Modeling fusion of cellular aggregates in biofabrication using phase field theories

A mathematical model based on the phase field formulation is developed to study fusion of cellular aggregates/clusters. In a novel biofabrication process known as bioprinting (Mironov et al., 2009a), live multicellular aggregates/clusters are used to make tissue or organ constructs via the layer-by-layer deposition technique, in which the printed bio-constructs are embedded in hydrogels rich in maturogens and placed in bioreactors to undergo the fusion process of self-assembly, maturation, and differentiation to form the desired functional tissue or organ products. We formulate the mathematical model to study the morphological development of the printed bio-constructs during fusion by exploring the chemical-mechanical interaction among the cellular aggregates involved. Specifically, we treat the cellular aggregates and the surrounding hydrogels as two immiscible complex fluids in the time scale comparable to cellular aggregate fusion and then develop an effective mean-field potential that incorporates the long-range, attractive interaction between cells as well as the short-range, repulsive interaction due to immiscibility between the cell and the hydrogel. We then implement the model using a high order spectral method to simulate the making of a set of tissues/organs in simple yet fundamental geometries like a ring, a sheet of tissues, and a Y-shaped, bifurcating vascular junction by the layer-by-layer deposition of spheroidal cellular clusters in the bioprinting technology.