  Understanding the visocoelastic properties of soft biological tissues is
important for progress in the field of human healthcare. 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, namely liver, breast, and skeletal muscle tissues, using a
plate--plate rheometer. We found that some soft biological tissues have
non-minimum phase properties; that is, 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 a fractional
dynamics model with the fractional Hilbert transform to represent these
non-minimum phase properties. 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.
