A discrete-time nonlinear Wiener model for the relaxation of soft biological tissues

The present paper is devoted to introducing discrete-time models for the relaxation function of soft biological tissues. Discrete-time models are suitable for the analysis of sampled data and for digital simulations of continuous systems. Candidate models are searched for within both linear ARX structures and nonlinear Wiener models, consisting of an ARX element followed in cascade by a polynomial function. Both these discrete-time models correspond to sampling continuous-time exponential function series, thus preserving physical interpretation for the proposed relaxation model. The estimation data set consists of normalized stress relaxation curves drawn from experiments performed on samples of bovine pericardium. The normalized relaxation curves are found to be almost insensitive to both the magnitude of strain and the loading direction, and so a single model for the whole relaxation curves is assumed. In order to identify the parameters of the Wiener model an iterative algorithm is purposely designed. Over the ARX one, the nonlinear Wiener model exhibits higher capability of representing the experimental relaxation curves over the whole observation period. The stability of the solution for the iterative algorithm is assessed, and hence physical interpretation as material properties can be attached to the parameters of the nonlinear model. Suitable features of the Wiener model for computational application are also briefly presented.