CAREER: MPS-BIO: Mathematical Modeling and Experiments of Neuromechanical Pumping

The broad goal of this proposal is to create mathematical models of the electrophysiology and neuromechanics of an organ and organism whose dynamics rely on environmental cues and electrical activation through the action of pacemaker cells. Recent advancements in computational fluid dynamics have enabled researchers to efficiently explore problems that involve moving elastic boundaries immersed in fluids for problems such as cardiac fluid dynamics, fish swimming, and the movement of bacteria. These advances have also made modeling the interaction between a fluid and a neuromechanical model of an elastic organ or organism feasible. This project will focus on the development and implementation of such models for two problems: 1) fluid transport through the pumping of tubular hearts, and 2) feeding currents generated by the pulsation of jellyfish bells. This proposal leverages existing computational algorithms for fluid-structure interactions, whereas the mathematical novelty lies in coupling this technology to living boundaries. The models will integrate feedback between the conduction of action potentials, the contraction of muscles, the movement of tissues, and fluid motion. For example, mathematical models will be developed that couple action potentials triggered by noisy pacemaker cells to the generation of tension through appropriate muscle and Ca2+ models. The non-Hookean material properties and geometry of highly deformable heart tubes and jellyfish bells will also be quantified and accurately modeled using discrete differential geometry.

This work will combine computational, mathematical, and experimental tools to ultimately answer some of questions posed in one of the five grand challenges in organismal biology: Integrating living and physical systems. Integrative mathematical models of the neurobiology, muscular mechanics, elasticity, and fluid dynamics of pumping tubular hearts and jellyfish bells will be developed. While great strides have been made in the modeling and simulation of each of these components separately, coupling these fields remains elusive. The working proposition that motivates this research is that modeling the complete neuromechanical system is more tractable for the two selected problems than almost any other given their relative simplicity. The results of this research may also provide a framework for the development of integrative models of other fundamental biological problems such as the movement and regulation of waste through the intestines, air through the lungs, and lymph through the lymphatic system. The educational focus of this proposal is to implement a unified training program for mathematicians and biologists centered on mathematical modeling in biology. The proposed educational activities will include a first year seminar in epidemiology, a course and associated text on mathematical modeling in comparative biomechanics for biologists and mathematicians, and a summer program for mathematical biologists at the UNC Galapagos Center. This educational program is motivated by the fact that it will be critical to train mathematics and biology students at this interface in order to rise to the scientific challenges that will be posed during the 21st century.