A tissue in the tissue: models of microvascular plasticity.

The microcirculation is a dense space-filling network that, with few exceptions, invests every tissue in the body. To maintain an optimal function, any lasting change in volume or physiological activity level of a tissue is met with a corresponding structural change in the supplying microvascular network. The pronounced plasticity and the inherently complex nature of vascular networks have spurred an enduring interest in mathematical modeling of the microcirculation. This has been advanced by the continuous increase in computing power over recent decades enabling simulation of increasingly detailed models of microvascular rarefaction, remodeling and growth. In the present paper we review some of the models of microvascular adaptation that have appeared in the literature within the last two decades. We focus on models in which local vessel structure and/or network structure is allowed to change, either in an adaptive manner or as consequence of directly imposed alterations. Most of the early models are concerned primarily with vessel diameter and flow simulations and do not, in many cases, explicitly take into consideration the vascular wall. More recent models typically include the structural and mechanical properties of the vascular wall itself. This has allowed the emerging concept of tone as a pervasive factor in remodeling to enter microvascular models and this concept may become a cornerstone in future modeling work. The main goal in the present paper is briefly to review and discuss some of the mechanisms in the different models which govern microvascular adaptation and to point to some possible future directions for models of microvessels and microvascular networks.