Wide-band multifrequency MR elastography with a fractional viscoelastic model and nonlinear inversion for enhanced viscoelastic parameter mapping
Bibliographic record
Abstract
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 ( ), fractional exponent ( ), and reference frequency ( ) parameters from which frequency-dependent storage ( ), loss ( ), and magnitude ( ) shear moduli are derived. Robustness was verified in COMSOL models containing three stiff inclusions; even with 5% Gaussian noise, was recovered with 12% accuracy and and with 5 % accuracy, while spatial contrast was preserved. Tofu–polyvinyl alcohol (PVA) phantom tests produced two-fold contrast and clear and 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 ( ), 1.10 ( ) and 1.65 ( ), comparable to clinical T2-weighted contrast (∼1.8). A representative colorectal metastasis with a necrotic core showed low and but elevated and 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, (baseline stiffness), (power-law dispersion), and (transition frequency), and corresponding frequency-dependent moduli ( , , ). 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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".