Physically-based simulation of elastic-plastic fusion of 3D bioprinted spheroids

Spheroids are microtissues containing cells organized in a spherical shape whose diameter is usually less than a millimetre. Depending on the properties of the environment they are placed in, some nearby spheroids spontaneously fuse and generate a tissue. Given their potential to mimic features typical of body parts and their ability to assemble by fusing in permissive hydrogels, they have been used as building blocks to 3D bioprint human tissue parts. Parameters controlling the shape and size of a bioprinted tissue using fusing spheroid cultures include cell composition, hydrogel properties, and their relative initial position. Hence, simulating, anticipating, and then controlling the spheroid fusion process is essential to control the shape and size of the bioprinted tissue. This study presents the first physically-based framework to simulate the fusion process of bioprinted spheroids. The simulation is based on elastic-plastic solid and fluid continuum mechanics models. Both models use the 'smoothed particle hydrodynamics' method, which is based on discretizing the continuous medium into a finite number of particles and solving the differential equations related to the physical properties (e.g. Navier-Stokes equation) using a smoothing kernel function. To further investigate the effects of such parameters on spheroid shape and geometry, we performed sensitivity and morphological analysis to validate our simulations with in-vitro spheroids. Through our in-silico simulations by changing the aforementioned parameters, we show that the proposed models appropriately simulate the range of the elastic-plastic behaviours of in-vitro fusing spheroids to generate tissues of desired shapes and sizes. Altogether, this study presented a physically-based simulation that can provide a framework for monitoring and controlling the geometrical shape of spheroids, directly impacting future research using spheroids for tissue bioprinting.