Introduction

Magnetic resonance elastography (MRE) has shown promise in resolving local mechanical properties related to the microstructure of the human brain.^1-3 The nonlinear inversion (NLI) algorithm provides an avenue for more accurate and reliable property maps through its inhomogeneous finite-element formulation.^4-6 In order for NLI-MRE to provide patient-specific estimates, it is necessary to accurately reconstruct viscoelastic material properties in relatively small heterogeneous regions in the brain.⁴ To reduce computational burden,¹ NLI decomposes the entire domain into a set of overlapping smaller regions of a specified size (subzones), where an iterative conjugate gradient (CG) optimization process updates an estimate of the mechanical properties. The subzone solutions are collected, smoothed, and the subzone process is repeated with new randomly generated subzones until the property estimate converges. This study aims to characterize the effect of two major inversion parameters – subzone size and CG iterations – on the reconstruction of local mechanical properties. The parameters are chosen based on independent measurements with dynamic mechanical analysis (DMA) in phantoms and convergence criteria in a human subject.

Methods

One healthy subject underwent eight repeated MRE experiments, with diffusion tensor imaging (DTI) and high-resolution T1-weighted anatomical imaging for registration^1,8 acquired in tandem. A Resoundant pneumatic driving system applied 50 Hz vibrations to the head to generate shear waves; MRE phase imaging captured the complex displacement field;⁷ and NLI estimated the material property maps.^4,5 Imaging was performed on a Siemens 3T Trio scanner with 32-channel head coil. MRE imaging parameters included: two-shot in-plane spiral readout with SENSE (R = 2); ten slabs of eight sampling planes with 25% slab overlap; TR/TE = 1800/73 ms; four (4) temporal phase offsets; and FOV = 240x240x120 mm with 2x2x2 mm³ isotropic spatial resolution.¹ All experimental conditions were consistent between datasets, leaving scanner each time. We processed displacement datasets using NLI with a range from 1 to 5 CG iterations and subzone sizes based on expected shear wavelength, $$$L_s = \frac{1}{f} \sqrt{G’/\rho}$$$. We prescribed cubic subzones with edge lengths of $$$L_s/4$$$, $$$L_s/2$$$, $$$0.64L_s$$$, $$$3L_s/4$$$, and $$$L_s$$$. The reference shear wavelength for the phantom is $$$23.5 ~\mathrm{mm}$$$ and $$$30.6~\mathrm{mm}$$$ for the human brain. The $$$0.64L_s$$$ subzone is included as the "standard" size, which, along with CG=2, was chosen based on the experience of stability and convergence in numerical, phantom, and in vivo studies described in previous works.^1-3,5-7

Results and Discussion

The size of the subzones and the CG iterations are two of the most dominant parameters affecting the reconstruction of the viscoelastic shear modulus (G = G' + i G''); see Figures 1 and 2. Figure 1, and the accompanying statistics for an inclusion (large bottom-right) in Figure 3, show an optimal subzone size near $$$3L_s/4$$$ and increasing CG iterations improves the estimate towards the DMA results. The much softer surrounding silicone appears to affect the NLI material reconstruction. Figure 2 shows results from this subzone size have pronounced rigidity in the region of the falx cerebri, known to be stiff compared to healthy brain tissue, but only for the largest subzone ($$$L_s$$$). Figure 4 shows a proposed convergence criteria defined relative to the variation of properties with last ten global iteration in NLI: variation relative to mean (“percent”) and variation relative to [Pa] threshold (“constant”). The convergence criteria highlight the stability of the reconstructed values on a voxel-wise basis. Specifically, we report the percent of voxels in the region mask that are converged according to the specific criteria. Figure 5 shows the effect of the convergence criteria on the reported statistics (average and standard deviation) for the superior longitudinal fasciculus (SLF) white matter region. The statistics for each convergence criteria are nearly identical and unchanged above 300 global iterations, but decreasing the threshold level improves the confidence in the final statistics.

Conclusions

Choosing the optimal MRE-NLI parameters is a balance between the subzone containing sufficient spatial resolution to capture complex internal property features while not allowing regions not appropriately modeled, like the falx, to corrupt surrounding tissue estimates. In the phantom, the NLI reconstructions matched the expected contrast but did not exactly match the DMA results; however, increasing the number of CG iterations improved the estimate and was likely affected by the surrounding soft background. The proposed convergence criteria show the capability of capturing the full statistics of an important white matter region while improving the confidence in the final reported statistics. This allows NLI-MRE to be tailored to the material or tissue under investigation by choosing the subzone based on expected bulk properties and a priori convergence criteria can ensure accurate estimations.

Acknowledgements

Support for ATA and JGG was provided by NSF Grant CMMI-1437113. Partial support was provided by the Biomedical Imaging Center of the Beckman Institute for Advanced Science and Technology at the University of Illinois at Urbana-Champaign (UIUC), NIH Grant R01-EB018230, and NIH/NIBIB Grant R01-EB001981. This research is part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (awards OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications.

References

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