Spatially-realistic and reduced models for integrative biomedical computing

Abstract

Biomedical computing will greatly benefit from a progressive and adaptive approach to modelling, combined with novel adaptive methods for multiphysics and multiscale simulation. Both symbolic and hierarchical characterizations of the various components should be allowed for, as well as shape reconstruction from high-resolution imaging techniques [2]. Managing finer and finer details and transforming them into additional parameters for coarse-grain models is of the greatest importance. However, it is also essential to be able to analise complicated shapes and patterns, in order to identify their salient features, using computational topology methods based on Morse theory [7]. We apply such ideas to modelling of spatially realistic and reduced domains of structures and ultrastructures of the nervous tissues, where running numerical simulations of the functional behaviour of neurons. In particular, we generate spatially realistic reconstructions of dendrites, axons, glia, and extracellular space domains, using quality surface meshing algorithms to make these reconstructions ready for realistic modeling of dendritic signaling. Reconstruction and modeling tools are used to quantify the variation in surface area and volume of axons, den- drites, glia, extracellular space, synapses, and core subcellular organelles, that could impact electrical signaling. To bridge the gap to one-dimensional models that have been used for electrophysiological simulations, we develop appropriately reduced domain models. In this paper we introduce a novel method to compute a minimal fat skeleton, made by hexahedral elements, starting form a point sampling of shape boundary and from the one-dimensional and two-dimensional unstable manifolds of the the index 1 and index 2 saddle points of the Morse structure induced by the shape. The result is a cell decomposition with a minimal number of cells, that yet approximate well the shape. The output mesh can be used for simulation of physical behaviour of neural tissue with a minimal number of degrees of freedom.