The timely remodeling of the cervix from a mechanical barrier into a soft, compliant structure, which dilates in response to uterine contractions is crucial for the safe delivery for a term baby. A cervix which softens too early in the pregnancy is implicated in spontaneous preterm births (sPTB). Currently, 15 million babies are affected by PTB annually, early diagnosis is difficult, and 95% of all PTBs are unmanageable by available therapies. These statistics highlight the need to better understand the biological processes involved in cervical remodeling and its downstream effects on material properties. To address this need, we propose the development of a hormone-mediated material constitutive model for the cervix where steroid hormone actions on key tissue constituents are incorporated into a microstructure-inspired material model. As the first steps towards the development of this model, the main objective of this dissertation work is to understand the key structure-mechanical function relationships involved in pregnancy. To understand cervical material property changes, the equilibrium swelling and tensile response of the nonpregnant and pregnant mouse cervix is measured, a porous fiber composite material model is proposed, and the model is fit to the mechanical data then validated. To better understand key tissue constituents involved, the evolution of intermolecular collagen crosslinks is determined in normal pregnancy and the role of the small proteoglycan, decorin, and elastic fiber structure on cervical mechanical function is investigated. The results presented here demonstrate that a porous, continuously distributed fiber composite model captures the three-dimensional mechanical properties of the nonpregnant and pregnant cervix. The material property changes of the cervix in a 19-day mouse gestation is described as a four order of magnitude decrease in the parameter associated with the fiber stiffness. We provide quantitative evidence to demonstrate the role of collagen crosslinks on tissue softening in the first 15 days, but not in the latter stages of a mouse pregnancy. A role of elastic fiber structure on cervical mechanical function is demonstrated, as well as distinct roles of estrogen on elastic fiber structure and progesterone on collagen fibril structure. Lastly, an analysis of the time-dependent response of cervices from nonpregnant, normal pregnant, and induced PTB mice are presented. This dissertation concludes by reviewing the presented data within the context of the proposed framework to suggest future directions towards its development.

Thesis (Ph. D.)--Civil and Environmental Engineering, Georgia Institute of Technology, 2008. / Committee Chair: Germanovich, Leonid; Committee Co-Chair: Skrinjar, Oskar; Committee Member: Mayne, Paul; Committee Member: Puzrin, Alexander; Committee Member: Rix, Glenn.

We propose a new approach for defining mechanical properties of the brain tissue in-vivo by taking MRI or CT images of a brain response to ventriculostomy operation, i.e., the relief of the elevated pressure in the ventricular cavities. Then, based on 3-D image analysis, the displacement fields are recovered from these images. Constitutive parameters of the brain tissue are determined using inverse analysis and a numerical method allowing for computations of large strain deformations. We tested this approach in controlled laboratory experiments with silicone brain models mimicking brain geometry, mechanical properties, and boundary conditions. The ventriculostomy was simulated by inflating and deflating internal cavities that model cerebral ventricles. Subsequently, the silicone brain model was described by a hyperelastic (neo-Hookean) material. The obtained mechanical properties have been verified with direct laboratory tests. Properties of real brain tissue are more complicated, but the proposed approach requires only conventional medical images collected before and after ventriculostomy. Breast cancer is the second most prevalent cancer in women, and an operative mastectomy is frequently a part of the treatment. Women often choose to follow a mastectomy with a reconstruction surgery using a breast implant. Furthermore, there is a growing demand for breast augmentation for the sake of aesthetic improvement. In this dissertation, we also developed a quantitative large-strain 3-D mechanical model of female breast deformation. The results show that the stiffness of skin and the constitutive parameters of the breast tissue are important factors affecting breast shape. Our results also suggest that the published Mooney-Rivlin parameters of breast tissue are underestimated by at least one or two orders of magnitude. Scale analysis, representing female breast as a cantilever beam, confirms these conclusions. Subdural hematoma (tearing and bleeding between scull and brain) is one of the major complications of the ventriculostomy operations. Understanding the mechanism of subdural hematoma is critically important for development of more effective medical treatments. In this work, we developed a simple, spherically-symmetrical poroelastic model of the ventriculostomy operation and studied brain response to the pressure change in the ventricles. The observed effect of the material properties on the occurrence of subdural hematoma may be useful for making clinical decisions.

There is a growing consensus that life-threatening cardiac arrhythmias like ventricular tachycardia (VT) or ventricular fibrillation (VF) arise because of the formation of spiral waves of electrical activation in cardiac tissue; unbroken spiral waves are associated with VT and broken ones with VF. Several experimental studies have shown that inhomogeneities in cardiac tissue can have dramatic effects on such spiral waves. In this thesis we try to understand these experimental results by carrying out detailed and systematic studies of the interaction of spiral waves with different types of inhomogeneities in mathematical models for cardiac tissue. In Chapter 1 we begin with a general introduction to cardiac arrhythmias, the cardiac conduction system, and the connection between electrical activation waves in cardiac tissue and cardiac arrhythmias. As we have noted above, VT and VF are believed to be associated with spiral waves of electrical activation on cardiac tissue; such spiral waves form because cardiac tissue is an excitable medium. Thus we give an overview of excitable media, in which sub-threshold perturbations decay but super-threshold perturbations lead to an action potential that consists of a rapid stage of depolarization of cardiac cells followed by a slow phase of repolarization. During this repolarization phase the cells are refractory. We then give an overview of earlier studies of the effects of inhomogeneities in cardiac tissue; and we end with a brief description of the principal problems we study here. Chapter 2 describes the models we use in our work. We start with a general introduction to the cable equation and then discuss the Hodgkin-Huxley-formalism for the transport of ions across a cell membrane through voltage-gated ion channels. We then describe in detail the three models that we use for cardiac tissue, which are, in order of increasing complexity, the Panfilov model, the Luo Rudy Phase I (LRI) model, and the reduced Priebe Beuckelmann (RPB)model. We then give the numerical schemes we use for solving these model equations and the initial conditions that lead to the formation of spiral waves. For all these models we give representative results from our simulations and compare the states with spiral turbulence. In Chapter 3 we investigate the effects of conduction inhomogeneities (obstacles) in the three models introduced in Chapter 2. We outline first the experimental results that have provided the motivation for our study. We then discuss how we introduce obstacles in our simulations of the Panffilov, LRI, and RPB models for cardiac tissue. Next we present the results of our numerical studies of the effects, on spiral-wave dynamics, of the sizes, shapes, and positions of the obstacles. Our Principal result is that spiral-wave dynamics in these models depends sensitively on the position of the obstacle. We find, in particular, that, merely by changing the position of a conduction inhomogeneity, we may convert spiral turbulence (the analogue in our models of VF) to a single rotating spiral (the analogue of VT) anchored to the obstacle or vice versa; even more exciting is the possibility that, at the boundary between these two types of behaviour, we find a quiescent state Q with no spiral waves. Thus our study obtains all the possible qualitative behaviours found in experiments, namely, (1) VF might persist even in the presence of an obstacle, (2) it might be suppressed partially and become VT, or (3) it might be eliminated completely. In Chapter 4 we extend our work on conduction inhomogeneities (Chapter 3) to ionic inhomogeneities. Unlike conduction inhomogeneities, ionic inhomogeneities allow the conduction of activation waves. We find, nevertheless, that they too can lead to the anchoring of spiral waves or even the complete elimination of spiral-wave turbulence. Since spiral waves can enter the region in which there is an ionic inhomogeneity, their behaviours in the presence of such an inhomogeneity are richer than those with conduction inhomogeneities. We find, in particular, that a single spiral wave anchored at an ionic inhomogeneity can show temporal evolution that may be periodic, quasiperiodic, or even chaotic. In the last case the spiral wave shows a chaotic pattern inside the ionic inhomogeneity and a regular one outside it. Defibrillation is the control of arrhythmias such as VF. Most often defibrillation is effected electrically by administering a shock, either externally or via an internally implanted defibrillator. The development of low-amplitude defibrillation schemes, which minimise the deleterious effects of the applied shock, is a major challenge in the treatment of cardiac arrhythmias. Numerical studies of models for cardiac tissue provide us with convenient means of studying the elimination of spiral-wave turbulence by the application of external electrical stimuli; this is the numerical analogue of defibrillation. Over the years some low-amplitude defibrillation schemes have been suggested on the basis of such numerical studies. In Chapter 5 we discuss two such schemes that have been shown to suppress spiral-wave turbulence in two-dimensional models for cardiac tissue and also scroll-wave turbulence in three-dimensional models. One of these schemes uses local electrical pacing, typically in the centre of the simulation domain; the other applies the external electrical stimuli over a mesh. We study the efficacy of these schemes in the presence of conduction inhomogeneities. We find, in particular, that the local-pacing scheme, though effective in a homogeneous simulation domain, fails to control spiral turbulence in the presence of an obstacle and, indeed, might even facilitate spiral-wave break up. By contrast, the second scheme, which uses a mesh, succeeds in eliminating spiral-wave turbulence even in the presence of an obstacle. We end with some concluding remarks about the possible experimental implications of our study in Chapter 6.