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Modeling Fusion of Cellular Aggregates in Biofabrication Using Phase Field Theories


A 2011 Preprint by X. Yang, V. Mironov, and Q. Wang

  • 2011:03
  • A mathematical model based on a phase field formulation is developed to study fusion of cellular aggregates/clusters. In a novel biofabrication process known as bioprinting [25], live multicellular aggregates/clusters are used to make tissue or organ constructs via the layer-by-layer deposition technique in compatible hydrogels rich in maturogen; the bio-constructs embedded in hydrogels are then 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 between cellular aggregates involved. Specifically, we treat the cellular aggregates and the surrounding hydrogels as two immiscible complex fluids 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 geometries like a ring or a sheet of tissues and a Y- or T-shaped vascular junction by the layer-by-layer deposition of spheroidal cellular clusters in the bioprinting technology.

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