Methods for theoretical simulation of microvascular networks

The microcirculation consists of an extensive network of small blood vessels. It is responsible for transport of substances including oxygen, nutrients and waste products to all parts of the body. Microcirculatory function can be studied experimentally using microscopic imaging techniques. However, many aspects of microvascular function are difficult to observe directly, and theoretical models and simulations have made valuable contributions to our understanding of the microcirculation. Here we review several theoretical approaches for investigating several key aspects of microvascular networks, including blood flow in microvessels, exchange of oxygen and other substances between blood and tissue, short-term local regulation of blood flow, and long-term structural adaptation and remodeling, including angiogenesis. A recurrent theme is the impact of the heterogeneous structure of the networks on the functional properties of the microvasculature. This heterogeneity arises from geometrical constraints and from the stochastic nature of microvessel growth. Theoretical simulations can be used to investigate how active mechanisms of flow regulation and remodeling can compensate for the inherent heterogeneity, and how failure of these mechanisms can contribute to impaired tissue function in diseases.