Virtual angiogenesis : mathematical and multiphysics approach for directed tissue engineering (2019)

Background Adding a blood vessel network to cultured tissues is an essential step for clinical application. A physiological organization of these networks is important for the functioning of the blood vessels. Endothelial cells seeded in a hydrogel can give rise to microvascular networks. In reaction to external chemical (growth factor gradients) and mechanical forces (matrix stiffness, interstitial fluid flow), the networks grow into adjacent empty matrix [1,3]. A range of cell-cell interactions leading to microvascular network formation have been proposed [2,4]. However, the cell-based models (cellular potts model) studying these mechanisms, often fail to include factors as opposed by the environment. Objective We developed a framework for studying the effect of extracellular regulating factors such as chemical gradients, matrix stiffness, interstitial flow, coupled with cellular component in a single model for predicting the evolution of microvascular network in a given geometry. Methods An hybrid cellular potts – partial differential equation (CPM-PDE) model is presented to study the microvascular network formation. This hybrid model consisting of a CPM component for cellular representation, and a PDE component solving mathematical equations for the distribution of chemicals. Individual cells are represented in a 2D discrete space. The cells secrete and react to chemicals in their environment, which diffuse and decay in the ECM. Results and Discussion The model in this study is based upon the previous work of the lab of Roeland Merks.We modeled the network formation in a microfluidic device setting as shown in figure. From the cells seeded in the hydrogel matrix and their local interactions, network structures emerge. The shapes of arising structures are studied and correlated to calculated properties and parameter values. New boundary conditions were set-up as to be comparable to experimental data and an external Vascular Endothelial Growth Factor (VEGF) source was added. Figure. Modeling chemotaxis of microvascular angiogenesis Future plans We anticipate our model framework to be a starting point for more sophisticated experimental driven (microfluidic-based) insilico testing tool for tissue engineering applications. For example, the possible addition of aptamer binding kinetics coupled to the mechano-chemical parameters could be used to study the network organization within a spatiotemporal controlled growth factor release system. This would help us to predict the emerging network types within the tissue constructs of specific extracellular regulating parameter values. Furthermore, it would be used to design the quantitative assay for in vitro testing. References 1. J T Daub and R M H Merks, A Cell-based model of extracellular-matrix guided endothelial cell migration during angiogenesis, Bull Math Biol, 2013 2. R F M van Oers et.al., Mechanical cell-matrix feedback explains pairwise and collective endothelial cell behavior in vitro, PLoS One, 2014 3. Y Abe et.al., Balance of interstitial flow magnitude and vascular endothelial growth factor concentration modulates three-dimensional microvascular network formation, APL Bioeng, 2019 4. Xu Z et.al., A multiscale model of thrombus development, J.R.Soc.Interface, 2008 Acknowledgements This work is supported by an ERC Consolidator Grant under grant agreement no 724469