Measuring cardiac output

in hemodialysis patients

MSc thesisJana van Gerwen

November 2009BMT 09.43

Committee:Prof. dr. ir. F.N. van de Vosse 1

Prof. dr. ir. P.A.J. Hilbers 1

Dr. ir. B.E. Westerhof 2

Dr. T. Delhaas 3

Dr. ir. E.M.H. Bosboom 1,3

Ir. W. Huberts 1,3

1Eindhoven University of Technology2BMEYE B.V.3Maastricht Universitary Medical Center

1

Abstract

End-stage renal disease (ESRD) is often treated with hemodialysis, which is fa-cilitated by surgically creating an arteriovenous fistula (AVF). An AVF requiresapproximately six weeks of maturation, before it can be used for dialysis. Despiteextensive preoperative vessel assessment, non-maturation occurs frequently. To beable to better predict if an AVF will mature, insight into the hemodynamics of theinvolved vessels is required. It is currently investigated whether a patient-specificone-dimensional wave propagation model can help to gain this insight by predictingthe early postoperative blood flow through the AVF. Flow through the aorta (orcardiac output) is an input for this model which has to be measured to make thewave propagation model patient-specific. Another reason to measure cardiac outputin ESRD and hemodialysis patients, is to monitor a patient’s cardiac function afterAVF creation, as cardiac failure is common in these patients.

Non-invasive techniques to measure cardiac output are Doppler echocardiogra-phy and phase-contrast MRI (PC-MRI), of which the latter is the most accurate.Unfortunately, MRI techniques are expensive, time consuming and not always pos-sible. Ultrasound dilution is a technique that combines ultrasound with the classicindicator dilution method, which can be performed during hemodialysis. Disadvan-tage of ultrasound dilution is that measurements are invasive and thus not suitableto measure cardiac output for the preoperative patient-specific wave propagationmodel. Because of the disadvantages of both techniques, this study aims at inves-tigating the feasibility of Nexfin CO, for determining the wave propagation modelinput and for monitoring hemodialysis patients.

Nexfin CO cardiac output measurements on both hands were compared to PC-MRI for 10 healthy volunteers. Mean bias was was 17% and 18% for the right andleft hand respectively. Precision was 36% for both hands. Simultaneous Nexfin COand ultrasound dilution measurements were performed in 10 hemodialysis patientsand revealed a bias of 17% and a precision of 45%.

To obtain insight into the working of the Nexfin CO algorithm, it was comparedto the patient-specific wave propagation model. This comparison revealed that thetransfer from finger to brachial blood pressure is similar for both models, but trans-formation of brachial pressure to stroke volume differs. Furthermore, the Nexfinalgorithm is very sensitive to small changes in the brachial pressure waveform. Asensitivity analysis of the effect of inaccuracy of several input parameters on theoutput of the wave propagation model showed that the inaccuracy in the cardiacoutput of the Nexfin CO has a smaller influence on the simulated pressure and flowthan the inaccuracy of the arterial radii. The finger pressure waveforms obtained inthe sensitivity study of the wave propagation model were also used as input for theNexfin CO algorithm. Variations in the cardiac output assessed by the Nexfin COalgorithm were smaller than the variations applied in the wave propagation model.

It can be concluded that Nexfin CO cardiac output measurements are less ac-curate and can thus not replace PC-MRI and ultrasound dilution cardiac outputmeasurements. However, as an input of the wave propagation model, cardiac outputmeasurements with Nexfin CO are sufficiently accurate, due to the large influenceof inaccuracies in the arterial radii.

2

Samenvatting

Nierfalen wordt vaak behandeld met hemodialyse, waarvoor het nodig is om chirur-gisch een arterioveneuze fistel (AVF) te creeren. Een AVF heeft ongeveer zes wekennodig om te matureren, voordat het voor hemodialyse kan worden gebruikt. On-danks uitgebreide preoperatieve vaatonderzoeken komt non-maturatie vaak voor.Om beter te kunnen voorspellen of een AVF zal matureren, is er meer inzicht in dehemodynamica van de betrokken vaten nodig. Het wordt momenteel onderzocht ofeen patient-specifiek een-dimensionaal golfvoortplantingsmodel hieraan kan bijdra-gen, door de postoperatieve flow door de AVF te voorspellen. Aorta flow (of cardiacoutput) is een input voor dit model die moet worden gemeten om het golfvoort-plantingsmodel patient-specifiek te maken. Een andere reden om de cardiac outputvan nier- en hemodialysepatienten te meten is het monitoren van de hartfunctievan de patienten na de creatie van een AVF, omdat voor deze patienten hartfalenveelvoorkomend is.

Niet-invasieve technieken om cardiac output te meten zijn Dopper echocardio-grafie en fase-contrast MRI (PC-MRI), de laatste is het meest nauwkeurig. Denadelen van MRI zijn de hoge kosten, hoge tijdsbelasting en de contra-indicaties.Ultrasound dilutie combineert ultrasound met de klassieke indicator dilutie methodeen kan worden uitgevoerd tijdens hemodialyse. Het nadeel van ultrasound dilutie isdat metingen invasief zijn en dus niet geschikt om cardiac output te meten voor hetpreoperatieve patient-specifieke golfvoortplantingsmodel. Door de nadelen van beidetechnieken, is het doel van deze studie om de toepasbaarheid van Nexfin CO, voorhet bepalen van de input van het golfvoortplantingsmodel en voor het monitorenvan hemodialyse patienten, te onderzoeken.

Nexfin CO cardiac output metingen aan beide handen zijn vergeleken met PC-MRI metingen voor 10 gezonde personen. De systematische fout was 17% en 18%voor de rechter en linkerhand. De precisie was 36% voor beide handen. Nexfin CO enultrasound dilutie metingen zijn gelijktijdig uitgevoerd op 10 hemodialyse patienten.Een systematische fout van 17% en een precisie van 45% werden gevonden.

Om inzicht te krijgen in de werking van het Nexfin CO algoritme, werd ditvergeleken met het patient-specifieke golfvoortplantingsmodel. Uit deze vergelijk-ing bleek dat de transformatie van vinger naar brachiale bloeddruk overeenstemt,maar dat de transformatie van brachiaaldruk naar slagvolume verschilt. Bovendienbleek het Nexfin algoritme zeer gevoelig voor kleine veranderingen in de brachialedrukgolf. Een sensitiviteitsanalyse van het effect van onnauwkeurigheid van verschil-lende input parameters op de output van het golfvoortplantingsmodel, liet zien datde onnauwkeurigheid van de cardiac output metingen met Nexfin CO een kleinereinvloed op de gesimuleerde druk en flow heeft dan de onnauwkeurigheid van de ar-teriele diameters. De vingerdrukgolven die verkregen zijn in de sensitiviteitsstudievan het golfvoortplantingsmodel zijn ook gebruikt als input voor het Nexfin COalgoritme. Variaties in cardiac output waargenomen door het Nexfin CO algoritmewaren kleiner dan de variaties op de input van het golfvoortplantingsmodel.

Het kan worden geconcludeerd dat Nexfin CO cardiac output metingen mindernauwkeurig zijn dan PC-MRI and ultrasound dilutie cardiac output metingen en dezetechnieken daardoor niet kan vervangen. Als input van het golfvoortplantingsmodel,zijn cardiac output metingen met Nexfin CO nauwkeurig genoeg, door de invloedvan grote onnauwkeurigheden op de arteriele stralen.

3

Contents

1 Introduction 8

2 Measuring cardiac output 122.1 Nexfin CO . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

2.1.1 Measuring finger pressure . . . . . . . . . . . . . . . . . . . . 122.1.2 Calculating brachial blood pressure with a transfer function . 152.1.3 Determining cardiac output . . . . . . . . . . . . . . . . . . . 16

2.2 Echocardiography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.3 Phase-contrast MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.4 Ultrasound dilution . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.4.1 Cardiac output measurements . . . . . . . . . . . . . . . . . . 222.4.2 Access flow measurements . . . . . . . . . . . . . . . . . . . . 24

2.5 Clinical studies of accuracy . . . . . . . . . . . . . . . . . . . . . . . 242.5.1 Nexfin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.5.2 Phase-contrast MRI and Doppler echocardiography . . . . . . 262.5.3 Ultrasound dilution . . . . . . . . . . . . . . . . . . . . . . . 26

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Measurement protocol and data processing 303.1 Nexfin versus PC-MRI in healthy volunteers and end-stage renal dis-

ease patients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.1.1 Measurement protocol . . . . . . . . . . . . . . . . . . . . . . 313.1.2 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 Nexfin versus ultrasound dilution in hemodialysis patients . . . . . . 323.2.1 Measurement protocol . . . . . . . . . . . . . . . . . . . . . . 323.2.2 Data processing . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.3 Statistical analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4 Measurement results 384.1 Nexfin cardiac output versus PC-MRI stroke volume in healthy vol-

unteers and end-stage renal disease patients . . . . . . . . . . . . . . 384.2 Nexfin cardiac output versus ultrasound dilution cardiac output in

hemodialysis patients . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

5 Nexfin CO and wave propagation model 485.1 Wave propagation model . . . . . . . . . . . . . . . . . . . . . . . . . 485.2 Wave propagation model input parameters . . . . . . . . . . . . . . . 49

5.2.1 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4

5.2.2 Arterial wall properties . . . . . . . . . . . . . . . . . . . . . 535.2.3 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 53

5.3 Sensitivity analysis of the wave propagation model . . . . . . . . . . 545.3.1 Input flow (cardiac output) . . . . . . . . . . . . . . . . . . . 545.3.2 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555.3.3 Young’s modulus . . . . . . . . . . . . . . . . . . . . . . . . . 555.3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.4 Nexfin CO algorithm input and sensitivity analysis . . . . . . . . . . 56

6 Modeling results 586.1 Nexfin CO versus wave propagation model (reference situation) . . . 586.2 Sensitivity analysis of the wave propagation model . . . . . . . . . . 626.3 Sensitivity analysis of the Nexfin CO model . . . . . . . . . . . . . . 66

7 Discussion and conclusion 687.1 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

7.1.1 Nexfin cardiac output versus PC-MRI cardiac output . . . . 687.1.2 Nexfin cardiac output versus ultrasound dilution in hemodial-

ysis patients . . . . . . . . . . . . . . . . . . . . . . . . . . . . 707.1.3 Nexfin CO algorithm versus wave propagation model . . . . . 717.1.4 Future research . . . . . . . . . . . . . . . . . . . . . . . . . . 73

7.2 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

Bibliography 75

A MR parameters 82

B Nexfin and PC-MRI data of healthy volunteers and end-stage renaldisease patients 83

C Nexfin and ultrasound dilution data of hemodialysis patients 87

D Patient specific input for the one dimensional wave propagationmodel 88

E Output of the sensitivity analysis of the wave propagation model 93

F Pressure and flow waveform output of the sensitivity analysis ofthe wave propagation model 97

G Output of the sensitivity analysis of the Nexfin model 106

H Effect of omitting the convection term in the wave propagationmodel 108

5

List of Figures

2.1 Inflatable finger cuff . . . . . . . . . . . . . . . . . . . . . . . . . . . 132.2 Stylized p-d diagrams during in vivo measurements . . . . . . . . . . 142.3 The Plethysmogram . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.4 The systolic area under the arterial pressure waveform . . . . . . . . 162.5 Bipolar gradients . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.6 Example of image obtained with PC-MRI . . . . . . . . . . . . . . . 212.7 Ultrasound dilution set up for cardiac output measurements during

hemodialysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222.8 A dilution curve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232.9 Reversed connection of the hemodialysis blood lines to measure access

flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

3.1 Error-gram for determining the limits of agreement between two tech-niques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

4.1 Nexfin measurements plotted against PC-MRI measurements for 10healthy volunteers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.2 Bland-Altman percentage plot of PC-MRI cardiac output comparedto indicator dilution cardiac output . . . . . . . . . . . . . . . . . . . 40

4.3 Bland-Altman percentage plots comparing Nexfin stroke volume withPC-MRI stroke volume . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4.4 Nexfin measurements plotted against ultrasound dilution measure-ments for 10 patients . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.5 Bland-Altman percentage plot of the Nexfin ultrasound dilution com-parison . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.6 Profile plot of Nexfin and ultrasound dilution measurements . . . . . 46

5.1 A diagram of simulations with the wave propagation model and theNexfin CO model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

5.2 Model geometry of the arm arteries . . . . . . . . . . . . . . . . . . . 515.3 The classical arterial patterns of the hand . . . . . . . . . . . . . . . 525.4 The three element windkessel model of the end-segments . . . . . . . 54

6.1 Pressure waveforms, measured with Nexfin and simulated with thewave propagation model and Beatscope. . . . . . . . . . . . . . . . . 61

6.2 Sensitivity of brachial artery pressure and flow . . . . . . . . . . . . 636.3 Sensitivity of finger artery pressure and flow . . . . . . . . . . . . . . 646.4 Sensitivity of the pressure and flow waveforms of patient nr. 2 for

changes in the diameter of the finger artery . . . . . . . . . . . . . . 65

6

6.5 Sensitivity of cardiac output, calculated by Nexfin, for finger pressurechanges . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66

6.6 Sensitivity of brachial blood pressure, calculated by Nexfin, for fingerpressure changes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

F.1 Simulated pressure waveforms of healthy volunteer nr. 1 . . . . . . . 98F.2 Simulated flow waveforms of healthy volunteer nr. 1 . . . . . . . . . 99F.3 Simulated pressure waveforms of healthy volunteer nr. 2 . . . . . . . 100F.4 Simulated flow waveforms of healthy volunteer nr. 2 . . . . . . . . . 101F.5 Simulated pressure waveforms of patient nr. 1 . . . . . . . . . . . . . 102F.6 Simulated flow waveforms of patient nr. 1 . . . . . . . . . . . . . . . 103F.7 Simulated pressure waveforms of patient nr. 2 . . . . . . . . . . . . . 104F.8 Simulated flow waveforms of patient nr. 2 . . . . . . . . . . . . . . . 105

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Chapter 1

Introduction

End-stage renal disease (ESRD) is a progressive loss of kidney function. The diseaseis best treated by renal transplantation, however due to the shortage of organ donors,35% of all ESRD patients in the Netherlands are treated with hemodialysis [Renine,2008]. During hemodialysis, water and waste products are removed from the bloodby a diffusion and ultrafiltration process across a semipermeable membrane in adialyzer. The best option to facilitate the withdrawal of blood for hemodialysis,is to create a vascular access by surgically connecting an artery and a vein, thisis called an arteriovenous fistula (AVF). Cannulas are inserted into the AVF andconnected to the dialyzer to lead the blood to the dialyzer and back to the body.

Fistulas are preferably placed in the upper extremities. Different types of fistulascan be used, autogenous arteriovenous fistulas are favorable because they show alower complication rate than non-autogenous arteriovenous grafts [van Tricht et al.,2005]. Complications of fistulas, such as infections, thrombosis, stenosis, aneurysmformation, ischaemia, steal syndrome and heart failure often occur [van Tricht et al.,2005], [Padberg et al., 2008]. The radial-cephalic wrist arteriovenous fistula (RC-AVF), where the radial artery and the cephalic vein are surgically connected, isthe best option for creating a vascular access, due to the low complication rateand the high long-term patency rate [van Tricht et al., 2005]. RC-AVF have lowerflow rates than upper-arm AVF, such as the brachial-cephalic elbow AVF and thebrachial-basilica elbow AVF, which prevents steal syndrome. When a RC-AVF iscreated, proximal vessels are preserved for possible placement of an upper-arm AVFin case the RC-AVF fails. After surgical creation, an AVF requires approximately sixweeks of maturation for the draining vein to dilate, to a minimum venous diameterof 4 mm, and a AVF blood flow of 500 mL/min or higher [Robbin et al., 2002].Only mature AVF can be used for hemodialysis, but unfortunately up to 50% ofall created RC-AVF do not mature [Tordoir et al., 2003], [Miller et al., 1999]. Thematuration of an AVF depends on the quality and size of the inflow arteries and theoutflow veins and on the ability of the vessels to adapt to the increased blood flow.Preoperative vessel assessment, such as physical examination, duplex ultrasoundand magnetic resonance angiography, are used to choose adequate vessels. However,despite these extensive preoperative examinations, non-maturation still occurs. Tobe able to better predict if an AVF will mature, insight into the hemodynamics ofthe involved vessels is required. It is currently investigated whether use of a patient-specific one-dimensional wave propagation model [Bessems, 2007], that can simulatepressure and flow waveforms throughout the body, can help to gain this insight. A

8

predictor of non-maturation of an AVF is the early postoperative blood flow throughthe AVF ([Kim et al., 2001], [Tordoir et al., 2003]). When the patient-specific modelcan predict this flow it should ultimately be able to predict whether an AVF willmature successfully for every individual patient. With the help of the model, onewill be able to select the best AVF configuration. Flow through the aorta or cardiacoutput is an input for the wave propagation model. In order to validate the modelfor ESRD patients, cardiac output has to be measured prior to AVF creation topredict postoperative AVF flow.

Another reason to measure cardiac output of ESRD patients is that it gives infor-mation about cardiac functioning. It is important to monitor cardiac functioning ofan ESRD patient, since over 50% of patients that start dialysis have a history of car-diovascular disease [Foley, 2003]. Furthermore, the placement of an AVF decreasesthe vascular resistance in the arm and this increases the demand on the heart. Itwas shown before that stroke volume and cardiac output can increase by 15 - 25%within 14 days after AVF placement ([Ori et al., 1996], [Iwashima et al., 2002]).Another study by Ori et al. [2002] found an increase in the cardiac index of 12%and 15% for respectively 1 and 3 months after surgery. Cardiac index is the cardiacoutput of a subject, divided by the subject’s body surface area. The study of Ungeret al. [2002] assessed the reduction of cardiac output during temporary occlusion ofthe fistula and 3-10 weeks after fistula closure. They found a reduction of 21% afterboth temporary occlusion and fistula closure. An increased cardiac output imposescontinuous cardiac loading and can cause high-output cardiac failure ([van Trichtet al., 2005], [Padberg et al., 2008]). Especially patients with high vascular accessflow are thought to be at risk for this [MacRae et al., 2004], [MacRae, 2006]. Thisconcept is strengthened by the significant relation between access flow and cardiacoutput that was found by Wijnen et al. [2005] and Pandeya and Lindsay [1999].

To measure cardiac output, thermodilution is considered the current gold stan-dard in the clinic. However, this method is invasive and this is not desired forroutine patient examination. The most frequently used methods to non-invasivelydetermine cardiac output are based on echocardiography and magnetic resonanceimaging. Phase-contrast MRI (PC-MRI) [Breeuwer, 2005/8] and Doppler echocar-diography [Mathews and Singh, 2008] calculate total flow per unit of time in theascending aorta from the blood flow velocity at this point and the aortic cross sec-tional area. Although echocardiography is the most popular technique for clinicallymeasuring cardiac output, PC-MRI has proven to be more accurate than Dopplerechocardiography when applied to flow in a phantom ([Kondo et al., 1991], [Leeet al., 1997], [Summers et al., 2005]). PC-MRI also showed to be accurate comparedto the indicator dilution technique in healthy volunteers [Møgelvang et al., 1992] andto thermodilution in the pulmonary artery of patients with pulmonary hypertension[Hoeper et al., 2001]. Unfortunately, MRI techniques are generally expensive andtime consuming due to the complex logistics and measurements cannot be performedwhen the subject suffers from claustrophobia or has a pacemaker.

Ultrasound dilution is a methodology to determine cardiac output during dialy-sis [Krivitski and Depner, 1999]. Briefly, measurements are done by injecting salineinto the venous blood line leading away from the dialysis machine. The concen-tration of the injected saline that eventually flows through the arterial blood lineis a measure for cardiac output. To perform this measurement it is necessary toinject 30 mL of saline in the blood lines, this is unwanted for a hemodialysis patient

9

since the kidneys of these patients are unable to clear it from the blood. Anotherdisadvantage is that this technique is only possible during dialysis, making it im-possible to compare the patient’s cardiac output prior to vascular access placementto the postoperative cardiac output with the same technique. Furthermore, cardiacoutput during hemodialysis can be different from cardiac output at another timepoint, because the withdrawal of blood during hemodialysis puts extra load on theheart.

Due to the disadvantages of PC-MRI and ultrasound dilution and the inaccuracyof echocardiography, it would be beneficial to find an accurate method to non-invasively determine cardiac output. It was chosen to investigate the feasibility ofNexfin CO, since unlike PC-MRI this method is inexpensive, easy to perform andcan be used when a subject is claustrophobic or has a pacemaker. Furthermore,Nexfin can be used to measure cardiac output at any point in time as opposed toultrasound dilution. The latter can only be applied postoperatively during dialysis,which makes it impossible to use these measurements as an input for the wavepropagation model.

Cardiac output measurements with Nexfin CO are based on finger pressure mea-surements with an inflatable finger cuff. A large advantage of this method for clinicaluse is that finger and brachial pressure can be determined continuously. The brachialblood pressure is determined from the finger blood pressure with the use of a general,frequency dependent transfer function based on a population of healthy volunteers,hypertensive patients and patients suffering from arteriosclerotic vascular disease[Gizdulich et al., 1997]. Systolic and diastolic pressure obtained from finger pressurewith this transfer function have been validated against Riva-Rocci/Korotkoff (theclassical method with the upper arm cuff) blood pressure measurements and provedto be accurate [Eeftinck-Schattenkerk et al., 2009]. Measurements in the latter studywere done in hypotensive, normotensive and hypertensive subjects.

Nexfin calculates cardiac output from brachial blood pressure by using systolicpulse contour analysis on a beat-to-beat basis. The systolic area of the blood pressurewaveform is integrated and divided by a statistically determined aortic impedance.This impedance depends on the age, height, weight and gender of the subject and wasdetermined from brachial pressure measurements and thermodilution measurementson patients during open heart surgery [Wesseling et al., 1993], [Jansen et al., 2001],on healthy volunteers undergoing a passive head-up tilt [Harms et al., 1999] and onpatients during septic shock [Jellema et al., 1999].

To summarize, it might be advantageous to use Nexfin CO to measure cardiacoutput in ESRD-patients with and without an AVF. Unfortunately, the accuracy ofNexfin cardiac output measurements is unknown. Moreover, no information aboutthe effects of an altered vessel anatomy, which hemodialysis patients have, on cardiacoutput measurements with Nexfin is available either. Therefore, it is the purposeof this study to investigate whether Nexfin CO can be used to determine cardiacoutput as an input for the wave propagation model to simulate fistula creation andfor monitoring a patient’s change in cardiac output after vascular access surgery.

Before Nexfin CO can be used in practice, its results have to be validated first.To assess whether Nexfin cardiac output is accurate enough as an input for the wavepropagation model and to monitor a patient before surgery, Nexfin CO measure-ments will be compared to PC-MRI measurements in young, healthy volunteers andin ESRD-patients without a vascular access. The group of healthy volunteers was

10

included in the analysis to be able to measure with Nexfin CO in a homogeneousgroup, since in this group the most optimal agreement between Nexfin CO and PC-MRI cardiac output measurements was expected. In the ESRD-population accuracyof Nexfin measurements might be influenced since older ESRD-patients are prone tovascular disease. In order to monitor the cardiac output of a hemodialysis patient,Nexfin should also be accurate when a patient has a vascular access. It is unknownwhat the influence of a vascular access is on the relation between finger pressureand cardiac output. Therefore, Nexfin will be compared to ultrasound dilution inhemodialysis patients during their regular hemodialysis treatment. An advantage ofultrasound dilution measurements is that it can be performed simultaneously withNexfin CO measurements.

After determining the accuracy of cardiac output measurements with Nexfin, bycomparing it to PC-MRI and ultrasound dilution measurements, it is important toinvestigate whether the error in the Nexfin measurements has an effect on resultsfrom simulations with the wave propagation model of Bessems [2007] and how theeffect of the accuracy of cardiac output compares to the effect of the accuracy ofother input parameters. Therefore, a sensitivity analysis of patient-specific modelsfor cardiac output, radii of arteries and Young’s modulus was done. Patient-specificgeometries for the wave propagation model were made for two healthy volunteersand two ESRD-patients without an AVF, only one arm per subject was considered.

The Nexfin CO algorithm bases its calculation on gender, age, height and weightof a subject. This statistical model was not based on physiological and physicalrelations. Therefore, it is not possible to directly assess the response of the NexfinCO algorithm on changes of radii and Young’s moduli of the arteries. However,the simulated finger pressure obtained with the sensitivity analysis of the wavepropagation model provide an unique opportunity to give insight in the working ofthe Nexfin CO algorithm and the sensitivity of the cardiac output estimations bythe Nexfin CO algorithm and this is thus also investigated.

In Chapter 2 the basics behind different techniques to measure cardiac output,i.e. Nexfin CO, echocardiography, PC-MRI and ultrasound dilution, are described.In addition, the accuracy of these techniques is discussed. In Chapter 3 it is explainedhow measurements with Nexfin, PC-MRI and ultrasound dilution were performedand how data was processed. Chapter 4 lists the results of the comparison of Nexfinmeasurements with PC-MRI and ultrasound dilution measurements. In Chapter 5,all input for the patient-specific wave propagation model and the Nexfin CO algo-rithm is described and explained. Chapter 6 includes the results of the comparisonof the Nexfin CO algorithm and the wave propagation model, the sensitivity of thewave propagation model and the Nexfin CO algorithm for changes in input parame-ters of the wave propagation model. In the final chapter, the study is discussed andconcluded.

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Chapter 2

Measuring cardiac output

The two most frequently used methods to non-invasively determine cardiac outputare phase-contrast MRI (PC-MRI) and echocardiography, of which the latter ismost popular in the clinic due to costs, availability and the possibility of bedsidemeasurements.

The thermodilution technique has become the clinical standard for cardiac out-put determination, since it is thought to be the most accurate [Mathews and Singh,2008]. A similar technique, called ultrasound dilution, can be used to determinecardiac output during hemodialysis.

In this chapter, the basics behind all techniques that were mentioned above aredescribed. In addition, an evaluation of the accuracy of all methods is given and itis concluded which techniques are useful to compare Nexfin CO with. The theorybehind Nexfin CO cardiac output measurements is given first.

2.1 Nexfin CO

Nexfin CO (BMEYE B.V., Amsterdam, the Netherlands) can be used to non-invasively and continuously measure finger blood pressure, from which brachial bloodpressure and cardiac output are estimated. The modality measures finger blood pres-sure with an inflatable cuff and brachial blood pressure is determined from this witha frequency dependent transfer function. The systolic part of the brachial bloodpressure curve is integrated and the result is divided by an impedance that dependson the patient’s gender, age, length and weight to obtain stroke volume. Cardiacoutput is calculated by multiplying stroke volume with heart heart.

2.1.1 Measuring finger pressure

Finger blood pressure is measured with an inflatable cuff placed around the finger.The transmural pressure across the arterial wall is defined as the difference betweenintra-arterial and extra-arterial pressure. When transmural pressure is zero, there isno pressure across the arterial wall and arterial pressure can be determined from cuffpressure, since in this case cuff pressure equals arterial pressure [Wesseling et al.,1995]. By keeping the diameter of the artery constant, full transmission of arterialpressure to cuff pressure is achieved. The diameter at zero transmural pressureis called the setpoint diameter. An infrared light source and a photocell that aremounted inside the cuff and form a built-in photo-electric plethysmograph (Figure

12

Figure 2.1: Inflatable finger cuff

2.1) are used to keep the diameter constant. Because blood absorbs infrared light,the diameter of the finger artery can be determined from the plethysmograph, i.e. thetransmission spectrum. A fast pneumatic servo system is used to keep the arterialdiameter constant. Nexfin records finger blood pressure with a sample frequency of200 Hz.

At startup, cuff pressure is increased stepwise and held constant by Nexfin, untilone beat is detected for each step level, to determine a first estimate of the pressureat zero transmural pressure [Imholz et al., 1998]. The plethysmographic amplitudeincreases with increasing cuff pressure since blood is pressed out from under the cuff.Of all pressure steps, the plethysmogram with the largest amplitude is detected. Thispressure is a first estimate of mean arterial finger pressure.

The Physiocal (short for physiological calibration) procedure [Wesseling et al.,1995] was implemented in Nexfin because smooth muscle in the arterial wall cancontract or relax due to various conditions of the arterial system, such as changesin temperature, pain, blood loss or other stressors. When the arterial diameter ischanged due to modulations of smooth muscle tone, the cuff has to change its set-point diameter to maintain zero transmural pressure. The need of the Physiocal pro-cedure is emphasized by the difference in pressure-diameter relations of relaxed andcontracted finger arteries in Figure 2.2, which were obtained by studying segments ofhuman finger arteries in vitro [Langewouters et al., 1986]. Both pressure-diametersrelations are clearly nonlinear with the steep part located near zero transmural pres-sure. A fully open diameter was never reached since the arterial diameter continuesto increase with higher pressures. However, the diameter increases relatively littleat higher pressures. It is clear that to avoid errors, changes in smooth muscle tonemust somehow be followed by the setpoint diameter. In Nexfin this is done by thePhysiocal procedure.

The Physiocal protocol is as follows: for one beat cuff pressure is set at mid-pressure, half way between systolic and diastolic pressure, of the previous beat andthe finger plethysmogram is observed for one beat. This is repeated once at a cuffpressure which is one quarter of the pulse pressure lower than mid-pressure. Thissuffices to open the artery even when smooth muscle is contracted. The finger

13

Figure 2.2: Stylized p-d diagrams after in vivo measurements, with transmural pres-sure pt plotted against arterial diameter d [Langewouters et al., 1986]

Figure 2.3: In the upper panel: finger pressure in black and cuff pressure in blue.In the lower panel: the associated plethysmographic pulsations. Circles indicate theplethysmogram in diastole. Adapted from Wesseling et al. [1995]

14

arterial plethysmogram is observed and its shape examined. It can be derived fromthe shape of a single plethysmographic wave whether cuff pressure is above, belowor at arterial mid-pressure (Figure 2.3). If cuff pressure is set at a constant levelnear diastolic pressure (first cuff pressure in Figure 2.3), transmural pressure will bepositive during a large fraction of the heart beat. In diastole transmural pressureis negative for a small period. However, the artery will not fully collapse and someinfrared will be absorbed by the remaining blood and the light output will not bemaximal. The plethysmogram in diastole, which is in the blue circle on the left inFigure 2.3, will be sharp. When cuff pressure is adjusted to be near the systoliclevel (last cuff pressure in Figure 2.3) in systole the artery is collapsed most ofthe time and will only open briefly to a small diameter. The artery will absorbthe infrared only moderately and the light output will not drop very deep. Thisleads to an obtuse plethysmogram in diastole (the blue circle on the right in Figure2.3). When cuff pressure is approximately half way between systolic and diastolicpressure an intermediate curve as in the middle section of Figure 2.3 will occur. Awaveform shape factor, based on the sharpness of the plethysmogram in diastole atpositive deflection, is computed and the setpoint diameter is reset in proportion tothis factor. When the sharpness criteria have not been met during two beats, extrapressure steps are taken or the interval to the next Physiocal is shortened.

2.1.2 Calculating brachial blood pressure with a transfer function

Pressure pulsations in the finger differ in shape and level compared to pulsations inthe brachial artery, therefore a frequency dependent transfer function is implementedin Nexfin to transfer finger blood pressure to brachial blood pressure. Gizdulichet al. [1997] have studied the differences in the waveforms recorded invasively in thebrachial artery and noninvasively at the finger of the ipsilateral hand with TNOFinapres Model 5 for 53 subjects. The patient group consisted of 22 healthy volun-teers, 31 hypertensive patients and 7 patients suffering from arteriosclerotic vasculardisease. Fourier analysis was used to establish a ’forward‘ (brachial to finger artery)complex frequency transfer function:

H(f) = K(1 + if/f0)2

1 + 2iDf/f1 − (f/f1)2, (2.1)

with i the imaginary unit. This model is equivalent to a gain (K), a second-orderhigh pass section at frequency f0, followed by a second-order underdamped low passsection at resonance frequency f1, with damping D<1. The transfer function wasforced to unity transfer at high frequencies by linking f0 and f1 by the equation:f0 = f1

√K. The model was least-squares fitted to the complex transfer functions

of every subject, thereby estimating K, f1 and D. A general model for the groupwas computed by taking the average of each model parameter. The values of theparameters for the general model were: K = 0.84 (range 0.63 - 0.98), f1 = 7.34 Hz(4.26 - 10.58) and D = 0.36 (0.07 - 0.83).

Since mean pressure was subtracted from the pulses prior to Fourier analysislevel correction has to be applied after using the transfer function. To obtain thislevel correction the full finger pressure (without the mean pressure subtracted) wasinverse modeled, i.e. the forward transfer function of Equation 2.1 was inversely ap-plied, to approach full brachial artery pressure. The remaining differences in systolic,

15

diastolic and mean levels between measured finger and brachial artery pressure, andbetween the modeled full brachial artery pressure and the measured brachial pres-sures were computed. A significant relation was found between the difference of themodeled full diastolic brachial artery pressure and the measured diastolic brachialpressure (∆pD) and the modeled full brachial artery systolic (pS) and diastolic (pD)pressure. Differences in mean pressure also related significantly to systolic and di-astolic pressure. Therefore, a level correction that depends on systolic and diastolicpressure was defined:

∆pD = k1 − k2 · pS + k3 · pD, (2.2)

With k1 = -13.3 mmHg, k2 = 0.194 mmHg and k3 = 0.574 mmHg. ∆pD has to besubtracted from the systolic, diastolic and mean blood pressure levels.

Hydrostatic pressure changes due to differences in height between the fingerand the heart are compensated by a heart reference system that consist of a liquidcolumn. The hydrostatic pressure is calculated by positioning one end of the columnat heart level and the other end, that includes the sensor, to a finger adjacent to theone with the pressure cuff.

Figure 2.4: The systolic area under the arterial pressure waveform. With Td as thediastolic period and Ts as the systolic period, the systolic area is displayed in blue.Figure was adapted from Mathews and Singh [2008].

2.1.3 Determining cardiac output

Nexfin determines stroke volume on a beat-to-beat basis with systolic pulse contouranalysis. This method combines the nonlinear effect of mean pressure and heart ratewith the influence of age, height, weight and gender of the subject on aortic mechan-ical properties. In the three element windkessel model, the pulsatile systolic area(AS) and stroke volume (Vstroke) are related by means of characteristic impedanceof the aorta (ZA):

Vstroke = ASZA,

where AS =∫ t1t0

(p(t)− pD)dt (2.3)

In which AS is the area under the pressure curve (p(t)), corrected for the diastolicpressure (pD) as depicted in Figure 2.4, from the onset of systole (t0) to the end

16

of ejection (t1). Characteristic impedance ZA depends on age, height, weight andgender.

Thermodilution cardiac output and intra-arterial radial or brachial pressure ornoninvasive finger pressure data measured by Wesseling et al. [1993], Harms et al.[1999], Jellema et al. [1999] and Jansen et al. [2001] were used to determine thecharacteristic impedance, details about these population studies can be found inTable 2.1. Wesseling et al. [1993] and Jansen et al. [2001] measured on patientsduring open heart surgery. The population used for the measurements in the studyof Harms et al. [1999] consists of healthy volunteers undergoing a passive head-uptilt. Jellema et al. [1999] measured on patients during septic shock and treatmentwith catecholamines. In order to compare thermodilution cardiac output to cardiacoutput determined by the systolic pulse contour analysis, finger and radial pressurewaveforms were transformed to a brachial waveform. Finger pressure was trans-formed to brachial pressure with one transfer function, to transform radial pressureto brachial pressure another filter was employed.

2.2 Echocardiography

Echocardiography is the most popular image modality to assess cardiac functionin the clinic due to costs, availability and possibility of using the technique at thebedside. The modality is based on the propagation of ultrasound waves, transmit-ted by the transducer, through tissue. Measurements can be done by placing thetransducer on the chest of the patient, this is called transthoracic echocardiography,or by inserting the transducer into the esophagus, to produce a transesophagealechocardiogram [Mathews and Singh, 2008]. The last procedure has a better imagequality and there is no interference of the patient’s ribs. It is, however, unpleasantfor the patient.

One can look at two phenomena with echocardiography: reflection of ultrasoundwaves at a transition between two tissue types and the Doppler shift that is inducedby a moving scatterer, for example a blood cell. The first phenomenon can be usedto look at the anatomy of a subject. The ultrasound waves, transmitted by thetransducer, travel through the human body. When the waves reach a transitionbetween two tissue types, the sound waves will be partially reflected back to thebody’s surface, where they are detected by the transducer. With this technique,stroke volume can be measured by determining the difference between the end sys-tolic volume (ESV) and end diastolic volume (EDV) of the left ventricle. With 2Dechocardiography, the ESV and EDV are determined by assuming an ellipsoid thatis calculated from two perpendicular long axis views of the ventricle. 3D echocar-diography can give a better representation of the ventricle volume, but accuracy ofcontour detection is limited due to low image quality and low contrast.

Techniques that rely on Doppler shifts of ultrasound are more reliable and there-fore used more often in the clinic to determine cardiac output. When ultrasoundis scattered by a moving object, such as a red blood cell, the ultrasound picked upby the receiving transducer differs slightly in frequency from the transmitted wave[Gill, 1985]. This change, called the Doppler shift, is given by:

∆f = 2vcos(θ)f0/c, (2.4)

17

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18

where ∆f represents the Doppler shift, v is the scatterer’s velocity, θ is the anglebetween the ultrasound beam and the direction of motion, f0 is the frequency of thetransmitted ultrasound and c is the speed of propagation of ultrasound in blood. f0

and c are known and v · cosθ can be calculated from the measured Doppler shift. θmust be accurately determined before v can be determined.

In reality, the Doppler sample volume contains a large number of red cells thatscatter the ultrasound [Gill, 1985]. Therefore, the detected Doppler shift signalcontains a spectrum of frequencies representing the range of red cell velocities presentin the sample volume.

Modern ultrasound machines use pulsed Doppler to measure velocity. Duringpulsed Doppler measurements, the transducer alternates transmission and receptionof ultrasound. The frequency shift of each pulse is ignored, but the relative phasechanges of the pulses are used to obtain the frequency shift. The latter can be done,since frequency is the rate of change of phase. The advantage of pulsed Doppler isthat distance information can be obtained and thereby localized measurements arepossible.

Blood flow can be determined with ultrasound from velocity and area with severalmethods [Gill, 1985]. One way is to first determine the velocity in all elements (∆Ai)of the cross section of the vessel and then determine the flow contribution in eachelement, which are summed up, to give the total blood flow (Q) in the vessel, suchthat:

Q =∑i

(vi∆Ai) (2.5)

High resolution is necessary for this technique, i.e. the sample volume must be smallcompared to the diameter of the vessel. Therefore, this technique is best suited forlarge blood vessels with a diameter in the order of 10 mm or above [Gill, 1985]. Thesmall size of the subcutaneous vessels accessible with pulsed Doppler suggests thatthe profile integration technique is not preferred for accurate transcutaneous volumeflow measurements.

Another possibility to calculate blood flow is to compute the average velocity ofthe entire cross section and multiply this by the cross-sectional area. This approachuses the relationship between the mean Doppler shift and the average blood velocitywithin the sample volume. The sample volume has to be made sufficiently large toencompass the entire vessel cross section, this is difficult to achieve in very largevessels such as the aorta.

The most frequently used method to perform flow measurements in the aorta isbased on the assumption of a flat profile in the aorta. Measurements are done withthe transducer placed at the apical window and the sample volume positioned in themiddle of the outflow tract around the point where the aortic leaflets come together.It is known that a flat profile occurs when blood is subjected to high acceleration.The maximum frequency is taken to represent the velocity in the area of interest.This velocity is multiplied by the cross sectional area to obtain flow per unit of time.A second assumption is that the angle θ is 0◦. Thus, ultrasound is transmitted inthe direction of flow.

In the case of valve insufficiency, the aorta can no longer be considered circular,the diameter cannot be measured at the same point as the velocity measurementsand has to be measured at a more distal point in the aorta, where the aorta mighthave a different radius. The latter makes the measurement unreliable.

19

Time

GBP

(a) Positive

Time

GBP

(b) Negative

Figure 2.5: Bipolar magnetic field gradient (GBP ) pulses

2.3 Phase-contrast MRI

MRI is a medical imaging technique used primarily to visualize the internal structureand function of the body. When tissue is placed in the powerful magnetic field ofthe MRI scanner, the magnetic moments (or spins) of the protons of hydrogenatoms align with the direction of the field. A radio frequent electromagnetic field isthen briefly turned on, causing the protons to alter their alignment relative to thefield. After turning off this field the protons return to the original magnetizationalignment, thereby creating a signal which can be detected by the scanner.

Every MR imaging data acquisition provides information about the signal mag-nitude and the phase of each voxel. In conventional imaging sequences, signal in-tensities are processed into an anatomic image (magnitude image) and the phaseinformation is discarded. In phase-contrast measurements, the phase information isused to calculate the velocity of the spins in each voxel in the form of a phase orvelocity image [Lotz et al., 2002].

Spins moving along a magnetic field gradient acquire a shift in their phase of ro-tations ∆φ in comparison to stationary spins. For linear field gradients, the amountof this phase shift is proportional to the velocity of the moving spin [Moran et al.,1985]. Phase shifts of stationary tissue are compensated for with the help of a bipo-lar magnetic field gradient (GBP ). A bipolar gradient pulse is one in which thegradient is turned on in one direction for a period of time and then turned on inthe opposite direction for an equivalent amount of time. A positive bipolar gradientpulse has the positive lobe first and a negative bipolar gradient has the negativelobe first (Figure 2.5). Spins exposed to the positive (+) and negative (-) lobes ofthe positive bipolar gradient acquire a shift in radians given by

φ+ = 2πγ∫xt1GBPdt and

φ− = −2πγ∫xt2GBPdt, (2.6)

where γ is the gyromagnetic ratio.It is clear that when the gradients of the two lobes are equal and the position (x) ofa spin is equal during the two pulses at t1 and t2, φ+ equals −φ−, thus there is noeffect on stationary spins. However, spins which have a velocity component in thedirection of the gradient will be effected by the bipolar gradient pulse. For thesespins, xt1 and xt2 are not equal and the phase difference on the spins between the

20

Figure 2.6: Example of an anatomical image (on the left) of the aorta and a phaseimage (on the right) obtained with PC-MRI. The red contour indicates the regionof interest.

two lobes is proportional to the velocity of a spin. By repeating the measurementwith an negative bipolar gradient, phase shift induced by field inhomogeneities areeliminated. The phase difference that remains after subtraction of these two datasets can be used for calculation of velocities in every voxel.

An accurate first guess of peak velocity is of importance to prevent aliasing ortoo much noise. Phase shifts should be within a range of ±180◦, therefore thepeak velocity has to correspond to a phase shift of 180◦ [Lotz et al., 2002]. Tosynchronize the MR imaging with the cardiac cycle, a trigger is required to start thedata acquisition. Usually, the acquisition is triggered to the R peak of the subject’selectrocardiographic waveform. To prevent motion artifacts due to breathing, thesubject has to hold his breath. When all phase-contrast images have been acquired,an area of interest has to be specified. Theoretically, flow in the vessels is notinfluenced when the area is a bit too large, since tissue in voxels at the outside ofthe aorta has no velocity in the direction of interest. However, to ensure accurateresults, contours that precisely envelope the aorta are acquired both manually andautomatically from the magnitude image, an example can be found in Figure 2.6.The contours are then copied to the phase-contrast images, from which the flow isquantified [Breeuwer, 2005/8]. The stroke volume can be calculated by integratingthe flow and cardiac output is the product of stroke volume and heart rate.

2.4 Ultrasound dilution

A vascular access provides an unique opportunity to assess cardiac output usingultrasound employing the classic indicator dilution method. The advantage of ul-trasound dilution is that it is minimally invasive since catheterization as in thethermodilution procedure is not necessary. Furthermore, ultrasound dilution mea-surements can be executed during dialysis and therefore are not time-consumingfor the patient. A minor modification of the regular ultrasound dilution technique

21

B

C D

A

V

Figure 2.7: Ultrasound dilution during hemodialysis, canulas are inserted in thevascular access of the patient. The arterial blood line (A) leads the blood throughthe ultrasonic sensor (B) to the blood pump and dialyzer. The venous blood line(V) returns the blood to the patient. D represents the injected saline.

can be used to also measure access flow at the start of the hemodialysis session.This paragraph will explain the use of ultrasound dilution for both cardiac outputmeasurements and access flow measurements.

2.4.1 Cardiac output measurements

After dialysis is started, cardiac output can be measured with ultrasound dilution byinjecting a bolus of indicator in the venous blood line [Krivitski and Depner, 1999].The indicator travels through the heart and lungs, a portion of the indicator isthen detected in the arterial blood line leading towards the vascular access. Cardiacoutput can be calculated from this portion. An ultrasonic sensor is clamped onthe arterial blood line, as in Figure 2.7, to measure the indicator. Isotonic saline isused as an indicator. Ultrasound velocity in blood can be 1560 - 1585 m/s, whereasultrasound velocity in saline is about 1533 m/s, making it useful as an indicator[Krivitski, 1995]. The ultrasonic sensor measures the changes in blood ultrasoundvelocity caused by the injected saline. Body temperature saline injected in thevenous line passes through the cardiopulmonary system and is then detected as adilution curve in the arterial line leading towards the vascular access. An exampleof such a dilution curve can be found in Figure 2.8. Cardiac output (QCO) iscalculated based on the standard Stewart-Hamilton equation [Krivitski, 1995]:

QCO =Vinj∫c(t)dt

, (2.7)

in which Vinj is the volume of injected saline, measured by the venous sensor andc(t)[%] is the concentration of saline with respect to time during the first pass ofthe indicator measured by the arterial sensor,

∫c(t)dt is the area under the dilution

curve, displayed in green in Figure 2.8.Indicator concentration has to be derived from ultrasound velocity measured by

the arterial sensor. Since ultrasound velocity in blood is a function of total blood

22

Figure 2.8: A dilution curve; the blue line represents the injected saline and theblack line represents the concentration of saline detected by the ultrasound sensoron the arterial blood line.

protein concentration, temperature and average ion concentration in plasma, thearea under the arterial dilution curve will depend not only on cardiac output butalso on these other factors. For example, for the same cardiac output in a patientwith high hemoglobin, the area under the dilution curve measured by the arterialsensor will be larger than the area under the curve in diluted blood of a patientwith low hemoglobin. To eliminate this effect, the difference between the ultrasoundvelocity of the injected saline and that of the patient’s blood is also measured bya venous sensor that is clamped on the venous blood line [Tsutsui et al., 2009]. Inpatients with high hemoglobin this difference will be larger than in patients withlow hemoglobine. Equation 2.7 has to be modified as follows:

QCO = (vblood − vsaline)Vinj∫va(t)dt

(2.8)

where vblood − vsaline is the difference between ultrasound velocity of blood and salinemeasured by the venous sensor and va(t) refers to changes over time in arterial bloodultrasound velocity measured by the arterial sensor.

There are a few pitfalls that should be taken into account [Krivitski and Depner,1999]. First, dialyzed blood may circulate through the vascular access directly backto the dialyzer, preventing an accurate assessment of systemic dilution. This caneither occur continuously, this means that the pumped blood flow is greater than theflow in the vascular access, or momentarily, in which case it is caused by the bolusinjection of indicator. To prevent recirculation, the pump flow of the hemodialyzerneeds to be decreased to 200 mL/min.

Second, the access device acts as a peripheral arterio-venous shunt providing afast route for blood return to the heart known as cardiopulmonary recirculation.After the first pass of the injected saline through the heart, the shunt can causea very quick second pass of indicator that may interfere with the first. To reducethe influence of this second pass, the bolus must be injected quickly within 4 to6 seconds. A fast injection will decrease the duration of the first indicator curve,decreasing the chance of overlap with the second pass. Furthermore, the curvesof the first and second pass can be separated by extrapolating the down-slope of

23

Figure 2.9: Reversed connection of the hemodialysis blood lines to measure accessflow, adapted from Krivitski [1995]. Large arrows indicate the direction of flow,small arrows show the movement of the indicator.

the first pass. To optimize this separation, the timing of the first pass through thecardiopulmonary circuit is used to calculate the expected timing of the second pass.

The saline that is injected ultimately diffuses out of the blood and into thetissues. Moser and Kenner [1988] showed that in the lung microcirculation 0.08%of the injected saline is lost. This means that the loss of saline indicator during thefirst pass is not a significant factor.

2.4.2 Access flow measurements

Flow through the vascular access can be measured by reversing the dialysis bloodlines [Krivitski, 1995]. The venous blood line is connected to the arterial site of thevascular access and the arterial blood line is connected to the venous site of thevascular access, creating a recirculation through the AVF as can be seen in Figure2.9. The venous outlet now faces the access flow stream, this creates a good mixingzone upstream from the venous outlet. The flow through the vascular access can becalculated analogous to cardiac output in Equation 2.8, QCO now becomes vascularaccess flow.

2.5 Clinical studies of accuracy

A drawback of all techniques for in vivo measurements of blood flow is the lack of astandard of reference. Therefore, the error of measurements of the different method-ologies is difficult to estimate. In research studies, the thermodilution technique is

24

considered the gold standard. However, this is an invasive technique and this is notdesired for routine examination of a patient’s condition. The results of validationstudies done with noninvasive techniques (in this study Nexfin, echocardiography,PC-MRI and ultrasound dilution) are listed in this paragraph. A small paragraphabout the accuracy of access flow measurements with ultrasound dilution was alsoincluded since this technique was also used in this study, to determine the effect ofa vascular access on the accuracy of Nexfin.

2.5.1 Nexfin

Validation studies for Nexfin are limited since the device is relatively new. Sofar, Nexfin brachial blood pressure has been validated against ipsilateral Riva-Rocci/Korotkoff (RRK) blood pressure measurements simultaneously performed bytwo observers [Eeftinck-Schattenkerk et al., 2009]. RRK measurements are auscul-tatory blood pressure measurements with an arm cuff which are frequently used inclinical practice; in the study by [Eeftinck-Schattenkerk et al., 2009] an automatedarm cuff was used. The Association for the Advancement of Medical Instrumenta-tion (AAMI) prescribes that, for a validation such as this, mean differences betweenthe new technique and the golden standard must be ±5 mmHg or less, with a stan-dard deviation of 8 mmHg or less. When the mean of three observations per subjectis used to assess accuracy, standard deviations not larger than 5.2 and 6.5 mmHg forsystolic and diastolic pressure respectively are allowed according to AAMI standards.

Eeftinck-Schattenkerk et al. [2009] used three 30 seconds averages per subject,in 104 subjects. The subjects had blood pressures ranging from hypotensive tohypertensive. Mean systolic blood pressure was 134 ± 24 mmHg and mean diastolicblood pressure was 81 ± 14 mmHg. The mean difference between Nexfin and RRKblood pressure (defined as Nexfin - RRK blood pressure) was 4.3 ± 9.3 mmHgand -2.5 ± 8.1 mmHg for systolic and diastolic pressure respectively. Analysis ofwithin-subject precision showed a standard deviation of 3.8 mmHg for systolic bloodpressure and 2.4 mmHg for diastolic blood pressure.

When the mean of three observations per subject was analyzed, Eeftinck-Schattenkerket al. [2009] found a standard deviation of 8.7 and 7.9 mmHg for systolic and diastolicblood pressure.

Despite slightly exceeding AAMI guidelines, Eeftinck-Schattenkerk et al. [2009]conclude that Nexfin provides accurate blood pressure measurements with goodwithin-subject precision. It should be noted that AAMI guidelines are not intendedfor continuous noninvasive blood pressure measurements.

A shortcoming of the study by Eeftinck-Schattenkerk et al. [2009] is that RRKblood pressure measurements cause temporal occlusion of the brachial artery andtherefore, simultaneous measurements were not possible.

Although good precision between Nexfin and RRK blood pressure measurementswas shown, the accuracy of RRK measurements should be kept in mind. Studies thathave compared auscultatory pressure measurements to intra-arterial measurementshave found frequent discrepancies and large variations in measurement error withinand between patients [Bergen et al., 1954], [Gravlee and Brockschmidt, 1990].

Information about the accuracy of finger pressure measurements is not available,because the small diameter of the finger arteries makes intra-arterial measurementsimpossible.

25

Cardiac output measurements with Nexfin have not been validated either. Adisadvantage of Nexfin CO is that cardiac output is only determined per beat andaortic flow waveform cannot be determined.

2.5.2 Phase-contrast MRI and Doppler echocardiography

[Summers et al., 2005] and [Kondo et al., 1991] found good accuracy and correlationsbetween PC-MRI and phantom flow, goodness of fits of R2 > 0.99 and r > 0.99respectively were found. Cardiac output determined with PC-MRI also showedto be highly correlated (r=0.96, p=0.001) to simultaneously performed indicatordilution measurements in healthy volunteers [Møgelvang et al., 1992]. PC-MRI flowin the pulmonary artery was compared to measurements done with a thermodilutioncatheter in this artery for patients with pulmonary hypertension by Hoeper et al.[2001]. A mean bias between both techniques of 0.1 L/min was found. In all but twocases, an acceptable overall agreement was found. These two cases however increasedthe 95% confidence interval of the difference between the two techniques to 2.0L/min. The measurements in the study by Hoeper et al. [2001] were not performedsimultaneously, but within a time frame of 24 hours. Since the patients showedhigh variation in stroke volume measured with both techniques, nonsimultaneouslyperforming measurements is a possible cause for the large differences found in somepatients.

When the image plane was chosen at a sufficient distance from the aortic valve,valvular disease has no influence on the measurement [Lotz et al., 2002]. Since thecoronary arteries bifurcate before the blood flows through the image plane approxi-mately 5% of the cardiac output is lost [Mymin and Sharma, 1974].

Magnin et al. [1981] compared Doppler echocardiographic flow measurementswith pulsatile flow in a phantom and found a correlation of r = 0.86. They alsoperformed measurements on patients undergoing cardiac catheterization and founda correlation of r = 0.83. However, the latter comparison showed a large bias ofabout 3 L/min.

PC-MRI measurements are often compared to Doppler echocardiographic mea-surements, since this is considered the gold standard in the clinic. However, Leeet al. [1997] proved that PC-MRI correlates much better with flow in a phantom(r>0.99) than Doppler echocardiography (r = 0.78). Errors in echocardiographycould be caused by the flat profile that is assumed. PC-MRI takes into account thevariation of flow in the vessel within the spatial resolution. Furthermore, Dopplerechocardiography is more prone to errors in the area of the aorta since this areais determined from a manually determined diameter, meaning that the aorta is as-sumed to be circular. PC-MRI is less sensitive to the area chosen, since all pixelsin the aorta are considered. When the area of the aorta for PC-MRI measurementsis chosen too large, the pixels outside the aorta have no contribution since, in thosepixels, there is no velocity in the direction of interest.

2.5.3 Ultrasound dilution

Cardiac output measurements

Kisloukhine and Dean [1996] compared the ultrasound dilution method against mea-surements with an ultrasound flow probe that was placed on the ascending aorta.

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These measurements were done on anesthetized pigs whose right femoral artery andvein were cannulated for hemodialysis. They also placed the animals on right atrialto left atrial bypass and compared pump flow to cardiac output from ultrasounddilution. Ultrasound dilution compared favorably with both methods, the goodnessof regression between dilution and flow probe was r= 0.95 and r was 0.99 for thecomparison of ultrasound dilution and pump flow.

Ultrasound dilution was also validated against thermodilution in intensive careunits in humans during detoxification by Nikiforov et al. [1996]. Again good agree-ment was demonstrated (r=0.97). However, it is impossible to simultaneously per-form ultrasound dilution and thermodilution measurements. Differences in cardiacoutput measured with the techniques can thus also be caused by unstable hemody-namics of the patient. Tsutsui et al. [2009] therefore tried to assess cardiac stabilityby measuring cardiac output with thermodilution before and after ultrasound dilu-tion measurements. When the two thermodilution measurement deviated too much,those series of measurements were neglected. Tsutsui et al. [2009] concluded thatultrasound dilution provides an accurate estimate of cardiac output, since the biaswas 0.02 L/min and when the fraction of differences between measurements andmean of measurements were calculated a 95% confidence limit of about 24% wasfound. According to the criterium of Critchley and Critchley [1999] that takes theaccuracy of the reference method (in this case thermodilution) into account, the twotechniques could be interchangeably used to measure cardiac output in patients.The criterium of Critchley and Critchley [1999] will be explained further in Para-graph 3.3. For the experiments of Tsutsui et al. [2009] blood lines were connectedto a catheter in the radial artery and a central venous catheter. This deviates fromthe setup during dialysis, but is thought to be comparable since the indicator stilltravels through the cardiopulmonary system.

Access flow measurements

There is no gold standard for noninvasive vascular access flow measurements andvalidation studies of the ultrasound dilution technique are therefore difficult. Kriv-itski [1995] has compared ultrasound dilution measurements of access flow to flowin a phantom. Access flow of 200 to 2200 ml/min were simulated and it was con-cluded that flow can be measured within an error of 5%. An increase of access flowincreases measurement errors. Smaller access diameters create better mixing condi-tion and better accuracy [Krivitski, 1995]. When flow becomes very high (> 2500ml/min) mixing presumable becomes difficult. To ensure good mixing of saline andblood, the needle tips should have a minimal distance of 3 cm and the venous outletshould face the access stream as in Figure 2.9. Bosman et al. [1996] compared invivo measurements with magnetic resonance angiography (MRA), which they con-sidered the most reliable technique to measure vascular access flow, for 22 patients.MRA measurements were performed immediately before hemodialysis. The corre-lation between MRA and ultrasound dilution access flow measurements was r=0.91(p<0.001).

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2.6 Conclusion

A technology that provides cardiac output estimates for patient diagnostics and in-put for the wave propagation model, should ideally be noninvasive, accurate andreliable. Nexfin CO is a noninvasive technique that can measure cardiac output ona beat-to-beat basis. Unfortunately, Nexfin CO has not been validated and it isunknown how a vascular access effects the measurements. Therefore, Nexfin will bevalidated for both healthy volunteers and hemodialysis patients. Both PC-MRI andechocardiography are popular techniques for measuring cardiac output in the clinic.The advantage of echocardiography is the possibility of measuring simultaneouslywith Nexfin. However, PC-MRI showed to be more accurate than echocardiographyand it was therefore decided to compare this technique with Nexfin cardiac outputmeasurements to assess the accuracy of Nexfin. Ultrasound dilution measurementscan only be performed on hemodialysis patients during their treatment, making itimpossible to use these measurements to obtain cardiac output for the wave propaga-tion model. However, it provides an unique opportunity to determine the accuracyof Nexfin cardiac output measurements in patients with an AVF, since measure-ments can be performed simultaneously and during the regular dialysis treatmentof a patient. Furthermore, with this technique it can be determined whether Nexfincan accurately measure cardiac output in patients with a vascular access. Thus,Nexfin measurements will also be compared to ultrasound dilution measurements ina population of hemodialysis patients.

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Chapter 3

Measurement protocol and dataprocessing

In this chapter, the measurement protocol for the comparison of Nexfin with phase-contrast MRI (PC-MRI) and with ultrasound dilution is described. Nexfin wascompared to PC-MRI in healthy volunteers and end-stage renal disease patients,prior to AVF placement, to assess whether Nexfin can accurately determine cardiacoutput. The measurement protocol and data processing can be found in Paragraph3.1. Since it is important to monitor cardiac output in hemodialysis patients andan AVF might have influence on Nexfin measurements, Nexfin was also compared toultrasound dilution for hemodialysis patients. Details about this comparison can befound in Paragraph 3.2. Statistical analyses applied in both studies are described inParagraph 3.3.

3.1 Nexfin versus PC-MRI in healthy volunteers andend-stage renal disease patients

Measurements were performed on 10 healthy volunteers (4 males and 6 females,all non-smokers) and 3 end-stage renal disease patients (3 males, 1 smoker). Mea-surements on patients were performed a few months prior to AVF placement, noneof the patients had an old AVF. Characteristics of the population can be foundin Table 3.1. Nexfin and phase-contrast MRI measurements of healthy volunteerswere performed within 1 to 5 hours. Patients were scanned 13-22 days after Nexfinmeasurements. All measurements were performed as a part of a larger study pro-tocol (ARCH-project), all subjects signed a written informed consent before theyparticipated in the study protocol.

Table 3.1: Characteristics of healthy volunteers and hemodialysis patients, displayedin means and ranges

Subjects Number of subjects Age [years] Height [cm] Weight [kg]Healthy 10 26 (22 - 36) 176 (159 - 188) 71 (56 - 86)Patients 3 76 (72 - 77) 175 (168 - 180) 78 (69 - 85)

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3.1.1 Measurement protocol

Both PC-MRI and Nexfin measurements were performed while the subject was insupine position and at rest. To determine whether the output of the Nexfin mea-surements depends on which hand was measured on, both left and right hand weremeasured simultaneously with two Nexfin machines. Cuffs were applied on the mid-dle finger of each hand and connected, together with the heart reference system, tothe wrist unit, which is a unit that is strapped around the wrist and connects thecuff and heart reference system to the Nexfin monitor. All Nexfin cuffs were appliedby the same person. A medium size cuff was used for all subjects except for one, asmall size cuff had to be used for this person.

Both Nexfins were started and while waiting for the Physiocal interval to in-crease, ultrasound measurements of the brachial artery were started with the Picuswith ART.LAB functionality (ESAOTE, Maastricht, the Netherlands). Distension,i.e. diameter change, measurements of the brachial artery were used to determinethe Young’s modulus of the arteries, used as input for the model in Chapter 5.The brachial artery, at mid upper arm level, was located with ultrasound. After 10minutes rest, from the moment the Nexfin cuffs were applied, at least three mea-surements of 6 seconds of the distension of the brachial artery were done in B-mode.Nexfin analogue output was connected to the ultrasound machine, in order to si-multaneously record brachial blood pressure with ultrasound brachial distension.Moreover, two Nexfin recordings were made of 70 heart beats in which no Physiocalwas executed. These two recordings for each hand were used for data analysis. Inone subject (the one with the small size cuff) intervals of only 60 heart beats with-out a Physiocal could be reached. A marker was set simultaneously in each of thetwo Nexfin recordings, to be able to retrospectively synchronize the blood pressuremeasurements of the two hands performed by the two Nexfin machines.

Only one Nexfin with a cardiac output and analogue output module was avail-able. The analoge output module of Nexfin had to be connected to the ultrasoundmachine during the distension measurements. The cables that connect the wristunit to the Nexfin monitors were exchanged to also perform cardiac output andultrasound distension measurements on the contralateral arm. Finger cuffs werenot removed. The above described measurements of distension and Nexfin CO wererepeated.

PC-MRI measurements were done with a 1.5 Tesla MR scanner (Intera R9.1,Philips HealthCare, Best, the Netherlands). After performing a survey scan todetermine the measurement location in the ascending aorta, the subject was told tohold his breath and a PC-MRI measurement was done. ECG was used to triggerthe data acquisition to the R peak of the ECG. During one PC-MRI measurementthe flow in the aorta is measured during approximately 20 heart beats. Every heartbeat, a part of the k-space that makes up an image, at a certain time after the Rpeak on the ECG, is filled. Multiple k-spaces are partially filled or filled up duringone heartbeat and this is repeated for the following heart beats, until all k-spacesare fully filled. Eventually, 20 images in time are obtained. This measurement wasperformed three to five times. MR parameters can be found in Appendix A.

Nexfin and PC-MRI measurements could not be performed simultaneously, sinceNexfin is not MR compatible. To study the influence of this on measurements, Nexfinmeasurements were repeated a few weeks later for four subjects. Due to cost and

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availability, it was not possible to repeat the PC-MRI measurements.

3.1.2 Data processing

Nexfin data was exported and processed with Matlab 7.5 (The MathWorks, Nat-ick, USA). The mean and standard deviation of the cardiac output, stroke volume,heart rate and finger blood pressure in each of the two recordings were calculatedfor analysis. Simultaneously recorded blood pressure data of the right and left handwas exported from Nexfin and synchronized retrospectively, to be able to determinewhether there was an effect of the measured hand on finger pressure in this popula-tion. Synchronization was done with help of the location in time of the marker. Thelocation of the diastolic blood pressure closest to the marker was used to determinethe timing difference between both Nexfin machines. The difference in time thatwas found, was corrected for.

PC-MRI results were obtained with MR Cardiac Analysis implemented in View-forum 6.1 software (commercially available from Philips Medical Systems Nether-lands B.V., Best, The Netherlands). First, the contour of the aorta was manuallydetermined in the magnitude image at diastole. This contour was propagated au-tomatically through every image and manually corrected when necessary. Thesecontours were copied to the phase-contrast images, from which the flow was quanti-fied. Viewforum calculated the flow in 20 time points in the cardiac cycle and fromthis stroke volume and cardiac output were determined. Average heart rate wasdetermined from the length of the flow profile.

3.2 Nexfin versus ultrasound dilution in hemodialysispatients

Simultaneous Nexfin and ultrasound dilution measurements were performed in 11hemodialysis patients (5 males and 6 females, 1 smoker) during their hemodialy-sis treatment. It was chosen to perform the measurements during the first hourof hemodialysis, since this hour is the period in which patients are hemodynami-cally most stable. Only patients without an old AVF in the contralateral arm wereincluded. It was desired to perform Nexfin measurements on this arm, since mea-surements on the fingers of the arm used for dialysis are very difficult due to lowpressure in the finger arteries. The average length of these patients was 170 cm(range 161 - 183 cm), the average weight was 73 kg (58 - 102 kg) and the averageage was 68 years (55 - 81 years). For nine patients the Nexfin finger cuff was rappedaround the right middle finger and for 2 patients around the middle finger of theleft hand. All patients signed a written informed consent before participating.

3.2.1 Measurement protocol

Nexfin and ultrasound dilution measurements were performed simultaneously. First,cuffs were applied at the middle finger of the arm contralateral to the arm with theAVF and Nexfin was started. Ultrasound dilution measurements were done withHD03 (Transonic Systems Inc, Ithaca, New York, USA). The ultrasound dilutionmeasurements were not started until Nexfin executed a Physiocal for a few timesand blood pressure measurements were stable. Cardiac output was measured with

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ultrasound dilution by injecting 30 mL of body-temperature saline in the venousline. Since the kidneys of hemodialysis patients are unable to clear the saline out ofthe blood, it was decided to repeat this measurement only once.

With regard to the vascular access flow, an access flow measurement of eachpatient, obtained as a part of the standard clinical treatment, was considered. Inthis way, the effect of access flow on the accuracy of Nexfin measurements, couldbe determined. The measurement that was performed closest to the cardiac outputmeasurements were taken for analysis. Measurements were performed with ultra-sound dilution at the beginning of a dialysis session, 1.5 to 2.5 months after thecardiac output measurements with ultrasound dilution, by reversing the blood linesas described in Chapter 3.

3.2.2 Data processing

Unfortunately, exact synchronization of the ultrasound dilution and the Nexfin mea-surements was not possible. It was assumed, from observations during several mea-surements, that the ultrasound dilution measurement device started measuring thedilution curve in the arterial blood line 10 seconds after saline injection and that thismeasurement lasted 10 seconds. Nexfin cardiac output values were thus averagedfor these last 10 seconds. When a Physiocal occurred during these 10 seconds, thesevalues were removed.

3.3 Statistical analysis

In medical literature, measurement techniques are often compared to a gold standardin a Bland-Altman plot [Bland and Altman, 1986]. This bias and precision statis-tics involves plotting the differences between comparative measurements, called thebias, against the mean values of each pair of readings. 95% confidence limits (µ±2σ), which are referred to as the limits of precision, can be drawn. µ refers to themean bias and σ to the standard deviation of the mean bias. Using the limits ofprecision, judgement can then be made regarding the precision and acceptability ofthe new technique against the reference technique. Critchley and Critchley [1999]recommended to report the statistical results of bias and precision for cardiac outputmeasurements in percentages, since Bland and Altman’s method does not compen-sate for relationships between the magnitude of the cardiac output and the size ofthe error. Furthermore, validation studies of new techniques to determine cardiacoutput often state absolute values of the precision limits and compare these to theprecision limits of the reference technique. However, absolute values are only usefulwhen the mean cardiac output measured with the reference technique equals themean cardiac output of the measurements with the method to be tested.

The Bland and Altman analysis lacks criteria with respect to the bias and pre-cision statistics; it is unclear when a technique is precise enough to replace an oldermore established method. Therefore, Critchley and Critchley [1999] advised to judgethe acceptance of a new method A to measure cardiac output against the precision ofthe current reference method B. The limit of precision of the validation experimentdepends on the limits of precision of the methods A and B. An error-gram (Figure

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Figure 3.1: Error-gram adapted from Critchley and Critchley [1999] enabling one tographically determine the limits of agreement between two techniques that measurecardiac output. The x-axis refers to the limits of precision in percentages (± 2 σ/µ),of the method being tested A. The isolines refer to the limit of precision (%) of thereference method B. The y2-axis shows the resultant limit of agreement betweenmethods. The y1-axis shows the corresponding absolute limits of agreement for atypical study with an overall mean cardiac output of 5 L/min. An example is shownwhere the limits of precision for both the test and reference methods are ±20% andpredicted limits of agreement are shown to be ±28.3% and ±1.42 L/min.

3.1) based on the following equation:

σA+B =√σ2A + σ2

B, (3.1)

was constructed to enable a graphical determination of the limit of agreement ofexperiments done with the two techniques to measure cardiac output. For Equation3.1 it is assumed that the measurement results for method A and B are independentof each other. The limit of agreement is the maximal limit of precision when com-bining method A and B that is allowed. When the combined limit of precision issmaller or equal to the limit of agreement, the reference technique can be replacedby the new technique. The method developed by Critchley and Critchley [1999]was used for comparison of Nexfin with PC-MRI and ultrasound dilution. SinceNexfin and MRI measurements were not done simultaneously, it was chosen to usestroke volume instead of cardiac output for this analysis, to eliminate the effect ofa different heart rate.

Repeatability of the measurement method is relevant when comparing meth-ods, because the repeatabilities of the two methods limit the amount of agreementwhich is possible [Bland and Altman, 1986]. In the case that one method has poorrepeatability, i.e. there is considerable variation in repeated measurements underthe same circumstances, the agreement between the two methods is bound to bepoor. Repeatability is therefore determined by assessing the standard deviation of

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the 3-5 repeated PC-MRI measurements, the standard deviation of the 2 Nexfinmeasurements of the right hand and the standard deviation of the 2 measurementsof the left hand. Repeatability of ultrasound dilution and Nexfin measurementswas determined by assessing the standard deviations of both techniques. Repeatedmeasures analysis of variance (ANOVA) was used to determine whether there was adifference in standard deviation between Nexfin and PC-MRI, and between Nexfinand ultrasound dilution.

Repeated measures ANOVA was also used to evaluate the effect of several factorson measured cardiac output or stroke volume. For the comparison of Nexfin withPC-MRI the factors tested for their effect were the use of a certain method (Nexfin orPC-MRI) and the hand (left or right) that was measured on with Nexfin. Thus, withthe method -factor, the differences between stroke volume determined by Nexfin andPC-MRI was investigated. The hand -factor can be used to investigate the differencein stroke volume determined by Nexfin on the left and right hand. The latter wasalso done for the pressure differences between hands.

For every subject three to five PC-MRI stroke volume measurements were avail-able. However, since a repeated measures ANOVA will ignore all data of one subjectwhen there is a missing value, when five measurements were available three were ran-domly picked to make analysis possible. The method-factor consisted of seven levels:the three PC-MRI measurements, two measurements on the right hand and two onthe left hand with Nexfin. Since it was not of interest to compare the seven levelsof the method-factor, contrasts were used. These contrasts made it possible to com-pare a group of three levels of PC-MRI and a group of two Nexfin levels of eitherthe right or left hand, by making a linear combination of the different levels. It ispossible that the subjects experience more stress in the MRI than during the Nexfinmeasurements. To study the influence of stress, the effect of the method -factor onheart rate was investigated as well. For four subjects, Nexfin measurements wererepeated a few weeks later. Differences in stroke volume between these time pointswere also assessed with repeated measures ANOVA.

For the Nexfin ultrasound dilution comparison, the influence of the followingfactors was investigated: method, age and access flow. This time the method-factorconsisted of four levels: two consecutive ultrasound dilution measurements and twosimultaneously performed Nexfin measurement. Again contrasts were used to makea group of ultrasound dilution measurements and a group of Nexfin measurements.The possible effect of age was investigated by making two age categories: patientswere divided among the 50-69 years category and the 70-89 years category, resultingin five patients per group. The access flow factor was also subdivided in normalaccess flow (access flow ≤ 30% of cardiac output measured with ultrasound dilution)and high access flow (access flow > 30% of cardiac output measured with ultrasounddilution) as defined by MacRae et al. [2004].

In the ANOVA test F-tests are used to determine the significance of a certaineffect. F-tests assess the proportion of variance of a factor that can be explained bythe ANOVA model and the variance that cannot be explained by the model. F-testsare valid under three assumptions:

• Normality: the data arise from populations with normal distribution.

• Homogeneity of variance: the variances of the assumed normal distributionsare equal across groups.

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• Sphericity: the variances of the differences between all pairs of the repeatedmeasurements are equal. Sphericity is not an issue when testing between-subject factors.

Of these assumptions, the third is the most important when testing within-subjectfactors. All ANOVA tests were done using SPSS version 17.0. The significance valuewas placed at a p-value of 0.05.

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Chapter 4

Measurement results

In this chapter, results of cardiac output measurements with Nexfin are presentedand compared to phase-contrast MRI (PC-MRI) and ultrasound dilution measure-ments. PC-MRI measurements were executed on healthy volunteers and on end-stage renal disease patients. The patients were measured prior to AVF creation.Nexfin cardiac output was compared to ultrasound dilution cardiac output for hemodial-ysis patients during hemodialysis treatment.

4.1 Nexfin cardiac output versus PC-MRI stroke vol-ume in healthy volunteers and end-stage renal dis-ease patients

In total, measurements were performed on 10 healthy volunteers and 3 end-stagerenal disease patients without AVF. Data of one patient was discarded from furtheranalysis, since it was impossible to measure cardiac output with Nexfin in one handdue to distortions in the finger pressure recording. All raw measurement results canbe found in Appendix B. Only healthy volunteers were included for the analysesdescribed below, since patients were short of breath or had chest pain and a highlyvariable heart rate. This indicates that the hemodynamics of these patients mightbe unstable and therefore large differences can occur between the measurement withthe two different methodologies due to the fact that measurements were not donesimultaneously.

Figure 4.1 shows the comparison of the stroke volume measured with Nexfinand with phase-contrast MRI for the healthy volunteers. For this figure all Nexfinmeasurements of one hand and all PC-MRI measurements were averaged, since aspecific Nexfin measurement cannot be linked to a specific PC-MRI measurement.Nexfin overestimates stroke volume measured on the right hand for 7 subjects andon the left hand for 8 subjects. To judge whether Nexfin is accurate enoughto replace PC-MRI cardiac output measurements, the method described before byCritchley and Critchley [1999] was used. First, the limit of precision of the PC-MRImeasurements needs to be known. Møgelvang et al. [1992] have compared PC-MRIto indicator dilution and displayed their results in a regression plot. A Bland-Altmanplot (Figure 4.2) was constructed from this. The mean indicator dilution cardiacoutput was 7.0 L/min, the mean PC-MRI cardiac output was 6.9 L/min. The meanbias was -0.1 L/min, the upper limit of precision was 0.7 L/min and the lower limit

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Figure 4.1: Average of Nexfin measurements of each hand plotted against the averageof PC-MRI measurements for 10 healthy volunteers

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Figure 4.2: Bland-Altman plot of PC-MRI cardiac output (CO) compared to indi-cator dilution CO, data was based on Møgelvang et al. [1992]. Bias was defined asPC-MRI CO - indicator dilution CO.

was -0.9 L/min. The limit of precision (± 2 σ /µ) was 11%. When the criteriumis used that Nexfin has to be as precise as PC-MRI, i.e. Nexfin also has a limit ofprecision of 11%, it can be calculated with Equation 3.1 that the combined limit ofagreement of the Nexfin and PC-MRI measurements is 16%.

Figure 4.3 depicts the Bland-Altman comparison between the average of the 2Nexfin measurements of the right or left hand and the 3 PC-MRI measurements.The mean PC-MRI stroke volume was 89.0 mL, the mean stroke volume for theNexfin right hand measurements was 105 mL, for the left hand the mean was 106mL. For the comparison with the right hand, mean bias was 16.2 mL, the upperlimit of precision was 51.9 mL, the lower limit was -19.4 mL. For the left hand thesevalues were 17.2 mL, 52.6 mL and -18.2 mL respectively. The limits of precision forthe comparison between PC-MRI stroke volume and Nexfin stroke volume of boththe right and left hand were 36%. This is much higher then the limit of agreementof 16% calculated with the criterium of Critchley and Critchley [1999].

Repeatability was assessed by determining whether the difference of the standarddeviation of the PC-MRI measurements and the Nexfin measurements was signifi-cant. This was done with a repeated measures ANOVA. The data was distributednormally and homogeneity of variance and sphericity was not of importance sincethere is only one group and only two measurements for each subject are compared.The standard deviation of Nexfin stroke volume determined on the right and lefthand were both significantly different from the standard deviation of PC-MRI strokevolume for the 10 healthy volunteers (p < 0.01 in both cases). Mean standard devi-ation of PC-MRI, Nexfin right hand and Nexfin left hand measurements were 4.30

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Figure 4.3: Bland-Altman plots comparing Nexfin stroke volume (SV) with PC-MRISV, for healthy volunteers. Bias was defined as Nexfin - PC-MRI stroke volume.

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mL, 1.28 mL and 1.30 mL respectively. Thus, Nexfin has a better repeatability thanPC-MRI.

Two of the healthy volunteers had arrhythmias. To determine the effect of ar-rhythmias on the analyses, Bland-Altman analyses were repeated without the valuesof the two subjects with arrhythmias. The limit of precision for the comparison be-tween Nexfin stroke volume on the right hand and PC-MRI stroke volume remainedunchanged while the limit of precision for the left hand decreased to 31%.

Subjects could possibly experience more stress in the MRI scanner than duringthe Nexfin measurements. To assess this effect, a repeated measures ANOVA wasdone, to compare heart rates between measurements. The data was distributednormally. Homogeneity of variances was not of importance, since there is only onegroup. Due to the use of contrasts there are only two levels that are compared (heartrate during PC-MRI and during Nexfin measurements) and therefore variances ofdifference between pairs cannot be assessed. A significant difference (p < 0.02)between heart rate during PC-MRI and Nexfin measurements was found. Howeverthe difference was small, the mean of the Nexfin and PC-MRI measurements were60 bpm (confidence interval: 58 - 61) and 64 bpm (confidence interval: 61 - 67)respectively.

Measurements with the two different modalities were not done simultaneously.To investigate this effect on stroke volume measurements, Nexfin measurements of4 healthy volunteers were repeated a few weeks later. Measured data can be foundin Appendix B. Again, a repeated measures ANOVA was done. The data had anormal distribution, homogeneity of variances and sphericity was not of importance.No significant difference was found between the stroke volume measured by Nexfinon day 1 and on day 2 in this population. A Bland-Altman percentage plot revealeda limit of precision of 14% for the right hand and 33% for the left hand. The largelimit of precision of the left hand was due to the measurements on one subject. Thishealthy volunteer had a right-to-left stroke volume difference of 0.5 mL during theNexfin measurements on day 1 and a difference of 18 mL when measurements wererepeated. Since this was the subject that needed the S size cuff, it was possibly verydifficult for Nexfin to find the setpoint diameter and the difference in stroke volumethus likely was a measurement error. The limits of precision without this subjectwere 11% and 6% for the right and left hand respectively.

To investigate the effect of the hand in which the stroke volume was determinedon the measured stroke volume, finger pressure was measured simultaneously onboth hands of all healthy volunteers and end-stage renal disease patients. Unlikefinger blood pressure, stroke volume could not be measured simultaneously on bothhands because only one Nexfin with a cardiac output module was available. But,since all healthy volunteers were hemodynamically stable, their left and right handstroke volume could be compared, even for non-simultaneous measurements. AnANOVA repeated measures analysis was done to determine the effect. The data wasdistributed normally, homogeneity of variance is not an issue since there is only onegroup. Sphericity is no issue either since due to the use of contrasts the hand factorhas only two levels (left and right). No significant difference was found betweenthe systolic, diastolic and mean blood pressure and stroke volume of the right andleft hand of the healthy population. Despite this, there can still be differences inblood pressure in individuals that lead to differences in stroke volume. For example,one healthy volunteer showed an average systolic finger blood pressure difference of

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about 20 mmHg between left and right and as a result a stroke volume difference ofabout 15 mL, which is about 17% of the subjects stroke volume.

Nexfin cardiac output, stroke volume and heart rate measurements on patientsshowed signs of cardiac instability. The standard deviation of Nexfin stroke volumeand heart rate measurements of patient 1 in Table B.2 of Appendix B shows thatthis patient had highly variable stroke volumes and heart rates due to arrhythmias.The standard deviation of the measured stroke volume reaches up to 29% of themean stroke volume, the standard deviation of the heart rate was approximately18% of the mean heart rate. Patient 2 showed a large difference in heart rate ofapproximately 30 beats/min between Nexfin measurements of the right and lefthand that were only 15 minutes apart. The two patients had a systolic left-to-rightfinger pressure difference of 43 and 25 mmHg, because Nexfin uses systolic pulsecontour analysis to determine stroke volume, this will certainly lead to significantlydifferent stroke volume between hands.

Stroke volume measured with Nexfin were higher than stroke volume measuredwith PC-MRI for both patients. For patient 1, PC-MRI stroke volume differed with28 L/min from Nexfin stroke volume measured on the right hand and with 6 L/minfrom left hand Nexfin stroke volume. Patient 1 showed differences of 29 L/min and55 L/min between PC-MRI stroke volume and Nexfin stroke volume of the rightand left hand respectively. Reasons for these differences are difficult to assess dueto the cardiac instability of the patients.

4.2 Nexfin cardiac output versus ultrasound dilutioncardiac output in hemodialysis patients

In total, Nexfin cardiac output and ultrasound dilution cardiac output of 11 hemodial-ysis patients was collected. Nexfin was unable to perform pressure recordings on thefinger artery of one patient. One out of two measurements of another patient wasignored since the standard deviation of the Nexfin measurement was extremely highdue to motion artifacts. All data can be found in Appendix C.

The comparison between Nexfin cardiac output and ultrasound dilution cardiacoutput can be found in Figure 4.4. Nexfin overestimated cardiac output in six pa-tients. A difference in Nexfin cardiac output between older patients and youngerpatients was found. This difference was not present in the ultrasound dilution mea-surements (Figure 4.4).

Tsutsui et al. [2009] found a limit of precision of 23.5% for the ultrasound dilutiontechnique. If Nexfin is desired to be as precise as this, this leads to a combinedlimit of agreement criterium of 33% (Equation 3.1). The Bland-Altman plot ofNexfin cardiac output compared to ultrasound dilution cardiac output is shown inFigure 4.5. The mean ultrasound dilution cardiac output is 4.5 L/min, while themean Nexfin cardiac output is 5.4 L/min. Mean bias is 0.86 L/min, with upperand lower limits of precision of 3.5 and -1.7 L/min respectively. In percentage thelimit of precision reads 45%. Critchley and Critchley [1999] stated that consecutivemeasurements can be averaged to improve their accuracy. In our study, this hasvery little effect on the limit of precision, which was 44% after averaging. The biaswas also similar.

Repeatability was assessed by determining the standard deviation of the ultra-

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ac o

utpu

t [L/

min

]

50−69 year70−89 yearNexfin = Ultrasound dilutionPatient with one data point

Figure 4.4: Nexfin cardiac output measurements plotted against ultrasound dilutionmeasurements for 10 patients, with error bars indicating ± standard deviation.

3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5

−60

−40

−20

0

20

40

60

Mean CO [l/min]

Bia

s [%

]

Figure 4.5: Bland-Altman percentage plot of the Nexfin ultrasound dilution com-parison. Bias was defined as Nexfin - ultrasound dilution cardiac output.

44

sound dilution and Nexfin measurements. A repeated measures ANOVA was doneto determine whether the difference between the standard deviations was significant.Data of 9 patients was included, since of one patient only one good measurementwas available. The data was distributed normally and homogeneity of variance andsphericity was not of importance since there is only one group of patients and onlytwo standard deviations for each subject were compared. Mean standard devia-tion of ultrasound dilution cardiac output and Nexfin cardiac output measurementswere 0.25 L/min and 0.12 L/min respectively. No significant difference was foundbetween the standard deviation of Nexfin cardiac output and ultrasound dilutioncardiac output for the patients.

Repeated measures ANOVA tests were done to determine the effects of the fac-tors method (Nexfin or ultrasound dilution), age and access flow on cardiac outputmeasurements. The age factor consisted of two categories: 50-69 years old and 70-89years old, resulting in two groups of five patients. With regard to the access flow,the patients were divided in normal access flow (access flow ≤ 30% of cardiac outputmeasured with ultrasound dilution, n = 7) and high access flow (access flow > 30%of cardiac output measured with ultrasound dilution, n = 3) as defined by MacRaeet al. [2004]. Data was distributed normally. Homogeneity of variance is not of im-portance because there is only one group. Sphericity is not an issue, since due to theuse of contrast there are only two levels for each factor. The results of the ANOVAtests can be found in Table 4.1. The significance of a source is derived from theF-test. The ANOVA test revealed no significant difference in cardiac output for thetwo methodologies. Although there seems to be a difference between the accuracy ofNexfin in the 50 - 69 year old patients and the 70 - 89 year old patients (Figure 4.4and Figure 4.6), the interaction effect of method and age category was not signifi-cant. There was no significant difference between the accuracy of Nexfin for patientswith normal access flow and for patients with high access flow. The interaction ef-fect between method and access flow category has the lowest mean square and thusthis factor explained the least variance on the cardiac output. When this interactionfactor was excluded from the model, the error decreased and both the method-factorand the interaction between method and age category were significant (p = 0.03 forboth factors).

45

Table 4.1: Results of ANOVA test. The mean square is derived from the sum ofsquared differences between the cardiac output of a certain group and the cardiacoutput of the population, and the number of observations in a certain group. Frepresents the results of the F-tests which is the ratio between the variance of asource explained by the model (the mean square of a source) and the variance thatis unexplained by the model (the mean square of the error). The significance of asource is derived from the F-test.

Model Source Mean Square F Significance1 method 1.27 4.14 0.09

method · access flow category 0.07 0.23 0.65method · age category 0.81 2.63 0.16error 0.31

2 method 2.03 7.46 0.03method · age category 1.89 6.94 0.03error 0.27

Ultrasound dilution Nexfin3

4

5

6

7

8

9

CO

[L/m

in]

50 − 69 year70 − 89 year

Figure 4.6: Profile plot of Nexfin and ultrasound dilution measurements for thedifferent age categories. Error bars indicate the 95% confidence interval.

46

47

Chapter 5

Nexfin CO and wavepropagation model

Both Nexfin CO and the patient-specific wave propagation model relate finger pres-sure to cardiac output. To obtain more insight into the working of the Nexfin COalgorithm, the differences in outcome between the patient-specific wave propagationmodel and the Nexfin CO algorithm are studied. In Chapter 4, the precision ofNexfin CO cardiac output calculations was determined. A sensitivity study of themost important input parameters of the wave propagation model was done to as-sess whether the effect of Nexfin CO measurement inaccuracies on simulated fingerand brachial blood pressure is relatively large compared to other input inaccura-cies. The input parameters that were chosen for the sensitivity study in additionto cardiac output are: arterial radius and Young’s modulus. In addition, the ef-fect of variations in arterial diameters, cardiac output and Young’s modulus on theNexfin CO algorithm is studied. It is not possible to directly study the influenceof these parameters on the cardiac output determined by Nexfin. However, thefinger pressure simulated by the wave propagation model can be used as input forthe Nexfin CO algorithm, thereby using the wave propagation model as an artificial‘patient’, to give insight into the sensitivity of Nexfin CO to changes in cardiac out-put, arterial radius and Young’s modulus. To clarify this approach, the procedureis described schematically in Figure 5.1. Simulations with Beatscope are includedto generate the brachial pressure waveforms, as this is not possible with Nexfin CO.The Beatscope program (BMEYE, Amsterdam, the Netherlands) transfers fingerpressure to brachial pressure with a transfer function, similar to the one used byNexfin CO (described by Gizdulich et al. [1997]) except for age-dependence.

In this chapter, first the basics behind the wave propagation model will brieflybe described. Information about the input parameters and boundary conditions ofthe model will be given, in addition to the input of the Nexfin CO algorithm. Thevariations applied on several input parameters for the sensitivity analysis of boththe wave propagation model and the Nexfin CO model will also be described.

5.1 Wave propagation model

All simulations were done with the wave propagation model of Bessems [2007]. Inthis model, the conservation of one-dimensional mass and momentum equations were

48

Figure 5.1: A diagram of simulations with the wave propagation model and theNexfin CO model (in black), the simulation with Beatscope is displayed in blue.The pictogram indicates whether a waveform was available. The finger pressurewaveform simulated by the wave propagation model was used as input for the NexfinCO algorithm and Beatscope. SV = stroke volume.

solved considering blood as an incompressible Newtonian fluid. To be able to solvethe wave propagation model for pressure and flow, a velocity profile, which dependson the Womersley number, was introduced based on a boundary layer model. In thisstudy, the convection term in the momentum equation was omitted to ensure numer-ical stability. The arterial wall was modeled as a thick walled linear-elastic material.The governing equations were solved by applying a spectral element method. A timediscretization step of 0.001 seconds was chosen, output was registered every 0.01 sand started after 8 seconds. For more details about the numerical implementation,we refer to Bessems [2007]. Input parameters and boundary conditions are explainedin the next paragraph.

5.2 Wave propagation model input parameters

To make the wave propagation model patient-specific, the geometry, Young’s mod-ulus and input flow of the upper arm of four subjects were obtained. The imple-mentation of these parameters in the model will be explained in the paragraphsbelow.

5.2.1 Geometry

Patient-specific geometries were obtained for four subjects, i.e. two healthy volun-teers and two patients. Characteristics of all subjects can be found in Table 5.1.

The input geometry of the model was divided into three regions: the centralarteries, the arm arteries and the arteries in the hand. Diameters, lengths and wallthickness of the central artery segments were adapted from Stergiopulos et al. [1992],who based their data on Westerhof et al. [1969]. For every subject the diameterswere scaled with the factor between on the most proximally measured arm diameterand diameter from Stergiopulos et al. [1992] at this point. Wall thicknesses werescaled accordingly to [Westerhof et al., 1969], to remain the same wall thicknessdiameter ratio.

49

Table 5.1: Characteristics of healthy volunteers and hemodialysis patients, whosedata were used for the sensitivity analysis

Geometry ob-Subjects Number Gender Age [years] Height [cm] Weight [kg] tained ofHealthy 1 Female 36 180 77 Left arm

2 Male 28 187 84 Right armPatient 1 Male 77 168 85 Left arm

2 Male 72 176 81 Right arm

The geometry of the arm arteries was determined from contrast-enhanced MRIscans of the upper arm (the proximal scan) and the lower arm (the distal scan)which were available since all four subjects were included in the ARCH protocol. Toperform the proximal and distal contrast-enhanced MRI scans, low concentrationGadovist (20 ml x 0.5mmol/L at 3 ml/s) and subsequent NaCl flush (20 ml at 3ml/s) were injected in the contralateral arm. Philips SENSE-body and Synergy-Flex-L coil were used. Parameters for the contrast-enhanced MRI measurementscan be found in Appendix A. Diameters of the subclavian, brachial, radial, ulnarand interosseous artery were determined at the proximal, mid and distal level asdisplayed in Figure 5.2 using manually placed calipers. The diameters were aver-aged over five repeated measurements at each level. The length of the segmentswas determined by calculating the distance between the locations of the points ofdiameter determination. The distal and proximal contrast-enhanced scan overlap inthe area of the bifurcation of the brachial artery to the ulnar and radial artery, andthus, all segments were complete on at least one scan. The proximal and distal scanhave different pixel resolutions (Appendix A). This has an effect on the measure-ment errors in the diameters. It was chosen to use the diameters determined fromthe distal contrast-enhanced MRI scan for the most distal brachial artery diameter.The diameters of the radial and ulnar artery and the interosseous are also deter-mined from the distal scan. The diameters of the nodes between the measurementpoints were determined by linear interpolation. These nodes were included in thegeometry to make the lengths of the segments sufficiently small to ensure numericalconvergence.

The hand was not included in the scan volume and therefore, information abouhand geometry and radii have to be taken from literature. Figure 5.3 shows theclassical pattern of the arteries in the hand, often found in textbooks. In the classicalanatomy the ulnar and radial artery fuse together to form a superficial and a deeppalmar arch. However, several variations on these patterns are found, such as anincomplete superficial and/or deep palmar arch or a median artery that anastomoseswith the superficial palmar arch. A complete superficial palmar arch was found in47.5 - 84.4% of hands (Coleman and Anson [1961], Ruengsakulrach et al. [2001],Gellman et al. [2001], Bilge et al. [2006] and Fazan et al. [2004]). The complete deeppalmar arch was present in 90 - 100 % off all hands ([Coleman and Anson, 1961],[Ruengsakulrach et al., 2001] and [Gellman et al., 2001]). Since the anatomy of thehand arteries was unknown for the individual subjects it was chosen to take the mostcommon anatomy, i.e. both palmar arches were assumed to be complete. Gellmanet al. [2001], Fazan et al. [2004] and Bilge et al. [2006] have studied the lumen

50

Right subclavian artery

Left carotid artery

Vertebral artery

Left subclavian artery

Brachial artery

Radial arteryUlnar artery

Interosseous

Digital arteries

Palmar

Arch

Aorta

Abdominal

Aorta

Figure 5.2: Model geometry of the arm arteries. Measurement points are indicatedby a square. Three measurement points are located at the bifurcation of the brachialartery: the distal brachial artery and the proximal radial and ulnar artery. Thedashed square indicates a measurement of the interosseous only.

51

Figure 5.3: The classical arterial patterns of the hand (adapted from Gellman et al.[2001])

Table 5.2: Vessel lumen diameters adapted from Gellman et al. [2001]

Vessel diameter [mm]Radial artery 2.6Ulnar artery 2.5Superficial arch 1.8Deep arch 1.5Common digital arteries (superficial arch) 1.6Metacarpal arteries (deep arch) 1.2

diameters of the hand, the results found by Gellman et al. [2001] (Table 5.2) wereused in this study since this was the most complete data set and the diameters of theradial and ulnar arteries corresponded best with the mean diameters measured inthis study. For simplicity and to ensure numerical stability, it was chosen to modelonly one palmar arch. In literature, a reciprocal relation was found between thedeep and the superficial palmar arch. Moreover, since the difference between thediameter of the superficial palmar arch and the deep palmar arch was small (table5.2), the diameter of the single palmar arch in the model geometry was taken to bethe average of the diameter of both arches found by Gellman et al. [2001].

Coleman and Anson [1961] have found considerable variations in the anatomy ofthe digital arteries. However, 77.3 % of the hands examined had 5 common digitalarteries and 50.5 % had 5 metacarpal arteries, similar to the classical anatomyin Figure 5.3. The single palmar arch of the model was therefore given 5 digitalarteries. Since Coleman and Anson [1961] usually found a reciprocal relationshipwith respect to size between the common digital arteries and the metacarpal arteriesit was decided to use the average of the common digital and metacarpal lumendiameters found by Gellman et al. [2001]. Fazan et al. [2004] and Bilge et al. [2006]found no significant differences between the first four digital arteries and thereforeit was chosen to use the same diameter for the 5 digital arteries. They also foundno differences between the left and right hand.

The diameters of the palmar arch and the digital arteries, of every patient-specific

52

model, were scaled with the ratio between the diameters determined by Gellmanet al. [2001] and the subjects’s diameters, to ally the diameter of the palmar archwith the arm artery at the level of the ulnar and radial artery.

5.2.2 Arterial wall properties

Diameter and distension of the mid-brachial artery, were measured for every subjectwith ultrasound as mentioned in Chapter 3. Brachial pressure was measured simul-taneously with Nexfin CO. ART.LAB (ESAOTE, Maastricht, the Netherlands) wasused to analyse the results and assess the distension and the diameter. Since de-tection of the arterial walls was difficult in some measurements, only measurementswith a distension waveform following the pressure were taken into account. Thedistensibility (D) was determined from:

D =2 · r ·∆r + ∆r2

r2 ·∆p(5.1)

with radius r, distension ∆r and pulse pressure ∆p. Young’s modulus for a thickwalled tube was calculated from the distensibility, radius and wall thickness (h),such that:

E =3( rh + 1)2

D(2 rh + 1)(5.2)

It was assumed that the radius of the brachial artery was five times the wall thicknessas Kaiser et al. [2001] and Westerhof et al. [1969] have found.

Young’s moduli of the radial and ulnar artery were chosen to be twice that of thebrachial artery and the Young’s moduli of the hand and interosseous were chosenfour times the Young’s modulus of the brachial artery, analogous to Westerhof et al.[1969].

5.2.3 Boundary conditions

Input flow (cardiac output)

The average flow profile of the PC-MRI measurements was prescribed to the firstnode of the aorta segment of the model. The first 11 Fourier coefficients of thepatient specific profile were calculated and these coefficients were used as input.

End-segments

The total peripheral resistance (Rp) can be calculated from the mean pressure (p),the cardiac output (q), such that

Rp =p

q(5.3)

Mean pressure in Equation 5.3 was determined by assuming that the mean arte-rial blood pressure was equal to the patient-specific mean brachial blood pressuremeasured with Nexfin (Appendix D).

At the end of each truncated artery, a three element windkessel model, as dis-played in Figure 5.4, is prescribed. Since the time average wall shear stress isassumed to be equal for all extremities, it is found from a Poiseuille profile that each

53

Z0

RV

CV

Figure 5.4: The three element windkessel model of the end-segments

total resistance at extremity j, Rp,j is inversely proportional to the third power ofthe radius rj :

Rp,j =p

q

∑Nj1 r3

j

r3j

= Z0 +Rv, (5.4)

where Z0 =√

LC is the characteristic impedance of the segment, with:

L = ρπr2

C =2πr2(

2r2(1−ν2)

h2 +(1+ν)( 2rh

+1))

E( 2rh

+1)

(5.5)

determined by assuming a thick walled tube instead of a thin walled tube as inBessems [2007]. In which E is the Young’s modulus, ν the Poisson ratio, r theinternal arterial radius and h the wall thickness of the artery. Mean pressure inEquation 5.4 was determined by assuming that the mean arterial blood pressurewas constant across the entire geometry. The patient-specific mean brachial bloodpressure measured with Nexfin (Appendix D) was used for this. τ = RvCv, the timeconstant that defines the decay of the pressure signal, was assumed to be 1.5 seconds[Stergiopulos et al., 1999].

5.3 Sensitivity analysis of the wave propagation model

It was chosen to determine the local sensitivity of input parameters cardiac output,radius and Young’s modulus on the brachial and finger pressure and flow waveforms.These input parameters were chosen, because these are patient specific parameterswhich can be measured and are thought to have the largest effect on the output of themodel. The reference parameters set that was used for the sensitivity analysis can befound in Appendix D. For the sensitivity analysis the parameters were varied withtheir inaccuracy, these are described below. To determine the linearity of the effecton the output, also a variation of 50% of the inaccuracy was applied. Interactionsbetween parameters are neglected.

5.3.1 Input flow (cardiac output)

In Chapter 4 it was established that Nexfin CO can estimate the cardiac outputwith approximately 40% precision. Therefore, a 20% and 40% increase and decreasewas simulated for every subject. For the sensitivity analysis, the patient specificprofile was scaled to one second, while keeping the stroke volume unchanged beforethe Fourier coefficients were calculated.

54

Table 5.3: Measurements of brachial artery radius with contrast-enhanced MRImeasurements and with ultrasound measurements

Subjects Number Radius determinedwith MRI [mm]

Radius determinedwith ultrasound [mm]

Healthy 1 2.15 1.752 2.30 1.70

Patient 1 2.11 2.552 2.46 2.42

5.3.2 Geometry

To estimate the error on the diameter, the mid-brachial diameter determined withMRI was compared to the mid-brachial radius determined with ultrasound duringthe ultrasound distension measurements, (measurements are listed in Table 5.3).Ultrasound was chosen as the gold standard since from accuracy studies in thecarotid artery a standard error of 0.1 mm was found [Weber and Brands, 2008]. ABland-Altman percentage plot for the measurements of the four subjects revealed a40% limit of precision. For the sensitivity analysis, this variation was applied to theentire geometry.

No patient specific information was available for the diameters of the hand ar-teries, while errors in this region of the geometry are likely to have a large influenceon the pressure and flow in the finger. To investigate the effect of inaccuracy ofthe diameters of the hand arteries, only the hand artery diameters were changed,while the other diameters were unaltered. It was chosen to use the same maximalvariation of 40%.

5.3.3 Young’s modulus

The error in the determination of Young’s modulus with ultrasound cannot be com-pared to a gold standard. Therefore, this error is estimated from the variation of theparameters r, ∆r and ∆p on which the Young’s modulus depends on. The standarderror of the mean Young’s modulus (SE) was calculated with Equation 5.6 for eachsubject.

SE =

√(∂E

∂r· Sr)2 + (

∂E

∂∆r· S∆r)

2 + (∂E

∂∆p· S∆p)

2 (5.6)

The standard errors of the mean Young’s modulus for healthy volunteer nr. 2 andpatient nr. 1 and nr. 2 were 20, 10 and 11 % respectively. For healthy subject nr.1, it could not be determined as there was only one distension measurement. It waschosen to vary the Young’s modulus with 20%.

5.3.4 Summary

To study the sensitivity of the wave propagation model for the inaccuracy in inputparameters, the parameters are changed as displayed in Table 5.4.

55

Table 5.4: Sensitivity analysis of the wave propagation model

Input parameter Error 50% error Error based on the pre-cision of:

Cardiac output ±40% ±20% Nexfin CORadius of the entire geometry ±40% ±20% CE-MRI vs ultrasoundRadius of the hand arteries ±40% ±20% CE-MRI vs ultrasoundYoung’s modulus ±20% ±10% Ultrasound distension

5.4 Nexfin CO algorithm input and sensitivity analysis

The finger pressures simulated by the wave propagation model, for the referencegeometry of four subjects, were used as input for the Nexfin CO algorithm. Inaddition, also the finger pressures resulting from a 20 % change on diameter, cardiacoutput and Young’s modulus were used as input. In this way, the sensitivity of theNexfin CO algorithm could be studied. Other patient-specific inputs for the NexfinCO algorithm were gender, age, height and weight, which were chosen such thatthey could represent the subject and can be found in Table 5.1. Brachial pressurewaveforms calculated by the Nexfin CO model are not available. Therefore, theBeatscope programm, which transfers finger pressure to brachial pressure with atransfer function similar to the one used by Nexfin CO, was used to generate thesewaveforms.

56

57

Chapter 6

Modeling results

The results of the comparison of the Nexfin CO algorithm and the wave propagationmodel can be found in this chapter. In addition, the sensitivity of the wave propa-gation model to variations in cardiac output, arterial radius and Young’s modulusis given. The last paragraph describes the effect of variations in these parameterson the Nexfin CO algorithm. The latter is done by using the simulated finger pres-sures of the wave propagation model as an input for the Nexfin CO algorithm, asdescribed in Chapter 5.

6.1 Nexfin CO versus wave propagation model (refer-ence situation)

In this paragraph, the Nexfin CO algorithm is compared to the wave propagationmodel for the reference situation. The cardiac output from PC-MRI is used toderive a finger pressure with the wave propagation model. These finger pressuresare used as input for the Nexfin CO algorithm. Besides finger pressure, the wavepropagation model also simulates brachial pressure. Nexfin CO determines brachialpressure from finger pressure to calculate cardiac output. Thus, cardiac outputand finger and brachial pressure simulated by the wave propagation model and theNexfin CO algorithm for four subjects can be compared (Table 6.1). PC-MRI andNexfin measurement results were also included for comparison and to clarify inputof the models.

If the wave propagation model and the Nexfin CO algorithm would behave ex-actly equal, PC-MRI stroke volume (which is the input of the wave propagationmodel) would be equal to the stroke volume calculated by Nexfin. However, Table6.1 shows that the stroke volume calculated by the Nexfin CO algorithm overesti-mates the PC-MRI stroke volume for both healthy volunteers and underestimatesPC-MRI stroke volume for both patients. Differences in stroke volume for the foursubjects were 15%, 18%, 13% and 12% of PC-MRI stroke volume.

Figure 6.1 depicts the available brachial and finger pressure waveforms: the wave-forms measured with Nexfin, the waveforms simulated with the wave propagationmodel and a brachial pressure waveform calculated with the Beatscope programmthat is calculated in a similar way as the brachial pressure waveform which Nexfin

58

Table 6.1: Input stroke volume and finger and brachial blood pressure (BP) andflow simulated by the wave propagation model

Healthyvolun-teer nr.1

Healthyvolun-teer nr.2

Patientnr. 1

Patientnr. 2

Measurements

Nexfin fingerpressure

Systolic BP [mmHg] 136 115 169 170Diastolic BP [mmHg] 59 63 35 57Mean BP [mmHg] 80 79 67 93

Nexfin brachialpressure

Systolic BP [mmHg] 134 116 166 181Diastolic BP [mmHg] 70 68 60 74Mean BP [mmHg] 95 87 169 170

Nexfin stroke volume [mL] 119 108 102 78PC-MRI stroke volume [mL] 97 85 48 72

Wave propagation modelInput : PC-MRI stroke volume [mL] 97 85 48 72

Output : fingerartery

Systolic BP [mmHg] 169 195 230 192Diastolic BP [mmHg] 85 120 148 115Mean BP [mmHg] 111 144 173 142

Output : brachialartery

Systolic BP [mmHg] 181 196 229 196Diastolic BP [mmHg] 87 123 150 117Mean BP [mmHg] 115 146 174 144

Nexfin CO algorithmInput : finger BPsimulated by wavepropagation model

Systolic BP [mmHg] 169 195 230 192Diastolic BP [mmHg] 85 120 148 115Mean BP [mmHg] 111 144 173 142

Output : brachialartery

Systolic BP [mmHg] 183 194 224 195Diastolic BP [mmHg] 95 118 140 115Mean BP [mmHg] 123 144 168 145

Output : stroke volume 112 100 42 64

uses to estimate cardiac output. The duration of the measured waveforms wasdetermined by the length of the shortest heart beat during the Nexfin measurementfor each subject.

Table 6.1 and Figure 6.1 show that the simulated brachial and finger pressuredeviate from the measured pressure, especially the mean pressure. However, thebrachial blood pressure simulated by the wave propagation model and the brachialpressure calculated by Beatscope from the simulated finger blood pressure corre-spond for both the mean and the waveform. This means that the transition betweenfinger and brachial pressure in the Nexfin CO algorithm and the wave propagationmodel are similar.

Nexfin CO can calculate stroke volume from pressure waveforms at differentsites. Besides finger pressure, brachial pressure can also be used as input. Table6.2 lists the stroke volume calculated by the Nexfin CO algorithm when differentbrachial artery waveforms are used as input. For simulation 1 the brachial pressure

59

simulated by the wave propagation model is used as input and for simulation 2brachial pressure calculated with Beatscope is used as input. Since the brachialartery systolic, diastolic and mean pressure level of the brachial artery waveformused in simulation 1 and 2 do not differ much, one would expect that the strokevolume derived in simulation 1 and 2 does not differ much either. However, itappears that there are large differences for some subjects (10% of PC-MRI strokevolume for healthy volunteer nr. 1, 8% for healthy volunteer nr. 2, 14% for patientnr. 1 and 7% for patient nr. 2). This suggest that the Nexfin CO algorithm issensitive to small changes in the brachial pressure waveform.

The transfer function that transfers finger pressure to brachial pressure imple-mented in Beatscope is different from the transfer function in Nexfin CO, but agood substitute as differences in brachial pressure are small. The latter is apparentwhen comparing the brachial pressure levels simulated by the Nexfin CO algorithmlisted in Table 6.1 and the brachial pressures from simulation 2 in Table 6.2. How-ever, even such small differences in brachial pressure lead to 12% changes in strokevolume. Again, this emphasizes that the Nexfin CO algorithm is sensitive to smallchanges in the brachial pressure waveform.

Table 6.2: Stroke volumes calculated by the Nexfin CO algorithm for different inputpressures

Healthyvolun-teer nr.1

Healthyvolun-teer nr.2

Patientnr. 1

Patientnr. 2

Simulation

Input: brachial pressure simulated by the wave propagation modelSystolic brachial BP [mmHg] 181 196 229 196Diastolic brachial BP [mmHg] 87 123 150 117 1Mean brachial BP [mmHg] 115 146 174 144Stroke volume [mL] 108 80.8 31.8 51.8Input: brachial pressure calculated by BeatscopeSystolic brachial BP [mmHg] 181 191 225 196Diastolic brachial BP [mmHg] 95 119 140 115 2Mean brachial BP [mmHg] 123 143 168 145Stroke volume [mL] 98.5 88.3 36.8 55.8

60

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250Healthy subject nr. 1

t[s]

p[m

mH

g]

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250

t[s]

p[m

mH

g]

Healthy subject nr. 2

Measured by NexfinSimulated with the WP model

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250Patient nr. 1

t[s]

p[m

mH

g]

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250Patient nr. 2

t[s]

p[m

mH

g]

(a) Finger pressure waveforms

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250Healthy subject nr. 1

t[s]

p[m

mH

g]

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250Healthy subject nr. 2

t[s]

p[m

mH

g]

Nexfin measurementsSimulated with the WP modelCalculated with Beatscope

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250Patient nr. 1

t[s]

p[m

mH

g]

0 0.2 0.4 0.6 0.8 10

50

100

150

200

250Patient nr. 2

t[s]

p[m

mH

g]

(b) Brachial pressure waveforms

Figure 6.1: Pressure waveforms, measured with Nexfin and simulated with the wavepropagation (WP) model and Beatscope. Nexfin measurement data was obtainedby averaging all waveforms measured during the two recordings of 70 heart beatswithout a Physiocal as described in Chapter 3.

61

6.2 Sensitivity analysis of the wave propagation model

Changes in brachial and finger pressure as a results of changes in cardiac output,radius and Young’s modulus are displayed in Figure 6.2 and 6.3. Exact values canbe found in Appendix E. Aortic, brachial and finger pressure waveforms of allsimulations in the sensitivity study for all four subjects can be found in AppendixF. The relation between the change in cardiac output and the change in systolic anddiastolic blood pressure is roughly linear. Mean flow in the finger and brachial arteryalmost exactly follows the increase of flow, as expected. The inaccuracy on arterialradii determined with MRI has the largest influence on systolic and diastolic pressurein both the brachial and the finger artery. Changing the radii in the entire arterialgeometry has a larger effect than changing only the radii of the hand arteries. Theincrease in systolic blood pressure and decrease in diastolic blood pressure resultingfrom a decrease in arterial radius can be explained from a decrease of the complianceas described in Paragraph 5.2. Increasing the radius of the aorta has a much largereffect on the total arterial compliance than increasing the hand arterial radii, dueto the large radius of the aorta. This explains the large effect on blood pressurewhen all radii are varied. The opposite holds for flow in the arteries: varying allradii hardly affects the blood flow in the fingers, while varying the hand radii has alarge effect. This is due to the fact that in the model the flow through the daughterbranches at a bifurcation depends on the radius of the branches. Furthermore, theperipheral resistance highly depends on the radius. The 50% error bars indicatethat the response of blood pressure and flow to an increase of radius is not linear.

Effects of changes in Young’s modulus are negligible, which also becomes clearwhen observing the waveforms in Appendix F.

An example of the changes in pressure and flow waveforms in the aorta, brachialartery and finger artery can be found in Figure 6.4. It is apparent that variations ofthe arterial radii of the hand affect the systolic, diastolic pressure and the maximaland minimal blood flow. However, the shape of the pressure and flow waveformsdoes not change.

62

-100

-50

0

50

100

CO * 0.6

and * 0.8

CO * 1.4

and * 1.2

r * 0.6

and * 0.8

r * 1.4

and * 1.2

r hand * 0.6

and * 0.8

r hand * 1.4

and * 1.2

E * 0.8

and * 0.9

E * 1.2

and * 1.1

Incre

ase [%

]

Systolic BP

healthy subject 1

healthy subject 2

patient 1

patient 2

-100

-50

0

50

100

CO * 0.6 and * 0.8

CO * 1.4

and * 1.2

r * 0.6

and * 0.8

r * 1.4 and * 1.2

r hand * 0.6

and * 0.8

r hand * 1.4

and * 1.2

E * 0.8

and * 0.9

E * 1.2

and * 1.1

Incre

ase [%

]

Diastolic BP

-100

-50

0

50

100

150

200

CO * 0.6

and * 0.8

CO * 1.4

and * 1.2

r * 0.6

and * 0.8

r * 1.4

and * 1.2

r hand * 0.6 and * 0.8

r hand * 1.4

and * 1.2

E * 0.8

and * 0.9

E * 1.2

and * 1.1

Incre

ase [%

]

Mean flow

Figure 6.2: Sensitivity of brachial artery pressure and flow. The 50% error levelsare displayed in bold boxes.

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-100

-50

0

50

100

CO * 0.6 and * 0.8

CO * 1.4

and * 1.2

r * 0.6

and * 0.8

r * 1.4

and * 1.2

r hand * 0.6

and * 0.8

r hand * 1.4

and * 1.2

E * 0.8

and * 0.9

E * 1.2

and * 1.1

Incre

ase [%

]

Systolic BP

healthy subject 1

healthy subject 2

patient 1

patient 2

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100

CO * 0.6

and * 0.8

CO * 1.4

and * 1.2

r * 0.6

and * 0.8

r * 1.4

and * 1.2

r hand * 0.6

and * 0.8

r hand * 1.4

and * 1.2

E * 0.8

and * 0.9

E * 1.2

and * 1.1

Incre

ase [%

]

Diastolic BP

-100

-50

0

50

100

150

200

CO * 0.6

and * 0.8

CO * 1.4

and * 1.2

r * 0.6

and * 0.8

r * 1.4

and * 1.2

r hand * 0.6

and * 0.8

r hand * 1.4

and * 1.2

E * 0.8

and * 0.9

E * 1.2

and * 1.1

Incre

ase [%

]

Mean flow

Figure 6.3: Sensitivity of finger artery pressure and flow. The 50% error levels aredisplayed in bold boxes.

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0 0.2 0.4 0.6 0.8 1100

110

120

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t[s]

p[m

mH

g]

Aortic blood pressure

0 0.2 0.4 0.6 0.8 1100

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p[m

mH

g]

Patient nr. 2Brachial blood pressure

0 0.2 0.4 0.6 0.8 1100

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0 0.2 0.4 0.6 0.8 1−0.2

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r hand * 1.4r hand * 1.2referencer hand * 0.8r hand * 0.6

Figure 6.4: Sensitivity of the pressure and flow waveforms of patient nr. 2 forchanges in the diameter of the finger artery

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6.3 Sensitivity analysis of the Nexfin CO model

For the sensitivity analysis of the Nexfin CO algorithm, the finger pressures simu-lated by the wave propagation model after changing the cardiac output, radii andYoung’s modulus by 20%, were used as input for the Nexfin CO algorithm. Fig-ure 6.5 shows that the Nexfin CO algorithm does not follow the change in cardiacoutput of 20%, but only estimates a change of 9%. This is caused by the relativelylow change in finger pressure in the wave propagation model when cardiac outputis changed (Figure 6.3) whereas the Nexfin CO algorithm bases its calculation onfinger pressure. Change of all arterial radii has a large effect on Nexfin cardiac out-put, while change in hand radii has a small effect, corresponding with the changesin Figure 6.3. Also for the Young’s modulus, changes are in line with the changesin simulated finger pressures. When comparing Figure 6.6 to Figure 6.2, the latterfigure can be considered as input changes, it can be seen that changes in systolic anddiastolic finger blood pressure are damped, thereby changing pulse pressure and asa result cardiac output.

−25

−20

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Incr

ease

[%]

Cardiac output

CO * 0.8 CO * 1.2 r * 0.8 r * 1.2 r hand * 0.8 r hand * 1.2 E * 0.8 E * 1.2

healthy subject 1healthy subject 2patient 1patient 2

Figure 6.5: Sensitivity of cardiac output calculated by Nexfin for finger pressurechanges of Figure 6.3.

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-20

-10

0

10

20

CO * 0.8 CO * 1.2 r * 0.8 r * 1.2 r hand * 0.8 r hand * 1.2 E * 0.8 E * 1.2

Incre

ase [%

]Systolic BP

healthy subject 1

healthy subject 2

patient 1

patient 2

-20

-10

0

10

20

CO * 0.8 CO * 1.2 r * 0.8 r * 1.2 r hand * 0.8 r hand * 1.2 E * 0.8 E * 1.2

Incre

ase [%

]

Diastolic BP

-20

-10

0

10

20

CO * 0.8 CO * 1.2 r * 0.8 r * 1.2 r hand * 0.8 r hand * 1.2 E * 0.8 E * 1.2

Incre

ase [%

]

MAP

Figure 6.6: Sensitivity of brachial blood pressure, calculated by Nexfin for fingerpressure changes of Figure 6.3.

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Chapter 7

Discussion and conclusion

The goal of this study was to investigate whether Nexfin CO can be used to monitorcardiac output in a patient after vascular access creation and to determine cardiacoutput with an accuracy that suffices for the wave propagation model. The analysesof the Nexfin cardiac output measurements will be discussed in the first two para-graphs of this chapter. Furthermore, the outcome of the wave propagation modelwas compared to the outcome of the Nexfin CO algorithm. The Nexfin CO algo-rithm was compared to the wave propagation model and a sensitivity analysis wasperformed. This will be discussed in Paragraph 7.1.3. The next paragraph describesthe directions for further research on Nexfin CO validation. A conclusion of theentire study can be found in the last paragraph.

7.1 Discussion

7.1.1 Nexfin cardiac output versus PC-MRI cardiac output

Nexfin CO and PC-MRI cardiac output measurements were performed on healthyvolunteers and ESRD-patients to determine the accuracy of Nexfin in measuringcardiac output as input for the wave propagation model. Unfortunately, data of thepatients had to be discarded from the analysis due to their hemodynamic instability.A limit of precision of 36% was found for the comparison of PC-MRI stroke volumeand the stroke volume determined with Nexfin in both the left and the right hand.This does not suffice the limit of agreement of 16% that was calculated with the cri-terium by Critchley and Critchley [1999]. A number of factors could have influencedthe measurements performed for the comparison of Nexfin CO and PC-MRI. Thesewill be discussed below.

The Bland-Altman percentage plot for comparing PC-MRI and indicator dilutionmeasurements (Figure 4.2) was only based on 7 simultaneous measurements. Takingthis into account, a limit of agreement of 16% for Nexfin CO measurements is ratherstrict. However, the determined combined limit of precision of 36% will alwaysresult in high limits of precision for Nexfin. For instance, a limit of precision of 20%for PC-MRI, will results in a limit of agreement of 30% for the analysis of Nexfinmeasurements compared with PC-MRI, which is lower than the found combinedlimit of precision of 36%. It can thus be concluded that Nexfin is not as accurate asPC-MRI cardiac output measurements.

A repeated measures ANOVA of the standard deviation of the PC-MRI data

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and Nexfin data of every subject revealed that Nexfin had a significantly betterrepeatability than PC-MRI. However, this could also be caused by the fact thatNexfin stroke volume calculations depend for a great deal on constant factors suchas age, height, weight and gender of the subject and are therefore not influenced bysmall variations in blood pressure.

The analysis with Nexfin are performed on intervals, without a Physiocal, ofabout 60 - 70 heart beats. This is different from the approximately 20 heart beatsthat are needed for a PC-MRI measurement. The variation in the Nexfin strokevolume measurements in healthy volunteers, without arrhythmias, is due to tidalbreathing, and does thus not differ much when 20 or 70 heartbeats are taken intoaccount, since a breath cycle lasts about 3-5 seconds. Effects of tidal breathingon the Nexfin stroke volume measurements are canceled out by taking the meanover a certain time period. During the PC-MRI cardiac output measurements, itis necessary to hold one’s breath. Verschoor et al. [1996] and Endresen and Hill[1976] investigated whether breath holding influences stroke volume with impedancecardiography and found no significant difference in rest. Thus, despite the differ-ence in the number of heart beats taken into account between Nexfin and PC-MRIcardiac output measurements and the holding of one’s breath during PC-MRI mea-surements, it is valid to compare Nexfin cardiac output measurements to PC-MRIcardiac output measurements.

Two of the healthy volunteers had arrhythmias. In these subjects, the differencein number of heart beats taken for PC-MRI and ultrasound dilution could haveeffected the comparison. During the PC-MRI measurements of these two healthyvolunteers, the criteria to disregard heart beats had to be made less strict. Ac-curacy of Nexfin stroke volume during arrhythmias has not been investigated sofar. However, when the data of the subjects with arrhythmias were discarded fromthe Bland-Altman analyses, only small changes of the limits of precision were found,meaning that arrhythmias had little effect in the comparison between Nexfin cardiacoutput and PC-MRI cardiac output measurements and did not effect our conclusion.

It is not unlikely that the volunteers experienced more stress in the MRI scannerthan during the Nexfin measurements. To assess this effect, heart rates betweenmeasurements were compared. A significant difference was found, but differenceswere very small. The average difference was only 4 beats/min, which does notnecessarily have to be a result of stress alone. Such small differences easily occurdue to the biological variation of the heart rate of a person. It is therefore unlikelythat stress caused by the MRI causes the large differences in stroke volume betweenthe two modalities.

To investigate whether results were affected because Nexfin and PC-MRI mea-surements were not performed simultaneously, Nexfin measurements of 4 healthyvolunteers were repeated a few weeks later. When comparing the stroke volumesof the Nexfin measurements on the two time points, limits of precision of 11% and6% were found, for the right and left hand respectively. The large combined limitof precision of Nexfin and PC-MRI measurements (36%) can thus not be entirelyexplained by non-simultaneous measurements. When an 11% limit of precision isused for the non-simultaneously performed measurements, the combined limit ofprecision of Nexfin and PC-MRI measurements should be 19% for Nexfin to be asaccurate as PC-MRI (which has a limit of precision of 11%).

ESRD-patients are often of older age and therefore vascular anomalies are thought

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to occur more frequently than in younger, healthy volunteers. To investigate if vas-cular anomalies effect the accuracy of Nexfin cardiac output measurements, mea-surements were also performed in a population of ESRD-patients. Unfortunately,due to the small group of patients that were measured in this study and their hemo-dynamic instability, it was not possible to determine the accuracy of Nexfin strokevolume measurements for ESRD-patients. It was, however, possible to comparefinger pressures between both hands, for these patients. This is of interest, sincevascular anomalies, such as a stenosis, can induce a pressure difference in the fingerarteries between hands, which could have an effect on the stroke volume determinedby Nexfin. Differences in systolic blood pressure are most important, since Nexfinuses systolic pulse contour analysis to determine stroke volume. Large differencesin systolic finger pressure between hands were found for both patients. This meansthat stroke volume determined with Nexfin can depend on the hand that is measuredon. This influences the accuracy of Nexfin for ESRD patients.

7.1.2 Nexfin cardiac output versus ultrasound dilution in hemodial-ysis patients

Nexfin CO cardiac output measurements were compared to ultrasound dilution mea-surements to determine whether Nexfin can be used to monitor a patient’s cardiacoutput. In contrast to the analysis discussed in the previous paragraph, measure-ments with both methods could be performed simultaneously. Comparison betweenNexfin and ultrasound dilution was performed on hemodialysis patients, who havean altered vessel anatomy. This could have an effect on the accuracy of Nexfincardiac output measurements, since the statistical algorithm implemented in NexfinCO is not based on patients with an altered vessel anatomy.

A limit of precision of 45% was found for the comparison between Nexfin CO andPC-MRI cardiac output measurements, which is much higher than the calculatedlimit of agreement of 33%. This shows that Nexfin cannot replace the ultrasounddilution measurements; the combined limit of precision of the measurements is toohigh.

Difference in repeatability of Nexfin and ultrasound dilution was assessed bycomparing the standard deviation of repeated measurements with both techniques.No significant difference was found between the standard deviation of ultrasounddilution and Nexfin. However, this could also be due to the fact that cardiac outputis generally less variable in older subjects.

The timing of the ultrasound dilution measurement with respect to Nexfin mea-surements was not exact, but the effect on the results of the comparison is negligiblesince this was a matter of seconds and the standard deviation of a series of Nexfinmeasurements was very small. When a Physiocal occurred during the 10 seconds ofmeasurement, these values were removed. Again this had little influence due to thesmall standard deviation in a series of Nexfin measurements.

In our study, Nexfin was able to estimate cardiac output more accurately inpatients of 70-89 years old than for patients of 50-69 years old. This indicates thatNexfin is as precise as ultrasound dilution for patients above 70. Caution should betaken to base consequences on this conclusion as the study population was small.Furthermore, no explanation could be found for the differences between patients of70-89 and of 50-69 year old as the Nexfin algorithm was based on measurements of

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subjects of various ages as can be seen in Table 2.1. However, this is an interestingfinding for future research.

As mentioned before, the altered vessel anatomy of hemodialysis patients, canhave an effect on stroke volume calculations with the Nexfin algorithm. To inves-tigate this effect, it was determined whether the accuracy of Nexfin cardiac outputmeasurements is influenced by the size of the flow through the vascular access. Usingan access flow - cardiac output ratio of 30% to separate high from normal accessflow, no significant difference was found for the accuracy of Nexfin measurementsbetween access flow categories. The 30% ratio was taken from literature, however itwas not clinically validated. Bakran et al. [2003] proposed a ratio of 20%. Using the20% ratio a significant difference of the accuracy of Nexfin CO was found betweensubjects with normal and high access flow. However, with this ratio eight out often patients had a high access flow. Thus, no conclusions regarding the effect ofvascular access flow on the accuracy of Nexfin CO cardiac output measurements canbe drawn, but further research with a large population is required.

7.1.3 Nexfin CO algorithm versus wave propagation model

To obtain more insight in the Nexfin CO algorithm, a comparison was made witha patient-specific wave propagation model. A sensitivity analysis of both the wavepropagation model and the Nexfin CO algorithm was performed to assess the effectof inaccuracies in the Nexfin on the modeling results.

The Nexfin CO algorithm was compared to the patient-specific wave propagationmodel for four subjects by using the finger pressure simulated by the wave prop-agation model as input for the Nexfin CO algorithm. Mean simulated finger andbrachial blood pressures largely deviated from measured pressures with Nexfin CO,suggesting that the peripheral resistance in the wave propagation model was toohigh or the distribution of flow through the geometry was incorrect. This could bedue to the fact that the radii of the hand were not correctly put in the model as nopatient information was available. Furthermore, only one palmar arch was modeled,whereas both a deep and superficial arch are usually present. This arch was giventhe average diameter of the superficial and deep system, thus modeling the archesin series, while they are in parallel. The used resistance for the palmar arch and thefingers is thus too high, resulting in a too high mean pressure.

The brachial blood pressure waveform calculated by Nexfin CO, from the sim-ulated finger pressure, was similar to the brachial blood pressure calculated by thewave propagation model for both the mean and the waveform. However, stroke vol-ume calculated by the Nexfin CO algorithm deviated from PC-MRI stroke volume,which was used as input for the wave propagation model, by 15% on average. Itcan thus be concluded that the transfer from finger pressure to brachial pressurewas similar for both models, but transformation of brachial blood pressure to strokevolume was different.

When the brachial blood pressure simulated by Beatscope and the brachial bloodpressure simulated by the wave propagation model were both put in the Nexfin COalgorithm, differences between the calculated stroke volumes in the order of 10% werefound. This is remarkable, since the systolic, diastolic and mean brachial pressurecalculated by the Nexfin CO algorithm is almost equal to the pressure calculatedby Beatscope. In addition, differences between the stroke volume derived by the

71

Nexfin CO algorithm from the finger pressure of the wave propagation model andthe stroke volume derived from the brachial pressure calculated with Beatscope werealso in the order of 10%. This means that the Nexfin CO algorithm is very sensitiveto small changes in the brachial pressure waveform.

For most patients, differences in stroke volume derived from the brachial bloodpressures simulated by the wave propagation model and by Beatscope, were ap-proximately equal to the area under the systolic pressure curve. As described inChapter 2, this area is used to calculate stroke volume. However, for healthy sub-ject nr. 1, the area under the brachial pressure curves only differed 2%, while thestroke volumes differed 10%. This suggests that the characteristic impedance of theaorta depends on more factors than age, height, weight and gender, or that NexfinCO determines the area under the systolic pressure curve differently than what weassumed.

To determine how the accuracy in Nexfin cardiac output affects the pressure andflow in the wave propagation model compared to inaccuracies of other input param-eters, a sensitivity analysis was done. The effect of variations in cardiac output,arterial radius and Young’s modulus on the brachial and finger blood pressure wasdetermined. The brachial and finger pressures in the wave propagation model weremore sensitive to variations in arterial radii than to variations in cardiac output.The brachial and finger flows were more sensitive to variations in hand radii thanto variations in cardiac output. To conclude, since effects of the accuracy of thearterial radii measurements are larger than the effects of the accuracy on NexfinCO measurements, it suffices to use Nexfin cardiac output as input for the wavepropagation model. It has to be investigated whether this is also the case after AVFcreation.

To obtain insight into the working of the Nexfin CO algorithm, the finger pres-sures simulated for the sensitivity study of the wave propagation model, were usedas input for the Nexfin CO algorithm. Although it was found that Nexfin CO issensitive to small changes in the brachial blood pressure waveform, variations ap-plied on the input aorta flow of the wave propagation model were not fully recordedby the Nexfin CO algorithm. This can be explained by the relatively low changesin finger pressure and the fact that the Nexfin CO algorithm damped the brachialpulse pressure changes, by lowering the diastolic blood pressure changes comparedto the brachial blood pressure changes in the wave propagation model. The decreasein pulse pressure changes causes lower systolic area changes and therefore also lowerstroke volume changes compared to the stroke volume changes applied on the wavepropagation model input. When using different brachial blood pressure waveforms,diastolic and systolic pressure were almost equal and differences in stroke volumes,calculated by the Nexfin CO algorithm, were merely caused by a slightly differentwaveform. The effects in changes in all arterial radii, in the hand radii and in Young’smoduli on the Nexfin CO algorithm corresponded with the effect of changing thoseparameters on the finger pressures simulated by the wave propagation model forvariation of these parameters.

The variations in the input parameters for the sensitivity study were based onthe accuracy of the measurement techniques. To calculate the inaccuracy in thedetermination of the Young’s modulus of the brachial artery with ultrasound dis-tension measurements, a diameter-wall thickness ratio of 5 was taken, based onmeasurements by Westerhof et al. [1969] and Kaiser et al. [2001]. In addition, it

72

was assumed that this ratio was 100% accurate. However, Mourad et al. [1997] andKu et al. [2006] have found smaller ratios of 0.08 and 0.11 respectively. An errorin the diameter-wall thickness ratio could mean that the inaccuracy in the Young’smodulus is larger than the 20% that was used in the sensitivity analysis in thisstudy. However, since variations in Young’s modulus had little influence on brachialpressure and flow, it is unlikely that a higher variation would change our conclusions.

The variations in diameter were based on the comparison of MRI brachial arterydiameter measured with MRI and with ultrasound. The Bland-Altman plots showedan error of 40%. However, MRI and ultrasound measurements were not performedsimultaneously and this could have had an effect: the differences are partly causedby inaccuracy of MRI and partly by temporal changes in arterial radii. The lattercan be the result of factors such as a temperature change, pain or hemodynamicalinstability. Since the variations in diameter of the arm arteries had a large influenceon simulated blood pressures, more measurements should be performed to determinethe inaccuracy of diameter measurements with MRI.

To ensure numerical stability in all geometries for the sensitivity studie, the non-linear convection term in the momentum balance of Bessems [2007] was omitted.This had very little influence on pressure and flow as can be seen in the Figure inAppendix H, where pressure and flow waveforms for the subject on which omittingthe convection term had most influence are depicted. When the convection termwas omitted, for this subject, systolic pressure increased 1% at the brachial andfinger artery, diastolic pressure was unchanged. Mean brachial pressure decreased2% while mean finger pressure increased with 1%. Mean flow in the brachial andfinger artery increased with 1%. All other subjects had smaller or no changes. Thus,for the analysis of the arterial pressure and flow in this study, the convection termis not of great importance.

7.1.4 Future research

In this study, the group of ESRD-patients without an AVF was very small. SinceESRD-patients are prone to cardiovascular diseases [Foley, 2003] and this can ef-fect Nexfin CO measurements, it is important to study the accuracy of Nexfin COmeasurements in a larger population. This is emphasized by the large right-to-leftpressure differences that were found in the two ESRD-patients that were successfullymeasured with Nexfin.

When Nexfin was compared to ultrasound dilution in hemodialysis patients,Nexfin seemed to be accurate and precise for patients older than 70. However, sincemeasurements used to develop the Nexfin CO algorithm were done in subjects ofvarious ages, no explanation could be found for this observation. In addition, theeffect of vascular access flow on Nexfin CO measurements was investigated, butdifferent criteria of high access flow led to inconclusive results. Thus, to draw solidconclusions about the accuracy of Nexfin and the influence of age and vascular accessflow, measurements should be repeated on a larger group of hemodialysis patients.

Nexfin is not MRI compatible, and therefore, Nexfin and PC-MRI measurementscannot be performed simultaneously. To overcome this, Nexfin CO measurementscould be performed simultaneously with thermodilution which is the gold standardfor cardiac output measurements. As thermodilution is an invasive technique, apossibility would be to perform measurements during surgery.

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Results of the sensitivity study of the wave propagation model suggested thataccurate arterial radii are the most important for simulations of both blood pressureand flow. To obtain more accurate arterial radii, measurements could be donewith ultrasound. Unfortunately, the morphology of the arteries is more difficultto assess with ultrasound. Hand arteries are very small and are therefore verydifficult to measure with both MRI and ultrasound. In our study, no patient-specificinformation was available about the anatomy and radii of the palmar arch and digitalarteries as input for the wave propagation model. The sensitivity study of the wavepropagation model showed that variations in hand diameters have great influence onflow through the brachial and finger artery. Hence, to be able to accurately predictpostoperative AVF flow, more patient-specific information about hand arteries hasto be obtained. An alternative could be to tune the radii of the hand arteries untilthe simulated finger pressures equal the measured finger pressures. However, theaccuracy of such a protocol has to be validated, for example by comparing brachial,radial and ulnar pressures and flows.

7.2 Conclusion

Comparison of Nexfin cardiac output with PC-MRI and ultrasound dilution cardiacoutput indicates that Nexfin measurements cannot replace either technique.

Breath holding, arrhythmias, stress during PC-MRI measurements and the factthat the PC-MRI and Nexfin measurements were not performed simultaneously, allwere excluded as confounding factors. It seems that, especially in older subjects,the results of the Nexfin CO measurements depend on the hand measured on, whichwarrants extra caution in performing Nexfin CO measurements in ESRD-patients.

The higher reproducibility of Nexfin compared to that of PC-MRI suggests thatNexfin depends largely on the patient-specific information (age, length, height andgender) needed for the statistical algorithm, to determine cardiac output. Effect ofhigh age and access flow on the accuracy of Nexfin should be examined further.

The sensitivity of the wave propagation model was assessed for the followinginput parameters: cardiac output, arterial radii and Young’s modulus. Simulatedbrachial and finger pressure were very sensitive to changes in arterial radii andless to changes in cardiac output. Variation of the hand arterial radii had a largeinfluence on brachial and finger flow, whereas this influence was again larger than theinfluence of changes in cardiac output. Varying the Young’s modulus hardly effectedboth pressure and flow. Thus, until arterial radii can be measured more accurately,Nexfin CO suffices as an input for the wave propagation model, when PC-MRI is notavailable. However, information about the aortic flow waveform cannot be providedby Nexfin.

The patient-specific wave propagation model was also used to obtain insight intothe Nexfin CO algorithm and its sensitivity to changes in finger pressure resultingfrom changing input parameters of the wave propagation model. Small changes inthe brachial pressure waveform led to significant changes in stroke volume calculatedby the Nexfin CO algorithm. The transfer from finger pressure to brachial pressurewas similar for both models, but transformation of brachial blood pressure to strokevolume was different. Changes in the input stroke volume of the wave propagationmodel were not fully recorded by the Nexfin CO algorithm. This was a result of

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the relatively low changes in finger pressure and the brachial artery pulse pressurechanges being damped by the Nexfin CO algorithm.

To summarize, this study suggests that Nexfin CO cannot replace PC-MRI andultrasound dilution cardiac output measurements for monitoring of patients. Due tothe large influence of inaccuracies in arterial radii, cardiac output estimations withNexfin CO are sufficiently accurate as an input for the wave propagation model.

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Appendix A

MR parameters

Table A.1: PC-MRI parameters

TR [ms] 5.44TE [ms] 3.50Flip angle [degrees] 15Pixel spacing [mm] 1.25 x 1.25Slice thickness [mm] 8.0Slice distance [mm] 8.0Image matrix 256 x 256Number of slices 1Number of dynamics (images in time) 20

Table A.2: Contrast-enhanced MRI

Proximal scan Distal scanTR [ms] 1.54 1.59TE [ms] 5.39 5.33Flip angle [degrees] 40 40Pixel spacing [mm] 0.63 x 0.63 0.84 x 0.84Slice thickness [mm] 1.68 2.5Slice distance [mm] 0.84 1.25Image matrix 512 x 512 512 x 512Number of slices 125 90Number of dynamics (measurements in time) 4 4

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Appendix B

Nexfin and PC-MRI data ofhealthy volunteers andend-stage renal disease patients

Table B.1: Nexfin and PC-MRI cardiac output (CO), stroke volume (SV) and heartrate (HR) of the healthy volunteers. Nexfin data is reported as mean ± standarddeviation.

Healthy volunteer Measurement CO [L/min] SV [mL] HRPC-MRI 1 5.75 87.10 69.28

2 6.68 99.70 67.003 6.75 105.50 66.89

1 Nexfin 1 6.89 ± 2.57 106.20 ± 27.72 63.33 ± 13.56right hand 2 7.15 ± 2.10 112.44 ± 20.21 62.67 ± 12.50Nexfin 1 6.13 ± 1.59 95.49 ± 16.27 63.71 ± 11.50left hand 2 6.63 ± 2.85 99.82 ± 35.26 65.51 ± 14.61PC-MRI 1 4.67 94.60 59.94

2 5.39 81.9 59.823 5.25 88.9 62.57

2 Nexfin 1 4.92 ± 0.29 83.55 ± 4.61 58.96 ± 3.65right hand 2 4.70 ± 0.37 83.57 ± 3.92 56.26 ± 4.64Nexfin 1 5.90 ± 0.35 97.75 ± 3.53 60.38 ± 3.46left hand 2 6.01 ± 0.29 98.55 ± 3.12 60.98 ± 3.47PC-MRI 1 4.83 82.90 58.31

2 5.43 92.90 58.483 5.11 90.00 56.82

3 Nexfin 1 7.82 ± 0.73 128.95 ± 6.65 60.67 ± 4.93right hand 2 7.53 ± 0.85 128.08 ± 6.76 58.97 ± 7.79Nexfin 1 7.26 ± 0.85 123.18 ± 6.17 58.98 ± 7.02left hand 2 6.66 ± 0.46 121.14 ± 4.46 55.03 ± 4.03PC-MRI 1 6.00 83.30 75.47

2 6.50 87.90 77.923 6.31 84.20 78.64

4 Nexfin 1 7.03 ± 0.66 110.17 ± 5.77 63.95 ± 6.01

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right hand 2 6.62 ± 0.33 106.28 ± 4.63 62.39 ± 4.06Nexfin 1 6.53 ± 0.50 103.22 ± 4.31 63.30 ± 4.92left hand 2 6.62 ± 0.29 106.19 ± 4.92 62.52 ± 4.42PC-MRI 1 4.68 79.80 60.85

2 5.09 85.30 59.703 5.04 82.50 61.104 4.99 83.50 59.76

5 5 5.29 88.00 60.12Nexfin 1 7.63 ± 0.31 122.08 ± 3.73 62.57 ± 2.68right hand 2 7.46 ± 0.26 123.70 ± 3.90 60.38 ± 2.44Nexfin 1 7.09 ± 0.29 117.57 ± 4.49 60.39 ± 3.50left hand 2 7.05 ± 0.24 119.51 ± 4.51 59.02 ± 2.75PC-MRI 1 4.80 72.40 66.30

2 4.99 77.70 64.243 5.08 77.80 65.364 4.83 75.30 64.10

6 5 5.08 75.80 67.04Nexfin 1 4.11 ± 0.27 70.85 ± 3.50 58.05 ± 3.18right hand 2 4.08 ± 0.26 70.55 ± 3.79 57.92 ± 2.62Nexfin 1 3.99 ± 0.35 69.49 ± 3.95 57.47 ± 3.99left hand 2 4.01 ± 0.27 70.92 ± 2.97 56.50 ± 2.26PC-MRI 1 9.26 135.70 68.26

2 8.06 126.60 63.693 8.17 124.30 65.72

7 Nexfin 1 7.12 ± 0.62 119.17 ± 5.15 59.75 ± 4.84right hand 2 6.67 ± 0.85 118.36 ± 9.20 56.44 ± 6.95Nexfin 1 7.11 ± 1.68 115.17 ± 15.63 61.23 ± 10.72left hand 2 6.67 ± 0.85 113.86 ± 17.97 61.88 ± 10.07PC-MRI 1 5.04 72.10 69.85

2 4.55 69.70 65.293 5.47 78.10 70.014 4.63 73.00 63.42

8 5 4.95 68.50 72.29Nexfin 1 6.67 ± 0.41 99.03 ± 4.38 67.41 ± 4.05right hand 2 6.44 ± 0.23 101.45 ± 3.52 63.56 ± 3.42Nexfin 1 6.94 ± 0.45 106.83 ± 3.60 64.99 ± 4.60left hand 2 7.13 ± 0.26 107.53 ± 3.01 66.38 ± 3.18PC-MRI 1 4.26 69.20 61.54

2 4.67 72.10 64.793 4.28 69.40 61.604 4.23 66.10 63.97

9 5 4.15 65.10 63.69Nexfin 1 5.44 ± 0.42 94.13 ± 4.05 57.88 ± 4.21right hand 2 5.29 ± 0.25 93.31 ± 3.76 56.80 ± 3.36Nexfin 1 5.85 ± 0.50 98.33 ± 4.23 58.46 ± 4.55left hand 2 5.77 ± 0.24 97.55 ± 3.50 59.21 ± 3.01PC-MRI 1 4.94 102.10 48.39

2 4.85 98.90 49.02

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3 5.32 102.00 52.1310 Nexfin 1 5.96 ± 0.85 116.88 ± 8.58 51.04 ± 6.51

right hand 2 5.71 ± 0.28 115.79 ± 4.95 49.35 ± 2.36Nexfin 1 6.51 ± 0.99 127.95 ± 11.32 50.83 ± 6.17left hand 2 6.53 ± 0.46 129.68 ± 6.73 50.43 ± 3.99

Table B.2: Nexfin and PC-MRI cardiac output (CO), stroke volume (SV) and heartrate (HR) of the end-stage renal disease (ESRD) patients. Nexfin data is reportedas mean ± standard deviation.

ESRD Patient Measurement CO [L/min] SV [mL] HR1 PC-MRI 1 4.53 67.30 67.26

2 5.22 77.20 67.643 4.71 70.40 66.89

Nexfin 1 6.88 ± 2.33 100.13 ± 24.87 67.20 ± 11.63right hand 2 6.80 ± 2.55 99.26 ± 27.06 66.60 ± 12.44Nexfin 1 5.03 ± 1.87 76.98 ± 22.60 63.48 ± 10.78left hand 2 5.15 ± 1.91 77.97 ± 22.63 64.34 ± 10.84

2 PC-MRI 1 3.98 50.00 79.682 3.95 48.40 81.523 3.56 45.10 78.95

Nexfin 1 5.71 ± 0.20 76.27 ± 2.58 74.84 ± 2.19right hand 2 5.80 ± 0.19 76.54 ± 2.84 74.44 ± 1.14Nexfin 1 9.60 ± 0.83 101.83 ± 5.22 94.18 ± 5.94left hand 2 9.41 ± 0.28 103.26 ± 4.08 91.13 ± 1.89

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Table B.3: Repeated stroke volume (SV) measurements with Nexfin of 4 healthyvolunteers. Measurements on t0 are the measurements done for the comparison ofNexfin with PC-MRI

Healthy SV [mL] SV [mL]subject Hand Measurement during 1st Physiocal interval during 2nd Physiocal interval

3 Right t0 128.95 ± 6.65 128.08 ± 6.76Right t1 121.73 ± 3.81 122.24 ± 5.35Left t0 123.18 ± 6.17 121.14 ± 4.46Left t1 123.69 ± 6.56 124.68 ± 4.46

7 Right t0 70.85 ± 3.50 70.55 ± 3.79Right t1 78.15 ± 4.49 78.32 ± 4.00Left t0 69.49 ± 3.95 70.92 ± 2.97Left t1 94.95 ± 3.79 97.54 ± 4.27

8 Right t0 119.17 ± 5.15 118.36 ± 9.20Right t1 111.55 ± 19.99 114.30 ± 7.81Left t0 115.47 ± 15.63 113.86 ± 17.97Left t1 110.68 ± 28.16 109.79 ± 40.09

9 Right t0 99.03 ± 4.38 101.45 ± 3.52Right t1 106.13 ± 4.34 104.21 ± 4.52Left t0 106.83 ± 3.60 107.53 ± 3.01Left t1 103.68 ± 4.78 104.88 ± 4.34

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Appendix C

Nexfin and ultrasound dilutiondata of hemodialysis patients

Table C.1: Nexfin and ultrasound dilution (UD) cardiac output (CO) of hemodialysispatients. Nexfin data is reported as mean ± standard deviation. The measurementdisplayed in Italic was ignored for data analysis due to motion artifacts.

Age category UD CO [L/min] Nexfin CO [L/min] UD accessPatient [years] 1 2 1 2 flow [mL]

1 50-69 4.68 4.95 4.52 ± 2.18 5.97 ± 0.22 10232 50-69 6.11 4.89 5.67 ± 0.13 5.51 ± 0.12 14033 50-69 6.77 6.12 9.56 ± 0.16 9.69 ± 0.18 11734 50-69 3.63 3.59 5.52 ± 0.05 5.61 ± 0.07 10075 50-69 3.96 4.20 6.64 ± 0.18 6.16 ± 0.07 5706 70-89 4.01 4.24 3.86 ± 0.06 3.84 ± 0.05 16707 70-89 3.49 3.80 3.84 ± 0.41 3.65 ± 0.26 10878 70-89 3.37 3.34 4.27 ± 0.12 4.33 ± 0.23 12379 70-89 4.03 3.65 4.54 ± 0.09 4.21 ± 0.11 116710 70-89 5.87 5.98 4.68 ± 0.28 4.89 ± 0.26 2140

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Appendix D

Patient specific input for theone dimensional wavepropagation model

Healthy volunteer nr. 1Stroke volume measured with PC-MRI: 97.4 mLHeart rate during PC-MRI measurement: 60 /sMean brachial blood pressure: 90 mmHg

Table D.1: Model geometry of healthy volunteer nr. 1

Element Segment Radius Radius Wall thick- Wall thick- Young’slength node 1 node 2 ness node 1 ness node 2 modulus

[m] [m] [m] [m] [m] [Pa]Ascending aorta 1 2.00e-02 8.67e-03 8.61e-03 9.68e-04 9.68e-04 7.70e05Ascending aorta 2 2.00e-02 8.61e-03 8.50e-03 9.50e-04 9.50e-04 7.70e05Aortic arch A1 1.00e-02 6.61e-03 6.61e-03 7.79e-04 7.79e-04 7.70e05Aortic arch A2 1.00e-02 6.61e-03 6.61e-03 7.79e-04 7.79e-04 7.70e05Innominate a. 3.40e-02 3.70e-03 3.70e-03 5.07e-04 5.07e-04 7.70e05Aortic arch B 3.90e-02 6.31e-03 6.31e-03 7.49e-04 7.49e-04 7.70e05L. carotic a. 4.10e-02 2.18e-03 2.18e-03 3.72e-04 3.72e-04 1.54e06Thoracic aorta 5.20e-02 5.89e-03 5.89e-03 7.08e-04 7.08e-04 7.70e05L. subclavian a. A 3.40e-02 2.49e-03 2.48e-03 3.95e-04 3.95e-04 7.70e05L. vertebral a. 4.90e-02 1.11e-03 1.10e-03 2.71e-04 2.71e-04 1.54e06L. subclavian a. B1 2.79e-02 2.48e-03 2.31e-03 3.97e-04 3.70e-04 7.70e05L. subclavian a. B2 2.79e-02 2.31e-03 2.13e-03 3.70e-04 3.62e-04 7.70e05L. brachial a. 1 5.89e-02 2.13e-03 2.14e-03 3.62e-04 4.28e-04 7.70e05L. brachial a. 2 5.89e-02 2.14e-03 2.15e-03 4.28e-04 4.30e-04 7.70e05L. brachial a. 3 6.73e-02 2.15e-03 1.90e-03 4.30e-04 3.80e-04 7.70e05L. brachial a. 4 6.73e-02 1.90e-03 1.66e-03 3.80e-04 3.32e-04 7.70e05L. radial a. 1 3.81e-02 1.31e-03 1.38e-03 3.54e-04 3.73e-04 1.54e06L. radial a. 2 3.81e-02 1.38e-03 1.45e-03 3.73e-04 3.92e-04 1.54e06

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L. radial a. 3 5.22e-02 1.45e-03 1.38e-03 3.92e-04 3.73e-04 1.54e06L. radial a. 4 5.22e-02 1.38e-03 1.31e-03 3.73e-04 3.54e-04 1.54e06L. ulnar a. A 3.45e-02 1.61e-03 1.52e-03 3.70e-04 3.50e-04 1.54e06L. interosseous a. 4.62e-02 1.31e-03 1.46e-03 3.93e-04 4.38e-04 3.08e06L. ulnar a. B1 3.45e-02 1.52e-03 1.42e-03 3.50e-04 3.27e-04 1.54e06L. ulnar a. B2 5.47e-02 1.42e-03 1.39e-03 3.27e-04 3.20e-04 1.54e06L. ulnar a. B3 5.47e-02 1.39e-03 1.36e-03 3.20e-04 3.13e-04 1.54e06L. p. arch ulnar site 2.00e-02 1.36e-03 8.66e-04 3.13e-04 2.60e-04 3.08e06L. palmar arch 1 5.00e-03 8.66e-04 8.66e-04 2.60e-04 2.60e-04 3.08e06L. palmar arch 2 5.00e-03 8.66e-04 8.66e-04 2.60e-04 2.60e-04 3.08e06L. palmar arch 3 5.00e-03 8.66e-04 8.66e-04 2.60e-04 2.60e-04 3.08e06L. digital a. 1 5.00e-03 7.35e-04 7.35e-04 2.21e-04 2.21e-04 3.08e06L. p. arch radial site 5.00e-03 8.66e-04 8.66e-04 2.60e-04 2.60e-04 3.08e06L. digital a. 2 5.00e-03 7.35e-04 7.35e-04 2.21e-04 2.21e-04 3.08e06L. digital a. 3 5.00e-03 7.35e-04 7.35e-04 2.21e-04 2.21e-04 3.08e06L. digital a. 4 5.00e-03 7.35e-04 7.35e-04 2.21e-04 2.21e-04 3.08e06L. digital a. 5 5.00e-03 7.35e-04 7.35e-04 2.21e-04 2.21e-04 3.08e06

Healthy volunteer nr. 2Stroke volume measured with PC-MRI: 85.1 mLHeart rate during PC-MRI measurement: 77 /sMean brachial blood pressure: 88 mmHg

Table D.2: Model geometry of healthy volunteer nr. 2

Element Segment Radius Radius Wall thick- Wall thick- Young’slength node 1 node 2 ness node 1 ness node 2 modulus

[m] [m] [m] [m] [m] [Pa]Ascending aorta 1 2.00e-02 1.13e-02 1.12e-02 1.26e-03 1.26e-03 6.10e05Ascending aorta 2 2.00e-02 1.12e-03 1.11e-03 1.24e-03 1.24e-03 6.10e05Aortic arch A1 1.00e-02 8.62e-03 8.62e-03 1.02e-03 1.02e-03 6.10e05Aortic arch A2 1.00e-02 8.62e-03 8.62e-03 1.02e-03 1.02e-03 6.10e05Innominate a. 3.40e-02 4.80e-03 4.80e-03 6.62e-04 6.62e-04 6.10e05Aortic arch B 3.90e-02 8.24e-03 8.24e-03 9.78e-04 9.78e-04 6.10e05L. carotic a. 4.10e-02 2.85e-03 2.85e-03 4.84e-04 4.84e-04 1.22e06Thoracic aorta 5.20e-02 7.69e-03 7.69e-03 9.24e-03 9.24e-03 6.10e05L. subclavian a. A 3.40e-02 3.26e-03 2.51e-03 5.16e-04 5.16e-04 6.10e05R. carotid a. 4.40e-02 2.85e-03 2.85e-03 4.85e-03 4.85e-03 1.22e06R subclavian a. 3.40e-02 3.26e-03 3.26e-03 5.16e-04 5.16e-04 6.10e05R. vertebral a. 4.90e-02 1.45e-03 1.41e-03 3.54e-04 3.54e-04 1.22e06R. subclavian a. B1 3.75e-02 3.26e-03 2.91e-03 5.22e-04 4.66e-04 6.10e05R. subclavian a. B2 3.75e-02 2.91e-03 2.55e-03 4.66e-04 4.34e-04 6.10e05R. brachial a. 1 5.89e-02 2.55e-03 2.42e-03 4.34e-04 4.84e-04 6.10e05R. brachial a. 2 5.89e-02 2.42e-03 2.30e-03 4.84e-04 4.60e-04 6.10e05R. brachial a. 3 5.55e-02 2.30e-03 2.11e-03 4.60e-04 4.22e-04 6.10e05

89

R. brachial a. 4 5.55e-02 2.11e-03 1.93e-03 4.22e-04 3.84e-04 6.10e05R. radial a. 1 3.88e-02 1.63e-03 1.61e-03 4.40e-04 4.35e-04 1.22e06R. radial a. 2 3.88e-02 1.61e-03 1.59e-03 4.35e-04 4.29e-04 1.22e06R. radial a. 3 6.43e-02 1.59e-03 1.53e-03 4.29e-04 4.13e-04 1.22e06R. radial a. 4 6.43e-02 1.53e-03 1.48e-03 4.13e-04 4.00e-04 1.22e06R. ulnar a. A 4.50e-02 1.91e-03 1.81e-03 4.39e-04 4.16e-04 1.22e06R. interosseous a. 1 6.95e-02 1.59e-03 1.54e-03 4.77e-04 4.62e-04 2.44e06R. interosseous a. 2 4.62e-02 1.54e-03 1.42e-03 4.62e-04 4.26e-04 2.44e06R. ulnar a. B1 4.50e-02 1.81e-03 1.71e-03 4.16e-04 3.93e-04 1.22e06R. ulnar a. B2 6.39e-02 1.71e-03 1.64e-03 3.93e-04 3.77e-04 1.22e06R. ulnar a. B3 6.39e-02 1.64e-03 1.57e-03 3.77e-04 3.61e-04 1.22e06R. p. arch ulnar site 2.00e-02 1.57e-03 9.90e-04 3.61e-04 2.97e-04 2.44e06R. palmar arch 1 5.00e-03 9.90e-04 9.90e-04 2.97e-04 2.97e-04 2.44e06R. palmar arch 2 5.00e-03 9.90e-04 9.90e-04 2.97e-04 2.97e-04 2.44e06R. palmar arch 3 5.00e-03 9.90e-04 9.90e-04 2.97e-04 2.97e-04 2.44e06R. digital a. 1 5.00e-03 8.40e-04 8.40e-04 2.52e-04 2.52e-04 2.44e06R. p. arch radial site 5.00e-03 9.90e-04 9.90e-04 2.97e-04 2.97e-04 2.44e06R. digital a. 2 5.00e-03 8.40e-04 8.40e-04 2.52e-04 2.52e-04 2.44e06R. digital a. 3 5.00e-03 8.40e-04 8.40e-04 2.52e-04 2.52e-04 2.44e06R. digital a. 4 5.00e-03 8.40e-04 8.40e-04 2.52e-04 2.52e-04 2.44e06R. digital a. 5 5.00e-03 8.40e-04 8.40e-04 2.52e-04 2.52e-04 2.44e06

Patient nr. 1Stroke volume measured with PC-MRI: 47.8 mLHeart rate during PC-MRI measurement: 80 /sMean brachial blood pressure: 101 mmHg

Table D.3: Model geometry of patient nr. 1

Element Segment Radius Radius Wall thick- Wall thick- Young’slength node 1 node 2 ness node 1 ness node 2 modulus

[m] [m] [m] [m] [m] [Pa]Ascending aorta 1 2.00e-02 1.09e-02 1.08e-02 1.21e-03 1.21e-03 1.60e06Ascending aorta 2 2.00e-02 1.08e-02 1.07e-02 1.19e-03 1.19e-03 1.60e06Aortic arch A1 1.00e-02 8.29e-03 8.29e-03 9.77e-04 9.77e-04 1.60e06Aortic arch A2 1.00e-02 8.29e-03 8.29e-03 9.77e-04 9.77e-04 1.60e06Innominate a. 3.40e-02 4.60e-03 4.60e-03 6.36e-04 6.36e-04 1.60e06Aortic arch B 3.90e-02 7.90e-03 7.90e-03 9.40e-04 9.40e-04 1.60e06L. carotic a. 4.10e-02 2.74e-03 2.74e-03 4.66e-04 4.66e-04 3.20e06Thoracic aorta 5.20e-02 7.39e-03 7.39e-03 8.88e-04 8.88e-04 1.60e06L. subclavian a. A 3.40e-02 3.12e-03 3.11e-03 4.96e-04 4.96e-04 1.60e06L. vertebral a. 4.90e-02 1.39e-03 1.38e-03 3.40e-04 3.40e-04 3.20e06L. subclavian a. B1 7.23e-02 3.11e-03 2.75e-03 4.98e-04 4.40e-04 1.60e06L. subclavian a. B2 8.03e-02 2.75e-03 2.13e-03 4.40e-04 3.62e-04 1.60e06L. brachial a. 1 3.15e-02 2.13e-03 2.12e-03 3.62e-04 4.24e-04 1.60e06

90

L. brachial a. 2 3.15e-02 2.12e-03 2.11e-03 4.24e-04 4.22e-04 1.60e06L. brachial a. 3 5.26e-02 2.11e-03 2.01e-03 4.22e-04 4.02e-04 1.60e06L. brachial a. 4 5.26e-02 2.01e-03 1.91e-03 4.02e-04 3.82e-04 1.60e06L. radial a. 1 5.61e-02 1.49e-03 1.49e-03 4.02e-04 4.02e-04 3.20e06L. radial a. 2 5.61e-02 1.49e-03 1.49e-03 4.02e-04 4.02e-04 3.20e06L. radial a. 3 5.54e-02 1.49e-03 1.45e-03 4.02e-04 3.92e-04 3.20e06L. radial a. 4 5.54e-02 1.45e-03 1.41e-03 3.92e-04 3.81e-04 3.20e06L. ulnar a. A 6.65e-02 1.67e-03 1.58e-03 3.84e-04 3.61e-04 3.20e06L. interosseous a. 1 4.00e-02 1.39e-03 1.39e-03 4.17e-04 4.17e-04 6.40e06L. ulnar a. B1 6.65e-02 1.58e-03 1.50e-03 3.61e-04 3.45e-04 3.20e06L. ulnar a. B2 4.45e-02 1.50e-03 1.42e-03 3.45e-04 3.27e-04 3.20e06L. ulnar a. B3 4.45e-02 1.42e-03 1.34e-03 3.27e-04 3.08e-04 3.20e06L. p. arch ulnar site 2.00e-02 1.34e-03 8.91e-04 3.08e-04 2.67e-04 6.40e06L. palmar arch 1 5.00e-03 8.91e-04 8.91e-04 2.67e-04 2.67e-04 6.40e06L. palmar arch 2 5.00e-03 8.91e-04 8.91e-04 2.67e-04 2.67e-04 6.40e06L. palmar arch 3 5.00e-03 8.91e-04 8.91e-04 2.67e-04 2.67e-04 6.40e06L. digital a. 1 5.00e-03 7.56e-04 7.56e-04 2.27e-04 2.27e-04 6.40e06L. p. arch radial site 5.00e-03 8.91e-04 8.91e-04 2.67e-04 2.67e-04 6.40e06L. digital a. 2 5.00e-03 7.56e-04 7.56e-04 2.27e-04 2.27e-04 6.40e06L. digital a. 3 5.00e-03 7.56e-04 7.56e-04 2.27e-04 2.27e-04 6.40e06L. digital a. 4 5.00e-03 7.56e-04 7.56e-04 2.27e-04 2.27e-04 6.40e06L. digital a. 5 5.00e-03 7.56e-04 7.56e-04 2.27e-04 2.27e-04 6.40e06

Patient nr. 2Stroke volume measured with PC-MRI: 71.6 mLHeart rate during PC-MRI measurement: 67 /sMean brachial blood pressure: 99 mmHg

Table D.4: Model geometry of patient nr. 2

Element Segment Radius Radius Wall thick- Wall thick- Young’slength node 1 node 2 ness node 1 ness node 2 modulus

[m] [m] [m] [m] [m] [Pa]Ascending aorta 1 2.00e-02 1.13e-02 1.12e-02 1.26e-03 1.26e-03 1.41e06Ascending aorta 2 2.00e-02 1.12e-03 1.11e-03 1.24e-03 1.24e-03 1.41e06Aortic arch A1 1.00e-02 8.62e-03 8.62e-03 1.02e-03 1.02e-03 1.41e06Aortic arch A2 1.00e-02 8.62e-03 8.62e-03 1.02e-03 1.02e-03 1.41e06Innominate a. 3.40e-02 4.80e-03 4.80e-03 6.62e-04 6.62e-04 1.41e06Aortic arch B 3.90e-02 8.24e-03 8.24e-03 9.78e-04 9.78e-04 1.41e06L. carotic a. 4.10e-02 2.85e-03 2.85e-03 4.85e-04 4.85e-04 2.82e06Thoracic aorta 5.20e-02 7.69e-03 7.69e-03 9.24e-04 9.24e-04 1.41e06L. subclavian a. A 3.40e-02 3.26e-03 2.51e-03 5.16e-04 5.16e-04 1.41e06R. carotid a. 4.40e-02 2.85e-03 2.85e-03 4.85e-04 4.85e-04 2.82e06R subclavian a. 3.40e-02 3.26e-03 3.24e-03 5.16e-04 5.16e-04 1.41e06R. vertebral a. 4.90e-02 1.45e-03 1.41e-03 3.54e-04 3.54e-04 2.82e06

91

R. subclavian a. B1 4.89e-02 3.24e-03 2.91e-03 5.18e-04 4.66e-04 1.41e06R. subclavian a. B2 4.89e-02 2.91e-03 2.58e-03 4.66e-04 4.39e-04 1.41e06R. brachial a. 1 5.64e-02 2.58e-03 2.52e-03 4.39e-04 5.04e-04 1.41e06R. brachial a. 2 5.64e-02 2.52e-03 2.46e-03 5.04e-04 4.92e-04 1.41e06R. brachial a. 3 5.23e-02 2.46e-03 2.51e-03 4.92e-04 5.02e-04 1.41e06R. brachial a. 4 5.23e-02 2.51e-03 2.57e-03 5.02e-04 5.14e-04 1.41e06R. radial a. 1 5.15e-02 1.67e-03 1.54e-03 4.51e-04 4.16e-04 2.82e06R. radial a. 2 5.15e-02 1.54e-03 1.40e-03 4.16e-04 3.78e-04 2.82e06R. radial a. 3 5.34e-02 1.40e-03 1.42e-03 3.78e-04 3.83e-04 2.82e06R. radial a. 4 5.34e-02 1.42e-03 1.43e-03 3.83e-04 3.86e-04 2.82e06R. ulnar a. A 3.64e-02 1.41e-03 1.35e-03 3.24e-04 3.11e-04 2.82e06R. interosseous a. 1 3.43e-02 1.34e-03 1.44e-03 4.02e-04 4.32e-04 5.64e06R. interosseous a. 2 6.33e-02 1.44e-03 1.29e-03 4.32e-04 3.87e-04 5.64e06R. ulnar a. B1 3.64e-02 1.35e-03 1.30e-03 3.11e-04 2.99e-04 2.82e06R. ulnar a. B2 5.31e-02 1.30e-03 1.28e-03 2.99e-04 2.94e-04 2.82e06R. ulnar a. B3 5.31e-02 1.28e-03 1.26e-03 2.94e-04 2.90e-04 2.82e06R. p. arch ulnar site 2.00e-02 1.26e-03 8.66e-04 2.90e-04 2.60e-04 5.64e06R. palmar arch 1 5.00e-03 8.66e-04 8.66e-04 2.60e-04 2.60e-04 5.64e06R. palmar arch 2 5.00e-03 8.66e-04 8.66e-04 2.60e-04 2.60e-04 5.64e06R. palmar arch 3 5.00e-03 8.66e-04 8.66e-04 2.60e-04 2.60e-04 5.64e06R. digital a. 1 5.00e-03 7.35e-04 7.35e-04 2.21e-04 2.21e-04 5.64e06R. p. arch radial site 5.00e-03 8.66e-04 8.66e-04 2.60e-04 2.60e-04 5.64e06R. digital a. 2 5.00e-03 7.35e-04 7.35e-04 2.21e-04 2.21e-04 5.64e06R. digital a. 3 5.00e-03 7.35e-04 7.35e-04 2.21e-04 2.21e-04 5.64e06R. digital a. 4 5.00e-03 7.35e-04 7.35e-04 2.21e-04 2.21e-04 5.64e06R. digital a. 5 5.00e-03 7.35e-04 7.35e-04 2.21e-04 2.21e-04 5.64e06

92

Appendix E

Output of the sensitivityanalysis of the wave propagationmodel

Table E.1: Sensitivity of systolic blood pressure in the brachial artery

Change of output parameter systolic brachial blood pressure [%]Change of input param-eter [%]

Healthy vol-unteer nr. 1

Healthy vol-unteer nr. 2

Patient nr. 1 Patient nr. 2

Cardiac output -20 -5.63 -5.15 -4.59 -5.52+20 +7.50 +5.20 +4.00 +5.30-40 -14.56 -9.80 -8.30 -10.78+40 +14.93 +10.14 +8.39 +10.95

Radius -20 +29.67 +18.40 +14.84 +19.20+20 -11.71 -5.70 -7.40 -7.08-40 +90.74 +62.26 +50.36 +65.02+40 -19.68 -12.17 -11.18 -14.92

Radius in hand -20 +4.06 +1.77 +0.14 +0.55+20 -0.68 -2.33 -0.30 -1.03-40 +6.14 +3.53 +0.23 +1.12+40 -2.98 -4.21 -3.95 -1.89

Young’s modulus -10 -1.81 -1.31 -1.06 -1.37+10 +1.83 +1.31 +0.97 +0.97-20 -3.84 -2.85 -2.20 -2.54+20 +3.62 +2.31 +1.90 +1.90

93

Table E.2: Sensitivity of diastolic blood pressure in the brachial artery

Change of output parameter diastolic brachial blood pressure [%]Change of input param-eter [%]

Healthy vol-unteer nr. 1

Healthy vol-unteer nr. 2

Patient nr. 1 Patient nr. 2

Cardiac output -20 +7.86 +2.50 +0.92 +2.67+20 -4.16 -2.67 -1.82 -2.98-40 +9.10 +5.62 +2.99 +5.55+40 -8.71 -5.68 -3.17 -5.54

Radius -20 -14.90 -9.21 -5.61 -9.78+20 +8.35 +4.48 +2.78 +5.39-40 -68.06 -30.57 -29.44 -52.00+40 +13.78 +7.54 +4.56 +7.95

Radius in hand -20 +0.55 -0.26 +0.05 -0.30+20 +0.25 -0.50 +0.01 -0.28-40 +0.97 -0.09 +0.02 -0.24+40 -0.18 -0.53 -0.38 -0.19

Young’s modulus -10 +1.48 +0.92 +0.40 +0.41+10 -0.95 -0.84 -0.41 -0.93-20 +3.07 +1.71 +0.73 +1.21+20 -1.83 -1.68 -0.81 -1.85

Table E.3: Mean brachial flow in the reference situation

Healthy vol-unteer nr. 1

Healthy vol-unteer nr. 2

Patient nr. 1 Patient nr. 2

Mean flow [mL/s] 1.69 1.15 0.56 0.61

Table E.4: Sensitivity of mean flow in the brachial artery

Change of output parameter mean brachial flow [%]Change of input param-eter [%]

Healthy vol-unteer nr. 1

Healthy vol-unteer nr. 2

Patient nr. 1 Patient nr. 2

Cardiac output -20 -18.89 -19.47 -19.88 -19.89+20 +18.84 +19.39 +19.64 +19.35-40 -38.35 -39.17 -39.68 -39.66+40 +37.02 +38.52 +39.12 +38.84

Radius -20 -20.74 -2.73 -1.84 -2.68+20 -12.27 +2.82 +0.58 +2.36-40 -34.24 -12.86 -7.04 -9.28+40 -10.97 +3.39 +105.68 +1.01

Radius in hand -20 -29.63 -24.27 -21.44 -23.33+20 +8.26 +35.70 +31.43 +33.77-40 -39.10 -39.18 -34.50 -37.31+40 +37.95 +84.67 +327.36 +80.56

Young’s modulus -10 +0.15 +0.19 0.00 -0.22+10 +0.06 +0.04 -0.10 -0.26-20 +0.23 +0.56 -0.09 -0.20+20 +0.19 -0.23 -0.15 -0.37

94

Table E.5: Sensitivity of systolic pressure in the finger artery

Change of output parameter systolic finger blood pressure [%]Change of input param-eter [%]

Healthy vol-unteer nr. 1

Healthy vol-unteer nr. 2

Patient nr. 1 Patient nr. 2

Cardiac output -20 -2.87 -4.00 -3.98 -4.49+20 +5.28 +3.91 +3.22 +4.31-40 -9.61 -7.62 -7.35 -8.94+40 +10.36 +7.61 +6.75 +8.86

Radius -20 +4.85 +8.93 +8.51 +11.35+20 -3.16 -2.03 -5.91 -4.08-40 +37.44 +24.82 +23.29 +32.79+40 -8.99 -7.96 -8.86 -11.64

Radius in hand -20 +8.89 +2.53 -0.03 +0.71+20 -0.88 -4.13 -0.47 -1.68-40 +10.64 +4.45 -0.22 +0.58+40 -7.04 -8.13 -11.17 -3.67

Young’s modulus -10 -1.70 -1.13 -0.90 -1.15+10 +1.88 +1.11 +0.81 +0.80-20 -3.62 -2.45 -1.82 -2.07+20 +3.59 +1.90 +1.61 +1.60

Table E.6: Sensitivity of diastolic blood pressure in the finger artery

Change of output parameter diastolic finger blood pressure [%]Change of input param-eter [%]

Healthy vol-unteer nr. 1

Healthy vol-unteer nr. 2

Patient nr. 1 Patient nr. 2

Cardiac output -20 +8.52 +2.80 +1.05 +2.90+20 -4.66 -2.97 -1.95 -3.18-40 +10.34 +6.27 +3.30 +6.07+40 -9.63 -6.25 -3.42 -5.91

Radius -20 -18.31 -10.49 -6.55 -10.76+20 +9.69 +4.76 +3.19 +5.73-40 -62.91 -32.59 -22.40 -39.51+40 +15.97 +8.38 +4.66 +8.77

Radius in hand -20 -0.16 -0.56 +0.27 -0.36+20 +0.42 -0.39 -0.28 -0.28-40 -0.39 -0.68 +0.30 -0.40+40 -0.19 -0.56 -3.04 -0.34

Young’s modulus -10 +1.48 +0.80 +0.39 +0.33+10 -0.77 -0.87 -0.37 -0.80-20 +2.73 +1.71 +0.68 +1.23+20 -1.72 -1.77 -0.72 -1.75

Table E.7: Mean finger flow in the reference situation

Healthy vol-unteer nr. 1

Healthy vol-unteer nr. 2

Patient nr. 1 Patient nr. 2

Mean flow [mL/s] 0.16 0.12 0.06 0.06

95

Table E.8: Sensitivity of mean flow in the finger artery

Change of output parameter mean finger flow [%]Change of input param-eter [%]

Healthy vol-unteer nr. 1

Healthy vol-unteer nr. 2

Patient nr. 1 Patient nr. 2

Cardiac output -20 -18.52 -19.18 -19.91 -20.07+20 +18.49 +19.69 +19.35 +18.98-40 -37.89 -39.04 -39.70 -39.67+40 +36.14 +38.81 +38.86 +38.42

Radius -20 -39.63 -3.56 -2.07 -3.05+20 -28.46 +3.62 +0.34 +2.24-40 -51.37 -15.02 -9.28 -11.75+40 -27.17 +3.56 +235.70 +0.68

Radius in hand -20 -64.19 -48.39 -48.66 -48.83+20 +17.75 +71.84 +71.20 +71.22-40 -84.89 -78.20 -78.26 -78.44+40 +82.28 +170.03 +742.88 +169.59

Young’s modulus -10 +0.13 +0.42 -0.10 -0.35+10 +0.07 +0.36 -0.28 -0.48-20 +0.25 +0.82 -0.20 -0.37+20 +0.19 -0.16 -0.26 -0.56

96

Appendix F

Pressure and flow waveformoutput of the sensitivity analysisof the wave propagation model

97

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105

Appendix G

Output of the sensitivityanalysis of the Nexfin model

Table G.1: Sensitivity of Nexfin cardiac output

Change of output parameter cardiac output [%]Change of input of thewave propagation model

Healthy vol-unteer nr. 1

Healthy vol-unteer nr. 2

Patient nr. 1 Patient nr. 2

Cardiac output -20% -10.73 -10.20 -7.54 -9.0220% +7.25 +9.78 +7.54 +8.51

Radius -20% +20.39 +29.33 +24.35 +25.7720% -16.62 -15.78 -15.94 -16.49

Radius in hand -20% +0.45 +0.56 +0.29 +0.5220% -0.15 +0.14 -0.87 +0.26

Young’s modulus -20% -4.53 -5.73 -5.51 -4.9020% +3.63 +5.59 +4.06 +4.12

Table G.2: Sensitivity of Nexfin systolic blood pressure of the brachial artery

Change of output parameter systolic brachial blood pressure [%]Change of input of thewave propagation model

Healthy vol-unteer nr. 1

Healthy vol-unteer nr. 2

Patient nr. 1 Patient nr. 2

Cardiac output -20% -8.39 -6.70 -6.07 -7.0320% +9.78 +6.86 +5.92 +7.17

Radius -20% +36.34 +26.14 +22.54 +26.5820% -17.53 -9.31 -10.26 -10.55

Radius in hand -20% +0.25 0.00 +0.14 0.0020% +0.13 -0.16 0.00 -0.42

Young’s modulus -20% -5.34 -4.09 -3.47 -4.2220% +5.08 +3.59 +3.18 3.52

106

Table G.3: Sensitivity of Nexfin diastolic blood pressure of the brachial artery

Change of output parameter diastolic brachial blood pressure [%]Change of input of thewave propagation model

Healthy vol-unteer nr. 1

Healthy vol-unteer nr. 2

Patient nr. 1 Patient nr. 2

Cardiac output -20% +1.00 -0.52 -0.69 -0.4720% +1.00 +0.26 +0.46 +0.24

Radius -20% +4.48 +2.08 +2.54 +1.6520% +4.48 +2.08 +2.54 +1.65

Radius in hand -20% -1.99 +0.26 -0.69 +0.4720% 0.00 -0.26 0.00 -0.24

Young’s modulus -20% -0.25 0.00 -0.23 -0.4720% +0.50 0.00 +0.23 -0.24

Table G.4: Sensitivity of Nexfin mean arterial pressure of the brachial artery

Change of output parameter mean brachial blood pressure [%]Change of input of thewave propagation model

Healthy vol-unteer nr. 1

Healthy vol-unteer nr. 2

Patient nr. 1 Patient nr. 2

Cardiac output -20% -2.11 -2.56 -2.46 -2.6320% +3.83 +2.56 +1.89 +2.63

Radius -20% +14.56 +9.38 +7.56 +9.7620% -7.09 -2.56 +1.89 +2.63

Radius in hand -20% 0.00 -0.21 0.00 -0.1920% 0.00 -0.21 +0.19 -0.38

Young’s modulus -20% -2.11 -1.49 -1.32 -1.6920% +2.11 +1.07 +1.13 +1.13

107

Appendix H

Effect of omitting theconvection term in the wavepropagation model

0 0.5 180

100

120

140

160

180

200

t [s]

P [m

mH

g]

Brachial artery

0 0.5 180

100

120

140

160

180

200

t [s]

P [m

mH

g]

Finger artery

0 0.5 1−1

0

1

2

3

4

5

6

7

8

t [s]

Flo

w [m

L/s]

Brachial artery

δ1 as in Bessems [2007]

δ1 = 0

0 0.5 1−2

0

2

4

6

8

t [s]

Flo

w [m

L/s]

Finger artery

Pressure and flow curves of simulations with and without convection term for healthyvolunteer nr. 1

108