Characterization of Mechanical Properties and Identification of Constitutive Parameters for Soft Tissues

Surgical reconstruction of pathological or injured living tissues has become a generalized clinical practice over the last thirty years. Most of these tissues are connective soft tissues, whose primary function is bearing or transmitting loads: arterial tracts, heart valves, joint ligaments are only some examples among the most popular replacements. However, in spite of the wide spread of this practice, in many cases consistent long-term clinical results are still far from being obtained. A perfect knowledge of the mechanical properties of living materials is essential for the reliability of tissue reconstruction, since the structural function of the tissue depends on such properties; moreover living tissues are the interfaces of the prosthetic substitutes, and determine their boundary conditions. Last, knowledge of mechanical properties of living tissues allows their use as biomaterials for bioprostheses and regenerative patches manufacturing once they have been subjected to a proper treatment of sterilization and preservation. The mechanical behavior of a material is usually described by means of constitutive equations. The constitutive equations of tissues can be used to derive the target properties required for the reconstruction of an unhealthy tissue, or to design the application of a given tissue as a biomaterial. Constitutive equations are also employed in numerical simulations, in order to solve boundary problems and to predict the effectiveness of a prosthetic device or of a restorative operation. The mechanical behavior of soft tissues is characterized, even if at different degrees, by some common features, like finite elasticity, strain rate effects, creep, stress relaxation, plasticity after the first loading cycles. Several approaches have been proposed in the past to model such properties, but they were often focused only on part of the mechanical characteristics, or were restricted to specific applications of the tissue. However, it would be appealing to include all the features presented by soft tissues within a single theory, thus allowing a compact description of their properties. Continuum-based theories that are consistent with the basic principles of mechanics and thermodynamics, are adequate to handle different mechanical behaviors within a comprehensive framework, and thus should prove to be adequate to the scope. In the development of a constitutive theory, physical modeling and experiments are equally important; the experiment, by giving a general knowledge of the material behavior, allows to define the general constitutive framework (elasticity, viscoelasticity, plasticity, or other) inside of which the constitutive equations must be set; within this framework, a constitutive model consistent with the general principles of physics is formulated: such model describes the overall behavior by means of mathematical equations containing constitutive parameters which are specific for any particular material; experiments are then required as the final step in order to identify the actual constitutive parameters for the given material. The first objective of the present work is to formulate a constitutive theory which includes the different mechanical features of soft tissues, which is consistent with the general principles of physics, and which does not require an expensive experimental program in order to identify the properties of the tissue under consideration. The second objective is consequently to develop an experimental procedure that allows a straight characterization of the mechanical properties of the tissue within the general constitutive framework. Setting up mathematical expressions for the constitutive equations can be compromised from scarce physical knowledge of some features of the tissue mechanics. It will be shown how suitable expressions can be built by applying to the theory of system identification. The third objective is to check the suitability of the proposed constitutive theory by means of its application to the characterization of a specific tissue, i.e. preserved bovine pericardium.