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.

The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years. Many aspects of these problems are now wellunderstood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation. In this perspective paper we review the state of the field and highlight open questions, challenges, and avenues for further development.

During human brain development, the cerebral cortex undergoes substantial folding, leading to its characteristic highly convoluted form. Folding is necessary to accommodate the expansion of the cerbral cortex; abnormal cortical folding is linked to various neurological disorders, including schizophrenia, epilepsy, autism and mental retardation. Although this process requires mechanical forces, the specific force-generating mechanisms that drive folding remain unclear. The two most widely accepted hypotheses are (1) folding is caused by differential growth of the cortex and (2) folding is caused by mechanical tension generated in axons. Direct evidence supporting either theory, however, is lacking. Here we show that axons are indeed under considerable tension in the developing ferret brain, but the patterns of tissue stress are not consistent with a causal role for axonal tension. In particular, microdissection assays reveal that significant tension exists along axons aligned circumferentially in subcortical white matter tracts, as well as those aligned radially inside developing gyri (outward folds). Contrary to previous speculation, however, axonal tension is not directed across developing gyri, suggesting that axon tension does not drive folding. On the other hand, using computational (finite element) models, we show that differential cortical growth accompanied by remodeling of the subplate leads to outward folds and stress fields that are consistent with our microdissection experiments, supporting a mechanism involving differential growth. Local perturbations, such as temporal differences in the initiation of cortical growth, can ensure consistent folding patterns. This study shows that a combination of experimental and computational mechanics can be used to evaluate competing hypotheses of morphogenesis, and illuminate the biomechanics of cortical folding.

A simple phenomenological model is used to study interrelations between material properties, growth-induced residual stresses, and opening angles in arteries. The artery is assumed to be a thick-walled tube composed of an orthotropic pseudoelastic material. In addition, the normal mature vessel is assumed to have uniform circumferential wall stress, which is achieved here via a mechanical growth law. Residual stresses are computed for three configurations: the unloaded intact artery, the artery after a single transmural cut, and the inner and outer rings of the artery created by combined radial and circumferential cuts. The results show that the magnitudes of the opening angles depend strongly on the heterogeneity of the material properties of the vessel wall and that multiple radial and circumferential cuts may be needed to relieve all residual stress. In addition, comparing computed opening angles with published experimental data for the bovine carotid artery suggests that the material properties change continuously across the vessel wall and that stress, not strain, correlates well with growth in arteries.

In humans and many other mammals, the cortex (the outer layer of the brain) folds during development. The mechanics of folding are not well understood; leading explanations are either incomplete or at odds with physical measurements. We propose a mathematical model in which (i) folding is driven by tangential expansion of the cortex and (ii) deeper layers grow in response to the resulting stress. In this model the wavelength of cortical folds depends predictably on the rate of cortical growth relative to the rate of stress-induced growth. We show analytically and in simulations that faster cortical expansion leads to shorter gyral wavelengths; slower cortical expansion leads to long wavelengths or even smooth (lissencephalic) surfaces. No inner or outer (skull) constraint is needed to produce folding, but initial shape and mechanical heterogeneity influence the final shape. The proposed model predicts patterns of stress in the tissue that are consistent with experimental observations.

Cardiac looping is a vital morphogenetic process that transforms the initially straight heart tube into a curved tube normally directed toward the right side of the embryo. While recent work has brought major advances in our understanding of the genetic and molecular pathways involved in looping, the biophysical mechanisms that drive this process have remained poorly understood. This paper examines the role of biomechanical forces in cardiac rotation during the initial stages of looping, when the heart bends and rotates into a c-shaped tube (c-looping). Embryonic chick hearts were subjected to mechanical and chemical perturbations, and tissue stress and strain were studied using dissection and fluorescent labeling, respectively. The results suggest that (1) the heart contains little or no intrinsic ability to rotate, as external forces exerted by the splanchnopleure (SPL) and the omphalomesenteric veins (OVs) drive rotation; (2) unbalanced forces in the omphalomesenteric veins play a role in left-right looping directionality; and (3) in addition to ventral bending and rightward rotation, the heart tube also bends slightly toward the right. The results of this study may help investigators searching for the link between gene expression and the mechanical processes that drive looping.

Stress-modulated growth in the aorta is studied using a theoretical model. The model is a thick-walled tube composed of two pseudoelastic, orthotropic layers representing the intima/media and the adventitia. Both layers are assumed to follow a growth law in which the time rates of change of the growth stretch ratios depend linearly on the local smooth muscle fiber stress and on the shear stress due to blood flow on the endothelium. Using finite elasticity theory modified to include volumetric growth, we computed temporal changes in stress, geometry, and opening angle (residual strain) during development and following the onset of sudden hypertension. For appropriate values of the coefficients in the growth law, the model yields results in reasonable agreement with published data for global and local growth of the rat aorta.

A method is proposed to measure transverse blood flow by using photoacoustic Doppler broadening of bandwidth. By measuring bovine blood flowing through a plastic tube, the linear dependence of the broadening on the flow speed was validated. The blood flow of the microvasculature in a mouse ear and a chicken embryo (stage 16) was also studied.