Spatially-Realistic and Reduced Models for Integrative Biomedical Computing C. Bajaj 1 , A. DiCarlo 2 and A. Paoluzzi 3 1 Dept of Computer Sciences & ICES, Center for Computational Visualization, 201 East 24th Street, Austin, TX 78712-0027, USA 2 Dept of Studies on Structures, Modelling & Simulation Laboratory Via Corrado Segre 6, I-00146 Roma, Italy 3 Dept of Informatics and Automation, Geometric Computation Laboratory Via della Vasca Navale 79, I-00146 Roma, Italy 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 numeri- cal simulations of the functional behaviour of neurons. In par- ticular, we generate spatially realistic reconstructions of den- drites, axons, glia, and extracellular space domains, using quality surface meshing algorithms to make these reconstruc- tions ready for realistic modeling of dendritic signaling. Re- construction and modeling tools are used to quantify the varia- tion in surface area and volume of axons, den- drites, glia, ex- tracellular space, synapses, and core subcellular organelles, that could impact electrical signaling. To bridge the gap to one- dimensional models that have been used for electrophysiologi- cal 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 behav- iour of neural tissue with a minimal number of degrees of free- dom. Keywords— Geometry generation & processing, computational geometry and topology, computational physiology. I. INTRODUCTION The biological and medical research must deal with prob- lems of higher and higher complexity, for which the tradi- tional approach—based on the subdivision of biological systems by dimensional scales, scientific disciplines or by anatomical sub-systems—is inadequate. It is therefore nec- essary to give computational support to an integrative ap- proach aimed to combine observations, theories and predic- tions across temporal and dimensional scales, scientific dis- ciplines and anatomical sub- systems. This intuition gave origin to a number of initiatives such as integrative biology, system biology, Physiome, VPH, etc. The physiome term hence refers to human modelling using mathematics and computational methods, accommodating cross-disciplinary science (chemistry, biology, physics, computer science) and several dimensional and temporal scale (sub-cellular to or- gans, sub-microsecond to tens-of-years). The Physiome Project [8] is a worldwide efort to pro- vide a computational framework for understanding human and other eukaryotic physiology. It aims to develop integra- tive models at all levels of biological organisation, from genes to the whole organism. The VPH (Virtual Physiologi- cal Human) is a European initiative intending to provide a unifying architecture for the integration and cooperation of multi-scale physiome models [6]. It is foreseen that matur- ing physiome activities will increasingly influence medicine and biomedical research. The novel computational frame- work proposed for Proto-PLASM [2] is a specialized and high-performance extension of the geometric language Plasm [9 ] strongly inspired by the functional language FL, designed after Backus’ earlier FP programming language [1], providing specific support for what Backus termed function-level programming, and oriented to work on pro- grams as mathematical objects. Our goal is to obtain spatially realistic reconstructions of dendrites, axons, glia, and extracellular space domains within representative hippocampal and cortical mouse neu- ropil (see Figure 1). Modeling of electrical signals in den- drites has typically been done on simplified cases that treat the complex dendritic arbor and local variation in dendritic structure as a series of cylinders. Reconstruction from serial section transmission electron microscopy (ssTEM), how- ever, reveals substantial deviation from these cylindrical 1 final.pages