Combining quasi-static and high frequency experiments for the viscoelastic characterization of brain tissue

TL;DR

This study addresses the challenge of inconsistent brain tissue mechanics across time and length scales by integrating quasi-static large-strain rheology and tabletop magnetic resonance elastography on porcine brain regions corona radiata, putamen, and thalamus. It uses region-specific measurements and calibrates a fractional Kelvin-Voigt model with two fractional elements in parallel to unify the low- and high-frequency responses, aided by a two-term Prony series in the quasi-static domain. The main findings show consistent regional trends across domains, with the corona radiata remaining the stiffest and showing stronger viscous contributions at high frequency; the model accurately captures the wide-frequency behavior. The work provides a practical framework for comprehensive brain tissue characterization, with implications for neurosurgical planning, injury prediction, and disease modeling.

Abstract

Mechanical models of brain tissue are a beneficial tool to simulate neurosurgical interventions, disease progression, or brain development. However, the accuracy and predictive capacity of such a model relies on a precise experimental characterization of the tissue's mechanical behavior. Such a characterization is yet limited by inconsistent or contradictory experimental responses reported in the literature, particularly when measurements are performed in different time or length scales. Although brain tissue has been extensively investigated in previous studies, the combination of experimental findings from different scales has received limited attention. In this study, we combine ex vivo mechanical responses of porcine brain tissue obtained at different time scales in a mechanical model. We investigated the mechanical behavior of three different brain regions in the quasi-static domain with multi-modal large strain rheometer measurements and at high frequencies with magnetic resonance elastography (MRE). A comparative analysis of the mechanical parameters obtained from both experimental techniques demonstrated consistent regional variations in the viscoelastic behavior across the two domains. However, the mechanical behavior changes from a higher elasticity in the quasi-static and low frequency domain to a dominating viscosity at high frequencies. Based on the quasi-static and the high frequency behavior, we calibrated a fractional Kelvin-Voigt model and consequently unified the two responses in a single mechanical model to obtain a comprehensive characterization of the tissue's mechanical behavior.

Figures (10)

• Figure 1: Exemplary samples of a) the rheometer experiment on brain, b) the tabletop MRE on the thalamus and c) the corona radiata with gray matter. The white bars have a length of 10mm
• Figure 2: Comparison of the averaged storage and loss modulus for the corona radiata samples in which the full image was used for the data analysis (CR Full, $n = 7$) and in which gray matter parts were excluded from the image (CR, $n = 9$).
• Figure 3: Comparison of the stress response obtained in multi-modality rheometer experiments for the corona radiata (CR), the putamen (P) and the thalamus (T). The averaged response under a) cyclic compression-tension, b) compression relaxation, c) tension relaxation, d) 15% shear strain and e) 30% shear strain with the corresponding maximum and minimum stresses under cyclic loading and the relaxed stress after 300s in the relaxation test. Statistically significant differences between the groups are marked with '*' for $p < 0.05$.
• Figure 4: Comparison of hyperelastic parameters. Shear moduli $\mu_i$ and nonlinearity parameters $\alpha_i$ of the two-term Ogden model and the initial shear modulus $\mu_0$ for the corona radiata (CR), the putamen (P) and the thalamus (T). Solid lines donate the medians, dashed lines the mean values and outliers are marked in red. Statistically significant differences between the groups are marked with '*' for $p < 0.05$.
• Figure 5: Comparison of the viscoelastic parameters. Prony parameters $g_i$ and $k_i$ and the relaxation times $\tau_i$ of the two-term Prony series for the corona radiata (CR), the putamen (P) and the thalamus (T). Solid lines donate the medians, dashed lines the mean values and outliers are marked in red. Statistically significant differences between the groups are marked with '*' for $p < 0.05$ and '**' for $p<0.01$.