Microvascular hemodynamic variations accompanying microvessel dimensional changes

Microvascular repair: post-angiogenesis vascular dynamics

Vascular compromise and the accompanying perfusion deficits cause or complicate a large array of disease conditions and treatment failures. This has prompted the exploration of therapeutic strategies to repair or regenerate vasculatures, thereby establishing more competent microcirculatory beds. Growing evidence indicates that an increase in vessel numbers within a tissue does not necessarily promote an increase in tissue perfusion. Effective regeneration of a microcirculation entails the integration of new stable microvessel segments into the network via neovascularization. Beginning with angiogenesis, neovascularization entails an integrated series of vascular activities leading to the formation of a new mature microcirculation, and includes vascular guidance and inosculation, vessel maturation, pruning, AV specification, network patterning, structural adaptation, intussusception, and microvascular stabilization. While the generation of new vessel segments is necessary to expand a network, without the concomitant neovessel remodeling and adaptation processes intrinsic to microvascular network formation, these additional vessel segments give rise to a dysfunctional microcirculation. While many of the mechanisms regulating angiogenesis have been detailed, a thorough understanding of the mechanisms driving post-angiogenesis activities specific to neovascularization has yet to be fully realized, but is necessary to develop effective therapeutic strategies for repairing compromised microcirculations as a means to treat disease.

On the pressure and flow-rate distributions in tree-like and arterial-venous networks

A solution algorithm yielding the pressure and flow-rate distributions for steady flow in an arbitrary, tree-like network is provided. Given the tree topology, the conductance of each segment and the pressure distribution at the boundary nodes, the solution is obtained from a simple recursion based on perfect Gauss elimination. An iterative solution method using this algorithm is suggested to solve for the pressure and flow-rate distributions in an arbitrary diverging-converging (arterial-venous) network consisting of two tree-like networks which are connected to each other at the capillary nodes. A number of special solutions for tree-like networks are obtained for which the general algorithm is either simplified or can be replaced by closed form solutions of the pressure and flow-rate distributions. These special solutions can also be obtained for each tree of diverging-converging networks having particular topologies and conductance distributions. Sample numerical results are provided.

Effect of dispersion of vessel diameters and lengths in stochastic networks. I. Modeling of microcirculatory flow

A microvascular network model is proposed with random arrangement and random dimensions of vessels. In addition to stochasticity of the topological characteristics of the model networks, as previously introduced by Fenton and Zweifach (1981, Ann. Biomed. Eng., 9, 303-321), the vessel diameters and lengths are treated as random variables following certain probability distributions for each vascular order. Flow and pressure distributions are calculated for each network configuration assuming a linear relationship between the blood flow rate and pressure drop for each vascular segment. The mean, coefficient of variation, skewness, kurtosis, and histograms of the hemodynamic variables are computed using an ensemble of random networks. The results indicate that dispersion of vessel diameters and lengths may significantly affect the distributions of microvascular variables such as capillary flow and pressure, and the flow distribution at bifurcations. It is shown that the dispersion of vessel diameters causes a decrease of total flow whereas the dispersion of lengths causes its increase.