Publications

Fluid shear stress has been implicated as a regulator of sprouting angiogenesis. However, whether endothelial cells within capillary sprouts in vivo experience physiologically relevant shear stresses remains unclear. The objective of our study is to estimate the shear stress distribution along the length of a capillary sprout through computational modeling of blood flow in a blind ended channel branching off a host vessel. In this model, we use sprout geometries typical for rat mesenteric microvasculature and consider three types of boundary conditions: 1) non-permeable vessel wall, 2) uniformly permeable vessel wall, and 3) a non-permeable vessel wall with open slots (representative of endothelial clefts). Our numerical simulation predicts that for each boundary condition a local maximum shear stress (13.9, 8.9, and 13.3 dyne/cm2 respectively) occurs at the entrance of a 50 um long, 6 um diameter sprout branching at 90 degrees off of a 11 um diameter host vessel. The shear stress drops below 0.2 dyne/cm2, a threshold for endothelial cell activation, within 4.1 um of the entrance for the non-permeable wall case and 4.2 um for the uniformly permeable wall case. Shear stress magnitudes within the sprout are above 0.2 dyne/cm2 for longer sprout scenarios and peaked at 5.9 dyne/cm2 at endothelial cell clefts. These results provide a first estimate of relative fluid shear stress magnitudes along a capillary sprout and highlight the importance of investigating endothelial cell responses to flow conditions during angiogenesis in tumors and other altered microenvironments.

We present a Navier-Stokes/Oldroyd-B immersed boundary algorithm that captures the interaction of a flexible structure with a viscoelastic fluid. In particular, we study the effects of bulk viscoelasticity on freely decaying shape oscillations of an Oldroyd-B fluid droplet suspended in an Oldroyd-B matrix. Our numerical data indicate that if the fluid viscosity is low, viscoelasticity plays a modulating role in the drop shape relaxation; specifically, it increases the oscillation frequency and decreases the decay rate when the fluid relaxation time is above a critical value. In the high-viscosity limit, i.e., when a Newtonian droplet is expected to return to a spherical shape with an aperiodic decay, an increase in the relaxation time eventually results in the reappearance of the oscillations. Both these results are in line with the prediction of small deformation theory for viscoelastic droplet oscillations. The algorithm was also validated by direct comparison with linear asymptotics.

Wall slip effects in a rheometer with double concentric cylinder geometry may lead to significant errors in measurement of the apparent viscosity. Previously, we proposed to use a slotted rotor design to reduce these effects. In this paper, we conduct two- as well as three-dimensional computational fluid dynamics (CFD) simulations to determine the differences in rheological measurements of yield stress fluids between the slotted and non-slotted rotor designs. The test fluid and the slip wall boundary of a rotor are characterized in our computational model by the constitutive equation of Zhu et al. (2005) and the wall-slip length method, respectively. The model has been validated against the existing rheological data measured using a vane rheometer. The results of this study indicate that the rheometer equipped with a slotted rotor can measure the fluid properties with enhanced accuracy and less sensitivity to the wall slip velocity than a rheometer with a non-slotted rotor. We also show that the wall slip effects can be further reduced by either increasing the slot ratio or adding more slots to the rotor. This work illustrates that CFD analysis can be a powerful tool in rheometer design.

White blood cells (WBCs), also known as leukocytes, migrate to sites of infection to destroy pathogenic microorganisms. The ability of WBCs to deform is essential for this function but it is also an important determinant of healthy vasculature. This chapter analyzes the effects of leukocyte deformability on leukocyte–endothelial interactions, presents the evidence for the critical role of the cytoskeleton in bulk mechanical properties of leukocytes, summarizes recent advances in rheological measurements of leukocytes, and discusses pathologies associated with leukocyte activation and reduced deformability of these cells.