Bio-fabrication methods utilize mechanical means to manufacture products with living cells incorporated. During the fabrication process, cells are involuntarily manipulated and/or exposed to mechanical disturbances that may not be present in the normal physiological environment. One of fundamental questions that need to be answered is whether cells remain viable and/or functional when subjected to mechanical disturbances. This paper presents the development of a theory that can address relation between applied mechanical forces and cellular response from a mechanics point of view. Specifically, a 3D multi-scale numerical model is developed and applied to determine the stress and deformation fields at the cellular level when the tissue construct is subjected to macro-level loads. Based on the detailed information rendered for the micro stress and deformation fields, a general theory is then formulated. A simulation for a 3D alginate tissue construct with encapsulated cells under uniform compression is conducted to illustrate the solution technique. Comparison between the predicted cell viability and experimental data demonstrates that the proposed theory is capable of capturing the experimental trend.

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