An optimized differential evolution algorithm for constitutive model fitting of arteries

The mechanical properties of arteries are often assessed with biaxial testing. Constitutive models are fitted to the experimental stress-stretch responses to determine relations describing the intrinsic characteristics of the material. Nonlinear least square-based optimization routines and the Levenberg-Marquardt and Trust-Region-Reflective algorithms are commonly used for fitting. But they may not always produce the best fit for the experimental data. We describe a different optimized fitting routine that can significantly improve the constitutive model fit quality. Experimental stress-stretch data were obtained from biaxial testing of 16 human superficial femoral arteries. A metaheuristic population-based algorithm, Differential Evolution (DE), and loss functions based on the Minkowski and Chebyshev Distance functions were used to improve the fit with common constitutive relations. Hyperparameter tuning by grid search method was performed to determine how algorithm settings affect the fit quality. The DE algorithm showed a superior fit in all samples compared to the traditional algorithms. The loss functions based on Minkowski Distance and Chebyshev relations rather than the square error produced better fits. This allows describing the experimental data with simpler constitutive relations that have fewer material parameters, which reduces the complexity and improves the efficiency of computational implementations.