near the center of the increased stiffness inclusion were compared to the MR magnitude inclusion to determine the spatial accuracy, and manual segmentation of the background and inclusion using the MR magnitude image allowed the quantitative accuracy of each inversion technique to be evaluated, by comparison with DMA measurements. 4 RESULTS Figure 2 shows images from 3 phantom datasets. From left to right, images are MR magnitude, iterative MRE stiffness shear modulus of the background and inclusion for the 4 phantom datasets, along with SNR and DMA results. Table 1: Modulus estimates of the background and inclusion shear modulus of the gelatin phantoms shown in figure 2, for iterative MRE, Direct inversion MRE, and independent dynamic mechanical analyzer measurements (units of kPa, given as median ±standard deviation). Manual segmentation of the inclusion using the MR magnitude image was used to produce the MRE values, which use data from the full 3D modulus estimate. Background Inclusion Iterative Inversion Direct Inversion DMA Iterative Inversion Direct Inversion DMA 3.1±0.5 3.7 ±1.5 3.3 ±0.8 8.3±1.2 7.9±2.7 8.8±0.9 3.0±0.4 2.9 ±1.0 3.3 ±0.8 8.2±1.2 7.2±2.3 8.8±0.9 2.25±0.35 2.9 ±0.9 3.3 ±0.8 6.0±0.4 20±5 8.8±0.9 5 DISCUSSION Results in gelatin phantoms presented in Fig. 2 show both iterative and direct inversion MRE achieve good spatial accuracy, boundaries of the stiff inclusions are clear in the shear modulus images for both techniques. Direct inversion appears to resolve the point of the conical inclusion better than iterative inversion, most likely because of the spatial continuity requirement enforced by the finite element support of the shear modulus in the iterative inversion algorithm, which is effectively a smoothing operation in areas of rapid spatial changes in shear modulus. Numerical accuracy of the iterative inversion is better, direct inversion shows both over and underestimation of the inclusion stiffness, however background stiffness estimates were accurate for both techniques. The choice of which inversion technique to use is dependent on many factors. Obviously, accurate images are desirable so that artifacts and inaccuracies do not affect the diagnostic information provided by the images. If this was the only consideration, results form this study indicate that iterative inversion would be the most appropriate method. However, another important factor is the processing time, where Direct Inversion is orders of magnitude faster than iterative methods (seconds on a desktop computer compared to hours on a specialized multi-processor cluster). The iterative algorithm used in this study is not optimized for speed, development of robust convergence criteria could cut down on unnecessary iterations, and more efficient optimization strategies could also provide a speedup, however processing time would likely still be on the order of hours. Faster inversions fit much better into a clinicians workflow, MRE processing could be performed immediately after imaging, rather than having to wait hours for processing to be complete. Each MRE application must decide whether the better quantitative accuracy of iterative inversion is worth the increase in computational load and processing time. Iterative methods have the advantage of being able to use different material models, such as poroelasticity [9, 10], which regarded as an appropriate model for fluid saturated materials such as brain tissue. There is currently no comparable direct inversion technique for poroelastic materials such as brain tissue, due to the increase in complexity of the governing constitutive equation. A more detailed analysis of the advantages and disadvantages of iterative and direct inversion MRE, involving a larger collection of phantoms, and in vivo biological data is required to provide enough information to allow the important decision of which inversion strategy to use to be made. This work is currently underway. 53 estimate, Direct Inversion MRE stiffness estimate images, and a line profile through the inclusion. Table 1 gives the median
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