Extensive experimental studies have identified vascular endothelial growth factor (VEGF) concentrations and concentration gradients as major factors in angiogenesis; however, localized in vivo measurements of these parameters have not been possible. We developed a three-dimensional computational model of skeletal muscle fibers, blood vessels, and interstitial space. Here it is applied to rat extensor digitorum longus. VEGF isoforms are secreted by myocytes, diffuse through extracellular matrix and basement membranes, and bind endothelial cell surface receptors on blood vessels. In addition, one isoform, VEGF164, binds to proteoglycans in the interstitial space. VEGF secretion rate is determined from the predicted tissue oxygen level through its effect on the hypoxia inducible factor-1alpha transcription factor. We estimate VEGF secretion and its concentrations and gradients in resting muscle and for different levels of exercise. The effects of low levels of inspired oxygen are also studied. We predict that the high spatial heterogeneity of muscle fiber VEGF secretion in hypoxic tissue leads to significant gradients of VEGF concentration and VEGF receptor activation. VEGF concentration gradients are predicted to be significant in both resting and exercising muscle (4% and 6-8% change in VEGF over 10 microm, respectively), sufficient for chemotactic guidance of 50-microm-long sprout tip cells. VEGF gradients also result in heterogeneity in VEGF receptor activation--a possible explanation for the stochasticity of sprout location. In the absence of interstitial flow, gradients are 10-fold steeper in the transverse direction (i.e., perpendicular to the muscle fibers) than in the longitudinal direction. This may explain observed perpendicular anastomoses in skeletal muscle.

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.

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