Relationship Between Structure and Mechanics for Membranous Tissues

Abstract

Professor Yoram Lanir has pioneered the development of structurally based constitutive relations to describe the stressstrain response of soft biological tissues. This approach relates the mechanical response of the tissue to the intrinsic micro-structural properties of its constituents, such as collagen. This article summarises some of the work by the Auckland Bioengineering Institute contributing towards the goal of understanding the structure–function relationship of soft membranous tissue. Key aspects of our work are to (1) develop constitutive relations based on quantitative information of tissue structure; and (2) use rich sets of experimental data to aid in accurate and reliable constitutive parameter identification. We first outline several common techniques to quantify tissue structure, such as collagen fibre orientations. A detailed description of an extended-volume imaging system, developed in our laboratory, is then provided along with a few application examples. The gathered imaging data is incorporated into structural constitutive models by means of fitting to mathematical distributions. Based upon the observations made from some imaging studies, a conceptual fibre distribution model is proposed for modelling the collagen network in skin. We then introduce a selection of constitutive models, which have been developed to characterise the mechanical behaviour of soft connective tissues (skin in particular), with particular emphasis on structurally based models. Finite element models, used with appropriate constitutive relations, provide a means of interpreting experimental results. Some of our recent efforts in developing instrumentation to measure the two-dimensional and three-dimensional response of soft tissues are described. This includes a biaxial tensile rig, which is capable of deforming membranes in up to 16 directions, and a force-sensitive micro-robot. We highlight some of the challenges often associated with constitutive parameter identification using commonly used model based fitting approaches. These issues were examined and illustrated in depth by performing controlled studies on silicon gel phantoms, which allowed us to focus our attention solely on the identification problem. Lastly, future directions of applying structurally based models to understanding the biomechanics of soft tissues are discussed.