Recovery of cellular traction in three-dimensional nonlinear hyperelastic matrices

The traction exerted by a cell on the extra-cellular matrix (ECM) is critical to understanding and manipulating important biological processes such as stem cell differentiation, cancer cell metastasis, and embryonic morphogenesis. This traction is typically quantified through traction force microscopy (TFM). In TFM, the displacement of select markers inside the ECM is tracked, and is used in conjunction with an elasticity problem to reconstruct the traction field. Most applications of this technique thus far have assumed that the matrix behaves as a linear elastic solid that undergoes small deformation and infinitesimal strains. In this manuscript, we develop and implement a robust and efficient TFM methodology that overcomes these limitations by accounting for geometric and material nonlinearities in the ECM. We pose the TFM problem as an inverse problem and develop efficient adjoint-based minimization techniques to solve it. We test the effect of measurement noise on the proposed method, and examine the error incurred by not including nonlinear effects when solving the TFM problem. We present these results for in-silico traction fields that are applied to realistic geometric models of microglial and neuronal cells

Characterization of carotid artery plaques using noninvasive vascular ultrasound elastography

L'athérosclérose est une maladie vasculaire complexe qui affecte la paroi des artères (par l'épaississement) et les lumières (par la formation de plaques). La rupture d'une plaque de l'artère carotide peut également provoquer un accident vasculaire cérébral ischémique et des complications. Bien que plusieurs modalités d'imagerie médicale soient actuellement utilisées pour évaluer la stabilité d'une plaque, elles présentent des limitations telles que l'irradiation, les propriétés invasives, une faible disponibilité clinique et un coût élevé. L'échographie est une méthode d'imagerie sûre qui permet une analyse en temps réel pour l'évaluation des tissus biologiques. Il est intéressant et prometteur d’appliquer une échographie vasculaire pour le dépistage et le diagnostic précoces des plaques d’artère carotide. Cependant, les ultrasons vasculaires actuels identifient uniquement la morphologie d'une plaque en termes de luminosité d'écho ou l’impact de cette plaque sur les caractéristiques de l’écoulement sanguin, ce qui peut ne pas être suffisant pour diagnostiquer l’importance de la plaque. La technique d’élastographie vasculaire non-intrusive (« noninvasive vascular elastography (NIVE) ») a montré le potentiel de détermination de la stabilité d'une plaque. NIVE peut déterminer le champ de déformation de la paroi vasculaire en mouvement d’une artère carotide provoqué par la pulsation cardiaque naturelle. En raison des différences de module de Young entre les différents tissus des vaisseaux, différents composants d’une plaque devraient présenter différentes déformations, caractérisant ainsi la stabilité de la plaque. Actuellement, les performances et l’efficacité numérique sous-optimales limitent l’acceptation clinique de NIVE en tant que méthode rapide et efficace pour le diagnostic précoce des plaques vulnérables. Par conséquent, il est nécessaire de développer NIVE en tant qu’outil d’imagerie non invasif, rapide et économique afin de mieux caractériser la vulnérabilité liée à la plaque. La procédure à suivre pour effectuer l’analyse NIVE consiste en des étapes de formation et de post-traitement d’images. Cette thèse vise à améliorer systématiquement la précision de ces deux aspects de NIVE afin de faciliter la prédiction de la vulnérabilité de la plaque carotidienne. Le premier effort de cette thèse a été dédié à la formation d'images (Chapitre 5). L'imagerie par oscillations transversales a été introduite dans NIVE. Les performances de l’imagerie par oscillations transversales couplées à deux estimateurs de contrainte fondés sur un modèle de déformation fine, soit l’ « affine phase-based estimator (APBE) » et le « Lagrangian speckle model estimator (LSME) », ont été évaluées. Pour toutes les études de simulation et in vitro de ce travail, le LSME sans imagerie par oscillation transversale a surperformé par rapport à l'APBE avec imagerie par oscillations transversales. Néanmoins, des estimations de contrainte principales comparables ou meilleures pourraient être obtenues avec le LSME en utilisant une imagerie par oscillations transversales dans le cas de structures tissulaires complexes et hétérogènes. Lors de l'acquisition de signaux ultrasonores pour la formation d'images, des mouvements hors du plan perpendiculaire au plan de balayage bidimensionnel (2-D) existent. Le deuxième objectif de cette thèse était d'évaluer l'influence des mouvements hors plan sur les performances du NIVE 2-D (Chapitre 6). À cette fin, nous avons conçu un dispositif expérimental in vitro permettant de simuler des mouvements hors plan de 1 mm, 2 mm et 3 mm. Les résultats in vitro ont montré plus d'artefacts d'estimation de contrainte pour le LSME avec des amplitudes croissantes de mouvements hors du plan principal de l’image. Malgré tout, nous avons néanmoins obtenu des estimations de déformations robustes avec un mouvement hors plan de 2.0 mm (coefficients de corrélation supérieurs à 0.85). Pour un jeu de données cliniques de 18 participants présentant une sténose de l'artère carotide, nous avons proposé d'utiliser deux jeux de données d'analyses sur la même plaque carotidienne, soit des images transversales et longitudinales, afin de déduire les mouvements hors plan (qui se sont avérés de 0.25 mm à 1.04 mm). Les résultats cliniques ont montré que les estimations de déformations restaient reproductibles pour toutes les amplitudes de mouvement, puisque les coefficients de corrélation inter-images étaient supérieurs à 0.70 et que les corrélations croisées normalisées entre les images radiofréquences étaient supérieures à 0.93, ce qui a permis de démontrer une plus grande confiance lors de l'analyse de jeu de données cliniques de plaques carotides à l'aide du LSME. Enfin, en ce qui concerne le post-traitement des images, les algorithmes NIVE doivent estimer les déformations des parois des vaisseaux à partir d’images reconstituées dans le but d’identifier les tissus mous et durs. Ainsi, le dernier objectif de cette thèse était de développer un algorithme d'estimation de contrainte avec une résolution de la taille d’un pixel ainsi qu'une efficacité de calcul élevée pour l'amélioration de la précision de NIVE (Chapitre 7). Nous avons proposé un estimateur de déformation de modèle fragmenté (SMSE) avec lequel le champ de déformation dense est paramétré avec des descriptions de transformées en cosinus discret, générant ainsi des composantes de déformations affines (déformations axiales et latérales et en cisaillement) sans opération mathématique de dérivées. En comparant avec le LSME, le SMSE a réduit les erreurs d'estimation lors des tests de simulations, ainsi que pour les mesures in vitro et in vivo. De plus, la faible mise en oeuvre de la méthode SMSE réduit de 4 à 25 fois le temps de traitement par rapport à la méthode LSME pour les simulations, les études in vitro et in vivo, ce qui pourrait permettre une implémentation possible de NIVE en temps réel.Atherosclerosis is a complex vascular disease that affects artery walls (by thickening) and lumens (by plaque formation). The rupture of a carotid artery plaque may also induce ischemic stroke and complications. Despite the use of several medical imaging modalities to evaluate the stability of a plaque, they present limitations such as irradiation, invasive property, low clinical availability and high cost. Ultrasound is a safe imaging method with a real time capability for assessment of biological tissues. It is clinically used for early screening and diagnosis of carotid artery plaques. However, current vascular ultrasound technologies only identify the morphology of a plaque in terms of echo brightness or the impact of the vessel narrowing on flow properties, which may not be sufficient for optimum diagnosis. Noninvasive vascular elastography (NIVE) has been shown of interest for determining the stability of a plaque. Specifically, NIVE can determine the strain field of the moving vessel wall of a carotid artery caused by the natural cardiac pulsation. Due to Young’s modulus differences among different vessel tissues, different components of a plaque can be detected as they present different strains thereby potentially helping in characterizing the plaque stability. Currently, sub-optimum performance and computational efficiency limit the clinical acceptance of NIVE as a fast and efficient method for the early diagnosis of vulnerable plaques. Therefore, there is a need to further develop NIVE as a non-invasive, fast and low computational cost imaging tool to better characterize the plaque vulnerability. The procedure to perform NIVE analysis consists in image formation and image post-processing steps. This thesis aimed to systematically improve the accuracy of these two aspects of NIVE to facilitate predicting carotid plaque vulnerability. The first effort of this thesis has been targeted on improving the image formation (Chapter 5). Transverse oscillation beamforming was introduced into NIVE. The performance of transverse oscillation imaging coupled with two model-based strain estimators, the affine phase-based estimator (APBE) and the Lagrangian speckle model estimator (LSME), were evaluated. For all simulations and in vitro studies, the LSME without transverse oscillation imaging outperformed the APBE with transverse oscillation imaging. Nonetheless, comparable or better principal strain estimates could be obtained with the LSME using transverse oscillation imaging in the case of complex and heterogeneous tissue structures. During the acquisition of ultrasound signals for image formation, out-of-plane motions which are perpendicular to the two-dimensional (2-D) scan plane are existing. The second objective of this thesis was to evaluate the influence of out-of-plane motions on the performance of 2-D NIVE (Chapter 6). For this purpose, we designed an in vitro experimental setup to simulate out-of-plane motions of 1 mm, 2 mm and 3 mm. The in vitro results showed more strain estimation artifacts for the LSME with increasing magnitudes of out-of-plane motions. Even so, robust strain estimations were nevertheless obtained with 2.0 mm out-of-plane motion (correlation coefficients higher than 0.85). For a clinical dataset of 18 participants with carotid artery stenosis, we proposed to use two datasets of scans on the same carotid plaque, one cross-sectional and the other in a longitudinal view, to deduce the out-of-plane motions (estimated to be ranging from 0.25 mm to 1.04 mm). Clinical results showed that strain estimations remained reproducible for all motion magnitudes since inter-frame correlation coefficients were higher than 0.70, and normalized cross-correlations between radiofrequency images were above 0.93, which indicated that confident motion estimations can be obtained when analyzing clinical dataset of carotid plaques using the LSME. Finally, regarding the image post-processing component of NIVE algorithms to estimate strains of vessel walls from reconstructed images with the objective of identifying soft and hard tissues, we developed a strain estimation method with a pixel-wise resolution as well as a high computation efficiency for improving NIVE (Chapter 7). We proposed a sparse model strain estimator (SMSE) for which the dense strain field is parameterized with Discrete Cosine Transform descriptions, thereby deriving affine strain components (axial and lateral strains and shears) without mathematical derivative operations. Compared with the LSME, the SMSE reduced estimation errors in simulations, in vitro and in vivo tests. Moreover, the sparse implementation of the SMSE reduced the processing time by a factor of 4 to 25 compared with the LSME based on simulations, in vitro and in vivo results, which is suggesting a possible implementation of NIVE in real time

Volumetric quantitative optical coherence elastography with an iterative inversion method

It is widely accepted that accurate mechanical properties of three-dimensional soft tissues and cellular samples are not available on the microscale. Current methods based on optical coherence elastography can measure displacements at the necessary resolution, and over the volumes required for this task. However, in converting this data to maps of elastic properties, they often impose assumptions regarding homogeneity in stress or elastic properties that are violated in most realistic scenarios. Here, we introduce novel, rigorous, and computationally efficient inverse problem techniques that do not make these assumptions, to realize quantitative volumetric elasticity imaging on the microscale. Specifically, we iteratively solve the three-dimensional elasticity inverse problem using displacement maps obtained from compression optical coherence elastography. This is made computationally feasible with adaptive mesh refinement and domain decomposition methods. By employing a transparent, compliant surface layer with known shear modulus as a reference for the measurement, absolute shear modulus values are produced within a millimeter-scale sample volume. We demonstrate the method on phantoms, on a breast cancer sample ex vivo, and on human skin in vivo. Quantitative elastography on this length scale will find wide application in cell biology, tissue engineering and medicine.Publisher PDFPeer reviewe

Heterogeneous Material Characterization Using Incomplete and Complete Data with Application to Soft Solids

This dissertation proposes and develops novel features into the existing inverse algorithms for characterizing nonhomogeneous material properties of soft solids. Firstly, a new feature that material properties are defined as a piece-wise constant in each element has been implemented in the inverse program. Secondly, to reduce boundary sensitivity of the solution to the inverse problem in elasticity, we modify the objective function using a spatially weighted displacement correlation term. Compared to the conventional objective function, the new formulation performs well in preserving stiffness contrast between the inclusion and background. Then, we present an approach to estimate the nonhomogeneous elastic property distribution using only boundary displacement datasets. We further improve this approach by using force indentation measurements to quantitatively map the elastic properties and analyze the sensitivity of this approach to a variety of factors, e.g., the location and size of the inclusion. Furthermore, we present a method to quantitatively determine the shear modulus distribution using full-field displacements with partially known material properties on the boundary and without any traction or force information. We test its performance using two different types of regularization: total variation diminishing (TVD) and total contrast diminishing (TCD) regularizations. We observe that TCD regularization is capable of mapping the absolute shear modulus distribution, while TVD regularization fails to achieve this. Furthermore, we investigate the feasibility of using the linear elastic inverse solver to solve inverse problems for nonlinear elasticity for large deformations. We conclude that the linear elastic approximation will overestimate the stiffness contrast between the inclusion and background. We also extend the inverse strategy to map the orthotropic linear elastic parameter distributions. The reconstructions reveal that this method performs well in the presence of low displacement noise levels, while performing poorly with 3% noise. Finally, a feature that maps the viscoelastic behavior of solids using harmonic displacement data has been implemented and tested. In summary, these new features not only strengthen our understanding in solving the inverse problem for inhomogeneous material property characterization, but also provide a potential technique to characterize nonhomogeneous material properties of soft tissues nondestructively that could be useful in clinical practice

Biomechanical Modeling and Inverse Problem Based Elasticity Imaging for Prostate Cancer Diagnosis

Early detection of prostate cancer plays an important role in successful prostate cancer treatment. This requires screening the prostate periodically after the age of 50. If screening tests lead to prostate cancer suspicion, prostate needle biopsy is administered which is still considered as the clinical gold standard for prostate cancer diagnosis. Given that needle biopsy is invasive and is associated with issues including discomfort and infection, it is desirable to develop a prostate cancer diagnosis system that has high sensitivity and specificity for early detection with a potential to improve needle biopsy outcome. Given the complexity and variability of prostate cancer pathologies, many research groups have been pursuing multi-parametric imaging approach as no single modality imaging technique has proven to be adequate. While imaging additional tissue properties increases the chance of reliable prostate cancer detection and diagnosis, selecting an additional property needs to be done carefully by considering clinical acceptability and cost. Clinical acceptability entails ease with respect to both operating by the radiologist and patient comfort. In this work, effective tissue biomechanics based diagnostic techniques are proposed for prostate cancer assessment with the aim of early detection and minimizing the numbers of prostate biopsies. The techniques take advantage of the low cost, widely available and well established TRUS imaging method. The proposed techniques include novel elastography methods which were formulated based on an inverse finite element frame work. Conventional finite element analysis is known to have high computational complexity, hence computation time demanding. This renders the proposed elastography methods not suitable for real-time applications. To address this issue, an accelerated finite element method was proposed which proved to be suitable for prostate elasticity reconstruction. In this method, accurate finite element analysis of a large number of prostates undergoing TRUS probe loadings was performed. Geometry input and displacement and stress fields output obtained from the analysis were used to train a neural network mapping function to be used for elastopgraphy imaging of prostate cancer patients. The last part of the research presented in this thesis tackles an issue with the current 3D TRUS prostate needle biopsy. Current 3D TRUS prostate needle biopsy systems require registering preoperative 3D TRUS to intra-operative 2D TRUS images. Such image registration is time-consuming while its real-time implementation is yet to be developed. To bypass this registration step, concept of a robotic system was proposed which can reliably determine the preoperative TRUS probe position relative to the prostate to place at the same position relative to the prostate intra-operatively. For this purpose, a contact pressure feedback system is proposed to ensure similar prostate deformation during 3D and 2D image acquisition in order to bypass the registration step

Doctor of Philosophy

dissertationImage-based biomechanics, particularly numerical modeling using subject-specific data obtained via imaging, has proven useful for elucidating several biomechanical processes, such as prediction of deformation due to external loads, applicable to both normal function and pathophysiology of various organs. As the field evolves towards applications that stretch the limits of imaging hardware and acquisition time, the information traditionally expected as input for numerical routines often becomes incomplete or ambiguous, and requires specific acquisition and processing strategies to ensure physical accuracy and compatibility with predictive mathematical modeling. These strategies, often derivatives or specializations of traditional mechanics, effectively extend the nominal capability of medical imaging hardware providing subject-specific information coupled with the option of using the results for predictive numerical simulations. This research deals with the development of tools for extracting mechanical measurements from a finite set of imaging data and finite element analysis in the context of constructing structural atlases of the heart, understanding the biomechanics of the venous vasculature, and right ventricular failure. The tools include: (1) application of Hyperelastic Warping image registration to displacement-encoded MRI for reconstructing absolute displacement fields, (2) combination of imaging and a material parameter identification approach to measure morphology, deformation, and mechanical properties of vascular tissue, and (3) extrapolation of diffusion tensor MRI acquired at a single time point for the prediction the structural changes across the cardiac cycle with mechanical simulations. Selected tools were then applied to evaluate structural changes in a reversible animal model for right ventricular failure due to pressure overload

The use of digital image correlation in the biomechanical area: a review

This paper offers an overview of the potentialities and limitations of digital image correlation (DIC) as a technique for measuring displacements and strain in biomechanical applications. This review is mainly intended for biomechanists who are not yet familiar with DIC. This review includes over 150 papers and covers different dimensional scales, from the microscopic level (tissue level) up to macroscopic one (organ level). As DIC involves a high degree of computation, and of operator- dependent decisions, reliability of displacement and strain measurements by means of DIC cannot be taken for granted. Methodological problems and existing solutions are summarized and compared, whilst open issues are addressed. Topics addressed include: preparation methods for the speckle pattern on different tissues; software settings; systematic and random error associated with DIC measurement. Applications to hard and soft tissues at different dimensional scales are described and analyzed in terms of strengths and limitations. The potentialities and limitations of DIC are highlighted, also in comparison with other experimental techniques (strain gauges, other optical techniques, digital volume correlation) and numerical methods (finite element analysis), where synergies and complementarities are discussed. In order to provide an overview accessible to different scientists working in the field of biomechanics, this paper intentionally does not report details of the algorithms and codes used in the different studies

Variational methods for modeling and simulation of tool-tissue interaction

Ph.DDOCTOR OF PHILOSOPH

Capture and Modeling of Non-Linear Heterogeneous Soft Tissue

This paper introduces a data-driven representation and modeling technique for simulating non-linear heterogeneous soft tissue. It simplifies the construction of convincing deformable models by avoiding complex selection and tuning of physical material parameters, yet retaining the richness of non-linear heterogeneous behavior. We acquire a set of example deformations of a real object, and represent each of them as a spatially varying stress-strain relationship in a finite-element model. We then model the material by non-linear interpolation of these stress-strain relationships in strain-space. Our method relies on a simple-to-build capture system and an efficient run-time simulation algorithm based on incremental loading, making it suitable for interactive computer graphics applications. We present the results of our approach for several non-linear materials and biological soft tissue, with accurate agreement of our model to the measured data.Engineering and Applied Science