VEGF Distribution Modeling in Mouse Tissue

The basis of this mouse model is the human model developed by Stefanini and co-workers that was used to explore the VEGF distributions in humans in health and disease [8] (link), [18] (link), [19] (link), [21] (link); the model is significantly expanded as explained below. The mouse is divided into the blood compartment and tissue compartment (Figure 1). As an approximation, the tissue compartment is represented by skeletal muscle that comprises the majority of its mass (43% of total body mass [22] (link)). To build the tissue compartment, the skeletal muscle is represented as cylindrical fibers (myocytes) aligned in parallel with cylindrical microvessels dispersed between the muscle fibers. The space between the muscle fibers and microvessels is designated as the interstitial space, which is itself composed of the basement membranes of the parenchymal cells/myocytes (PBM) and endothelial cells (EBM), in addition to the extracellular matrix (ECM). VEGF is secreted by the myocytes into the interstitial space where it can bind to VEGF receptors VEGFR-1, VEGFR-2, and NRP-1 on the abluminal surface of the endothelial cells, as well as to glycosaminoglycan chains (GAG) in the basement membranes and extracellular matrix. The binding of VEGF to NRP-1 on the surface of the myocytes is also included. VEGF can be transported to the blood via the lymphatics at a rate k_L and can be exchanged between the blood and interstitium via microvascular permeability at a rate k_p. VEGF in the blood can bind to receptors on the luminal surface of the endothelial cells and can be removed via plasma clearance at a rate c_V. Receptors and VEGF/receptor complexes can be internalized at a rate k_int.Figure 2 summarizes the molecular interactions of VEGF₁₂₀ and VEGF₁₆₄ with their receptors and with GAG chains in the PBM, EBM, and ECM.
In our model, we include an anti-VEGF agent that can bind to and form a complex with VEGF in both the blood and tissue. The unbound anti-VEGF agent and the complex are also subject to intercompartmental transport via permeability and lymphatic drainage, and can also be cleared from the blood. The molecular interactions between the two VEGF isoforms and the anti-VEGF agent are illustrated in Figure 2.
We incorporate pore theory in modeling the interstitial space to reflect the available volume for VEGF to diffuse. The VEGF molecules are free to diffuse in the available interstitial fluid volume, denoted K_AV, which is defined as the available fluid volume (U_AV) divided by the total tissue volume (U). Based on the geometry of the pores in the basement membranes and extracellular matrix, the partition coefficient and available fluid volume can be calculated as follows: