Abstract
Cortical spreading depression (CSD) is the propagation of a relatively slow wave in cortical brain tissue that is linked to a number of pathological conditions such as stroke and migraine. Most of the existing literature investigates the dynamics of short term phenomena such as the depolarization and repolarization of membrane potentials or large ion shifts. Here, we focus on the clinically-relevant hour-long state of neurovascular malfunction in the wake of CSDs. This dysfunctional state involves widespread vasoconstriction and a general disruption of neurovascular coupling. We demonstrate, using a mathematical model, that dissolution of calcium that has aggregated within the mitochondria of vascular smooth muscle cells can drive an hour-long disruption. We model the rate of calcium clearance as well as the dynamical implications on overall blood flow. Based on reaction stoichiometry, we quantify a possible impact of calcium phosphate dissolution on the maintenance of F0F1-ATP synthase activity.
Publication
PLOS Computational Biology (16)
Assistant Professor
Shixin Xu is an Assistant Professor of Mathematics at Duke Kunshan University. His research interests are machine learning and data-driven models for diseases, multiscale modeling of complex fluids, homogenization theory, and numerical analysis. Xu has a B.Sc. in mathematics (honors) from Ocean University of China and a Ph.D. in mathematics from the University of Science and Technology China. From 2013 to 2017, he held postdoctoral positions at the National University of Singapore, the University of Notre Dame, the University of California, Riverside, and the Fields Institute for Research in Mathematical Sciences, Canada.
Professor
Huaxiong Huang is Professor of Mathematics at the York University. He is VP (Academic) and Executive Director of Research Center of Mathematics (Zhuhai, China). He has served as Deputy Director of the Fields Institute and Director of the Fields Centre for Quantitative Analysis and Modelling. His wide array of publications in applied mathematics focus on fluid mechanics and scientific computing, finance, biology, physiology, energy and medicine.