The mechanics of soft biological systems

This special issue is dedicated to the behavior of soft biological systems and, in particular, to the contributions by experts in continuum mechanics of solids. Increasing numbers of researchers are becoming involved in this multidisciplinary area and huge investments are being made to promote the subject. In the last few years many leading universities have established new departments devoted to different aspects of biological engineering and of mechanics of soft tissue. The number of international conferences focusing on biomechanics has grown dramatically and many new journals have been spawned. Biomechanics has achieved a great deal since its coming of age as a distinct discipline in the mid-1960s, but there remain many challenging problems for mechanics to address within the biological and medical fields, as the excellent review article by JD Humphrey points out in the January 2003 issue of the Proceedings of the Royal Society of London [1]. Humphrey defines biomechanics as ‘the development, extension and application of mechanics for the purposes of understanding better physiology and pathophysiology as well as the diagnosis and treatment of disease and injury’. Here we focus on broader aspects of the subject that relate to the description of material behavior and changes in that behavior as a result of changes in the mechanical environment. Soft biologically based materials are inherently nonlinear in the mechanical response and are subject to large strains ‘in service’. The prediction and possible alteration of the mechanical response, which is best described using the theory of nonlinear elasticity or pseudo-elasticity, is essential for the intended functions. For example, many biological materials stiffen as they are stretched, thereby preventing excessive deformations that could threaten tissue integrity. Therefore, the mechanical properties play a key role in development, stability, growth, regeneration and remodeling. It is also well known that the internal structure of biomaterials has an essential influence on mechanical response. For example, important constituents of many cells and tissues are filamentous proteins, such as silk and collagen (in its various forms), which are relatively stiff (compared with the surrounding material) and endow the material with anisotropic properties. The development of the mechanics of biological systems has reached a point where it can benefit enormously from the contributions of experts in nonlinear continuum mechanics. Understanding the mechanical behavior of soft tissue and the changes in that behavior due to growth, remodeling and adaptation requires a significant input from such expertise. The objective of this special issue is to apply biological and engineering principles towards the development of mathematical models to describe the response of biological systems and the solution of prototype initial boundary value problems for predictive purposes. In the paper by Holland et al., the authors present a mathematical and computational framework to simulate differential growth of isotropic and transversely isotropic thin films in living structures. Specialized to classical model problems in plant biology, the theory shows that differential growth generates axial tension and residual stresses, which can be released by the peeling of individual layers. The theory can be adapted to biomedical applications such as asthma, gastritis, obstructive sleep apnea, brain development and tumor invasion. Cardiac electrophysiology is the focus of the paper by Nardinocchi and Teresi. The model presented by the authors couples the electro-mechanical activities occurring along the cardiac cycle using the active strain format as opposed to the active stress. The structure of the myocardium is characterized by two families of oriented