A silicone gel (Sylgard 527, Dow Corning, Elizabethtown, KY) was repeatedly tested with dualMRI to analyze the precision of this technique. A separately validated loading device33 (link) was used to compress a 1.5-cm thick imaging phantom within the 3.0 T clinical MRI system to 18.5 N for 1.5 s, every 3.0 s. Spatial resolution was varied by using different acquisition matrix sizes (256 × 256/384 × 384/512 × 512 pixels) while maintaining a fixed slice thickness (3 mm) and field of view (180 × 180 mm). Image acquisition parameters necessarily changed with the varying acquisition matrix size and were as follows: echo time (TE) = 62/72/82 ms respectively, effective repetition time (TR) = 3000 ms, number of averages (NA) = 8. To compute precision, 16 evenly spaced points of interest were selected within the deformed image of the silicone phantom. The pooled standard deviation of the displacement and strain values at these points of interest, across five repeated experimental measures, were defined as the precision33 (link)34 (link)36 (link) and computed as a function of the number of smoothing cycles (Fig. 3A,B).
Simulated deformations were generated using a model of contact between femoral and tibial cartilage ROIs in finite element analysis software (COMSOL Multiphysics v3.2, Burlington, MA) (Fig. 3C). The Monte Carlo method was used to study the propagation of error to strain calculations using MATLAB (Mathworks, Natick, MA) with 100 repeated simulations and randomly distributed noise51 (link). Within each simulation, displacement noise was added according to the standard deviation of displacements before smoothing, as determined for the 384 × 384 acquisition matrix, and noisy displacements were smoothed (Fig. 3D) to permit estimation of strain. The displacement and strain bias was computed as the difference between the ideal values and the values after smoothing in 12 evenly distributed points within the ROIs across the 100 simulations, similar to previous studies51 (link).
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