Mathematical Tools for Simulation of 3D Bioprinting Processes on High-Performance Computing Resources: The State of the Art

Three-dimensional (3D) bioprinting belongs to the wide family of additive manufacturing techniques and employs cell-laden biomaterials. In particular, these materials, named “bioink”, are based on cytocompatible hydrogel compositions. To be printable, a bioink must have certain characteristics before, during, and after the printing process. These characteristics include achievable structural resolution, shape fidelity, and cell survival. In previous centuries, scientists have created mathematical models to understand how physical systems function. Only recently, with the quick progress of computational capabilities, high-fidelity and high-efficiency “computational simulation” tools have been developed based on such models and used as a proxy for real-world learning. Computational science, or “in silico” experimentation, is the term for this novel strategy that supplements pure theory and experiment. Moreover, a certain level of complexity characterizes the architecture of contemporary powerful computational resources, known as high-performance computing (HPC) resources, also due to the great heterogeneity of its structure. Lately, scientists and engineers have begun to develop and use computational models more extensively to also better understand the bioprinting process, rather than solely relying on experimental research, due to the large number of possible combinations of geometrical parameters and material properties, as well as the abundance of available bioprinting methods. This requires a new effort in designing and implementing computational tools capable of efficiently and effectively exploiting the potential of new HPC computing systems available in the Exascale Era. The final goal of this work is to offer an overview of the models, methods, and techniques that can be used for “in silico” experimentation of the physicochemical processes underlying the process of 3D bioprinting of cell-laden materials thanks to the use of up-to-date HPC resources.