Particle Swarm Optimization Method for Hyperelastic Characterization of Soft Tissues

Hyperelastic constitutive models such as Ogden and Mooney-Rivlin are commonly used for nonlinear characterization of soft materials and especially biomaterials such as brain tissue. The parameters of these models are usually found by curve-fitting to the experimental or in some cases, the numerical data. Most of the times, common non-linear least square curve fitting method known as Levenberg-Marquardt (LM) is employed for this purpose. In this paper, we show that the result of this method is highly dependent to the initial guesses. In some cases, the approximated curve-fitting solution can be very close to the experimental data, however, the hyperelastic parameters can be very different to the actual ones despite the fact that a very good curve-fitting solution (high coefficient of correlation) may be achieved. To overcome this problem, we demonstrate the application of a derivative free (black box) optimization method called particle swarm optimization (PSO) for hyperelastic characterization of nonlinear materials using least square method. Using multiple search agents in PSO makes this method highly inclined to end up with global optimum points in the search space. In this study, the hyperelastic parameters for Ogden and Mooney-Rivlin hyperelastic models are found for bovine brain tissue by using the experimental uniaxial compression test data. The PSO method yields high coefficient of correlation for curve fitting and its results is comparable to the LM method in terms of accuracy of parameters. It is concluded that PSO can be successfully used for nonlinear hyperelastic characterization of soft materials such as brain tissue.