Modified Kelvin-Voigt fractional derivative model for viscoelasticity measurement in optical coherence elastography

Optical coherence elastography(OCE) can quantitatively obtain the viscoelasticity of tissues using rheological models and is widely applied to the clinical diagnosis of diseases. However, commonly used rheological models in OCE do not account for the distinctive dependence of high-frequency storage and loss moduli on frequency in tissues, which results in the rheological models failing to accurately measure the viscoelastic properties of tissues. In this paper, a modified Kelvin-Voigt fractional derivative model is presented based on the power-law behavior of soft tissues and the dependence of high-frequency complex shear modulus on frequency in living cells. In the rheometer and OCE tests, the modified model can provide the prediction of the power-law relationship between the low-frequency shear viscosity and frequency; compared with the Kelvin-Voigt and Kelvin-Voigt fractional derivative models, the modified model has a higher goodness-of-fit(accuracy >96%)for the high-frequency storage moduli of gelatin phantoms. Furthermore, the proposed model can reduce the root mean square error of fit by approximately 83% for the high-frequency(1–128 kHz) storage modulus of the polydimethylsiloxane phantoms obtained from publicly available data. Overall, the modified model accurately predicts the mechanical properties of biomimetic materials over a wide frequency range, with the potential to more accurately reflect pathological changes in tissues.