Modeling Skeletal Muscle Angiogenesis from the Molecular to the Tissue Level

We present a multiscale model of angiogenesis that integrates individual modules representing blood flow, oxygen transport, growth factor distribution and signaling, cell sensing, cell movement and cell proliferation. This integration will be used to better understand underlying biological mechanisms from the molecular level up through the organ systems level; examine the effects of pathological conditions on skeletal muscle capillary growth; and test new therapeutic strategies. Model methodology includes partial differential equations, stochastic models, complex logical rules, and agent‐based architectures. Spatial and time scales range from ligand‐receptor interactions and intracellular signaling occurring on the order of seconds and minutes, to cell‐level movement and cell‐matrix interactions over minutes to hours, to vessel formation and tissue level responses over hours to days. We introduce the individual modules and describe our methodology for integration, which involves wrapping models (written in different programming languages) in a Java‐based dynamic link library format that allows for a central controller to readily pass parameters between the models. We present results from the coordination of modules: the effects of hypoxia in skeletal muscle from the molecular‐detailed changes in HIF1‐initiated VEGF secretion and VEGF‐VEGFR signaling; to endothelial cell activation, cell movement in response to VEGF gradients, and capillary branching as a function of the Notch ligand DLL4; to the resulting new capillary network and altered pattern of blood flow. This angiogenesis multiscale modeling and integration will be a tool in rational drug development and therapeutic regime design, and encourage related angiogenesis experiments.