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Improved interface for deep venous thrombosis screening using B-mode ultrasound Guerrero, Julian 2002

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Improved Interface for Deep Venous Thrombosis Screening using B-Mode Ultrasound by Julian Guerrero B.Eng., Instituto Tecnologico y de Estudios Superiores de Monterrey, Campus Morelos, Mexico, 1999 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE THE FACULTY OF GRADUATE STUDIES (Department of Electrical and Computer Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA December 2002 © Julian Guerrero, 2002 In presenting t h i s thesis i n p a r t i a l f u l f i l l m e n t of the requirements for an advanced degree at the Univ e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e for reference and study. I further agree that permission for extensive copying of t h i s thesis for s c h o l a r l y purposes may be granted by the head of my department his or her representatives. It i s understood that copying or pu b l i c a t i o n of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of ^^£gl-oe»\l (Xt^Jj uViw^uW £>A -^<'*giMN\ The U n i v e r s i t y of B r i t i s h Columbia Vancouver, Canada Abstract This work presents a system for the screening of deep venous thrombosis by processing B-mode ultrasound images, and by using information from additional force-torque and location sensors. It is known that deep venous thrombosis (DVT) is a disease that affects the venous system, where blood clots are formed and obstruct the venous pathways, causing serious consequences such as pulmonary embolism. Identifying D V T using conventional ultrasound principally relies on identifying incompressible veins which contain clots by using the B-mode imaging modality to view vessels in a transverse plane. A model-based contour detection method is presented which assumes that the transverse section of a vein can be described by an ellipse. By using the image brightness values a modified Star-Kalman filter is used to detect the vessel contour, and a validation scheme is implemented in order to accept or reject the detected curve. Additional information from a six degree-of-freedom force-torque sensor and a six degree-of-freedom location sensor allow the ultrasound image and detected contour to be placed in a three-dimensional virtual environment, were they are displayed in correct perspective. By stitching together several detected contours, a three-dimensional model of the examined vessel can be con-structed and displayed. The force-torque information is combined with the vessel area obtained via the contour detection method, and an objective compression assessment can be obtained for the examined vessel segment. B y repeating this procedure, a complete vessel can be screened for D V T , with an objective measure as a result. Additionally, this information can be mapped to the previously constructed virtual model. ii Contents Abstract ii Table of Contents iii List of Tables vii List of Figures viii Glossary xi Acknowledgements xiii 1 Introduction 1 1.1 Background 1 1.1.1 Description of Deep Venous Thrombosis 2 1.1.2 Diagnosis Methods for Deep Venous Thrombosis 2 1.1.3 Drawbacks and Limitations 5 1.2 Motivation 6 1.3 Research Objectives 7 1.4 Thesis Outline 8 2 Problem Formulation 10 2.1 Deep Venous Thrombosis Detection 10 2.1.1 Clinical Need 10 2.1.2 Detection Using Ultrasound 12 2.1.3 Compression Ultrasound Examination Procedure 13 CONTENTS iv 2.2 Image Feature Detection 14 2.3 Position, Orientation and Force Detection 23 2.3.1 Justification for Sensing Force, Position and Orientation 23 2.3.2 Force Sensing Background and Basics 25 2.3.3 Position and Orientation Sensing Background and Basics 26 2.3.4 Proposed Configuration and Requirements 28 2.4 User Interface and Data Integration 31 2.5 Summary 33 3 Methodology 34 3.1 Vein Contour Extraction From Ultrasound Images 34 3.1.1 Overview of the Star - Kalman Algorithm 35 3.1.2 Elliptical Contour Model 40 3.1.3 Estimation of Parameters for Elliptical Contour Model 45 3.1.4 Estimation of Ellipse Center 51 3.1.5 Edge Detector Selection 52 3.1.6 Contour Validation 58 3.1.7 Variation of the Search Area 62 3.1.8 Propagation of Information over Image Frames 63 3.1.9 Summary of Image Processing Procedure 64 3.2 Force, Position and Orientation Sensing 66 3.2.1 Position and Orientation Sensing 66 3.2.2 Force Sensing 68 3.3 User Interface 71 3.3.1 Vein Model Construction 71 3.3.2 Compression Examination Assessment 73 3.3.3 Displaying Virtual Objects 79 3.4 Summary 80 4 Validation 82 4.1 Evaluation of Parameter Estimation Algorithm 82 4.1.1 Feature Detection Comparison 87 CONTENTS v 4.1.2 Results of Parameter Estimation Algorithm 89 4.2 Maximum Search Area Variation 89 4.3 Transverse Area Ratio Validation 94 4.4 Ultrasound Phantom 98 4.5 Summary 102 5 E x p e r i m e n t s 103 5.1 Experimental Setup 103 5.2 Experimental Results 107 5.2.1 Phantom Reconstruction 107 ' Healthy Vein . 107 Thrombosed Vein 110 Ultrasound Phantom Limitations 112 5.2.2 Reconstruction of Human Vessels 115 5.3 Summary 121 6 Conc lus ions a n d Recommenda t ions 123 6.1 Summary 123 6.2 Recommendations and Future Work 125 B i b l i o g r a p h y 127 A p p e n d i c e s 135 A Phys ic s of U l t r a s o u n d 135 A . l Physical Properties Of Sound And Transmission Media 135 A.1.1 Interactions Between Sound A n d The Medium 137 A.2 Basic Ultrasound Imaging 140 A.2.1 Transmit Gain .145 A.2.2 Amplification 145 A.2.3 Time Gain Compensation 145 A.2.4 Signal Processing 145 A.2.5 Scanner Types 146 CONTENTS vi A . 3 Brightness(B)-Mode Imaging 147 A.3.1 Frame Rate Limitations 148 A.3.2 Real-time Scanners 149 A . 3.3 Focusing Ultrasound Beams 151 B Deep Venous Thrombosis Examination 154 B . l D V T 154 B.2 Current Methods of Detection of D V T 155 B . 2.1 Contrast Venography 155 B.2.2 Plethysmography 156 B.2.3 Ultrasonography (US) 157 B.2.4 Compression Ultrasound 158 B.2.4.1 Continuous Wave Doppler 158 B.2.4.2 Colour Duplex scanning 158 B.2.5 1251-Fibrinogen scanning (IFS) 159 B.2.6 Computer Assisted Tomography and Magnetic Resonance Imaging 159 B.2.7 Laser Doppler Fluxometry (LDF) 159 B.2.8 Blood Tests 160 B.2.9 Near-IR Time-Resolved Spectroscopy 160 B.3 Venous Anatomy of the Lower Limbs 160 B.4 Examination of the Lower Limbs 163 B.4.1 Examination Protocol 165 B.5 Diagnosis of the Lower Limbs 167 B.6 Drawbacks and Limitations of D V T Examinations 169 C Examples of Contour and Parameter Estimation Algorithm 171 List of Tables 3.1 Characterization of Various Edge Detectors 54 3.2 Ellipse Estimation Accuracy based on Error Measure 60 3.3 Full-Scale Loads - Nano25 69 4.1 Estimated Ellipse Parameters (a, b) from First Image Set - Verified Manually . . . . 85 4.2 Estimated Ellipse Parameters (a, b) from First Image Set - Verified using Error Measure 85 4.3 Estimated Ellipse Parameters (a, 6) from Field II© generated Ultrasound Images -Verified using Error Measure 85 4.4 Estimated Ellipse Parameters <f> 86 4.5 Comparison of Ellipse Parameter Estimation 88 4.6 Transverse Area Ratio for Healthy Veins - Manual Calculation 94 4.7 Transverse Area Ratio for Diseased Veins - Manual Calculation 95 4.8 Transverse Area Ratio for Healthy Veins - Contour Detector 97 4.9 Transverse Area Ratio for Diseased Veins - Contour Detector 97 5.1 Values of Slope m 117 5.2 Values of Slope m 119 5.3 Values of Slope m 121 vii List of Figures 1.1 Veins of the Lower Limb (after [3]) 3 2.1 Typical Compression Ultrasound Image 13 2.2 Ellipse 21 2.3 Error Measure 22 2.4 Ultrasound Probe, with different orientations 24 3.1 Edge Detection using Probabilistic Data Association Filter 38 3.2 5x3 Smoothing Kernel 53 3.3 Average Errors for Several Edge Detectors on Image with Gaussian Noise 55 3.4 Expanded View of Average Errors for Several Edge Detectors on Image with Gaus-sian Noise 56 3.5 Average Errors for Several Edge Detectors on Simulated Ultrasound Image 57 3.6 System Flowchart 65 3.7 Ultrasound Force Transducer 70 3.8 Raw Contour Data in World Frame 72 3.9 Surface Mesh 72 3.10 Maximum Distance Between Contours 74 3.11 Flowchart of the Compression Examination Assessment 77 3.12 Normalized Force vs. Normalized Area 78 3.13 Virtual Objects within Virtual Environment 80 4.1 Examples of Simulated Ultrasound Images generated using Field II© 83 4.2 Results of Contour and Parameter Estimation 90 viii LIST OF FIGURES ix 4.3 Error Values Using Different Rmax 91 4.4 Relative Error Values Using Different Rmax 92 4.5 Relative Error Values Using Different Rmax 93 4.6 Healthy Vein Compression Sequence 95 4.7 Diseased Vein Compression Sequence 96 4.8 Ultrasound Phantom Container 101 5.1 Ultrasound Screening System 104 5.2 Screen-Shot Ultrasound Screening System Interface 105 5.3 Building Vein Model 108 5.4 Vein Model with Compression Information 109 5.5 Cross Section of Uncompressed Healthy Vessel Phantom . 109 5.6 Cross Section of Compressed Healthy Vessel Phantom 110 5.7 Model of Thrombosed Vessel Phantom I l l 5.8 Minimum Transverse Vessel Area by Location Along Vessel 112 5.9 Maximum Force by Location Along Vessel 113 5.10 Cross Section of Uncompressed Thrombosed Phantom 113 5.11 Cross Section of Compressed Thrombosed Phantom 114 5.12 Reconstructed Human S F V 115 5.13 Location of Compression Examination Measurements 116 5.14 Compression Examination Data 116 5.15 Compression Examination Data - Curves Fi t to Data 118 5.16 Reconstructed Human S F V 118 5.17 Typical Compression Examination Data 119 5.18 Typical Compression Examination Data - Curves Fi t to Data 119 5.19 Typical Compression Examination Data II 120 5.20 Typical Compression Examination Data II - Curves Fi t to Data 120 5.21 Transverse Image Human P O P 120 5.22 Typical Compression Examination Data for Artery • . . 121 B . l Veins of the Lower Limb (after [3]) 161 LIST OF FIGURES x C l Results of Contour and Parameter Estimation, Phantom Vessels - I 173 C.2 Results of Contour and Parameter Estimation, Phantom Vessels - II 174 C.3 Results of Contour and Parameter Estimation, Phantom Vessels - III 175 C.4 Results of Contour and Parameter Estimation, Human Vessels - I 176 C.5 Results of Contour and Parameter Estimation, Human Vessels - II 177 Glossary CFA CFV CUS Distal DOF DVT LSV Negative Predictive Value P E PER Perforator Veins POP Positive Predictive Value PROF Prone Proximal PT Sensitivity SFV Specificity Common Femoral Artery. Common Femoral Vein. Compression Ultrasound. Farther from the heart. Degrees of freedom. Deep Vein Thrombosis. Long Saphenous Vein. Ratio of true negatives over total negatives detected. Pulmonary Embolism. Peroneal Vein. Veins connecting superficial and deep venous systems. Popliteal Vein. Ratio of true positives over total positives detected. Profunda Femoris or Deep Femoral Vein. Patient lies on front. Nearer to the heart. Posterior Tibial Vein. Ability of a test to pick up an abnormality. Superficial Femoral Vein. Ability of a test to yield true positives. xi GLOSSARY xii ssv Short Saphenous Vein. Supine Patient lies on back. US Ultrasound. Ak System matrix. a Semi-major axis of ellipse equation. b Semi-minor axis of ellipse equation. Ck Measurement matrix. E{X) Expectation of random variable X. Vk Measurement noise (at the kth instant). Gk Kalman gain matrix. Tk System noise matrix. Pk\k Estimate (error) covariance matrix. Angular displacement of ellipse equation. Qk Variance matrix of random vector £k-Rk Variance matrix of random vector r)k-rk The detected radius at instant k. Sk Covariance matrix of £fc and T]k-0 Ellipse parameter vector. 0 Optimal estimate of ellipse parameter vector. Vk Measurement data (at the kth instant). Var(X) Variance of random variable X. Xk State vector (at the fcth instant). XkjX^k Optimal filtering estimate of Xk-xk\k-l Optimal prediction of Xk-Zk System noise (at the kth instant). Acknowledgements • First of all, I would like to thank my co-supervisors Tim Salcudean and Jim McEwen for their guidance and support, which helped me develop a project such as this and bring it to term. I also thank them for making me work hard, because now I am very proud of what I accomplished. I am also very grateful to Dr. Bassam Masri and Dr. Savvas Nicolaou, without whom I could not have learned so much. Their expertise in the clinical setting was invaluable and necessary in order to get this project of the ground, and greatly enriched my program by making it truly an interdisciplinary initiative. • I would also like to thank all my lab mates, to whom I owe a great deal. Everyone helped me so much that I don't even know how to start listing them all. From Purang, who guided me through learning ultrasound and implementing image processing, to Daniela and Shahin who were always present helping me figure out ways to implement my Kalman filters. Also Simon DiMaio and Emre, for their help with tissue mimics, You Wei, king of programmers, Simon Bachmann for getting all my requests built. Of course I've left Andrew for the end, 'cause I know it'll bug him, and Parvaneh and Danny... thank you all. • I cannot write more without thinking about my family. Their support has been incredible, and I hope that the least that my stay here has done is made them proud. Mom and Papa, ultimately you are the ones who made me who I am, and made me capable of achieving this. Koa, Kati, I'm glad there will always be sister-power there to help me. Thank you, family. • All of this would have meant nothing, had I not been so fortunate as to have the everlasting love and support of my wife, Liz. You are my drive, my inspiration, my desire to be better. I could not be at the place I am today without you. Thank you. xiii Chapter 1 Introduction 1.1 Background It has been established in the literature that deep venous thrombosis (DVT) of the lower limbs is a frequent condition, and if left untreated, carries a high risk of mortality and morbidity [80]. The annual incidence of a first episode of clinically suspected venous thrombosis has been estimated at 2-4 per 100 in the general population [47]. The thrombi obstruct venous pathways, not permitting blood to flow. Thrombi may break off and flow through the vascular system, where they are a potential cause for pulmonary embolism (PE). It has been reported that 50% of patients with proximal DVT have lung scan evidence of PE [80, 97]. It is known that untreated deep vein thrombosis in 30% of cases can lead to PE, which might be immediately fatal [41]. Each year in the United States approximately 200,000 patients die as a result of pulmonary embolism [9] and it has been reported that the overall mortality of untreated deep vein thrombosis is approximately 2.5% [75]. Results from a population-based study indicate that there are approximately 170,000 new cases of clinically recognized venous thromboembolism in patients treated in short-stay hospitals in the United States each year and 99,000 hospitalizations for recurrent disease [4]. Because of this it is imperative to be able to adequately detect, quantify and characterize thrombi, specifically in the veins of the lower extremities, permitting a correct diagnosis of DVT to be able to administer appropriate treatment. An adequate DVT screening system would aid in this task. 1 1.1 Background 2 1.1.1 Description of Deep Venous Thrombosis The most common site of onset of DVT in both postoperative and symptomatic patients is in the deep veins of the calf [50]-, due to the sluggishness of blood flow in this area. More rarely, DVT may originate in the ileo-femoral-popliteal veins, particularly as a consequence of trauma or surgery on the thigh. The thrombi usually originate from valvular pockets lined by normal endothelium, and are composed mainly of red cells and fibrin. Even though there are usually very few platelets in the head of the thrombus, there are substantial amounts of them in the thrombus tail which grows proximally. The length of venous thrombi may range from a few millimeters to long enough to fully occlude large veins. Thrombus extension occurs in the direction of the blood flow by deposition of successive layers; thrombi may contain a fluctuating segment that may dislodge and cause emboli. Pulmonary emboli can sometimes originate from calf vein thrombi, but this is rare and usually of little clinical consequence because the corresponding emboli are small and occlude only the most peripheral segments of the pulmonary artery. Thrombi originating from proximal veins (popliteal, femoral and iliac) are usually much larger and carry a greater risk of clinically severe PE [80]. There is some controversy related to the importance of detecting calf vein thrombosis, and its relation to fatal PE. Aside from this controversy, it is generally accepted that calf DVTs can cause significant pulmonary emboli if they propagate proximally beyond the calf. This proximal propagation occurs in approximately 20 - 30% of cases of calf DVT [46,76,89]. DVT can be diagnosed by several methods. It is the doctor's responsibility as to which tests to order and methods to use, and the results from the imaging methods commonly have to be interpreted to obtain pertinent information. 1.1.2 Diagnosis Methods for Deep Venous Thrombosis There are several established techniques used in the diagnosis of DVT, and they may be broadly classified as physiological or anatomical. The physiological or functional studies provide indirect evidence of venous disease and reflect the hemodynamic or biochemical consequences of its presence. The anatomical studies demonstrate directly the presence of disease, localizing and quantifying the extent of venous disease and characterizing the pathological processes involved. Anatomical 1.1 Background 3 Figure 1.1: Veins of the Lower Limb (after [3]) techniques directly visualize thrombus and can demonstrate the pattern of obstruction [57]. Of these detection techniques, the two most common are contrast venography (CV) and com-pression ultrasound (CUS). Contrast venography (CV) has been the reference method for the diagnosis of DVT [47]. CV establishes presence, precise location and extent and occlusiveness of venous thrombi. Contrast medium is injected into a vein through the patient's foot, and it is permitted to flow through the patients venous system. After a short period of time, radiographic images are taken of the filling of the veins by the contrast medium. Healthy veins will fill up completely and show up on the radiographic images, but diseased veins will not. By correctly interpreting this absence of filling of the veins, DVT can be diagnosed. Until recently, contrast venography was considered the 'gold standard' for the diagnosis of DVT. 1.1 Background 4 At present, contrast venography is the only method with proven accuracy for the detection of asymptomatic DVT in high-risk patients [80]. The disadvantages of this technique are that this is an invasive procedure, and may cause pain to the patient. It is also a difficult technique to interpret. Another disadvantage is that CV cannot be performed in up to 10% of patients, because of inability to acquire venous access, allergic reactions, local infections, or because of renal insufficiency [47]. Contrast venography is a physiological method, as a positive DVT finding consists of an inad-equate filling of the veins, as observed with contrast medium. The objective of a compression ultrasound examination is to assist in the detection of DVT of the lower limbs by observing the transverse area of the veins in order to ascertain whether the venous system is obstructed. Loss of compressibility of a thrombus filled vein under gentle probe pressure, i.e. CUS, is the most accurate, simple and useful diagnostic criterion for the diagnosis of DVT and has now been used by some to be the primary diagnostic criterion [6]. This lack of venous compressibility when gentle pressure is applied accurately indicates high probability anechoic thrombus. If a vein does completely collapse, the possibility of DVT in that section of the vein is, on the contrary, very small. It is well documented that the diagnostic value of compression US equals that of contrast venog-raphy [5,19,81]. A recent meta-analysis pooled all of the studies of the diagnostic performance of ultrasonography for symptomatic proximal deep vein thrombosis. The sensitivity of ultrasonog-raphy was reported to be 97% and its specificity was 98% [75], while another source reports the sensitivity in the range from 89% to 100%, the specificity in the range 97% - 100%, the posi-tive predictive value in the range from 96 - 100% and negative predictive value in the range 88 -100% [47].' It is also known that no fatal pulmonary emboli were subsequently diagnosed in patients with normal compression ultrasonograms obtained for suspected deep venous thrombosis. Research shows that in patients with low clinical probability of DVT, negative ultrasonic findings lower the probability to less than 1%, and positive findings increment the probability to 54%. Patients with a high clinical probability but with negative ultrasonic findings were found to still have a 24% probability of having DVT in the lower extremity, but with positive ultrasonic findings the probability of DVT approaches 100% [9]. 1.1 Background 5 Because of this, along with its non-invasive nature, compression ultrasound is the technique of choice for the screening and diagnosis of DVT. Other modalities such as Doppler and color flow imaging may also be used for these purposes, but are not within the scope of this project. The protocol for deep venous thrombosis screenings varies from institution to institution. Gen-erally they involve assessing the risk factors of the patient, performing a DVT screening, and then interpreting the results based on the risk factors. The time it takes for one compression ultrasound examination varies widely, as reported from 13.5 minutes [67] to more than 40 minutes for examin-ing both extremities. A typical reported examination time for a duplex examination1 was 20 - 30 minute per extremity [83]. 1.1.3 Drawbacks and Limitations It is conceivable that while performing a compression examination a thrombus may dislodge and travel through the vascular system as a result of the force applied by the probe. An extensive literature search was performed, and only three cases where this occurred were reported [28,84]. In all reported cases, a thrombus was observed using ultrasound and upon compression was seen to disappear. Afterwards, the patients developed symptoms of PE over the next few minutes to several hours, and pulmonary embolism was subsequently diagnosed in each patient. Considering that this technique has been widely used over the past 20 years, and a very small number of reported cases were found where a thrombus is dislodged because of a compression ultrasound exam, we can say that the probability of this happening is very low. Even so, it is recommended that compression exams be performed by applying as little force as possible to obtain results. There are some other drawbacks and limitations to compression ultrasound. It was found that 76% of patients require a repeat test [75], which mean extra time and money spent on each patient for an adequate diagnosis. Moreover, 50% to 67% of the deep vein thromboses seen on repeat ultra-sound examination are false-positive results, further exposing patients to the risks of unnecessary anticoagulant treatment. Serial ultrasound (performing a second ultrasound examination at day 7 on all patients with a negative initial test) was the most expensive strategy ($1,482 per patient), though the results of serial ultrasound examinations have the lowest false negative rate (0.02%) as 'Consisting of B-mode images as well as Doppler ultrasound information 1.2 Motivation 6 well as the highest false positive rate (3.0%) [75]. The outcome of a compression examination may be highly dependant on the experience of the examining technician [12,31,67], and therefore lead to possible undesirable variations in the results. These variations can reduce the effectiveness of the compression examination, leaving more room for error. As well, not much has been easily observed about the natural evolution of clots in the lower extremities, especially those arising from the calf veins because of the existing limitations for calf examinations. The most ample information about clot evolution comes from postmortem studies [42,85], but studies based on repeated phlebography, which examines the changes in bioelectrical impedance of an area of tissue due to changes in blood flow, have also been reported [90]. 1.2 Motivation Since it has been established that DVT is a dangerous condition, and one which has diagnostic procedures that may be long, costly and may be dependant on the experience of the technician who performs them, the need for a fast and reliable DVT screening system has been identified. Methods currently used for identifying DVT may be used and improved upon, in order to generate a system that can screen patients for DVT with quick and accurate results. Even though ultrasound systems are accurate, they still rely heavily on the experience and skill of the technician doing the tests and physician who interprets them. This skill and experience permits the examination of more difficult areas, and therefore a more complete examination. There is a need for a system that identifies DVT that is much less subjective, and provides equally high accuracy independent of the operator. In this manner, repeat screenings could be carried out more effectively and in a less costly manner, as less skilled operators could be trusted with the examination. As well, studies have shown that positive results from CUS examinations for asymptomatic patients are not as common as those for symptomatic patients, which casts doubt on whether general screening tests for patients are accurate. The results of these studies contribute to the consensus that general screenings are not cost effective, because the strength of diagnosis using 1.3 Research Objectives 7 ultrasound is for symptomatic patients. Therefore there is a need to equalize and improve results of CUS examinations, in order to make high quality screenings cost effective. Currently, when DVT CUS exams are performed, a crude schematic mapping of the thrombus on a paper chart is all the information that is recorded regarding its localization for subsequent examinations or for the diagnostic procedure. This information is particularly important when the diagnosing physician would like to establish the possibility of thrombus migration, an issue which currently is under much debate. There is no current agreement on whether thrombi from calf veins contribute to the occurrence of DVT or PE, and if calf veins should be routinely examined for thrombi. More information is needed about thrombus migration in order to resolve this matter. A tool that could repeatedly and precisely locate and map a thrombus would provide much useful information. Similarly, a screening tool that could provide information for comparative evaluations of differ-ent DVT treatments would be extremely beneficial for evaluating the effectiveness of the applied treatments. By generating detailed vascular maps with information such as thrombus number, lo-cation, and the progression of these thrombi over time, valuable data for the treatment procedures could be obtained, and more so if the information could be obtained by using a quick and simple screening test. It is also desirable to develop an adequate user interface for a DVT detection system that would include these improvements. An increase in the amount of acquired information during an exam would necessitate the proper display of this new information. 1.3 Research Objectives The desired outcome of this work is to obtain a deep venous thrombosis screening system that provides a fast, accurate, objective and thorough mapping of the venous system based on com-pression ultrasound examinations, which may be performed by a person with minimal instruction. With this in mind, the specific objectives to be achieved are: (i) providing means to accurately obtain position and orientation measurements from an appropriate ultrasound probe, as well as the forces applied by a technician to a patient through the probe; (ii) developing an image processing algorithm that incorporates the measured data in order to asses a vein/venous segment for com-1.4 Thesis Outline 8 pression using the principles of a standard ultrasound compression examination; (iii) developing a user interface to properly display the acquired and processed data in order to present the possibility of deep venous thrombosis of a vein/venous segment; and (iv) establishing that this new screening system results in an accurate and objective deep venous thrombosis examination of the lower limbs. 1.4 Thesis Outline In this chapter, a brief introduction was given on the condition of deep venous thrombosis. An overview of incidence and mortality, as well as the main methods of diagnosis of this condition were presented. In summary it can be stated that the motivation of this work was the need for an objective and intuitive system for identifying deep venous thrombosis with a spatial mapping for a more complete examination. The research objectives were presented and hereinafter an outline of this thesis is presented. Chapter 2 presents the problem formulation and description. The necessary requirements are stated, and the manner in which the problem will be solved is presented. It is identified that the system will consist of three main parts, namely a feature detection algorithm and subsequent processing, a novel transducer setup, and an intuitive user interface for accessing the acquired information. Chapter 3 describes how the formulated problems were solved. The feature detection algorithm, transducer, and user interface are presented in detail. Additionally, contour validation metrics are presented, as well as the definition of the measures to quantify the presence of deep venous thrombosis in the examined vessel. The feature detection algorithm as well as the validation metrics are evaluated in Chapter 4. Also, a physical simulator that was used initially to validate the detection system is presented. Afterwards, the detection system was tested and validated on our physical simulator as well as on human volunteers. These results are presented in Chapter 5. Finally, Chapter 6 presents the conclusions of this research together with the recommendations for future work. In Appendix A a description of the physics of ultrasound is presented, as well as an overview 1.4 Thesis Outline 9 of some of the details of image and data acquisition using ultrasound. In Appendix B, a detailed description of the venous anatomy of the lower limbs is given, as well as an overview of detection methods for DVT, while focusing on compression ultrasound as the main detection method. Diagnostic criteria for DVT are presented, as well as some drawbacks and limitations. Several examples of results obtained from applying the contour detection algorithm presented in Chapter 3 are presented in Appendix C. Chapter 2 Problem Formulation In this chapter the requirements for a DVT screening system are stated, and the necessary components are identified. A statement of the clinical need for an improved DVT screening system is formulated, as well as a description of the process from which this originated. 2.1 Deep Venous Thrombosis Detection 2.1.1 Clinical Need As presented in the previous chapter, there are many sources in the literature that indicate the importance of adequately detecting deep venous thrombosis. Additionally, members of the local health care and health care training communities were contacted and interviewed, and a informal survey on the current detection procedures was performed, resulting in a consolidated view of the importance and frequency of deep venous thrombosis. Over a period of several months, regular visits were scheduled several times a week in order to observe the DVT detection procedure at Vancouver General Hospital. Ultrasound compression examinations were observed as they were performed on individuals who were either high risk or symptomatic, and in varying states of health. The difficulties and benefits of the ultrasound compression examinations were seen first-hand, as well as the process by which the information was recorded and archived. 10 2.1 Deep Venous Thrombosis Detection 11 Patients with varying signs, symptoms and conditions were scanned. It was observed that DVT scans are routinely recommended and performed on high-risk in-patients who have undergone major surgery, mainly total hip replacement and total knee replacement, as a preventive measure. As well, other in-patients who are classified as high risk because of other factors such as cancer, being bedridden for more than three days, localized tenderness or swelling in the lower limb, or a strong family history of DVT [9,97] may undergo compression exams as a preventive step. A small percentage of the patients scanned are out-patients with symptoms indicative of DVT. Concurrent with the visits to the hospital, the protocol for a venous compression ultrasound examination was reviewed based on the literature [10,19,59,79,83,101] and compared to the infor-mation obtained in the field. Educational videos created for the sole purpose of correctly identifying deep venous thrombosis were also reviewed and studied, in order to gain a complete understanding of the procedures, methods and concepts involved in compression ultrasound examinations. Several registered ultrasound technicians were contacted in order to provide instruction on the DVT detection process. The ultrasound technicians included both technicians employed in health care, and technicians employed in instruction. Instructional meetings were arranged with the ultrasound technicians in order to precisely document the examination protocol, discuss the more critical points of the examination, such as correctly identifying anatomy and correct probe placement, and the author and instructing technician examined healthy volunteers in order to completely understand the compression ultrasound examination. The result of this process was a familiarity of the human anatomy of the lower limbs, principally the vascular system, an in-depth understanding of the compression ultrasound examination which comprises the deep venous thrombosis detection procedure, a synthesis of the concepts on which this examination is based, and as well as the drawbacks and limitations that this technique may present. Throughout this period, as a result of informal interviews and direct observation, confirmed as well by an extensive literature review, the need for a reliable, accurate and fast screening system was identified. A system that is less operator dependent and provides a good measure of reliability for the compression examinations is also desirable. The need for objective and quantitative information resulting from a compression ultrasound examination was also identified, so that precise records of the information obtained in an examination could be created. 2.1 Deep Venous Thrombosis Detection 12 2.1.2 Detection Using Ultrasound Thrombosis detection using compression ultrasound can be reduced to a simple concept. It is assumed that a healthy vein will completely collapse upon compression, this is, if a small amount of pressure is applied to a vein the opposing walls of the vessel will come into contact with one another, completely displacing the blood within with little effort. Veins and arteries are easily distinguishable from one another since there is, in general, a greater pressure within arteries because the heart continuously pumps our blood. During a compression ultrasound examination, an additional characteristic can also be used to identify veins and arteries. An ultrasound probe produces an ultrasonic wave which travels through tissue and detects the returning echoes, forming an image of the examined volume. Different tissues have different properties, which in turn create changes in impedance for the ultrasound wave. These changes in impedance create reflections mainly at the tissue boundaries, which then show up in an ultrasound image. Blood, for example is characteristically non-echogenic and therefore does not show up in an ultrasound image, which means that there are no large changes in impedance throughout a blood vessel and subsequently strong echoes are not produced. Instead, a generally black1 area will appear in the image at the place where a vein or artery is located. A thrombus, which consists of the building blocks of blood, mainly red cells and fibrin, will also be non-echogenic and not show up in an ultrasound image. This is especially true for younger thrombi, and it is very difficult to identify a thrombus based only on one image. But thrombi do differ from blood in that they are generally uncompressible, providing a manner to locate them within a vein. Therefore, using these two premises, namely that veins are compressible and thrombi are not, a venous compression examination can take place. Once a vein has been located, it is compressed. If the opposing walls are seen to collapse, then the vein is free from thrombi. If not, the probability that the patient has DVT is very high. This is the basic concept of the compression ultrasound examination. There are several other modalities such as Doppler ultrasound and colour flow imaging that may assist in the detection of DVT, but they were not considered for the present system because 1 The color depends on the color-scale setting of the ultrasound machine used. 2.1 Deep Venous Thrombosis Detection 13 of factors such as time limitations. 2.1.3 Compress ion Ul t rasound Examina t ion Procedure As mentioned above, compression ultrasound is based on the loss of compressibility of a throm-bus filled vein under gentle probe pressure, which has been reported as being the most accurate, simple and useful diagnostic criterion for the presence of DVT [53,79]. The B-mode modality is used to present the anatomical features, such as vein valves, vein walls, and vein size, and therefore is used for the compression examinations. The use of a 5 - 7.5 MHz linear transducer is most suitable, because it provides sufficient penetration, with typical axial resolutions better than a millimeter (about 0.1 to 0.3 mm). A more detailed description of B-mode imaging can be found in Section A.3. Figure 2.1: Typical Compression Ultrasound Image. The examining technician will perform a complete mapping of the patient's venous system throughout the compression ultrasound examination. Generally, the examination begins at the level of the groin, scanning the common femoral artery (CFA) in a transverse plane, in order to observe the vessel cross-section. Gentle probe pressure is applied and the vessel cross-section is observed in order to confirm that the vessel has completely collapsed. If the vessel does not 2.2 Image Feature Detection 14 completely collapse, there is a high probability that there is a thrombus present in that section of the vein. The probe is then translated distally in order to image the next vessel section, and the procedure repeated. The patient's veins are scanned in this manner, from the thigh, then into the popliteal fossa (behind the knee), and into the deep veins of the calf. It is important to obtain images of bifurcations in the vessels, as this is a common location for thrombus to form. Each section is assessed for compression as the probe is repositioned. The deep veins of the lower limb must be imaged from different points of view in order to obtain the best possible image. The upper thigh is best imaged medially, while the popliteal fossa and the upper sections of the calf can be imaged better from a posterior approach. For each vessel section, the best images should be obtained. Each examination is documented by acquiring and saving split images that present the uncom-pressed vein and the compressed vein side by side, as shown in Figure 2.1. The right hand side shows an uncompressed image, while the left shows the same area under compression. Note that the common femoral vein has collapsed completely. Typically, 10 to 20 sets of images may be saved for a compression examination. If any abnormalities are found, a split image of the area is also obtained, and a paper chart or diagram roughly indicating the location of the anomaly is prepared. Therefore, the size of the thrombus is recorded as only the two vessel cross-section images, and the location is recorded on the chart. A detailed description of the compression ultrasound examination protocol and diagnosis pro-cedure can be found in Appendix B, Section B.4. 2.2 Image Feature Detection Any application that we want to develop that includes correctly identifying an object within an image will require some type of feature detection algorithm. It may seem like a trivial task at times for a human to look at an image or picture, and identify an object within it, but it is not. There are several advantages of describing an image based on features extracted from it. The extraction of image features greatly reduces the amount of information we have to deal with. By 2.2 Image Feature Detection 15 constructing a higher level representation of what an image contains, the bulk of the data that we must manipulate is reduced. It is therefore important that the feature detection is accurate, so that the necessary information is preserved. As well, cues from visual perception can be incorporated into any automated or semi-automated system that detects and processes the features. In this manner, we can include human experience and knowledge into these systems. An additional advantage of extracting features from an image is that we can reduce the variance of detected features from one image to another that is a result of changes in scale, brightness, orientation, and location. This in turn reduces the complexity of our systems as the information is standardized, and complex operations are not needed in order to process the data. Some of the goals or applications of feature detection in medical images are screening or detec-tion, diagnosis or classification, therapy and treatment planning, and image guided surgery. Features within an image that we can identify normally correspond to objects within a scene that have been captured by some means and converted into a two-dimensional image. It is the ultimate goal of these applications to be able to correctly identify these objects [87]. In many cases, the features may be distinct from the background image in shape or coloring, in which case feature detection is straightforward. Simple feature detection algorithms such as masks or templates are used in order to detect an object within an image [56,69,86,87]. In order to extract the location of the arterial wall from an ultrasound image of the carotid artery, [69] applied a low pass filter on the ultrasound image, and then used a Canny edge detector. Afterwards a Hough transform was implemented as a template in order to locate the location and size of the artery, assuming that this is described by a circle. Texture can also be used to segment or track a region of interest [33]. But in many other cases, more complex schemes must be developed, such as model driven detection. A model that defines the characteristics of the feature is derived, and a method must be developed to use image intensity values in order locate the feature. This is true for features that are very irregular in shape, size and coloration, and without clearly delimited boundaries, as is the case with medical images. For example, ultrasound images contain speckle, which is a noisy artifact, and this noise makes ultrasound images especially hard to analyze. In many instances, even humans have problems identifying medical features [3]. Feature or object identification by 2.2 Image Feature Detection 16 machines becomes more difficult with these images, and therefore the algorithms used to detect them may increase in complexity as well. As we stated in Section 2.1.2 detecting the change in shape and size of a vessel contour forms an integral part of a standard compression ultrasound examination. In order to include this diagnostic criterion into a DVT screening system, an algorithm must be developed that can adequately detect a contour of a vein in a ultrasound image of a transverse plane. There have been several methods presented for detecting anatomical features across several imaging modalities [15,30,93]. One of these methods is known as deformable contours or surfaces (snakes) [13,39,40,51,58], which have been used for detecting various anatomical features across different imaging modalities. A snake is an energy-minimizing spline guided by external constraint forces and influenced by image forces that pull it towards features such as lines and edges [51]. Several methods have also been developed to extract carotid artery contours from ultrasound images [2,37,69]. Additionally, there are various techniques that have been developed to detect boundaries in ultrasound images, a few of which are presented in [38,55]. An automatic ventricular cavity boundary detection algorithm is described in [32]. Ultrasonic images undergo three processes: decimation by a low pass filter in order to decrease image size, determining the center of gravity using a Star algorithm, and then using a simulated annealing optimization algorithm in order to detect the optimal location of the edge. A method called 'live-wire' for interactively detecting the contour of an image feature has been presented in [68]. This method uses a dynamic programming approach in order to determine a mathematically optimal path between a user-selected seed point, and another dynamically selected 'free' point in the image. By defining a cost matrix based on image gradient magnitude and orientation, as well as geometric cost measures such as length of a path, a minimum cost path can be found from the seed point to another 'free' point in the image of interest. In this manner, the user's notion of object recognition is used, as well as the computer's efficiency at boundary delimitation. The results report that this particular method accurately detects low-contrast boundaries. Several systems have implemented 'live-wire' based detection systems, such as [26,27] for C T and MRI images with good results. The drawback of these systems from our point of view is that they are designed as user-interactive methods for edge detection. It would be ideal that our 2.2 Image Feature Detection 17 application had the least amount of user-interaction in the feature detection process as possible. A cross-correlation speckle-tracking technique was used to measure longitudinal median nerve movement in ultrasound images [24] with good 'phantom' experimental results at velocities of 1 to 10 mm/s. An in depth review of feature extraction techniques has been presented in [1], where a number of feature extraction procedures have been compared on the basis of accuracy and possibility of real-time implementation. Methods such as template matching are only accurate for tracking a feature in a series of images when there are no large changes in pixel brightness, i.e. when the features remain similar throughout consecutive frames. Because of the nature of the compression ultrasound examination where the vessel cross sections are constantly changing, and because ultrasound images may contain large amounts of speckle, this method does not constitute a good choice. In [39], the authors developed a method for segmenting the human left ventricle in ultrasonic images using a combination of Snakes or active contour models and active shape models. This method supposes an application where human guidance is needed on a frame-to-frame basis, and the method must be trained in order to develop a model of the feature to be extracted. A three-dimensional snake-based segmentation technique is reported in [34]. A volume is man-ually initialized, and internal forces drive a dynamic balloon model outward until external image forces, such as brightness and its gradient, create an equilibrium. Good agreement has been re-ported between this segmentation technique and manual segmentation. In [58], an active contour method is used for successful semiautomatic segmentation of 2-D structures in MRI images. Contours are initialized at a single point and an initial estimate of the contour is obtained using a 'balloon' algorithm, which is an extension of an active contour with an internal energy that propels the border outwards. Afterwards, a second phase is implemented where a conventional active contour algorithm fine tunes the location of the edges. A snake-based segmentation is performed on intravascular ultrasound images of coronary arter-ies, as presented in [37], while in [54] ultrasound images of human organs, such as gallbladders and kidneys, are segmented using the same techniques. For the general case of deformable models or active contours, several disadvantages arise. One 2.2 Image Feature Detection 18 example is that careful initialization must be performed in order for some active contour meth-ods to converge. It has also been reported that some snake algorithms may show good feature tracking throughout a sequence of images, but the actual boundary detection is coarse, while other algorithms may show more accurate contour detection, but they are also very susceptible to noise and unclear boundaries, as reviewed in [1]. Additionally, many of the active contour methods are relatively complex, and therefore difficult to implement in real-time. Four different boundary detection algorithms were implemented and tested for identifying the human carotid artery in ultrasound images [38]. The first was a dynamic programming approach that identified the boundary by minimizing a cost-function, after having performed a training procedure. The second algorithm was based on finding points of maximum gradient. The third method used a mathematical model to describe the intensity profile of the desired edge, which also required training. The fourth method was based on defining a template of the intensity profile of the boundary, and applying a matched filter procedure in order to determine the location of the edge. In all cases, operator assistance was needed in order to obtain a more accurate edge. The dynamic programming algorithm was best in terms of accuracy and robustness, but depended greatly on the training that this algorithm underwent. Three speckle-tracking techniques that can be used in cross-correlation methods to. measure movement of features in ultrasound images are evaluated and compared in [33]. It was shown that Sum of Absolute Differences (SAD) and normalized correlation performed well, even for small kernel sizes. Non-normalized correlation did not perform well for smaller kernel sizes, but its performance improved as kernel size increased. A segmentation technique for carotid arteries in ultrasound images using a deformable model method is described in [61]. The image gradient, as well as a desired gray level contrast are used as driving or 'external' forces while the geometry of the contour defines the 'internal' force. These forces deform a contour through an iterative process until convergence requirements are met, in this manner locating the contour. The method presented in [2] identifies the contour of a cross-section of a human vessel using a modified Star algorithm [32] and a Kalman filter. This algorithm has been also known to perform well in detecting features even with echo drop-outs and shadowing artifacts. 2.2 Image Feature Detection 19 In general, there is an underlying model that defines what the final feature or contour will be, and a model, which is modified by image forces in order to approximate the shape of the anatomical feature. The model and process by which it can be modified varies from method to method, but generally the image forces used are those which arise from edges within an image. One of the simplest forms of edge detection is to define the location of an edge at places where the image gradient is large. Assuming we have an u, v coordinate system, and the brightness of the image is denoted by f(u,v), the gradient is defined as Vf(u,v) = df(u,v) du df(u,v) dv (2.1) If we assume that we have a model-based feature detection algorithm, the image forces of this model can be set to be proportional or equal to (2.1) (the gradient of the image), and the underlying models are then iteratively deformed by these images forces, and the result is a detected image feature which depends on both image intensity values and a model describing the shape of the feature. The step of identifying edges within an image is a very important one, as the final output of a feature detection algorithm will be driven by the result of the edge detection process. If this edge detection process is flawed and produces inadequate results, the final detected feature will also be inadequate, independent of the accuracy of the underlying model of the feature detection algorithm. Therefore, an appropriate edge detection function must be used if a simple gradient function does not produce acceptable results. Referring to the feature detection method presented in [2], the authors developed a Star-Kalman algorithm in order to detect the contour of a carotid artery from an ultrasound image. The algorithm assumes that the underlying model of the cross section of the vessel is a circle, and using image intensity data from an ultrasound machine, detects the most probable location of the vessel lumen based on a probabilistic edge detection function. The low processing requirements and performance results of the algorithm make it a good candidate for our application. Even so, there are several drawbacks to this approach when it is extended to detect cross-sections of compressed veins. Considering that the underlying circular model is generally robust and 2.2 Image Feature Detection 20 adequate for arteries, a vein under enough compression is deformed to the point that the detected contour does not correspond to the actual vessel cross-section. In this case the assumption that the contour is a circle does not hold. A manual parameter modification is required to reduce the error between the detected contour and the actual (established by a trained ultrasound operator) vessel lumen. It is therefore necessary for this application to use a model other than a circle for the feature detection. A characteristic of image feature detection in ultrasound images (and in medical images in general) which is central and can be considered a drawback from an application point of view is the validation of the detected feature. In most cases, we are looking for an unknown feature in an image, and we only have a general idea of what it looks like. In humans, experience and knowledge of anatomy and physiology are the basis for the model of the feature, and validation may be performed by obtaining a second opinion. Even in this case validation may be a difficult process. In order to develop a system that performs the procedure in which a feature is identified, a validation of the detected feature must also be performed. One way to establish whether the detected contour corresponds to the real vessel cross-section, and in this manner validate the feature, is to take advantage of the properties of human vessels in ultrasound images as mentioned above. Since the interior of the vessels is generally dark and free of any speckle pattern, as compared to the surrounding tissue, an average brightness value of the pixels within the detected contour can be calculated, and a simple thresholding process can indicate whether the detected feature is valid or not. Unfortunately, this threshold value must also be constantly updated depending on the average image intensity of the generated ultrasound image. This dependence on the brightness level increases the possibility of erroneously validating an incorrect contour. It is therefore necessary to include two characteristics into our feature detection algorithm. Firstly, the detected vein contour in a transverse ultrasound image plane should be represented by an appropriate model, one which can correctly represent a vein under compression as well as an uncompressed vein by using data obtained from an edge detection function. And secondly, a validation scheme must be developed in order to ensure that our detected contour is correct, as much as possible. Both of these characteristics can be included into the feature detection algorithm by modifying 2.2 Image Feature Detection 21 the model in the Star - Kalman filter. As published, the Star - Kalman contour detection algorithm models the detected contour in polar coordinates as r{6) = a (2.2) where r is the radius of the circle, and equals a for all 6. 6 simply indicates the angle at which r projects from the center of the circle, or that r is a function of 6. The vein, both in compressed and uncompressed states, can be more accurately modeled by exchanging equation (2.2) with the ellipse equation r{8) = a b = (2.3) ^Jb2 cos(0 - (j))2 + a2 sm(6 - 4>)2 where r is the radius, 9 is the angle with respect to the image plane, <f> is the angular displacement of the major axis of the ellipse with respect to the image plane, a is the semi-major axis, and b is the semi-minor axis. In this model, the parameters a and b describe the size and eccentricity of the ellipse, and (f> indicates the orientation of the ellipse. By setting the parameters a, b and (f> with different values, a vein can be accurately modeled in all cases. A compression examination is a dynamic procedure and therefore throughout one cycle of the examination, which comprises compressing and releasing a vein, the vessel may change drastically 2.2 Image Feature Detection 22 in shape. One set of parameters for the model in equation (2.3) will not suffice for all possible vein contours. By including the parameters into our feature detection algorithm as well as an estimator for them, we can obtain an iterative process that presents as its output a series of points defining the optimal estimate of the location of the vessel contour2, as well as values for the parameters of the ellipse equation (2.3). In this manner we will have information describing the detected contour, as well as information for an ellipse that has been fitted to the data, which represents the vein. This information will have been extracted using an edge detection function, and processed using a feature detection algorithm, so that the detected contour closely represents the actual vessel lumen. We can then create an error measure by calculating the mean squared distance from each detected point on the contour and the corresponding point on the ellipse generated with the detected parameters. Figure 2.3: Error Measure This measure is independent of the brightness of the image in that it does not depend on an average grayscale value within the detected contour, and can be easily and quickly calculated. It will be shown that if the error measure is greater than a certain threshold, indicating that the detected contour and estimated ellipse parameters do not correspond, the probability of having detected a correct contour decreases, while a small error value will indicate a correctly detected contour (as verified by an experienced ultrasound operator). Therefore, if the edges are missed 2Assuming the parameters are estimated using an extended Kalman filter. 2.3 Position, Orientation and Force Detection 23 and the correct contour is not detected a high error measure is expected, and the feature detection algorithm can be executed again with a slight change in initial parameters, as will described ahead. Even so, there is a very slight possibility that the detected contour may be similar to an ellipse, but will not correspond to the correct contour. In this case, our error measure will be small, and the possibility exists that an incorrect contour will be accepted. But as our results in the next chapters indicate, this is very unlikely. 2.3 Position, Orientation and Force Detection The requirements for the measurement of applied force through an ultrasound probe while performing a screening for the detection of deep venous thrombosis, as well as those requirements for the measurement of the position and orientation of said ultrasound probe are presented below. 2.3.1 Justification for Sensing Force, Position and Orientation It has already been established that compression ultrasonography is the most important in-dicator in the detection of deep venous thrombosis. In order for the detection procedure to be automated in any way, the force that is applied to the patient must be measured. The applied force could conceivably be approximated through the use of image processing techniques, correlating the size of the vein with the applied force, but since the positive diagnosis of DVT is based on non-compressibility of the veins, a force transducer must be included. This also ensures that the patient is not harmed because of use of excessive force during the examination. Once a clot or thrombus has been detected, to be able to completely characterize it, the location of the thrombus within the patient must be known. Since the venous anatomy of a patient can be relatively variable, it may not be obvious what area is being imaged based on the resulting picture. Also, if a vascular map is to be produced from the acquired information, be it a 2D or a 3D record, the position and orientation of the ultrasound probe must be known for each acquired image in order to perform a successful reconstruction. Therefore, a position and orientation sensor must be used. Also, since the examination is being performed on a patient, this requires that the ultrasound 2.3 Position, Orientation and Force Detection 24 (c) Figure 2.4: Ultrasound Probe, with different orientations probe be translated in all three X — Y — Z directions3 and rotated about all three axes (rotation about X Y Z), indicating that a 6 degree-of-freedom (DOF) sensor is needed. As illustrated in Figure 2.4, it can clearly be seen that the probe must be moved in such a manner that requires a 6 DOF sensor. The probe can be translated in any direction by the examining technician, as well as rotated freely. An additional advantage of measuring position and orientation information is that each image plane that is acquired can be placed in 3D space, as well as all features that are detected on each frame. By storing all the image data and feature information, a 3D representation of the scanned vessel can be built, permitting the visualization of the complete vessel, as opposed to only one slice or image. In this manner, the results of compression examinations could be mapped to different easily identifiable regions on the reconstructed vessel, and improperly scanned areas could quickly 3Assuming a Cartesian reference frame is used. 2.3 Position, Orientation and Force Detection 25 and intuitively be identified thereby verifying the completeness of a CUS exam. This 3D reconstruction could also benefit the diagnosis procedure. Currently, for example, after a standard compression examination, the examining technician schematically indicates where a thrombus has been detected (if the case is so) on a paper chart, giving only a rough estimate of the location of the thrombus. Detecting if a thrombus has migrated proximally may become more complicated as the location is not exact. A precise three dimensional record of thrombus location could greatly improve the reliability in diagnosing thrombus migration. Also, in general, the cognitive load on the examining technician is reduced. 2.3.2 Force Sensing Background and Basics It has been found that several systems have been developed that require sensing the pressure or force exerted by an ultrasound probe on a patient. Some of these systems calculate the force through the use of an activated mechanical linkage, which positions and orients the probe as well. Through the calculation of the inverse kinematics of the mechanical linkage, the applied force can be obtained and controlled. Also in some cases with mechanical linkages, a 3-axis force sensor is used to measure the pressure and forces exerted on the end effector [65,100], directly measuring the force exerted on the end effector. The disadvantage of these systems is that they are bulky and may interfere with the examination process. Another system was found that measured the pressure exerted by an ultrasound probe while obtaining ultrasound information in order to calculate the material properties of the tissue being examined [99]. 'A low profile Entran compressive load cell calibrated for a 10 N range was connected in series with the ultrasound transducer . . . a load cell driver/amplifier (an Entran PS-30A) was used to drive the load cell, and the output signal was digitized by a 12 bit ADC . . . the accuracy of the force was better than 0.003 N within the 10 N range.' The probe used was a single element transducer. Ideally for our application, the force sensor should be as unobtrusive as possible, so as to not interfere with the examination. 2.3 Position, Orientation and Force Detection 26 2.3.3 Position and Orientation Sensing Background and Basics There are several ways in which to measure the position and orientation in space of an object, including mechanical linkages, cameras, sound generators and microphones, infrared sensors, and through the use of electromagnetic sensors. Those of which have been applied with relation to the detection of the position and orientation of an ultrasound probe will be explained in greater detail. In general there are two categories into which the measurement of position and orientation can be divided. These are mechanical and freehand techniques. A brief description is presented below. One of the most simple ways to measure position and orientation is through the use of mechanical assemblies or mechanical arms. In the former case, the ultrasound probe is mounted on a mechanical assembly, which moves the probe along a predefined path while the whole assembly is held fixed during acquisition, thereby obtaining position information, but the examiner cannot directly modify the trajectory. Technical problems include inaccuracy in the motor drive and vibrations, making the distance between scan planes uncertain. However, the most important shortcoming of using a mechanical system on the abdomen is the restricted movement and angulation of the transducer [63]. Some of the shortcomings of mechanical assemblies can be overcome to some extent by using a mechanical linkage or arm. The dimensions of the arm are known, and by measuring the respective angles at each link, the position and orientation of the end of the linkage can be determined. If a probe is included in this set-up, through an additional mathematical transformation, the position and orientation of the probe can be found. Various configurations have been used in practice, from commercially available products [14,36,64,70], to custom-made linkages [65,100]. There are also several drawbacks to this method. First of all, the linkage may be bulky and could interfere with the examination process. As well, there exists a limited range of motion defined by each configuration, that is, a specific workspace exists where the ultrasound probe can be moved. On the other hand, 'freehand 3D ultrasound preserves one of the inherent advantages of ultra-sound over CT and MRI; namely, the ability for the clinician to move the probe in an unrestricted manner' [91]. An example of a freehand system used for detecting position and orientation information is based on an acoustic ranging system described by Brinkley et al. (1978), King et al. (1990), Moritz 2.3 Position, Orientation and Force Detection 27 et al. (1983) and Levine et al. (1989) [45]. Three sparking electrodes are placed on a small platform on the ultrasound transducer, which produce an acoustic signal at specific time intervals. An array consisting of four microphones is placed on a stationary 'L' shaped bar, and the time of flight is calculated for each acoustic signal. In this manner, the distance between the spark gaps and the microphones is calculated and the position of the probe is triangulated. The drawbacks to this system are that the examiner must remain clear of the line of sight between the sparking electrodes and the microphones in order to obtain an accurate measurement. Also it was reported that the sparking acoustic sound source is frightening to some patients [62]. To avoid significant errors, the air temperature must be continually monitored as the velocity of sound in air changes at a rate of about 2% per 10 degrees C [45]. Another freehand technique is based on locating the position and orientation through the use of electromagnetic sensors. These identify their 3D position and 3D orientation in space with respect to the position of a magnetic field generator. 'The basic measurement concept involves using a set of transmitter coils to generate 3 orthogonal dipole fields in a time sequence. A sensor is used that can detect the field strength in 3 orthogonal directions. Therefore, in a measurement cycle three orthogonal fields are sequentially produced and 3 measurements are made each time. This gives 9 field strength measurements from which the 3D position in space with respect to the transmitter is identified and the 3D orientation of the sensor with respect to the Cartesian axes of the transmitter are also identified. Together this information provides information in six different dimensions' [62]. The disadvantages of this last type of system are its susceptibility to nearby metal, and stray electromagnetic signals, which can cause significant errors in the measurements. Also, the accuracy of the measurements decrease as the distance between the emitter and receiver is increased [45,62]. Even so, there have been several applications where this type of sensor has been used with ultrasound imaging equipment [11,45,63,71,91]. It has been reported that the static accuracy of one of these systems (Polhemus 3Space Fastrak System, which emits a 8013 Hz E M signal) in a metal-free environment is specified as 0.8 mm RMS and 0.15 degrees (2.618 x 10~3 radians) RMS, and the resolution, 0.005 mm per cm of range and 0.025 degrees (2.181 x 10 - 3 radians). These values apply when the receiver is within 76 cm of the center of the transmitter [45]. To achieve this, the system must be properly calibrated in order to determine the geometric relation of the receiver and the object [71]. 2.3 Position, Orientation and Force Detection 28 2.3.4 Proposed Configuration and Requirements It has been reported that the approximate pressure to be exerted by the ultrasound probe to compress a normal vein during a compression examination should be just enough to dimple the skin, or approximately 104 Pa (which corresponds to approximately 0.18 psi) [19,20,98]. It seems reasonable to think that the pressure needed to completely compress a vein will vary, especially depending on the patient's anatomy and other causes, such as swelling or edema. A range of 0 to 5 psi is suggested for the instrumentation, and a resolution of at least 0.01 psi is thought to be adequate for this purpose. Therefore, assuming that the pressure will be initially obtained as an analog value, an analog to digital conversion should be done using at least a 9-bit resolution (divide 5 by 0.01 = 500, closest is 9 bits: 29 = 512). The resolution of an ultrasound image will be initially defined by the equipment with which the image is acquired. Typically, for B-mode imaging, resolution of better than 1 mm in the axial direction is obtainable (using a 7.5 MHz signal) [101]. Resolution varies depending on the equipment and settings, for example the lateral resolution depends on the size of the ultrasound field and the position of the object within it [101]. It is also typical to digitize this information into 512 x 512 arrays for each image (although other sizes can be used such as 640 x 480), while an 8-bit grayscale resolution is adequate for each element or pixel. The frame rate will vary anywhere from 5 to 60 frames per second, depending on several ultrasound image settings such as number of focal points, the depth being imaged, and the number of modalities being combined into one image (frame rate decreases for Colour imaging, for example, which superimposes colour information onto B-mode information) [3,101]. A frame rate of 30 frames per second is typical for B-mode only imaging, using a 5 MHz probe. In order to maintain the resolution of the information, the images must be digitized with an appropriate data acquisition card or frame grabber. An 8-bit grayscale array of 512 x 512 at a frame rate of 20 to 25 fps is considered suitable. Furthermore, if only a fraction of the ultrasound image is being acquired, such as when the ultrasound image is being 'zoomed in' on the equipment, over-sampling may occur, but the resolution of the equipment will be maintained (if the ultrasound equipment provides 1 mm per 'pixel' resolution, and once digitized we have 0.3 mm per pixel, our minimum resolution will still be 1 mm). 2.3 Position, Orientation and Force Detection 29 The ultrasound image resolution must also be considered when denning the requirements for the position and orientation sensor. If the maximum spatial resolution of the ultrasound equipment is 1 mm 4, then a position and orientation measurement, or location, should be obtained with similar degree of accuracy. If our location has a resolution of 5 mm, the ultrasound probe will acquire a range of images for what seems to be one position and orientation, and this will lead to errors. The setting at which we will be obtaining images provides 1 pixel per 0.1 mm both in the axial and lateral directions. All measurements being made should be done on a similar timescale. Position, orientation, and pressure values should all be sampled at the frame rate frequency, to be able to construct a complete and unique data set consisting of an ultrasound image, the pressure measurement for that image, and the position and orientation of the transducer that was used to acquire the image. For this, a data acquisition card capable of the resolution mentioned above for the pressure with an acquisition rate of at least 20 to 25 samples per second (Hz). As well, the position and orientation must be sampled at this same rate. It would also be advantageous to have all these measurements synchronized, so that the correct pressure, position and orientation measurements are all linked to the correct image. As mentioned in the literature, a 5 MHz linear probe is the most common transducer to use for a DVT examination [6,19,20,60,79,83,98]. It is also noted that even though the grayscale or B-mode image is acquired using this center frequency, the Doppler modality as well as the colour imaging modality is typically performed using a lower center frequency such as 3.5 MHz [19,79], because echoes from blood are weaker than from soft tissue [52]. For our system, a primary probe with these characteristics should be used. Even so, it is suggested that a secondary probe (or configuration) be used at a lower center frequency for B-mode, 3 or 4 MHz, possibly in combination with the primary probe/configuration. This would be in order to compensate for lack of penetration, because higher frequencies are attenuated in tissue more than lower frequencies, with a sacrifice in resolution as axial resolution is better for higher frequencies. In order to choose any type of sensor, several considerations must be made. First of all, since our system will be in direct contact with patients, all sensors, the signals produced by them, and the conditioning applied to the signals should be within certain limits in order not to harm the 4 Two interfaces which generate two 'peaks' separated by 1 mm will be detectable 2.3 Position, Orientation and Force Detection 30 patients. Secondly, this system will not be used as part of a life support system, but even so, its purpose is to detect a potentially life threatening disease. Therefore, all instrumentation used should be highly reliable, as a malfunction because of unreliable instrumentation of the system may imply that a person may die as a result. It is suggested that guidelines presented by the Association for the Advancement of Medical Instrumentation be consulted. Lastly, all sensor as well as their conditioning circuits should remain relatively small. It can be considered that an ultrasound probe is constructed of a certain size to easily fit into a person's hand. The cord connecting the probe to ultrasound equipment has been said to be too heavy and cumbersome [Personal Communication]5, so an effort should be made in order not to increase the size nor the weight of the probe and attached cord, to the extent that it is possible. It has been estimated that the volume in which the ultrasound technician performs the diagnos-tic exam comprises approximately 50 cm horizontally x 60 cm vertically x 100 cm longitudinally. As well, it has been observed that there are several positions and orientations used during the examination, such as examining the thigh medially, the knee joint posteriorly, and the leg anterior and posteriorly 6 . If the patient is completely mobile, the examination may require less movement and reorientation of the probe, but these considerations are being made based on low mobility pa-tients. So, in order to measure the position and orientation of the ultrasound probe, the preferred configuration would include an electromagnetic 6 DOF sensor. This type of sensor provides the mobility needed, as well as the workspace for this particular examination. A more limited exam could be performed with the use of a mechanical linkage. One of the main problems that may occur is interference between the sensor readings, including the detection of the ultrasound information. It has been reported that the direct placement of an electromagnetic location sensor onto the ultrasound probe caused skewing of the outlines of the image [45]. The authors of said report overcame this problem by placing the transducer on an extended plastic shell (or rod). Because of the possibility of interference as well, neither variable inductance nor variable ca-pacitance pressure transducers should be used as pressure sensors. Also, regardless of which type of sensors is used, it must be verified that the associated electronics 5Vancouver General Hospital ultrasound technicians. 6Please refer to Appendix B for greater detail. 2.4 User Interface and Data Integration 31 do not interfere with any measurements, nor causing any image distortion because of interference with the signals generated by the ultrasound probe. And as mentioned before, the addition of instrumentation to the probe itself is bound to cause an increase in volume and weight, which may be of such a magnitude to be bothersome or cumbersome to the examiner while performing a DVT screening. Several sources of error are expected from this system setup, in varying degrees and at various stages. Small errors may arise from the ultrasound image and the feature detection algorithm applied to the image, because of improper matching of the gain settings and image brightness values, and the corresponding parameters on the feature detection algorithm. Also, the ultrasound image plane is being considered to be an infinitely thin plane, while in reality it is far from that. As well any nonlinearities in the ultrasound image will not be taken into account. Larger errors are expected from a combination of the sensor measurements, as well the calibra-tion of these sensors. Complete faith was placed on the factory-provided calibrations for the force and location sensors, and no attempt was made to verify these values. As well, some errors are expected from the location sensor because of the known problems with electromagnetic interference caused by signals and nearby metal. The most significant errors in this system are considered to come from the deformability and movement of the patient. Since a soft, deformable tissue is being examined, we do not expect a series of detected contours from the exact same vessel segment under different compression values to be located at the same fixed location, say our location sensor base frame. Additionally, if the patient moves during an examination, the same point on the patient will no longer be at the same point in the location sensor reference frame, causing misalignments. 2.4 User Interface and Data Integration Once an ultrasound probe has been fitted with the appropriate sensors to be able to carry out an adequate compression examination, new possibilities arise as to how the acquired information can be processed and displayed. In conventional ultrasound, the examining technician examines a two-dimensional image on 2.4 User Interface and Data Integration 32 a screen which presents a 'slice' of the anatomy being examined. Since there are no organs or structures in the human body solely in two dimensions, the examiner must translate and rotate the ultrasound probe in such a manner so that the whole volume of interest is examined, one slice at a time. The examining technician must form a mental image of the examined area, using all the information from the constant stream of images generated by the ultrasound machine. This also implies that the examiner must have a good knowledge of anatomy in order to identify certain landmarks and organs. This process becomes increasingly difficult as the anatomical structures become more com-plicated. More complex three-dimensional structures, such as tortuous veins, may become more difficult to visualize based only on two-dimensional images. A three dimensional representation of the anatomy would be a very useful tool. As mentioned above, it is a relatively simple step to transform the detected image features from the two dimensional image plane into a three dimensional reference frame, once the position and orientation of the ultrasound probe are known, as well as the transformation constants between image, probe and world frames. From these vessel contours, now represented in 3-D, a complete model of the examined vein can be built and displayed alongside the conventional ultrasound image. Several references of model building have been found in the literature that are similar in that a contour or boundary is detected in an image, and boundaries from consecutive frames are then stitched together to form a three dimensional representation of the examined anatomy [58,69,74,93-96]. The imaging methods include X-ray, MRI and ultrasound, both external and intravascular. As well, a dense volume may be constructed of the imaged area, by using the entire image information that was acquired, instead of building a sparse model [29,77]. It is also possible to perform the feature extraction from a three-dimensional data set [34]. Once the geometric model has been built, it is possible to display this model in 3-D space, as well as displaying the information that was used to construct the model in the same space [93,94]. One of the major limitations of the systems mentioned in the literature is that the information takes time to process, and the visualization is usually done off-line. It is our goal to overcome this limitation through the use of a fast image processing algorithm, so that the complete current ultrasound image frame can be displayed in 3-D space alongside the 3-D vein model constructed in real-time, giving the user a precise relative reference as to where the probe is located with respect 2.5 Summary 33 to the vessel. Once we have a model of the uncompressed examined vein, information can be mapped to this model, giving the user an intuitive interface, and an indication of the results and completeness of the examination. For example, color can be used to represent the results of a compression exam at a certain location of the vein. If an area is green, for example, it would indicate that there is a very low probability of DVT at this location, and if this area is presented as red in colour, then this would indicate high probability of DVT at this location. A color such as black could be used to indicate that a certain area of the vein had not been properly scanned. This color scheme is used as an example, and other parameters such as hue or opacity could also be modified to represent different data. A 3-D model of the vessel deformation can also be built, by using the detected contours at the maximum applied compression force, instead of visualizing an uncompressed vessel with color mapped to its surface. All contours would be sorted by location, as well as by applied force. Problems may arise if we wanted to view both the uncompressed vessel model and the compressed vessel model at the same time, because of the deformation of the tissue would result in that an uncompressed contour of a vessel section would be mapped to a different location than the location of the compressed contour of that same vessel section. An additional visualization option would be to construct an animated 3-D model using all detected contours, in order to view the compressibility of a vessel segment, by using the contours corresponding to a specific force interval at different time intervals. All contours would have to be aligned along a common axis, and information on the vessel geometry may be lost in the process. 2.5 Summary By processing the ultrasound images obtained during an ultrasound compression examination, the change in transverse area of an observed vein can be automatically quantified. In this manner a standard quantitative measure for the identification of DVT can be obtained, which results in a more objective analysis. Also, with additional position and orientation sensing equipment, a precise localization of a detected thrombus may be achieved. This can permit consistent, repeatable examinations, and a 3D description of the thrombus. Chapter 3 Methodology In this chapter, a feature detection algorithm is derived which includes a contour detection process, a parameters estimation process, and a contour validation process. Additionally, it is presented how the force, position and orientation measurements are incorporated into a deep venous thrombosis screening system, as well as presenting a user interface for the system. 3.1 Vein Contour Extraction From Ultrasound Images It has been defined in Chapter 2 that the transverse view of a vein in an ultrasound image cannot be modeled by a simple circle because of the changes that this feature undergoes. This is especially true when referring to the images of a vein during a compression exam because of the implicit nature of the test, which requires deforming the vein in order to obtain a diagnosis. There have been several methods reported to extract features from ultrasound images, such as template matching, active contours, and the star - Kalman algorithm. It has been established that the feature detection algorithm presented in [1,2] is an efficient, fast and reliable way of extracting vessel contours in transverse ultrasound images. In order to perform our examination we require a measurement of transverse vessel area, which will be supplied by the feature extraction algorithm. Therefore, an algorithm that can only detect and/or track the center point of the vessel is of no use to us. As well, we would like user interaction in the image segmentation step to be minimal as possible. 34 3.1 Vein Contour Extraction From Ultrasound Images 35 The star - Kalman algorithm therefore proves to be an adequate launching platform, and is used as a starting point for a vessel contour detection algorithm to be implemented in the deep venous thrombosis screening system. Afterwards, the contour detection algorithm's model is changed, and a Kalman filter is devel-oped using an ellipse as the model. This model will initially be developed considering constant parameters, and subsequently a parameter identification scheme will be developed in order to esti-mate the parameters that describe the ellipse model. 3.1.1 Overview of the Star - Kalman Algorithm As described in [2], the Star - Kalman algorithm functions as follows. An ultrasound image of a vein seen on the transverse plane is acquired, and a seed or center point xc, yc is selected1 so that this point lies somewhere inside the contour of the desired vessel. N angularly equispaced radii are then projected from the center point, and the brightness values along each radii are processed by an edge detection function. M number of candidate points pi are selected based on the results of an edge detection function, and a probability distribution function describing the actual location of the edge is constructed from these points for each radius. The contour that we wish to detect is modeled by the system Zk = rk + Vk where rk is the radius of the boundary point along radius k, which shows the state of the system at iteration k. Also, zk is the measured version of the real rk at iteration k, and £ and rj are sequences of zero-mean, white, Gaussian process and measurement noise values with covariances Qk and Rk, respectively. It is known [7,8,17] that we can apply a Kalman filter to the system (3.1) to obtain an estimate fk of rk. J B y automatic or manual means. 3.1 Vein Contour Extraction From Ultrasound Images 36 Indeed, consider that we have a linear system described in a general manner by xk+i = Ak xk + rk £k VK = CKXK + T]K where Ak, Tk, Ck, are nxn, nxp, qxn known constant matrices, respectively, with 1 < p, q < n, xk is the state vector (analogous to rk in (3.1)), vk is a vector of measurements, and £fc and rjk are unknown system and observation noise sequences, respectively. We assume that the system noise and observation noise £ k and r]k are sequences of zero-mean, Gaussian white noise such that the variance of the process noise Var(£k) = Qk and that the variance of the measurement noise Var(nk) = Rk- We assume that Qk and Rk are symmetric, positive definite matrices and the expected value EfekWi^) = 0 for all k and I, and are therefore uncorrelated. The initial state Xo is also assumed to be independent of £ k and r)k. The Kalman filter will obtain an optimal estimate of the state vector xk. The optimality is in the sense of least-squares, giving an unbiased estimate of xk, i.e. E(xk) = E(xk), which follows from choosing the optimal weight matrix Wk that gives a minimum variance estimate of xk, by minimizing the variance of the measurement error for all positive definite symmetric weight matrices Wk [7,8,17], where the error has been defined as a function of Wk. We can use the following recursive formula to compute xk in real-time &k\k - *k|fc-i + Gk(vk - Ckxk\k_{) (6.6) &k\k-l = A f e x f c _ 1 | f e _ 1 where is the estimate of xk and £j.|fc_i is the prediction of xk at iteration k, and Gk are the recursively calculated Kalman gain matrices. The prediction xk\k_i is calculated using the estimate of the previous iteration, and then this predicted value is used to calculate the estimate Xk\k a * the current iteration k. The starting point is the initial estimate of XQ = XQ|O - Since XQ is an unbiased estimate of the initial state XQ, we can use x0 = E(x0). (3.4) 3.1 Vein Contour Extraction From Ultrasound Images 37 It can also be shown [7,8,17] that the Kalman gain matrices can be calculated by Gk = Pk,k-i CkT (Cfc Pk,k-i C^ + Rk)~X (3.5) where Pk,k-i is the prediction covariance at iteration fc given the data at fc — 1. The term (Ck Pk,k-i Cj + Rk) is known as the measurement prediction covariance. The initial condition may be set as P0|o = Var{x0) (3.6) and for all fc can be calculated as Pk,k-i = Ak-i Pk-\,k-i Ak-\T + Tk-i Qk-i r*:-i T . (3.7) It is evident that we need to calculate Pk\k-i> which can be done using [7,8,17] Pk\k = (I ~ GkCk) Pk\k-i • (3-8) In this case, Xk = rk, Ak — 1, Tk = 1, Ck = 1, and the process and measurement noises are to be determined by trial and error. The output obtained once we apply the Kalman filter to the system (3.1) is f j .^, a list of fc points, representing the estimated distance of the detected edge from the initial seed, at an angle 6k = 2 7r k/N with respect to the image plane (x,y). Each ?k\k is the estimated edge location of rk, calculated by the Kalman filter in the following manner fk\k = rk\k-\ + Gk{yk) Vk = Zfc - ?k\k-i where fk\k-\ IS the predicted value of at iteration fc, yk is the correction term of the Kalman filter, Gk is the value of the Kalman gain at iteration fc, and Zk is the measurement as before. Typically, an edge within an image can be defined as the change in pixel brightness in a neigh-3.1 Vein Contour Extraction From Ultrasound Images 38 borhood, as defined in (2.1). The magnitude of the edge for our specific case is calculated by where f(r, 0) represents the brightness values of the image, and therefore its partial derivative with respect to r will be the derivative of the image brightness along the radial direction from the central seed point. The edge function will produce a higher output value when pixel brightness along a radius varies by a larger amount, and the output will be smaller when pixel values along a radius are more homogeneous. For an ideal image, we can consider that the edge is located at the position that has the maximum gradient as defined by (3.10). In an ultrasound image, we cannot obtain the edge location by applying (3.10) directly and obtaining the maximum because of speckle and boundaries that may not be clearly delimited. Speckle may create peaks in the gradient that may be larger in magnitude than the true edge, and the edge itself may have a smaller intensity because the ultrasound beam does not strike the vessel boundary at an optimal angle. Because of the nature of ultrasound images, there is no single measurement value for the edge location, and therefore the measurement Zfc in (3.9) is unknown. A more complex measurement must be used in order to find the edge location. df{r,0) (3.10) dr e Edge (xo, Vo) Figure 3.1: Edge Detection using Probabilistic Data Association Filter In [2], a combination of different candidate vessel edge points along each radius k is constructed 3.1 Vein Contour Extraction From Ultrasound Images 39 as an alternative value for yk in (3.9), as described by M Vk = ^2iPi,kPi,k (3-11) i=l where each P^k are weighting factors that describe the probability that each of the candidate points Pifc on radius k is the actual vessel edge. This is based on the assumption that there will be a normal distribution of edge points around the actual vessel boundary, with edge function magnitudes that also vary with a normal distribution. In this manner, edge location and edge magnitude are included into the alternate measurement yk, as shown by [8] Pi,k where (3.12) Pi,k = T y ^ F e x P ( : I Fedge(pi:k) (3.13) represents the probability distribution function of the correct measurement. In order to obtain Fedge(Pi,k) for each k, the gradient function as previously defined in (3.10) is applied to the image brightness values in the radial direction. The result is then ordered by magnitude, starting with the greatest value. We then define Fe(ige(pitk) as the first M points of the ordered gradient, so that we have the magnitude of the edge at the ith candidate point (pitk) of iteration k, for i = 1 to M , as shown schematically in Figure 3.1. Additionally, Sk is the measurement prediction covariance, and Tk\k-i defined as before. Sk is also determined by trial and error. As can be seen from (3.13), the effect of the magnitude of the edge on piik is given by Fedge(pi,k), while the effect of the edge location is present in the squared term (pitk — rk\k-i)2 • The predicted edge location Tk\k-\, along with Sk will determine the mean and variance of the normal distribution used to represent the true edge. By introducing the measurement yk into the system, the Kalman filtering process must be modified from its form presented in equations (3.3) - (3.8). In the equation (3.11), yk is generated by using a probabilistic data association filter [8], which assumes that there is only one target of interest, and is known as the combined innovation. The probabilistic data association filter assumes that for each sample time k, the measurements 3.1 Vein Contour Extraction From Ultrasound Images 40 Pi will be normally distributed around the actual location of the edge, according to the latest estimate and covariance matrix. Based on this assumption, we can divide pi into two sets of events, those pi which originate from the actual edge, and those pi that do not. Each of these sets will have an associated probability, Pi^ for those measurements that originated from the vessel edge, and /?o,fc for those that did not. In this way, we rate or grade our measurements Pi based on the probability that they originated from the actual vessel contour using equation (3.11). We can now calculate the error covariance Pk\k presented in equation (3.8) by [8] ^ 1 * = Po,k Pk\k-i + [1 - Po,k] Pk\k + h (3-14) where Pk = Gk and M ~^2Pi,k Vk y'k - Vk y'k »=i G'k (3-15) pCk\k = [J " GkCk)Pk\k-i (3-16) where /?o,fc indicates the probability that none of the measurements are correct, and is associated with the prediction covariance Pk\k-\ which indicates that there is no update. It follows then that 1 — Po,k indicates the probability that the correct measurement is available, and is associated with the update covariance P^k- The term presented in (3.15) will increase the covariance of the updated state because of measurement uncertainty, since it is not known which of the M measurements are correct [8]. Through the implementation of the Star - Kalman filter to 'solve' the system, the state which describes the location of the contour points, is estimated in the optimal least-squares sense. 3.1.2 Elliptical Contour Model An ellipse can be represented in Cartesian coordinates by the equation 54= i <3i7» which represents an ellipse centered at (0,0) that has its semi-major and semi-minor axes aligned 3.1 Vein Contour Extraction From Ultrasound Images 41 with the reference frame. In polar coordinates, an ellipse can be represented by a b v/62 cos(6> - <j>)2 + a 2 sin(0 - <f>)2 (3.18) where r is the radius, 6 is known as the eccentric angle which is formed with respect to the image plane, 0 is the angular displacement of the major axis of the ellipse with respect to the image plane, a is the semi-major axis, and b is the semi-minor axis. Both r and 9 are measured from the center of the ellipse, and it is assumed that the ellipse is centered at the origin of the coordinate system. A modified version of 3.17 can be written as (x - x0)2 (y - y0)2 a 2 + b2 (3.19) which represents an ellipse centered at (xo>2/o)- I n order to include the angular displacement <j> of an ellipse, a description of the rotation can be included into this equation. The resulting ellipse equation can be written as [x - x 0 ] T R ( 0 ) T A R(<f>) [x - XQ] = 1 (3.20) where and rcos(0) x0 x 0 = — r sin(#) yo R(0) cos(</>) sin(</>) — sin(</>) cos(</>) (3.21) (3.22) (3.23) where the coordinates (x, y) have been written in their polar form, and (3.20) is a function of 6, r is the radius from the center of the ellipse, (xo,yo) is the displacement of the center of the ellipse from the origin of the coordinate system, and R(</>) includes the effect of the angular displacement of the ellipse. 3.1 Vein Contour Extraction From Ultrasound Images 42 The ellipse is a more suitable representation for the. venous contour, which as mentioned under-goes much more drastic changes in shape than an artery. With the appropriate set of parameters 0 , defined as 0 = [ab(p}T (3.24) for the ellipse defined by (3.18), or 0 = [ab4>x0y0}T (3.25) for the ellipse defined by (3.19), the vessel contour can be more accurately and precisely described than if using a circular model. Also an advantage is the fact that by having a parametric represen-tation of the vessel contour, operations such as area and perimeter can be computed very rapidly. The manner in which 0 is chosen will be described in detail below. In order to use the Kalman filtering process for contour detection using an ellipse as our model, we must create the state-space description. As in the system described by (3.1) it is our goal to estimate rk for all fc. Therefore, we include equation (3.18) in our state by writing _ _ _ 2TT ab ( a 2 - f t 2 ) cos(ek-4>) sin(6k-<t>) . £ fe+1 fc N ( 6 2 cos{ek-<t,Y+a? sin(9 f c-<A) 2) 3 / 2 ^ (3 26) Zk = r k + rjk where rk+i is the estimated contour, Zk is the measurement of at iteration fc, and £ and 0 are sequences of zero-mean, white, Gaussian process and measurement noise values with covariances Qk and Rk, respectively, as before. The parameters of the ellipse equation remain as stated above, with Ok calculated by 2 TT k/N for each cycle. The system was obtained by using a first order approximation dr de e=ek A6> {vk-vk^) { 3 2 7 ) where A0 is the 'angular step' which is 2ir/N, and obtaining and expression for rk- Afterwards, the indices were modified in order to obtain an expression for rk+i-3.1 Vein Contour Extraction From Ultrasound Images 43 This results in a state-space description of a non-linear system of the form xk+i = fk{xk) + ^kik ^32g^ "fe = 9k(xk) + Vk and it is known [7,8,17] that we can apply the extended Kalman filtering process, which linearizes the system, in order to obtain the estimated contour, as in equation (3.2). We define as our state at iteration k, and it is our desire to calculate the estimated location ff.\k of the vessel contour described by the state, which we can calculate using rk\k = fk\k-i + Gk(vk-Ck rk\k-i) • (3.29) This includes the prediction rk\k_i of the state, the Kalman gain matrix Gk, as well as the mea-surements Vk and matrix Ck which are known, all at iteration k. In order to calculate the prediction fk\k-i we can define rk\k-i = fk-i(rk-i\k-i) (3-30) which in this case is simply _ _ 2TT ab (a2 - b2) cos(8k-i - <j>) s in(4-i - <i>) N ib2 cos(^_1 - 4>)2 + a2 sin(0k-i ~ <t>)2f2 ' where 0k_i is given for each iteration as _ 2 7t(fc-l) ffk-i = ^ • (3.32) As part of the linearization procedure, the equivalent equations for (3.3) through (3.8) are 3.1 Vein Contour Extraction From Ultrasound Images 44 defined in general terms as fc|fe-i d/fc-l / A \ fc-i|fe-i [eac^ilfc-i (*fc-i|fe-i)] + ^k-iQk-i^k-iT Gk = Pk\k-x |§£(*fc|fc-i) iT ^ ( * f c i f c - i ) | pk\k-i |il£(*fc|fc-i) Rk Pk\k — I-Gk f§r(*fc|fc-i) pk\k-i where we have used the notation dfk-i ,~ \ dfk-i , . —\xk-\\k-\) = -zz—:—\xk-i\k-i) ^fc-iifc-i = ^ fe-iifc-i dxk-i\k-i dxk-i\k-i and the state Xk = rk for our case. In the specific case of the ellipse model, the Kalman filtering equations are simplified to Pk\k-l (3.33) (3.34) Gk Pk\k-1 + P-k (3.35) Pk\k-l — -Pfc-llfc-1 + Qk-1 (3.36) and Pk\k — (I — Gk) Pk\k-1 • (3.37) The only requirement now needed in order to implement the Kalman filtering process is to set the initial conditions. We may set P 0 | 0 = Var(ro) (3.38) and choose adequate values for Q and R. An additional system was implemented using equation (3.20) as the system in an extended 3.1 Vein Contour Extraction From Ultrasound Images 45 Kalman filter. The system was denned as (3.39) where we analytically obtained dr 36 e=ek b2 sm(6k-4>)\-rk cos(ek-<t>)+cos(4>)xo+sm(4>)yo}+q2 cos(ek-<t>)[rk sin(8k-<p)+s\n(<f>)x0-cos(4>)yo] / o An\ k b2 cos(0k-4>)[rk c o s ( 6 / f e - < £ ) - c o s ( # E 0 + s i n ( ^ ) y 0 ] + a 2 sin{6k-4>)[rk sm(ek-<t>)+sm(4>)x0-cos(4>)y0] V<J.W) where r has been substituted by r^, as part of the approximation. This results in a state-space description described by (3.28), to which we can also apply the extended Kalman filter in order to obtain a linearized system, and therefore estimate a contour as before. 3.1.3 Estimation of Parameters for Elliptical Contour Model A possible improvement of a feature detection algorithm has been presented in Section 3.1.2 which can be used to more accurately characterize the contour of a vessel presented in a transverse plane. This detection, though, relies on having knowledge of the model parameters, namely those in equation (3.24), in order to detect the feature. Since there is no fixed set of parameters that can describe all situations, a parameter estimation process is performed concurrently with the feature detection process, optimizing the feature detection. It is advantageous that a Kalman filter is used to detect the image feature, because the pa-rameter estimation can be included into this process. One application of extended Kalman filters is adaptive system identification which serves our purposes perfectly. By a straightforward lin-earization procedure, we may use our state-space model described by (3.26) with a few minor modifications, to further estimate the parameters of the ellipse equation within the same iteration cycle. 3.1 Vein Contour Extraction From Ultrasound Images 46 Suppose that we can describe our system as xk+1 = Ak(Q, xk) + rk(@)£k vk = C f c(0) xk + rjk (3-41) We assume that Ak(@, xk), Tk(&) and Ck(@) are all known matrix valued functions of some unknown constant vector 0 which we want to identify. In this specific case, we will use 0 as defined in equation (3.24), which is repeated here 0 = [ab<p]T All the parameters that describe the system are in 0 , and once identified could accurately describe our contour in a parametric manner. In order to estimate 0 , there are two requirements [17]. First, we must treat 0 as a random constant vector, such as that described by Gk+1 = ek + <;k (3.42) where Cfc is any zero-mean Gaussian white noise sequence uncorrelated with r}k and with preassigned positive definite variance Sk- The values chosen for Sk may be set as Sk = S > 0 (3.43) for all k. If we set Sk = 0 and thus consider the unknown constant vector 0 to be deterministic, then we will not be able to identify the vector 0 via the extended Kalman filtering procedure, as we will only obtain 0^ = 0fc-i for all k, independently of the measured data. We then rewrite our system (3.41) along with (3.42) as xk+\ Ak{&k, xk) + rfc(0fc) £*: = 0fc+l ®k sk vk = [Cfc(0fc) 0] xk 0 f c Vk (3.44) 3.1 Vein Contour Extraction From Ultrasound Images 47 in such a manner that the state vector of our system now also contains &k and its components. In this manner the system described by (3.41) is now represented by a non-linear model, and the extended Kalman filtering procedure can be applied to estimate the state vector and thereby obtain the estimate 0fc+i [17]. By substituting the values of xk and 0^, Ak(@k,Xk) can be written as Ak(@k, xk) = y/bk2 cos2(6»fc - (pk) + ak2 sin2(t?fe - 0fc) and for our particular case, equation (3.44) becomes (3.45) s/bk2 coS2(9fc-0fc)+afc2 sin2(9k-d)k) ak + ?i,fc — bk+i bk <?2,fc 4>k+i _ 4>k _ <?3,fc (3.46) and vk = [1 0 0 0] rk a-k bk <Pk Vk (3.47) It is now possible to apply the extended Kalman filtering procedure to this system and obtain an estimate Xk of the state vector, which includes 0^ and its components. We recall from the previous section that Xk indicates the state vector of the system, and that Xk indicates the estimate of the state vector at iteration k. The estimate can also be written as Xf.\k-, while xk\k-i is the prediction of the state for time step k. Both the notations Xk and xk\k are used interchangeably throughout. In general form, the estimated output can be written as [17] xk\k _ xk\k-\ ®felfe ©fclfc-1 Gk (vk - Ck(®k\k-i)xk\k-^j (3.48) 3.1 Vein Contour Extraction From Ultrasound Images 48 After substituting the values of our system then becomes ?k\k fk\k-i "fc|fc-i bk\k H\k-i _ <t>k\k-i Gk (vk~fk\k-i) (3.49) where Gk is a matrix of size 4 x 4 . It is known [17] that the Kalman gain Gk in the case of system identification is in general now calculated by using Gk = Pk\k-i Ck(&k\k-i) o Ck(®k\k-i) o] P f c | f c_! [Ck(&k\k-i) o] +Rk and the prediction covariance calculation is updated by Pk\k-l = Afc_l(0fc_l, Xfe - l ) 0 d & k - i A f c_i(0fe_i, xfc_i)] I Pk-1\fc-1 (3.50) Afc_i(0fc_i, xk-i) 0 Afc-i(0fc_i, J (3.51) rfc_i(6fc_i)Qfe_irfc_iT(6fc_i) o 0 Sfc-1 where we use the notation Ak-i(@k-i, xk-i) fc-i [Ak-i(®k-i, Xk-i)} (3.52) 3.1 Vein Contour Extraction From Ultrasound Images 49 It is evident from equation (3.51) that we must calculate d dBk-i [Afc_i(©fc_i, £fc-i)] ©fc-i = ©it (3.53) in order to proceed. Since we have previously denned Ak(@k, &k) m (3.45) for our specific case, and we know that we may generally calculate (3.53) as d [Afc_l(©fc-1, Xk-l) @k-i=e>k. d[Ak-i(®k-i,xk-i)] 9®l , f e - l 8 | i t - i ( 8 t - i , i t - i ) ] _ d{Ak-i(®k-i,Xk-i)) &k-i=®k-i ' 9@ 2 f c - i e fc_i=e fc_i > 9 @ 3 k-i efc_i=e, where the notation Q^k-i is used to indicate the ith element of ©fe- i , we can then substitute (3.45) into (3.53), using the correct indices and Xk-i = Xk-i, to obtain dAk-i(@k-i, Xk-i) dcik-i © * _ ! = © * _ ! 1 - — v ^ w ^ - ^ ) + a f c2 s in 2(0 f c -0 f c) V h * 2 c o s 2(^ - + a * 2 s i n 2 (^ - **) (3.54) dAk-\{®k-\, Xk-i) dbk-i efc_i=efc_i ak \Jbk2 cos2(Ok - 4>k) + ak2 sm2(6k - <pk) 1 -bk2cos2(ek - 4>k) bk2 cos2(9k - <pk) + ak2 sin2(0fc - cpk) (3.55) dAk-i{&k-i, Xfc - i ) d<j> fc-i O-k bk ( Q f c 2 ~ b f c 2 ) cos(et-0fc)sin(9fc-0fc) 6fc2 cos2(ek-(pk)+ak2 sm2(0k-cf)k) (3.56) We must also calculate P^*. to update the Kalman gain at each cycle. In order to initialize the 3.1 Vein Contour Extraction From Ultrasound Images 50 0|0 (3.57) filter, we can set r Var(x0) 0 0 S0 where Var(a;o) is the variance of the initial state xo, which is known, and So is the variance of the noise sequence, which is also known or can be assigned. In order to update Pk\k, which obviously at the next iteration will be Pk-i\k-i, we can use [17] Pk\k = [I -Gk [Ck(®k\k-i) 0]] Pk\k-i (3.58) which will provide the prediction covariance for the next cycle. The initial conditions of the state must also be set as x0 E(x0) do 00 (3.59) The predicted values xuk-i and ®k\k-i be calculated in a straightforward manner by evaluating [17] xk\k-l -Afc-l (®fc-l lfc-l> xk-l\k-l) ® f c l k - l ® f c - l l f c - l (3.60) and by substituting equations (3.45) and (3.24) into (3.60) we obtain °fc- i|fc- i frfc-i|fc-i rk\k-i "fe|fc-i bk\k-i 4>k\k-l 6fc_i | fc_i 2 cos 2(6» f c-0 f c_ 1| f c_ 1)+a f c_ 1| f c_ 1 2 s i n 2 ( 6 l f c - 0 f c _ 1 | f c _ i ) a f c - l | f e - l ° f c - l | f e - l <f>k-l\k-\ (3.61) Once we have defined our matrices, we can then perform the Kalman filtering process, and estimate values for our parameter vector as well. We can then easily reconstruct an ellipse based on the estimated parameters, and obtain measures such as area in an analytical manner. 3.1 Vein Contour Extraction From Ultrasound Images 51 The system defined by (3.39) and (3.40) was implemented and tested along with the parameter estimation. It was observed that except for cases that had very accurate initial conditions (the actual known parameter values) and small error covariance values, the system did not converge to the correct values, or did not converge at all. Also, for covariance values of £k a n d rjk greater than 0.5, the system became unstable and did not converge. Therefore, an alternate method for estimating the parameters (xo,yo) was implemented, which will be described below. Throughout the estimation process, there are several parameters that we can modify in order to obtain a better estimation. By modifying the values for the variance of the process and measurement noise Q and R, we can control how much the output will follow either the ellipse model or the measured edge points. By assuming a large R and therefore larger variance in the measurement, the output will follow the model. By assuming a large Q we assume that our process noise has large variance, and therefore we trust our measurements more which results in the output following the detected edge points. These are the most sensitive of our parameters. Other parameters that we may modify are the number of radii that are projected from the seed point, the number of iterations N as well as the maximum allowable search radius. The processing time is directly proportional to all of these parameters. An in-depth exploration of the maximum allowable search radius is presented in the following chapter. 3.1.4 Estimation of Ellipse Center By implementing the contour detection described above, we will obtain the values of the pa-rameters a, b, and <j>. But in order to completely characterize an ellipse anywhere in the plane we also need a value for the location of the center of the ellipse, (XQ, J/O )• Since integrating equation (3.19) into a linear system did not produce desirable results, we must find another solution. One iteration of the extended Kalman filter for estimating the parameters of an ellipse consists of computing the Kalman equations that have been derived in the previous sections N times, where N is the number of points that we use to describe our closed curve. In order for our filter to converge, several iterations are typically needed. 3.1 Vein Contour Extraction From Ultrasound Images 52 The center coordinates of the ellipse can be estimated by updating the original seed point at each iteration. When we have finished an iteration, we will have N points that correspond to the currently detected edge. From these points, we can easily calculate a center of mass, by simply averaging the (x, y) coordinates of the JV points. These new points can then be combined with the center or seed point that was used at the beginning of the iteration, in order to create a new seed or center point. In this manner, at the end of each iteration of the extended Kalman filter, a new seed point is calculated. This approach was implemented, and it was observed that the center of the ellipse converged to the true center. The method used to combine the newly calculated center of mass and the previous seed point at each iteration was simply an averaging function, although other schemes can also be implemented. 3.1.5 Edge Detector Selection We now have a contour detection algorithm that uses an ellipse as a model for the detected boundary. There is still one matter to deal with, though. We must have measurement values vk for each k in order to calculate the predicted output. An edge detection function was presented in Section 3.1.1 and can be implemented by modifying (3.49) as follows . f^c|fc ^fc|fe-i Ofc|fc _ &k\k-l °k\k °k\k_i _ 4>k\k J L 4>k\k-l including in this manner the implementation of the probabilistic data association filter (3.11) in our parameter estimation scheme. This is possible because the model does not influence the manner in which the measurements are obtained. We expect that there will always be an error when using one measurement to describe an edge, especially with ultrasound images. By using the values obtained from an edge function, as is the case with the probabilistic data association filter, the location of the edge will be approximated in a better fashion. It is for this reason that we incorporate it into our extended Kalman filter, by + Gk {yk) , (3.62) 3.1 Vein Contour Extraction From Ultrasound Images 53 using (3.62). Even so, there are several options [38] that we can choose from in order to obtain an edge function that will most accurately describe the edge in our image. Several tests were performed for the purpose of selecting the best possible edge detection function Fedge (pi,k) (3-63) for our system. As mentioned above, the magnitude of the edge is calculated simply as the gradient in the radial direction in [2]. This seems the most common edge detection technique in ultrasound [32,34,54,68]. Because of the nature of ultrasound images, the presence of speckle is expected to influence the gradient in that the edge location may not correspond to the location of the highest gradient. The negative effect of speckle can somewhat be reduced by smoothing the image [32,69] using different low-pass filters. Edge x Location / 1 (x0, y0) 1 r Figure 3.2: 5x3 Smoothing Kernel The effect of smoothing using Gaussian and averaging filters, removal of outliers and curve fitting on the edge detection function (3.63) were investigated. Two sets of simulated images were generated for this purpose. One set consisted of images generated using the ellipse function (3.18) and adding preset brightness offsets and Gaussian and random noise. The other set consisted of simulated ultrasound images, generated using the Field II© package [48]. The images consisted of elliptically shaped cysts, very similar to vessel cross -sections. The ellipses in this second set were also generated according to the function (3.18), and 3.1 Vein Contour Extraction From Ultrasound Images 54 therefore the 'true' edge location in all images was known. The effect of smoothing on edge detection was observed by applying 3x1 and 5x1 normalized Gaussian kernels, as well as smoothing using an average filter using the same sizes, and then calculating the gradient as defined in (3.10). An alternative smoothing procedure using a kernel of size 3 x 5 , for both Gaussian and average filters, was used. This smoothing filter included pixels that were perpendicular to the radial direction, as well as pixel values along it, in order to include more pixels possibly located on an edge, as presented schematically in Figure 3.2. In order to perform outlier removal, two types of filters were implemented. A median filter was implemented that used 5 consecutive pixels along the radial direction, which returned the value of the statistical median. Additionally, a filter that returned the average pixel value from a maximum neighborhood of 5 pixels was implemented. An initial mean and standard deviation were calculated from the brightness values, and pixels were classified as valid if that pixel had a brightness value that was within one standard deviation of the mean. All resulting valid pixels were then used to calculate an average. The gradient was then calculated on the resulting pixel values for both cases in preparation for the edge detection as described below. Table 3.1: Characterization of Various Edge Detectors Edge Detector Number in Figure No Smoothing 1 Curve Fitting 2 Median Filter 3 Outlier Removal 4 3 x 1 Gaussian 5 5 x 1 Gaussian 6 3 x 1 Average 7 5 x 1 Average 8 3 x 5 Average 9 3 x 5 Gaussian 10 A final method was implemented by using a least squares approach to fit a first order curve to a neighborhood of 5 pixels in the radial direction. For each pixel location the slope of the resulting curve was saved, in this manner constructing a map of the derivatives of the curves for all candidate pixel locations, which can be interpreted as the gradient in the radial direction. 3.1 Vein Contour Extraction From Ultrasound Images 55 300 250 ® 200 o l5 150 -o CD i 03 | "100 c CD CD 50 - * - Maximum — Threshold (Max - min)/2 - Threshold Max/2 O PDAF \ \ \ \ / \ / \ 1 1 1 \ 1 1 1 1 / / \ \ \ \ \ - - _ _ - - -N N N / / / / / / • sfr . — — — ® $ _J L_ _ l I I I I L_ 3 4 5 6 7 Edge Detection Algorithms 10 Figure 3.3: Average Errors for Several Edge Detectors on Image with Gaussian Noise For each of the aforementioned algorithms, a set of error measures were generated to evaluate their performance, using edges defined in three different ways. The error measures were generated by summing the squared distance from the detected edge to the actual edge location for each method. The first edge detection method consisted of taking the maximum gradient as the location of the edge. The location of the maximum slope was used for the curve fitting method. The second and third consisted of defining a threshold for the gradient value. The first pixel with a value above the threshold was then selected to be the edge location, starting from the center of the feature. The threshold for the second edge was set as half the difference between the maximum and minimum values of the gradient, or _, , maxGradient — minGradient , „ „ , v Threshold = (3.64) where maxGradient is the maximum value of the gradient, and minGradient is the minimum 3.1 Vein Contour Extraction From Ultrasound Images 56 10r Figure 3.4: Expanded View of Average Errors for Several Edge Detectors on Image with Gaussian Noise value of the gradient. The threshold for the third error measure was defined as half the value of the maximum gradient, or ™, , , , maxGradient .„ Threshold = (3.65) where the quantities are the same as defined above. It should be mentioned that the edge that we want to detect will produce a positive gradient value. We are assuming that the center point is within the feature, and we will search outwards. Generally, the pixel values within the vessel will have a lower brightness level than those outside, and will therefore produce a positive gradient. A negative gradient value will be produced when the pixel brightness values are high, and they become lower as we travel in the radial direction. This also holds for the values of the slopes of the fitted curves for the curve fitting method. Additionally, an error measure using a probabilistic data association filter (PDAF) as defined by (3.11) to find the edge location was also implemented. The true location of the edge was used 3.1 Vein Contour Extraction From Ultrasound Images 57 Figure 3.5: Average Errors for Several Edge Detectors on Simulated Ultrasound Image as the estimated value r f c | f c _ 1 in (3.13) and the edge was assumed to have a constant Sk = 5, also needed for (3.13). For each radius, an error value was then obtained. These values were squared and averaged, in this manner obtaining a value analogous to the mean squared error value of the previous measures. Figures 3.3 through 3.5 show the results of applying the edge detectors to the two different sets of images. In each figure, the methods by which the image was processed are numbered as listed in Table 3.1. In these figures, the four different error measures (maximum gradient, threshold gradient using (3.64), threshold gradient using (3.65), and error obtained using PDAF as edge detector) generated as described above are plotted. In Figures 3.3 and 3.4, it can be observed that the best results are obtained when using the maximum gradient value and when applying the probabilistic data association filter because the mean squared error values obtained are much smaller for these edge detectors. Figure 3.4 shows an expanded view of Figure 3.3 where these small error values are presented in more detail. When using a threshold to select the edge location, large errors appear. Even so, it can be seen that most 3.1 Vein Contour Extraction From Ultrasound Images 58 of the edge detection schemes do not greatly affect the error, except when using the larger Gaussian and average smoothing kernels. It can also be observed that the smallest error is obtained when the edge is detected using the curve fitting method (edge detector #2). Similar observations can be made for Figure 3.5, with the exception that defining the edge location by using the maximum gradient now has an error much larger than when using the PDAF. An interesting thing to note is that when using the line fitting method the errors increase when using the maximum gradient or the PDAF, but decrease when the thresholding methods are used to determine the location of the edge. It can be observed that, in general, the algorithms that include the probabilistic data association filter (3.11) generally perform better than those that do not, i.e., the error between the actual edge location and the detected edge location are the smallest. Also, it can be seen that with the exception of the line fitting method, there is no substantial difference between which method is used to define edge location, especially when using the PDAF. The most useful filters for this case are the median filter and the 5 x 1 average filter, as these are the ones that presented the least error. Therefore, the PDAF was implemented for our system, using either a median filter or an average filter for smoothing the image before the edge detection. 3.1.6 Contour Validation Once a vessel contour has been detected, it must be validated in order to undergo further processing. The identification of DVT revolves around correctly identifying the vessel contours in order to assess the results of a compression examination, so we must be certain that the detected contours are valid. The validation is done in the following manner. It can be stated that the feature extraction algorithm presented here returns two important pieces of information. The first is a list of points fk of length N, which describe the detected contour as the radial distance from the initial seed point xc,yc at an angle Ok = 2 TT k/N with respect to the image plane. The second is a set of parameters 0 which describe an ellipse that optimally fits the detected contour in a least squares sense. From the list ?k we can obtain a new center point x™ew , y™ew by computing the average 3.1 Vein Contour Extraction From Ultrasound Images 59 coordinate of the detected contour rnew _ Y.k=\ xk .new _ Ylk=l Vk (3.66) b c ~ N ' Vc ~ N v ' where xk = rkcos9k + xc , yk = fksm6k + yc (3-67) have been previously calculated, for k from 1 to N. Additionally, using the estimated parameters 0 along with x^ew , y™ew from (3.66), we can now calculate the location of the contour represented by the estimated ellipse. The center of the ellipse can be set to be located at x™ew , y^ewand the parametric ellipse equation (3.18) in polar coordinates, modified to use the estimated parameters as follows & h (3.68) \Jb2 cos(0 - ct>)2 + a2 sin(0 - 0) 2 can be used to calculate r. We can now generate an error measure by using the mean squared distance from each detected point xk,yk to the corresponding point on the curve of the ellipse that is described by the estimated parameters. This can be written as E r r o r = EE* (** -*? + (fo - yf . ( 3 . 6 9 ) where x and y are calculated using equation (3.68) by setting 0 = tan"1 (~ y™W) (3.70) and then converting r to Cartesian coordinates by x = rcos6 + xncew , y = rsin(9 + y™w • (3-71) The result is a measure that gives a degree of reliability to the detected contour because we are quantifying the error or distance between the detected contour point, and the corresponding point 3.1 Vein Contour Extraction From Ultrasound Images 60 on the estimated ellipse, as illustrated in Figure 2.3. Since it is assumed that a vessel's contour can be represented by an elliptical model, large deviations from this model would indicate that the detected contour is incorrect. Smaller values resulting from equation (3.69) would indicate that the contour is more elliptical and therefore can be used for processing in order to obtain a diagnosis. Since there will always be exceptions to the rule, it is possible that even though a contour receives a higher error value from (3.69) the detected contour is still accurate. This can be overcome by an adequate selection of the error cut-off value or threshold. Any contour that deviates from the ellipse generated by the estimated parameters by more than the threshold value will not be used for processing. Alternate measures such as the curvature of the detected contour can also help indicate the validity of a detected contour. It is known that a vessel contour will in general have lower values of curvature along its contour and if a region of a contour has a large curvature, indicating that sections of the contour may be 'jagged', the contour can be discarded. It has been found through experimentation that a threshold value of 10 - 20% of the maximum radial search distance (Rmax) is appropriate, this is if the mean squared error between the detected contour rk and the ellipse generated by 0 and calculated using 3.69 is more that 0.2 • Rmax, that contour will not be used. The average error values obtained for several ellipse estimations (approximately 100) are presented in Table 3.2. The contour detection algorithm was executed, and the resulting contour was evaluated to see if the estimation was accurate. When the parameter estimation was good the average error, presented as a percentage of the maximum search distance Rmax, was low. However, when the estimation was not accurate, the error measure generated was large. Table 3.2: Ellipse Estimation Accuracy based on Error Measure Average Error Value Estimation accurate ? 6.01% Rmax Yes 39.64% Rmax No The parameter settings for the generation of the ultrasound image will affect the contour de-tection, and therefore the error validation. The ultrasound gain settings will be the ones that most affect the contour detection. Higher settings will provide stronger signals from the vessel lumen, 3.1 Vein Contour Extraction From Ultrasound Images 61 but may also increase the speckle of the surrounding tissue and generate false edge locations. The imaging depth also has a large influence on the detected contour because of the attenuation of the ultrasound beam. Other settings such as focal point (s) will not have such a large impact on the output. There are several situations where this validation scheme will fail. The current system does not handle branching vessels and therefore the contours detected in these situations may not be identified as two separate vessels, and they will not be validated. Also we may have problems at any location where another anatomical structure is present that looks like vessels on a transverse plane, especially if the boundaries on the ultrasound image are not clear throughout because of, for example, shadowing or because the structures are parallel to the incident ultrasound beam. In these cases, since the complete edge is not visible, the detected contour may 'jump around' the image even though the probe is not being moved. Regions with high brightness values close to the vessel in the ultrasound image may also cause errors by generating large signals that indicate a strong edge at locations far away from the actual feature. There are two options once a contour has been discarded. The contour detection algorithm can be executed again with a slight modification of input parameters, namely reducing the maximum search radius2, or if the algorithm has failed a successive number of iterations to accurately detect a contour, the user can be informed that a new image or probe location is needed for detecting the vein contour. An additional validation step can be implemented by using information from the previously detected contour. For the general case it can be assumed that the change from one ultrasound image frame to the next will be minimal. Therefore, the change in the detected contour should also be minimal. If the difference of the values of the detected parameters of the previous contour from the values generated by the contour that we are validating are greater than a specified threshold, then we can discard the current contour. We can write this as €>,_! - <=>,• > Thresholde (3.72) 2Reducing the search radius improves contour detection, as long as the complete vessel contour remains inside the search area, as is presented below. 3.1 Vein Contour Extraction From Ultrasound Images 62 where Qj-i represents the parameters from the previous contour, ©.,• are the parameters from the currently detected contour that we want to validate, and Threshold^ are the threshold values for each parameter. We can define Threshold^ as a fraction of the maximum value allowable for each parameter. Thus, we now have a manner in which to verify our contour detection algorithm. This verifica-tion method is independent of the image brightness values, and does not need to be modified every time an ultrasound technician changes the brightness settings of the equipment. This is a great advantage compared to, for example, a verification method based on measuring the average pixel brightness within a detected contour. 3.1.7 Variation of the Search Area Generally in feature detection applications, it is reasonable to assume that by constraining the search area to the smallest possible region, while still containing the image feature to be detected in its entirety, the resulting match will be more accurate. This is because structures in the image belonging to other objects that we do not want to detect will not be included in a smaller region. In this manner, image forces will only arise from the feature that we want to detect, and therefore the detection itself will be better. Additionally, in this particular application, the size of our features will be changing constantly, as veins will vary in size throughout a single compression-release cycle, as well as throughout the lower limb. It is therefore necessary to investigate the effect of the maximum search area with relation to the size of the feature. Since we don't know what the size of the vein that will be detected is beforehand, we must make sure that our system can deal with vessels of different sizes. A scheme was devised as follows in order to provide accurate contour detection for large and small vessels. • When a seed point is selected, set a predefined initial MaxR value for the maximum radial search distance. An example of a predefined value for MaxR is the value of MaxR from a previous correctly detected contour, plus an increment. • Execute the feature detection algorithm. 3.1 Vein Contour Extraction From Ultrasound Images 63 • Analyze the error value, as presented in Section 3.1.6. If the error is less than the specified threshold, return an indicator of successful completion along with the detected contour. If the error is greater than the specified threshold, decrease the search distance by a predefined step, and repeat second and third steps. • If the search distance is less than a minimum predefined value, indicate an unsuccessful completion of the feature detection algorithm. This process will always start out with a large search area, and work its way down to find the correct contour. The initial increment in the first step would permit an adequate detection when the area is getting larger over several image frames, while the repeated reductions in search-area would allow a smaller area to be detected. In this manner, an appropriate value for the maximum radial search distance will be used for vessels of different sizes. See Section 4.2 for details on the validation of this process. 3.1.8 Propagation of Information over Image Frames In an image sequence in our application, it can be assumed that two consecutive image frames will be very similar to each other, unless a drastic movement occurs. Therefore, propagating information from one frame to the next can prove very useful, especially for setting initial conditions for our contour detection algorithm. For setting the initial conditions in the next image it is a simple matter of using the estimated ellipse parameters 0 from the previous image for the contour detection algorithm. It will be assumed that there is not a large variation of the shape of the vessel between images. What may vary more drastically though is the center or seed point for the ellipse, for which we use a more complex solution. If we assume that the seed point varies from image to image by a constant velocity, we can 3.1 Vein Contour Extraction From Ultrasound Images 64 write X fc+i where the state is defined by 1 At 0 1 zk = [i o] xk + 4>k Xk = [xk xfc] Xk + £fc (3.73) (3.74) and Xk is the position (x, y) of the seed point, x*, is the velocity of the seed point, and A i is the time-step. We now have a linear system that describes the movement of the seed point, and it is known [17] that we can implement a Kalman filter to estimate the location of the seed in the next frame, using the estimated seed from the previous frame as the measurement vk. 3.1.9 Summary of Image Processing Procedure A flow chart describing the general operation of the algorithm can be found in Figure 3.6. One contour detection cycle will be briefly overviewed. The system starts by acquiring the necessary data, in this case an image, location and force measurements. The contour detection algorithm is initialized by setting a predefined maximum search radius Rmax, and setting the initial values of the extended Kalman filter accordingly. The contour detection is then performed for a predefined number of iterations. From the resulting edge points f and parameters 0 , an error measure is generated as described above, and a decision is taken on whether the contour is valid or not. If the contour is not valid, and Rmax has not reached its minimum value, the contour detection algorithm is repeated. If Rmax has already reached its minimum value, a 'Contour Not Valid' message is returned, and the system moves on to the next image. If the contour is valid, the image coordinates are transformed to world coordinates as described below, and a decision is made on how to use the detected contour. If the force value for this specific image is above a predefined threshold, the contour will be used to characterize the compressibility of the location being examined. If the force is not above the 3.1 Vein Contour Extraction From Ultrasound Images 65 Start Acquire Image Location, Force Reduce Rmax Yes Input Seed Initialize Rmax a = b = r0= Rmax/2 7 = 0 Execute Contour Detection ( 1 ) a, b, y, rk Calculate Error Measure Yes Transform Contour to World Contour NOT Detected Build Vein Model Do Compression Exam Processing Figure 3.6: System Flowchart 3.2 Force, Position and Orientation Sensing 66 threshold, the contour will be used for the three-dimensional model to be displayed. Alternately, a flag may be set by the user to indicate whether to use contours for characterizing the compressibility or for building the virtual model. The alternate method was implemented in our system, so that the user indicated the destination of the detected contours by clicking a button on the user interface. Values of 0.3 to 1 N were used for the predefined force threshold for testing purposes, obtained from trial and error. The system then moves on to the next set of data. 3.2 Force, Position and Orientation Sensing The previous section describes a method for obtaining and validating a vessel contour. Now these vessel contours must be ordered in order to obtain useful information from them. What is important to us is where the contour was detected, and also how hard the probe was being pressed against the patient when the contour was detected. 3.2.1 Position and Orientation Sensing As was mentioned before, there are several methods to obtain a measurement of where a tool is located in space, as well as how it is oriented in that space. For our application a 6 degree-of-freedom (DOF) electromagnetic position and orientation sensor is used (PCIBird, Ascension Technology Corporation [18]). The position and orientation in space of any object can be represented by a 4 x 4 transformation matrix such as M R T 0 1 i?l l R 1 2 R 1 3 Tx P-21 R 2 2 R 2 3 Ty F-31 R 3 2 R 3 3 Tz 0 0 0 1 (3.75) where Tx, Ty, and Tz are the translations along the x, y, and z axes, respectively, of a reference frame Fw and the 3 x 3 matrix R describes the rotations about the x, y, and z axes. 3.2 Force, Position and Orientation Sensing 67 The above mentioned position sensor provides us with the values of matrix M in equation (3.75) that permit us to locate the receiver with respect to the emitter. In this case, the reference frame Fw is centered within the emitter. Additionally, the receiver must be fixed to the ultrasound probe(s) that will be used for the system. Because of our implementation constraints, the sensor is not located exactly where the image is generated, nor is it aligned with the image plane. Therefore, a secondary transformation must be included to convert all points x, y located in the image plane to points described within the reference frame Fw. In this manner, any point x, y located on the acquired image plane will have x, y, z coordinates x" M™ M? xl 0 1 0 1 (3.76) where x" XW y W ^ 0 i T xl y% z% 0 (3.77) (3.78) and Ml represents the transformation between image frame and sensor frame, and M™ is the transformation between the sensor frame and the reference or world frame Fw. In general, z1 = 0, as an image is information represented in two dimensions. As mentioned before, all the values of Mf are obtained directly from the electromagnetic sensor at each iteration, and do not need to undergo further processing. The values for Mf are constant, and depend on the configuration of the sensor with respect to the ultrasound probe. Based on the method described in [72], our ultrasound system was calibrated using a custom built calibration phantom. As a result of this calibration we obtained the values for Ml, which were combined with 3.2 Force, Position and Orientation Sensing 68 values obtained by measuring the setup, and result in the transformation 0.0 -1.0 Rl3 20.1419 1.0 0.0 # 2 3 -1.9203 (3.79) 0.0 0.0 -R33 3.1809 0 0 0 1 where it should be noted that .R13, R23 and R33 may take arbitrary values because zi = 0, as mentioned before. It should also be noted that these values of Ml are specific to a certain configuration of the ultrasound machine, depending specifically on the size of the region that is being imaged. In our case, our 2-D ultrasound image is approximately 5 cm x 3.7 cm. If any settings affecting the size of the region of interest are modified, a new transformation matrix must be obtained. An additional scaling factor must also be included in order to obtain image coordinates in appropriate units, in this case, millimeters. The scaling factor is 10 pixels per millimeter. This value was obtained using a measuring tool available with the ultrasound machine being used. Several measurements were taken where values were given in millimeters, and then the number of pixels for each measurement were counted. The scaling factor was obtained in this manner. A very important assumption was made, and that was that the on-screen ultrasound measuring tool was accurate. Therefore, during each iteration, a set of values that will compose Mf is read from the position sensor, and xw is computed using (3.76) for each estimated contour point ffc. In this manner, fk can be described in frame Fw for all k, and a succession of detected vein contours can be used to build a three dimensional representation of the scanned vein. 3.2.2 Force Sensing The pressure exerted by a technician through an ultrasound probe during a compression exam is approximately 0.2 psi [19,20,98], for a normal individual in the thigh area. It is expected that this value will vary greatly, depending on the physical characteristics of the person examined. For example, the force needed to completely compress a healthy femoral vein at mid-thigh is expected 3.2 Force, Position and Orientation Sensing 69 to be greater than the force needed to completely compress a healthy popliteal vein in the popliteal fossa because of the greater depth of the femoral vein, and therefore greater amount of tissue between the vein and the ultrasound probe. Also, the build of the individual being examined, say thin, regular or heavy-set, will also affect the amount of force needed because of varying amounts of tissue present between the probe and the vein being examined. Another factor that may influence the amount of force applied through the probe is swelling or edema, because of increased internal pressure. In all cases though, we are interested in the force applied axially through the probe. A force-torque sensor (Nano25 SI-125-3, ATI Industrial Automation, Inc.) is used with a novel ultrasound probe shell in order to measure the amount of applied pressure. Additionally, the position and orientation sensor is also fixed to the shell. Table 3.3 shows the full-scale loads for the force-torque sensor. Table 3.3: Full-Scale Loads - Nano25 Fx (N) Fy (N) Fz(N) Tx (N-m) Ty (N-m) Tz (N-m) 125 125 500 3 3 3 The novel force transducer comprises two shells that surround the ultrasound probe. The interior shell is fixed to the ultrasound probe itself, in such a manner that there is ideally no movement or deflection between the probe and this inner shell. A second shell encases both the ultrasound probe and the inner shell to which it is attached at the rear, or opposite end from which the ultrasound images are acquired. Both shells are connected through the 6 DOF force-torque sensor at the rear of the casings. Both shells combined add approximately 70 grams and increase the size of the ultrasound probe by a few millimeters. The interior of the ultrasound probe is not modified in any way, nor is its structural integrity. The force-torque sensor is read by a 16-bit resolution data acquisition card (PCI-6034E, National Instruments Corporation), capable of obtaining a maximum throughput of 28.5 K datasets per sec-ond. The location is obtained using an electromagnetic sensor (PCIBird, Ascension Technology Corporation), capable of providing up to 105 measurements per second. The sensor specifications characterize the static resolution as 0.5 mm for the position measurements and 0.1 degree for the angular measurements, with an accuracy of 1.8 mm and 0.5 degrees for position and orientation, 3.2 Force, Position and Orientation Sensing 70 respectively. Our ultrasound image resolution is approximately 0.2 - 0.3 mm, almost twice that of the location sensor. This will create some ambiguity about the location of a 0.1 mm feature, and therefore be a source of error when deciding the location of a vessel. Since we are not inter-ested in locating the vessel with respect to a fixed reference frame, the accuracy for the position measurements will not affect our models as much as the resolution. The examining technician takes hold of the outer shell as he or she would in a regular exami-nation and caries out a compression exam in a regular manner. Figure 3.7: Ultrasound Force Transducer Since the outer shell is held by the examiner, and not the probe itself, all the force applied is transferred through the outer shell to the inner shell through the force torque sensor, and in this manner the applied force can be measured. The data acquisition card is used to read the sensor, and can be read during the time that each image is acquired, as well as each position and orientation measurement. This way, a force reading can be matched to a detected contour, once the acquired image has been processed. 3.3 User Interface 71 3.3 User Interface The current system differs from a conventional compression ultrasound examination in that much more concrete information is acquired, namely the force, position and orientation measure-ments, as well as the possibility of saving a larger amount of image data. In order to obtain benefits from this increase in amount of information a proper method of display must then be developed. The user interface includes three specific advances for displaying our data. Firstly, a 3D topo-graphical vein model is constructed based on the detected vein contours, which shows the general geometry of the vein. Secondly, the vein is displayed as a 3D object, along with a representation of the image plane in the correct location and orientation, as well as a similar representation of the ultrasound probe itself. And lastly, the colour of the surface of the three-dimensional vein model is mapped according to the amount of vessel compression that was attained for a specific segment, translating the numerous detected contours along with the associated pressure, position and orientation measurements into a simple, intuitive representation that indicates the results of a compression ultrasound examination. 3.3.1 Vein Model Construction The process for building the three dimensional vein model from the detected contours, as well as the position and orientation measurements, is relatively straightforward. Once a contour has been validated, an additional decision must be made before it is included into the vein model. The force reading that was acquired for the frame from which the contour came must be analyzed. A threshold is set in order to identify contours that correspond to model measurements and those that correspond to force measurements. Model measurements are the contours that were extracted from images obtained under minimal compression of the vessels. These contours are representative of what the transverse vessel section would be with no force applied, and therefore in a normal state. These detected contours are the ones that will be used to build the model, as well as for assessing a location by means of a compression examination. 3.3 User Interface 72 Figure 3.8: Raw Contour Data in World Frame Figure 3.9: Surface Mesh Once a contour has been tagged as a model measurement, the location of each of the estimated contour points fk are converted to world frame by using equation (3.76), and are stored in a list. Once two contours have been detected, the three dimensional vein model construction can begin. Each point now represents a vertex in a three dimensional structure, and several methods can be used to generate a polygonal mesh, which will represent the surface of the vein model. Any appropriate method can be used for this purpose, such as fitting a surface to a point set or simply using the detected points in 3D as vertices for polygons. A default initial color is assigned to each 3.3 User Interface 73 section of surface. When a contour is detected and is labeled as a force measurement, a different process takes place. In this case, the information that is stored corresponds to the detected parameters © , as well as the resulting seed point x™ew, y™ew and the transformation Mf for that specific contour. Additionally, the detected boundary as well as the image frame, partially or completely, can be stored for review at a later time. This information will be used for assessing the results of a compression examination. 3.3.2 Compression Examination Assessment The main objective of this system is to adequately assess a vein for compression. The data collected is now processed for this purpose. In general, the data labeled as force measurements is used to determine the compressibility of a vessel segment. In order to this, all force contours must be divided into groups of measurements taken at the 'same location.' Afterwards, we can obtain several measures of compressibility, such as the Transverse Area Ratio, presented below. Let E be the complete set of detected contours Ci of a given examination, so that E (3.80) where N is the number of detected contours in the set. Initially E is an empty set, i.e. N = 0, and as images are processed along with the force, position and orientation measurements, this set grows. Now, let C be subset of E, or C C E (3.81) comprising all contours that have center points xnew, y™ew within a volume in world frame of predefined size, or in other words, a volume in world frame where no center point of one contour within that volume has a distance to any other center point within that same volume greater than a specific amount, MaxDistance. This can be written as \J(xJ - xj+l)2 + (yV - yj+l)2 < MaxDistance (3.82) 3.3 User Interface 74 where x™, yj is the center point of a detected contour in world frame and xj+1, yf+i is an additional center point of another detected contour, within the same set C. This is shown schematically in Figure 3.10. Alternately, a user can toggle between using contours for force measurements and model measurements, as stated in Section 3.1.9. MaxDistance was chosen by trial and error taking into account our sensor resolution, so that all detected contours from one compression-release cycle would be grouped together. It is intended that any detected contours from adjacent compression-release cycles would be organized into a separate group. A value of 10 mm was used for MaxDistance during testing, but the alternate method where the user manually toggles between force and model measurements was implemented. Figure 3.10: Maximum Distance Between Contours Each set C must have a minimum number of elements in order to be processed, which must be greater than MinContours, or N > MinContours (3.83) where N is typically larger than 8. Another requirement is that two contours within the subset C have a minimum force difference, 3.3 User Interface 75 between the element of the set with lowest force as read by the force-torque sensor, and the element with the highest force. Suppose that the element c\ is that which has the highest force in subset Ci, and C2 has the lowest force, where ForceCi represents the force measurement for the element Ci, this last requirement can be expressed as {ci,c2}eCi maxForce = Forcecl , minForce = ForceC2 (3.84) maxForce — minForce > MinForceDif ference and this will ensure that an adequate compression examination has taken place. By ensuring that there is a minimum force difference between two images within a set C, it can be veri-fied if a compression examination has been performed correctly. A value of 3 N was used for MinForceDif ference, but this value may need to vary depending on the build and region of the patient being examined. An additional measure using the force data can be implemented in order to insure a correct examination. During a compression examination the maximum force applied at one location is expected to be very similar in magnitude to the maximum force applied at an adjacent location. We can therefore compare the maximum values of the force applied to adjacent locations and generate another measure to determine whether or not we have the data necessary for a correct compression examination. If the current maximum force value, plus a predetermined constant to account for variations from one location to another, is less than the maximum force measurement at an adjacent location, then we do not have a complete compression examination. We can express this as maxForcej + constant > maxForcej-i (3.85) where maxForcej is the current maximum force value, maxForcej-i is the maximum force value of a directly adjacent location, and constant is a predefined constant such as 10 - 15% of the maximum force allowable, also chosen by trial and error. Once a subset C is generated with A?" > MinContours detected contours, while at the same time there is a force difference of at least MinForceDif ference between two elements of C and 3.3 User Interface 76 the condition stated in (3.85) is met, then the area of each detected contour can be approximated by Area = TT a b (3.86) by using the parameters 0 . All the area values for a volume are computed and stored, and a final ratio is generated as Transverse Area Ratio = — (3.87) jweajxitxx where Areamin is the minimum value of area within the subset, and Areamax is the maximum area within the same subset C. The value for Areamax can be obtained from the contour within the set C that was used to generate a section of the model. Figure 3.11 shows the compression assessment flowchart. The Transverse Area Ratio or TAR is a concrete measure of the outcome of the compression examination. It indicates to what percentage of the original transverse area of the vein is reduced to when compression is applied. This value, along with the measurement of the applied force can help indicate the presence of DVT. A high TAR value would indicate less reduction in transverse area, and therefore an indication of higher probability of deep venous thrombosis. A final procedure can be used in order to classify and distinguish healthy and diseased veins. For each location area and force measurements are obtained, which are then normalized using the maximum values for that location. This data can be arranged in a two dimensional space, which maps force vs. area. We can then obtain a set of points to which we can fit a first order curve in the least-squares sense, which will represent the compressibility of the examined vessel at a specific location. We approximate our data by y = m x + b or (3-88) area = m force + b where the value of ra, or slope, will indicate the compressibility. When m « 0, it is an indication of almost no compression of the vein, and when m < — 1 then we have an indication of a properly compressed vein. Figure 3.12 illustrates two generated data sets, one representing a healthy vein 3.3 User Interface 77 Figure 3.11: Flowchart of the Compression Examination Assessment 3.3 User Interface 78 and one representing a diseased vessel. For this Figure, m = —0.8036 for the healthy data set and m = —0.0070 for the diseased data set. 0.9 0.8 30.7 0.6 TO e I 0.5 0.4 0.3 0.2 Approx Curve Healthy Approx Curve Diseased Healthy Vein Diseased Vein 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Normalized Force Figure 3.12: Normalized Force vs. Normalized Area By observing the change of m over several locations, we can use the force and detected area information to indicate the presence of DVT. This measure will also give us more information on the compressibility of the region being examined, as opposed to simply the result presented by the TAR. The results of a compression examination can therefore be interpreted through the Transverse Area Ratio, and this information is mapped to the surface of the generated vein model and displayed as a color. Alternately, we can map the slope information from (3.88) to the constructed vein model, instead of using simply the TAR. In this way, a color scheme can be selected so that one color, such as green, can represent a healthy vein, while another color, such as red, represents a vein with high probability of DVT. Intermediate colors can be used in order to indicate inappropriate or incomplete examinations. There are many ways in which the additional information that has been acquired can be dis-played. Aside from the images that are acquired for a normal compression ultrasound examination, we now have the position and orientation of each of the images in a three dimensional space, the force applied at each images, and a set of extracted contour points for each frame. 3.3 User Interface 79 Additionally, as described above, the information is processed in order to obtain measures such as the Transverse Area Ratio or TAR, as well as a characterization of the applied force vs. detected area. It has been suggested that the TAR or the applied force vs. detected area be mapped to the constructed vessel model in order to be displayed. This need not be the manner in which the information is conveyed to the user. A more extensive and detailed output can be presented to the user, describing the exact force applied or range of forces, or an image sequence with the overlaid detected area. Indeed, all this information is stored and will provide a very accurate picture of the venous system of the patient. 3.3.3 Displaying Virtual Objects The user interface comprises two basic displays. The first is similar to a conventional ultrasound display, where a standard two dimensional ultrasound image is displayed. The examiner can view the generated image in the same manner as he or she would regularly do. The other display presents a virtual environment, where several objects can be represented. Two of these objects always appear, while others may be added. A representation of the ultrasound image plane is displayed in the correct perspective, position and orientation. On this image plane, the current frame that is being displayed on the first display is presented, or simply the image area that corresponds to the observed anatomy. The plane is idealized as an infinitely thin plane only for display purposes, as the actual ultrasound beam does have a specific thickness perpendicular to the image plane. Additionally, a representation of the ultrasound probe is also presented, in relation to the image plane, so that it appears that the image is at the tip of the ultrasound probe. Both the plane and the probe are updated as the real ultrasound probe is moved through space using the electromagnetic sensor measurements. In this manner, the virtual environment mimics the actual workspace, with one benefit being that the image plane can actually be seen with respect to the probe. Other virtual objects may appear, namely vein models that have been reconstructed using the extracted contours from the various image planes. The vein models also appear in correct relation to both the probe and image plane, permitting the user to easily locate a vein once a model has 3.4 Summary 80 Figure 3.13: Virtual Objects within Virtual Environment been constructed3, as ilustrated in Figure 3.13. Since the vein model will display which venous segments have been examined, along with the results of the examination, it is easy to detect areas that have been improperly scanned, or areas that may require closer attention. This can contribute to insuring that a basic level of quality is achieved in compression exams. Offline analysis of the collected data is also possible. After a compression examination has been completed the resulting vein model, which contains information about which sections were examined and has the results intuitively mapped to the surface of the model as colors, can be examined through a similar interface and a more detailed analysis can be performed if necessary. 3 . 4 Summary The development of a contour detection algorithm, a novel pressure transducer, and a user interface for a deep venous thrombosis screening system were presented in this chapter. The contour detection algorithm comprises an extended Kalman filter applied to an elliptical 3 A s s u m i n g the patient does not move. 3.4 Summary 81 model which also includes parameter identification of the model. From the detected contour and estimated parameters, a validation measure is created in order to assign a degree of validity to each detected contour. A force transducer is presented for a free-hand system, which measures the pressure that an examining technician applies during a DVT compression ultrasound examination. Also, a position and orientation sensor are incorporated into the system, in order to locate the acquired data in space. Lastly, a user interface for viewing the additional information is also presented. Chapter 4 Validation This chapter presents the results of using the deep venous thrombosis screening system presented in Chapter 3 to characterize a deformable vessel in a physical simulator. Variations of the maximum search area are explored, and the effect on the output of the contour detection algorithm. As well, the Transverse Area Ratio measurement presented in the previous section is validated for a series of image data collected for this purpose. A physical simulator or phantom is presented, including the process used to manufacture it. 4.1 Evaluation of Parameter Estimation Algorithm The parameter estimation subsection of the contour detection algorithm was evaluated in order to identify its performance. Image data was generated and the system defined by (3.46) and (3.47) was processed by the Kalman filter in order to achieve this. Two image data sets were generated. The first consisted of generating nine ellipses by using equation (3.18) with different sets of parameters a,b,(j). Care was taken to simulate the brightness values from a transverse ultrasound image of a vein surrounded by tissue. The location of the edge of the ellipse was calculated, and the brightness values were modified so that the edge location was described by a line at most 3 pixels in width. The edge brightness values corresponded to typical values obtained for vessel boundaries in an ultrasound image. The brightness values of pixels inside 82 4.1 Evaluation of Parameter Estimation Algorithm 83 each ellipse were set to a typical value of the inside of a vessel lumen, and the area outside the ellipse was set to a value typical of soft tissue, which is greater or brighter than that of the vessel lumen. Afterwards, noise was added to the whole image to simulate speckle and noise inherent in ultrasound images. The image was visually similar to an actual ultrasound image. The second set of images was generated using the Field II® program, as described by [48]. Nine ellipses were generated using the same parameters as for the previous set, and were modeled as highly anechoic tissue, so that they would simulate the properties of blood vessels. A highly reflective region was created as well, surrounding the 'blood vessel' to simulate the vein lumen. (a) (b) Figure 4.1: Examples of Simulated Ultrasound Images generated using Field II® Two sets of estimations were performed on the first data set. The first set of estimations consisted of manually validating the detected contour, and recording the estimated values. A seed point was chosen, and if the resulting contour was considered an adequate fit by the author, then the contour was accepted. The second set of estimations consisted of using the validation scheme presented in Section 3.1.6 to validate the detected contours. An error measure was calculated using equation (3.69), and only contours with an error measure below a predefined threshold were accepted. 4.1 Evaluation of Parameter Estimation Algorithm 84 For the second data set only one set of estimations was performed, using the error measure (3.69) presented in Section 3.1.6. Only contours that met the validation criteria were accepted. All estimations were performed for 5 iterations, with 50 radii for each feature, and a maximum search area of 80 pixels. Additional initial conditions were set to Q = 3, R 10 0 0 0 0 10 0 0 0 0 10 0 0 0 0 10 , and S 0.5 0 0 0 0.5 0 0 0 0.1 as well as setting a0|o = °o\o = MaxRadius/2 0o|o = 0° where MaxRadius is the initial maximum search radius length from the center point, in pixels. A large error threshold of 0.35 MaxRadius was used. A set of estimations were performed for each case, and an average value for the estimated pa-rameter was obtained, denoted d for simplicity, as well as a standard deviation s. The error between the average estimate and the real parameter value was also calculated. At least 30 estimations were performed for each case. If the absolute error between the average estimated parameter and the actual parameter, e.g. |a — d|, was less than the value of the calculated standard deviation s, the parameter estimation was considered very good. The results of both series are presented in Tables 4.1, 4.2 and 4.3, along with the actual param-eters used to generate the ellipses. The values of the estimated parameter d are very good for all sets of data. It can be seen that, except for a limited number of cases, the error between the average estimated value and the true value is less than the value of the standard deviation s, for both the automatically and manually verified contours. This can be considered to indicate very good parameter estimation. On the other hand, the estimation of b varies between the parameters verified manually and 4.1 Evaluation of Parameter Estimation Algorithm 85 Table 4.1: Estimated Ellipse Parameters (a, b) from First Image Set - Verified Manually a a s of d | a — a | b b s of b \b-b\ 40 40.56 3.204 0.56 40 40.003 1.894 0.003 26.67 28.991 4.059 2.321 40 37.676 4.246 2.324 20 21.057 1.9718 1.057 40 40.07 3.716 0.07 16 16.921 1.3633 0.921 40 42.655 5.178 2.655 13.3 14.166 1.8679 0.866 40 41.385 5.5343 1.385 11.43 12.012 1.3245 0.582 40 38.092 4.3184 1.908 10 10.299 1.6627 0.299 40 41.198 6.2869 1.198 8.9 8.879 1.8856 0.021 40 41.686 6.5217 1.686 8 8.154 1.3456 0.154 40 37.889 4.6984 2.111 Table 4.2: Estimated Ellipse Parameters (a, b) from First Image Set - Verified using Error Measure a d s of d | a — d | b s s of b \b-h\ 40 41.3306 1.1728 1.3306 40 37.4458 1.7758 2.5542 26.67 24.8724 1.7650 1.2024 40 40.3134 1.5083 0.3134 20 18.1351 1.5446 1.8649 40 38.9236 0.9043 1.0764 16 13.3075 1.6961 2.6925 40 38.3673 0.8353 1.6327 13.3 11.9108 1.6891 1.3892 40 38.1169 0.7149 1.8831 11.43 9.9197 1.5089 1.5103 40 37.7866 1.4829 2.2134 10 8.4829 1.3309 1.5171 40 36.6122 1.5383 3.3878 8.9 7.0063 1.5498 1.8937 40 36.0948 3.0605 3.9052 8 6.5843 1.4497 1.4157 40 35.5166 3.7389 4.4834 Table 4.3: Estimated Ellipse Parameters (a, b) from Field II© generated Ultrasound Images -Verified using Error Measure a d s of d | a — d | b s s of b | 6-6 | 55 53.7275 2.0504 1.2725 55 53.1096 1.6081 1.8904 36.67 37.5439 0.7915 0.869 55 52.8498 2.5104 2.1502 27.5 27.7206 1.3493 0.2206 55 50.3563 2.0702 4.6437 22 22.1884 1.3821 0.1884 55 46.4812 1.7612 8.5188 18.29 18.4537 1.4997 0.1637 55 50.4168 2.8738 4.5832 15.72. 15.7113 1.3650 0.0087 55 46.2513 4.4787 8.7487 13.75 14.2659 1.6660 0.5159 55 47.2696 4.0271 7.7304 12.24 14.2313 1.5886 1.9913 55 45.0617 2.9669 9.9383 11 10.1903 1.5088 0.8097 55 44.2599 5.3493 10.7401 4.1 Evaluation of Parameter Estimation Algorithm 86 those verified using the error measure (3.69) from Section 3.1.6. The errors between the estimated parameter b and the actual b are small for the data set presented in Table 4.1, and in general the standard deviation s is large. Even so, the result is that the parameter estimation remains 'very good' in the manual case because the error between the average estimated parameter and the real value is less than one standard deviation. For the data presented in Table 4.2, in general the errors between b and the actual b ave larger than the values for the standard deviation s. In this case, we cannot say that the parameter estimation is 'very good' as we defined above. In many cases though, the difference between the error and the standard deviation is minimal. The results are similar for the data set using the simulated ultrasound images using the Field II© program, as presented in Table 4.4. The values for the estimated parameter a can be considered very good, while the values for the estimated parameter b are not. It can be seen though, that the error between the estimated parameter b and the true value of the parameter is not greater than two standard deviations. Table 4.4: Estimated Ellipse Parameters <j> Ellipse Parameters Data Set 1 Data Set 2 a, b 0 S of 0 4> S of 0 a = b -8.0153 26.0284 -47.9625 50.2503 a = | b 2.3752 2.3512 5.3618 18.9435 a=\b 0.8056 2.5155 0.9440 9.3613 a=\b 0.0456 3.6501 -4.5836 9.9141 a=\b 0.3290 2.7759 -0.2210 10.9124 a=^b 1.8268 2.3766 0.7783 5.6282 a=\b 1.2935 3.3689 3.4335 4.5106 a = I b 1.7870 3.7721 -1.7347 8.8842 a=\b 1.5840 3.8675 1.5358 7.3998 In general, it can be seen that the parameters verified visually in general have larger standard deviations, but the error between the average value of the estimated parameter and the known value is much less than those parameters obtained with automatic verification. It can also be noted that the accuracy of the estimation for b (which remains a constant value) decreases as the value for a decreases. 4.1 Evaluation of Parameter Estimation Algorithm 87 A high error threshold was used during the parameter estimation with automatic verification, this is even though high error values were produced when applying equation (3.69), the contour was still considered valid. In this manner, all contours detected were validated and none were discarded. By reducing this threshold, the results in Table 4.2 will tend towards the results in Table 4.1, by discarding inadequate parameter values. Because of the nature of the ellipse equation, and ellipse can be represented by values a\, b\ and 0 i or by the parameters ai, 62 and 02, where 0-2 = h, 62 = a,i, and 02 = 01 + 9 0 ° . (4.1) The values presented above for a and b were corrected taking this into account, as were the results for the estimation of the value of 0. For all ellipses, the value of 0 was 0°. As is shown in Table 4.4, where all values of ij> are in degrees, the estimation of 0 is good for all cases, except for when a = b. This is expected since for this case, the ellipse equation will describe a circle, and the angular displacement 0 cannot be uniquely identified. 4.1.1 Feature Detection Comparison A comparison between the contour detection algorithm developed herein, and an alternate method was performed. The alternate method consisted of using the Star-Kalman algorithm pre-sented in [2] in order to obtain a series of contour points, and then obtaining the parameters of the minimum volume ellipsoid that contained all the detected points. The minimum volume ellipsoid was obtained in the manner described by [92]. The two methods were applied to the simulated ultrasound images, and the extracted parameters were compared to the known true values. As well, the time taken for the algorithms to converge was measured. All test were performed in Matlab©, and the minimum volume ellipsoid parameters were obtained using the Parameter Estimation Toolbox. Our contour detection algorithm, described by (3.46) and (3.47), was initialized as in Section 4.1. The results are presented in Table 4.5. The values for the estimated parameters a and b are 4.1 Evaluation of Parameter Estimation Algorithm 88 presented for each of the methods, as well as an error between the estimated values a and b, and the known values a and b, respectively. The time taken to complete the estimation is presented in seconds. Table 4.5: Comparison of Ellipse Parameter Estimation Method a \ a — a \ s \b-b\ Time (s) Min Vol Ellipsoid Extended Kalman filter 55.3588 55.0278 0.3588 0.0278 56.5798 53.2653 1.5798 1.7347 1.8433 0.3287 Min Vol Ellipsoid Extended Kalman filter 50.0467 49.3912 4.9533 5.6088 41.2580 38.6469 4.5880 1.9769 3.5363 0.3230 Min Vol Ellipsoid Extended Kalman filter 47,2062 48.1812 7.7938 6.8188 34.2704 29.8789 6.7704 2.3789 3.6407 0.3120 Min Vol Ellipsoid Extended Kalman filter 44.1632 45.3087 10.8368 9.6913 27.9855 24.0977 5.9855 2.0977 3.5517 0.3020 Min Vol Ellipsoid Extended Kalman filter 42.9579 46.1075 12.0421 8.8925 26.4960 20.9811 8.2060 2.6911 3.5730 0.3227 Min Vol Ellipsoid Extended Kalman filter 43.2305 42.8300 11.7695 12.1700 25.6730 18.5280 9.9530 2.8080 3.9533 0.3127 Min Vol Ellipsoid Extended Kalman filter 39.3706 40.6489 15.6294 14.3511 22.0675 16.1812 8.3175 2.4312 3.5360 0.3073 Min Vol Ellipsoid Extended Kalman filter 35.0103 38.5269 19.9897 16.4731 21.2273 15.7249 8.9873 3.4849 3.5727 0.3177 Min Vol Ellipsoid Extended Kalman filter 34.2355 38.2430 20.7645 16.7570 16.6312 12.1249 5.6312 1.1249 3.8700 0.3177 It can be observed that the error between the true value and the estimated value of the ellipse parameters is in general smaller for the extended Kalman filter presented herein. Of more interest is the time taken for each algorithm to converge, as the difference in time taken is almost an order of magnitude less for the extended Kalman filter. This is a great advantage, as we seek to detect the contour as fast as possible. It should also be noted that the error values are in general much larger than those presented in Section 4.1, where the feature detection algorithm is validated, because a fixed search area was used in all cases. From the results that have been presented, it can be easily observed that our feature detection method is a fast and accurate way to determine a contour within an ultrasound image, when 4.2 Maximum Search Area Variation 89 compared to similar methods. 4.1.2 Results of Parameter Estimation Algorithm In this section, a few concrete examples of detected contours and parameters are presented. Various images obtained from our ultrasound phantom (Figures 4.2(a) through 4.2(f)), as well as images from deep veins of several volunteers (Figures 4.2(g) through 4.2(i))were used as input for the contour detection algorithm. In general, the detected contour points are presented as circles, while the detected ellipse equa-tion parameters were used to plot an ellipse on the image. The semi-major axis is represented by the solid line, while the semi-minor axis is presented as a dotted line. Care was taken to include images that included varying degrees of image brightness by ad-justing the gain control from the ultrasound machine, as well as including different vessel sizes by compressing them in order to present the results of the feature detection algorithm over a broad range of situations. Other settings such as zoom were not altered, so that the scaling factors would remain the same. The same settings were used for the image feature detection algorithm for all cases, except for the maximum search area which was adjusted for the size of the vessel. Many more examples can be found in Appendix C. 4.2 Maximum Search Area Variation The effect of the size of the search area was briefly studied, and is presented as follows. The contour detection algorithm developed herein was applied to several images depicting human vessels on a transverse plane. The seed point for each of these images was selected manually with a mouse. The maximum search radius for the algorithm was set to different values, with a minimum value that would still include the complete vessel and the generated error measures presented in Section 3.1.6 were analyzed. Each contour was also visually inspected and rated as correct or incorrect by the author. Figure 4.2: Results of Contour and Parameter Estimation 4.2 Maximum Search Area Variation 91 300 r Search Radius (pixels) Figure 4.3: Error Values Using Different Rmax The values used for the algorithm were <2 = 3, R = as well as setting and 20 0 0 0 0 20 0 0 0 0 20 0 0 0 0 20 , and S = 0.5 0 0 0 0.5 0 0 0 0.1 do|o = &o|o = Max Radius/2 4>o\o = o° ^0|0 = 10 0 0 0 10 0 0 0 10 4.2 Maximum Search Area Variation 92 0.18r 6 1 , , , , , , , 30 40 50 60 70 80 90 100 Search Radius (pixels) Figure 4.4: Relative Error Values Using Different Rmax In Figure 4.3, the error value obtained from equation (3.69) is plotted against the maximum search area. Each line indicates the error value obtained when applying the contour detection algorithm to 5 different images, with different values of Rmax, as indicated. A clear tendency can be seen indicating that the smaller the search area is, the less error there is between the detected contour and generated ellipse using the estimated parameters. The only disruption in this trend is when the lower values of Rmax are reached, as is anticipated. If the search area does not contain the complete feature to be detected, an increase in the error between an estimated ellipse and detected contour is expected. Therefore it is natural to conclude that the error will decrease as long as the search area contains the complete vessel. One other matter must be addressed, though. It seems obvious that if the search area is smaller, the detected ellipse and contour will be smaller as well, even if a feature is not properly detected. This, in turn, will also reduce the error calculated by (3.69) without necessarily guaranteeing better detection. Only if the error is normalized by Rmax can it be stated that there is an improvement in detection of the image feature. 4.2 Maximum Search Area Variation 93 0.35 0.3 0.25 ra E or 0.2 .- 0.15 o 0.1 0.05 30 40 — Image 3 — Image 4 Image 5 50 60 70 80 Search Radius (pixels) 90 100 Figure 4.5: Relative Error Values Using Different Rmax In Figures 4.4 and 4.5 the detected error has been normalized by dividing the error value by the Rmax used for that iteration. It is obvious from these that the error indeed tends to be reduced. The error obtained for different values of Rmax for one of the test images is presented in Figure 4.4. The dotted vertical line indicates the minimum value of Rmax that contains the complete feature. It can be seen that the error decreases monotonically with Rmax until the point that the feature is no longer contained completely within the search area. Even so, after a slight increase in the error with a reduction in the search area, the error continues to diminish. Figure 4.5 shows a special case. It is known that the minimum value of Rmax that will contain the complete image feature is 60, as indicated by the dotted line. Once Rmax is less than this predetermined value, it can be seen that the normalized error drastically increases. Through this characterization it may be possible to develop a more comprehensive scheme to validate an estimated ellipse and detected contour, as it is known that the error can dramatically increase once the search area is smaller than the image feature. These results validate the method presented in Section 3.1.7 in order to properly detect the 4.3 Transverse Area Ratio Validation 94 desired features. 4.3 Transverse Area Ratio Validation In order to verify the validity of the Transverse Area Ratio presented in Section 3.3.2 a series of images of compression ultrasound examinations were analyzed. These images were obtained from instructional videos. Each image series consisted of several frames of one compression-release cycle of a compression examination of both healthy and thrombosed veins. Within each frame, a vein from the lower limb was presented in the transverse plane. It was assumed that each series of images was acquired at approximately the same location, and therefore represented the same venous segment. For most of these image series, force or pressure measurements were not available. Even so, through visual inspection of the individual images and in sequence, it was possible to infer which images were acquired while more pressure was being applied through the probe, even though it was not numerically quantified. A reference measurement was created for each image frame, by manually outlining the vessel contour. The contours were traced by the author, with great care taken so that the correct contours were represented. Once the contour for each of the images in a series had been traced, the area within each contour was calculated, and normalized. The normalization procedure consisted of dividing all area measurements from a series by the maximum area of that specific series. Usually either the first or last image was the one with largest transverse area. The results of calculating the ratio of the minimum area over the maximum area in a series of images are presented in Tables 4.6 and 4.7, which present data from healthy veins and diseased veins, respectively. Table 4.6: Transverse Area Ratio for Healthy Veins - Manual Calculation 1.788% 1.357% 0.128% 0.0% 0.0% 0.0% 1.744% 0.0% 0.0% 0.0% From Table 4.6 it can be seen that the minimum area is less than 2% of the original uncompressed 4.3 Transverse Area Ratio Validation 95 Table 4.7: Transverse Area Ratio for Diseased Veins - Manual Calculation 73.457% 50.5855% 61.16% transverse area in all cases. In the cases were the Transverse Area Ratio is presented as 0.0%, it indicates that the vein compressed completely, and therefore had no discernable transverse area. The results from a typical image series of a healthy vessel is shown in Figure 4.6, which shows the normalized area through a series of images, where the vein is being compressed. This maps the transverse area vs. the applied force. Image Sequence Figure 4.6: Healthy Vein Compression Sequence In Table 4.7, the results of a compression examination performed on a diseased vein can be seen. In this case, one compression-release cycle is performed. Of the images examined that presented vessels with intraluminal matter, in no case was the minimum area less than 50% of the original area. This is a large difference when compared to healthy veins. The normalized transverse area for a typical image series depicting a thrombosed vessel is 4.3 Transverse Area Ratio Validation 96 presented in Figure 4.7. As can be seen, at no time during the compression examination does the transverse vein area become smaller than 50% of the original area. o 0.4 -0.3 -0.2 -0.1 -0 I 1 1 , 1 , 1 1 1 2 3 4 5 6 7 8 Image Sequence Figure 4.7: Diseased Vein Compression Sequence From these results, it can clearly be identified that if a vein is healthy, i.e. is clear of thrombus, then the minimum transverse area will be less than 2% of its uncompressed or maximum area. On the other hand, if the vein does contain intraluminal matter, it will not collapse as easily which will result in a larger minimum transverse area, as the results show. Veins in which thrombi were identified had a minimum area of 50% or more of the original transverse area. These results indicate a very clear difference between healthy and thrombosed vessels, and such a wide margin will be very advantageous when automatically identifying diseased veins. Additionally, the contour detection algorithm presented herein was applied to the same image series, using the error measure (3.69) presented above in order to validate the contours. The results obtained from the contour detection algorithm were compared to the results obtained manually. For each image, a seed or center point was generated in order to initialize the algorithm. This 4.3 Transverse Area Ratio Validation 97 seed point was set as the average point obtained from the manually generated contour for each image. As well, the values used for the algorithm were Q = 3, R 20 0 0 0 0 20 0 0 0 0 20 0 0 0 0 20 , and S = 0.5 0 0 0 0.5 0 0 0 0.1 as well as setting *0|0 &o|o = Max Radius/2 0o |o 0° and Po\o = 10 0 0 0 10 0 0 0 10 where MaxRadius is the initial maximum search radius length from the center point, in pixels. The results obtained for the respective image sequences by using the algorithm developed herein, are presented in Tables 4.8 and 4.9. Table 4.8: Transverse Area Ratio for Healthy Veins - Contour Detector 3.55% 6.12% 2.59% 24.65% 15.63% 17.0% 13.79% 25.99% 15.27% 5.0% Table 4.9: Transverse Area Ratio for Diseased Veins - Contour Detector 57.54% 64.53% 56.82% Figures 4.6 and 4.7 also contain the data that was generated using the contour detection algo-rithm for the specific image sequences. It can be seen that the estimated areas are very similar in both cases. A large difference can be seen in Figure 4.7 between the manually segmented contour and the contour obtained from the feature detection algorithm. This is due to the feature detection algorithm detecting the edge location of the thrombus itself which is relatively strong, instead of 4.4 Ultrasound Phantom 98 the vessel lumen itself. From the results presented in Tables 4.8 and 4.9, it can easily be seen that the same tenden-cies as with the manually segmented images are present. The difference between healthy veins is slightly less, but still substantial. That is, for healthy veins, the minimum area is always less than approximately 25% of the original area, while the minimum transverse area for a diseased vein will be no less than approximately 50% of the original transverse area. For all cases where the TAR was above 10%, the initial, uncompressed cross-section of the vessels was relatively smaller than for the cases with a Transverse Area Ratio below 10%. This indicates that the size of the vein within the image may affect the calculation of the Transverse Area Ratio. From these results, it is suggested that a threshold value of 20% be used to identify healthy veins. Any vein that returns a Transverse Area Ratio greater than 20% but less than 50% can be flagged as intermediate and those with a value greater than 50% can be considered as veins with high probability of DVT. Even so, the Transverse Area Ratio information is mapped to the vein model and the intermediate results can be observed. 4.4 Ultrasound Phantom A phantom is a device that generally mimics human or biological tissue and anatomy for use in training, experimentation and validation of image-processing algorithms, or to assess the capabilities of various imaging techniques. These applications include biopsies and medical imaging techniques such as x-ray CT and angiography, and B-mode, power Doppler and colour Doppler ultrasound. Phantoms are used when there is a difficulty in accessing the real tissue and when algorithms are in their laboratory stages. An ultrasound phantom is a device that not only mimics human tissue or structures at anatom-ical level, but also mimics how these tissues and structures appear when imaged using ultrasound. Therefore, not only should the anatomy and properties like compliance or stiffness match the or-gans that the phantoms are representing, but also the acoustical properties should match as well, meaning that they should have the same ranges of speed of sound, attenuation coefficients, and 4.4 Ultrasound Phantom 99 scattering coefficients of soft tissue, in order to obtain adequate images. An ultrasound phantom for testing and validating the current DVT screening system was con-structed which was intended to be a realistic model of human vasculature and surrounding tissue, according to the following requirements: • The phantom should represent at least one vessel segment, which corresponds to a human vein. Preferably, two vessels should be located side by side, representing a vein and an artery, which is a common configuration in reality. • The vessels should be compressible under gentle pressure, mimicking a healthy human vein. Under this same requirement, if two vessels are present, the one corresponding to the artery should at least be not as compressible as the vein. It has been reported that the Young's modulus for a femoral artery is in the range 1.23 to 5.50 MPa [25]. • The vessels should be surrounded by a material with properties similar to those of a human leg. It has been reported that Young's modulus E for relaxed human muscle is 0.0062 MPa [25]. Therefore, the phantom should have a similar modulus. • The vessels should appear as bright circles or boundaries in an ultrasound image, while the interior of the vessel should remain black1. Additionally, the surrounding material should contain a degree of ultrasound speckle. • Means should be included for allowing a section of the vein to become at least partially incompressible, in this manner simulating a thrombus. These means should not be visible on an ultrasound image, and should be localized to a specific area. • The properties of the tissue-mimicking materials used at room temperature should be ap-proximately equal to the properties of the corresponding tissues at 37°C. Aside from these requirements, it was also desirable to include the possibility of providing flow through the vessels, for validation of future improvements in the detection procedure. Several authors [16,21,66,73,82] have experimented with different materials for constructing ultrasound phantoms representing sections of vasculature, for different applications. In general, a 1 Assuming a standard grayscale B-mode image. 4.4 Ultrasound Phantom 100 mold is constructed and filled with tissue mimicking material. This material contains structures, created by different means, which represent the vessels. Agar based tissue-mimics are among the materials most used in phantoms for tissue surrounding a vessel, because of both its physical and acoustical properties. It has been demonstrated that blocks of agar gels have elastic moduli similar to that of muscle [73]. Since a great part of the lower limb is composed of muscle, agar gels then seem to be the material of choice. For constructing the vessels, it was decided that polyvinyl-alcohol (PVA) cryogels [16] would be used for the vein and artery. PVA has ultrasound properties similar to tissue, such as a speed of sound 1540-1580 m/s, and an attenuation factor of 3.0 dB/cm when imaged at 5 MHz. Also, the elastic modulus of PVA is 0.19 MPa, which is similar to tissue. The average speed of sound for soft tissues is 1540 m/s, and an attenuation factor of soft tissues is approximately 3.5 dB/cm when isonated at 5 MHz [25]. First of all, a container was constructed of 1/4" Plexiglas to hold the vessels as well as the surrounding tissue. The container is 6 inches long by 3.5 inches wide, and 4 inches deep. There are two openings on each end of the container, and a fixture passes through each of them. The fixtures extended into the interior of the container and are beveled, so that the previously constructed PVA vessels can be fixed to them so that they are sealed. On the exterior of each of the fixtures, a screw on cap is provided. In this manner, the interior of the vessels can be sealed off from the outside of the container, and from the inside as well. For the construction of each vein, a tubular plastic mould was constructed with an inner diam-eter of approximately 12 mm. A 8 mm rod was inserted into the mold and coaxially aligned, in this manner creating a 2-mm gap between the rod and the inner diameter of the out tube. The moulds were positioned vertically and sealed at the bottom, leaving only the top accessible. 10 % PVA cryogel was prepared as described by [16]. The gel was heated in boiling water for 30 minutes, and then poured into the moulds. Afterwards, the moulds were sealed at the top, and the gel was permitted to cool off for approximately 24 hours. Each vessel then underwent 3 freeze-thaw cycles, to obtain the desired properties. The vessels were then extracted from their moulds and ready for use in the phantom. Agar is composed of about 70 % of agarose and about 30 % of agaropectin which has sulfate 4.4 Ultrasound Phantom 101 Figure 4.8: Ultrasound Phantom Container groups in its molecule. By mixing agar with water in different proportions, the compliance of the resulting gel can be modified. A mixture of about 5 % agar and about 95 % water generated a gel with compliance similar to sections of the lower limb. Once the vessels have been placed on the fixtures, a rod is inserted through the PVA vessels and supported at each end by the fixtures, so that when the tissue-mimic is poured they do not collapse. The rods also will determine the location of the vessels within the agar. The tissue-mimic is prepared based on the recipe in [82], which has a measured acoustic impedance of 3.5 dB/cm at 4 MHz and sound velocity of 1560 m/s [82]. A solution of 8 % Glycerol and distilled water is mixed with 3 % agar (by mass), as well as 3 % (by mass) 50 /j,m cellulose particles. The Glycerol is added to increase the acoustic velocity of the tissue, and the added cellulose particles provide the desired acoustic attenuation. This mixture is then heated to approximately 90°C, and then permitted to cool off slightly without congealing. The tissue mimic must cool to about 40°C, so that when it is poured into the phantom mould, the PVA cryogel vessels do not melt. Once the agar mixture is cool but still liquid, it is poured into the container and permitted to cool off completely. 4.5 Summary 102 When the tissue mimic has completely congealed, the phantom is ready for use. The vessels can be filled with water or another suitable liquid that will act as blood. A blood mimic is also presented in [82] and can be used for a DVT evaluation that comprises pulsed or colour Doppler. Since in our case we do not consider the blood flow for DVT diagnosis, it is not critical that the blood mimic be used. If a healthy vein is being simulated, the vessels should not contain anything other than the blood mimicking fluid, which should not cause any significant ultrasound reflections. For these simulations water was used to simulate blood because of the imaging properties, and for ease of use. If the phantom is to be used to simulate a thrombosed vein, then a thrombus must be con-structed. A material with stiffness close to that of a thrombus is needed, and which also displays the adequate ultrasonic properties. Possible thrombi include the tissue mimic described above, only that the cellulose particles are not added to it, or PVC. Both of these materials present almost no speckle at all, which matches a thrombus quite well. The physical properties of these materials adequately approximate a thrombus. The results of using the phantom as a 'human simulator' are presented in the following chapter. 4.5 S umma r y In this chapter, the results of validations and simulations were presented. It was demonstrated that the feature detection algorithm has a reduced error when the search area is smaller and contains only the feature to be detected. Also, it was confirmed that the ratio of minimum area over maximum area of a compression-release cycle in a compression ultrasound exam can be used as an objective indicator as to the possibility of the intraluminal matter within a vessel. Finally, a physical simulator for the DVT screening system was presented. Chapter 5 Experiments In this chapter, the DVT screening system is implemented and tested on a custom ultrasound phantom as well as on healthy human subjects. A description of the working system is presented, as well as the procedure that was used to scan a series of volunteers for DVT. The collected data was then analyzed and the results are presented below. 5.1 Experimental Setup All of the elements of the deep venous thrombosis screening system that have been previously described were included in the experimental system. A 6-9 MHz linear probe connected to a prototype PC-based ultrasound machine (Ergosonix 500) developed by Ultrasonix Medical Corporation was used for all scans. The probe was fitted with the novel force transducer as previously described, and the electromagnetic sensor was fixed to the shell. During each of the scans, the ultrasound image brightness was adjusted in order to obtain the best image quality possible, while using a center frequency of 6 MHz. By using these settings, the ultrasound image frame-rate was 12Hz. Two PCs were used in our system, connected over a Local Area Network (LAN). The first was the ultrasound machine, which acted as an image server. The second contained the data 103 5.1 Experimental Setup 104 acquisition cards for the sensors, and was used as the main computer, on which the system was executed. The user interface, the contour detection algorithm, and the compression examination assessment procedure were all modularly coded in C++. This is shown schematically in Figure 5.1. Figure 5.1: Ultrasound Screening System The position and orientation of the probe was read through a PCIBird (Ascension Technology Corporation) and the pressure was read through a Nano 25 six-axis force-torque sensor (ATI In-dustrial Automation). A continuous video stream was displayed on the user interface as previously described through a conventional 2-D ultrasound image display, as well as through the virtual environment depicting the probe and image plane in 3-D. The image size was 664 x 508 pixels. 5.1 Experimental Setup 105 Upon initial execution of the program, the main computer established a connection with the Ultrasonix machine, in order to transfer images. Upon input from the user, the system would then start acquiring images and sensor data, and display the appropriate ultrasound image, as well as the 3-D representation of the ultrasound image plane in the virtual environment. A screen shot of the interface is shown in Figure 5.2 imaging the vessels of the phantom in a transverse plane. Afterwards, the user could then choose from a variety of actions, such as performing a simple scan, building a 3-D venous model, and also performing a compression exam once a model had been constructed. A contour tracking subsystem as described previously was implemented to continuously detect and track a contour of a vessel in the transverse plane acquired using the ultrasound probe. The virtual vein model can be constructed by using these continuously detected and tracked contours, as well as by using contours selected one at a time from the detected images. A compression examination can be performed in the same manner, by using the continuously detected contours or contours obtained in a one by one manner. Initially, the system was tested and refined for the ultrasound phantom and afterwards it was evaluated on human subjects. Healthy adults were recruited in order to represent normal individuals in the general population in order to test the deep venous thrombosis screening system, according to U B C Office of Research Services ethical guidelines. Since the system is still in an experimental QEH2E32E3EE (a) (b) Figure 5.2: Screen-Shot Ultrasound Screening System Interface 5.1 Experimental Setup 106 stage, only healthy volunteers were examined instead of patients, with or without symptoms of DVT, in order to reduce possible complications. The examination protocol followed for each exam was based on that presented in Section B.4.1. In general the examination was divided into smaller subsections, each of which represented a venous segment. Each examination is divided into the model building procedure, and the compression examination procedure. The exam roughly comprises • Examining the common femoral vein (CFV). • Examining the insertions of the superficial femoral vein (SFV) and the long saphenous vein (LSV). • Examining the SFV, moving distally along the thigh. • Examining the popliteal vein (POP). • Moving distally towards the thigh, and examining the posterior tibial (PT), anterior tibial (AT) and peroneal vessels (PER) to the extent that it is possible. The subject is asked to remain as still as possible throughout each section. The model building procedure consists of placing the probe at the desired region of interest in order to image a vessel in a transverse plane. As little force as possible is applied in order to not compress the examined vessel. Then, the contour tracking is activated and an initial seed point is selected. The probe is then moved slowly along the longitudinal axis of the vessel, in order to acquire contours of that same vessel at different locations. Alternatively the contour tracking can be disengaged, and the contours are obtained individually by placing the probe in the desired location and selected a seed point for the contour detection algorithm, while also applying as little force as possible. Once a vessel model has been constructed, the probe is then moved to a location where the image plane intersects the vein model, and a compression exam is performed. As with the model construction scenario, the compression examination can be done by activating the contour tracking and selecting an initial seed point, or by individually selecting seed points for each contour. Once a compression examination has been performed, it is validated by verifying that there are enough 5.2 Experimental Results 107 contours for that region and that the force applied was enough. The result of the compression examination is then mapped to the appropriate region of the recently constructed vessel contour. Once a compression examination has been completed the data is then saved, and a new segment is examined until the patient's complete deep venous system has been examined. The DVT detection system was set up beside an examination bed, on which the volunteers lay. The electromagnetic transmitter was located on a wheeled table so that it could be positioned in such a way so that the examined vessel's longitudinal axis would appear parallel to the screen on which it was displayed. The transmitter was not moved during an examination. 5.2 Experimental Results 5.2.1 Phantom Reconstruction The deep venous thrombosis screening system presented in this thesis was initially evaluated in the laboratory using the ultrasound phantom that was described in Section 4.4. Two specific cases were tested, representing a completely healthy vein and a almost completely thrombosed vein. The results of these test are presented below. For the healthy vein case, the vessel-mimicking tubes were purged of any substance, and filled again with the selected blood mimic. An agar-based thrombus was constructed as described above, and sized to a cylinder approximately 3 mm in diameter, and 10 mm in length. When the phantom was used for the case of a vein with thrombosis the vessels were purged, and the thrombus-mimic was inserted into the vessel that was to represent the vein. The thrombus was located at approximately the middle of the vessel. Healthy Vein The phantom was imaged throughout only on the transverse plane, depicting the vessel phantom as generally circular or elliptical structures. The examination was carried out by the author. First, a general vein model was constructed with the system. The examiner positioned the 5.2 Experimental Results 108 Figure 5.3: Building Vein Model probe on one end of the phantom, making sure the vessel of interest was completely within the image plane and uncompressed, as indicated by the force reading and by proprioceptive feedback. A seed point within the vessel was selected, and a contour was detected and stored. The probe was then translated along the axial direction of the vessel by approximately 1 cm, and the process repeated. Once enough data had been collected for an adequate vein model, then this appeared in the virtual environment display. As more data was collected, the vein appeared to grow. The color the vein was presented in indicated a neutral state. No compression information for those sections of vessel had been acquired to that point. A partially completed vein model can be seen in Figure 5.3, as well as a view of the image plane. When the far end of the phantom was reached, the model building procedure was completed. Once the model had been constructed, the compression examination of the phantom began. The examiner positioned the probe so that the image plane in the virtual environment was aligned with one end of the vessel model. The examiner then pressed down by a small amount and held the transducer in place, without completely compressing the vein while selecting a seed point. The contour was detected and stored. The examiner then pressed down by another small amount, and repeated the process. When the vessel had been seen to completely compress, or alternatively when the maximum 5.2 Experimental Results 109 Figure 5.4: Vein Model with Compression Information pressure was reached, the vessel was uncompressed and the probe translated along the axial direction of the vessel by about 1 cm to a new location for the next compression-release cycle. In this manner the complete phantom was assessed for compression, and the results were displayed as can be seen in Figure 5.4. Figure 5.5: Cross Section of Uncompressed Healthy Vessel Phantom As is clearly evident from the results that the vessel reconstruction in Figure 5.4 corresponds to the vessel within the phantom. The vessel is roughly tubular and straight in shape, and therefore so is the resulting model. There are small errors that originate from several sources, such as the deformability of the vessels and tissue mimic, position and orientation measurements, and the 5.2 Experimental Results 110 Figure 5.6: Cross Section of Compressed Healthy Vessel Phantom feature detection algorithm, as well as from movement of the phantom. These account for the fact that the reconstructed model is not a perfect straight tube, for the most part because of the location measurements as well as the tissue deformability. Also, it can be observed from the model that the results of the compression exam correspond to that of a healthy vein. A curious artifact is generated because the phantom is used. Since the vessels are fixed at each end, and the fixtures to which they are attached are extremely stiff, the minimum transverse area of the vessels closer to the ends of the phantom are greater than those in the middle. This results in the vein model indicating a higher probability of DVT at the ends of the examined segment than in the center. Figures 5.5 and 5.6 show the ultrasound images acquired from the phantom mimicking a healthy vein, and the results of the boundary detection algorithm as well as the ellipse constructed using the estimated parameters. It can be seen that the vessel is compressed almost completely. Thrombosed Vein The procedure for generating the vessel model is exactly the same as that presented in Section The only difference is that the phantom now mimicks a vessel containing a thrombus. Therefore, it is expected that the results will reflect this change. This is so, as can be seen in Figure 5.7. The vessel model that was generated is basically the 5.2 Experimental Results 111 Figure 5.7: Model of Thrombosed Vessel Phantom same in geometry as the model generated with a healthy vein, but the corresponding compression data mapped to the model is different. This vein model also contains artifacts generated by the fixtures to which the vessels are at-tached, but also contains a large area near the middle indicating high probability of intraluminal matter. We know that this is actual location of our thrombus, because of our knowledge of the phantom. Figure 5.8 shows the minimum area obtained at specific locations along the vessel for both the healthy and diseased cases. By observing Figure 5.8 it can clearly be seen that towards the center of the vessel, the minimum transverse vessel area is more than 50 % of the maximum area, indicating with high probability that matter is contained within the vessel for the diseased case. The vessel that represents the healthy vein can clearly be seen to compress to less than 30 % of the original area, indicating a low probability of intraluminal matter. Figure 5.9 shows that a relatively uniform amount of force was used throughout the vessel, though small variations in force from one location to another can be seen. This is expected, especially when performing exams on human subjects, because of the inhomogeneity of the tissues throughout the area being examined. Even so, it can clearly be seen that there is no correlation between the applied force and the minimum area, indicating that the compression exam was carried 5.2 Experimental Results 112 0.1 -gl 1 1 1 1 1 1 1 1 5 10 15 20 25 30 35 40 Translation along Vessel (Axial) Figure 5.8: Minimum Transverse Vessel Area by Location Along Vessel out adequately. The force values were normalized using the maximum applied force. As can be seen from the image of minimum area in Figure 5.11, it is clear that the vessel phantom was not compressed completely. By analyzing this image alone, it is impossible to ascertain whether there is something inside the vessel or not. But since we know the forces applied by the transducer as well as the area of the vessel at different applied forces, such as that obtained from Figure 5.10, it is clear that there is something within the vessel phantom. Ultrasound Phantom Limitations It was found during the experiments, that the ultrasound phantom presented certain limitations. The image quality of the phantom was excellent. The formula used to create the phantom produced adequate amount of speckle in the image, as well as producing adequate boundaries where the vessels met the agar gel. The interior of the vessels was also very good, as it was very non-echogenic, and did not produce strong echoes. 5.2 Experimental Results 113 0.3 h 0.2 -0.1 -Ql 1 1 1 , ! 1 1 1 5 10 15 20 25 30 35 40 Translation along Vessel (Axial) Figure 5.9: Maximum Force by Location Along Vessel Figure 5.10: Cross Section of Uncompressed Thrombosed Phantom 5.2 Experimental Results 114 Figure 5.11: Cross Section of Compressed Thrombosed Phantom The major drawback of our phantom was observed during the compression examinations. Be-cause of the nature of the compression ultrasound examination, the probe was repeatedly pressed and released on the surface of the phantom. This procedure, along with a relatively thin ultrasound probe head, would literally dig into the phantom and break the agar gel apart. The effect of the repeated compressions was partially solved by placing a sheet of plastic on top of the phantom, but after several compression examinations the agar, especially near the surface, had completely crumbled. The main effect on the ultrasound image was that unwanted reflections due to air bubbles became present. T h e air bubbles could be removed by submerging the phan tom in water, or by using ultrasound gel to fill in the gaps. Several phantoms had to be constructed throughout the validation and testing procedure. As well, there are differences between the system in the phantom when compared to the human vascular system. The phantom is a closed fluid system, and when force is applied to it in the form of a compression exam, the blood mimic within the vessels has nowhere to go. On the other hand, when a compression exam is performed on a human, the displaced fluid may be displaced throughout an intricate vascular system. The effect of this is that it will be more difficult to completely compress a phantom vessel, and larger Transverse Area Ratio values may be obtained. Another drawback to our ultrasound phantom is that we do not yet have enough data to 5.2 Experimental Results 115 validate our simulator, in the sense that it we do not specifically know how accurately it represents a thrombus filled vessel. Though the images depict a non-echoic area surrounded by a highly echoic area, it is still a very simplified model. 5.2.2 Reconstruction of Human Vessels Several human vessel segments were scanned, reconstructed, and had compression examinations performed on them using the DVT detection system. (a) (b) Figure 5.12: Reconstructed Human SFV A proximal section of the SFV was reconstructed, as shown in the screen-shot in Figure 5.12. It can be noted in the corresponding ultrasound image, that the characteristic 'Mickey Mouse head' can be seen were the SFV and the LSV branch off from the CFV. A compression examination was then performed on the venous segment. The data was acquired from a small volume, as can be seen in Figure 5.13, where each point represents the locations of each compression measurement taken. The scale of the venous segment can also be observed. All axes units are centimeters. Figure 5.14 shows the results of the compression examinations, as the detected transverse area of the vessel vs. applied force. The area values have been normalized and all x-axes are force. It can be seen that for this specific segment, twelve compression cycles were performed. These are typical compression examination results, and are meant to reflect the data collected throughout the examination process. It is clearly evident that not all compression cycle data indicates a healthy vein. The first 5.2 Experimental Results 116 Compression Examination Location 29 Figure 5.13: Location of Compression Examination Measurements : 0.5 : 0.5 : 0.5 0 1 I ; 0.5 5 v 10 10 10 0.5 : 0.5 10 10 10 "» • • ) 5 10 « ; 0.5 •• • a • : 0.5 • • • 0 1, V 0.5 5 10 10 4 . 10 Force 20 10 Force ea 9 • • < g 0.5 • z 0 20 10 20 Force Figure 5.14: Compression Examination Data 5.2 Experimental Results 117 two charts in the top row show examples of incomplete compression cycles. It can be seen that the maximum force reached was only about 5 N, and that the detected contours did not vary significantly. Another example of an incomplete exam is the first plot in the third row. Only 4 measurements were taken at this location, and the results do not present conclusive evidence. The plot in the second row, second column shows a data set that does not present a clear result. It can be seen that one data point describes a small contour with a relatively large force, and as we move along the force axis we encounter a data point representing a large contour with an even larger force. This, to say the least, does not intuitively describe a healthy vein. By using the discrepancy between the TAR measure (which indicates a healthy vessel) and the value of the slope obtained by fitting a curve to the data (which indicates an unhealthy vessel), this data set can be labeled as invalid and discarded. It can be seen in general that as more data is collected, the results tend towards those expected of healthy veins. Even though there are some outliers in some cases, in can be seen that as more pressure is applied, the transverse area is decreased. The outliers are due to inadequate tracking of the vessel center because of a low frame rate from the ultrasound machine. Therefore there is a large change from one image frame to the next, and the feature detection algorithm starts at an incorrect location, detecting an incorrect large vessel area. A large force value is associated with this large area. Examples of this are first row, third column, and third row, second and third column. The force data was also normalized and curves were fit to the each data set, as shown in Figure 5.15. All x-axes are normalized force. It can be seen that the slopes for the incomplete data sets could indicate the presence of DVT, but for the complete examinations the values are as expected for a healthy vein. Table 5.1 shows the corresponding values for the slopes in Figure 5.15. Table 5.1: Values of Slope m -0.0608 -0.158 -0.422 -0.884 -0.293 -0.885 -0.483 -0.379 -0.271 -1.112 -0.917 -0.518 An additional segment of the SFV located distally with respect to the first was examined. 5.2 Experimental Results 118 Figure 5.15: Compression Examination Data - Curves Fit to Data A model was generated, and a compression examination was performed. Once the compression examination had been concluded, the information obtained from the examination was mapped to (a) (b) Figure 5.16: Reconstructed Human S F V the three-dimensional model, as shown in Figure 5.16. 5.2 Experimental Results 119 Some typical results are shown in Figure 5.17 for this distal segment. It should be noted that the maximum force needed in order to obtain compression of the vessel is less than in the previous case. This vessel segment is located in the mid thigh, as compared to near the groin for the previous case. It is expected that the force needed to compress a vein near the groin will be larger because of the surrounding anatomy. : 0.5 : 0.5 2 4 6 Force 2 4 6 Force Figure 5.17: Typical Compression Examination Data Figure 5.18: Typical Compression Examination Data - Curves Fit to Data Table 5.2: Values of Slope m -0.706 -0.634 -0.081 An approximation was also obtained for this data set, as shown in Figure 5.18. In general the results indicate a healthy vein, except for the data in the third column. This is because of the limitations of using a linear approximation. Even so, the Transverse Area Ratio obtained indicates a healthy vessel. This an example of using two of our DVT indicators in order to classify a vessel. A data set obtained from another volunteer shows similar results, as shown in Figure 5.19. In 5.2 Experimental Results 120 0.5 : 0.5 : 0.5 •• • 10 15 20 5 Force 10 Force 15 5 10 15 Force Figure 5.19: Typical Compression Examination Data II this case, we collected data from behind the knee (popliteal fossa), and the vein examined was the popliteal vein. A n interesting variation is the maximum force values in order to obtain complete compression of the vessel. 0.5 1 Norm. Force 0.5 1 Norm. Force 0.5 1 Norm. Force Figure 5.20: Typical Compression Examination Data ff - Curves Fit to Data (a) (b) Figure 5.21: Transverse Image Human P O P In all cases the minimum cross sectional area of the vessel is less than 10% of the original area. As well, the slopes obtained from the linear approximation indicate a healthy vessel, as shown in 5.3 Summary 121 Figure 5.20 and Table 5.3. Table 5.3: Values of Slope m 1.4508 -1.3586 -0.8602 Examples of two popliteal vessel cross-sections, as well as the extracted contours are presented in Figure 5.21. In both images, the popliteal artery can clearly be distinguished on the right side, and the detected contour indicate that the vessel has almost completely collapsed. Additional tests were performed mapping different venous and arterial segments. Since we were examining healthy individuals, we did not expect to find any incompressible venous segments. In order to simulate a positive DVT finding, the arteries were examined during a compression examination. It is expected that an artery will not compress as easily as a vein would. Typical results are presented in Figure 5.22. It can easily be seen that for all force levels applied to the region, the area of the detected contour remains relatively constant. This fact was also reflected on the vessel model that was constructed. < E 0.5 0 2 4 6 8 10 Force < E 0.5 0 0.2 0.4 0.6 0.8 1 Norm. Force Figure 5.22: Typical Compression Examination Data for Artery The value of the slope for this data set was m = —0.0098, indicating that the vessel is almost incompressible. 5.3 Summary In this chapter we have presented experimental results of a deep venous thrombosis screening system. Ultrasound compression examinations were performed on simulated and real human vessels 5.3 Summary 122 in accordance with our method and system, with promising results. Chapter 6 Conclusions and Recommendations 6.1 Summary In this thesis, a system for screening for deep venous thrombosis by processing B-mode ultra-sound images has been presented. An overview of deep venous thrombosis, as well as current diagnostic methods was presented. The compression ultrasound examination was closely examined and it was proposed that by measur-ing a vessel contour in a transverse plane during a compression examination, an objective measure to quantify DVT could be produced. The image feature detection problem was addressed and a model-based contour detection method was proposed, implemented and tested as presented in Chapter 4 in order to detect the vessel cross-sections. The contour detection method consists of a modified Star-Kalman algorithm that uses image brightness values, data from previous contours and an elliptical model in order to accurately detect a contour in an ultrasound image. The ellipse parameters a, b and c/>, where a is the semi-major axis, b is the semi-minor axis, and <j> is the angular displacement of the semi-major axis, were estimated to within 4.03%, 7.81% and 1.79°, respectively, of known ellipse parameters during the validation of the contour detection algorithm. Several validation metrics were developed in order to establish whether the detected contours were accurate or not. These metrics are not computationally intensive and are easily adaptable to 123 6.1 Summary 124 real-time systems. Sensors were included in our DVT detection system, which included a force-torque sensor and a location sensor, mounted unobtrusively on the ultrasound transducer. The data from the force-torque sensor indicated the amount of force applied through the ultra-sound probe on the tissue being imaged (ranging from 0 to approximately 20 N), and combined with the detected vessel contour produced data that indicated whether or not a vessel was healthy. By combining area and force measurements, a stiffness plot of the examined area was generated. With the data obtained from the 6 DOF location sensor, the ultrasound image and the detected contours were placed in a 3-D virtual environment. This environment was displayed to the user portraying the ultrasound probe, the ultrasound image and the detected contours all in correct perspective. Three-dimensional vessel models were constructed by stitching together the detected contours, and were incorporated into a user interface that augments the traditional ultrasound machine interface. The additional information acquired during a modified compression examination was mapped to the surface of the virtual model of the vessel, displaying the information in an intuitive way to the user. This is the first time to the knowledge of the author that information on the compressibility of a vessel has been mapped to a three dimensional model of that vessel, by integrating information from various sensors. The performance of this system was good, as seen in Chapter 5. Anatomically correct three dimensional models were constructed of vessel segments, and compression information was mapped to the corresponding locations. It should be mentioned that we have developed a screening examination that is potentially faster than the current screening methods, as accurate and highly operator independent. The system presented herein also has the potential of providing a means for performing a DVT screening without requiring that an experienced ultrasound technician be present. The existence of a fast, operator-independent screening system can in turn potentially reduce operating costs. The system that has been presented can also serve as an adequate tool for comparative eval-uation of DVT treatment techniques, creating accurate records of thrombus size, location and number within the venous system. Repeat examinations can yield objective measurements that 6.2 Recommendations and Future Work 125 can help describe thrombus migration throughout the vessels, as well as possible changes in vessel and thrombus stiffness over time. 6.2 Recommendations and Future Work There are several research directions which could improve the current work, as listed below. (1) Modification of the Star-Kalman algorithm. In this thesis, the feature detection algorithm uses an ellipse equation as the dynamic system to represent a contour. Several configurations were tested while a other promising ones were not. A promising option for the current system is to include the ellipse equation as a measurement for a Kalman filter, instead of including it in the state equations. This was briefly examined, but not developed. (2) An alternate tissue mimicking material should be used for the construction of the phantom for compression examinations. It was observed that under repeated compressions the agar gel did not hold up. Also, extensive force vs. area data from healthy and diseased human subjects as well as additional phantom development is needed in order to validate the phantom as an accurate representation of a vessel and thrombus within. (3) In our system, all vessels were identified based on the gray-scale B-mode images produced by the ultrasound machine, and the screening was performed based on the compression ultrasound examination. There are still other ultrasound imaging modalities that we could include in our screening system in order to correctly identify a vessel. One such example is the use of colour flow imaging, which can display the blood moving through the imaged vessels. By extending our screening system in order to also include colour information, it is expected that our vessel detection will improve. (4) One important issue is accurately identifying when a vessel has completely collapsed. The current system cannot currently identify a completely collapsed vessel. An adequate method to determine whether a vein has completely collapsed is needed. (5) Several improvements in the manner in which the gathered information is displayed are possible. Since our system relies on acquiring data at different force intervals, it would be advan-tageous to indicate to the user the force that is being applied through the probe. By means of a 6.2 Recommendations and Future Work 126 visual indicator, either located on the screen or on the probe itself, the user could be informed of the force level, and therefore the type of data the system is acquiring. It could be easily indicated whether the acquired images are being used to construct the vessel model, or to assess the vessel for compression by using, for example, a LED (or a set of LEDs) mounted on the probe by the colour that they display or by the rate at which they flash. Auditory feedback could be used as well in order to assist in informing the user the amount of force applied to the patient. For example, force intervals that we would want to indicate would be the upper force level (highest allowable force) for a model measurement to be valid, and the force interval at which compression data can be obtained. An additional safety measure could be implemented as well, by using the mentioned indicators to inform the user that they are pressing down too hard on the patient. (6) Two steps are necessary in order to use different depth or scale settings on the ultrasound machine. First, a transformation from image frame to sensor frame JWf for each depth setting must be generated, or alternately develop a general description of the transformation Mf that is dependent on the depth and scale settings on the ultrasound machine. Secondly, a program module which reads the depth or scale setting from the ultrasound machine must be included, so that the correct transformation and scaling factors are used to process the acquired data. Access to the variables which contain this data in the ultrasound machine is possible in the current configuration. (7) Concerning the commercialization of this system, a representative of Ultrasonix was con-tacted and asked about the possibility of integrating our system into a single-unit ultrasound machine. It was established that such a system would be possible without increasing the cost by much more than the value needed to include our system's sensors and software. The price increase would be approximately $10,000 - 15,000 CND, which would represent a 16 to 25% increase in total price. (8) Some problems did occur during the contour tracking through successive image frames, because the frame rate obtainable over the Ethernet connection was marginally acceptable. 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An Ultrasound Indentation System For Biomechanical Properties Assessment Of Soft Tissues In-Vivo. IEEE Trans. On Biomed Eng, 43(9):912-918, 1996. [100] W.H. Zhu, S.E. Salcudean, S. Bachmann, and P. Abolmaesumi. Motion/Force/Image Control Of A Diagnostic Ultrasound Robot. In International Conference on Robotics and Automation, pages 1580-1585, San Francisco, U.S., April 2000. IEEE. [101] W.J. Zwiebel. Introduction To Vascular Ultrasonography. W.B. Saunders Company, 4 edition, 2000. Appendix A Physics of Ultrasound Below is presented a brief description of ultrasound imaging modalities, encompassing the different physical interactions of sound with tissue, as well as basic instrumentation and a description of the system processes that take place [3,43,49,101]. A . l Physical Properties O f Sound A n d Transmission Media In general, an ultrasound imaging system acquires data through the generation of an ultrasound wave directed towards the area to be examined, and receives an echo signal generated by the interaction of the ultrasound wave with the tissue in the examined area. Sound is mechanical energy that is transmitted through a medium. Forces acting on the molecules, causing them to vibrate or oscillate about their mean positions, create periodic changes in the pressure of the medium. There is no net displacement of particles, and there is no mass transported, sound is only a disturbance in the medium. These changes in pressure are conveyed from one location to another through molecular interactions, transmitting the force from the source to a region distant to it. The energy propagates into the medium and is attenuated, scattered and reflected by interfaces. Sound requires an elastic, deformable medium for transmission. A sound wave can be characterized in a simple manner through its amplitude and its frequency. These characteristics depend on the medium the wave is being propagated through. The amplitude describes what the largest displacement a molecule has from its mean position, which can be translated into the maximum increase (or decrease) in the pressure due to the presence of the sound wave. The frequency describes how fast the oscillations occur or how many oscillations at a 135 A.l Physical Properties Of Sound And Transmission Media 136 given point per unit of time, generally described in cycles per second or Hertz (Hz). This can be presented mathematically as where A describes the amplitude of the wave at time t, AQ the peak amplitude, and / the frequency of the oscillations. An ultrasound wave is the same as a sound wave, only in a higher frequency range, that is higher than 20,000 Hz. Ultrasound has the same physical properties as sound and can be described in the same manner. Aside from amplitude and frequency, a sound wave has other properties to describe it. The period t is the amount of time necessary for one cycle to complete, or the inverse of the frequency. The wavelength spatially describes one complete cycle, as it is the distance from crest to crest of the waveform defined by equation A- l . Other properties that are specifically dependent on the medium that sound travels through are acoustic velocity and particle velocity. Acoustic velocity describes the speed at which a wave propagates through a medium, and depends on the density and compressibility of the medium. For soft tissues, the average speed has been found to be 1540 m/s and most ultrasound equipment is calibrated assuming this speed. Variations are small and generally ignored. Particle velocity is the speed at which particles vibrate back and forth around their mean positions. This velocity is proportional to the period of the sound wave. A medium will have certain properties that will describe how well sound will propagate through it, such as elasticity, density and compressibility. Elasticity is the ability of an object to return to its original shape after a force that has been acting on it is removed. Density p describes the mass of a medium per unit of volume ( kg/m3 ). The speed of sound in a certain medium will be proportional to the inverse of the root of the density of that medium. The compressibility K indicates the fractional decrease in volume when pressure is applied to the medium. The propagation speed of sound in a medium will be where po' s the mean density, and K is the adiabatic compressibility, assuming that there is no net A = A0 sin(2 ir f t) (A- l ) (A-2) transfer of energy from the wave to the medium. K is expressed in m2/N. A.l Physical Properties Of Sound And Transmission Media 137 If we assume that the pressure disturbance from the wave is much smaller that the equilibrium pressure, then the wave propagation will be linear. A.1.1 Interactions Between Sound And The Medium As sound travels through a medium, if the physical properties of the medium remain constant, the properties of the sound wave such as velocity, frequency, wavelength and period will remain constant. The amplitude of the sound wave will decrease or be attenuated in a manner proportional to the distance the wave has traveled. The intensity of a sound or ultrasound wave can be decreased through reflection, refraction, scattering, diffraction, divergence and absorption. The attenuation coefficient a of the medium describes this attenuation, and is expressed in decibels per centimeter ( dB/cm ). The value of this coefficient is dependent on the medium that the sound wave is traversing and the frequency of the sound wave. With respect to ultrasound imaging, the attenuation coefficient for soft tissue (fluid filled tissue) is nearly proportional to the frequency. For large organs, the attenuation coefficient has an intermediate value, and is relatively high for muscle and skin. Closely related to the attenuation is the acoustic impedance. The acoustic impedance is de-scribed by the density times speed, or Z = pc (A-3) where Z is the acoustic impedance, p the density and c is velocity. This quantity is a measure of the resistance to sound that is passing through a medium. It is expressed in kilograms per square meter per second ( kg/m2/s). Other sources of attenuation are through the reflection and scattering of the sound wave at boundaries between media with different densities, sound speed, or absorption properties. For ultrasound imaging, reflection is considered differently from the other attenuating factors. This is because the imaging principle is based on the assumption that when an ultrasound wave is directed at a patient, a percentage of that sound will reflect back to the transducer. This reflected sound contains the information necessary to create the images. Reflection occurs when an ultrasound beam comes upon an interface formed by two tissues with different acoustic impedance, or also called an impedance mismatch. The interface must be smooth and larger than the width of the ultrasound beam to be classified as a specular reflector A.l Physical Properties Of Sound And Transmission Media 138 and fit within this first analysis. These interfaces are responsible for the major organ outlines seen in diagnostic ultrasound examinations. For maximum detection of the reflected signal, the transducer must be positioned so that the generated sound beam will strike the interface being imaged perpendicularly. A fraction of the beam is transmitted through the interface, and part is reflected back. The amplitude of the reflected wave will be proportional to the difference of acoustic impedance between the two tissues. The greater the difference of acoustic impedance is between the two mediums, the greater the amplitude of the reflected echo. Large mismatches can be found at tissue-to-air, and tissue-to-bone interfaces. The ratio R of the reflected to the incident amplitude is described by R = (f 2 - ll\ (A-4) (Z2 + Zi) V ' where Z\ is the acoustic impedance of the first medium or tissue and Z2 is the acoustic impedance of the second tissue. By squaring equation A-4 we can obtain the ratio of reflected to incident power, or R?. This is also called the reflection coefficient an, which can be written as Since this coefficient is the square of the ratio R, the direction in which the sound wave traverses through the interface does not affect the amount of reflection that interface will generate. The amount of reflection will always be the same for a specific interface. If we subtract the reflection coefficient a/j from 1, we obtain the transmission coefficient ax, which can be also be expressed as * - imrr Another type of reflection is caused by an interface that reflects sound in multiple directions because the interface has a rough surface and is called diffuse reflection. The result is a weaker reflected signal, which presents a loss of coherence with respect to the emitted ultrasound. And unlike specular reflectors where the direction of the reflected echo depends greatly on the angle of incidence, diffuse reflectors reflect sound with various angles of reflection and are less dependent A.l Physical Properties Of Sound And Transmission Media 139 on the orientation of the interface with respect to the sound beam. Most tissue presents diffuse reflections. Scattering is also a type of reflection, called non-specular reflection. Scattering provides the texture of the organs in an ultrasound image. In this case, the interfaces are small, and less then several wavelengths across. Each interface acts as a separate sound source, and sound is reflected in all directions. Scattering is highly frequency dependent (/ 2 to / 6 ). Scattering is also the physical phenomenon that makes the detection of blood velocities possible. Ultrasound scanners are optimized to show the backscattered signal, which is considerably weaker than that found from reflecting boundaries. Backscatter from organs and tissue produce what is known as speckle, formed because structures are much smaller than the ultrasound wavelength, and does not reveal a physical structure. Speckle is the constructive - destructive interference of scattered signals from all those small structures. If an ultrasound beam strikes an interface at an angle of 90°, the transmitted beam will continue in a straight line along its path. If the angle that the beam strikes the interface at is different than 90°, the transmitted beam will bend away or be refracted. Refraction obeys Snell's Law, given by sin<j>j = Cj. sin 4>t ct where <j>i is the incident angle, <pt is the transmitted angle, Cj is the velocity of sound in the incident medium and Ct is the velocity of sound in the transmitted medium. The angles are measured from a line perpendicular to the interface. In this manner, the velocities of sound in the two media are related to the angle of transmission. Diffraction causes the ultrasound beam to diverge or spread out as the waves move farther from the sound source. This is more severe the smaller the sound sources. The lateral resolution of the beam and the sensitivity of the ultrasonic system are both affected by divergence. Interference can be described by the algebraic summation of waves. Interference can be con-structive or destructive, including every combination in between. Constructive interference results in increased amplitude and destructive interference results in decreased amplitude. Because of this, interference does not necessarily have to be considered as attenuation. Interference affects the uniformity of the beam intensity throughout the ultrasonic field, and is A.2 Basic Ultrasound Imaging 140 important in the design of an ultrasonic transducer. As well, focusing in real-time is accomplished by applying the principles of wave interference. Absorption is the only process whereby sound energy is dissipated in a medium. All other interactions mentioned until now only redirect the energy. In the absorption process, the sound energy is converted into different energy forms, namely heat. The absorption of sound by a medium depends on the beam's frequency, and the viscosity and relaxation time of the medium. The ability of molecules to move past one another determines the viscosity of a medium and the relaxation time describes the rate at which molecules return to their original positions after being displaced. The higher the viscosity (greater resistance to molecular flow) and the longer the relaxation times, the more absorption occurs. Also viscosity and relaxation time must be considered with respect to the frequency of the beam. The higher the frequency, the more energy is absorbed. A . 2 Basic Ultrasound Imaging For a general image to be obtained from an ultrasound system a sound beam must be generated, the reflected echo must be detected, and the received signals must be processed for display. All ultrasound scanning systems are derived from the Amplitude mode (A-mode) system, and is used as an example. A-mode is based on the echo-ranging principle. A pulsed ultrasound wave is directed at an area to be interrogated, and echoes from different boundaries and interfaces are detected. Only structures that lie along the direction of propagation are interrogated. This is called the scan line, or the line of sight. The returning echoes are received, recorded and displayed as spikes, and represent the interfaces that were encountered along the examination path. In A-mode, the term amplitude refers to the magnitude of the echo that is detected from the echo signal. This magnitude is plotted along one axis, while time or depth (interchangeable because they are directionally proportional) is displayed on a perpendicular axis. The amplitude is determined by the backscattered ultrasound signal, and peaks will occur where there are interfaces between areas with different reflectivities (or acoustic properties) of the media through which the ultrasound wave is traveling. Each interface will produce a different echo. Time gain compensation is used to correct for attenuation loss of the wave. A-mode scans contain spatial information, since A.2 Basic Ultrasound Imaging 141 they register distance between interfaces. An A-mode system consists of a transducer that is excited to produce an ultrasound signal, which is directed into the tissue. A clock begins to measure the time from the emission of the pulse, until a certain depth limit is reached. The depth can be determined by the time of travel of the ultrasound wave as mentioned before, considering a constant speed in the tissue. Various averages for speed in tissue have been used, ranging from 1520 m/s to 1540 m/s. When an echo is received, the transducer produces an induced electrical signal through the piezoelectric effect. This signal is processed for display. The signal passes through a time gain compensator (TGC) which amplifies it, and the envelope of the signal is detected. This envelope produces a graph of the observed area along the line of sight, in the form of amplitude of the signal versus depth. Only one line can be observed at any given instant on the display. A transducer that consists of a piezoelectric crystal generates the ultrasound beam. A piezo-electric crystal has the property that if a voltage is applied across it, it either contracts or expands. If an alternating voltage wave is applied to it, it will oscillate and produce a mechanical vibration. Selecting the proper frequency and crystal thickness, an ultrasound wave of a desired frequency can be produced. If on the other hand the piezoelectric crystal is mechanically compressed, then a voltage will be induced across it. For this reason, a piezoelectric transducer is used to generate the ultrasound beam and to receive the reflected echo. The piezoelectric transducer is sensitive to electromagnetic noise, and is shielded in order to be able to detect weak signals. For imaging, the transducer sends out a short burst of ultrasound, followed by a period of silence to listen for returning echoes. These are the transmit and receive modes respectively, used in a pulsed system, as opposed to a continuous system where the transducer is driven to produce a constant ultrasound beam. A pulsed system is based on the echo ranging principle, were an ultrasound wave is transmitted into the body, strikes an interface, and is partially reflected back to the transducer. The amplitude of the reflected echo depends on the different acoustic impedance of the media, as discussed above. If the time between the emitted pulse and the detected echo is known, as well as the speed of sound in the medium, then the distance to the interface can be easily calculated. z = ct (A-8) 2R = ct A.2 Basic Ultrasound Imaging 142 where z is the distance traveled by the sound beam, c is the velocity of sound in the medium, t is the time elapsed between when the pulse was fired and the echo received, and R is the distance from the transducer to the interface. There are two ways to generate a pulsed wave output. The crystal can receive an electrical signal from a gated input connected to a sine wave generator. The master synchronizer controls how long the sine wave excites the crystal, and how long the crystal is left to be able to receive a reflected echo. In the second method, a capacitor can be charged during the listening time, and discharged through the piezoelectric crystal, which vibrates at its resonating frequency. The amount of charge in the capacitor (and discharge time) determines the pulse length. The number of times the crystal is pulsed per second is called the pulse repetition rate or frequency (PRF). There is an upper limit to the pulse repletion rate or frequency (PRFm) which depends on the maximum depth R sampled and the velocity of ultrasound c in the medium. PRFm = ^ (A-9) Substituting equation A-8 into A-9 we obtain PRFm = ^ . (A-10) From equations A-9 and A-10 we can see that the deeper the structures are that we want to obtain data from, the more time is needed and therefore a lower PRFm. In general the user cannot modify the PRF. The inverse of the PRF is the pulse repetition period PRP, which describes the time required to transmit a pulse plus the time needed to listen for the returning echoes. The spatial pulse length SPL is the length of the short duration pulse generated during transmit, and can be calculated by SPL = \n (A-ll) where A is the wavelength of the ultrasound frequency being used, and n is the number of cycles that are transmitted during the short pulse. The SPL can influence the axial resolution. For better resolution, a shorter pulse is desirable. The temporal pulse length, or pulse duration PD is a measure of the time in which the trans-A.2 Basic Ultrasound Imaging 143 ducer generates the ultrasound pulse. It is the elapsed time from the initiation of a pulse to a point 20 dB below the maximum peak-to-peak pressure amplitude of the wave, or the number of half cycles in which the peak amplitude is greater than 25% of the maximum amplitude in the pulse. The axial resolution also depends on the PD, which is calculated from the number of cycles n in a pulse and the period r of the wave PD = m (A-12) The SPL varies directly with the pulse duration, the constant of proportionality being equal to the velocity in the medium SPL = cPD . (A-13) The duty factor DF is the fraction of time the unit is active and is calculated by D F = Tip • ^ The DF has no units, since it is merely a ratio. The direction of travel of the sound beam produced by a diagnostic ultrasound transducer is parallel to the axis of the transducer. This sound beam has two components, called the near field and the far field. The near field extends axially to a distance of approximately a 2 /A, where a is the transverse radius and A is the wavelength of the ultrasound wave. Within the near filed, the amplitude and the intensity of the beam fluctuate from one place to another, but the beam remains collimated. Where the near field becomes the far field, the sound beam gradually becomes smooth and continues smooth throughout the far field, but the beam diverges as the distance from the transducer increases. For two transducers with the same dimensions, the divergence angle will be greater for lower frequencies than that for higher frequencies. The spatial resolution for a transducer is defined by the minimum spacing between two reflectors for which they can be distinguishable on the display. In the case of ultrasound images, the spatial resolution is defined by three elements, axial resolution, lateral resolution and slice thickness. The axial resolution specifies how close two objects can be along the axis of the beam and yet still be detected as two different entities. Axial resolution also specifies the smallest object detectable along the axis of the beam. A.2 Basic Ultrasound Imaging 144 Commonly the spatial pulse length is used as a specifier for axial resolution. The best possible axial resolution is the spatial pulse length divided by two. Other factors also influence axial reso-lution, but at a cost. The SPL depends on the number of cycles and the frequency of the wave. Fewer number of cycles increase the spatial resolution because the SPL decreases, but the number of cycles that can be produced cannot be made extremely small because of physical limitations. Higher frequency improves axial resolution, because this shortens wavelength which in turn reduces de SPL, but higher frequency implies less penetration into tissue. Focusing the transducer creates a region of higher intensity increasing the sensitivity, but may lengthen the pulse deteriorating the axial resolution. Lateral resolution describes the ability to resolve two objects adjacent to each other that are perpendicular to the beam axis. It also refers to the ability of the ultrasound beam to detect single small objects across the width of the beam. In general, decreasing the beam width improves lateral resolution. The more a beam diverges, the worse the lateral resolution. For single element transducers the lateral resolution can be improved by focusing the transducer crystal. The beam is focused within a focal zone. The focal zone is defined as the region where intensity has a value within 3 dB of the maximum along the transducer axis. The distance from the front face of the transducer to the focal point is called the focal length. The beam can be focused externally as with light, with acoustic lenses or mirrors, or can be focused internally through the use of a curved piezoelectric crystal. Focusing reduces the beam width over a volume called the focal region. In this region, the beam width can be approximated by r r r 1.2 A F . . . W * — (A-15) where F is the focal distance, 2a is the diameter of the radiating surface and A is the wavelength. Higher ultrasound frequencies provide narrower sound beams and higher lateral resolution. The thickness of the scanned section that contributes to the image is referred to as the slice thickness. This thickness depends on the width of the ultrasound beam perpendicular to the image plane. The focusing is achieved in this direction in most cases with the use of an acoustic lens, and is considered the worst aspect of the resolution of ultrasound transducers. A.2 Basic Ultrasound Imaging 145 A.2.1 Transmit Gain Most ultrasound units include an output, power or transmit gain control that can be adjusted to produce an acoustic pulse of higher intensity, resulting in a higher echo. Increased sound wave intensity enhances the detectability of weak reflectors. However, higher intensity levels increase patient exposure and unlimited power gain does not continue to improve sensitivity. In addition high intensity distorts the sinusoidal pressure wave, altering both the propagation and the reception of sound waves. Doubling the intensity results in a sensitivity change of 5%. A . 2.2 Amplification A reflected sound wave strikes the crystal and induces a radiofrequency RF signal via the piezoelectric effect. The waveform of the RF signal mimics the ultrasound waveform. The microvolt or millivolt RF signal is amplified to 1 V or 10 V for processing or display purposes. Combinations of linear, exponential, logarithmic, and variable amplifications can be used. The most common type of receiver gain is logarithmic. The amount of gain is adjustable by the user. Weak signals undergo more amplification than strong signals. Dynamic range (dB) is the ratio of the largest to the smallest signal that can be accommodated by a system component. Logarithmic amplification reduces the dynamic range of the induced RF signals, and this is called compression. A.2.3 Time Gain Compensation Equally reflective interfaces will produce different intensity signals, depending on their relative distances from the transducer because of attenuation of the ultrasound beam. Time gain compen-sation TGC control is used to increase the amplitude of processed signals with time or depth. A.2.4 Signal Processing Normal processing includes either rectification of the RF signal, after it has been amplified and passed through the TGC control, or clipping the negative sections of the RF signal. Afterwards the signal is enveloped or demodulated, generally by using a low pass filter. After that, the envelope is mathematically integrated and presented as a spike or dot with height or brightness proportional to the result of the integration, respectively. Threshold or suppression control can also be added. A.2 Basic Ultrasound Imaging 146 Other techniques can also be incorporated, such as leading edge detection, peak detection or differentiation. Usually integration is used along with leading edge detection. A.2.5 Scanner Types Different types of scanners are and have been use to acquire information from a patient. Below is a general list of these. • Mechanical scanners. With these types of scanners, the ultrasound transducer is physically moved and reoriented to scan over a region of interest ROI. Generally, this is done by oscillating the transducer within the scan head, in this manner steering the sound beam over the ROI. Alternatively, the beam may be swept over the ROI using an acoustic mirror. • Linear array or sequential scanners. The image is formed by an array of separate rectangular transducer elements placed side by side, numbering approximately 120. The ultrasound beam is produced by simultaneously activating groups of approximately 15 to 20 elements, referred to as the active elements. The echoes are detected by the active elements and then these are shifted one over centering the beam over a different area, and the process is repeated. • Curvilinear array scanners. The transducer elements are arranged on a convex scanning surface on these types of scanners, resulting in a similar to linear arrays. The image is acquired in the same manner as for the linear arrays as well, but providing a wider image field while scanning from a narrower window on the patient surface. • Phased array scanners. These types of scanners consist of an array of about 120 very narrow elements arranged side by side. Each ultrasound beam line is produced by the combined use of all the elements simultaneously. The beam is 'steered' by introducing small time delays between transmit pulses applied to the individual elements. Time delays are also applied to echo signals picked up from individual elements during reception, in this manner steering the received directionality as well. An image is formed by using approximately 150 beams steered in different directions. In order to view the image as such in a suitable format, a scan converter is generally used. The image is converted into a format adequate for video monitor viewing and for video recording. Usually this is a digital device, which converts the ultrasound information into pixel values at A.3 Brightness(B)-Mode Imaging 147 specific locations, with brightness represented by a designated number of bits used for each pixel. In this manner, the brightness information is converted into a digital format thereby defining the brightness resolution with the number of bits per pixel. The amount of pixels vary, but the resulting image measures approximately 500 by 500 and resembles a television image. Some scanners can also store cine loops for viewing a sequence of images. A . 3 B r i g h t n e s s ( B ) - M o d e I m a g i n g It can be considered that a B-mode image is formed based on a series of A-mode images, repre-sented in a different manner, and including several A mode plots at a time. Instead of representing the amplitude of an echo along a vertical axis, this information is presented as brightness, hence the name B-mode (B for brightness). The location on the screen where this brightness information is placed depends on the position and orientation of the transducer, which corresponds to a location in the patient. In this way a two dimensional representation of the anatomy is presented. For a single element transducer, this position and orientation information was obtained through a me-chanical setup. The displayed position for each B-mode dot is determined from the beam angle at the time of echo detection and the echo return time T. For array transducers the relative position of the transducer elements is known and the image can be easily constructed. Real-time B-mode ultrasound makes dynamic studies possible. In static B-mode gray-scale imaging the transducer is placed at the starting position and in-formation is recorded along a single line of sight. All echoes from a single pulse are assumed to originate from reflections along that line of sight. The amplitude of each signal is represented by the brightness of the dot. To build up a two dimensional image, the sonographer moves the transducer manually to a different position or orientation to acquire information along a new line of sight. The previous line of sight data are retained. The image, or sonogram, is thus created by obtaining a large number of lines of sight over a 10 or 20 second period. The resolution of the image is improved as the number of lines of sight is increased. Static scanning depends on the object not moving, because lines of sight are acquired at different times and then combined to form a single image. Real time gray scale imaging requires the acquisition of data in a very rapid fashion to give the perception of motion. The ultrasound beam is swept or steered (electronically or mechanically) A.3 Brightness(B)-Mode Imaging 148 through the area of interest in a repetitive automated fashion. Instead of a single sonogram with multiple lines of sight, as in static B-mode scanning, multiple sonograms are formed each composed of multiple lines of sight. Every line requires one pulse of ultrasound waves to probe interfaces along its path. The ultrasound beam is first directed along one line of sight, and after the echoes are received for that line, the next line is probed. In this manner, an entire area is scanned by sweeping the beam over the region. This process is repeated to produce successive images of the region. If the detection of rapid motion is desired, a faster frame rate is necessary to display structures without jerkiness. The restrictions on the frame rate are imposed by the time it takes an ultrasound pulse to travel to the desired depth and back to the transducer, as well as the lateral resolution required in the image (how many vertical lines are sampled). The more lines of sight there are in an image, the better the resolution. Frame rates of 5 to about 60 images per second are available. The number of scan lines in a frame us usually between 50 and 200 depending on scan conditions. Commonly 120 to 150 scan lines are used. A.3.1 Frame Rate Limitations The number of complete scans carried out by transducer per second is known as the frame rate FR. The frame rate is limited by the speed with which the sound pulse propagates (which depends on the properties of the tissue), the depth setting of the scanner (defined by the PRF), and the number of beam lines forming the image. The maximum frame rate FR in frames per second fps is given by the following equation FR = s— = ™F (A-16) -r-n' 2RN N v ' where c is the velocity of ultrasound in the medium, R the depth of interest, N the number of lines of sight per frame ( Ipf ), and PRF the pulse repetition frequency. This equation indicates that if the scanning depth and/or the number of lines of sight are increased, the maximum frame rate must decrease. In the end, the speed of sound is what ultimately determines the frame rate. 13 msec is required for every cm of tissue. The sound must travel from the transducer, through the tissue to the maximum depth, and then return to the transducer to be detected for each line of sight. The frame rate is inversely proportional to the time it takes for the sound to travel this A.3 Brightness(B)-Mode Imaging 149 distance. Conventional B mode scanners operate at a PRF of between 200 and 2000 pulses per second. Real-time scanners reach 5000 pulses per second, in this manner maintaining lateral resolution as well as a high frame rate. A.3.2 Real-time Scanners The manufacturer of real time equipment sets the frame rate based on the field of view, depth of interest, and number of lines of sight required for the desired image quality. Several approaches are possible to compensate for an increase in scanning depth. The real time unit may automatically decrease the frame rate but maintain the same number of lines. On the other hand, both frame rate and number of lines may be adjusted downward. The number of lines may be reduced without a loss of resolution by narrowing the field of view. Often several transducers of different frequencies are available for use with a single ultrasound unit. Each frequency is optimized with respect to the number of lines of sight and frame rate as a function of sampling depth. Scan converters are not necessarily needed for real time B mode, but they can be used to allow for data manipulation and aid in the interpretation of the images. Since each line of sight is defined by a specific crystal position, we know the relative location the information is coming from to build a 2D image. This information can either be displayed immediately or stored. Scan converters are usually incorporated to obtain better grayscale images and provide freeze frame capability. Different types of real-time scanners can be used to acquire information. These are divided in the same manner as general scanners. • Mechanical scanners. The ultrasound beam is focused, and swept through the region of interest by mechanically moving the scanner. This is usually the simplest and least expensive type of real-time scanner. These are divided into contact and liquid path scanners. With contact scanners, the transducer makes physical contact with the patient and is mounted within a liquid medium. The transducer generally is attached to a motor and moved or wobbled. The transducers that comprise a liquid path scanner are placed in a liquid bath (usually a water and alcohol mix) and the transducer is moved from one end to the other, in this manner acquiring data. • Sequential (non-segmented) linear arrays. Consists of multiple crystals arranged in a straight A.3 Brightness(B)-Mode Imaging 150 row. Each crystal produces an ultrasound beam, and then receives the echo from that beam to build the 2D image. The crystals are activated sequentially to form the individual lines of sight. The number of crystals determines the number of lines of sight. The crystals are fired sequentially with a certain delay between firing to account for the ultrasound beam traveling through the tissue, and reflecting back to the transducer. The first crystal is fired and a certain time elapses, calculated from the desired depth, while the transducer collects information from reflected the ultrasound. Then the next crystal is fired, and information is collected until all crystals have been fired. This forms one image. Afterwards this process is repeated for the next image. The frame rate is determined by how long it takes all the crystals to be fired. • Segmental linear array. With this type of transducer, groups or segments of crystals in the linear array are stimulated, in order to produce a more desirable beam shape. Although the resultant ultrasonic field provides a more favorable beam pattern, fewer lines of sight for the same given area are used deteriorating the lateral resolution. In order to obtain good lateral resolution with these arrays, while maintaining the favorable beam pattern, a step-down procedure is implemented. For example, a set of four crystals is fired as a group or segment to produce the desired beam pattern and improved resolution is achieved by overlapping groups, in this manner increasing the number of lines of sight can be increased. • Phased arrays. These can be classified as linear, annular or rectangular arrays, and can vary in the amount of crystals that make up the transducer (16 to 128 elements). Unlike linear arrays, all elements are fired at once and only one line of sight is imaged at a time. Through the use of time delays between the excitation signal and the transducer elements, the beam can be steered throughout the field of view and allows data collection along different lines of sight. Small time delays can be implemented to achieve fixed transmit focusing, and the beam can also be dynamically focused in receive mode. Outside the central field of view the resolution deteriorates because of the increased difficulty of electronic focusing of beams when large-angle beam steering is used. A.3 Brightness(B)-Mode Imaging 151 A.3.3 Focusing Ultrasound Beams Ultrasound beams are focused to improve the lateral resolution and sensitivity. Because a linear array has a rectangular format, focusing must be applied in two directions. The length direction is also referred to as the in-plane direction because scan data collected with respect to this direction forms one dimension of the cross sectional image. Focusing along the width direction (out-of-plane) determines the slice thickness (thickness of tissue from which the data is collected) of the cross-sectional image. Focusing can be achieved mechanically or electronically. Mechanical focusing methods narrow the ultrasound beam in the width direction. This is done by using curved or concave acoustic lenses or using curved crystals, done in a uniform manner over the whole array. Electronic focusing is more complex. Since the sequence of firing one group of crystals (stepping down) and then firing the next group prohibits mechanical focusing of the ultrasound beam in the length direction, a dynamic focusing technique is needed. The relative position of a crystal in a group determines the focusing requirements for that crystal. Electronic focusing can be achieved during transmit or receive mode. The process of delaying the firing of crystals and changing the delay times to obtain different focal depths is called transmit focus. Implementing delays on the received echoes from different crystals is called receive focus. Transmit focusing involves the superimposition of ultrasound waves. Each crystal produces a particular wave pattern, and the overall pattern is the sum of all waves from all crystals. Electronic focusing is accomplished by offsetting the firing of various crystals in a group be a small delay (in the range of nanoseconds) compared to the time it takes the ultrasound wave to travel through tissue to the depth of interest. Varying the delay times between crystal firings alters the depth of the focal zone. This delay is accomplished by delay lines, which hold the command signal for a specified time. The exact nanosecond timing sequence depends on crystal position and the focal zone depth desired. The wave front generated by each crystal in the group is made to arrive at a specific point in the phase, and the result is a focused beam at that point. Improved spatial detail is obtained within the focal zone, because a narrow beam is used to scan the region of interest. Multiple transmit focal zones can be achieved at one time, but this capability is usually ac-companied by increased cost. For each focal depth all the information for a complete image must be obtained, thus increasing the scan time depending on the number of focal depths in the image. A.3 Brightness(B)-Mode Imaging 152 The frame rate for this case is calculated by F R = 2PTN-n <A"17> where c is the velocity of ultrasound in the medium, R the depth of interest, N the number of lines of sight per frame Ipf, and n is the number of focal zones. Combining multiple zones to form one image may cause a discontinuity at the boundary between focal zone areas, called the stitch line artifact. Co-processing the echoes restores the frame rate to the original value. The rate of data collection is increased by simultaneously acquiring multiple lines of sight. Select portions of each line of sight corresponding to the focal depth are retained for the final image. Data for all zones are obtained concurrently, with one area collecting short focus, another medium and another long, for example. Another manner in which transmit focus is achieved is through aperture focusing. This consists of varying the number of crystals that are fired as a group. This is based on beam aperture and its properties. If fewer crystals are excited, a smaller aperture beam is produced which results in a very short and narrow near field. This in turn results in a short focus. If more elements are used at a time, the near field is extended, and therefore a longer focus is obtained. Aperture focus is characterized by the / - number, defined as the ratio of focal length F to the size of the aperture in the length direction d, an is expressed by F f — number = — (A-18) d When the f-numbefs value is 2 the optimal focusing occurs. Many manufacturers combine time delayed firing and aperture focusing for the optimization of the beam focus. One disadvantage of aperture focusing is that it tends to decrease the frame rate. Receive focus is based on the premise that when an echo is generated at an interface, the echo arrives at different transducer elements at different times. Because of this time delays can be applied to the detected signals in manner similar to transmit focus to implement a receive focus. By delaying the received signals from different elements, these signals are brought into phase and afterwards summed, creating one single signal from each reflector detected by use of all the elements. During the reception of the echoes, the focal region changes dynamically by automatically A.3 Brightness(B)-Mode Imaging 153 varying the delays to the received signals with time, and therefore the depth, after the ultrasound pulse has been generated. This dynamic focusing improves the resolution over the entire image and is done by most instruments that use array transducers. One great advantage is that it does not slow the frame rate down the way multiple transmit focusing does. Appendix B Deep Venous Thrombosis Examination B . l D V T It has been established in the literature [78] that DVT of the lower limbs is a frequent condition, and if left untreated, carries a high risk of mortality and morbidity [80]. The thrombi obstruct venous pathways, not permitting blood to flow. Also, thrombi may break off and flow through the vascular system, and are a potential cause for pulmonary embolism (PE). 50 % of patients with proximal DVT have lung scan evidence of PE [80, 97] and if left untreated can cause fatal PE. Because of this it is imperative to be able to adequately detect, quantify and characterize thrombi, specifically in the veins of the lower extremities, permitting a correct diagnosis of DVT to be able to administer appropriate treatment. DVT usually originates in the deep veins of the calf, due to the sluggishness of blood flow in this area. More rarely, DVT may originate in the ileo-femoral-popliteal veins, particularly as a consequence of trauma or surgery on the thigh. The thrombi usually originate from valvular pockets lined by normal endothelium, and are composed mainly of red cells and fibrin. Even though there are usually very few platelets in the head of the thrombus, there are substantial amounts of them in the thrombus tail which grows proximally. The length of venous thrombi may range from a few millimeters to long enough to fully occlude large veins. Thrombus extension occurs in the direction of the blood flow by deposition of successive layers; thrombi may contain a fluctuating segment that 154 B.2 Current Methods of Detection of DVT 155 may dislodge and cause emboli. Pulmonary emboli can sometimes originate from calf vein thrombi, but this is rare and usually of little clinical consequence because the corresponding emboli are small and occlude only the most peripheral segments of the pulmonary artery. Thrombi originating from proximal veins (popliteal, femoral and iliac) are usually much larger and carry a greater risk of clinically severe PE [80]. DVT can be diagnosed by several methods. It is the doctor's responsibility as to which tests to order and methods to use, and the results from the imaging methods commonly have to be interpreted to obtain pertinent information. B . 2 Current Methods of Detection of D V T Patients with deep venous thrombosis can remain asymptomatic or may present with complaints of lower extremity pain, swelling and/or erythema. Data, however, demonstrate that only 50% of symptomatic patients have a documented deep venous obstruction [57]. The techniques used in the diagnosis of these disease processes may be broadly classified as physiological or anatomical. The physiological, or functional, studies provide indirect evidence of venous disease and reflect the hemodynamic or biochemical consequences of its presence. The anatomical studies demonstrate directly the presence of disease, localizing and quantifying the extent of venous disease and characterizing the pathological processes involved. Anatomical techniques directly visualize thrombus and can demonstrate the pattern of obstruc-tion [57]. 1251-labeled fibrinogen uptake and scanning, radionuclide venography, B-mode imaging and magnetic resonance imaging are classified as anatomical studies. Duplex imaging combines aspects of physiological and anatomical evaluation. B.2.1 Contrast Venography Contrast venography (CV) has been the reference method for the diagnosis of DVT [47]. CV establishes presence, precise location and extent and occlusiveness of venous thrombi. Contrast medium is injected into a vein through the patient's foot, then radiographic images are taken of the filling of the veins, which when interpreted correctly can diagnose DVT. At present, contrast venography is the only method with proven accuracy for the detection B.2 Current Methods of Detection of DVT 156 of asymptomatic DVT in high-risk patients [80]. The disadvantages are that this is an invasive procedure, and may cause pain to the patient. It is also a difficult technique to interpret. Another disadvantage is that CV cannot be performed in up to 10% of patients, because of inability to acquire venous access, allergic reactions, local infections, or because of renal insufficiency [47]. B.2.2 Plethysmography This technique is based on changes in blood volume in an extremity produced by venous ob-structions and can be used to non-invasively characterize valvular function and the hemodynamic consequences of chronic venous disease. Plethysmographic techniques have utilized changes in bioelectrical impedance to assess venous capacitance and outflow in response to temporary extrinsic venous compression. They provide a tool for identifying the presence of obstruction and for documenting the resolution of thrombotic obstruction and/or collateral development. This information yields quantitative descriptions of venous hemodynamics. Such objective information is not readily available with anatomical imaging techniques. However, the accuracy of the results will be affected if the patient does not breathe normally or keep the leg muscles relaxed. Compression of the veins because of pelvic tumors or decreased blood flow, due to shock or any condition that reduces the amount of blood the heart pumps, may also change the test results. There are several variations of plethysmography, which are listed below. Impedance Plethysmography (IPG) • This method takes into account that changes in blood volume lead to changes in electrical resistance or impedance. This resistance changes depending on the volume of blood flowing through the veins. Electrical resistance is measured using high frequency signals. • This method is not very accurate for calf vein thrombosis, but can be used to diagnose recurrent DVT in some cases. The accuracy varies between different machines. • Impedance plethysmography is also called an impedance test of blood flow or impedance phlebography. B.2 Current Methods of Detection of DVT 157 Strain gauge plethysmography (SGP) • This method detects volume changes by measuring circumferential changes using strain gauges. This change in circumference is proportional to the blood flow, which in turn can be used to decide if there is a thrombus or not. • This technique is not as extensively evaluated as impedance plethysmography. Photoplethysmography • Venous photoplethysmography employs a transducer incorporating an infrared light emitting diode and an adjacent photosensor. Variations in the amount of back-scattered light reflect capillary volume flow and are a function of arterial inflow, venous outflow and the presence and extent of venous reflux. B.2.3 Ultrasonography (US) This method has widespread clinical application, because it can non-invasively characterize valvular anatomy and physiology with fairly good resolution. It is based on the concept that ultrasound waves traversing biological structures are reflected from barriers or interfaces between structures with different acoustic impedance. These reflections are sensed and interpreted to form images. Two dimensional, direct visualization of the thrombus is possible. The imaging allows localization and quantification of the extent of thrombus present and permits the identification of non-occlusive thrombus. The sensitivities of real-time B-mode imaging with compression, duplex ultrasonography and color flow duplex imaging to proximal deep venous thrombosis do not appear to be significantly different. Sensitivity of calf vein thrombosis is low because of the small size and anatomic variations. Isolated thrombi in the iliac vein and in the superficial femoral vein within the adductor canal are difficult to detect. The non-invasive techniques described (CUS, IPG) are not suitable for the detection of asymp-tomatic proximal DVT because their sensitivity in asymptomatic patients is much lower than that in symptomatic patients [80]. B.2 Current Methods of Detection of DVT 158 B.2.4 Compression Ultrasound The most accurate, reliable and simple criterion for the presence of DVT is non-compressibility of the vein under gentle pressure known as compression ultrasound (CUS). Most studies are limited to compressibility of the common femoral vein and popliteal vein. Visualization may be difficult and not always reproducible. Although a normal CUS test result essentially excludes a diagnosis of proximal vein thrombosis, it does not exclude isolated calf vein thrombosis. Real-time B-mode ultrasonography yields an image that allows direct visualization of veins, as well as intraluminal thrombus. Imaging is generally combined with venous compression to further define the presence of intraluminal thrombus. Real-time US that applies the only qualitative crite-rion of full compressibility (CUS), has been proved to be of limited value because in a substantial proportion of patients the veins affected by a thrombotic process are not compressible, making it impossible to distinguish a recent thrombus from an old one. A more detailed description of CUS is presented in Section B.4. B.2.4.1 Continuous Wave Doppler The venous Doppler examination employs continuous-wave Doppler instrumentation to assess ve-nous flow characteristics (spontaneity, phasicity, augmentation and reflux) in the deep veins of the lower extremity. Deep venous thrombosis is characterized by the absence of spontaneous venous flow, the presence of continuous venous flow without phasic respiratory variation, and/or diminished augmentation on distal compression or proximal decompression. It has been established that Doppler sonography alone is not enough to asses DVT of the lower extremity [35]. B.2.4.2 Colour Duplex scanning This technique utilizes a combination of pulsed Doppler with two dimensional B-mode imaging, and the diagnosis is performed based on a combination of previous criteria. Duplex imaging has been used to assess valvular competence, to localize the levels of valvular insufficiency and to provide qualitative and quantitative descriptions of venous reflux. B.2 Current Methods of Detection of DVT 159 B.2.5 1251-Fibrinogen scanning (IFS) This method involves the incorporation of labeled fibrinogen into a thrombus, and then imaging the extremities to reveal where the label fibrinogen has accumulated. Some false positives can occur from other causes, and false negatives can occur from old or smaller thrombi. This method is insensitive in thigh and upper pelvic area. The disadvantages are that it is an invasive technique, uses radioactive materials, and there is a necessity for fibrinogen, which can only be derived from human plasma. Because of concerns with regard to disease transmission, the use of fibrinogen scanning has been abandoned. B.2.6 Computer Assisted Tomography and Magnetic Resonance Imaging There are not many trials and evaluations of C T and MRI, but from the information that has been acquired, it has been observed that C T is better for detecting thrombi in major veins than CV. Magnetic resonance imaging offers the potential for three-dimensional visualization of the deep veins without the use of contrast agents, and may provide increased sensitivity to iliac and pelvic vein obstruction. Comparison of studies evaluating MRI is complicated by the lack of uniform reporting standards, although the sensitivity and specificity exceed 90% in most series. Both these techniques are expensive and time consuming, which is their major downfall. B.2.7 Laser Doppler Fluxometry (LDF) The presence of DVT is likely to increase the venous pressure and, consequently, the venous volume distal to the thrombosis. This may trigger peripheral vasoconstriction responses, which result in a reduction of skin blood perfusion. Theoretically, the reduction of skin blood perfusion upon artificial venous occlusion would be less pronounced in the leg with DVT than the leg without DVT. LDF is useful for this purpose, as it can measure the peripheral vasoconstriction response upon an increase in venous pressure, which is hypothetically preactivated upon venous damming by a thrombus. Laser light is conducted through optical fibers to the skin, where it penetrates the skin and is partly reflected. When back scattered by moving objects, this light undergoes a frequency shift, which is proportional to the velocity and number of moving objects (flux) [23]. B.3 Venous Anatomy of the Lower Limbs 160 B.2.8 Blood Tests There are several biochemical methods developed for the diagnosis of DVT. These methods are beyond our scope, and it suffices to say that they cannot be used as the only diagnostic tool for the detection of DVT [47,57]. B.2.9 Near-IR Time-Resolved Spectroscopy This method has not been completely proven, and is only in development stages. It will be men-tioned only as a possible solution for diagnosis of DVT. NIR-TRS has been combined with frequency response analysis to provide a possible tool for the detection of DVT in two dimensions. Frequency response analysis is applied to analyze NIR-TRS spectra from a tissue with a thrombus. The value changes in parameters obtained from frequency response analysis are correlated with heterogene-ity position in three dimensions. The goal of this research is to non-invasively localize deep vein thrombosis in the human leg through the use of this combination [44]. B .3 Venous Anatomy of the Lower Limbs The anatomy of the venous system in the limbs is very complex and variable, more so than that of the arteries. The arterial system is in general much more regular, and even though it is a general rule that veins accompany arteries, it is not always so. Because of this, the location of the venous system is sometimes described with reference to the arterial system, and examination protocols suggest identifying the arterial system first to obtain a reference, as will be described further below. Two terms commonly used for describing the relationship between anatomical structures are proximal and distal. When used to describe the venous system, proximal describes locations that are nearer to the heart, and distal describes locations that are farther from the heart [3]. These terms are used differently when describing the arterial system, where they are used with respect to blood flow, and may cause some confusion. The portion of the lower extremity between the hip and the knee is known as the thigh. The segment between the knee and the ankle is known as the leg. On the leg, the posterior, muscular portion is called the calf. Sometimes, the term leg is used to reference the entire lower extremity, causing some confusion [101]. B.3 Venous Anatomy of the Lower Limbs 161 The veins of the lower limb are divided into the superficial and deep systems, which are con-nected by a number of veins called perforator veins. From distal to proximal, the deep venous system is the following. Starting with the calf, there are three main groups of veins, the posterior tibial (PT), peroneal (PER) and anterior tibial (AT). Usually, two veins accompany each artery of the same name, but there can be as many as 3 veins alongside the artery. In the calf itself there are sinuses or venous channels present, the largest of these being the gastrocnemius and the soleal veins. The gastrocnemius veins are branches of the popliteal vein located in the medial head of the gastrocnemius muscle and are a potential site for DVT. These venous channels progress proximally (upward) and in the upper calf area they join the other deep veins. Calf veins join to form the popliteal (POP) vein or veins, as there can be as many as 3 veins. The popliteal(s) runs up the popliteal fossa, usually posterior and medial to the artery [3], or posterior Anterior Tibial ~ . Short Saphenous Figure B.l: Veins of the Lower Limb (after [3]) B.3 Venous Anatomy of the Lower Limbs 162 and laterally to the popliteal artery [10]. The short saphenous vein (SSV) joins the popliteal vein at the saphenopopliteal junction, still within the fossa. At the upper (proximal) part of the popliteal fossa, the popliteal vein becomes the superficial femoral vein (SFV). Once the popliteal vein has passed through the adductor canal, it becomes the superficial femoral vein. Very rarely, the popliteal vein can join the profunda femoris vein, located deeper in the thigh. Even though the name of the SFV indicates otherwise, it is part of the deep venous system. The superficial location of the popliteal vein with respect to the popliteal artery is the inverse of that seen in the femoral area. The superficial femoral vein runs up the medial aspect of the thigh posterior to the superficial femoral artery and joins the deep femoral or profunda femoris (PROF) in the femoral triangle below the groin. The profunda vein is found posterior to the superficial femoral vein. After these veins have joined they form the common femoral vein, which lies medial to the common femoral artery. The common femoral vein is joined by the long saphenous vein at the saphenofemoral junction. This long saphenous vein is located medial to the superficial femoral vein and the common femoral vein at the level of the superficial femoral vein insertion. Progressing proximally, the common femoral becomes the external iliac vein (EIV) after it passes under the inguinal ligament, and then passes posteriorly along the posterior pelvis. Afterwards, the internal iliac vein (UV) joins the external iliac vein to form the common iliac vein (CIV). The two common iliac veins join to form the inferior vena cava, which eventually reaches the heart. With respect to the superficial venous system, there are two main veins that comprise this system. The long or greater saphenous vein (LSV or GSV) arises from the medial aspect of the dorsal venous arch of the foot and passes in front of the medial malleolus to run up the medial aspect of the calf and knee into the thigh. In the upper thigh the long saphenous vein curves laterally and deeply to join the common femoral vein as described above. The short saphenous vein arises from the lateral aspect of the dorsal venous arch of the foot, passing below and behind the lateral malleolus to run up the posterolateral aspect of the calf into the popliteal fossa, where it passes through the deep fascia to join the popliteal vein. Venous valves are commonly seen in the common femoral veins, superficial femoral veins and popliteal veins. Their function is to prevent the blood from flowing distally. Flow always goes from the superficial venous system in the direction of the deep venous system. Flow in the opposite direction is always abnormal. B.4 Examination of the Lower Limbs 163 All veins are thin walled and collapse easily with pressure, a fact that is exploited during the ultrasound examination to diagnose DVT. B . 4 Examination of the Lower Limbs Various examination procedures as well as modifications have been used to diagnose deep venous thrombosis (DVT). There are variations as to patient positions, decision of which veins to examine, and which indicators to use to diagnose as positive DVT. Even so, the most accurate, simple and useful diagnostic criterion for the presence of DVT has been the loss of compressibility of a thrombus filled vein under gentle probe pressure, known as compression ultrasound [53,79]. Other criteria include loss of respiratory phasicity, loss of flow accentuation when the calf is squeezed [79], visualization of the thrombus, the absence of vein extension upon a Valsalva maneuver [47] (a vein does not change size when patient holds breath and bears down), lack of color filling a vein when using color Doppler. When attempting to diagnose DVT using some of these other criteria, an accurate result may be difficult to ascertain, and these results aren't always reproducible [47]. Three imaging modalities are used while imaging the deep venous system, namely B-mode or grayscale, Doppler, and Color Doppler or Color Imaging. The B-mode modality is used to present the anatomical features and therefore used for the compression examinations. Vein valves, vein walls, vein size and thrombi themselves can also be viewed with this modality. Doppler or spectral analysis is used for assessing blood flow, and the distribution of speeds within a certain sample volume, usually positioned by a cursor overlying a B-mode image. When B-mode and Doppler are combined it is known as Duplex. Color Doppler or color imaging presents flow information over a broader volume, and velocity distributions are presented superimposed on a B-mode image. Color imaging is used to assess flow throughout the vein lumen. Since blood flow in the veins is relatively slow, the equipment should be set up for the detection of slower flows in general. The use of a 5 MHz linear transducer is most suitable, because it provides sufficient penetration, and typical resolution is within millimeter accuracy (Resolution depends on A, for 5MHz A = 300 mm; resolution will depend on the spatial pulse length (SPL), which depends on the wavelength A and the number of cycles n in a pulse. Assuming 2-4 cycles a pulse, the resolution is approximately 0.5 mm). The specific resolution depends on the equipment being used. Below is a general examination procedure, based on published works [10,19,59,79,83,101]. B.4 Examination of the Lower Limbs 164 It is recommended that the patient lay supine on an examination table tilted to 20° - 30° with their head elevated (known as the reverse Trendelenburg position). It is advantageous to have a tilting couch to produce some distension of the lower limb veins, which makes them easier to identify and the assessment of compression straightforward [3]. Also the patient should be warm to prevent vasoconstriction [101]. The involved lower extremity should be rotated externally 30° -45° with 20° - 40° of flexion at the hip and knee [88]. As well, the supine position is chosen because of the limitations in movement some patients may have, for example a recent surgery. Since the examination of the deep venous system in order to assess DVT requires a through mapping of the veins, it is unnecessary to perform a survey, and then a more detailed examination. Images can be obtained as the examination progresses. It is also recommended by some that both legs be examined for comparative purposes, even though symptoms may be restricted to one extremity [10]. This is not always the case, and factors such as time limitations are considered. A typical reported examination time was 20 - 30 minute per extremity [83]. The most important part of the ultrasound examination for the diagnosis of DVT is achieving the compression of the veins in order to see that there is no obstruction of the venous system. It is recommended that the compression examination be done in a transverse or short image plane, that is, imaging the veins along their transverse axis. When compression examinations are done in the longitudinal plane there is a possibility of orienting the ultrasound scanner such that the vein 'slips' from view, seeming as if complete compression was achieved even though this was not so, which would result in a possible false negative result. In order to assess compressibility, gentle pressure is applied to the patient via the ultrasound probe while imaging in B-mode. To assess respiratory phasicity and augmentation of flow, the veins are examined using Doppler or duplex ultrasound. Phasicity can be assessed by observing the spectral distribution of flow in a vein. Squeezing the calf gently will augment the flow or alternatively, the patient can be asked to plantar-flex their toes, contracting the calf muscles and emptying the calf veins [3]. The Doppler modality cannot be performed at the exact same time as a B-mode examination, and switching from one modality to the other is common practice. Color imaging is used to image the vein lumen as well as augmentation, and in some cases is used only as a road map [6]. Since venous flow is generally slow, the sensitivity must be set quite high. As well, in some cases augmentation must be performed in order to visualize adequate venous flow. Longitudinal imaging should also be performed so that no small thrombus is missed [10]. B.4 Examination of the Lower Limbs 165 B.4.1 Examination Protocol When compression exams are done, a split image is created showing the transverse image of the vein uncompressed alongside the same vein with pressure applied. For the Doppler findings, a duplex image is created which includes the grayscale image of the region being scanned along the longitudinal axis, plus the spectral display of the blood flow showing the phasicity and augmenta-tion. For color imaging findings, the grayscale longitudinal image is shown, with color information superimposed showing flow within the vessels. When possible, findings from all of these modalities should be obtained and recorded for each vein segment. In general the examination begins high on the thigh of the patient, at or above the level of the groin crease [10]. The following should be done: • The CFA (common femoral artery) and the C.FV are located. To confirm that the C F V has been located, scan slightly lower, where the SFV and LSV insertions should be seen. • The C F V should be assessed for compression every 1-2 cm, creating images along the way. • The probe should be moved to the longitudinal plane and the Doppler capabilities turned on to obtain a spectrum analysis. The cursor should be placed towards the flow while in this orientation. When using the Doppler from the transverse plane, the cursor should remain perpendicular to the probe [10]. A duplex image showing respiratory changes in the C F V should be generated. Color imaging should also be done. • Returning to the short plane using B-mode, move distally and locate insertion of LSV medially. The proximal portion of the LSV should be assessed for compression. Unless pathology is suspected, only assess this portion. • Assess the proximal LSV with Doppler and create image of results. • The C F V should be located again using grayscale, and then move distally to locate insertion of the PROF. This lies posterior and lateral to the SFV. The PROF should be followed as far as possible assessing compression, while obtaining images of the results. • Afterwards, return to the PROF insertion where a spectral.analysis of flow is done and documented. The flow is generally evaluated close to the insertion. B.4 Examination of the Lower Limbs 166 • In B-mode, return to the SFV insertion. The SFV should be followed all the way down the thigh, assessing for compressibility. Create split images at proximal, mid and distal thigh of vein compression. Also assess flow by Doppler at these locations as well as with the color modality, creating images of the spectral analysis and flow. It has been observed (by the author) that compression exams are performed every 3 -5 cm in this area, and images are only obtained of the aforementioned regions. Compression towards the distal thigh at the region of the adductor canal may become very difficult because of the tendons present there, and compression is better achieved by placing a hand behind the medial thigh and pushing up with the fingers against the transducer [3]. The popliteal fossa should be examined with either the patient prone, or supine with the knee bent and with external rotation if there is limited mobility. Also the decubitus position may be used or the leg can be elevated and supported off the couch by an assistant [3]. • The POP should be located posterior to the popliteal artery, and assessed for normal com-pression characteristics creating images to document the findings. There may be vessel dupli-cation, as it is common in this area. The popliteal vein should be followed as far as possible distally, if possible to level of the trifurcation into calf veins. The largest of these should be followed as far as possible as well, assessing for compression along the whole way. • Afterwards, return to the mid popliteal area ad assess with Doppler and color imaging. There are varying examination procedures for the calf. Some prefer performing calf examina-tions in the sitting position, with the leg of the patient hanging over the edge of the bed and the foot resting on the thigh of the examiner [98]. There are reported findings that this position greatly improves de reliability of the examination of the calf venous system [6]. Others choose the supine position with the knee flexed up off the mattress for this examination because 'as the subject starts to sit up the venous channels distend, especially in the upper calf, and the squeeze maneuver may be less effective in producing flow accentuation. In addition, the supine position is easier to manage for patients who have recently undergone surgical procedures [79].' A third option is with the patient in the decubitus position on a tilted couch. In the leg, arteries are used as landmarks and in some cases are identified with color imaging, to locate the position of the veins. B.5 Diagnosis of the Lower Limbs 167 • The posterior tibial vessels are more easily located scanning in the transverse plane from the medial side of the calf or posteromedial aspect of the leg and identifying the artery [101]. • The anterior tibial veins are best visualized from the anterolateral approach, with the trans-ducer positioned between the tibia and the fibula, and scanning transversely. The AT vessels are found in the superficial aspect of the interoseous membrane. • The deeper peroneal can be imaged using the same transducer position as the PT veins. If the same position cannot be used, a straight posterior approach may be tried. As well, the peroneal veins can best be seen from the anterolateral approach, as used to visualize the AT veins. Usually calf veins are not easily compressible. As well, the blood flow is generally not spon-taneous in calf veins, and augmentation must be done in order to visualize flow. In the mid and lower calf, squeezing the calf to augment blood flow may produce motion artifacts, so it is better to squeeze the foot, which produces enough flow to be detected. Compression examinations are done for the three mentioned pairs of calf veins to the extent that this is possible. Because flow is not necessarily spontaneous, Doppler examinations are limited to augmentation exams. Color examinations are used to show that the vein lumen is patent. Iliac veins are examined by following the external iliac vein upwards from the common femoral vein into the pelvis. A 3 or 4 MHz transducer is usually necessary for adequate penetration [3]. Because of the anatomy, compression exams are not possible, and the examination is limited to flow exams only. While examining the CFV, it is possible to perform augmentation exams and the Valsalva maneuver to rule out occlusion in the CIV [101]. B . 5 Diagnosis of the Lower Limbs Normal sonographic findings of a venous examination are [10]: • Appearance of vein and vein lumen. • Spontaneous flow. This is, there is blood flow throughout the vein from distal to proximal. • Respiratory phasicity, the flow within the lumen varies with the respiratory cycle. • Augmentation, blood flow increases upon distal compression of the calf, or plantar extension. B.5 Diagnosis of the Lower Limbs 168 • Valve competence, flow is unidirectional and there is no reflux. • Non-pulsatility, the flow does not vary with the heartbeat. • Valves can sometimes be seen. Indicators for the positive diagnosis of DVT are presented below. Lack of venous compressibility when gentle pressure is applied accurately indicates anechoic thrombus [60,83]. This is, when a lack of complete apposition of the opposing walls of the vein could be demonstrated on the transverse plane indicates high probability of acute DVT [79], and has been used by some to be the primary diagnostic criterion [6]. When there is a clot present, the vein lumen is usually enlarged and may contain low to medium echoes [10]. If there is an enlarged lumen, it is very important to show the change in caliber of the vessel in the longitudinal plane if possible [personal communication]. The lumen of a vein is normally anechoic although there are exceptions to blood being anechoic, such as during pregnancy, or where there is slow venous flow or hyperviscosity [3]. Anechoic venous thrombi may be missed in regions were venous compression is difficult, specifically the distal superficial femoral vein as it courses through the adductor canal and the deep calf veins [83]. Usually the walls of veins are smooth and unobtrusive, but after recanalization because of the occurrence of a thrombus, they become irregular, thickened and echogenic [3]. In general major veins are somewhat larger than the corresponding artery. If veins are substantially larger and size does not vary with respiration, thrombus should be suspected. Ultrasound does not perform exceptionally well in identifying thrombus age, but some indicators can be obtained. A fresh thrombus will have consistency of jelly, and may be compressed with strong pressure [3]. As well, sometimes an intraluminal thrombus can be directly observed and this can help indicate age, as older thrombi become more echogenic [3]. Another indicator of thrombus age is that fresh thrombus has a tendency to expand the vein, making it look rounder and fuller than normal [3]. Another indicator of thrombus age is obtained from the flow in collateral channels. At an acute stage, intramuscular channels still have not developed, but there is increased velocity and flow in the superficial venous system or portions of the deep venous system, depending on the location of the thrombus. In chronic cases, collateral channels have developed and are easily seen in the color imaging modality [3]. B.6 Drawbacks and Limitations of DVT Examinations 169 It is recommended that a longitudinal scan be included as well, because smaller and non-occlusive clots are more easily identifiable in this plane. Small size and this nonocclusive nature of DVTs, can cause them to be missed especially in large veins [22,83]. If there is a venous obstruction proximal to the examination area, venous flow may be decreased and/or continuous and often no respiratory changes are seen [10]. This information can be obtained from the Doppler spectral analysis, which should also show spontaneous flow. Phasic response may persist when thrombus does not substantially obstruct the lumen, so Doppler should not be used as the only criterion. Also as mentioned before, in normal small veins the flow may not be spontaneous. Absence of flow and of augmentation are considered to be (one of) the best signs of total occlusion of a venous segment [60]. The results of an augmentation exam should show an increase in flood flow and an increase in flow velocity. If the response is dampened or not present, this is an indicator of a venous obstruction between the area being examined and where the compression is being applied. For segments that cannot be examined directly, the Valsalva maneuver is a good indicator of obstruction. This maneuver comprises deep inspiration followed by bearing down, and results in a complete cessation of flow in normal patients. Abnormal results may indicate obstruction between the inferior vena cava and the area being examined. Color imaging results can also be used to help identify a thrombus. In one report, diagnosis of the thrombosis was based primarily on the presence of a focal void within the color-encoded blood flow image of the absence of the visible flow within the segment of a vessel. Usually the flow voids were accompanied by intraluminal echogenicity, vein distension, and absence of normal vein compressibility [83]. As mentioned the lumen of a vein is normally anechoic, but the vein should fill up with color when using this modality, especially when distal augmentation is performed. B.6 Drawbacks and L imi ta t ions of D V T Examinat ions As with any medical imaging technique, if it is not possible to adequately view the examined area complete information may not be obtained resulting in an inadequate diagnosis. It is therefore of extreme importance to completely and properly examine the patient, in order to obtain as much information as possible. The ability of Doppler and color imaging to detect blood flow decreases as depth increases. As B.6 Drawbacks and Limitations of DVT Examinations 170 well, the presence of soft-tissue edema, erythema, swelling and extensive collateral vein formation reduce the quality of the findings even more. Also, the sensitivity to low flows with the color modality is limited. The presence of swelling, fat and edema also limit the overall quality and depth of the images, from the B-mode modality to Color. When a patient presents with swelling of the lower limb, compression results may be more difficult to obtain, because the swelling itself causes the veins to compress. An anatomical problem may arise because of the formation of duplicated veins, and when varicose and/or collateral veins are present. The result is that imaging the correct vessel may become confusing [personal communication], because of the limited points of view the information is observed from and limited dimensions (restricted to a 2D image). There are many cases where the patient cannot be visualized correctly because of limited mo-bility, for example recent surgery or because there is an obstruction, for example a cast, bandage, or open wound. Complimentary views may be obtained, but there is a good possibility that infor-mation will be lost, misinterpreted or simply not obtained. As mentioned before, if the patient has limited mobility the optimal angle for an image may not always be available. But another difficulty may arise if the patient is extremely mobile. Limited quality images will be obtained if the patient does not stay still, especially with Doppler and Color flow information. Appendix C Examples of Contour and Parameter Estimation Algorithm Some concrete examples of detected contours and parameters are presented in this chapter. Var-ious images obtained from our ultrasound phantom, as well as images from deep veins of several volunteers were used as input for the contour detection algorithm presented in Chapters 3 and 4. The values used for the algorithm were Q = 3, R-. as well as setting and 20 0 0 0 0 20 0 0 0 0 20 0 0 0 0 20 , and S 0.5 0 0 0 0.5 0 0 0 0.1 a 0 | 0 '0|0 0O|o Max Radius/2 = 0° 10 0 0 ^0|0 = 0 10 0 0 0 10 where MaxRadius is the initial maximum search radius length from the center point, in pixels. 171 172 The initial MaxRadius was varied depending on the image, within the range of 80 to 40. Each contour was validated using the method presented in Section 3.1.6, and the final accepted contours are displayed. Care was taken to include images that included varying degrees of image brightness and ves-sel size, in order to present the results of the feature detection algorithm over a broad range of situations. In general, the detected contour points are presented as circles, while the detected ellipse equa-tion parameters were used to plot an ellipse on the image. The semi-major axis is represented by the solid line, while the semi-minor axis is presented as a dotted line. Figure C.I: Results of Contour and Parameter Estimation, Phantom Vessels -1 Figure C.2: Results of Contour and Parameter Estimation, Phantom Vessels - II 175 Figure C.3: Results of Contour and Parameter Estimation, Phantom Vessels - III 176 Figure C.4: Results of Contour and Parameter Estimation, Human Vessels - I 177 Figure C.5: Results of Contour and Parameter Estimation, Human Vessels - II 


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