Figure 5.

Simple timeline showing some key advances in modeling G&R, emphasizing in particular the seminal paper of Skalak in 1981, the introduction of a general constrained mixture theory twenty years after (submitted 2001, published 2002), and yet unimagined opportunities (?) again twenty years thereafter. Notwithstanding the importance of the theory of finite volumetric growth – formalized by Rodriguez and colleagues in 1994 and quickly shown to be useful by Taber, Rachev, and others – consistent with the review herein this timeline focuses primarily on key advances for the constrained mixture model (CMM), including the first finite element implementations in 2005/2006, fluid-solid-growth modeling first used in 2007 but advanced generally in 2009, the utility of such models in describing tissue engineered constructs (introduced in 2009, advanced in 2014, shown to be useful for scaffold design in 2015, and used to guide a clinical trial in 2020), the concept of mechanobiological stability introduced in 2014 and extended in 2019, and finally the computational efficiency engendered by the assumption of quasi-static mechanobiological equilibria shown in 2020 as well as the importance of coupling across scales, including with cell signaling models to appear in 2021. Note, too, some of the key reviews and books that address broader approaches to G&R.