Biomechanics of Growth, Remodeling, and Morphogenesis

Abstract

This review deals with biomechanical aspects of growth (mass change), remodeling (property change), and morphogenesis (shape change) in living systems. The emphasis is on theoretical models, but relevant experimental results also are discussed. As an aid to the reader, the fundamental biological terms and concepts are defined for the general problem and for each specific topic. At the outset, the processes involved in growth, remodeling, and morphogenesis are described and placed within the context of the evolution of species. Next, some of the analytical methods used in biomechanical models for these processes are presented. Then, applications of these and other techniques to specific systems are discussed, beginning at the cellular level and proceeding upward to the tissue and organ levels. At the cellular level, modeling and experimental studies are reviewed for cell division, cell movement, and pattern formation, and then morphogenetic mechanisms for epithelia (cell sheets) are discussed. At the tissue and organ levels, the musculoskeletal and cardiovascular systems are considered. Several models are described for growth, remodeling, and morphogenesis of bone, and mainly experimental results are examined in the cases of skeletal muscle, the heart, and arteries. Specific topics for the cardiovascular system include hypertrophy, residual stress, atherosclerosis, and embryonic development. Finally, some future research directions are suggested.

Theoretical study of Beloussov’s hyper-restoration hypothesis for mechanical regulation of morphogenesis

“…The specific mechanical stimulus for growth is a subject of ongoing debate (Humphrey, 2001;Taber, 1995;Cowin, 1996;Omens, 1998). Here, we assume that the local onedimensional growth/contractile response (in the x-direction) depends on stress through the morphomechanical law (5) where D gx is the growth rate per unit length of an element in the current zero-stress state, σ 0 is the target (homeostatic) stress, and a is a positive constant.…”

“…Some argue that cells contain no mechanism to directly sense the level of stress, just as there is no way for humans to experimentally measure stress inside a material. On the other hand, other researchers argue that Cauchy stress and strain rate are more likely candidates because, unlike strain, these quantities do not depend on a reference geometry, which may be somewhat arbitrary (Taber, 1995). To more clearly define a reference state for strain, Cowin (2004) recently proposed using the zero-stress configuration, but cells may never actually experience this configuration.…”

Computational modeling of morphogenesis regulated by mechanical feedback

“…A number of basic morphogenetic mechanisms can be simulated numerically using algorithms for volumetric growth (Taber, 1995). Examples include differential and directed growth, cytoskeletal contraction, and active cell-shape change.…”

“…Models for epithelial morphogenesis have been used to study cell rearrangement, pattern formation, and invagination (Taber, 1995). The classic paper of Odell et al (1981) presents an FE model for a blastula consisting of a circular ring of cells.…”

A 3D finite element model of ventral furrow invagination in the Drosophila melanogaster embryo

“…There have been a number of 2D mechanical models proposed to study invagination (Taber, 1995). In the early work of Odell et al (1981), trusses are located in cells which are controlled by a viscoelastic constitutive law that triggers their apical constriction, and a bistable mechanism that ensures the invagination process.…”