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Book
1 online resource (viii, 286 pages) : illustrations (some color)
Book
1 online resource.
Sarcomeres are the most basic contractile element of skeletal muscle, with lengths of around 3 μm in humans. The lengths and contractile dynamics of sarcomeres can greatly influence muscle function and be affected by disease, but the small scale of these structures deep within the body has made in vivo measurements difficult. Recently, second-harmonic generation (SHG) microendoscopy has been introduced to image sarcomeres in a minimally invasive manner. This thesis presents the first in vivo measurements of sarcomere lengths in important muscles for gait, the vastus lateralis and the soleus, and of contractile dynamics in a mouse model of ALS. We imaged sarcomeres in healthy humans in the vastus lateralis and the soleus muscles at multiple joint angles to better understand their force generating capacity across a range of joint angles. In the vastus lateralis, we acquired in vivo sarcomere images of several muscle fibers of the resting vastus lateralis in six healthy individuals. Mean sarcomere lengths increased from 2.84±0.16 μm at 50° of knee flexion to 3.17±0.13 μm (mean ± standard deviation) at 110° of knee flexion. The standard deviation of sarcomere lengths among different fibers within a muscle was 0.21±0.09 μm. Our results suggest that the sarcomeres of the vastus lateralis at 50° of knee flexion are near optimal length, enabling the muscle to generate approximately its peak isometric force. At a knee flexion angle of 110° the sarcomeres of vastus lateralis are longer than optimal length, reducing the muscle's active force-generating capacity to approximately 74% of its peak isometric force. In the soleus, we used microendoscopy to measure resting sarcomere lengths at 10° plantarflexion and 20° dorsiflexion in 7 healthy individuals. Mean sarcomere lengths at 10° plantarflexion are 2.84±0.24 μm (mean ± standard deviation), suggesting that the muscle generates near maximum force in this posture. Sarcomere lengths are 3.43±0.25 μm at 20° dorsiflexion, indicating that they are longer than optimal length when the ankle is in dorsiflexion and the muscle is inactive. Our results in both the vastus lateralis and the soleus indicate a smaller change in sarcomere length with joint flexion compared to estimates from musculoskeletal models and suggest why these models may underestimate the force-generating capacity of the soleus. We also measured muscle twitch contractile dynamics in a mouse model of ALS, a fatal disease in which motor neurons connected to muscles progressively die off. Through longitudinal measurements of motor unit twitch contractions in a B6.SOD1G93A mouse model of ALS from a presymptomatic stage to end stage, we observed a presymptomatic elongation in rise times and half relaxation times that increased in the later stage of the disease. We constructed a composite twitch time taken from measurements in each animal that effectively diagnoses individuals, and changes with progression of the disease. This quantitative, minimally invasive approach to assess motor unit contractile timing with ALS progression supports episodes of specific types of motor neuron loss, providing new information for preclinical and clinical studies. Together, these studies demonstrate the utility of muscle microendoscopy in research and the clinic.
Book
1 online resource.
The thesis presents the development, the mathematical analysis, as well as applications of a computational framework for the simulation of curvilinear crack propagation. At the core of the computational framework lies a novel finite element method, named the Mapped Finite Element Method (MFEM), for the optimal convergence of singular solutions. The main challenges in solving numerically the mathematical description of a propagating fracture can be identified in: the continuously evolving (cracked) domain, the singular nature of the elasticity fields, and the computation of the stress intensity factors for the prediction of crack growth. Current state-of-the-art methods are plagued by low order of accuracy, high computational cost, and complex data structures. The work herein addresses the aforementioned challenges by developing a computationally efficient, rapidly convergent, and non-intrusive algorithm consisting of three key ingredients: Universal Meshes, Mapped Finite Element Methods, and Interaction Integrals. First, Universal Meshes are introduced as a computationally efficient and robust meshing algorithm for the generation of conforming subdivisions of the evolving domain. Second, Mapped Finite Element Methods (MFEM) will be developed for the solution of the singular elasticity fields. The methods are shown to converge with optimal order for the same computational cost, preserving well conditioning and sparsity properties, and with no alteration to the data structure of standard Lagrange finite element methods (known to converge sub-optimally for this class of problems). The optimality of convergence is supported by mathematical analysis and applications of MFEM are showcased beyond brittle fracture (e.g. the resolution of boundary layers in flows around moving obstacle, real-space Kohn-Sham density functional theory calculations, etc). Third, the thesis presents the construct of a family of linear and affine functionals, named Interaction Integral functionals, for the rapidly convergent computation of the stress intensity factors (SIFs) for curvilinear fractures. The distinct feature of the Interaction Integral functionals is their ability to double the rate of convergence of the energy norm of the solution in the evaluation of the SIFs. Sketches of the mathematical analysis are provided to support the observed rapid rates of convergence. The propagation algorithm that combines the developed tools (Universal Meshes, Mapped Finite Element Methods, and Interaction Integrals) is presented and shown to be consistent (in the sense of being able to replicate observed experimental results) and predictive (in the sense of yielding crack paths that converge to a unique solution with refinement of the discretization). Lastly, the capabilities of the developed algorithm are exploited to study the formation of wavy crack patterns when brittle heat conductors are rapidly cooled.
Book
1 online resource.
The cornea provides the protective outer covering of the eye. Its almost perfect transparency allows light to pass through it with little loss and its external curvature and refractive index are responsible for most of the bending of light rays needed to focus light on the retina. In the simplest terms, the cornea is a fiber-reinforced fluid shell that supports the intraocular pressure (IOP) applied on its inner surface. Recent developments in imaging the organization of collagen fibers throughout the cornea have provided a quantification of collagen distributions that shed light on how the collagen maintains the cornea's shape and provides elastic resiliency. In addition to the collagen, another defining feature of the cornea is its high water content. The tissue hydration level plays a vital role in transparency, with deviations from normal resulting in corneal opacity. The interfibrillar water supports the tissue fluid pressure which has both hydrostatic (IOP) and osmotic pressure components, and the osmotic pressure is actively modulated to control tissue hydration. In this thesis a comprehensive model for these elements of tissue behavior is introduced with the goal of providing a predictive model for the living human cornea. Common defects in corneal shape lead to refractive errors (e.g. astigmatism). But most sources of refractive error do not have their prime origin in the cornea (e.g. myopia, hyperopia and presbyopia). However, in case of corneal disease such as keratoconus, refractive disruption due to corneal reshaping can be extreme. The surgical accessibility of the cornea makes it a desirable target for surgical correction of many refractive conditions, and not only those arising in the cornea. As a result, surgeons have great interests in being able to accurately predict changes in corneal curvature resulting from a wide range of surgical procedures, in which tissue is cut, removed, modified, added to or redistributed or in which synthetic implants are introduced. The list of surgical approaches is remarkably long and ever-increasing; this is an area of active innovation. In this thesis, a first-principles approach to modeling the biomechanics of the cornea is presented and is demonstrated to extend current predictive capabilities for refractive procedures. The research described in this thesis is organized into three major areas. (1) The active hydration control mechanism in the living cornea and its interaction with the collagen architecture, (2) the force mechanisms that maintain the regular order of the collagen fibrils within the stroma which are necessary for corneal transparency and (3) the influence of metabolic species on osmotic pressure, and the relationship between corneal edema and metabolic processes under normal and pathological conditions. For the studies of collagen-swelling interaction, we propose a structural model of the \textit{in vivo} cornea, which accounts for tissue swelling behavior and the three-dimensional organization of stromal fibers. The cornea is modeled as an electrolyte gel in which the osmotic pressure is modulated by the active endothelial ionic transport. The stromal fiber elasticity is modeled based on three-dimensional collagen orientation probability distributions for every point in the stroma obtained by synthesizing x-ray diffraction data and second harmonic-generated imaging data. The model is implemented in a finite element framework and employed to study the effect of fiber inclination in stabilizing the corneal refractive surface with respect to changes in tissue hydration and IOP. The transparency of the human cornea depends on the pseudohexagonal arrangement of the collagen fibrils and on the maintenance of an optimal hydration -- the achievement of both depends on the presence of negatively charged glycosaminoglycans (GAGs). While the GAGs produce osmotic pressure by Donnan effect, the means by which they exert positional control of the fibril arrangement is less clear. In this thesis, a theoretical model based on equilibrium thermodynamics is proposed to describe restoring force mechanisms that may control and maintain the fibril arrangement. Electrostatic-based restoring forces that result from local charge density changes induced by fibril motion, and entropic elastic restoring forces that arise from duplexed GAG structures that bridge neighboring fibrils, are described. A striking result is that the electrostatic restoring forces alone are able to reproduce the image-based distribution function of fibrils for the human cornea, and thus maintain the short-range order of the lattice-like fibril arrangement. The cornea contains cells, which require nutrient supply from the aqueous humor to maintain their metabolic activities. Disturbances in metabolite concentrations can cause corneal edema and result in loss of corneal transparency. In order to study the relationship between metabolic processes and corneal edema, we introduce a chemo-electro-mechanical model based on balance equations for the stromal fluid and metabolic species. The model describes interactions among metabolic species, charged GAGs and other mobile ions. The model is employed to predict corneal swelling with an intrastromal inlay for refractive correction of presbyopia. The results provide comprehensive explanations for clinical observations, and demonstrate the predictive capabilities of the proposed theory for refractive procedures.
Book
1 online resource.
Skin is our interface to the world, it protects our internal machinery, regulates our temperature, fluid exchange, and resists constant wear and tear. Skin has remarkable mechanical properties, it is a thin structure that can undergo large deformations without rupturing, letting us move around, interact with the objects in our surroundings, and express ourselves. Additionally, our integument is a living system and it can adapt to mechanical and environmental cues. In summary, mechanical integrity of skin is crucial to our survival. Understanding the mechanics and mechanobiology of skin is also important for the clinician since disruption of mechanical homeostasis appears often in disease and repair. This dissertation focuses on the problems of plastic and reconstructive surgery in which skin adapts to mechanical scenarios. These include tissue expansion, flap design and wound healing. Tissue expansion is a well-known technique to resurface large defects by growing skin in vivo. Skin grows in response to overstretch. Despite its numerous advantages and wide-spread, this technique does not lack complications and suboptimal outcomes. A major reason lies in the lack of quantitative tools to understand the fundamental aspects of skin growth to overstretch that can be then used to predict and guide preoperative planning. In this thesis, I show how applying the classical theories of mechanics and incorporating the description of finite growth by the multiplicative split of the deformation gradient into growth and elastic contributions, it is possible to get biological insight into the dynamics of skin growth in response to mechanical deformations. Furthermore, this approach is suitable for an efficient computational implementation using finite elements. I show how simulations can predict the effect of different expander geometries and sizes which are variables of clinical significance. The same set of tools can be used in patient specific scenarios. I demonstrate the use of computational simulations on geometries obtained from computer tomography scans of pediatric patients. In order to validate and calibrate the model, I designed and conducted animal experiments in collaboration with surgeons at Northwestern University. We established a novel experimental protocol that uses multi-view stereo and B-spline isogeometric analysis to capture the kinematics of expanded porcine integument. We show experimentally how overstretch triggers the growth of new skin. We compared different expander shapes and inflation protocols. We also quantified for the first time the development of residual stresses over a sizable patch of tissue. Tissue expansion is at the core of this dissertation, however, once new skin is grown there are two other processes of mechanical interest that become relevant: flap design and wound healing. These phenomena are also relevant for a vast majority of plastic and reconstructive surgery procedures and not only tissue expansion. I present the comparison of different flap designs on grown skin patches and show that the double back cut flap produces an overall lower stress distribution for the same size of defect as compared to the advancement flap. I also show how the orientation of the underlying collagen network plays an important role in the preoperative planning. Finally, another major concern regarding the restoration of mechanical homeostasis of skin is the process of wound healing and scarring. I present a generic framework for the coupled mechano-chemo-biological problem of wound healing. Starting from the mechanics perspective, I use state-of-the-art constitutive laws of skin to model it as an anisotropic hyperelastic material in terms of structurally motivated parameters. The load bearing properties of skin are attributed to the collagen content. When skin is wounded, the collagen architecture is abruptly disrupted. During healing, different cell populations act in coordination through various cell-signaling pathways in order to lay down and remodel the collagen microstructure. In the proposed framework, micro-structural parameters such as the collagen content become part of the evolving fields that have to be characterized as they change over time and space. I incorporate the mechanobiology coupling by making these parameters a function of cellular response. In turn, I introduce a new set of reaction-diffusion partial differential equations to model the dynamics of cell density fields and the chemical signals that regulate the cell behavior. The generic framework I propose is implemented in a monolithic finite element formulation. Simulations of a model problem of cutaneous wound healing shows good agreement with experiments from the literature, offering promise to more detailed simulations and experimental validation and calibration. In conclusion, the body of work presented in this dissertation is a significant step towards the better understanding of skin mechanics not only as a structure, but as a living tissue that can grow and heal. The computational tools developed are ultimately aimed at applications in clinically relevant problems of plastic and reconstructive surgery.
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Book
1 online resource.
The unique hierarchical structure of the human cornea results in a tissue which is remarkably transparent but mechanically resilient enough to protect the contents of the eye and maintain its shape for appropriate refraction of light onto the retina. Since the eye generates an intraocular pressure, the cornea can be thought of as part of a pressure vessel under constant mechanical stress. This work aims to use the latest knowledge and imaging at multiple length scales to produce a comprehensive biomechanical model of the cornea. Examining a cross-section of the human cornea with second harmonic-generated (SHG) imaging reveals that many lamellae (collagen-filled, tape-like fibers that make up the main stroma layer) have inclined trajectories that take them through the corneal thickness with a depth-dependent distribution. Transverse shear moduli from 1% shear strain oscillatory tests were found to be two to three orders of magnitude lower than tensile moduli reported in the literature and six times higher in the anterior third than the posterior third, confirming the hypothesis. In order to create a theoretical model that accounts for the 3-D collagen architecture, a multiscale model of stromal elasticity is developed. At the nanoscale, a collagen fibril is built by assembling tropocollagen molecules with enzymatic and non-enzymatic covalent crosslinks. Crosslink density, which is a function of age, disease, and therapeutic treatment, strongly influences fibril stiffness and is a key feature of the present model. At the microscale, aligned collagen fibrils are combined with other components to form a single lamella (fiber). For a continuum mechanics-based model of the lamella, a hyperelastic strain energy density is defined that is decomposed into three parts. At the macroscale, these directional lamellae organize to construct the stroma with a spatially-varying distribution of orientation. Stromal elasticity is calculated by a weighted average of individual lamella properties based on the spatially-varying orientation distribution. A fully 3-D representation of lamella orientation is synthesized by combining data from SHG imaging and X-ray diffraction. Inclined lamella orientation is extracted from SHG images and characterizes how the range and distribution of lamellae at inclined angles varies with depth through the stroma. Direct measurements from X-ray diffraction experiments give the depth-dependent orientation of lamellae in the tangent plane that follows the corneal surface. The model is calibrated with reference to macroscale in vitro inflation and torsional shear experiments. Nanoscale tropocollagen parameters and resulting fibril properties match well with molecular simulations and nanoscale experiments in the literature. Simulated experiments for model validation include in vivo indentation, in vitro strip extensiometry, and in vitro free swelling studies. Important features of the model are showcased by varying lamellar orientation distributions and non-enzymatic crosslink density.
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Book
1 online resource.
Computational methods for simulating blood flow have become powerful tools to gain insight into the physical behavior of the cardiovascular system in health and disease. This work is aimed at developing computational tools and models for the investigation of age-related arterial stiffening and its relationship to the underlying hemodynamics. Due to the complex geometry and spatially-varying material properties of the central arteries, and the hemodynamics therein, large-scale three-dimensional computational models of arterial mechanics can improve our ability to interpret current clinical hemodynamic metrics and to advance our fundamental understanding of the mechanisms of disease progression. We have built a novel computational model of fully three-dimensional and unsteady hemodynamics within the primary large arteries in the human systemic circulation from head to legs. We demonstrated that this virtual full body systemic arterial tree is able to reproduce many of the key local and global hemodynamic features of the human arterial circulation and is a promising first step toward further computational analyses of the relationship between blood flow and arterial stiffening. As part of this work, we have tested and implemented an important boundary condition for the arterial fluid-solid interaction problem that mimics the tethering effect of the external tissues and stabilizes simulations in large networks of vessels. The task of efficiently fitting large-scale 3-D models to patient-specific measurements is challenging due to the computational effort required for a single simulation and the number of model parameters involved. We implemented two different computational frameworks for parameter estimation: the first is based on computationally inexpensive one-dimensional analogues of the full 3-D system. The second method is based on sequential data-assimilation techniques, specifically, nonlinear Kalman filtering. We demonstrate that these frameworks may be used to rapidly estimate the parameters of large-scale 3-D models based on clinical measurements of blood flow, pressure, and vessel wall distensibility.
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Book
1 online resource.
The work presented herein is concerned with the development of biophysical methodology designed to address pertinent questions regarding the behavior and structure of select pathogenic agents. Two distinct studies are documented: a shock tube analysis of endospore-laden bio-aerosols and a correlated AFM/NanoSIMS study of the structure of vaccinia virus. An experimental method was formulated to analyze the biological and morphological response of endospores to gas dynamic shock waves. A novel laser diagnostic system was implemented to provide time resolved data concerning the structural decomposition of endospores in shock-heated flows. In addition, an ex situ methodology combining viability analysis, flow cytometry and scanning electron microscopy was employed to both assess the biological response of the endospore to the shock event, as well as to provide complementary data regarding the structural state of the treated endospore. This methodology was implemented to model the shock wave induced response of a variety of Bacillus endospores. The results are subsequently synthesized into a theoretical framework to be employed in modeling the interaction of endospore-laden bio-aerosols with blast waves. An analytical method combining atomic force microscopy (AFM) and nanometer-scale secondary ion mass spectrometry (NanoSIMS) was developed to examine the spatial localization and depth distribution of specific biological elements in viral systems. This methodology was implemented to analyze the distribution of 13C labeled fatty acids as well as 15N labeled thymidine in individual nanometer sized vaccinia viral particles. Based upon the 13C and 15N signals, three-dimensional depth-resolved data regarding the architecture and localization of the virion lipid membrane and the nucleoprotein complex was generated. In addition, this methodology was employed to provide direct correlation of architectural and chemical data for isolated sub-viral structures. The technique and results presented herein represent a novel tool for the structural and chemical study of both intact viral particles as well as specifically targeted sub-viral elements.
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Book
1 online resource.
The mitral valve is one of four heart valves that ensure unidirectional blood flow through the heart. Due to mitral valve failure approximately 44,000 people in the US alone undergo open heart surgery every year. Current treatment options include mitral valve replacement and mitral valve repair, neither of which have shown satisfying long-term success. A deepened understanding of mitral valve mechanics may help in improving current medical device designs and treatment options for mitral valve regurgitation. Here I provide an in depth analysis of the in vivo mechanics of the mitral valve using the theory of finite kinematics and based on this data develop non-linear in silico models of the mitral valve employing the finite element method. Using mechanical metrics such as strain and curvature I reveal the in vivo deformation of the mitral annulus and the mitral leaflet in the healthy, diseased, and repaired mitral valve. Furthermore, in silico I explore the effects of prestrain as well as growth and remodeling on the mechanics of the mitral valve. The results of my in vivo studies extend our current understanding of the healthy mitral valve, reveal new insight into disease characteristics and progressions, and evaluate the efficacy of current device designs. Furthermore, results from the in silico studies provide improved means to simulate mitral valve mechanics and predict long term adaptation for basic science research and medical device design. In conclusion, with the current work I take a large step toward a deepened understanding of mitral valve mechanics that may help to optimize medical device designs and treatment options.
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Book
1 online resource.
In this work we present a series of scientific contributions made to the study of the impact of projectiles into tissue-like materials, specifically the synthetic artificial tissue simulant Perma-Gel. These contributions consist of a combination of experimental observations, algorithmic ideas and numerical tools which demonstrate a series of problems and solutions to trying to simulate nearly incompressible soft tissues using finite elements. A number of experiments were performed by taking high-speed footage of the firing of spherical steel bullets at different speeds into Perma-Gel, a new thermoplastic material used as a proxy to human muscle tissue. This work appears to be the first publicly released experimental work using Perma-Gel and is part of the small amount of non-classified work looking at ballistic gelatin behavior. A number of experimental observations were made regarding the material behavior, elastic and plastic deformation around the projectile, and the possibility of cavitation. This work introduces an explicit dynamic contact algorithm that takes advantage of the asynchronous time stepping nature of Asynchronous Variational Integrators (AVI) to improve performance when simulating elastic-body rigid-wall contact. We demonstrate a number of desirable properties over traditional one-time-step methods for the simulation of solid dynamics and provide a number of examples highlighting the advantages of this method. The explicit contact algorithm and AVI was used to simulate the impact of a projectile into a simulated block of gelatin, but was hindered by difficulties using the realistic material parameters. Using a parallelized version of the algorithm, large-scale simulations were performed for progressively smaller shear moduli. As the simulations approached realistic values for the shear modulus, unstable element configurations formed which required infeasibly small time steps to successfully resolve. The behavior observed for the shear moduli we could numerically simulate with did not resemble the experimental results. To simulate with smaller values, we had to go to an axisymmetric setting. The axisymmetric setting increased the range of shear moduli which could be simulated and demonstrated the same dynamic behavior, though the issue of unstable element configurations continued to occur in extreme cases. To deal with the issue of unstable elements, we created an axisymmetric remeshing strategy to compensate for the unstable element configurations and insufficient spatial resolution. This strategy consists of periodically applying a remeshing and transfer algorithm that updates highly deformed finite element meshes with configurations formed with elements having uniform aspect ratios and local refinement in important areas. The axisymmetric setting with remeshing increased the range of potential shear modulus values that could be simulated. This allowed for the identification of qualitative similarities in the transient behavior between the numerical results and the experimental footage.
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Book
1 online resource.
The heart is an essential heterogeneous organ that depends on strong coupling between electrical, chemical, and mechanical dynamics to properly function as a pump that supplies blood to the rest of the body. Cardiac arrhythmias are common disorders characterized by irregular beating of the heart that lead to serious clinical conditions. It is estimated that approximately 2.2 million adults in the United States are affected by atrial fibrillation, a prevalent arrhythmia. Unfortunately, a clinician often does not have enough information to diagnose a patient's heart condition to determine the optimal treatment procedure. This is an area that computational mechanics can address. While development of mechanical and electrophysiological models of cardiac tissue primarily started in the 1950s, fully-coupled models have only more recently been developed due to factors regarding computational cost, difficulty in quantifying material properties, and difficulty in integrating complex models in a cohesive and efficient manner. Therefore, in order for simulation tools to have impact in the clinical or experimental setting, these tools must be efficient, fast, robust, and accessible. The focus of this thesis is to develop methods of addressing the aforementioned issues and then illustrate how efficient electromechanical finite element models can be developed for the heart such that their use in the clinical and experimental setting can be realized in several examples. In this thesis, a global-local variable splitting formulation borrowed from the field of plasticity is used to address the issues of complex model integration, and to maintain numerical stability at low costs. Through careful examination of classical phenomenological models and detailed biophysical ionic models of the electrophysiology of the heart, almost all models can be reformulated into this global-local splitting framework. The numerical properties of cost-expensive ionic models are briefly analyzed within the context of this framework. Use of implicit-time stepping in tandem with a simple iteration and error tolerance based adaptive time-stepping algorithm allows for reduction of computation time from hours to minutes. Flexibility and modularity of the framework are illustrated through the development of electrical, electro-chemical, electro-chemical-mechanical, and opto-electro-mechanical models of cardiac tissue. The heart is modeled efficiently using custom finite element ventricular cell models for physiological electrical simulations and large deformation excitation-contraction dry-pumping simulations of the heart. The results accurately model the physiological condition of the heart. The flexibility and multiscale nature of the framework is also leveraged in developing novel optical-induced cardiac cell excitation models of new genetically engineered Channelrhodpsin-2 (ChR2) cardiac myocytes. An ionic model was developed for these particular bio-engineered stem cells, calibrated with experimental data from collaborators, and was able to predict the electrical excitation behavior of the cells to a reasonable degree of accuracy. This model was then combined with ionic pacemaker cell models and also with ventricular cell models into respective finite elements to simulate experiments and predict future therapies using ChR2 genetically modified cardiac tissue. The thesis also addresses difficulties relating to identification and characterization of material parameter identification in inhomogeneous cardiac tissue. Metrics for determining smoothness in electrical conduction in tissue cultures were validated with stochastic finite element models of microelectrode array cell conduction experiments. The results indicate that these metrics are useful in characterizing different conduction patterns based on two metrics borrowed from texture analysis. Difficulties in obtaining structural fiber data from clinical images were addressed by developing an algorithmic method for designating approximate physiologically accurate fiber distributions for the heart using only geometrical information obtained from MRI scans of the surfaces of the heart. Poisson interpolation is used and results in a smooth continuous rotating fiber description that matches experimentally obtained fiber directions from MRI scans. The main benefits of this algorithm are its simplicity of implementation, physiologically accuracy, and generality in interpolating fiber distributions. Lastly, the thesis demonstrates possible benefits of GPU computing in order to achieve near-real-time electrical simulations of arrhythmias in the heart. The assembly and solver routines from the finite element code, FEAP from Berkeley, were ported to the GPU using CUDA. Even with a minimally optimized proof-of-concept, the GPU-only finite element code achieves performance comparable to twelve cores using only one GPU. To increase the overall efficiency of the method, current sparse matrix vector multiplication GPU algorithms are analyzed, and possible alternative algorithms are developed specifically with unstructured finite element meshes in mind. Altogether, the different methods developed in this thesis have been shown to be effective in addressing issues related to efficiency, numerical stability, modularity, and flexibility in real computational applications of the heart. Special consideration was taken in designing the different methods to be compatible with one another, such that a majority of the methods could be integrated and the benefits of each method could be leveraged with each other to gain maximum efficiency. While these developed methods can still be improved, the thesis work as a whole serves to demonstrate and highlight future uses for computational models within experimental and clinical settings.
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1 online resource.
In this thesis, a finite-element-based algorithm is presented to simulate plane-strain hydraulic fractures in an impermeable elastic medium where the crack path is not known a priori. The algorithm accounts for the nonlinear coupling between the fluid pressure and the crack opening and separately tracks the evolution of the crack tip and the fluid front. It therefore allows the existence of a fluid lag. The fluid front is advanced explicitly in time, but the crack tip is determined implicitly by enforcing Griffith's criterion and maximum energy release rate. A spatial discretization is created that conforms to the crack path by perturbing the nodes of a background mesh. The coupling between the fluid and the rock is enforced by simultaneously solving for the fluid pressure and the crack opening at each time step. Verification of the algorithm is provided for straight hydraulic fractures by performing sample simulations and comparing them to two known similarity solutions. Also, sample simulations are carried out for the general case of curvilinear fractures for which the crack path is not known a priori.
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1 online resource.
It is well known that blood vessels exhibit viscoelastic properties. Vessel wall viscoelasticity is an important source of physical damping and dissipation in the cardiovascular system. There is a growing need to incorporate viscoelasticity of arteries in computational models of blood flow which are utilized for applications such as disease research, treatment planning and medical device evaluation. However, thus far the use of viscoelastic wall properties in blood flow modeling has been limited. As part of the present work, arterial wall viscoelasticity was incorporated into two computational models of blood flow: (1) a nonlinear one-dimensional (1-D) model and (2) a three-dimensional (3-D) fluid-solid interaction (FSI) model of blood flow. 1-D blood flow model: In blood flow simulations different viscoelastic wall models may produce significantly different flow, pressure and wall deformation solutions. To highlight these differences a novel comparative study of two viscoelastic wall models and an elastic model is presented in this work. The wall models were incorporated in a nonlinear 1-D model of blood flow, which was solved using a space-time finite element method. The comparative study involved the following applications: (i) Wave propagation in an idealized vessel with reflection-free outflow boundary condition; (ii) Carotid artery model with non-periodic boundary conditions; (iii) Subject-specific abdominal aorta model under rest and exercise conditions. 3-D FSI blood flow model: 3-D blood flow models enable physiologic simulations in complex, subject-specific anatomies. In the present work, a viscoelastic constitutive relationship for the arterial wall was incorporated in the 3-D Coupled Momentum Method for Fluid-Solid Interaction problems (CMM-FSI). Results in an idealized carotid artery stenosis geometry show that higher frequency components of flow rate, pressure and vessel wall motion are damped in the viscoelastic case. These results indicate that the dissipative nature of viscoelastic wall properties has an important impact in 3-D simulations of blood flow. Future work will include simulations of blood flow in patient-specific geometries such as aortic coarctation (a congenital disease) to assess the impact of wall viscoelasticity in clinically relevant scenarios. In the present work, arterial viscoelasticity has been incorporated in 1-D and 3-D computational models of blood flow. The biomechanical effects of wall viscoelasticity have been investigated through idealized and subject-specific blood flow simulations. These contributions are significant and suggest the potential importance of wall viscoelasticity in blood flow simulations for clinically relevant applications.
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1 online resource.
The shoulder bones provide few constraints on motion. Therefore, stability must be maintained by muscles and ligaments. Shoulder mobility allows versatility of function, but makes the shoulder prone to injury. A better understanding of the role of muscle in shoulder mechanics is needed to improve the treatment of shoulder injuries and pathologies. Computational models provide a valuable framework for characterizing joint mechanics. Previous shoulder models have used simple representations of muscle architecture and geometry that may not capture the details needed to fully understand muscle function. The purpose of this dissertation was to create a detailed 3D finite element model of the deltoid and the four rotator cuff muscles. This model was then used to characterize the muscle contributions to joint motion and stability. The model was constructed from magnetic resonance images of a healthy shoulder. From the images, the 3D geometry of the muscles, tendons and bones was acquired. A finite element mesh was constructed and the 3D trajectories of the muscle fibers were mapped onto the finite element mesh. A hyperelastic, transversely-isotropic material model was used to represent the nonlinear stress-strain relationship of muscle. Bone motions were prescribed and the resulting muscle deformations were simulated using an implicit finite element solver. To characterize muscle contributions to joint motion, we calculated moment arms for each modeled muscle fiber. We found that 3D models predicted substantial variability in moment arms across fibers within each muscle, which is not generally represented in line segment models. We also discovered that for muscles with large attachment regions, such as deltoid, the line segment models under constrained the muscle paths in some cases. As a result, line segment based moment arms changed more with joint rotation than moment arms predicted by the 3D models. Glenohumeral instability is common, and difficult to treat. To better understand the mechanics of instability we used the 3D model to investigate the role of the muscles in stabilizing the glenohumeral joint by simulating joint translations. We found that at the neutral position, anterior deltoid provides the largest potential to resist anterior translation which counters the conclusions of conventional line segment models. This is the result of compression generated by muscle contact, which must be considered when characterizing the ability of muscle to resist joint translation. This dissertation provides a new computational method for analyzing shoulder mechanics, and demonstrates the importance of 3D analysis when investigating the complex function of shoulder muscles.
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Book
1 online resource.
Osteoarthritis (OA) of the knee is a prevalent and painful disease, yet there is no cure or robust treatment to slow disease progression. Improving solutions for patients with knee OA requires a better understanding of the disease mechanisms. While joint injuries are a significant risk factor in OA development (post-traumatic OA, PTOA), in many cases, the initial disease causation is unknown (idiopathic OA, IOA). Literature suggests that structural, mechanical, and biological factors on many scales are involved and interact in both PTOA and IOA development. Therefore, the overall goal of this thesis project was to test for differences in and interactions between structural, mechanical, and biological factors in populations at risk of developing PTOA and IOA. The first study in this dissertation tested a cohort of subjects at risk of developing PTOA due to partial medial meniscectomy. In this population, limb differences in both transverse and sagittal plane gait mechanics differed between walking and stair traversing activities. This study may provide novel information for post-operative care as the results indicate the need to sufficiently challenge the knee joint both in dynamic load and range of motion to elicit differences in clinically meaningful kinematic measures after meniscectomy. To test the whether these measured kinematic limb differences persist longer-term after medial meniscectomy, a sub-cohort of the post-meniscectomy population was tested again at 33 months post-operation. The results indicate that dynamic flexion angle ranges of motion (ROM) became more like that of a control population with time past surgery. Furthermore, these kinematic changes were correlated with between-time point changes in flexion and extension moments, suggesting that the observed kinematic changes may be attributable to increased thigh strength and/or activation at the time of follow-up. The first two studies presented in this thesis provide important insights into structural and mechanical factors involved in PTOA development after meniscectomy. The final two studies presented in this thesis focus on the development of idiopathic OA by utilizing a unique cohort of individuals who were asymptomatic with no prior knee or lower limb injury, but had magnetic resonance imaging (MRI) evidence of cartilage loss ("Pre-OA"). Here, the Pre-OA subjects were less extended near terminal stance and had decreased maximum extension moment in terminal stance than control subjects. The Pre-OA group also had greater systemic levels of inflammation (greater serum tumor necrosis factor-alpha concentrations, TNFα) compared to the control subjects. The fact that the observed gait alterations and elevated inflammatory markers in this population were consistent with differences seen in patients with medial compartment OA suggests a general response to the early stages of joint degeneration that is consistent with a continuum of structural, mechanical, and biological changes throughout the OA disease process beginning long before clinical diagnosis. The final study tested the interactions between gait mechanics, serum inflammation level, and cartilage structure (average cartilage thickness) in the aforementioned Pre-OA cohort. It was found that both systemic inflammation and coronal plane gait kinetics were positively correlated with femur and tibia regional average cartilage thickness values. In general, the results support a multi-factor, multi-scale model of OA pathogenesis. Furthermore, these results suggest measures for early disease detection and potential pre-OA disease modification. Together, this thesis presents four studies probing the pathogenesis of OA by testing for structural, mechanical, and biological differences in subjects at increased risk of developing post-traumatic and idiopathic OA.
Book
1 online resource.
Finite element simulations were introduced in the aviation industry in the 1970s and soon found their way into other industries as well as biomedical research. Since then, constitutive laws have been developed with the goal of building realistic organ level models and ultimately creating a whole human model. The attempts to model the fibrous soft tissue in the human body has led to the development of anisotropic models as conceived by Fung or Holzapfel and active muscle models as developed by Hill. These models have led to a better understanding of the underlying biomechanics in both passive and active systems and their interaction with devices or changing boundary conditions during disease. However, the human body's ability to adapt to boundary conditions, particularly in conjunction with devices or disease, has been ignored in most of these models. Here, I present constitutive laws for soft tissue adaptation, their implementation into general purpose finite element codes, and applications to clinically relevant problems. I applied a continuum mechanics framework to model the in-plane area growth of skin upon overstretch, the adaptation of skeletal muscle to changes in its mechanical environment, and the effect of annuloplasty ring sizes during mitral valve repair surgery. Our results demonstrate how the finite element method can be applied to model the interaction of adapting soft tissue with medical devices and changing mechanical changes in ite environment. We anticipate our models to open new avenues in surgical planning and to enhance the treatment of patients in both plastic and cardiovascular surgery. Furthermore, I expect these models to be used by medical device manufacturers as part of their computer-aided engineering pipelines.
Book
online resource (xviii, 275 pages) : illustrations (some color)
The mitral valve is one of four heart valves that ensure unidirectional blood flow through the heart. Due to mitral valve failure approximately 44,000 people in the US alone undergo open heart surgery every year. Current treatment options include mitral valve replacement and mitral valve repair, neither of which have shown satisfying long-term success. A deepened understanding of mitral valve mechanics may help in improving current medical device designs and treatment options for mitral valve regurgitation. Here I provide an in depth analysis of the in vivo mechanics of the mitral valve using the theory of finite kinematics and based on this data develop non-linear in silico models of the mitral valve employing the finite element method. Using mechanical metrics such as strain and curvature I reveal the in vivo deformation of the mitral annulus and the mitral leaflet in the healthy, diseased, and repaired mitral valve. Furthermore, in silico I explore the effects of prestrain as well as growth and remodeling on the mechanics of the mitral valve. The results of my in vivo studies extend our current understanding of the healthy mitral valve, reveal new insight into disease characteristics and progressions, and evaluate the efficacy of current device designs. Furthermore, results from the in silico studies provide improved means to simulate mitral valve mechanics and predict long term adaptation for basic science research and medical device design. In conclusion, with the current work I take a large step toward a deepened understanding of mitral valve mechanics that may help to optimize medical device designs and treatment options.
Medical Library (Lane)
Book
1 online resource.
Cardiomyocytes cultured from stem cells offer potential for use in regenerative tissue grafts, however the difficulty in manipulating and culturing these cells necessitates novel tools for both stimulating their development and assessing their mechanical and electrical function. Herein I introduce the tools for performing biomechanical investigations of cells and describe the challenges in working with cardiomyocytes and the development of two microfabricated sensors for quantifying the electricomechanical properties of immature cardiomyocytes throughout their development.
Special Collections
Book
online resource (xxii, 114 pages) : illustrations (some color)
In this work we present a series of scientific contributions made to the study of the impact of projectiles into tissue-like materials, specifically the synthetic artificial tissue simulant Perma-Gel. These contributions consist of a combination of experimental observations, algorithmic ideas and numerical tools which demonstrate a series of problems and solutions to trying to simulate nearly incompressible soft tissues using finite elements. A number of experiments were performed by taking high-speed footage of the firing of spherical steel bullets at different speeds into Perma-Gel, a new thermoplastic material used as a proxy to human muscle tissue. This work appears to be the first publicly released experimental work using Perma-Gel and is part of the small amount of non-classified work looking at ballistic gelatin behavior. A number of experimental observations were made regarding the material behavior, elastic and plastic deformation around the projectile, and the possibility of cavitation. This work introduces an explicit dynamic contact algorithm that takes advantage of the asynchronous time stepping nature of Asynchronous Variational Integrators (AVI) to improve performance when simulating elastic-body rigid-wall contact. We demonstrate a number of desirable properties over traditional one-time-step methods for the simulation of solid dynamics and provide a number of examples highlighting the advantages of this method. The explicit contact algorithm and AVI was used to simulate the impact of a projectile into a simulated block of gelatin, but was hindered by difficulties using the realistic material parameters. Using a parallelized version of the algorithm, large-scale simulations were performed for progressively smaller shear moduli. As the simulations approached realistic values for the shear modulus, unstable element configurations formed which required infeasibly small time steps to successfully resolve. The behavior observed for the shear moduli we could numerically simulate with did not resemble the experimental results. To simulate with smaller values, we had to go to an axisymmetric setting. The axisymmetric setting increased the range of shear moduli which could be simulated and demonstrated the same dynamic behavior, though the issue of unstable element configurations continued to occur in extreme cases. To deal with the issue of unstable elements, we created an axisymmetric remeshing strategy to compensate for the unstable element configurations and insufficient spatial resolution. This strategy consists of periodically applying a remeshing and transfer algorithm that updates highly deformed finite element meshes with configurations formed with elements having uniform aspect ratios and local refinement in important areas. The axisymmetric setting with remeshing increased the range of potential shear modulus values that could be simulated. This allowed for the identification of qualitative similarities in the transient behavior between the numerical results and the experimental footage.
Medical Library (Lane)
Book
online resource (xlvi, 313 pages) : illustrations (some color)
The heart is an essential heterogeneous organ that depends on strong coupling between electrical, chemical, and mechanical dynamics to properly function as a pump that supplies blood to the rest of the body. Cardiac arrhythmias are common disorders characterized by irregular beating of the heart that lead to serious clinical conditions. It is estimated that approximately 2.2 million adults in the United States are affected by atrial fibrillation, a prevalent arrhythmia. Unfortunately, a clinician often does not have enough information to diagnose a patient's heart condition to determine the optimal treatment procedure. This is an area that computational mechanics can address. While development of mechanical and electrophysiological models of cardiac tissue primarily started in the 1950s, fully-coupled models have only more recently been developed due to factors regarding computational cost, difficulty in quantifying material properties, and difficulty in integrating complex models in a cohesive and efficient manner. Therefore, in order for simulation tools to have impact in the clinical or experimental setting, these tools must be efficient, fast, robust, and accessible. The focus of this thesis is to develop methods of addressing the aforementioned issues and then illustrate how efficient electromechanical finite element models can be developed for the heart such that their use in the clinical and experimental setting can be realized in several examples. In this thesis, a global-local variable splitting formulation borrowed from the field of plasticity is used to address the issues of complex model integration, and to maintain numerical stability at low costs. Through careful examination of classical phenomenological models and detailed biophysical ionic models of the electrophysiology of the heart, almost all models can be reformulated into this global-local splitting framework. The numerical properties of cost-expensive ionic models are briefly analyzed within the context of this framework. Use of implicit-time stepping in tandem with a simple iteration and error tolerance based adaptive time-stepping algorithm allows for reduction of computation time from hours to minutes. Flexibility and modularity of the framework are illustrated through the development of electrical, electro-chemical, electro-chemical-mechanical, and opto-electro-mechanical models of cardiac tissue. The heart is modeled efficiently using custom finite element ventricular cell models for physiological electrical simulations and large deformation excitation-contraction dry-pumping simulations of the heart. The results accurately model the physiological condition of the heart. The flexibility and multiscale nature of the framework is also leveraged in developing novel optical-induced cardiac cell excitation models of new genetically engineered Channelrhodpsin-2 (ChR2) cardiac myocytes. An ionic model was developed for these particular bio-engineered stem cells, calibrated with experimental data from collaborators, and was able to predict the electrical excitation behavior of the cells to a reasonable degree of accuracy. This model was then combined with ionic pacemaker cell models and also with ventricular cell models into respective finite elements to simulate experiments and predict future therapies using ChR2 genetically modified cardiac tissue. The thesis also addresses difficulties relating to identification and characterization of material parameter identification in inhomogeneous cardiac tissue. Metrics for determining smoothness in electrical conduction in tissue cultures were validated with stochastic finite element models of microelectrode array cell conduction experiments. The results indicate that these metrics are useful in characterizing different conduction patterns based on two metrics borrowed from texture analysis. Difficulties in obtaining structural fiber data from clinical images were addressed by developing an algorithmic method for designating approximate physiologically accurate fiber distributions for the heart using only geometrical information obtained from MRI scans of the surfaces of the heart. Poisson interpolation is used and results in a smooth continuous rotating fiber description that matches experimentally obtained fiber directions from MRI scans. The main benefits of this algorithm are its simplicity of implementation, physiologically accuracy, and generality in interpolating fiber distributions. Lastly, the thesis demonstrates possible benefits of GPU computing in order to achieve near-real-time electrical simulations of arrhythmias in the heart. The assembly and solver routines from the finite element code, FEAP from Berkeley, were ported to the GPU using CUDA. Even with a minimally optimized proof-of-concept, the GPU-only finite element code achieves performance comparable to twelve cores using only one GPU. To increase the overall efficiency of the method, current sparse matrix vector multiplication GPU algorithms are analyzed, and possible alternative algorithms are developed specifically with unstructured finite element meshes in mind. Altogether, the different methods developed in this thesis have been shown to be effective in addressing issues related to efficiency, numerical stability, modularity, and flexibility in real computational applications of the heart. Special consideration was taken in designing the different methods to be compatible with one another, such that a majority of the methods could be integrated and the benefits of each method could be leveraged with each other to gain maximum efficiency. While these developed methods can still be improved, the thesis work as a whole serves to demonstrate and highlight future uses for computational models within experimental and clinical settings.
Medical Library (Lane)

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