In-silico analysis on biofabricating vascular networks using kinetic Monte Carlo simulations

We present a computational modeling approach to study the fusion of multicellular aggregate systems in a novel scaffold-less biofabrication process, known as 'bioprinting'. In this novel technology, live multicellular aggregates are used as fundamental building blocks to make tissues or organs (collectively known as the bio-constructs,) via the layer-by-layer deposition technique or other methods; the printed bio-constructs embedded in maturogens, consisting of nutrient-rich bio-compatible hydrogels, are then placed in bioreactors to undergo the cellular aggregate fusion process to form the desired functional bio-structures. Our approach reported here is an agent-based modeling method, which uses the kinetic Monte Carlo (KMC) algorithm to evolve the cellular system on a lattice. In this method, the cells and the hydrogel media, in which cells are embedded, are coarse-grained to material's points on a three-dimensional (3D) lattice, where the cell-cell and cell-medium interactions are quantified by adhesion and cohesion energies. In a multicellular aggregate system with a fixed number of cells and fixed amount of hydrogel media, where the effect of cell differentiation, proliferation and death are tactically neglected, the interaction energy is primarily dictated by the interfacial energy between cell and cell as well as between cell and medium particles on the lattice, respectively, based on the differential adhesion hypothesis. By using the transition state theory to track the time evolution of the multicellular system while minimizing the interfacial energy, KMC is shown to be an efficient time-dependent simulation tool to study the evolution of the multicellular aggregate system. In this study, numerical experiments are presented to simulate fusion and cell sorting during the biofabrication process of vascular networks, in which the bio-constructs are fabricated via engineering designs. The results predict the feasibility of fabricating the vascular structures via the bioprinting technology and demonstrate the morphological development process during cellular aggregate fusion in various engineering designed structures. The study also reveals that cell sorting will perhaps not significantly impact the final fabricated products, should the maturation process be well-controlled in bioprinting.