The bioprinting of heterogeneous organs is a crucial issue. To reach the complexity of such organs, there is a need for highly specialized software that will meet all requirements such as accuracy, complexity, and others. The primary objective of this review is to consider various software tools that are used in bioprinting and to reveal their capabilities. The sub-objective was to consider different approaches for the model creation using these software tools. Related articles on this topic were analyzed. Software tools are classified based on control tools, general computer-aided design (CAD) tools, tools to convert medical data to CAD formats, and a few highly specialized research-project tools. Different geometry representations are considered, and their advantages and disadvantages are considered applicable to heterogeneous volume modeling and bioprinting. The primary factor for the analysis is suitability of the software for heterogeneous volume modeling and bioprinting or multimaterial three-dimensional printing due to the commonality of these technologies. A shortage of specialized suitable software tools is revealed. There is a need to develop a new application area such as computer science for bioprinting which can contribute significantly in future research work.

Mathematical modeling for 3D bioprinting allows us to avoid widespread errors and also time and financial losses. It is necessary for such critical processes as tissue spheroids fusion and diffusion of nutrients in them. The reason is that tissue spheroids fusion is the base of the 3D bioprinting technology. In this work, we propose an approach for tissue spheroids fusion modeling considering a need to compromise between fidelity of the geometric form and viability of the whole bioconstruct.