Modeling biological growth and remodeling: Contrasting methods, contrasting needs

Abstract Biological growth and remodeling processes are necessarily time-dependent due to the finite periods needed for the material to be synthesized, deposited, degraded, and/or reorganized and, hence, so have been predominantly modeled for the past 20+ years. However, a full-spectrum examination of the timescales present in these processes reveals the need to explore a new class of models for which time-dependent effects are negligible. These mechanobiologically (quasi-) equilibrated formulations not only appear to apply well in many cases but also provide the modeler with those additional pieces of information, and intuition, always needed when modeling complex time-dependent responses. Material model determination, optimization involving long-term adaptations, and mechanobiological stability analyses could be leveraged by the simplicity and computational efficiency of time-independent models. Although this concept is general, we address it by means of two particular theories for which we also highlight crucial differences entailed by their diametrically different material memory and heterogeneity descriptions.

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