Recent advances in molecular and cell biology have emphasized the fundamental importance of mechanical factors in regulating the structure and function of cells and extracellular matrix in the vasculature. Consequently, there is an ever-greater motivation to calculate accurately the stress and strain fields in the arterial wall and how they change with disease, injury, and clinical treatment. Although there is an extensive literature on arterial mechanics, our understanding is still far from complete. In this paper, we review some of the salient findings with regard to wall properties, suggest some possible improvements in the calculation of wall stress, and identify some unresolved problems for further research.

Observations from diverse studies on cell biomechanics and mechanobiology reveal that altered mechanical stimuli can induce significant changes in cytoskeletal organization, focal adhesion complexes, and overall mechanical properties. To investigate effects of short-term equibiaxial stretching on the transverse stiffness of and remodeling of focal adhesions in vascular smooth muscle cells, we developed a cell-stretching device that can be combined with both atomic force and confocal microscopy. Results demonstrate that cyclic 10%, but not 5%, equibiaxial stretching at 0.25 Hz significantly and rapidly alters both cell stiffness and focal adhesion associated paxillin and vinculin. Moreover, measured changes in stiffness and focal adhesion area from baseline values tend to correlate well over the durations of stretching studied. It is suggested that remodeling of focal adhesions plays a critical role in regulating cell stiffness by recruiting and anchoring actin filaments, and that cells rapidly remodel in an attempt to maintain a homeostatic biomechanical state when perturbed above a threshold value.

A constrained mixture theory model was developed and used to estimate remodeling of F-actin in vascular smooth muscle cells that were subjected to 10% equibiaxial stretching for up to 30 minutes. The model was based on a synthesis of data on time-dependent changes in atomic force microscopy measured cell stiffness and immunofluorescence measured focal adhesion associated vinculin as well as data on stress fiber stiffness and pre-stretch. Results suggest that an observed acute (after 2 minutes of stretching) increase in cell stiffness is consistent with an increased stretch of the originally present F-actin plus an assembly of new F-actin having nearly homeostatic values of stretch. Moreover, the subsequent (after 30 minutes of stretching) decrease in cell stiffness back towards the baseline value is consistent with a replacement of the overstretched original filaments with the new (reassembled), less stretched filaments. That is, overall cell response is consistent with a recently proposed concept of "tensional homeostasis" whereby cells seek to maintain constant certain mechanical factors via a remodeling of intracellular and transmembrane proteins. Although there is a need to refine the model based on more comprehensive data sets, using multiple experimental approaches, the present results suggest that a constrained mixture theory can capture salient features of the dynamics of F-actin remodeling and that it offers some advantages over many past methods of modeling, particularly those based on classical linearized viscoelasticity.

Atomic force microscopy (AFM) is one of many new technologies available to study the mechanical properties and mechanobiological responses of living cells. Despite the widespread usage of this technology, there has been little attempt to develop new theoretical frameworks to interpret the associated data. Rather, most analyses rely on the classical Hertz solution for the indentation of an elastic half-space within the context of linearized elasticity. In contrast, we propose a fully nonlinear, constrained mixture model for adherent cells that allows one to account separately for the contributions of the three primary structural constituents of the cytoskeleton. Moreover, we extend a prior solution for a small indentation superimposed on a finite equibiaxial extension by incorporating in this mixture model for the special case of an initially random distribution of constituents (actin, intermediate filaments, and microtubules). We submit that this theoretical framework will allow an improved interpretation of indentation forcedepth data from a sub-class of atomic force microscopy tests and will serve as an important analytical check for future finite element models. The latter will be necessary to exploit further the capabilities of both atomic force microscopy and nonlinear mixture theories for cell behavior.