Computational Model of Vascular Endothelial Growth Factor Spatial Distribution in Muscle and Pro-Angiogenic Cell Therapy

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Abstract
Members of the vascular endothelial growth factor (VEGF) family of proteins are critical regulators of angiogenesis. VEGF concentration gradients are important for activation and chemotactic guidance of capillary sprouting, but measurement of these gradients in vivo is not currently possible. We have constructed a biophysically and molecularly detailed computational model to study microenvironmental transport of two isoforms of VEGF in rat extensor digitorum longus skeletal muscle under in vivo conditions. Using parameters based on experimental measurements, the model includes: VEGF secretion from muscle fibers; binding to the extracellular matrix; binding to and activation of endothelial cell surface VEGF receptors; and internalization. For 2-D cross sections of tissue, we analyzed predicted VEGF distributions, gradients, and receptor binding. Significant VEGF gradients (up to 12% change in VEGF concentration over 10 μm) were predicted in resting skeletal muscle with uniform VEGF secretion, due to non-uniform capillary distribution. These relative VEGF gradients were not sensitive to extracellular matrix composition, or to the overall VEGF expression level, but were dependent on VEGF receptor density and affinity, and internalization rate parameters. VEGF upregulation in a subset of fibers increased VEGF gradients, simulating transplantation of pro-angiogenic myoblasts, a possible therapy for ischemic diseases. The number and relative position of overexpressing fibers determined the VEGF gradients and distribution of VEGF receptor activation. With total VEGF expression level in the tissue unchanged, concentrating overexpression into a small number of adjacent fibers can increase the number of capillaries activated. The VEGF concentration gradients predicted for resting muscle (average 3% VEGF/10 μm) is sufficient for cellular sensing; the tip cell of a vessel sprout is approximately 50 μm long. The VEGF gradients also result in heterogeneity in the activation of blood vessel VEGF receptors. This first model of VEGF tissue transport and heterogeneity provides a platform for the design and evaluation of therapeutic approaches. It is not currently possible to experimentally quantify the gradients of protein concentration in the extracellular space in vivo. However, the concentration gradients of vascular endothelial growth factor (VEGF) are essential for both initiation and directed guidance of new blood vessels. The authors develop a computational model of VEGF transport in tissue in vivo (skeletal muscle, though the method is applicable to other tissues and other proteins) with realistic geometry and including biophysical interactions of VEGF, its receptors, and the extracellular matrix. Using this model, the authors predict for the first time the distribution of VEGF concentration and VEGF receptor activation throughout the tissue. VEGF concentration gradients are significant, up to 12% change in VEGF concentration over 10 μm in resting muscle. Transplanting VEGF-overexpressing myocytes (for therapeutic induction of blood vessel growth) increases the gradients significantly. Endothelial cells in sprouting vessels are approximately 50 μm long, and therefore the predicted gradients across the cell are high and sufficient for chemotactic guidance of the new vessels. The VEGF concentration gradients also result in significant heterogeneity in the activation of VEGF receptors on blood vessels throughout the tissue, a possible reason for the sporadic nature of sprout initiation.