Department of Mathematics, Applied Mathematics and Statistics

Friday, March 7, 2014 (3:00 p.m., Yost 306)

Title: Computational Models of Brain Energy
Metabolism at Different Scales

Speaker: Yougan Cheng (Case Western Reserve University)
Abstract: We propose a novel multi-domain formalism to assemble a three dimensional distributed model of brain cellular metabolism, which is governed by coupled reaction-diffusion equations in different cells and in the extracellular space, and it allows the inclusion of additional details, for example separate mitochondria for each cell type. We reduce the dimension and derive a computational model for a brain sample of the size of a Krogh cylinder, with spatial distribution in tissue along the radial component. For this model, the different availability of oxygen and glucose away from the blood vessel could affect the cells' aerobic or anaerobic metabolism and trigger the uptake of lactate, highlighting the important role of diffusion. This spatially distributed model indicates that drawing conclusions about a complex spatially distributed system from a simplified lumped model may lead to ambiguities. The computed results also reveal a significant sensitivity of parameters to scale change. This suggests that simple parameter estimation methods by model fitting may be inadequate, justifying the need for more sophisticated techniques. The results of our simulations offer a possible explanation why experimental data collected under similar conditions may have led to different conclusions when interpreted with models of low resolution, reinforcing the idea that a proper description of biological model parameters is not a single value, but rather a distribution of values. To capture more details, we perform intermediate reduction of the model from three to two spatial dimensions. The two dimensional model is then formulated in a variational form and some computed examples, using finite element methods, are presented.