CARGO: Approximation and Simulation of Neurons

Montana State University, Bozeman MT

Investigators

Abstract

DMS-0138065 Binhai Zhu In this project, we investigate a three-dimensional geometric problem that originated in neural maps, which model the motions of neurons so as to understand the human behavior. The problem is defined as follows: given a neuron, which is modeled as a polyhedron, compute a minimum set of (minimal) cylindrical segments to approximate the neuron. We plan to design a good approximation for this problem (i.e., the error between the cylindrical segments and the neuron is small). We also plan to have a good implementation, build a prototype system, and perform extensive empirical studies. Practically, a solution to this problem will have a great impact in computational biology. Theoretically, this problem generalizes the problem of finding a single line stabbing a set of balls in 3D (and has never been seriously studied to the best of our knowledge). Modeling the motions of human neurons is an important problem in biology, especially in understanding human behavior under different circumstances. To do that, we first need to model a single neuron, which is very much like a tree-shaped polyhedron, using a set of cylindrical segments. Different cylindrical segments of different radii have different functionality, so the union of the cylindrical segments should be as close to the neuron as possible. In practice this problem is estimated manually by technicians in the computational biology community. The process is time-consuming and error-prone. Our research will focus on automating this process with computers and a successful solution will have deep influence in the computational biology community. We will train two graduate students throughout this project.