Abstract
BackgroundMathematical 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.ResultsWe 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.ConclusionsThis 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.
Highlights
Mathematical modeling of angiogenesis has been gaining momentum as a means to shed new light on the biological complexity underlying blood vessel growth
As a first approximation, exercise-induced angiogenesis can be described as a sequence of the following events: i) Exercise increases oxygen consumption in tissue, followed by increased blood flow in the vasculature, affecting convectiondiffusion oxygen transport processes [2]; ii) As exercise continues, insufficient oxygen delivery to the tissue leads to tissue cellular hypoxia, which results in activation of the transcription factor hypoxia-inducible factor 1a (HIF1a) [3] and the transcription coactivator peroxisome-proliferator-activated-receptor-gamma coactivator 1a (PGC1a) [4]; iii) These factors induce the upregulation of vascular endothelial growth factor (VEGF) expression [5]
Using the integration strategy and simulation package described above, we performed a series of computational experiments to simulate activity-induced angiogenesis in extensor digitorum longus (EDL) during a single bout of exercise
Summary
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. Angiogenesis is a complex process whereby new capillaries are formed from pre-existing microvasculature It plays important roles in many physiological processes including embryonic development, wound healing and exercise-induced vascular adaptation. In such processes, robust control of capillary growth leads to new healthy pattern of physiological vessel network that matches the metabolic demands of development, wound repair, or exercise [1]. Spatial scales vary from nanometers at the molecular level to microns at the cellular level, to millimetres or centimetres at the tissue level
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