Doctor of Philosophy

dissertationSpinal cord injury (SCI) is extremely debilitating to patients and costly to our healthcare system. Since it is an important contributor to mortality and morbidity, various therapeutic strategies have been investigated, either experimentally or clinically, to improve patients' quality of life. Studies utilizing pharmacological methods to mitigate the inhibitory components of the glial scar and facilitate axonal regeneration have been the primary experimental approaches in the field. However, the results are still not satisfactory. In this research, we aimed to tackle the issue from a novel perspective by developing cell derived, tissue engineered biomaterials that can be used in combination with other therapeutic approaches to improve the efficacy of current treatments. In this dissertation, a simple method to create either cellularized or acellular ECM biomaterial constructs is described. In particular, by utilizing patterned surface ligands, organized orientation can be introduced to the entire astrocyte derived construct morphologically and with regard to its associated matrix proteins, which mimics the native astrocyte framework within the spinal cord fiber tracts and provides these constructs the ability to guide axonal regeneration in vitro. In addition, meningeal fibroblast based biomaterial constructs are also developed taking advantage of the same engineering approach. It has been demonstrated that repairing damaged dura mater with allografts also benefits the regeneration process of the damaged spinal cord. In particular, acellular meningeal ECM constructs preserve a similar matrix protein profile as the native rat dura mater and support allogeneic meningeal cell adhesion and promote proliferation. The results suggest these engineered biomaterial constructs derived particularly from cells residing within tissue targeted for repair may carry appropriate tissue specific biological cues and hold therapeutic potentials for spinal cord injury repair as well as dual defect reconstruction

A new approach for solving fractional partial differential equations

We propose a new approach for solving fractional partial differential equations based on a nonlinear fractional complex transformation and the general Riccati equation and apply it to solve the nonlinear time fractional biological population model and the (4+1)-dimensional space-time fractional Fokas equation. As a result, some new exact solutions for them are obtained. This approach can be suitable for solving fractional partial differential equations with more general forms than the method proposed by S. Zhang and H.-Q. Zhang (2011)

Generalized Variational Oscillation Principles for Second-Order Differential Equations with Mixed-Nonlinearities

Using generalized variational principle and Riccati technique, new oscillation criteria are established for forced second-order differential equation with mixed nonlinearities, which improve and generalize some recent papers in the literature

Asymptotic Properties of Solutions to Third-Order Nonlinear Neutral Differential Equations

The aim of this work is to discuss asymptotic properties of a class of third-order nonlinear neutral functional differential equations. The results obtained extend and improve some related known results. Two examples are given to illustrate the main results

Oscillation Theorems for Second-Order Forced Neutral Nonlinear Differential Equations with Delayed Argument

We are concerned with the oscillation of the forced second-order neutral nonlinear differential equations with delayed argument in the form (r(t)(x(t)+a(t)x(σ(t)))′)′+p(t)f(x(τ(t)))+∑i=1nqi(t)|x(t)|λisngx(t)=e(t). No restriction is imposed on the potentials p(t), qi(t), ande(t) to be nonnegative. Our methodology is somewhat different from those of previous authors