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Online Supplement

Wave Reflections, Assessed with a Novel Method for Pulse Wave Separation, are Associated with End-Organ Damage and Clinical Outcomes

Thomas Weber (1), Siegfried Wassertheurer (2), Martin Rammer (1), Anton Haiden (1), Bernhard Hametner (2), Bernd Eber (1)

1 ... Cardiology Department, Klinikum Wels-Grieskirchen, Austria 2 ... Austrian Institute of Technology, Vienna, Austria

Corresponding author: Thomas Weber, MD Cardiology Department Klinikum Wels-Grieskirchen Grieskirchnerstrasse 42 4600 Wels Austria Tel.: 0043 7242 415 2215 Fax: 0043 7242 415 3992 Email: thomas.weber3@liwest.at

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ARCSolver algorithm The amplitude of the antegrade and the reflected pressure wave was quantified, using Wave Separation Analysis (WSA) with the recently developed ARCSolver method. WSA uses pressure- and flow waves to perform frequency-domain based calculations to derive the amplitudes of the forward (Pf) and backward (Pb) travelling waves [1]. Pressure waves were transfer-function derived from radial tonometry (SphygmoCor system, AtCor Medical, Sydney, Australia) [2], and flow waves were estimated from three-element Windkessel models. Our method describes the outflow of the left ventricle (Qm) during systole based on an externally (in this study by SphygmoCor) provided central pressure waveform (Pm) similar to a 3-element Windkessel model by the means of a dynamic system of second order. We use a linear model with continuous parameter space for arterial resistance (RC), peripheral resistance (Rp) and arterial compliance (Ca). A mathematical description is given in three steps: (1) The Windkessel equations for (RC), (Rp) and (Ca), describes the outflow of the left ventricle based on an externally provided central pressure waveform by the means of a dynamic system using a second order ordinary differential equation. During systole the relation between pressure (p(t)), aortic root flow (q(t)) and peripheral aortic flow (x(t)) can be described as in ApEq. 1 and ApEq. 2.

q(t) = Rp*Ca*x'(t)+x(t) for 0 < t < ts (ApEq. 1) p(t) = Rc*q(t) + Rp*x(t) (ApEq. 2)

Here (Rp) is the peripheral resistance, (Rc) is the effective arterial resistance and (Ca) is the arterial compliance. The first derivative of the flow in the aorta with respect to time is denoted as (x'(t)), the end of the ejection time is marked as (ts). When the aortic valve is closed, the outflow is modeled to be zero, which is an assumption, resulting in an mono exponential decay for (x(t)) in diastole; see ApEq. 3 and ApEq. 4, where (td) denotes the end of diastole, which is synonymous with the end of the cardiac cycle.

q(t) = 0 for ts <= t <= td (ApEq. 3)

(ApEq. 4)

The initial value in ApEq. 4 is specified in the way that periodicity of the signal is guaranteed:

x(0) = x(td) (ApEq. 5)

The work of the heart over one cardiac cycle can now be calculated as:

W=∫0

t s

p( t )�q ( t )dt (ApEq. 6)

The aim is to minimize this integral (ApEq. 6) under the constraint that a certain stroke volume has to be reached:

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(ApEq. 7)

Furthermore the following physiological boundary conditions should be fulfilled

(see ApEq. 3):

q(0) = 0 (ApEq. 8) q(ts) = 0 (ApEq. 9)

This problem can be solved using the calculus of variations. Substituting (p(t)) and (q(t)) in ApEq. 6 using ApEq. 1 and ApEq. 2, the integrand can be written as a function (F=F(x,x’,t)). The isoperimetric constraint in ApEq. 7 can be incorporated to (F) using a Lagrange multiplier (µ). Hence (F) can be written as:

F(x,x’,t,µ) = (Rc+Rp)*x² + (2*Rp*Ca*Rc+R²p*Ca)*x*x’ + + R²p*C²a*Rc*x’² - µ*(Rp*Ca*x’+x) (ApEq. 10)

The solution for such a problem can be determined by the solution of the Euler-Lagrange-equation:

∂F∂ x

− ddt

∂ F∂ x'

= 0 (ApEq. 11)

Since (F) contains a first derivative of (x(t)) and the Euler-Lagrange equation includes a derivation with respect to time, the result is always an inhomogeneous linear second order ordinary differential equation, see ApEq. 12. The inhomogeneity results of course from the constraint incorporated in (F).

x’’ - α²*x = β (ApEq. 12)

The coefficients (α) and (β) are time-invariant but depend on several model parameters: (α=α(Rc,Rp,Ca)) and (β=β(Rc,Rp,Ca,µ)). Following the theory of ordinary differential equations, the solution has the following form:

x(t) = A*eα*t + B*e-α*t + C (ApEq. 13)

Inserting the general solution of the differential equation (ApEq. 13) to ApEq. 4, ApEq.7 and ApEq.9 yields to a system of three linear equations and therefore solutions for (A), (B) and (C) that can be found uniquely. Since (Vs) is unknown, it has to be approximated by:

(ApEq. 14)

The parameters (Rp), (Rc) and (Ca) are now varied over a certain physiological range to find their optimal values to fit the given pressure waveform. As optimization criteria the area under the pressure curve is used.

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As described above the proposed solution of the differential equation consists of three unknown parameters that have to be determined. But with ApEq. 4 and ApEq. 7-9 four boundary conditions were formulated. Therefore one constraint has to be omitted, and ApEq. 8 has been left out. The disadvantage of this kind of approach is that the resulting flow curve does reflect the right area of the flow curve but not reflect the real flow waveform due to the neglected initial condition ApEq. 8, which would inhibit its use for the wave separation analysis (see Figure S1).

(2) Therefore in an additional step the so calculated Windkessel flow is processed using a second order linear delay element to get the final flow wave shape (ApEq. 15). Here the initial conditions are set to be zero (b0=0, Q0=0). The time constants (T1) and (T2) of the delay depend on the slope of the pressure curve in early systole and naturally on the underlying time step. While (T1) is hold constant over time, (T2) is a time-dependent parameter decreasing linearly from (T1) to one, influencing the reshape of the flow curve mainly during systolic upstroke. (b) is an intermediate state variable and (Q) denotes the flow curve used for further processing in the wave separation analysis. Once more during diastole the flow is assumed to be zero (see Figure S1).

(bt+1

Qt+ 1)=(1− 1T 1

0

1T 2

1− 1T 2)�(bt

Qt)+(1T 1

�qt

0 ) (ApEqn. 15)

Flow curves calculated with the ARCSolver method were compared with ECHO-Doppler derived flow curves, assessed in the left ventricular outflow tract, in 148 patients. The timing of the flow curve maximum (tQmax), which is crucial for the pulse wave decomposition, shows for the measured (Doppler derived) flow a mean value of 0.084 (SD 0.008) sec and 0.088 (SD 0.006) sec for ARCSolver flow. To compare the shape of the different flow curves, the maximal slope (dQmax) can serve as an indicator. For the measured flow the mean maximal slope is 1491 (SD 227) AU, and for the ARCSolver flow 1646 (SD 131) AU. With the root mean square error (RMSE), the deviation of two curves based on the difference for each data point can be measured. The mean RMSE between the measured flow and the ARCSolver flow is 4.68 (SD 1.90) AU for a peak flow of 100 arbitrary units. (3) Transmission line theory, which is described in the next paragraph, is applied to these waveforms to assess wave reflection. To perform the separation, three variables are needed: The measured pressure (Pm) and modeled flow (Qm) wave in the aorta and furthermore the characteristic impedance (Zc), which represents the impact of the arterial wall and therefore the relation between pressure and flow. (Zc) is estimated in the frequency domain using the modulus of the complex input impedance (Zi) calculated from the ratio of the present pressure and flow in the frequency domain. The frequencies in the range of 4 to 10 Hz are taken into account, which is a commonly used procedure [7,8]. For higher frequencies there could be inaccuracy due to noise [2]. To minimize the influence of outliers, all input impedances greater than a factor of 3 of the median of the considered impedances, are not taken into account. Following the wave theory, the measurable pressure (Pm) in the aorta is the sum of forward (Pf) and backward (Pb) traveling waves [2]. The same is valid for the corresponding flow waves. To obtain the forward and backward going parts separately, these equations have to be transformed (Pf = 0.5 * [Pm + Zc * Qm] and Pb = 0.5 * [Pm - Zc * Qm]), in order to

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obtain explicit formulas for the requested parameters. Thus the calculated waves in forward and backward direction remain unchanged (see Figure S1). The WSA results for ARCSolver method were validated against the classical method of WSA, based on ECHO-Doppler derived flow curves, assessed in the left ventricular outflow tract, in 148 patients. In addition, both methods were compared against the method proposed by Westerhof and colleagues [7], adopting a triangular-shaped flow waveform: The starting point of the triangle was assigned to the beginning of the data set of the corresponding pressure curve, which marked the beginning of the pressure upstroke during systole. The maximum of the triangle was set to the moment of time when the inflection point of the pressure wave was detected. For the forward pressure wave (Pf), the mean amplitude calculated from the measured Doppler flow was 26.56 (SD 7.96) mmHg, taking the triangular flow 33.21 (SD 10.78) mmHg, and with the ARCSolver flow 26.17 (SD 7.54) mmHg. For the backward pressure wave (Pb), the mean amplitude calculated from the measured Doppler flow was 16.66 (SD 5.46) mmHg, taking the triangular flow 18.67 (SD 7.34 SD) mmHg, and with the ARCSolver flow 15.64 (SD 5.47) mmHg. Subsequently the mean differences for ARCSolver derived amplitudes against Doppler derived ones are -0.39 (SD 1.96) [-0.71|-0.07] mmHg and -1.02 (SD 1.31) [-1.24|-0.80] mmHg for the amplitudes of (Pf) and (Pb) respectively – Table S1. Supplemental References 1 … Westerhof N, Sipkema P, van den Bos GC, Elzinga G. Forward and backward waves in the arterial system. Cardiovasc Res. 1972;6:648-656. 2 … Nichols WW, O’Rourke MF, Vlachopoulos C. McDonald's Blood Flow in Arteries. Theoretical, Experimental and Clinical Principles. 6th ed. Hodder Arnold, London; 2011. 3 … Hämäläinen RP, Hämäläinen JJ. On the Minimum Work Criterion in Optimal Control Models of Left-Ventrikular Ejection. IEEE Transactions on Biomedical Engineering. 1985;BME-32,11:951-956. 4 … Wassertheurer S, Kropf J, Weber T, van der Giet M, Baulmann J, Ammer M, Hametner B, Mayer CC, Eber B, Magometschnigg D. A new oscillometric method for pulse wave analysis: comparison with a common tonometric method. J Hum Hypertens. 2010;24:498-504. 5 … Wassertheurer S, Mayer C, Breitenecker F. Modeling arterial and left ventricular coupling for non-invasive measurements. Simulation Modelling Practice and Theory. 2008;16:988-997. 6 … Yamashiro SM, Daubenspeck JA, Bennett FM. Optimal regulation of left ventricular ejection pattern. Appl Math Comput. 1979;5:41-54. 7 … Westerhof BE, Guelen I, Westerhof N, Karemaker JM, Avolio A. Quantification of wave reflection in the human aorta from pressure alone: a proof of principle. Hypertension. 2006;48:595– 601. 8 … Swillens A, Segers P. Assessment of arterial pressure wave reflection: methodological considerations. Artery Research. 2008;2:122-131.

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WSA parameter ARCSolver vs Echo TRIANGULAR vs Echo

RMSE, mmHg 0.82 (0.54 SD) [0.73|0.91]

2.34 (1.57 SD) [2.08|2.60]

(Pf)est – (Pf)echo, mmHg -0.39 (1.96 SD) [-0.71|-0.07]

6.66 (4.67 SD) [5.89|7.43]

R [(Pf)est vs (Pf)echo] 0.970 [0.959|0.978]

0.919 [0.890|0.941]

(Pb)est – (Pb)echo, mmHg -1.02 (1.31 SD) [-1.24|-0.80]

2.01 (3.87 SD) [1.37|2.65]

R [(Pb)est vs (Pb)echo] 0.971 [0.960|0.979]

0.858 [0.809|0.895]

Table S1: Summary of WSA parameters derived from each introduced flow approximation approach (est=estimated) versus WSA parameters derived from Echo (Doppler) – upper line: differences, lower line: correlation coefficients. Values in brackets are 95 % confidence intervals for differences and correlation coefficients (Pf=forward pressure wave amplitude, Pb= backward pressure wave amplitude).

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Interaction between pulsatile arterial function and left ventricular systolic function Variable Normal systolic

function Slightly reduced systolic function

Moderately reduced systolic function

p-value

N 637 37 51 Ejection fraction (ECHO)

68 ± 8 53 ± 7 44 ± 8 <0.0001

bSBP mm Hg 137 ± 20 138 ± 20 132 ± 20 0.20 bDBP mm Hg 79 ± 10 80 ± 14 78 ± 13 0.55 MBP mm HG 99 ± 13 99 ± 17 95 ± 15 0.26 bPP mm Hg 57 ± 15 58 ± 12 54 ± 15 0.12 cSBP mm Hg 126 ± 20 127 ± 21 121 ± 20 0.17 cPP mm Hg 46 ± 15 46 ± 11 42 ± 14 0.11 P1 mm Hg 32 ± 9 33 ± 7 30 ± 9 0.11 AP mm Hg 14 ± 8 14 ± 8 12 ± 7 0.27 AIx 29 ± 11 29 ± 12 27 ± 12 0.33 AIx@75 23 ± 10 23 ± 11 21 ± 12 0.43 RM 0.62 ± 0.10 0.60 ± 0.12 0.57 ± 0.13 0.008 RI 0.38 ± 0.04 0.37 ± 0.04 0.36 ± 0.06 0.008 Pf mm Hg 30 ± 9 32 ± 12 28 ± 9 0.15 Pb mm Hg 19 ± 7 19 ± 8 16 ± 6 0.008 Table S2: Steady state and pulsatile hemodynamics in patients with normal, slightly reduced and moderately reduced systolic function. P-values are from Kruskal-Wallis ANOVA. Abbreviations see Table 1

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Arterial function and cardiac load / hypertensive end-organ damage in patients with normal / slightly reduced systolic function Arterial parameter Log Nt-proBNP GFR LA diameter LV mass E / E` PWV ao bSBP 0.19 ‡ -0.18 ‡ 0.20 ‡ 0.28 ‡ 0.34 ‡ 0.36 ‡ bDBP 0.07 -0.07 -0.04 0.09 0.08 * 0.05 MBP 0.04 -0.13 † 0.06 0.15 † 0.21 ‡ 0.19 ‡ bPP 0.31 ‡ -0.20 ‡ 0.30 ‡ 0.31 ‡ 0.39 ‡ 0.45 ‡ cPP 0.36 ‡ -0.22 ‡ 0.32 ‡ 0.25 ‡ 0.42 ‡ 0.43 ‡ AIx 0.25 ‡ -0.13 † 0.17 ‡ -0.07 0.22 ‡ 0.11 † AIx@75 0.20 ‡ -0.13 † 0.13 † -0.13 * 0.19 ‡ 0.15 † AP 0.35 ‡ -0.19 ‡ 0.27 ‡ 0.09 0.38 ‡ 0.30 ‡ P1 0.27 ‡ -0.18 ‡ 0.30 ‡ 0.34 ‡ 0.36 ‡ 0.43 ‡ RM 0.20 ‡ -0.10 † 0.15 † -0.09 0.20 ‡ 0.10 * RI 0.19 ‡ -0.10 † 0.15 † -0.08 0.19 ‡ 0.10 * Pf 0.34 ‡ -0.22 ‡ 0.29 ‡ 0.26 ‡ 0.38 ‡ 0.46 ‡ Pb 0.37 ‡ -0.23 ‡ 0.30 ‡ 0.18 † 0.42 ‡ 0.43 ‡ * p<0.05, † p<0.01, ‡ p<0.0001 Table S3: Relationship between measures of steady and pulsatile function and measures of cardiac load and end-organ damage in patients with normal and slightly reduced systolic function (n=674). Values are Pearson´s correlation coefficients. GFR … glomerular filtration rate, LA … left atrium, LV … left ventricle, PWV … pulse wave velocity. Data for LVmass were available for 402 patients. Univariate predictors of outcome Parameter Hazard ratio 95% CI p-value Age (per year) 1.043 1.026-1.061 <0.0001 Hypertension (yes=1 no=0) 1.658 1.097-2.505 0.002 Diabetes (yes=1 no=0) 1.965 1.366-2.826 0.0003 Smoking (yes=1 no=0) 1.540 1.014-2.341 0.04 Coronary artery disease (yes=1 no=0) 3.928 2.718-5.678 <0.0001 Angioscore (per unit) 1.108 1.069-1.148 <0.0001 Body mass index (per unit) 0.953 0.917-0.990 0.01 E / E`med (per unit) 1.052 1.031-1.073 <0.0001 LA diameter/BSA (per unit) 1.095 1.041-1.151 0.0005 Systolic function* 1.417 1.119-1.793 0.004 Prior myocardial infarction (yes=1 no=0) 2.403 1.4676-3.935 0.0005 Log BNP (per unit) 2.474 1.827-3.350 <0.0001 PWV aortic (per SD) 1.451 1.292-1.630 <0.0001 Table S4: Univariate predictors of the combined endpoint. * Coding was: normal function=1, slightly reduced function=2, moderately reduced function=3

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Measures of pulsatile arterial function and the risk of cardiovascular events – adjustment for brachial systolic blood pressure Arterial parameter

Univariate Model 1 Model 2 Model 3 Model 4

bPP 1.297 CI 1.147-1.467

(p<0.0001)

1.524 CI 1.116-2.080

(p=0.008)

1.545 CI 1.109-2.153

(p=0.01)

1.427 CI 0.996-2.044

(p=0.054)

1.442 CI 1.002-2.074

(p=0.049) cPP 1.270

CI 1.120-1.439 (p=0.0002)

1.364 CI 1.018-1.826

(p=0.04)

1.547 CI 1.083 –

2.208 (p=0.02)

1.493 CI 1.009-2.208

(p=0.046)

1.609 CI 1.078-2.402

(p=0.02) AIx 1.143

CI 0.960-1.362 (p=0.13)

1.134 CI 0.927-1.389

(p=0.22)

1.104 CI 0.867-1.406

(p=0.42)

1.169 CI 0.908-1.505

(p=0.23)

1.259 CI 0.976-1.624

(p=0.08) AIx@75 1.176

CI 0.987-1.402 (p=0.07)

1.221 CI 0.988-1.510

(p=0.07)

1.116 CI 0.890-1.399

(p=0.34)

1.194 CI 0.943-1.512

(p=0.14)

1.279 CI 1.008-1.621

(p=0.044) AP 1.236

CI 1.075-1.423 (p=0.003)

1.197 CI 0.953-1.503

(p=0.12)

1.265 CI 0.951-1.683

(p=0.11)

1.266 CI 0.934-1.716

(p=0.13)

1.401 CI 1.030-1.905

(p=0.03) P1 1.302

CI 1.140-1.488 (p=0.0001)

1.301 CI 0.989-1.710

(p=0.06)

1.350 CI 1.007-1.809

(p=0.046)

1.280 CI 0.949-1.726

(p=0.11)

1.244 CI 0.921-1.682

(p=0.16) RM 1.187

CI 0.995-1.418 (p=0.059)

1.192 CI 0.991-1.433

(p=0.06)

1.185 CI 0.967-1.453

(p=0.10)

1.205 CI 0.973-1.494

(p=0.09)

1.313 CI 1.056-1.633

(p=0.015) RI 1.177

CI 0.980-1.413 (p=0.08)

1.183 CI 0.979-1.430

(p=0.08)

1.174 CI 0.952-1.447

(p=0.14)

1.189 CI 0.955-1.481

(p=0.12)

1.299 CI 1.036-1.629

(p=0.02) Pf 1.226

CI 1.064-1.412 (p=0.005)

1.174 CI 0.859-1.604

(p=0.32)

1.225 CI 0.879-1.738

(p=0.22)

1.197 CI 0.815-1.758

(p=0.36)

1.260 CI 0.843-1.882

(p=0.26) Pb 1.276

CI 1.106-1.472 (p=0.0009)

1.356 CI 1.030-1.784

(p=0.03)

1.476 CI 1.068-2.040

(p=0.02)

1.423 CI 1.007-2.012

(p=0.047)

1.695 CI 1.182-2.430

(p=0.004) Table S5: Measures of pulsatile arterial function and the risk of cardiovascular events Model 1: adjusted for age, gender, systolic function, brachial systolic blood pressure, angioscore Model 2: adjusted for model 1 plus diabetes, smoking, hypertension, E/E`, heart rate Model 3: adjusted for model 2 plus PWV aortic, prior myocardial infarction, statin use, lognt-proBNP, GFR, CAD, medications (ACE/ARB, BB, CCB, nitrates) Model 4: adjusted for model 3 (except E/E´) plus LV enddiastolic pressure (invasive), LA diameter (660 pts)

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Arterial parameter

Univariate Model 1 Model 2 Model 3 Model 4

bPP 1.349 CI 1.194-1.527

(p<0001)

1.535 CI 1.088-2.166

(p=0.015)

1.674 CI 1.158-2.418

(p=0.006)

1.561 CI 1.049-2.321

(p=0.03)

1.607 CI 1.081-2.388

(p=0.02)cPP 1.319

CI 1.163-1.496 (p<0.0001)

1.327 CI 0.966-1.824

(p=0.08)

1.769 CI 1.187-2.636

(p=0.005)

1.697 CI 1.101-1.262

(p=0.017)

1.822 CI 1.176-2.823

(p=0.008)AIx 1.121

CI 0.928-1.353 (p=0.24)

1.074 CI 0.864-1.335

(p=0.52)

1.137 CI 0.877-1.475

(p=0.33)

1.191 CI 0.909-1.559

(p=0.21)

1.241 CI 0.947-1.627

(p=0.12)AIx@75 1.169

CI 0.968-1.413 (p=0.11)

1.197 CI 0.949-1.511

(p=0.13)

1.133 CI 0.889-1.443

(p=0.31)

1.194 CI 0.930-1.534

(p=0.17)

1.239 CI 0.984-1.593

(p=0.10)AP 1.270

CI 1.098-1.1.469 (p=0.001)

1.138 CI 0.897-1.444

(p=0.29)

1.344 CI 0.991-1.824

(p=0.059)

1.362 CI 0.983-1.887

(p=0.06)

1.464 CI 1.054-2.033

(p=0.02)P1 1.373

CI 1.202-1.569 (p<0.0001)

1.357 CI 1.001-1.840

(p=0.05)

1.448 CI 1.046-2.005

(p=0.027)

1.374 CI 0.992-1.903

(p=0.057)

1.364 CI 0.984-1.892

(p=0.06) RM 1.254

CI 1.027-1.530 (p=0.03)

1.284 CI 1.035-1.591

(p=0.02)

1.312 CI 1.040-1.655

(p=0.02)

1.342 CI 1.054-1.708

(p=0.018)

1.415 CI 1.108-1.806

(p=0.006) RI 1.263

CI 1.024-1.558 (p=0.03)

1.291 CI 1.030-1.6178

(p=0.03)

1.323 CI 1.035-1.691

(p=0.026)

1.346 CI 1.045-1.734

(p=0.02)

1.431 CI 1.104-1.853

(p=0.007) Pf 1.297

CI 1.122-1.498 (p=0.0004)

1.133 CI 0.799-1.607

(p=0.48)

1.338 CI 0.911-1.966

(p=0.14)

1.253 CI 0.817-1.923

(p=0.30)

1.369 CI 0.878-2.133

(p=0.17) Pb 1.358

CI 1.173-1.572 (p<0.0001)

1.378 CI 1.027-1.850

(p=0.03)

1.692 CI 1.189-2.407

(p=0.004)

1.666 CI 1.141-2.433

(p=0.008)

1.941 CI 1.315-2.864

(p=0.0009) Table S6: Measures of pulsatile arterial function and the risk of cardiovascular events in 674 patients with normal and slightly impaired systolic function Model 1: adjusted for age, gender, systolic function, brachial systolic blood pressure, angioscore Model 2: adjusted for model 1 plus diabetes, smoking, hypertension, E/E`, heart rate Model 3: adjusted for model 2 plus PWV aortic, prior myocardial infarction, statin use, lognt-proBNP, GFR, CAD, medications (ACE/ARB, BB, CCB, nitrates) Model 4: adjusted for model 3 (except E/E´) plus LV enddiastolic pressure (invasive), LA diameter (616 pts)

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Measures of pulsatile arterial function and the risk of cardiovascular events – adjustment for brachial diastolic blood pressure Arterial parameter

Univariate Model 1 Model 2 Model 3 Model 4

bPP 1.297 CI 1.147-1.467

(p<0.0001)

1.229 CI 1.065-1.419

(p=0.005)

1.175 CI 1.006-1.373

(p=0.04)

1.105 CI 0.935-1.307

(p=0.25)

1.149 CI 0.970-1.360

(p=0.11) cPP 1.270

CI 1.120-1.439 (p=0.0002)

1.214 CI 1.049-1.404

(p=0.01)

1.187 CI 1.008-1.398

(p=0.04)

1.123 CI 0.942-1.338

(p=0.20)

1.183 CI 0.992-1.410

(p=0.06) AIx 1.143

CI 0.960-1.362 (p=0.13)

1.205 CI 0.986-1.473

(p=0.07)

1.218 CI 0.953-1.557

(p=0.12)

1.267 CI 0.979-1.641

(p=0.07)

1.384 CI 1.066-1.795

(p=0.015) AIx@75 1.176

CI 0.987-1.402 (p=0.07)

1.340 CI 1.080-1.663

(p=0.008)

1.220 CI 0.969-1.535

(p=0.09)

1.285 CI 1.009-1.636

(p=0.04)

1.393 CI 1.093-1.776

(p=0.008) AP 1.236

CI 1.075-1.423 (p=0.003)

1.216 CI 1.039-1.424

(p=0.015)

1.214 CI 1.011-1.459

(p=0.04)

1.166 CI 0.958-1.420

(p=0.13)

1.261 CI 1.037-1.534

(p=0.02) P1 1.302

CI 1.140-1.488 (p=0.0001)

1.207 CI 1.037-1.407

(p=0.016)

1.164 CI 0.989-1.369

(p=0.07)

1.106 CI 0.934-1.310

(p=0.24)

1.160 CI 0.953-1.348

(p=0.16) RM 1.187

CI 0.995-1.418 (p=0.059)

1.201 CI 1.002-1.439

(p=0.049)

1.202 CI 0.984-1.469

(p=0.07)

1.214 CI 0.981-1.501

(p=0.076)

1.327 CI 1.070-1.646

(p=0.01) RI 1.177

CI 0.980-1.413 (p=0.08)

1.195 CI 0.993-1.439

(p=0.06)

1.195 CI 0.972-1.469

(p=0.09)

1.201 CI 0.966-1.493

(p=0.10)

1.318 CI 1.054-1.648

(p=0.016) Pf 1.226

CI 1.064-1.412 (p=0.005)

1.145 CI 0.981-1.338

(p=0.09)

1.110 CI 0.938-1.314

(p=0.23)

1.055 CI 0.877-1.269

(p=0.57)

1.146 CI 0.936-1.405

(p=0.19) Pb 1.276

CI 1.106-1.472 (p=0.0009)

1.228 CI 1.046-1.436

(p=0.01)

1.202 CI 1.005-1.438

(p=0.04)

1.140 CI 0.939-1.384

(p=0.19)

1.306 CI 1.061-1.609

(p=0.01) Table S7: Measures of pulsatile arterial function and the risk of cardiovascular events Model 1: adjusted for age, gender, systolic function, brachial diastolic blood pressure, angioscore Model 2: adjusted for model 1 plus diabetes, smoking, hypertension, E/E`, heart rate Model 3: adjusted for model 2 plus PWV aortic, prior myocardial infarction, statin use, lognt-proBNP, GFR, CAD, medications (ACE/ARB, BB, CCB, nitrates) Model 4: adjusted for model 3 (except E/E´) plus LV enddiastolic pressure (invasive), LA diameter (660 pts)

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Arterial parameter

Univariate Model 1 Model 2 Model 3 Model 4

bPP 1.349 CI 1.194-1.527

(p<0001)

1.270 CI 1.093-1.476

(p=0.002)

1.241 CI 1.050-1.468

(p=0.01)

1.194 CI 0.998-1.428

(p=0.054)

1.223 CI 1.029-1.453

(p=0.02) cPP 1.319

CI 1.163-1.496 (p<0.0001)

1.246 CI 1.069-1.453

(p=0.005)

1.269 CI 1.066-1.510

(p=0.008)

1.226 CI 1.016-1.479

(p=0.03)

1.265 CI 1.056-1.515

(p=0.01) AIx 1.121

CI 0.928-1.353 (p=0.24)

1.150 CI 0.927-1.427

(p=0.21)

1.290 CI 0.991-1.678

(p=0.059)

1.334 CI 1.013-1.758

(p=0.04)

1.413 CI 1.070-1.864

(p=0.015) AIx@75 1.169

CI 0.968-1.413 (p=0.11)

1.333 CI 1.051-1.691

(p=0.018)

1.275 CI 0.997-1.629

(p=0.054)

1.329 CI 1.029-1.718

(p=0.03)

1.399 CI 1.082-1.809

(p=0.01) AP 1.270

CI 1.098-1.469 (p=0.001)

1.221 CI 1.034-1.442

(p=0.019)

1.304 CI 1.075-1.581

(p=0.007)

1.289 CI 1.045-1.591

(p=0.019)

1.356 CI 1.104-1.665

(p=0.004) P1 1.373

CI 1.202-1.569 (p<0.0001)

1.267 CI 1.080-1.467

(p=0.004)

1.236 CI 1.038-1.472

(p=0.018)

1.202 CI 1.002-1.441

(p=0.049)

1.218 CI 1.020-1.454

(p=0.03) RM 1.254

CI 1.027-1.530 (p=0.03)

1.299 CI 1.052-1.605

(p=0.016)

1.329 CI 1.059-1.668

(p=0.015)

1.357 CI 1.069-1.721

(p=0.01)

1.439 CI 1.132-1.831

(p=0.003) RI 1.263

CI 1.024-1.558 (p=0.03)

1.309 CI 1.049-1.635

(p=0.018)

1.347 CI 1.061-1.712

(p=0.015)

1.368 CI 1.066-1.756

(p=0.01)

1.462 CI 1.133-1.885

(p=0.004) Pf 1.297

CI 1.122-1.498 (p=0.0004)

1.189 CI 1.009-1.401

(p=0.04)

1.198 CI 1.003-1.431

(p=0.048)

1.141 CI 0.940-1.384

(p=0.18)

1.253 CI 1.010-1.556

(p=0.04) Pb 1.358

CI 1.173-1.572 (p<0.0001)

1.282 CI 1.087-1.511

(p=0.003)

1.320 CI 1.097-1.588

(p=0.003)

1.275 CI 1.043-1.557

(p=0.018)

1.454 CI 1.169-1.801

(p=0.0008) Table S8: Measures of pulsatile arterial function and the risk of cardiovascular events in 674 patients with normal and slightly impaired systolic function Model 1: adjusted for age, gender, systolic function, brachial diastolic blood pressure, angioscore Model 2: adjusted for model 1 plus diabetes, smoking, hypertension, E/E`, heart rate Model 3: adjusted for model 2 plus PWV aortic, prior myocardial infarction, statin use, lognt-proBNP, GFR, CAD, medications (ACE/ARB, BB, CCB, nitrates) Model 4: adjusted for model 3 (except E/E´) plus LV enddiastolic pressure (invasive), LA diameter (616 pts)

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Figure S1: (1) Windkessel flow derived from (ApEq. 1 and 2). (2) Realistic flow pattern provided by ARCSolver after (ApEq. 15) has been applied to Windkessel flow. (3) ARCSolver derived aortic flow wave is used to decompose synthetic aortic pressure wave into forward and backward wave (Pf + Pb) with WSA.