Crossover Frequency as a Model-Independent Viscoelastic Constant for Soft Tissue Biomechanics

TL;DR

This study introduces the crossover frequency as a model-independent biomarker for soft tissue viscoelasticity, enabling consistent tissue characterization across different elastography models and fitting strategies.

Contribution

The paper proposes the crossover frequency as a universal viscoelastic constant, validated across tissues and independent of the chosen material model or fitting method.

Findings

Crossover frequency accurately reflects tissue viscoelastic behavior.

It distinguishes different brain regions and separates brain from liver tissue.

Median crossover frequencies vary significantly across tissue types.

Abstract

Magnetic resonance elastography (MRE) and related elastography techniques are emerging as quantitative diagnostic tools for assessing tissue microstructure and pathology. To determine descriptive parameters of the tissues' properties, a frequency-dependent viscoelastic material model is required, which is calibrated to the measured response in a parameter identification process. However, the selection of this model and the fitting strategy is challenging, since it may influence the identified viscoelastic parameters notably. Here, we address this limitation by proposing the crossover frequency (fc, defined as the frequency at which storage and loss moduli intersect G'(fc) = G''(fc)) as a model-independent viscoelastic constant for soft tissues. Fresh porcine specimens of the corona radiata, the putamen, the thalamus, and the liver were investigated using tabletop MRE and the frequency-dependent viscoelasticity was characterized with a fractional Kelvin-Voigt model. By validating the crossover frequency against the viscoelastic parameters, we demonstrated that the crossover frequency accurately reflects the viscoelastic behavior, independent of the material model or the fitting strategy. Across all samples, fc distinguished brain regions and separated brain from liver tissue by median frequencies of 85Hz (95% CI: 69-269Hz) in the corona radiata, 423Hz (95% CI: 316-575Hz) in the putamen, 426Hz (95% CI: 302-601Hz) in the thalamus and 1174Hz (95% CI: 1074-1300Hz) in the liver (p<0.001). These results suggest that crossover frequencies capture distinct viscoelastic fingerprints without requiring viscoelastic model selection. The crossover frequency may therefore serve as a practical, model-independent biomaterial constant to improve comparability of viscoelastic measurements across elastography studies.