Computational model of flow-tissue interactions in intussusceptive angiogenesis

Angiogenesis, the growth of vascular structures, is a complex biological process which has long puzzled scientists. Better physiological understanding of this phenomenon could result in many useful medical applications such as the development of new methods for cancer therapy. We report on the development of a simple computational model of micro-vascular structure formation in intussusceptive angiogenesis observed in vivo. The tissue is represented by a discrete set of basic structural entities and flow conditions within the resulting domain are obtained by solving the Navier-Stokes equations. The tissue is then remodelled according to the tangential shear stress while approximating advection by means of simple non-diffusive heuristics. The updated tissue geometry then becomes the input for the next remodelling step. The model, consisting of steady-state flow and a simple mechanistic tissue response, successfully predicts bifurcation formation and micro-vessel separation in a porous cellular medium. This opens new modelling possibilities in computational studies of the cellular transport involved in micro-vascular growth.     

A computational study of leukocyte adhesion and its effect on flow pattern in microvessels

Three-dimensional computational modeling and simulation are presented on the adhesive rolling of deformable leukocytes over a P-selectin coated surface in parabolic shear flow in microchannels. The computational model is based on the immersed boundary method for cell deformation and Monte Carlo simulation for receptor/ligand interaction. The simulations are continued for at least 1 s of leukocyte rolling during which the instantaneous quantities such as cell deformation index, cell/substrate contact area, and fluid drag remain statistically stationary. The characteristic ‘stop-and-go’ motion of rolling leukocytes, and the ‘tear-drop’ shape of adherent leukocytes as observed in experiments are reproduced by the simulations. We first consider the role of cell deformation and cell concentration on rolling characteristics. We observe that compliant cells roll slower and more stably than rigid cells. Our simulations agree with previous in vivo observation that the hydrodynamic interactions between nearby leukocytes affect cell rolling, and that the rolling velocity decreases inversely with the separation distance, irrespective of cell deformability. We also find that cell deformation decreases, and the cells roll more stably with reduced velocity fluctuation, as the cell concentration is increased. However, the effect of nearby cells on the rolling characteristics is found to be more significant for rigid cells than compliant cells. We then address the effect of cell deformability and rolling velocity on the flow resistance due to, and the fluid drag on, adherent leukocytes. While several earlier computational works have addressed this problem, two key features of leukocyte adhesion, such as cell deformation and rolling, were often neglected. Our results suggest that neglecting cell deformability and rolling velocity may significantly overpredict the flow resistance and drag force. Increasing the cell concentration is shown to increase the flow resistance and reduce the fluid drag. The reduced drag then results in slower and more stable rolling of the leukocytes with longer pause time and shorter step distance. But the increase/decrease in the flow resistance/fluid drag due to the increase in the cell concentration is observed to be more significant in case of rigid cells than compliant cells.     

Nonlinear simulation of the effect of microenvironment on tumor growth

In this paper, we present and investigate a model for solid tumor growth that incorporates features of the tumor microenvironment. Using analysis and nonlinear numerical simulations, we explore the effects of the interaction between the genetic characteristics of the tumor and the tumor microenvironment on the resulting tumor progression and morphology. We find that the range of morphological responses can be placed in three categories that depend primarily upon the tumor microenvironment: tissue invasion via fragmentation due to a hypoxic microenvironment; fingering, invasive growth into nutrient rich, biomechanically unresponsive tissue; and compact growth into nutrient rich, biomechanically responsive tissue. We found that the qualitative behavior of the tumor morphologies was similar across a broad range of parameters that govern the tumor genetic characteristics. Our findings demonstrate the importance of the impact of microenvironment on tumor growth and morphology and have important implications for cancer therapy. In particular, if a treatment impairs nutrient transport in the external tissue (e.g., by anti-angiogenic therapy) increased tumor fragmentation may result, and therapy-induced changes to the biomechanical properties of the tumor or the microenvironment (e.g., anti-invasion therapy) may push the tumor in or out of the invasive fingering regime.