Wide-band multifrequency MR elastography with a fractional viscoelastic model and nonlinear inversion for enhanced viscoelastic parameter mapping.

Abstract

Magnetic resonance elastography (MRE) typically relies on external vibrations, potentially missing diagnostically relevant low-frequency responses. This study presents a wide-band multifrequency MRE framework that combines intrinsic cardiac motion (≈1 Hz) with conventional 30-60 Hz actuation and reconstructs tissue mechanics with a three-parameter Kelvin-Voigt fractional-derivative (KVFD) model. Subzone nonlinear inversion estimates the baseline stiffness (θ₀), fractional exponent (α), and reference frequency (ω_o) parameters from which frequency-dependent storage (G^'), loss (G″), and magnitude (|G^*|) shear moduli are derived. Robustness was verified in COMSOL models containing three stiff inclusions; even with 5 % Gaussian noise, θ_o was recovered with 12 % accuracy and α and ω_o with 5 % accuracy, while spatial contrast was preserved. Tofu-polyvinyl alcohol (PVA) phantom tests produced two-fold θ_o contrast and clear α and ω_o differentiation between poroelastic tofu and stiff PVA, confirming sensitivity to both stiffness and dispersion. In-vivo, intrinsic-extrinsic MRE was performed in seven patients with hepatic metastasis. Across tumors, the mean contrast-to-noise ratios were 1.30 (θ_or), 1.10 (α_r) and 1.65 (ω_or), comparable to clinical T2-weighted contrast (∼1.8). A representative colorectal metastasis with a necrotic core showed low |G^*| and θ_o but elevated α and ω_o centrally, mirroring established MRE signatures of necrosis. Sensitivity analysis demonstrated < 5 % parameter drift for ±30 % initial-value perturbations and a 115 % error increase when the 1 Hz data point was omitted, underscoring the value of the low-frequency anchor. Overall, integrating low-frequency intrinsic motion with KVFD modeling yields stable, spatially resolved biomarkers that capture frequency-dependent behavior invisible to conventional high-frequency MRE, advancing lesion detection and characterization. STATEMENT OF SIGNIFICANCE: Magnetic resonance elastography (MRE) typically probes a narrow high-frequency band (30-60 Hz), missing diagnostically rich low-frequency behavior. We present a wide-band, multifrequency MRE framework that fuses intrinsic cardiac motion (∼1 Hz) with conventional external actuation and reconstructs viscoelasticity using a three-parameter Kelvin-Voigt fractional derivative (KVFD) model. The approach yields interpretable parameters, θ_o(baseline stiffness), α(power-law dispersion), and ω_o(transition frequency), and corresponding frequency-dependent moduli (G^'(ω), G″(ω), |G^*(ω)|). Validation across COMSOL simulations, tofu-PVA phantoms, and in-vivo liver metastasis shows robust convergence under noise, stable parameter recovery, and lesion contrast comparable to clinical MRI, while revealing dispersion not captured by standard MRE. This work expands MRE's mechanical bandwidth and delivers spatially resolved biomarkers relevant to oncology and to engineered biomaterials whose function depends on frequency-dependent mechanics.