Characterisation of the soft tissue viscous and elastic properties using ultrasound elastography and rheological models: validation and applications in plantar soft tissue assessment

Abstract

Objective. The mechanical behaviour of soft tissue is influenced by its elastic and viscous characteristics. Therefore, the aim of this study was to develop a validated method to characterise the viscoelastic properties of soft tissues based on ultrasound elastography data. Approach. Plantar soft tissue was chosen as the tissue of interest, and gelatine-phantoms replicating its mechanical properties were manufactured for validation of the protocol. Both plantar soft tissue and the phantom were scanned using Reverberant shear wave ultrasound (US) elastography at 400–600 Hz. Shear wave speed was estimated using the US particle velocity data. The viscoelastic parameters were extracted by fitting the Young’s modulus as a function of frequency derived from the constitutive equations of the eight rheological models (four classic and their fractional-derivative versions) to the shear wave dispersion data. Furthermore, stress-time functions derived from the eight rheological models were fitted to the phantom stress-relaxation data. Main results. The viscoelastic parameters estimated using elastography data based on the fractional-derivative (FD) models, compared to the classic models, were closer to those quantified using the mechanical test. In addition, the FD-Maxwell and FD-Kelvin–Voigt models showed to more effectively replicate the viscoelastic behaviour of the plantar soft tissue with minimum number of model parameters ( $R^2$ = 0.72 for both models) . Hence the FD-KV and FD-Maxwell models can more effectively quantify the viscoelastic characteristics of the soft tissue compared to other models. Significance. In this study, a method for mechanical characterisation of the viscoelastic properties of soft tissue in ultrasound elastography was developed and fully validated. An investigation into the most valid rheological model and its applications in plantar soft tissue assessment were also presented. This proposed approach for the characterisation of viscous and elastic mechanical properties of soft tissue has implications in assessing the soft tissue function where those can be used as markers for diagnosis or prognosis of tissue status.