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.

Partitioning of red blood cell (RBC) fluxes between the branches of a diverging microvessel bifurcation is generally not proportional to the flow rates, as RBCs preferentially enter the higher-flow branch. A two-dimensional model for RBC motion and deformation is used to investigate the effects of cell-cell mechanical interactions on RBC partitioning in bifurcations. The RBC membrane and cytoplasm are represented by sets of viscoelastic elements immersed in a low Reynolds number flow. Several types of two-cell interactions that can affect partitioning are found. In the most frequent interactions, a `trade-off' occurs, in which a cell entering one branch causes a following cell to enter the other branch. Other types of interactions include `herding,' where the leading cell is caused to enter the same branch as the following cell, and `following,' where the trailing cell is caused to enter the same branch as the leading cell. The combined effect of these cell-cell interactions is a tendency towards more uniform partitioning, which results from the trade-off effect but is reduced by the herding and following effects. With increasing hematocrit, the frequency of interactions increases, and more uniform partitioning results. This prediction is consistent with experimental observations on how hematocrit affects RBC partitioning.

Necrotizing enterocolitis (NEC) is a severe disease that affects the gastrointestinal (GI) tract of premature infants. Different areas of NEC research have often been isolated from one another and progress on the role of the inflammatory response in NEC, on the dynamics of epithelial layer healing, and on the positive effects of breast feeding have not been synthesized to produce a more integrated understanding of the pathogenesis of NEC. We seek to synthesize these areas of research by creating a mathematical model that incorporates the current knowledge on these aspects. Unlike previous models that are based on ordinary differential equations, our mathematical model takes into account not only transient effects but also spatial effects. A system of nonlinear transient partial differential equations is solved numerically using cell-centered finite differences and an explicit Euler method. The model is used to track the evolution of a prescribed initial injured area in the intestinal wall. It is able to produce pathophysiologically realistic results; decreasing the initial severity of the injury in the system and introducing breast feeding to the system both lead to healthier overall simulations, and only a small fraction of epithelial injuries lead to full-blown NEC. In addition, in the model, changing the initial shape of the injured area can significantly alter the overall outcome of a simulation. This finding suggests that taking into account spatial effects may be important in assessing the outcome for a given NEC patient. This model can provide a platform with which to test competing hypotheses regarding pathological mechanisms of inflammation in NEC, suggest experimental approaches by which to clarify pathogenic drivers of NEC, and may be used to derive potential intervention strategies.

Objective The development of earlier and less invasive treatments for peripheral arterial disease requires a more complete understanding of vascular responses following a major arterial occlusion. A mechanistic model of the vasculature of the rat hindlimb is developed to predict acute (immediate) changes in vessel diameters and smooth muscle tone following femoral arterial occlusion. Methods Vascular responses of collateral arteries and distal arterioles to changes in pressure, shear stress, and metabolism are assessed before and after occlusion. The effects of exercise are also simulated and compared with venous flow measurements from WKY rats. Results The model identifies collateral arteries as the primary contributors to flow compensation following occlusion. Increasing the number of capillaries has minimal effect on blood flow while increasing the number of collateral arteries significantly increases flow, since the primary site of resistance shifts upstream to the collateral arteries following occlusion. Despite significant collateral dilation, calf flow remains below pre‐occlusion levels and the deficit becomes more severe with increased activity. Conclusions Although unable to compensate fully for an occlusion, the model demonstrates the importance of the shear response in collateral arteries and the metabolic response in the distal microcirculation in acute adaptations to a major arterial occlusion.