Jay D. Humphrey

Not long ago it was thought that the most important characteristics of the mechanics of soft tissues were their complex mechanical properties: they often exhibit nonlinear, anisotropic, nearly incompressible, viscoelastic behavior over finite strains. Indeed, these properties endow soft tissues with unique structural capabilities that continue to be extremely challenging to quantify via constitutive relations. More recently, however, we have come to appreciate an even more important characteristic of soft tissues, their homeostatic tendency to adapt in response to changes in their mechanical environment. Thus, to understand well the biomechanical properties of a soft tissue, we must not only quantify their structure and function at a given time, we must also quantify how their structure and function change in response to altered stimuli. In this paper, we introduce a new constrained mixture theory model for studying growth and remodeling of soft tissues. The model melds ideas from classical mixture and homogenization theories so as to exploit advantages of each while avoiding particular difficulties. Salient features include the kinetics of the production and removal of individual constituents and recognition that the neighborhood of a material point of each constituent can have a different, evolving natural (i.e. stress-free) configuration.

Arterial stiffness, a leading marker of risk in hypertension, can be measured at material or structural levels, with the latter combining effects of the geometry and composition of the wall, including intramural organization. Numerous studies have shown that structural stiffness predicts outcomes in models that adjust for conventional risk factors. Elastic arteries, nearer to the heart, are most sensitive to effects of blood pressure and age, major determinants of stiffness. Stiffness is usually considered as an index of vascular aging, wherein individuals excessively affected by risk factor exposure represent early vascular aging, whereas those resistant to risk factors represent supernormal vascular aging. Stiffness affects the function of the brain and kidneys by increasing pulsatile loads within their microvascular beds, and the heart by increasing left ventricular systolic load; excessive pressure pulsatility also decreases diastolic pressure, necessary for coronary perfusion. Stiffness promotes inward remodeling of small arteries, which increases resistance, blood pressure, and in turn, central artery stiffness, thus creating an insidious feedback loop. Chronic antihypertensive treatments can reduce stiffness beyond passive reductions due to decreased blood pressure. Preventive drugs, such as lipid-lowering drugs and antidiabetic drugs, have additional effects on stiffness, independent of pressure. Newer anti-inflammatory drugs also have blood pressure independent effects. Reduction of stiffness is expected to confer benefit beyond the lowering of pressure, although this hypothesis is not yet proven. We summarize different steps for making arterial stiffness measurement a keystone in hypertension management and cardiovascular prevention as a whole.

Since its coming of age in the mid 1960s, continuum biomechanics has contributed much to our understanding of human health as well as to disease, injury, and their treatment. Nevertheless, biomechanics has yet to reach its full potential as a consis-tent contributor to the improvement of health-care delivery. Because of the inherent complexities of the microstructure and biomechanical behaviour of biological cells and tissues, there is a need for new theoretical frameworks to guide the design and interpretation of new classes of experiments. Because of continued advances in exper-imental technology, and the associated rapid increase in information on molecular and cellular contributions to behaviour at tissue and organ levels, there is a pressing need for mathematical models to synthesize and predict observations across multiple length- and time-scales. And because of the complex geometries and loading con-ditions, there is a need for new computational approaches to solve the boundary-and initial-value problems of clinical, industrial, and academic importance. Clearly, much remains to be done. The purpose of this paper is twofold: to review a few of the many achievements in the biomechanics of soft tissues and the tools that allowed them, but, more importantly, to identify some of the open problems that merit increased attention from those in applied mechanics, biomechanics, mathe-matics and mechanobiology.