A new approach to an old algorithm for the Simulation of Isinglike Systems

The importance and need for an integrative mathematical modeling approach in the biological and medical fields is currently well recognized. Such an approach is crucial in understanding the complexity of hierarchical biological systems increasingly revealed by active researches in molecular and cellular biology. Particularly in cardiac functioning, modeling must cover such diverse phenomena as solid mechanics, fluid dynamics, electricity and biochemistry. Recent advancements in computational science and the development of high-performance computers have enabled the creation of multi-scale, multi-physics simulation heart models using the finite element method. Although whole heart or ventricular models of electrophysiology involving electro-mechanics with or without blood flow dynamics have been reported, to our knowledge no single model has yet succeeded in completely reproducing the behavior of the heart from the subcellular to whole organ levels. In this article, we present a brief methodology-focused review on some of the essential components for multi-scale, multi-physics heart modeling. A perspective of heart modeling in the era of high performance computing is also presented.

Recent studies have revealed that Ca(2+) not only regulates the contraction of cardiomyocytes, but can also function as a signaling agent to stimulate ATP production by the mitochondria. However, the spatiotemporal resolution of current experimental techniques limits our investigative capacity to understand this phenomenon. Here, we created a detailed three-dimensional (3D) cardiomyocyte model to study the subcellular regulatory mechanisms of myocardial energetics. The 3D cardiomyocyte model was based on the finite-element method, with detailed subcellular structures reproduced, and it included all elementary processes involved in cardiomyocyte electrophysiology, contraction, and ATP metabolism localized to specific loci. The simulation results were found to be reproducible and consistent with experimental data regarding the spatiotemporal pattern of cytosolic, intrasarcoplasmic-reticulum, and mitochondrial changes in Ca(2+); as well as changes in metabolite levels. Detailed analysis suggested that although the observed large cytosolic Ca(2+) gradient facilitated uptake by the mitochondrial Ca(2+) uniporter to produce cyclic changes in mitochondrial Ca(2+) near the Z-line region, the average mitochondrial Ca(2+) changes slowly. We also confirmed the importance of the creatine phosphate shuttle in cardiac energy regulation. In summary, our 3D model provides a powerful tool for the study of cardiac function by overcoming some of the spatiotemporal limitations of current experimental approaches.

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Large deformation, nonlinear stress relaxation behavior was examined in the molten state for two types of ABS polymers, with one type containing well-dispersed rubber particles and the other, agglomerated rubber particles. These different morphologies were accomplished by adjusting the chemical composition of poly(styrene-co-acrylonitrile) (SAN) grafted on the rubber particles, such that the acrylonitrile content of the grafted SAN is equal to or different from that of the matrix SAN. The time-strain separability was found for the nonlinear relaxation of the matrix/grafted SAN chains in those ABS polymers. In the ABS polymer containing randomly dispersed rubber particles, the damping function h(γ) of the SAN chains was more strongly dependent on the strain γ than h(γ) of the pure matrix SAN chains. This difference was attributed to the filler effect in that ABS polymer. In contrast, in the ABS polymers containing networks of the agglomerated rubber particles, the SAN chains exhibited less γ-dependent h(γ) that is close to the pure matrix chains, possibly due to lack of the filler effect in large pockets formed in this network.