|Ph.D.,||Rensselaer Polytechnic Institute,||(2015)|
|B.S.,||University of Mumbai,||(2008)|
Back pain is a major public health problem, often due to the degeneration of one or several intervertebral discs. The intervertebral disc is the largest avascular tissue in the body and therefore depends on the end plates to diffuse needed nutrients. Nutrients are supplied to the disc cells from the blood vessels in the soft tissue surrounding the annulus periphery and from capillaries arising in the vertebral bodies, which penetrate the subchondral bone but not the cartilaginous endplates. In a healthy disc, transport is dominated by diffusion, however, when the vertebral endplates become sclerotic or proteoglycan content in the disc is diminished, this transport is reduced. A reduction in transport causes a reduction in biosynthesis, increase in up-regulation of catabolic activity, loss of matrix organization, and apoptosis. This leads to further reduction in proteoglycan synthesis, disc desiccation, and ultimately collapse. Thus, reduction in nutrient transport is a key factor in disc degeneration. The aim of my research project is to study the effects of mechanical loading on the transport of nutrients to the intervertebral disc using finite element methods.
The effect of diffusive nutritional supply has been well documented in the literature, however there is evidence that convection plays an important role in the nutrition of the intervertebral disc. Using the triphasic theory of mixtures, I aim to better understand the transient response of the nutritional flow to and from the disc. A new mechano-electrochemical theory is used to model the 4 nonlinear degrees of freedom, which are independently interpolated, using Newton-Raphson's iterative procedure. Using a mixed finite element formulation, the governing equations for the model are reduced to a set of ordinary differential equations (ODE), which are solved using a backward Euler scheme. The interdependence and nonlinear response of model parameters such as porosity and diffusivity of the solid matrix, rate of deformation under load, coupled with complex boundary conditions makes solving these ODE's a challenge. I aim to solve these equations using mixed finite element formulation coupled with perturbation methods. The finite element problem is solved using COMSOL Multiphysics. The developed model will be validated using experimental data reported in the literature. A sensitivity analysis for clinically measureable parameters such as disc height, porosity, diffusivity and proteoglycan content is performed to develop a patient specific model.
The final goal of the project is to provide an optimal exercise regime to patients to increase the nutrition to the intervertebral disc thereby alleviating the back pain caused due to degeneration of the intervertebral disc.