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.