Synopsis

Correlation time ($\tau_c$) is an intrinsic property of molecules that can be probed from $T_{1\rho}$ dispersion measurement. The aim of this study was to evaluate the effect of low and high spin-lock frequencies (SLFs) on $\tau_c$ fitting and to find the optimum SLFs set within the typical clinical range. One bovine and two human cartilage samples were scanned to obtain $T_{1\rho}$ dispersion with 22 SLFs between 10 to 2500 Hz. $\tau_c$ maps were obtained by fitting Lorentzian function to different subsets of $T_{1\rho}$ dispersion. Our results show that $\tau_c$ fitting is significantly affected by low SLFs compared to high SLFs.

Introduction

Methods

Samples

This study utilized cylindrical osteochondral plugs (diameter = 6mm) of patellar cartilage from bovine (one plug) and human cadavers obtained from donors (two plugs, one per knee).

MRI

MRI was performed at 9.4 T using a 19 mm quadrature RF volume transceiver and VnmrJ3.1 Varian/Agilent DirectDrive console. The samples were imaged at room temperature and relaxation time measurements were realized using a global preparation-block coupled to a single slice FSE readout (TR=5s, Echo spacing=5.5ms, ETL=8 with centric echo ordering, matrix=256x64 (bovine sample) or 256x80 (human samples), FOV=16x12.8mm (bovine sample) or 16x16mm (human samples) and 1mm slice thickness, yielding a resolution of 62.5µm along cartilage depth). A single imaging slice was positioned at the center of the specimen, perpendicular to the axis of specimen. The measurements included CW-$T_{1\rho}$ dispersion with 22 SLFs⁴ (10, 20, 30, 50, 75, 100, 125, 150, 200, 250, 300, 400, 500, 600, 700, 800, 1000, 1200, 1500, 1800, 2200, 2500 Hz) and five spinlock times (0, 24, 48, 96, 192 ms).

Data analysis

$T_{1\rho}$ maps were fitted pixel-wise using two-parametric mono-exponential function. $\tau_c$ maps were obtained by fitting a Lorentzian function⁵

$$\frac{1}{T_{1\rho}}=\frac{3A \tau_c}{1+4\omega_{SL}^{2}\tau_c^{2}}+B,$$

to $T_{1\rho}$ dispersion data, where ω_sl is the SLF, and A, B and $\tau_c$ are the fitting parameters. Outlier $\tau_c$ pixels, identified as those with values <1 ms in $T_{1\rho}$ maps at SLF of 0 Hz calculated from $\tau_c$ fitting function, were excluded from further analysis. Data analysis was performed using in-house developed MATLAB scripts and plugin functions for Aedes.⁶ To investigate the role of low and high SLFs on $\tau_c$ fitting, $\tau_c$ maps were fitted from different subsets of the $T_{1\rho}$ dispersion data. Influence of higher SLFs was explored by comparing datasets with different range of SLFs while fixing the lowest SLF (e.g. set1: 10-2500 Hz, set2: 10-2200 Hz,…). Similarly, low SLFs were studied by comparing datasets with different range of SLFs while fixing the highest SLF (e.g. set1: 10-2500 Hz, set2: 20-2500 Hz,...). Resulting $\tau_c$ maps were evaluated using mean difference and Pearson correlation coefficients with reference $\tau_c$ map (fitted using full-range dispersion, 10-2500 Hz). To find the optimum distribution of SLFs for $\tau_c$ fitting in frequency range 10-500 Hz, fitting was applied to data from all possible combinations for 4, 5, 6, 9 and 12 SLFs. Resulting $\tau_c$ maps were compared pixel-by-pixel with a reference $\tau_c$ map fitted using all 13 SLFs (10-500Hz). Percentage of absolute mean difference between each tested and reference $\tau_c$ map for each sample was calculated. Results of both human samples were averaged to form one dataset.

Results

After dropping more than two low-frequency SLFs from the fitting data, correlation of $\tau_c$ maps with the full-range $\tau_c$ reference map dropped from 0.63 to -0.10 (Figure 1-a and Figure 2-a). However, even after leaving out 13 high SLFs from fitting, $\tau_c$ map showed correlation of 0.59 compared to the full-range $\tau_c$ reference map (Figure 1-b and Figure 2-b). Best selections of 12, 9, 6, 5 and 4 SLFs resulted in $\tau_c$ maps with mean difference in the range of 1-10% in bovine sample, 5-46% in human samples, compared to the 13 SLFs reference map (Figure 3). $\tau_c$ maps fitted from best SLFs combinations showed similar laminar appearance to the reference $\tau_c$ map (Figures 4 and 5).

Discussion and Conclusion

Acknowledgements

Research funding from Jane and Aatos Erkko Foundation and support from the Academy of Finland (grants #285909 and #293970) are gratefully acknowledged. We also thank CSC-IT Center for Science in Espoo, Finland, for computing time.

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