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Atherosclerotic plaques with high probability of rupture show the presence of a hot spot due to the accumulation of inflammatory cells. This study utilizes two and three dimensional (2-D and 3-D) arterial geometries containing an atherosclerotic plaque experiencing different levels of inflammation and uses models of heat transfer analysis to determine the temperature distribution in the plaque region. The 2-D studies consider three different vessel geometries: a stenotic straight artery, a bending artery and an arterial bifurcation which model a human aorta, a coronary artery and a carotid bifurcation, respectively. The 3-D model considers a stenotic straight artery using realistic and simplified geometries. Three different blood flow cases are considered: steady-state, transient state and blood flow reduction. In the 3-D model, thermal stress produced by local inflammation is estimated to determine the effect of inflammation over plaque stability. For fluid flow and heat transfer analysis, Navier-Stokes equations and energy equation are solved; for structural analysis, the governing equations are expressed in terms of equilibrium equation, constitutive equation, and compatibility condition, which are are solved using the multi-physics software COMSOL 3.3 (COMSOL, Inc.). Our results indicate that the best location to measure plaque temperature in the presence of blood flow is recommended between the middle and the far edge of the plaque. The blood flow reduction leads to a non-uniform temperature increase ranged from 0.1 to 0.25 oC in the plaque/lumen interface. In 3-D realistic model, the multiple measuring points must be considered to decrease the potential error in temperature measurement even within 1 or 2 mm at centerline region of plaque. The most highly thermal stressed regions with the value of 1.45 Pa are observed at the corners of lipid core and the plaque/lumen interface. The mathematical model developed provides a tool to analyze the factors affecting heat transfer at the plaque surface. The results may contribute to the understanding of the relationship between plaque temperature and the likelihood of rupture, and also provide a tool to better understand arterial wall temperature measurements obtained with novel catheters.

<p> Atherosclerosis generally occurs near the branching in the arteries where there tends to be flow irregularities. A build up of fatty deposits (plaque) occurs in the blood vessel in such regions making it to lose its elasticity. Such hardening of the arteries and the narrowing of the lumen can cause severe atheromas and even high blood pressure and blockage of the vessels. It is observed in North America that nearly 47% of the deaths are caused due to cardiovascular diseases and hence determination of such regions becomes very critical and can be very beneficial if done at an earlier stage. In this thesis, we present: an approach to model the pulsating flow of blood through such an atherosclerosis affected region of the artery using finite element method and further discuss the statistical model used to implement the optimization techniques to estimate the region of maximum rigidity. Here within we present a numerical and non-invasive approach to predict such regions. The computational modeling is carried out under two categories: a. The mathematical model and b. The statistical model. </p> <p> The mathematical model which is the forward model, comprises of the artery and the cardiac muscle as hyperelastic material modeled with the neo-hookean model and the three dimensional Navier-Stokes equations solve for the blood flowing through it. We perform fluid dynamic analysis for the blood flowing through the vessel to compute the velocity at different time instances and mechanical analysis to compute the deformation of the artery which is a function of the elasticity of the vessel. The two models are interconnected to each other by boundary conditions as the normal component of the surface force provides the coupling between the two models. The shear modulus represents a measure of the elasticity of the vessel. We use linear spatial basis functions to model the shear modulus which spatially varies along the geometry of the vessel thus we have a region of atherosclerosis and the geometry shows the stenosis. The change in the shear modulus affects the velocity of blood through the vessel. </p> <p> In the statistical model, we propose an inverse computational model for estimating the elasticity profile of the arterial wall where we implement the inverse modeling approach to estimate the maximum shear modulus which helps us to predict the region of atherosclerosis. The velocity and the deformation obtained for a particular shear modulus from our COMSOL forward model provide the realistic simulated measurements that are made noisy by introduction of white Gaussian noise with different SNR and we try to estimate the shear modulus that minimizes the error-function. We use COMSOL with MATLAB for simultaneous iterative computations of velocity and deformation measurements by running the optimization code. We estimate these unknown parameters using optimization algorithm that minimizes the cost function of our model. For our estimation we use the least squares estimator and we derive the maximum likelihood estimator. The unconstrained optimization is carried out with Neider Mead Simplex Method and the Trust Region Method which uses only the function evaluations to find the minimum: making it a very robust algorithm and very efficient for problems that are nonlinear or have a number of discontinuities. Our preliminary results demonstrate significant change in velocity of the blood and occurrence of vortices in the region of less elasticity and the tendency of the artery to deform minimum in the hardened less elastic region. Our estimation results show that the parameters are identifiable. The mean square error of the estimate as a function of SNR shows accuracy of the estimation. </p> / Thesis / Master of Applied Science (MASc)

Inverse spectral techniques are developed in this dissertation for recovering the shear modulus and residual stress of soft tissues. Shear modulus is one of several quantities for measuring the stiffness of a material, and hence estimating it accurately is an important factor in tissue characterization. Residual stress is a stress that can exist in a body in the absence of externally applied loads, and beneficial for biological growth and remodeling. It is a challenge to recover the two quantities in soft tissues both theoretically and experimentally. The current inverse spectral techniques recover the two unknowns invasively, and are theoretically based on a novel use of the intravascular ultrasound technology (IVUS) by obtaining several natural frequencies of the vessel wall material. As the IVUS is interrogating inside the artery, it produces small amplitude, high frequency time harmonic vibrations superimposed on the quasistatic deformation of the blood pressure pre-stressed and residually stressed artery. The arterial wall is idealized as a nonlinear isotropic cylindrical hyperelastic body for computational convenience. A boundary value problem is formulated for the response of the arterial wall within a specific class of quasistatic deformations reflexive of the response due to imposed blood pressures. Subsequently, a boundary value problem is developed from intravascular ultrasound interrogation generating small amplitude, high frequency time harmonic vibrations superimposed on the quasistatic finite deformations via an asymptotic construction of the solutions. This leads to a system of second order ordinary Sturm-Liouville problems (SLP) with the natural eigenfrequencies from IVUS implementation as eigenvalues of the SLP. They are then employed to reconstruct the shear modulus and residual stress in a nonlinear approach by inverse spectral techniques. The shear modulus is recovered by a multidimensional secant method (MSM). The MSM avoids computing the Jacobian matrix of the equations and is shown to be convenient for manipulation. Residual stress is recovered via an optimization approach (OA) instead of the traditional equation-solving method. The OA increases the robustness of the algorithms by overdetermination of the problem, and comprehensive tests are performed to guarantee the accuracy of the solution. Numerical examples are displayed to show the viability of these techniques.

Atherosclerosis is often diagnosed using an ultrasound (US) examination in the carotid and femoral arteries and the abdominal aorta. A decision to operate requires two measures of disease severity: the degree of stenosis measured using B-mode US; and the blood flow patterns in the artery measured using spectral Doppler US. However other biomechanical factors such as wall shear stress (WSS) and areas of flow recirculation are also important in disease development and rupture. These are estimated using an image-guided modelling approach, where a three-dimensional computational mesh of the artery is simulated. To generate a patient-specific arterial 3D computational mesh, a 3D ultrasound (3DUS) system was developed. This system uses a standard clinical US scanner with an optical position sensor to measure the position of the transducer; a video capture card to record video images from the scanner; and a PC running Stradwin software to reconstruct 3DUS data. The system was characterised using an industry-standard set of calibration phantoms, giving a reconstruction accuracy of ± 0.17 mm with a 12MHz linear array transducer. Artery movements from pulsatile flow were reduced using a retrospective gating technique. The effect of pressure applied to the transducer moving and deforming the artery was reduced using an image-based rigid registration technique. The artery lumen found on each 3DUS image was segmented using a semi-automatic segmentation technique known as ShIRT (the Sheffield Image Registration Toolkit). Arterial scans from healthy volunteers and patients with diagnosed arterial disease were segmented using the technique. The accuracy of the semi-automatic technique was assessed by comparing it to manual segmentation of each artery using a set of segmentation metrics. The mean accuracy of the semi-automatic technique ranged from 85% to 99% and depended on the quality of the images and the complexity of the shape of the lumen. Patient-specific 3D computational artery meshes were created using ShIRT. An idealised mesh was created using key features of the segmented 3DUS scan. This was registered and deformed to the rest of the segmented dataset, producing a mesh that represents the shape of the artery. Meshes created using ShIRT were compared to meshes created using the Rhino solid modelling package. ShIRT produced smoother meshes; Rhino reproduced the shape of arterial disease more accurately. The use of 3DUS with image-guided modelling has the potential to be an effective tool in the diagnosis of atherosclerosis. Simulations using these data reflect in vivo studies of wall shear stress and recirculation in diseased arteries and are comparable with results in the literature created using MRI and other 3DUS systems.

The incidence of disease of the cardiovascular system is very high and increasing worldwide, especially in the developing world. The radial and ulnar arteries are implicated in some important ailments where blood flow related parameters such as flow rate (FR), wall shear rate (WSR), arterial wall motion (AWM) and pressure, all of which can be measured using ultrasound techniques, are useful in diagnosis and patient management. However these measurements are prone to error due to the manner of image formation and the complex flow conditions within the vessels. In this thesis, the errors in ultrasound-measured parameters in the radial and ulnar arteries are investigated using experimental phantoms, computer simulation and on volunteers. Using the Womersley theory, FR and WSR were estimated using a clinical ultrasound scanner with the pulsed wave (PW) mode and B mode. Experimental flow phantoms were designed to evaluate those measurements under different circumstances. A simulation technique which combined image-based computational fluid dynamics and ultrasound simulation was also used to evaluate ultrasound estimation of these parameters. A case study was then conducted on healthy volunteers to evaluate the method of measuring FR and WSR in-vivo. For the AWM in the radial artery, an auto-correlation method was used based on the radio-frequency (RF) data and validations were done by a flow phantom, simulation, and in-vivo trial. The blood pressure waveform in a volunteer’s radial artery was derived from the ultrasound measured AWM and compared with the waveform from a tonometry. FR and WSR were both found to be overestimated by up to 50%, mainly due to the beam-vessel angle in the PW Doppler ultrasound. Measurement of the vessel diameter and assumption of the blood flow direction can also influence the estimations. Other factors, such as flow amplitude, vessel size, imaging depth and flow waveforms, do not seem to affect the estimation of these two parameters. Results taken from the flow phantoms agree with those from simulation and the estimations from the in-vivo case study also agree with the published data. The auto-correlation method for the AWM was validated from the phantom and simulation. It is able to detect motion amplitude of about tens of micrometres. The trial on volunteers proved the feasibility of this motion detection method. Blood pressure waveforms at the radial artery of a volunteer, derived from this ultrasound-measured wall motion and from the tonometry, were very similar. The Womersley-based method is able to estimate the FR and WSR in the radial and ulnar arteries with high accuracy. Sources of the error and their magnitudes in estimation of the two parameters by ultrasound pointed out in this thesis are beam-vessel angle, vessel diameter measurement and flow direction assumption. Researchers and clinicians using these measurements in practice and research should be aware. The capability of ultrasound imaging to measure arterial AWM in the radial artery is demonstrated and it is found that the blood pressure waveform can also be derived from the arterial AWM.

京都大学 / 0048 / 新制・課程博士 / 博士(人間健康科学) / 甲第19970号 / 人健博第38号 / 新制||人健||3(附属図書館) / 33066 / 京都大学大学院医学研究科人間健康科学系専攻 / (主査)教授 杉本 直三, 教授 精山 明敏, 教授 黒田 知宏 / 学位規則第4条第1項該当 / Doctor of Human Health Sciences / Kyoto University / DFAM

La thèse s’axe sur l’identification des propriétés mécaniques des artères faciales. Elle s’inscrit dans le cadre du projet FlowFace, qui porte sur l’étude du réseau artériel facial par Imagerie de Résonance Magnétique (IRM). Elle s’appuie sur une campagne de mesures effectuées sur un échantillon de 30 témoins au CHU d’Amiens, qui a permis d’obtenir de manière non invasive l’évolution de la déformation des vaisseaux, ainsi que la mesure des débits les parcourant. Des pressions diastoliques et systoliques ont été mesurées au niveau du bras, indépendamment des mesures IRM. L’objectif de la thèse a été de modéliser la déformation patient-spécifique des vaisseaux sanguins et de mettre en place une technique d’optimisation, afin de déterminer leurs propriétés mécaniques par analyse inverse. Des simulations du comportement des vaisseaux sanguins ont été réalisées au moyen des logiciels d’ANSYS Inc., en modélisant les interactions fluide-structure aussi bien en couplage fort que faible. L’objectif a été de déterminer les déformations pariétales induites par les conditions hémodynamiques, ainsi que les pertes de charge dans les vaisseaux considérés. Les simulations ont mis en jeu des modèles hyperélastiques grande déformation pour simuler le comportement des parois. Les déplacements prédits par le modèle numérique ont été comparés aux déplacements expérimentaux mesurés par IRM. Les propriétés mécaniques des vaisseaux ont été identifiées au moyen de la technique d’optimisation proposée dans la suite ANSYS et basée sur les algorithmes de gradient et algorithmes génétiques. La méthode d’identification a été validée sur des fantômes de vaisseaux, consistant en des tubes cylindriques en élastomère, et pour lesquelles des mesures de déformation sous écoulement pulsé ont été acquises par imagerie IRM. Les valeurs des propriétés mécaniques ainsi déterminées ont été comparées à celles obtenues par tests de traction et tests de dilatation. Un des points cruciaux de l’identification a consisté en la détermination de l’état non pré-contraint. S’il est un paramètre connu pour les fantômes de vaisseaux, il est à déterminer pour les vaisseaux natifs. Le challenge de cette thèse a aussi été de déterminer les propriétés hyperélastiques des vaisseaux sanguins à partir des valeurs systoliques et diastoliques de pression et déformation. La méthode a permis de conclure que le module tangent en diastole avoisine 200 KPa alors que celui en systole se trouve dans un intervalle entre 300 KPa et 1 MPa. / This thesis is based on identifying the mechanical properties of facial arteries. It is part of FlowFace project, which focuses on the study of the facial arterial system by MRI imaging. It is based on a measurement campaign conducted on a sample of 30 people at the Hospital of Amiens, which allowed obtaining noninvasively the evolution of the blood vessel deformation and the measurement of the flow. Diastolic and systolic pressures were measured at the arm independently of the MRI measurements. The aim of the thesis was to model the deformation of blood vessels and to implement an optimization technique to determine their mechanical properties by inverse analysis using MRI measurements of deformation. Simulations of the behavior of the blood vessels were performed, using ANSYS Inc. software, modeling fluid-structure interactions both strong and weak coupling. The objective was to determine the parietal deformations induced by hemodynamic conditions and pressure drops in the vessels concerned. The simulations involved hyperelastic and large deflection models to simulate the behavior of the wall. They allow calculate the numerical displacements that we compared with experimental displacements measured by MRI, the aim is that the difference between numerical and experimental be as low as possible to deduce the adequate mechanical parameters for the artery. To identify the mechanical properties of the vessels, the optimization technique proposed in ANSYS based on genetic algorithms or gradient algorithms was used. The identification method was validated on cylindrical tubes (elastomer), for which deformation measurements were acquired by MRI imaging under pulsating flow. The values of mechanical properties determined were compared with those obtained by traction tests and dilatation tests. One of the crucial points of identification involves the determination of the non-stress state. If it is a known parameter for the elastic tube, it has to be determining for blood vessels. The challenge of this thesis is to determine from a "minimum" quantity of pressure and deformation information, the hyper-elastic properties of blood vessels. The method based on a patient-specific geometry deformation concluded that the tangent modulus in diastole is approximately 200kPa while that in systole is in a range of 300 kPa to 1 MPa.

Atherosclerosis is an arterial disease that occurs due to the build-up of lipids, cholesterol and other substances in the arterial wall, collectively called plaque, leading to narrowing of the vessel lumen and, in time, disruption to the blood supply. The study of flow through atherosclerotic vessels is especially important since plaques not only cause a reduction in the vessel lumen but can rupture from the arterial wall, causing a blood clot in the vessel that may ultimately lead to heart attack or a stroke. Elevated level of oxidated low density lipoprotein (LDL) is a known risk factor associated with the genesis of atherosclerosis in arterial walls. Previous studies reported in literature have explored the transport of LDL through the arterial wall using analytical and mathematical models. In this work, we have presented a computational framework for the study of LDL transport in the lumen and the porous arterial wall. We have employed a four-layer arterial wall model and used governing equations to model the transport of LDL. We have used physiological parameters for the wall layers from literature and have validated the model based on the calculated filtration velocities and LDL concentration profiles in the arterial wall. We have further used this established model to study the effect of change in permeability and pressure on the LDL concentration. We have also studied the effect of pulsatile flow on the transport of LDL through the porous walls to examine the validity of the initial assumption of steady state and have seen that pulsation increases the time averaged net flux of LDL species by about 20%. We have next modeled a drug-eluting stent (DES), which is one of the popular remedies to cure atherosclerosis. The validation of DES model is followed by a combined study to analyze the effect of stent placement on LDL transport. Although there is no chemical reaction between the drug and LDL, we have noticed recirculation zones near the stent strut which result in accumulation of LDL molecules in the arterial wall. Future studies are aimed at incorporating variable porosity and permeability and a stenosed region in the geometry. The deformation of arterial wall due to pulsatile blood flow may lead to alteration of wall properties, which can give a realistic view of macromolecular transport.

Cette thèse présente un ensemble de travaux qui s'inscrivent dans le domaine du génie biomédical pour des applications cliniques. L'objectif principal de ce travail est de fournir aux cliniciens un mode d'imagerie ultrasonore pour extraire simultanément la vitesse du flux et le mouvement de la paroi à des cadences d'imagerie élevées dans les artères. Les pathologies cardiovasculaires sont une cause majeure de décès et d'invalidité dans le monde. Bien que l'origine de ces maladies ne soit pas encore entièrement comprise, il semble que certains marqueurs pathologiques de la paroi et du flux pourraient permettre une détection plus précoce. Parce que les tissus artériels sont sujets à des phénomènes rapides et complexes, une modalité d'imagerie à haute cadence semble très pertinente pour étudier les pathologies du système cardiovasculaire. Malheureusement, aucune technique n'est actuellement utilisée cliniquement ni même approuvée pour l'extraction de marqueurs pathologiques du sang et de la paroi à des cadences d'imagerie élevées. C'est pourquoi, dans cette thèse, je propose de concevoir une séquence et un algorithme ultrasonore permettant d'extraire ces deux aspects, à des cadences d'imagerie élevées sur les artères, pour une application clinique potentielle. Trois contributions scientifiques principales sont présentées cette thèse : i) la conception de la séquence ultrasonore avec un estimateur de mouvement 2D, ii) une nouvelle approche adaptative de filtrage de paroi, et iii) un essai clinique. La séquence d'imagerie ultrasonore est basée sur la transmission d'ondes planes permettant d'obtenir des cadences d'imagerie allant jusqu'à 10 000 Hz sur la carotide. La méthode d'estimation de mouvement est basée sur une approche introduisant une oscillation latérale virtuelle dans les images qui, couplée à un estimateur de phase 2D basé sur des travaux antérieurs de la littérature, permet d'extraire des champs vectoriels de vitesses. Les validations pour l'estimation des vitesses du flux et du mouvement des parois ont été effectuées à l'aide d'un fantôme d'écoulement Doppler commercial et d'un fantôme de carotide réaliste conçu pour les expériences. Une technique de filtrage adaptatif de paroi a été développée et validée sur des volontaires à l'aide des estimations de vitesses tissulaires, ce qui permet d'éliminer précisément le signal du tissu des signaux du sang. Enfin, l'essai clinique a été réalisé à l'hôpital avec un groupe de volontaires et un groupe de patients. La séquence ultrasonore, l'algorithme d'estimation de mouvement et les approches adaptatives de filtrage de paroi ont été validés dans la thèse. La méthode permet d'extraire les vitesses du flux et de la paroi à haute cadence d'imagerie, avec de faibles erreurs et écarts-types. L'approche adaptative du filtrage de paroi permet de mieux extraire le flux par rapport à d'autres approches standard. Cette amélioration est particulièrement perceptible à proximité de la paroi, ce qui permettrait des mesures précises de l'écoulement et des contraintes le long des parois artérielles où les plaques peuvent se former et se développer. Pour conclure, l'essai clinique a démontré la faisabilité de notre approche dans un environnement clinique avec l'extraction des mouvements tissulaires, du flux et de paramètres artériels qui ont montré des différences entre et au sein des groupes. Cette thèse est donc un pas en avant vers l'utilisation clinique de l'imagerie ultrasonore à haute cadence pour la quantification du mouvement tissulaire et du flux pour la détection et le diagnostic des maladies cardiovasculaires / This thesis is focused on biomedical engineering for clinical applications. The main goal of this work is to provide to clinicians an ultrasound mode to simultaneously extract wall motion and flow at high frame rates in arteries. Cardiovascular pathologies are a major cause of death and disability worldwide. Although the formation of such diseases is still not fully understood, it appears that some pathological markers from both wall and flow could allow an earlier detection. Because tissues are subject to fast and complex phenomena in the arteries, a high frame rate imaging modality seems highly relevant to extract as much information as possible on the condition of the cardiovascular system. Unfortunately, no technique is currently clinically used or even approved for the extraction of both flow and wall pathological markers at high frame rates. Therefore, in this thesis, I propose to design an ultrasound sequence and algorithm permitting to extract both aspects, at high frame rates on arteries, for a potential clinical application. There are three main scientific contributions in this thesis: i) the design of the ultrasound sequence with a 2D motion estimator, ii) a new adaptive clutter filtering approach, and iii) a clinical trial. The ultrasound sequence is based on plane wave acquisition permitting to yield frame rates up to 10 000 Hz in the carotid. The pipeline used an approach introducing a virtual lateral oscillation in ultrasound images which, coupled with a 2D phase-based estimator based on previous works from the literature, allows to extract vectorial velocity fields. Validations for both flow and wall motion estimation were performed on a commercial Doppler flow phantom and an in-house realistic carotid phantom was designed for the experiments. An adaptive clutter filtering technique was also developed and validated on volunteers based on tissue estimates, which permit to precisely remove tissue clutter from flow signals. Finally, the clinical trial was performed at the hospital with a group of volunteers and a group of patients. The ultrasound sequence, motion estimation algorithm, and adaptive clutter filtering approaches were well validated in the thesis. The method can provide both wall motion and flow estimates at high frame rates, with low errors and standard deviations. The adaptive clutter filtering approach permits to better extract the flow compared to other standard approaches. This improvement is especially noticeable close to the wall, which would allow accurate flow and stress measurements along arterial walls where plaques can form and develop. To conclude, the clinical trial has demonstrated the feasibility in a clinical environment with the extraction of wall motion, flow, and arterial parameters that showed differences between and within groups. This thesis is then a step toward clinical use of high frame rate ultrasound imaging for quantification of both wall motion and flow for pathological detection of cardiovascular diseases