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

Hongmei Zhang, Ying Guo, Yan Zhou, Hongrui Zhu, Pengying Wu, Kai Wang, Litao Ruan, Mingxi Wan, Michael F. Insana

Research output: Contribution to journalArticle


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 (R2 > 0.99) compared with traditional elastic models (R2 < 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 α, and viscosity τ among healthy, benign, and malignant groups. Malignant breast tissues show low-value, broad-distributions in E0 and with high fluidity α as compared with healthy and benign tissues. Second, histograms of E0 and α provide distinctive features by fitting to Gaussian mixture (GM) models. The histograms of E0 and α 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 α 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: [Figure not available: see fulltext.].

Original languageEnglish (US)
JournalBiomechanics and Modeling in Mechanobiology
StateAccepted/In press - 2020


  • Cellular mechano-biology
  • Gaussian mixture (GM) model
  • Histopathology correlation
  • Indentation-type atomic force microscopy (IT-AFM)
  • Viscoelastic biomarker

ASJC Scopus subject areas

  • Biotechnology
  • Modeling and Simulation
  • Mechanical Engineering

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