Formation of functionally adequate vascular networks by angiogenesis presents a problem in biological patterning. Generated without predetermined spatial patterns, networks must develop hierarchical tree-like structures for efficient convective transport over large distances, combined with dense space-filling meshes for short diffusion distances to every point in the tissue. Moreover, networks must be capable of restructuring in response to changing functional demands without interruption of blood flow. Here, theoretical simulations based on experimental data are used to demonstrate that this patterning problem can be solved through over-abundant stochastic generation of vessels in response to a growth factor generated in hypoxic tissue regions, in parallel with refinement by structural adaptation and pruning. Essential biological mechanisms for generation of adequate and efficient vascular patterns are identified and impairments in vascular properties resulting from defects in these mechanisms are predicted. The results provide a framework for understanding vascular network formation in normal or pathological conditions and for predicting effects of therapies targeting angiogenesis.

Movement, deformation, and partitioning of mammalian red blood cells (RBCs) in diverging microvessel bifurcations are simulated using a two-dimensional, flexible-particle model. A set of viscoelastic elements represents the RBC membrane and the cytoplasm. Motion of isolated cells is considered, neglecting cell-to-cell interactions. Center-of-mass trajectories deviate from background flow streamlines due to migration of flexible cells towards the mother vessel centerline upstream of the bifurcation and due to flow perturbations caused by cell obstruction in the neighborhood of the bifurcation. RBC partitioning in the bifurcation is predicted by determining the RBC fraction entering each branch, for a given partition of total flow and for a given upstream distribution of RBCs. Typically, RBCs preferentially enter the higher-flow branch, leading to unequal discharge hematocrits in the downstream branches. This effect is increased by migration toward the centerline but decreased by the effects of obstruction. It is stronger for flexible cells than for rigid circular particles of corresponding size, and decreases with increasing parent vessel diameter. For unequallysized daughter vessels, partitioning is asymmetric, with RBCs tending to enter the smaller vessel. Partitioning is not significantly affected by branching angles. Model predictions are consistent with previous experimental results.

The vasculature is a dynamic structure, growing and regressing in response to embryonic development, growth, changing physiological demands, wound healing, tumor growth and other stimuli. At the microvascular level, network geometry is not predetermined, but emerges as a result of biological responses of each vessel to the stimuli that it receives. These responses may be summarized as angiogenesis, remodeling and pruning. Previous theoretical simulations have shown how two-dimensional vascular patterns generated by these processes in the mesentery are consistent with experimental observations. During early development of the brain, a mesh-like network of vessels is formed on the surface of the cerebral cortex. This network then forms branches into the cortex, forming a three-dimensional network throughout its thickness. Here, a theoretical model is presented for this process, based on known or hypothesized vascular response mechanisms together with experimentally obtained information on the structure and hemodynamics of the mouse cerebral cortex. According to this model, essential components of the system include sensing of oxygen levels in the midrange of partial pressures and conducted responses in vessel walls that propagate information about metabolic needs of the tissue to upstream segments of the network. The model provides insights into the effects of deficits in vascular response mechanisms, and can be used to generate physiologically realistic microvascular network structures.

Convective fluid motion through artery walls aids in the transvascular transport of macromolecules. Although many measurements of convective filtration have been reported, they were all obtained under constant transmural pressure. However, arterial pressure in vivo is pulsatile. Therefore, experiments were designed to compare filtration under steady and pulsatile pressure conditions. Rabbit carotid arteries were cannulated and excised from male New Zealand White rabbits anesthetized with pentobarbitol sodium (30 mg/kg i.v. administered). Hydraulic conductance was measured in cannulated excised rabbit carotid arteries at steady pressure. Next, pulsatile pressure trains were applied within the same vessels, and, simultaneously, arterial distension was monitored using Optical coherence tomography (OCT). For each pulse train, the volume of fluid lost through filtration was measured (subtracting volume change due to residual distension) and compared with that predicted from steady pressure measurements. At 60- and 80-mmHg baseline pressures, the experimental filtration volumes were significantly increased compared with those predicted for steady pressure (P < 0.05). OCT demonstrated that the excess fluid volume loss was significantly greater than the volume that would be lost through residual distension (P < 0.05). After 30 s, the magnitude of the excess of fluid loss was reduced. These results suggest that sudden onset of pulsatile pressure may cause changes in arterial interstitial hydration.

) demonstrated significantly increased filtration after initial onset of pulsatile pressure compared with that predicted by using parameters measured under steady pressure. To determine the role of the endothelium in this phenomenon, the following experiments were performed on five New Zealand White rabbits (anesthetized with 30 mg/kg pentobarbital sodium). One of each pair of carotid arteries was deendothelialized, and filtration measurements under steady and pulsatile pressure were compared with those made in intact vessels (Alberding JP, Baldwin AL, Barton JK, and Wiley E. Am J Physiol Heart Circ Physiol 286: H1827-H1835, 2004). To determine the effect of increasing pulsatile frequency on arterial filtration, transmural filtration was measured by using pulsatile pressure frequencies of 1 Hz, followed by 2 Hz, in another set of intact arteries (6 arteries and 3 animals). For deendothelialized vessels, the initial increase in filtration after onset of pulsatility was similar to that observed in intact vessels, but the subsequent reduction in filtration was less abrupt. When pulsatile frequency was increased from 1 to 2 Hz in intact arteries, an initial increase in filtration was observed, similar to that obtained after onset of pulsatile pressure subsequent to a steady pressure. The observed responses of arteries to pulsatile pressure, with and without endothelium, or undergoing a frequency change, suggest a dynamic role for the endothelium in regulating transvascular transport in vivo. interstitial hydration; deendothelialized vessels; convective transport CONVECTIVE FLUID FLOW through the artery wall has been demonstrated to greatly facilitate the transport of macromolecules into the arterial intima (8). Accumulation of macromolecules, such as LDL, in the arterial intima can lead to formation of fatty streaks, a precursor to atherosclerosis. Previous investigators (4) have examined the variation of hydraulic conductance (L p ), a parameter of convective fluid transfer, at different steady hydrostatic pressures. Our subsequent experiments (1) showed that the onset of a pulsatile pressure (1 Hz), superimposed on a baseline pressure of 60 or 80 mmHg, produced a large, but transient, burst of increased filtration. Over time, the transient burst of filtration was dampened, and filtration continued at a lesser rate, this rate still being three times greater than that predicted by steady-state measurements (1).Studies have shown that the endothelium plays a significant role in controlling fluid filtration through the artery wall under steady-state pressure. These experiments (15,19) demonstrated that the endothelium accounts for about half of the hydraulic resistance of the whole vessel wall. Therefore, one goal of the present study was to evaluate the role of the endothelium in the initial increase and subsequent decrease in filtration following the onset of pulsatility. It is important to examine arteries when they are exposed to pulsatile pressure with variations in frequency, because in vivo, pulsatile pumping o...