Real-time prediction of soft tissue deformation; a non-integer order modeling scheme and a practical verification for the theoretical concept

Abstract

This paper presents a practical study to verify the concept of non-integer order dynamic behavior of multi-dimensional soft tissue deformation. The stress-strain relationship of soft tissue is of non-integer order. However, this concept needs to be proven. To this aim, the stress-strain relationship is combined with the mechanical equations describing a continuum body. Then, a set of differential equations are obtained modeling the body deformation. Next, the parameters of the model are calculated considering data extracted from an experimental study. The dynamic behavior of the tissue -which is required in the identification of the order- is then simulated using Abaqus. After estimating the order in an adaptive scheme, the non-integer order model and the proposed identification method are verified using some experimental test on a silicone-gel cube.