Date of Award

Summer 2010

Document Type


Degree Name

Doctor of Philosophy (PhD)


Micro and Nanoscale Systems

First Advisor

Weizhong Dai


The main subject of this research is the neuromuscular junction (NMJ). The NMJ is a biological structure composed of the interface between a neuron and a muscle cell. Currently, there is not a fully three dimensional model of diffusion-reaction processes occurring in the NMJ. Developing a useful predictive model of this structure will assist in the therapeutic efforts to restore and rehabilitate NMJ function to humans and in developing strategies to prevent damage to the NMJ. This research work developed 1D mass transport and full 3D reaction diffusion models. A new finite difference scheme is presented for solving 1D mass diffusion with Neumann boundary condition in cylindrical coordinates, which can be applied in neuromuscular junction processes. This new scheme is obtained based on the Crank-Nicholson method, together with a non-traditional second-order finite difference approximation for the boundary condition. The scheme is proved to be unconditionally stable, and the solution system is a tri-diagonal linear system which can be easily solved by the Thomas algorithm. The scheme is tested by several examples. Results show that our scheme is promising. Finally, the scheme can be readily generalized to the multi-dimensional cases.

A three-dimensional model of the reaction-diffusion processes of a neurotransmitter and its ligand receptor in a disk-shaped volume is established which represents the transmission process of acetylcholine in the synaptic cleft in the neuromuscular junction. The behavior of the reaction-diffusion system is described by a three-dimensional diffusion equation with nonlinear reaction terms due to the rate processes of acetylcholine with the receptor. A new stable and accurate numerical method is used to solve the equations with Neumann boundaries in cylindrical coordinates. The simulation analysis agrees with experimental measurements of end-plate current and agrees well with the results of the conformational state of the acetylcholine receptor as a function of time and acetylcholine concentration of earlier investigations with a smaller error compared to experiments. An asymmetric emission of acetylcholine in the synaptic cleft and the subsequent effects on open receptor population is simulated. Sensitivity of the open receptor dynamics to the changes in the diffusion parameters and neuromuscular junction volume is investigated. The effects of anisotropic diffusion and non-symmetric emission of transmitter at the pre-synaptic membrane is simulated.