Fractional Order Models for Viscoelasticity of Soft Biological Tissues

Dynamic mechanical properties of soft tissues provide information that may be used in medical diagnosis. Developing a better fundamental understanding of the governing constitutive relations could improve diagnostic techniques. The mechanical behavior of soft tissues and tissue mimicking phantoms, such as gels, can be represented by viscoelastic material models. Static loading of viscoelastic materials yields information related to elasticity, creep and stress relaxation. However, a broader measure of rate-dependent properties that affect mechanical wave propagation and wave attenuation in such materials can only be extracted from measured response to dynamic excitation. The well known linear viscoelastic material models of Voigt, Maxwell and Kelvin cannot represent the more complicated frequency dependency of these materials over a broad spectral range. Therefore, fractional calculus methods have been considered to model the viscoelastic behavior of soft tissue-like materials. Fractional order models capture the viscoelastic material behavior using fractional orders of differential equations that may yield a more accurate representation of viscoelastic material behavior. This paper focuses on experimental measurements on the tissue mimicking phantom, CF11. Surface waves on the phantom material are studied experimentally and theoretically. Theoretical calculations using linear and fractional order methods are compared with experimental measurements.