Inverse Parameter Fitting of Biological Tissues: A Response Surface Methodology

D.R. Einstein, A.D. Freed, and I. Vesely (USA)


Response surface method, computational modeling, heart valves, LS-OPT, ADINA


In this paper, we present the implementation of a global inverse method based on the response surface method. We illustrate the approach by way of the parameter fitting of aortic sinus tissue. First, we investigated the sensitivity of the method to experimental noise and to initial parameter values. We found that the method was able to reliably recover parameters after few iterations, and that modest noise added to the data had little effect on the estimated parameters and on the rate of convergence. Parameters were then fit to a nonlinear anisotropic constitutive equation, for aortic sinus and aortic wall. Simulations and materials tests for the aortic sinus data consisted of two orthogonal uniaxial tests, the experimental targets being measured force at a given displacement. Predictions with converged parameters showed excellent agreement with the data in both cases. We found that the method was able to consistently identify model parameters and that it was robust in the presence of experimental noise. We believe the method will find wide application in tissue material characterization and in diagnostic imaging.

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