Quasi-Linear Soft Tissue Models Revisited

Di erent mechanical properties of biological tissues depend on mineral content. Thus, roughly, it can be distinguished two classes of biological tissues. Bones and tooth content mineral, they conform the group known as hard tissues. Whereas, skin, muscle, blood vessel and lungs conform the second group called of soft tissues. They do not content mineral, so they are much deformable than hard tissues. Modelling the mechanical behavior of soft tissues has much in common with those techniques used to model rubber elasticity. Thus, nite deformation theories useful for rubber elasticity are often used to describe soft tissue mechanical behavior. However, there are signi cant differences in the material structure of soft tissues and rubber elasticity. Moreover, in the way they respond under applied stress. Soft tissue material achieve initially large stretch under relatively low level of stress and subsequent sti ening at higher level extensions. This is shown in Figure( 1), where are compared the typical simple tension stress-stretch response of rubber (left-hand gure) with that of soft tissue (right-hand gure). For other side, collagen bres distribution leads to pronounced anisotropy in soft tissue, in contrast with from typical isotropic rubber [1, 2, 3]. In biomechanics an specimen (animal) is regarded as an assemble of rigid bodies connected by joins and muscles. Under this framework, Newton’s law balance of forces maybe could not be e cient to write equations of motion for each connectors, known their mechanical properties. Naturally, because the number of particles to be considered is excessively large, and the way to specify the interaction forces between particles becomes very complex. Instead, it is much better to consider the body as a continuum, searching for a simpli ed way to specify interaction forces between particles by means of constitutive equations, and so thus specifying realistic properties of materials. A stress-strain relationship describes the mechanical property of a material and it is therefore a constitutive equation. Research on modelling soft tissue mechanical behavior has a growing demand for applications in surgical simulations, pursuing for in real time fast and precise calculations of tissue deformations. In trying for these commitments, it has been introduced models accounting for the continuous nature of soft tissue. Within the limits of the employed constitutive model the nite element methods allows for physically correct simulation of the tissue mechanics [4, 5, 6]. For other side, alternative discrete approaches based on spring-mass model have also been applied[7, 8]. It seems that methods based on the continuum approach are more appropriated to describe much better realistic soft tissue mechanical behavior, whereas spring-mass based models being economics are less accurate than the former. The main issue of our research look for an appropriate way to establish an accurate comparison between these methodologies. In this work we review some physic models applicable to modelling soft tissue mechanical behavior and we also discuss some perspective in the eld. This work is organized as follow: In section II we present the continuum approach formalism, and we also consider particular mathematical results for linear elastic solids and uids. Important testing methods on physics necessaries to characterize soft tissue mechanical behavior, i.e, strain, creep and relaxation, are presented in section III. Next, in section IV are reviewed more general soft tissue mechanical properties. Section V is devoted to show basic mathematic models describing nonlinear elasticity and quasi-linear viscoelasticity, which are related to soft tissue mechanical behavior. In section VI, it is presented the basic vibrational spring-mass model, which is also extended to consider viscoelastic mechanical behavior. In section VII we presented some discussions and perspectives.