Simple empirical model for identifying rheological properties of soft biological tissues

Understanding the rheological properties of soft biological tissue is a key issue for mechanical systems used in the health care field. We propose a simple empirical model using fractional dynamics and exponential nonlinearity (FDEN) to identify the rheological properties of soft biological tissue. The model is derived from detailed material measurements using samples isolated from porcine liver. We conducted dynamic viscoelastic and creep tests on liver samples using a plate-plate rheometer. The experimental results indicated that biological tissue has specific properties: (i) power law increase in the storage elastic modulus and the loss elastic modulus of the same slope; (ii) power law compliance (gain) decrease and constant phase delay in the frequency domain; (iii) power law dependence between time and strain relationships in the time domain; and (iv) linear dependence in the low strain range and exponential law dependence in the high strain range between stress-strain relationships. Our simple FDEN model uses only three dependent parameters and represents the specific properties of soft biological tissue.