Module-based multiscale simulation of angiogenesis in skeletal muscle

Mathematical modeling of angiogenesis has been gaining momentum as a means to shed new light on the biological complexity underlying blood vessel growth. A variety of computational models have been developed, each focusing on different aspects of the angiogenesis process and occurring at different biological scales, ranging from the molecular to the tissue levels. Integration of models at different scales is a challenging and currently unsolved problem.

We present an object-oriented module-based computational integration strategy to build a multiscale model of angiogenesis that links currently available models. As an example case, we use this approach to integrate modules representing microvascular blood flow, oxygen transport, vascular endothelial growth factor transport and endothelial cell behavior (sensing, migration and proliferation). Modeling methodologies in these modules include algebraic equations, partial differential equations and agent-based models with complex logical rules. We apply this integrated model to simulate exercise-induced angiogenesis in skeletal muscle. The simulation results compare capillary growth patterns between different exercise conditions for a single bout of exercise. Results demonstrate how the computational infrastructure can effectively integrate multiple modules by coordinating their connectivity and data exchange. Model parameterization offers simulation flexibility and a platform for performing sensitivity analysis.

This systems biology strategy can be applied to larger scale integration of computational models of angiogenesis in skeletal muscle, or other complex processes in other tissues under physiological and pathological conditions.