Fluid-driven deformation of a soft granular material

Compressing a porous, fluid-filled material will drive the interstitial fluid out of the pore space, as when squeezing water out of a kitchen sponge. Inversely, injecting fluid into a porous material can deform the solid structure, as when fracturing a shale for natural gas recovery. These poromechanical interactions play an important role in geological and biological systems across a wide range of scales, from the propagation of magma through the Earth's mantle to the transport of fluid through living cells and tissues. The theory of poroelasticity has been largely successful in modeling poromechanical behavior in relatively simple systems, but this continuum theory is fundamentally limited by our understanding of the pore-scale interactions between the fluid and the solid, and these problems are notoriously difficult to study in a laboratory setting. Here, we present a high-resolution measurement of injection-driven poromechanical deformation in a system with granular microsctructure: We inject fluid into a dense, confined monolayer of soft particles and use particle tracking to reveal the dynamics of the multi-scale deformation field. We find that a continuum model based on poroelasticity theory captures certain macroscopic features of the deformation, but the particle-scale deformation field exhibits dramatic departures from smooth, continuum behavior. We observe particle-scale rearrangement and hysteresis, as well as petal-like mesoscale structures that are connected to material failure through spiral shear banding

Descriptive and Intuitive Population-Based Cardiac Motion Analysis via Sparsity Constrained Tensor Decomposition

International audienceAnalysing and understanding population-specific cardiac function is a challenging task due to the complex dynamics observed in both healthy and diseased subjects and the difficulty in quantitatively comparing the motion in different subjects. It was proposed to use affine parameters extracted from a Polyaffine motion model for a group of subjects to represent the 3D motion regionally over time for a group of subjects. We propose to construct from these parameters a 4-way tensor of the rotation, stretch, shear, and translation components of each affine matrix defined in an intuitive local coordinate system, stacked per region, for each affine component, over time, and for all subjects. From this tensor, Tucker decomposition can be applied with a constraint of sparsity on the core tensor in order to extract a few key, easily interpretable modes for each subject. Using this construction of a data tensor, the tensors of multiple groups can be stacked and collectively decomposed in order to compare and discriminate the motion in each group by analysing the different loadings of each combination of modes for each group. The proposed method was applied to study and compare left ventricular dynamics for a group of healthy adult subjects and a group of adults withrepaired Tetralogy of Fallot

Spatio-Temporal Tensor Decomposition of a Polyaffine Motion Model for a Better Analysis of Pathological Left Ventricular Dynamics

International audienceGiven that heart disease can cause abnormal motion dynamics over the cardiac cycle, which can then affect cardiac function, understanding and quantifying cardiac motion can provide insight for clinicians to aid in diagnosis, therapy planning, as well as to determine the prognosis for a given patient. The goal of this paper is to extract population-specific cardiac motion patterns from 3D displacements in order to firstly identify the mean motion behaviour in a population and secondly to describe pathology-specific motion patterns in terms of the spatial and temporal aspects of the motion. Since there are common motion patterns observed in patients suffering from the same condition, extracting these patterns can lead towards a better understanding of a disease. Quantifying cardiac motion at a population level is not a simple task since images can vary widely in terms of image quality, size, resolution and pose. To overcome this, we analyse the parameters obtained from a cardiac-specific Polyaffine motion tracking algorithm, which are aligned both spatially and temporally to a common reference space. Once all parameters are aligned, different subjects and different populations can be compared and analysed in the space of Polyaffine transformations by projecting the transformations to a reduced-order subspace in which dominant motion patterns in each population can be extracted and analysed. Using tensor decomposition allows the spatial and temporal aspects to be decoupled in order to study the different components individually. The proposed method was validated on healthy volunteers and Tetralogy of Fallot patients according to known spatial andtemporal behaviour for each population. A key advantage of the proposed method is the ability to regenerate motion sequences from the respective models, thus the models can be visualised in terms of the full motion, which allows for better understanding of the motion dynamics of different populations

Accurate determination and application of local strain for studying tissues with gradients in mechanical properties

Determination of the mechanical behavior of materials requires an understanding of deformation during loading. While this is traditionally accomplished in engineering by examining a force displacement curve for a whole sample, these techniques implicitly ignore local geometric complexities and local material inhomogeneities commonly found in biologic tissues. Techniques such as normalized cross correlation have been classically applied to address this issue and resolve deformation at the local level; however, these techniques have proven unreliable when deformations become large, if the sample undergoes a rotation, and/or if strain fields become incompatible (e.g. at or near failure). Presented here is a toolbox of techniques that addresses the limitations of the prior state-of-the-art for localized strain estimation. The first algorithm, termed 2D direct deformation estimation (2D-DDE), directly incorporates concepts from mechanics into non-rigid registration algorithms from computer vision, eliminating the need to consider displacement fields, as required for all of the prior state-of-the-art techniques. This results in not only an improvement in accuracy and precision of deformation estimation, but also relaxes compatibility of the deformation fields. A second algorithm, 2D Strain Inference with Measures of Probable Local Elevation (2D-SIMPLE), incorporates the results of 2D-DDE with results from algorithms that enforce strain compatibility to develop a robust detector of strain concentrations. While tracking local strain in a vinylidene chloride sheet in tension, 2D-SIMPLE detected strain concentrations which predicted the initiation of a crack in the material and the progression of the crack tip. The third and fourth algorithms generalize the two dimensional algorithms to analyze three dimensional deformations in volumetric images (3D-DDE and 3D-SIMPLE, respectively). Lastly, the 2D-DDE algorithm is modified to estimate two dimensional surface deformation from multi-view imaging systems. The robustness and adaptability of these techniques was then validated and demonstrated on a wide variety of biomedical applications. Using 2D-DDE, a microscale compliant region was discovered at the tendon-to-bone attachment, local heterogeneity of partially mineralized scaffolds was revealed, and gradients in stiffness of partially mineralized nano-fiber scaffolds were demonstrated. Using 2D-SIMPLE, mechanisms of embryonic wound healing and associated strain localizations were elucidated. 3D-DDE confirmed the existence of strain gradients across chordae tendineae in beating murine hearts as well as demonstrated dramatic localized changes in wall deformation before and after myocardial infarction in murine hearts. 2D-DDE was also used to develop a model system to study the effects of applied stress versus the effects of applied strain on cells. The model system was first theorized by considering a system in which gradients of cross sectional area or scaffold shape were composed with gradients in material stiffness. By combining these gradients in novel ways, it was theoretically determined that stress and strain could be locally isolated. A tensile bioreactor was constructed, techniques for fabricating scaffolds with gradients in stiffness and gradients in cross sectional area were developed, and theoretical strain gradients were confirmed experimentally using 2D-DDE. The model system was then validated for in vitro cell studies. Cell adhesion, proliferation, and viability following a seven day loading protocol were explored. Methods for determining single cell responses, which could be correlated back to a specific stress or strain states, were developed using immunocytochemistry and 2D-DDE approaches. Future studies will apply this model system to determine precise mechanotransduction responses of cells. These studies are critical to optimize stem cell tissue engineering strategies as well inform cell mechanobiology mechanisms

Modified mass-spring system for physically based deformation modeling

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented

Modified mass-spring system for physically based deformation modeling

Mass-spring systems are considered the simplest and most intuitive of all deformable models. They are computationally efficient, and can handle large deformations with ease. But they suffer several intrinsic limitations. In this book a modified mass-spring system for physically based deformation modeling that addresses the limitations and solves them elegantly is presented. Several implementations in modeling breast mechanics, heart mechanics and for elastic images registration are presented

Doctor of Philosophy

dissertationThe statistical study of anatomy is one of the primary focuses of medical image analysis. It is well-established that the appropriate mathematical settings for such analyses are Riemannian manifolds and Lie group actions. Statistically defined atlases, in which a mean anatomical image is computed from a collection of static three-dimensional (3D) scans, have become commonplace. Within the past few decades, these efforts, which constitute the field of computational anatomy, have seen great success in enabling quantitative analysis. However, most of the analysis within computational anatomy has focused on collections of static images in population studies. The recent emergence of large-scale longitudinal imaging studies and four-dimensional (4D) imaging technology presents new opportunities for studying dynamic anatomical processes such as motion, growth, and degeneration. In order to make use of this new data, it is imperative that computational anatomy be extended with methods for the statistical analysis of longitudinal and dynamic medical imaging. In this dissertation, the deformable template framework is used for the development of 4D statistical shape analysis, with applications in motion analysis for individualized medicine and the study of growth and disease progression. A new method for estimating organ motion directly from raw imaging data is introduced and tested extensively. Polynomial regression, the staple of curve regression in Euclidean spaces, is extended to the setting of Riemannian manifolds. This polynomial regression framework enables rigorous statistical analysis of longitudinal imaging data. Finally, a new diffeomorphic model of irrotational shape change is presented. This new model presents striking practical advantages over standard diffeomorphic methods, while the study of this new space promises to illuminate aspects of the structure of the diffeomorphism group

Volumetric MRI Reconstruction from 2D Slices in the Presence of Motion

Despite recent advances in acquisition techniques and reconstruction algorithms, magnetic resonance imaging (MRI) remains challenging in the presence of motion. To mitigate this, ultra-fast two-dimensional (2D) MRI sequences are often used in clinical practice to acquire thick, low-resolution (LR) 2D slices to reduce in-plane motion. The resulting stacks of thick 2D slices typically provide high-quality visualizations when viewed in the in-plane direction. However, the low spatial resolution in the through-plane direction in combination with motion commonly occurring between individual slice acquisitions gives rise to stacks with overall limited geometric integrity. In further consequence, an accurate and reliable diagnosis may be compromised when using such motion-corrupted, thick-slice MRI data. This thesis presents methods to volumetrically reconstruct geometrically consistent, high-resolution (HR) three-dimensional (3D) images from motion-corrupted, possibly sparse, low-resolution 2D MR slices. It focuses on volumetric reconstructions techniques using inverse problem formulations applicable to a broad field of clinical applications in which associated motion patterns are inherently different, but the use of thick-slice MR data is current clinical practice. In particular, volumetric reconstruction frameworks are developed based on slice-to-volume registration with inter-slice transformation regularization and robust, complete-outlier rejection for the reconstruction step that can either avoid or efficiently deal with potential slice-misregistrations. Additionally, this thesis describes efficient Forward-Backward Splitting schemes for image registration for any combination of differentiable (not necessarily convex) similarity measure and convex (not necessarily smooth) regularization with a tractable proximal operator. Experiments are performed on fetal and upper abdominal MRI, and on historical, printed brain MR films associated with a uniquely long-term study dating back to the 1980s. The results demonstrate the broad applicability of the presented frameworks to achieve robust reconstructions with the potential to improve disease diagnosis and patient management in clinical practice

A Tissue Engineering Platform to Investigate Effects of Finite Deformation on Extracellular Matrix Production and Mechanical Properties

It is estimated that more than 85,000 prosthetic heart valves are implanted annually in the US and ~275,000 worldwide. Although current heart valve replacements have extended the lives of many patients, there is to date still no ideal alternative. Pediatric applications, in particular, pose unique problems because current valve replacement options are unable to accommodate somatic growth of the patient. Since its inception, the tissue engineering paradigm has garnered widespread attention as a means to recapitulate native tissue structure, composition, and mechanical function in a controlled and reproducible manner by combining engineering and life science principles. Before fully functioning tissue surrogates can be developed for clinical use, many complex biological, chemical and mechanical aspects of native tissues must be addressed. Furthermore, contemporary literature lacks a consolidated approach, instead, presenting a wide variety of scaffold materials, cell sources, and mechanical conditioning regimes in efforts to restore native tissue function. These challenges coupled with the paucity of structurally based, finite deformation framework constitutive models hinders our understanding of engineered tissues and their ability to perform as tissue surrogates. The focus of this dissertation is to elucidate the effects of large deformation mechanical stimuli on the development of engineered leaflet tissues. With our ability to incorporate viable cells distributed throughout the scaffold via concurrent electrospraying and electrospinning of poly (ester urethane) urea (PEUU) fiber scaffolds, we are provided a unique, controllable platform to: (1) characterize the mechanical behavior of electrospun PEUU and cellular response to global deformation, (2) assess our ability to create functional cell integrated surrogates via dynamic culture, and (3) develop a generalized finite deformation framework than can be used to gain an understanding of how the evolving extracellular matrix phase contributes to the construct gross mechanical behavior. We contend that much can be learned about the mechanical modulation of functional tissue from electrospun PEUU scaffolds since they capture aspects of native tissue microstructure and exhibit the ability to endure large deformations while recovering completely. It is our hope that these studies will guide the emergence of new materials and processing methods to develop functional pulmonary valve (PV) tissue surrogates which serve a predominantly biomechanical function