Fluidity and elasticity form a concise set of viscoelastic biomarkers for breast cancer diagnosis based on Kelvin–Voigt fractional derivative modeling

Abstract

Cancer progression involves biomechanical changes within transformed cells and the surrounding extracellular matrix (ECM). The viscoelastic features of fluidity and elasticity that are based on a novel Kelvin–Voigt fractional derivative (KVFD) model were found capable of discriminating normal, benign and malignant breast biopsy tissues on the cellular scale. The improved specificity of KVFD model parameters derives from greater accuracy of fitting the entire approaching force-indentation measurement curve ($R^{2}$ > 0.99) compared with traditional elastic models ($R^{2}$ < 0.86). Moreover, model parameters can be interpreted in terms of histopathological features. First, statistical comparisons reveal there are significant differences (p < 0.001) in elasticity E₀, fluidity $\alpha$, and viscosity $\tau$ among healthy, benign, and malignant groups. Malignant breast tissues show low-value, broad-distributions in E₀ and with high fluidity $\alpha$ as compared with healthy and benign tissues. Second, histograms of E₀ and $\alpha$ provide distinctive features by fitting to Gaussian mixture (GM) models. The histograms of E₀ and $\alpha$ are best fit by two kernels GM for malignant tissues, indicating that the cells are soft but with high fluidity and the ECM is stiff but with low fluidity. However, the data suggest one-kernel GM model for benign tissue and a patched uniform distribution for healthy tissue. Third, using fluidity $\alpha$ as the test statistic, the area under the receiver operator characteristic curve (AUC) is 0.701 ± 0.012 (p < 0.0001) for control versus malignant and 0.706 ± 0.013 (p < 0.0001) for benign versus malignant group. Variations in tissue fluidity and elasticity offer a concise set of viscoelastic biomarkers that correlate well with histopathological features.

Graphic abstract