Non-integer Variable Order Dynamic Modeling And Identification Of Soft Tissue Deformation

This paper presents the concept of non-integer analytical dynamic modeling of soft tissue deformation. Soft tissue is known to exhibit a viscoelastic behavior. The main idea of the paper is to introduce a variable order equation for the single-dimensional viscoelastic stress-strain relation. A set of experimental data and an identification method are used to validate such idea. Afterwards, we extend the stress-strain relationship to the multi-dimensional case. Combining this equation with the equations of motion for a soft continuum body leads to the force-displacement equations. These equations are analyzed and compared with a previously developed integer-order model. Then the model is rearranged to form a standard state space dynamical system.