Study of capillary network directionality and irrigation of hypoxic tissue in an angiogenesis lattice model

To shed light on the understanding of the angiogenesis process, we study a simplified lattice model for the capillary network formation between an existing blood vessel and an initially hypoxic tissue. We consider that the cells of the tissue surface can release growth factors that will diffuse, leading to the formation of new capillaries that ultimately arrive at the tissue. Additionally, we consider the local production of growth factors by the growing capillary network. We also propose the existence of an inhibition mechanism at the hypoxic surface, i.e., a fixed number of neighboring sites of an already irrigated site of the hypoxic tissue stop releasing growth factors due to the arrival of nutrients. Particularly, the goal of this work is to study the effect of the release of local growth factors and the inhibition mechanism on properties such as the directionality of the growing network and the irrigation of the hypoxic tissue. Therefore we propose the quantification of these two relevant features for angiogenesis modeling. We establish a relationship between the model behavior without the release of local growth factors in the presence of the inhibition mechanism and a normal angiogenesis process. In this situation, the model gives a directional capillary network and a good irrigation of the hypoxic tissue. On the other hand, for a large number of released local growth factors in the absence of the inhibition mechanism, the model could be appropriate for the description of tumor angiogenesis. In this case, the model provides a rather small directionality for the growing structure, with a worse degree of irrigation of the hypoxic tissue, as well as a more tortuous capillary network with many closed branches and loops.