Calculation of material coefficients of viscoelastic gel for validating soft tissue deformations

As soft tissue modeling gains more importance in recent scientific research, improving the accuracy and thus the reality of the simulations becomes a nonignorable necessity when the applications in which these simulations used are considered. The mathematical models of the deformation behavior of the living tissues are integrated in many biomedical and biomechanical engineering applications such as virtual surgery simulators, implant designs, etc. Therefore, both enhancing the mathematical model and defining the simulated material better in the sense of its characteristic coefficients mean reducing the error of the application. Validation of the proposed model should be done by an artificial control material on which the requested material tests can be conducted and which produces reaction forces in the similar range with the target soft tissue. Artificial materials make the advantages of homogeneity, determined boundary conditions, isotropy, and repeatability of the tests. In this study, several material tests are conducted on a material which is Parker Labs AquaFlex Ultrasound Gel Pad. Two types of experiments are conducted on this material: static indentation and ramp–hold tests. The stress–strain curves obtained from the static indentation tests conducted on AquaFlex Ultrasound Gel material show the nonlinearity of the material. Ramp–hold tests present the relaxation characteristic and that shows that the material is viscoelastic. Coefficients of the Mooney–Rivlin type strain energy density function are computed via curve fitting method applied to the static indentation test data. Parameters related to the viscoelastic response of the material are calculated again by curve fitting to ramp–hold test data by using Prony series expansion. The obtained results of this study are to be used as initial parameters in inverse finite element computations where initial parameters are effective for convergence. It is obvious that a standard material testing methods to evaluate the material properties of living tissue under all possible loading conditions does not exist. The complex nature of the living tissue limits modeling capabilities to certain experimental conditions. This study basically aimed to provide physical test data for a synthetic material and proposed material constants to validate medical simulations in future studies.