Non-minimum phase viscoelastic properties of soft biological tissues

Understanding the viscoelastic properties of biological tissues is important because they can reveal tissue structure. This study analyzes the viscoelastic properties of soft biological tissues using a fractional dynamics model. We conducted a dynamic viscoelastic test on several porcine samples, i.e., liver, breast, and skeletal muscle tissues, using a plate-plate rheometer. We found that some soft biological tissues have non-minimum phase properties, i.e., the relationship between compliance and phase delay is not uniquely related to the non-integer derivative order in the fractional dynamics model. The experimental results show that the actual phase delay is larger than that estimated from compliance. We propose an empirical model to represent these non-minimum phase properties; a fractional Maxwell model with the fractional Hilbert transform term is proposed. The model and experimental results were highly correlated in terms of compliance and phase diagrams, and complex mechanical impedance. We also show that the amount of additional phase delay, defined as the increase in actual phase delay compared to that estimated from compliance, differs with tissue type.