Accuracy of Laparoscopic 3D Ultrasound

Accuracy of Laparoscopic 3D Ultrasound

L I S A N I L S S O N

Master’s Thesis in Biomedical Engineering (30 ECTS credits) at the School of Mechanical Engineering Royal Institute of Technology year 2008 Supervisor at CSC was Erik Fransén Examiner was Anders Lansner TRITA-CSC-E 2008:039 ISRN-KTH/CSC/E--08/039--SE ISSN-1653-5715 Royal Institute of Technology School of Computer Science and Communication KTH CSC SE-100 44 Stockholm, Sweden URL: www.csc.kth.se


Accuracy of Laparoscopic 3D Ultrasound Abstract In laparoscopic surgery the surgeon has to rely on endoscopic camera visualization within the abdomen, without haptic feedback. This limits the usefulness of laparoscopy. To improve laparoscopic surgery, the department of medical technology at SINTEF Health Research and St. Olavs Hospital in Trondheim Norway are developing a navigation system based on advanced tracking and imaging capabilities. The navigation system provides the surgeon with an overview of anatomy beyond the surface of organs seen with video laparoscope. The user is also able to control the visualizations interactively with the tracked surgical instruments. In this student project the specific task was to evaluate the accuracy of laparoscopic 3D ultrasound using an electromagnetic tracking system with miniaturized tracking sensors in combination with a laparoscopic ultrasound probe. It was also to compare 3D ultrasound acquired with the electromagnetic system to acquisitions made using an optical tracking system. Two conventional ultrasound probes were used in addition to the laparoscopic probe. The latter was flexible at the distal end and, hence, optical tracking was not feasible with this probe. In order to achieve proper geometric volume scans performed by freehand, a probe calibration procedure was performed for all combinations of ultrasound probe and sensor. For this, an in-house made, specially designed phantom containing a thin Bakelite plastic membrane of known geometry was used, while a commercial accuracy phantom containing two egg-shaped volumes of known sizes with vender specified dimensions was used for the 3D acquisitions. Several types of freehand acquisitions were performed for all of the probes and sensor combinations. The volumes were reconstructed into regular 3D volumes in the navigation system software, and later with software based on a pixel-based method that uses an ellipsoid truncated Gaussian kernel with Gaussian weighing. The egg structures were then segmented and the volumes were calculated and dimensions measured with an image processing application. The results showed a systematic error in dimension compared to the specifications of the phantom. A few acquisitions were not possible to process due to errors in the probe calibration. Unexpectedly, the results further showed that the best results were achieved using the laparoscopic probe with electromagnetic tracking.


Noggrannhet hos laparoskopiskt 3D ultraljud Sammanfattning Vid laparoskopisk kirurgi är kirurgen beroende av visualisering av arbetsområdet i buken med hjälp av endoskopisk videokamera, helt utan taktil feedback. Detta begränsar användandet av laparoskopi. För att förbättra laparoskopisk kirurgi pågår hos SINTEF (Stiftelsen för industriell och teknisk forskning) och St. Olavs Hospital i Trondheim Norge, utveckling av ett navigationssystem baserat på avancerade visualiserings- och navigeringstekniker. Detta navigationssystem förser kirurgen i fråga med en överblick över organ belägna bakom operationsområdet som annars inte syns med endoskopisk videokamera. Systemet kan kontrolleras och justeras interaktivt av dess användare, som oftast är kirurgen, så att denne kan styra vilket område som skall visualiseras och återges via positioneringssystemsspårning av de laparoskopiska operationsinstrumenten. Specifikt för detta examensarbete var att utvärdera noggrannheten hos laparoskopiskt 3D ultraljud, skapat genom användning av med ett elektromagnetiskt positioneringssystem spårade sensorer placerade på en laparoskopisk 2D ultraljudsprob. Ytterliggare en del av arbetet var att jämföra dessa resultat med 3D ultraljud åstadkommet användandes samma metod men med optiskt positioneringssystem istället för elektromagnetiskt. Två konventionella ultraljudsprober användes i arbetet förutom den tidigare nämnda laparoskopiska proben. Då den senare är flexibel i dess distala ände gick den av praktiska skäl inte att använda i kombination med optisk positionering. För att kunna genomföra korrekt volymscanning gjord på frihand, genomfördes först positioneringskalibrering av varje ultraljudsprob- och positioneringssystemskombination. Till detta steg användes en egenkonstruerad specialfantom innehållandes ett tunt bakelitmembran med känd geometri. För volymscanningen användes en kommersiell precisionsfantom vilken innehöll två äggformade volymer vars dimensioner specificerats av tillverkaren. Ett flertal scanningar genomfördes för de olika kombinationerna av ultraljudsprob och positioneringssystem. De scannade volymerna rekonstruerades till ”vanliga” 3D volymer i navigationssystemets mjukvara och senare med mjukvara vars grund var baserad på en pixelbaserad metod vilken använder sig av en ellipsoid stympad Gaussisk kärna med Gaussisk vägning. De äggformade volymernas strukturer segmenterades efter detta i ett bildbehandlingsprogram för att möjliggöra volymsberäkning samt dimensionsmätningar av dem. Resultaten visade ett systematiskt dimensionsfel jämfört med de specificerade dimensionerna för precisionsfantomen. Vissa av volymscanningarna gick inte att genomföra på grund av bland annat misslyckad probkalibrering. Det visade sig också att det mest precisa resultatet åstadkoms med den laparoskopiska ultraljudsproben använd i kombination med det elektromagnetiska positioneringssystemet.


Acknowledgements I would like to thank the staff at SINTEF Health Research, Department of Medical Technology in Trondheim, Norway for sharing both knowledge and time so generously. I would especially like to acknowledge my supervisor Thomas Langø without whom this master thesis would not have been possible. Last but not least, I want to thank my beloved family and friends, in particular Bert Nilsson, Kerstin Svanlund, Emil and Nutchanet Nilsson, Karin Nilsson and Kim Fagerholm for their encouragement and belief in me at all times.


Contents

1. Aims and limitations................................................................................................ 1

2. Background ............................................................................................................ 2

2.1 Introduction ....................................................................................................... 2

2.2 Ultrasound......................................................................................................... 4

2.3 Positioning systems .......................................................................................... 5

2.3.1 Optical Tracking systems ........................................................................... 5

2.3.2 Electromagnetic tracking systems .............................................................. 6

2.4 Probe calibration ............................................................................................... 7

2.5 Generating 3D Ultrasound ................................................................................ 8

3. Method.................................................................................................................... 9

3.1 Equipment......................................................................................................... 9

3.2 Experimental set-up .......................................................................................... 9

3.3 Probe calibration and image-to-world transformation...................................... 13

3.4 Reconstruction ................................................................................................ 16

3.5 Segmentation and volume calculations........................................................... 17

4. Result ................................................................................................................... 19

4.1 Protocol for 3D acquisitions ............................................................................ 19

4.2 Result observations......................................................................................... 20

5. Discussion ............................................................................................................ 21

5.1 Time synchronization ...................................................................................... 21

5.2 Probe calibration ............................................................................................. 21

5.3 Reconstruction ................................................................................................ 23

5.4 Segmentation.................................................................................................. 23

5.5 Volume calculations ........................................................................................ 26

5.6 Other sources of error and important aspects................................................. 26

6. Conclusion............................................................................................................ 27

7. Future work........................................................................................................... 27

8. Bibliography and references ................................................................................. 28


9. Appendix............................................................................................................... 30

9.1.1 Probe calibration information.................................................................... 30

9.1.2 Probe calibration matrices used for one specific acquisition .................... 31

9.2 Calibration and Acquisition Settings: System FiVe ......................................... 32

9.3 Accuracy of NDI tracking systems .................................................................. 33

9.4 Differences; measured and specified dimensions........................................... 34

9.5 Measurement Volumes of NDI Tracking Systems........................................... 35

9.6 Specification of Model 055 3D Ultrasound Calibration Phantom..................... 36


1

1. Aims and limitations The main objective of this project is to evaluate the accuracy of 3D laparoscopic ultrasound using a combination of a flexible laparoscopic ultrasound probe and a miniature electromagnetic tracking sensor attached to the distal end of the probe. For comparisons we will also perform similar analysis with two other ultrasound probes and optical tracking as well. The 3D acquisitions will be performed by freehand scanning. The evaluation outcome plays an important role regarding future work within this area. Mostly because it provides basic knowledge in order to determine whether or not the method is accurate enough to further develop and use for clinical solutions. Within laparoscopic surgery, every measure made that varies no more than ±1 cm compared to given specifications is rated accurate enough. The major limitations are due to limited time given to this project. Of course, wider research would be possible were there more time. For instance more acquisitions could be made; other ultrasound probes could be used for the tests and so forth. With this in mind, the major focus of this project has been set to answer the question: “Is laparoscopic ultrasound combined with electromagnetic tracking accurate enough to use clinically?”


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2. Background In order to provide the reader with useful information concerning concepts and theories used in this project, the background chapter provides basic knowledge within areas such as ultrasound and tracking systems in general. More detailed explanation regarding the specific use of these technologies is presented in the method chapter.

2.1 Introduction In all types of surgery, accuracy and precision are very important parameters. Although the human “factor” plays a significant role, it is possible to minimize the risks of her causing errors by using for example high-quality instruments and appropriate imaging modalities. In laparoscopic surgery, the procedure is performed without opening the abdomen itself. Instead the patient is operated through tiny holes in which instruments with a diameter of 5-12 mm are inserted. To diagnose and plan the surgery, a preoperative computed tomography (CT) or magnetic resonance imaging (MRI) procedure is usually performed. These images can also be reconstructed into a 3D volume for improved visualization and interpretation. The surgeon and/or radiologist can then mark and plan for important anatomic structures surrounding the pathology to be operated, in particular, nerves and blood vessels. During surgery, the surgeons use intraoperative imaging when needed, in order to see beyond the surface view of the endoscopic video camera inside the abdomen. Such imaging can be ultrasound or x-ray with a C-arm (mobile x-ray gantry). To be able to link such images and the preoperative ones, tracking systems and navigation principles have been introduced into surgery (Mårvik et al. 2005). Furthermore, the real-time imaging capabilities of ultrasound make it possible to combine 2D ultrasound probes with tracking systems to achieve 3D ultrasound during surgery. This has been demonstrated for many years in neurosurgery (Gronningsaeter et al. 2000). Ultrasound in combination with preoperative data presents many advantages to the surgeons performing minimal invasive therapy. The progress of the procedure can be visually followed in the intraoperative ultrasound, while the overview and plan can be seen in preoperative CT or MRI. The tumor can for instance be marked in advance in the MRI or CT, and the ultrasound volume acquired during surgery can show possible remaining tumor tissue. If there are any signs of tumor remaining, the ultrasound volume will show this, giving the surgeon the opportunity to remove that as well. In this project, we will investigate the accuracy of freehand 3D ultrasound scanning using a flexible laparoscopic ultrasound probe with electromagnetic tracking (Aurora, Northern Digital Inc (NDI), Canada). Furthermore, we will use other probes to compare optical based tracking (Polaris, NDI) for freehand 3D ultrasound scanning to electromagnetic based tracking.


3

An important step in reconstruction of freehand 3D ultrasound volumes and in navigated 2D and 3D ultrasound is the probe calibration process. This is also one of the largest sources of error (Lindseth et al. 2002). Probe calibration constitutes the process of determining the position and orientation of the ultrasound image coordinate system relative to the coordinate system of the tracking sensor attached to the probe. The sensor attached to the probe provides the navigation system continuously with position measurements. Since the probe plus tracking sensor and the ultrasound 2D real time imaging plane constitutes one rigid body it suffices to determine the probe calibration transformation once for a probe and sensor combination. Although ultrasound has some disadvantages compared to CT or MRI, it still presents many advantages:

• The probe is small and can be manipulated with great flexibility

allowing real-time images at user-controlled orientations and

positions

• The ultrasound systems are inexpensive, compact, mobile, and it

does not require special facilities to allow intermittent use in the OR

• Ultrasound image quality has improved in recent years, in particular

the use of ultrasound contrast and new processing techniques will

continue to improve the value of ultrasound images

• Ultrasound can provide real-time imaging of blood flow, blood and

tissue velocity, other tissue parameters and changes and

characterization allowing the physician to map vascular structures of

varying size

Nevertheless, ultrasound suffers from some drawbacks that should also be mentioned:

• The signal-to-noise ratio is often low

• The specular nature of the modality causing shadowing, multiple

reflection artifacts, and variable contrast

• The quality of the images may be somewhat operator dependent,

based on his/her experience with ultrasound scanning

• Limited size of volume acquisitions due to small probe size, short

imaging range/depth, and width constraints, which may give

orientation and interpretation difficulties

Nevertheless, the real-time imaging capabilities of ultrasound outweigh these deficiencies and ultrasound has therefore been used for years to guide interventions in breast, prostate, liver, and brain.


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2.2 Ultrasound Ultrasound has been utilized in medical care since the 1950ies and is still one of the most frequently used modalities when it comes to medical imaging. It has several advantages compared to other forms of imaging, such as X-ray or magnetic resonance imaging. In addition to the advantages mentioned above, ultrasound is not harmful to body tissue. It has been proved that a fetus consisting of only four cells is not damaged if exposed to ultrasound. The principle of ultrasound is echoes received, due to variations in acoustic impedance, when transmitting acoustic waves towards and / or through different materials. The acoustic impedance is defined as:

c⋅=Ζ ρ

where ρ is the mass density and c is the speed of sound, in the material. In humans, every type of body tissue has its’ own specific value of impedance thus making the use of medical ultrasound possible. At the front of each ultrasound probe, an array of transducer elements is located. These elements are a type of electrical capacitors, which consist of a plate of Piezoelectric ceramic material with two thin metal electrodes on each face. A Piezoelectric material changes physically when exposed to electrical voltage. Coupling an alternating voltage source to the two electrodes, will therefore cause the Piezoelectric plate to increase or decrease in thickness depending on the polarity of the voltage. When placing the probe against skin, the vibrations will cause acoustic waves. These waves propagate through the tissue and each time the wave hits a tissue with different acoustic impedance from the previous, the wave will partially reflect and partially be transmitted across the boundary. The amount of reflection and transmission is determined by the difference in impedance when passing over from one type of tissue to another. The reflection coefficient R and the transmission coefficient T are defined as (Angelsen 1995)

⎟⎟⎠

⎞⎜⎜⎝

⎛Ζ+ΖΖ−Ζ

=21

1212R ⎟⎟

⎠

⎞⎜⎜⎝

⎛Ζ+Ζ

Ζ⋅=

21

212

2T

If the pulse hits gases or solids, the density difference is so great that most of the acoustic energy is reflected (R close to 1) and it becomes impossible to see deeper. Values of R near zero means that most of the wave energy has been transmitted (T close to 1) to the neighboring tissue. The echo in this case is very low in amplitude. The transducer does not only emit acoustic waves, it can also transfer energy from acoustic vibration into an electric voltage which in fact means that it is both speaker and microphone at the same time. Settings such as depth of focus and transmission frequency are individually set by the user, on the ultrasound system.


5

2.3 Positioning systems All types of positioning systems (acoustic, optical, mechanical, electromagnetic) aim to measure position and orientation with respect to a reference point or state.

2.3.1 Optical Tracking systems When it comes to accuracy, no positioning system has yet provided such precise results as the optical positioning systems (Mercier et al. 2005). Although the basic concept of optical tracking is emitting and recording of infrared light beams, the procedure can be performed in two manners. The difference is whether active or passive markers (sensors) are used, but for both types a minimum of three sensors is required. When using passive markers, beams of infrared light is emitted from the system towards spheres or discs mounted asymmetrically on a rigid structure. These spheres or discs will reflect the light and return them back to the system where cameras detect their reflections. The geometry of the spheres or discs with respect to each other is determined before any tracking is done. The spheres or discs can never be too similar to one another due to the fact that this might confuse the positioning system in terms of which disc or sphere a reflection originates from. With an optical tracking system that uses passive markers, the light emitter and the camera (detector) are located in the same apparatus. With active markers, light-emitting diodes are used. The camera detecting the light emitted and the diodes are connected via a processing box. If more than one tool is being tracked at the same time, all of the tools (or e.g. all the sets of diodes) must be wired to the processing box in order for it to activate the diode sets and flash them one at a time. By doing this, the same sensor geometry can be used multiple times without confusing the system with regards to what tool is being tracked. (A) (B)

Fig 1: (A) and (B) displays the main difference between active and passive tracking (www.ndigital.com)


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2.3.2 Electromagnetic tracking systems Electromagnetic spatial measurement systems determine the location of objects that are embedded with sensor coils. When the object is placed inside controlled, varying magnetic fields, voltages are induced in the sensor coils. These induced voltages are used by the measurement system to calculate the position and orientation of the object. As the magnetic fields are of low field strength and safely can pass through human tissue, location measurement of an object is possible without the line-of-sight constraints of an optical spatial measurement system. Within the transmitter coils are placed, through which pulsed direct (pDC) or alternating (AC) current is sent thus generating a magnetic field. The size of the field is naturally dependent on the size of the coils and the amplitude of the current. The field is not exactly homogenous as it is dependent on distance and orientation with reference to the generator. Electromagnetic positioning systems have a limited field measurement volume. Both magnetic fields generated from pulsed direct current and alternating current, are sensitive to possible interference of metallic objects. Especially ferromagnetic materials will affect the electromagnetic field as eddy currents induced in them will change the homogeneity of the field, resulting in measurement distortions. If direct current is used to generate electromagnetism, the ferromagnetic interference is smaller than if alternating current is used. This is because of the fact that pulsed direct current fields “stabilizes” soon after each electrical pulse and that is when measurements are made. No new eddy currents are induced when the system is in this stable state. With alternating current that varies constantly, new eddy currents are induced every time the current shifts in polarity and the field might therefore be interfered with more often than when using pulsed direct current. In spite of this drawback of all electromagnetic positioning systems, the greatest advantage they supply is the fact that they do not demand direct line-of-sight between transmitter and sensor. This is a highly beneficial characteristic as it allows tracking within the body of the patient. It also facilitates the work of the surgical staff as they are allowed to move freely in the operation room without having to adapt their working positions with regards to possibly blocking a line-of-sight demanding positioning system.

Fig 2: Visualization of generated electromagnetic field (www.ndigital.com)


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2.4 Probe calibration

Fig 3: World, sensor and image coordinate systems The probe calibration step is represented in Fig. 3 as isT ← . The purpose of this calibration is to transform the coordinate system of the ultrasound image (i) to the coordinate system of the position tracker/sensor (s). As this is a difficult process containing several factors of possible orientation errors affecting the final result, the probe calibration is the biggest source of error when reconstructing a 3D ultrasound freehand scanned volume. Calibration can be achieved by using a calibration phantom of known geometric properties. An ultrasound acquisition of the phantom is made, with a positioning sensor placed on the ultrasound probe. By sampling image and positions simultaneously and knowing the geometrical properties of the phantom it is possible to calculate the probe transformation matrix. The probe calibration technique used in this project is outlined in the method chapter.


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2.5 Generating 3D Ultrasound Although the most common way to display ultrasound is as 2D images, 3D volumes can be constructed using one of four general methods (Mercier et al. 2005). The methods have been classified into the following categories:

1. constrained sweeping techniques 2. 3D probes 3. sensorless techniques 4. 2D tracked probe techniques

Explanations of the categories are given below.

1. When using the constrained sweeping techniques, a 2D ultrasound probe is swept in a controlled manner over the object of interest, with for example a motor attached to the probe. The course of sweeping is predefined, and the slices are either acquired in a wedge pattern, in a series of parallel slices or with a rotation around a central axis.

2. There are different types of 3D probes but they generally consist of 2D arrays that allow explicit imaging in 3D. 3D probes that are mechanically or electronically steered within the probe housing are also available.

3. Sensorless techniques try to estimate the 3D position and orientation of a probe in space. This can be done by analyzing the speckle in the ultrasound images using decorrelation or linear regression. Unfortunately the accuracy of sensorless tracking is not nearly as good as the accuracy when using tracked ultrasound probes.

4. The technique using a tracked 2D ultrasound probe is also referred to as freehand technique. Usually, these systems consist of a tracking system used in combination with the ultrasound probe. By attaching a position sensor on the probe body, the position system calculates the sensor’s position and orientation at any point in time. With this information, the 3D coordinates of each pixel in the ultrasound image can be computed. But in order to be able to perform this step, probe calibration is required. A big advantage with using this technique is that not only can the image easily be registered to for instance a patient, but also to images originating from other imaging modalities by using for example the same fiducial markers previously placed on the patient.


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3. Method

3.1 Equipment • Ultrasound scanner: System FiVe, GE Vingmed Ultrasound, Norway • Probes: Flat phased array 5 MHz, Curved linear array 3.5 MHz, Linear array

probe (Laparoscopic) 6 MHz (frequencies given are center frequency for the probes)

• Tracking systems: Aurora, Northern Digital Inc (NDI), Canada, Polaris Spectra (NDI)

• Phantoms: Model 055 3D Ultrasound Calibration Phantom, CIRS, USA, Multimodal (CT, MR, Ultrasound) phantom 1997, SINTEF Health Research Medical Technology, Trondheim, Norway

• Desktop: Macintosh Power PC, Running OS 10.4.8 • Video grabber: The Imaging Source Model DFG / 1394-1e (Video-to-Fire Wire

converter) • Software: Custus X version 1.4 (in-house developed software based on open

source libraries from Insight Tool Kit and Visualization Tool Kit), Image J version1.37, OsiriX version 2.7.5

3.2 Experimental set-up We wanted to evaluate the accuracy of 3D ultrasound using the electromagnetic positioning system Aurora compared to the Polaris Spectra optical positioning system. In order to achieve this, probe calibration acquisitions together with 3D freehand translation- and tilt acquisitions were performed with different types of ultrasound probes for both positioning systems. The Polaris Spectra optical positioning system was used together with a curved linear array (CLA) probe (Fig 4) and a flat phased array (FPA) probe (Fig 5), and the Aurora electromagnetic system was used with a CLA probe, a FPA probe and also the laparoscopic probe (Fig 6). Two different types of phantoms were used. One was an in-house made phantom containing a thin Bakelite plastic membrane of known geometry used for probe calibration, and an accuracy phantom from CIRS (USA) (Fig 7a-c), containing two egg-shaped volumes of known sizes with hyper echoic surfaces and hypo echoic contents, used for 3D acquisitions. Four probe calibrations acquisitions and twelve 3D acquisitions were performed for each ultrasound probe and tracking system combination. Only the electromagnetic system was used for the laparoscopic probe, while both optical and electromagnetic tracking was used for the other probes. The acquisitions were: • Three translation acquisitions of the large accuracy phantom egg volume

• Three tilt acquisitions of the large accuracy phantom egg volume

• Three translation acquisitions of the small accuracy phantom egg volume

• Three tilt acquisitions of the small accuracy phantom egg volume


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Each translation acquisition was performed by movement of the probe parallel to the surface over an approximate distance of 8 cm during approximately 5 seconds, and during the tilt acquisitions the probe was angled above the center point of each egg during approximately 6 seconds with a total angle of approximately 70 degrees.

Fig 4: CLA probe with Polaris Spectra reflectors

Fig 5: FPA probe with Aurora sensor

Fig 6: Laparoscopic ultrasound probe


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Fig 7a: CIRS Accuracy phantom: animated cross section (www.cirsinc.com)

Fig 7b: CIRS Accuracy phantom: animated (www.cirsinc.com)

Fig 7c: CIRS Accuracy phantom during laparoscopic probe acquisition


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Fig 8: Free-hand acquisition: FPA and Polaris Fig 9: Free-hand acquisition: Laparoscopic probe

and Aurora

Fig 10: Probe calibration: CLA and Aurora

All of the acquisitions were used to reconstruct and segment the 3D-volumes that provide necessary information needed to compute the size of the volumes generated. Reconstruction and segmentation will be explained further on in this chapter. Most likely, size variations in computed volumes generated with the same acquisition method but with different tracking systems will occur, thus enabling comparison of the two tracking systems used.


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3.3 Probe calibration and image-to-world transformation The idea of probe calibration is to align the image plane from the ultrasound probe by 2D real time scanning with a submerged, extremely thin, but stiff and jagged membrane oriented approximately perpendicular to the bottom of a water tank. When the image is such that the membrane and the scan plane can be assumed to be coplanar, the positions of the sensor on the probe and the positions of the membrane are sampled. The positions of the membrane corners are found by pointing at them with a pre-calibrated pointer. The ultrasound image of the membrane is transferred to the computer and the five corners are marked by pointing at them manually with the mouse. These image points are denoted Pi, a five column position matrix, where each column represents the position of a corner of the membrane in the figure below.

Fig 11: Probe calibration with an optical tracking system The corresponding phantom points marked by the pre-calibrated pointer in the worldly (or global) position sensor system are represented by Pw. The pseudo-inverse matrix for transformation between the two systems (see fig 3, page 8), i.e. between the image system and the worldly system is given by:

( ) 1−← ⋅⋅⋅= T

iiT

iwiw PPPPT where the upper index T means transposed, lower index w refers to the worldly coordinate system, often named patient or the reference system, and the matrix iwT ← transforms the points sampled in the image system to the worldly coordinate system such that

iiwiw PTP ⋅= ←,


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iwT ← is transformed into a homogeneous coordinate matrix representation and the following matrix multiplication then gives us the desired calibration transformation

iwwsis TTT ←←← ⋅= The matrix wsT ← is not available, so in order to perform the calculation above, the

known matrix swT ← is inversed and used since ( ) wssw TT ←−

← =1 . Thus the final equation is

( ) iwswis TTT ←−

←← ⋅= 1 where w sT ← is the position sensor reading for the frame attached to the probe as the

image and membrane are assumed coplanar. A point [ ]Tiii zyx ,, in the ultrasound

image may be transformed into the global coordinate system by

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

⋅⋅=

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

←←

11,

,

,

i

i

i

isswiw

iw

iw

zyx

TTzyx

All of the equations show that the probe calibration transformation is only one of two transformations required when constructing a tracked ultrasound image. As seen in Fig. 3 (page 8), transformations of sensor-world and of world-phantom are also necessary. When a phantom (or patient / reference) is used its’ coordinate system must also be transformed and considered in the calculations needed to reconstruct a point originating from an ultrasound image into one in the coordinate system of “world space”. The transformation swT ← , representing the transformation of the sensor coordinate system to the tracking system coordinate system, is previously determined by the manufacturers of the positioning system utilized.


15

Combining all of the transformations provides all the information necessary to calculate the coordinates for a point in world space representing one of the points in the tracked ultrasound image.

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡•

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

•

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

←←

i

i

i

iziziyixi

yiziyixi

xiziyixi

iszszsysxs

yszsysxs

xszsysxs

sw

w

w

w

w

zyx

Ptrrrtrrrtrrr

Ttrrrtrrrtrrr

Tzyx

P

10001000,,3,3,3

,,2,2,2

,,1,1,1

,,3,3,3

,,2,2,2

,,1,1,1

iP = a point in the ultrasound image

isT ← = the translation and rotation of the image coordinate system to the sensor

coordinate system

swT ← = the translation and rotation of the sensor coordinate system to the world coordinate system

wP = a point in world space This probe calibration transformation is applicable in general since the probe and sensor constitutes a rigid body. A problem with this method is that it is dependant on how accurately the user can align the probe image plane and the membrane. This can be difficult given that the thickness and widening of the ultrasound beam increases as a function of depth. In addition, the accuracy of pointing at the membrane corners in the ultrasound images is subject to error. Furthermore, the membrane may have to be built in more than one size given the fact that different probes have highly varying array sizes and maximum scan depths. The probe calibration process is time consuming and the inter-operator variability may be large due to the fact that manual alignment is necessary and difficult.


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3.4 Reconstruction The reconstruction accuracy plays an important role regarding the final results of the volume calculations. A reconstruction algorithm is chosen, and then used to reconstruct the tracked 2D ultrasound images into 3D volumes. Apart from the reconstruction algorithm itself, other factors and parameters such as position data accuracy, imaging medium sound speed, the finite thickness (elevation direction) of ultrasound images, in addition to the general quality of the ultrasound imaging system, affect the final accuracy of the reconstructed volumes. There are three different types of reconstruction algorithms (Solberg et al. 2007):

1. Voxel-based methods 2. Pixel-based methods 3. Function-based methods

In this project, a pixel-based method that uses an ellipsoid truncated Gaussian kernel with Gaussian weighing (Ohbuchi et al. 1992) is used to reconstruct the ultrasound volumes. What the algorithm in fact does is to convolve each pixel in the input slices with a 3D ellipsoid truncated Gaussian kernel. For each voxel, three values are stored:

1. The reconstruction value, which is an added sum of all of all convolutions between the pixel and the 3D kernel that intersects the voxels,

2. The weight value, which is the sum of the values of the 3D kernels that intersect the voxels, and

3. The age, these are values of the pixels used to calculate a decay factor that can be used for making sure that newer pixels get higher significance than older ones.

Reconstruction time per image is estimated at 1.5 seconds (based on updated values from the Ohbuchi et al. 1992 article). The size of the input image is 128 x 128 pixels, reconstructed into a 128 x 128 x 128 volume.

Fig 12: Pixel-based method with a 3D ellipsoid Gaussian kernel around a pixel. The lines represent the input images and the points in the lines illustrate the centers of the pixels.


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3.5 Segmentation and volume calculations The program chosen for these two steps is OsiriX, a radiologic DICOM image processing software firstly designated for medical images produced by MR, CT, PET (amongst others). But since its’ segmentation algorithms rely on variations in grey scale it is also applicable on ultrasound images imported as raw volume data. The segmentation procedure is carried out as follows:

1. A set of reconstructed ultrasound images, together making up a volume, is imported to the program. Pixel resolution in x, y and z, image size and number of images must be stated (Fig 13).

2. Grey scale contrast of the images is manually set. 3. A region of interest (ROI) for the entire series of 2D images imported is

calculated by using a segmentation algorithm that relies on lower and upper threshold values of grey intensity. The goal is to narrow down the ROI to only the object of interest, in the case of this project, the egg shaped volumes of the accuracy phantom.

4. A new set of image series is computed by the program, now only containing the segmented part of the images.

5. The new set of images is set to be viewed in 3D, and a shading filter is added for clearer display of the volume constructed.

6. Should the ROI consist of more than the object of interest, a 3D scissor available in the software can be applied to remove possible excess parts of the ROI. The changes in the 3D volume are also displayed in the 2D view (Fig 14).

7. When the volume is satisfactory cut and as precise as possible, a new ROI is computed in the modified 2D view (now only containing the segmented object of interest).

Fig 13: View of imported image, after step 1 Fig 14: View of 3-D volume, after removal of excess parts after step 6


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Calculating the volume of the segmented object is done by marking a point on the new ROI boundary and running a volume calculation algorithm. The volume is displayed in a new window, with size given in cubic centimeters.


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4. Result

4.1 Protocol for 3D acquisitions Table 1 d1 [cm] d2 [cm] v [cm³] D1 [cm] D2 [cm] V [cm³] Phantom specifications 1.8 3.9 6.7 4.0 7.0 65.0 Probe Scan Aurora tracking system

Translation 1 1.550 3.792 5.4351 4.472 6.831 63.7753 Translation 2 1.702 3.789 5.3233 4.617 6.859 66.0904 Translation 3 NA NA NA 4.586 6.945 63.5580 Tilt 1 NA NA NA NA NA NA Tilt 2 NA NA NA NA NA NA

CLA

Tilt 3 NA NA NA NA NA NA Translation 1 1.824 3.525 5.0347 3.882 6.420 48.9662 Translation 2 1.660 3.452 5.1553 4.166 6.445 57.0659 Translation 3 1.701 3.473 5.4102 4.355 6.412 55.4215 Tilt 1 1.477 3.681 5.5212 4.056 6.397 65.4473 Tilt 2 1.605 3.647 5.4965 4.040 6.471 66.0330

FPA

Tilt 3 1.646 3.598 5.7514 4.207 6.408 64.3018 Translation 1 1.676 3.499 6.9047 NP NP NP Translation 2 1.697 3.718 6.9567 NP NP NP Translation 3 1.801 3.696 6.9673 NP NP NP Tilt 1 1.779 3.696 6.7992 NP NP NP Tilt 2 1.724 3.693 6.4183 NP NP NP

Lap.

Tilt 3 1.748 3.772 6.5701 NP NP NP Mean Aurora 1,685 3,645 5,982 4,265 6,576 61,184 STD Aurora 0,095 0,117 0,740 0,258 0,229 5,992 Polaris Spectra tracking system

Translation 1 1.530 3.663 5.6124 3.811 6.844 59.9363 Translation 2 1.543 3.601 6.3551 3.952 6.856 58.2514 Translation 3 1.575 3.574 5.4313 3.305 6.824 61.1523 Tilt 1 NA NA NA NA NA NA Tilt 2 NA NA NA NA NA NA

CLA

Tilt 3 NA NA NA NA NA NA Translation 1 1.640 3.298 5.3845 3.973 6.346 51.9486 Translation 2 1.651 3.390 5.3550 4.020 6.256 57.6340 Translation 3 1.676 3.203 5.3889 4.030 6.310 55.1604 Tilt 1 1.842 3.416 6.0847 4.285 6.206 59.1139 Tilt 2 1.838 3.413 5.8333 4.137 6.342 60.0481

FPA

Tilt 3 1.940 3.256 5.6215 4.302 6.260 59.2151 Mean Polaris 1,693 3,424 5,674 3,979 6,472 58,051 STD Polaris 0,147 0,160 0,352 0,298 0,281 2,860 Mean Total 1.688 3.558 5.861 4.122 6.524 59.618 STD Total 0.112 0.168 0.612 0.299 0.247 4.696 NA=Not available due to erroneous acquisition. NP=Not possible due to limited maximum probe depth for imaging. Table 1 shows measured diameters and calculated volumes of the eggs placed within the accuracy phantom reproduced with 3D ultrasound acquisitions. Index d and v refer to the diameter and volume of the smaller of the two eggs while D and V refer to the same dimensions of larger one. Index 1 represents the “width” diameter of the eggs, while index 2 represents the “height” diameter of the eggs.


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4.2 Result observations Based on results found in Table 1, observations are summarized below. Index explanations: m = measured dimensions of reconstructed acquisitions

s = vender specified dimensions.

d, v, D, V = dimensions of the smaller and bigger egg, respectively

d1, D1 = “width” diameter of the eggs

d2, D2 = “height” diameter of the eggs.

AURORA For Aurora in general:

md1 < sd1 while mD1 > sD1

md2 < sd2 and mD2 < sD2 Aurora CLA:

Practically all measured values except for mD1 are smaller than specified values. Aurora FPA: ntranslatiomd ,1 > tiltmd ,1 while ntranslatiomd ,2 < tiltmd ,2 ntranslatiomv , < tiltmv , < sv

The calculated volume of the first translation acquisition of the big egg using this probe, is as seen very small compared to the specification (circa 48 cm³ compared to specified 65 cm³). Comments on possible variables causing this, is discussed in the following chapter.

Aurora Laparoscopic probe: tiltmv , < sv < ntranslatiomv , POLARIS For Polaris in general:

md2 < sd2 and mD2 < sD2 Polaris CLA: All measured values are smaller than the specified values Polaris FPA: ntranslatiomd ,1 < sd1 < tiltmd ,1 ntranslatiomV , < tiltmV , < sV The ultrasound probe – tracking system combination providing the most accurate results according to these acquisitions was the laparoscopic probe used together with the Aurora electromagnetic positioning system.


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5. Discussion Ultrasound is an imaging modality that often provides images containing artifacts. Although it is precise, boundaries between tissues with differences in acoustic impedance will always appear rather blurry, which in the case of this project affects segmentation and thus volume calculations. Other sources of error also exist, the biggest one being probe calibration. Some of the steps affecting final results are discussed below.

5.1 Time synchronization No time synchronization calibration has been used in this project more than very slow free-hand scans in order to align plane scan input with positioning data input. Although slow scans should be enough to generate accurate plane – position combination, it could affect the final results. If scans were not made slow enough, input data from the positioning systems may not be correct in relation to the true position of the ultrasound plane being scanned thus resulting in errors when reconstructing the acquisitions.

5.2 Probe calibration Although the probe calibrations for the FPA and laparoscopic probes were satisfactory the probe calibration of the CLA probe was less good as the tilted acquisitions were not possible to reconstruct into proper ultrasound volumes. This is a result of incorrect probe calibration. Although all of the four probe calibration acquisitions that were made were used and tested to achieve a proper reconstruction of the images of the CLA probe, none of them were good enough to provide an accurate result of the tilt acquisitions thus leaving gaps in the volume calculations table. A good example showing the probe calibration for the CLA tilt acquisition producing an incorrect 3D reconstruction can be seen to the left in Fig. 15 below, and for comparison the right figure represents the reconstruction of a tilt acquisition with the FPA probe with accurate probe calibration.

Fig 15: Incorrect probe calibration CLA probe tilt acquisition (left), and correct probe calibration FPA probe tilt acquisition (right)


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The source of this error is mainly an offset-value error in the probe calibration matrix used. Changing the offset values could result in proper probe calibrations, but since not all of the values needed for this altering in the probe calibration matrix are available, it is not possible to perform that type of change for this project. Considering other possible methods in order to deal with this type of error, the best way to solve the problem is probably to develop and use a probe calibration method that is more stable and / or robust as the CLA probe is the most challenging, of the three probes used, to calibrate. The most probable explanations of why this error occurred in the first place are that:

1. The ultrasound plane is very thick, which in our case means that the thin Bakelite membrane used for calibration will be visible also when it is not located directly under the probe which is desirable when performing the probe calibration acquisition.

2. The origin of the image plane is located within the probe, and its’ exact location is very difficult to decide.

In order to test the stability of the chosen probe calibration method, reconstruction of a single acquisition was performed. Using all of the four different probe calibration matrices for the Polaris tracking system in combination with the FPA probe, one of the translation acquisitions was reconstructed, segmented, volumes were calculated and dimensions were measured. The result can be seen in Table 2 below, and the four calibration matrices used can be found in appendix 9.1.2. Table 2 shows, that for this combination of tracking system and probe the calibration method is rather stable as the dimensions and volumes does not vary much in spite of different calibration matrices used. Table 2

Polaris and Flat Phased Array Probe, Translation acquisition 1 (big egg)

Probe calibration matrix 1 3,897 6,442 54,3216 Probe calibration matrix 2 3,967 6,378 56,5560 Probe calibration matrix 3 3,937 6,376 54,6097 Probe calibration matrix 4 4,049 6,360 55,4232

D1 [cm] D2 [cm] V [cm³] Phantom specifications

4.0 7.0 65.0


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5.3 Reconstruction As all of the results showed significantly smaller dimensions in “height” of both the eggs, dimension measurements were made using images from the System FiVe acquisitions (these were compared to the RAW-data images, which are in fact the ultrasound images before they are reconstructed to determine equal dimensions). The dimensions of the eggs in the RAW-images were accurate which means

• The video grabbing step was successful, as the input data of the eggs were still of correct size.

• The decrease in length is most probably due to a systematic error in the reconstruction step. Though only in the beam direction as the width of the eggs still remained rather accurate after reconstruction.

Fig 16: Image taken from System FiVe acquisition (left) and imported in OsiriX (right) after reconstruction

5.4 Segmentation Previous tests to segment the acquisitions using for instance the ITK SnAP software have been made, though with very poor and inaccurate results. Although OsiriX is one of the better software to use in order to segment ultrasound volumes, it is still a semi-automatic algorithm where user-specified values are used which will of course affect results in some ways. Contrast differences in the original imported ultrasound images make similar segmentation in all of the acquisitions even more challenging to achieve since the segmentation algorithm used is dependent of grey scale intensities as mentioned earlier, thus resulting in being one of the variables affecting the calculated volumes the most from a segmentation point of view. An example of how difficulties arise due to poor contrast is demonstrated in the four following figures. They represent different steps of the segmentation process with the OsiriX software. All figures belong to the translation acquisition of the big egg, using the FPA probe and the Aurora positioning system. This particular acquisition was chosen because after segmentation, the size of the calculated volume was no more than 48.9662 cm³ (see table 1) which is approximately 24.6 % less than the vender specifications (65 cm³).


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The figures will help explain the most probable reason of why the volume size became so small further.

Fig 17: One out of an imported set of ultrasound images (Aurora FPA translation 1, big egg)

Already in Fig 17, representing the set of ultrasound images imported from the acquisition, it is clear that the edges of the egg are blurry, and the intensity of grey within the tip of the egg is quite similar to the intensity of grey in the surrounding areas. Fig 18 located on the following page, displays that in order to compute the region of interest without loosing any parts of the egg, the range in between upper and lower threshold values (that are user-set) must be rather wide. This unfortunately means that a great part that is not part of the egg is also included. The region of interest is surrounded by a thin light (green) line in Fig 18 and after region of interest has been computed and a new set of series only containing the chosen region can be viewed as shown in Fig 19. The step of cutting excess parts is done in the 3D view displayed in Fig 20. It is clear that precise cutting and revealing of only the egg is very difficult.


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Fig 18: Marking of region of interest

Fig 19: Segmented region of interest Fig 20: 3-D volume rendering of region of interest


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5.5 Volume calculations From Table 1 containing results it is clear that in general, the laparoscopic probe used with the Aurora tracking system provides the results with values closest to the specification. Unfortunately the laparoscopic probe with Aurora lack possibilities to be compared to the Polaris.

5.6 Other sources of error and important aspects The most important origins of error has already been mentioned and discussed, but other smaller contributors might still be worth mentioning. For instance: Speed of sound: The speed of sound within the accuracy phantom is specified to 1540 m / s, while the reconstruction algorithms speed of sound is set at 1560 m / s. The difference between the two values is approximately 1.3 %. Not very much but still a contributing factor. Human error: The scanning was done by free-hand which means that the accuracy might be affected. Identical scans can never be expected and velocity of probe movement will vary, if not much but still enough to be affecting the acquisitions to some extent. Sampling frequency: It is important to check that the sampling frequency rate of the positioning systems is not lower than for the imaging system. In the case of this project the sampling frequency of the imaging modality is 25 frames / second. If the sampling frequency rate of the positioning systems were to be lower, that would mean that two neighboring image planes might get the same positioning data. For instance if the imaging modality registers say 25 images per second, whilst the positioning data only registers 20 positions during this time, some of the images will be faulty linked to the same position when in fact they are located at different positions. The Aurora tracking system has a sampling frequency rate of 40 Hz and the Polaris Spectra 60 Hz, hence no problems of this kind has occurred during the acquisitions of this project. Probe differences: Increasing the distance between image plane and tracking sensor on the probe, means increasing error regarding probe calibration. The laparoscopic probe has the shortest distance between sensor and plane, which could be an explanation of why the measurements with Aurora and the laparoscopic probe are the most accurate ones. Also worth mentioning is the fact that this tracking system – probe combination is the one with the sensor closest to the Aurora transmitter. The further away the sensor is from the origin of the transmitter the higher the root mean square error (according to vender specifications, see appendix 10.3). In other words, the measurements of Aurora – laparoscopic probe could have benefited from this fact. Since the imaging plane of the laparoscopic probe is very thin, the probe calibration acquisitions is most likely to be significantly more accurate than for the CLA probe, whose imaging plane is far thicker than both the laparoscopic and FPA probe.


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6. Conclusion According to our acquisitions, measurements and calculations the tracking system – ultrasound probe combination providing the most accurate results is the Aurora electromagnetic positioning system used in combination with the laparoscopic ultrasound probe. Although the results might even be accurate enough for the combination to be used for future clinical applications it is important to keep in mind the fact that it is rather value reduced due to the systematic error discovered.

7. Future work First and foremost the systematic error causing inaccurate dimensions and volumes in the reconstructions most be corrected in order to further develop this project. As mentioned earlier in the report, lack of time is the reason it has not yet been done. Another step worth changing is how the acquisitions were performed. For instance a good follow up would be to redo the tests using only one probe and increasing the number of acquisitions made in order to achieve improved statistics. Also, using manual segmentation instead of semi-automatic would result in more precise segmentation thus generating more accurate final results, most likely decreasing the standard deviation for all acquisitions made. A better probe calibration method for the CLA probe must be developed to minimize difficulties due to its’ thick imaging plane and the fact that the origin of the plane is located within the probe itself. To perform time synchronization calibration would also be recommended for future development. An easy way of doing this is to use a water-filled tank and move a chosen ultrasound probe up and down vertically while scanning, while tracking it with a positioning system. A curve resembling a sinus curve will be generated for both the ultrasound probe and the tracking system due to the specific movement and these two can be compared in order to compare position and time for the image and the position. Finally, the Aurora sensor must be integrated in the probe to make sure it is electrically safe before inserting it into patients. No leakage of current is acceptable, unless it tested and shown to be completely safe. Of course, before any clinical use involving humans is done clinical porcine tests must be performed. It is clear that a lot of improvements can be made regarding the follow-up on this project, although it should be remembered that the results provided from acquisitions made for this project is a good start.


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8. Bibliography and references Angelsen BAJ; Waves, Signals and Signal Processing in Medical Ultrasonics, Volume I, 1995, chapters 1-2 Bates J; Abdominal Ultrasound – How, Why and When, Second edition 2004 ISBN: 0 443 027243 4 Gronningsaeter A, Kleven A, Ommedal Steinar. Aarseth T E, Lie T, Lindseth F, Lango T, Unsgard G; SonoWand, an Ultrasound-based Neuronavigation System. Instrumentation and Application Neurosurgery 47, Vol 6, December 2000, pp 1373-1380 Jacobsson B; Medicin och Teknik, Fourth edition 1995, pp 450-466 ISBN: 91-630-3338-0 Kaspersen JH, Sjølie E, Wesche J, Åsland J, Lundbom J, Ødegård A, Lindseth F, Nagelhus Hernes TA; Three-dimensional Ultrasound-Based Navigation Combined with Preoperative CT during Abdominal Interventions: A Feasibility Study Cardiovascular and Interventional Radiology, No 26, 2003, pp 347-356 Lindseth F, Bang J, Langø T; A Robust and Automatic Method for Evaluating Accuracy in 3D Ultrasound-Based Navigation Ultrasound in Medicine and Biology, Vol 29, No 10, 2003, pp 1439-1452 Lindseth F, Tangen GA, Langø T, Bang J; Probe Calibration for Freehand 3D Ultrasound Ultrasound in Medicine and Biology, Vol 29, No 11, 2003, pp 1607-1623 Mercier L, Langø T, Lindseth F, Collins DL; A Rewiew of Calibration Techniques for Freehand 3D Ultrasound Systems Ultrasound in Medicine and Biology, Vol 31, No 4, 2005, pp 449-471 Mårvik R, Langø T, Tangen GA, Andersen JON, Kaspersen JH, Ystgaard B, Fjösne HE, Fougner R, Toril A. Nagelhus Hernes; Tredimensjonal navigasjon i laparoskopisk kirurgi Nor Lægeforen, No 5, 2004, pp 617-619 Mårvik R, Langø T, Tangen GA, Lindseth F, Yavuz Y, Hernes TAN; Image-guided laparoscopic surgery – Review and current status. Minerva Chirurgica, October, Vol 60, No 5, 2005, pp 305-325 Nagelhus Hernes TA, Ommedal S, Lie T, Lindseth F, Langø T, Unsgaard G; Stereoscopic Navigation-Controlled Display of Preoperative MRI and Intraoperative 3D Ultrasound in Planning and Guidance of Neurosurgery: New Technology for Minimally Invasive Image-Guided Surgery Approaches Minimally Invasive Neurosurgery, Vol 46, 2003, pp 129-137


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Ohbuchi R, Chen D, Fuchs H; Incremental Volume Reconstruction and Rendering for 3-D Ultrasound Imaging Proceedings of Visualization in Biomedical Computing, Vol 1808, 1992, pp 312-323 Pluim JPW, Maintz JBA, Viergever MA; Mutual-Information-Based Registration of Medical Images: A Survey IEEE Transactions on medical imaging, Vol 22, No 8, August 2003, pp 986-1004 Rygh OM, Cappelen J, Selbekk T, Lindseth F, Nagelhus Hernes TA, Unsgaard G; Endoscopy Guided by an Intraoperative 3D Ultrasound-Based Neuronavigation System Minimally Invasive Neurosurgery, Vol 49, 2006, pp 1-9 Solberg OV, Lindseth F, Torp H, Blake RE, Nagelhus Hernes TA; Freehand 3D Ultrasound Reconstruction Algorithms – A Review Ultrasound in Medicine and Biology, in press Unsgaard G, Rygh OM, Selbekk T, Müller TB, Kolstad F, Lindseth F, Nagelhus Hernes TA; Intra-operative 3D Ultrasound in Neurosurgery Acta Neurochir, Vol 148, 2006, pp 235-253 Web site references: CIRS Inc., USA: http://www.cirsinc.com ITK-SNAP Software: http://www.itksnap.org Northern Digital Inc., Canada: http://www.ndigital.com OsiriX Imaging Software: http://www.osirix-viewer.com


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9. Appendix 9.1.1 Probe calibration information The form of the probe calibration matrix is

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

=←

1000,,3,3,3

,,2,2,2

,,1,1,1

ziziyixi

yiziyixi

xiziyixi

is trrrtrrrtrrr

T

where index r means rotation which are scaled vectors of values between 0 and 1, and index t means translation which are offset values given in millimeters.

isT ← Polaris FPA 0.910164 -0.0460601 0.0782659 29.57

0.0453443 0.913501 0.0102987 -3.20254 -0.0786833 -0.00636783 0.911271 61.7618

0 0 0 1

isT ← Aurora FPA -0.0509242 -0.919688 0.0428665 7.10386 0.197994 -0.052867 -0.899033 -55.6733 0.899146 -0.0404462 0.200397 4.44465

0 0 0 1

isT ← Polaris CLA 0.968844 -0.00951764 0.0869645 28.5987�

0.00905761 0.972728 0.00555145 -4.79358 -0.0870135 -0.00471916 0.968875 17.4569

0 0 0 1

isT ← Aurora CLA Translation Acquisitions 0.0120965 -0.977664 0.0530434 3.06428 0.154955 -0.050468 -0.965519 -36.3008 0.966762 0.020322 0.154092 -7.23102

0 0 0 1

isT ← Aurora Laparoscopic Probe 0.0383196 -0.913213 -0.322888 -33.6847 0.931545 -0.0537959 0.262702 -0.500642 -0.265401 -0.320674 0.87545 -2.88047

0 0 0 1


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9.1.2 Probe calibration matrices used for one specific acquisition These are the four different probe calibration matrices used for reconstruction of Polaris FPA translation acquisition 1 (big egg) in the discussion and conclusions chapter.

isT ← Polaris FPA Probe Calibration Matrix 1 0.910164 -0.0460601 0.0782659 29.57

0.0453443 0.913501 0.0102987 -3.20254 -0.0786833 -0.00636783 0.911271 61.7618

0 0 0 1


0.0726375 0.915954 0.00944636 -4.43731 -0.0971577 -0.00171853 0.913726 60.6643

0 0 0 1


0.0455199 0.914372 0.00296283 -4.26848 -0.0603341 4.34867e-05 0.913519 60.5227

0 0 0 1


0.0355884 0.920154 0.00757846 -4.47568 -0.0708197 -0.00482275 0.918133 60.9753

0 0 0 1


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9.2 Calibration and Acquisition Settings: System FiVe Table 3 Frequency

[MHz] Depth [cm]

Frames per second

Application optimized for

Focus (circa) [cm]

Polaris Spectra Probe Calibration Settings

FPA 5.7 12.0 6.8 Brain Surgery 7.25 CLA 4.4 11.0 23.8 Abdomen 5

Polaris Spectra Acquisition Settings

FPA 8.0 11.0 15.0 Neonatal Head 1, 2, 3, 4.25, 6.5, 11 CLA 4.4 11.0 23.8 Abdomen 5

Aurora Calibration Settings

FPA 5.7 12.0 14.7 Brain Surgery 4.6, 6.15 CLA 4.4 11.0 23.8 Abdomen 5 Lap. 8.0 6.5 16.0 Liver 7.2

Aurora Acquisition Settings

FPA 8.0 11.0 16.0 Neonatal Head 4.15, 5.3, 6.7, 9 CLA 4.4 11.0 23.8 Abdomen 5 Lap. 8.0 8.0 11.6 Long Acquisition 8.3, 9.8, 11.3, 14.5,

17.8


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9.3 Accuracy of NDI tracking systems Table 4 Manufacturer Model Accuracy

Polaris (optical) Position: 0.35 mm 3D RMS**, 95-240 cm range

Polaris Spectra (optical) Position: 0.25mm 3D RMS, 0.35 mm for

extended volume set-up, 95-300 cm range

Polaris Vicra (optical) Position: 0.25mm 3D RMS, 56-134 cm range

Optotrak Certus (optical) Position: 0.1 mm RMS at 2.25 m distance for x,

y coordinates, 0.15 mm for z coordinate

3D Resolution at 2.25 m distance: 0.01 mm

Aurora 5 DOF*** sensors (electromagnetic)

Sensor: 8 mm x 0.8 mm

Position: 0.9-1.3 mm RMS within 10-50 cm

distance from field generator

Orientation: 0.3° within measurement volume

Northern Digital

www.ndigital.com

Single marker in tracking

volume

Passive and active wireless tool

types

Aurora 6 DOF sensors (electromagnetic)

Sensor: 9 mm x 1.8 mm

Position: 0.9-1.6 mm RMS within 25-45 cm


Orientation: 0.8°-1.1° RMS within 25-45 cm


* Caution must be taken when comparing the accuracy of the different models because the given statistics are often not equivalent. ** RMS signifies Root Mean Square value. *** DOF signifies Degrees of Freedom.


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9.4 Differences; measured and specified dimensions Table 5 d1m - 1.8 d2m - 3.9 v m -6.7 D1m - 4.0 D2m - 7.0 V m - 65.0 Probe Scan Aurora tracking system

Translation 1 -0,250 -0,108 -1,265 0,472 -0,169 -1,225 Translation 2 -0,098 -0,111 -1,377 0,617 -0,141 1,090 Translation 3 NA NA NA 0,586 -0,055 -1,442 Tilt 1 NA NA NA NA NA NA Tilt 2 NA NA NA NA NA NA

CLA

Tilt 3 NA NA NA NA NA NA Translation 1 0,024 -0,375 -1,665 0,118 -0,580 -16,034 Translation 2 -0,140 -0,448 -1,545 0,166 -0,555 -7,934 Translation 3 -0,099 -0,427 -1,290 0,355 -0,588 -9,579 Tilt 1 -0,323 -0,219 -1,179 0,056 -0,603 0,447 Tilt 2 -0,195 -0,253 -1,204 0,040 -0,529 1,033

FPA

Tilt 3 -0,154 -0,302 -0,949 0,207 -0,592 -0,698 Translation 1 -0,124 -0,401 0,205 NP NP NP Translation 2 -0,103 -0,182 0,257 NP NP NP Translation 3 0,001 -0,204 0,267 NP NP NP Tilt 1 -0,021 -0,204 0,099 NP NP NP Tilt 2 -0,076 -0,207 -0,282 NP NP NP

Lap.

Tilt 3 -0,052 -0,128 -0,130 NP NP NP Mean Diff. Aurora -0,115 -0,255 -0,718 0,265 -0,424 -3,816 Polaris Spectra tracking system

Translation 1 -0,270 -0,237 -1,088 -0,189 -0,156 -5,064 Translation 2 -0,257 -0,299 -0,345 -0,048 -0,144 -6,749 Translation 3 -0,225 -0,326 -1,269 -0,695 -0,176 -3,848 Tilt 1 NA NA NA NA NA NA Tilt 2 NA NA NA NA NA NA

CLA

Tilt 3 NA NA NA NA NA NA Translation 1 -0,160 -0,602 -1,316 -0,027 -0,654 -13,051 Translation 2 -0,149 -0,510 -1,345 0,020 -0,744 -7,366 Translation 3 -0,124 -0,697 -1,311 0,030 -0,690 -9,840 Tilt 1 0,042 -0,484 -0,615 0,285 -0,794 -5,886 Tilt 2 0,038 -0,487 -0,867 0,137 -0,658 -4,952

FPA

Tilt 3 0,140 -0,644 -1,079 0,302 -0,740 -5,785 Mean Diff. Polaris -0,107 -0,476 -1,026 -0,021 -0,528 -6,949 Mean Diff. Total -0,112 -0,342 -0,839 0,122 -0,476 -5,382 NA=Not available due to erroneous acquisition. NP=Not possible due to maximum probe depth for imaging. For d1m, d2m, D1m, D2m, v m, V m lower index m means measured values. Diameters are given in [cm]; volumes are presented in [cm³].


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9.5 Measurement Volumes of NDI Tracking Systems

Fig 21: Measurement volume Polaris Spectra

Fig 22: Measurement volume Aurora

Both images are taken from the NDI Homepage.


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9.6 Specification of Model 055 3D Ultrasound Calibration Phantom

Figures and information from www.cirsinc.com

TRITA-CSC-E 2008:039 ISRN-KTH/CSC/E--08/039--SE

ISSN-1653-5715

www.kth.se

Accuracy of Laparoscopic 3D Ultrasound

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