Using uniaxial pseudorandom stress stimuli to develop soft tissue constitutive equations

A nonlinear systems identification method was used to develop constitutive equations for soft tissue specimens under uniaxial tension. The constitutive equations are developed from a single test by applying a pseudorandom Gaussian (PGN) stress input to the specimen, measuring the resulting strain, and calculating the Volterra-Wiener kernels. First and second order kernels were developed for two tissues with widely different properties, rat medial collateral knee ligaments, and rat skin. These kernels were used to predict the strain response to a variety of sinusoidal stress inputs. These predicted strains were compared with the measured strain response using the normalized mean squared error (NMSE). Results showed NMSEs in the range of 0.01-0.08 provided that the magnitudes of the applied stresses were present in the original PGN stress input. Overall, the method provides a means to develop soft tissue constitutive equations that can predict both nonlinear and viscoelastic behavior over a wide range of stress inputs.