An optimization based 3D1D coupling strategy for tissue perfusion and chemical transport during tumorinduced angiogenesis
Abstract
A new mathematical model and numerical approach are proposed for the simulation of fluid and chemical exchanges between a growing capillary network and the surrounding tissue, in the context of tumorinduced angiogenesis. Thanks to proper modeling assumptions the capillaries are reduced to their centerline: a well posed mathematical model is hence worked out, based on the coupling between a threedimensional and a onedimensional equation (3D1D coupled problem). Also the application of a PDEconstrained optimization formulation is here proposed for the first time for angiogenesis simulations. Under this approach no mesh conformity is required, thus making the method particularly suitable for this kind of application, since no remeshing is required as the capillary network grows. In order to handle both the evolution of the quantities of interest and the changes in the geometry, a discretehybrid strategy is adopted, combining a continuous modeling of the tissue and of the chemicals with a discrete tiptracking model to account for the vascular network growth. The tiptracking strategy, together with some proper rules for branching and anastomosis, is able to provide a realistic representation of the capillary network.
 Publication:

arXiv eprints
 Pub Date:
 November 2022
 DOI:
 10.48550/arXiv.2212.00692
 arXiv:
 arXiv:2212.00692
 Bibcode:
 2022arXiv221200692B
 Keywords:

 Quantitative Biology  Tissues and Organs;
 Mathematics  Numerical Analysis;
 65N30;
 65N50;
 68U20;
 8608;
 35Q92;
 92B05;
 92C17