Laurel Hales^{1} and Feliks Kogan^{2}

^{1}Electrical Engineering, Stanford University, Stanford, CA, United States, ^{2}Radiology, Stanford University, Stanford, CA, United States

Given the use of T1rho as a measure of cartilage health and an early indicator for osteoarthritis, it is important to understand the T1rho relaxation mechanism including its somewhat unexplained angular dependence. In the hope of finding a range of spin-lock frequencies (FSLs) with a decreased angular dependence, we generated T1rho maps of in-vivo femoral knee cartilage at various FSLs from 100Hz to 1kHz. We found a visible angular dependence in T1rho measurements for all FSLs including 1kHz. If there exists a range of FSL with little or no angular dependence it is higher than 1kHz.

Using the qDESS data and an open source deep-learning analysis pipeline [10], we generated a segmentation of the femoral cartilage in the first qDESS echo (adjusted manually) and a T2 map [7]. The T1rho weighted images were registered to the first TSL image using affine image registration and then to the first qDESS echo using rigid and b-spline image registration. A T1rho map was then generated for each FSL by a pixel-wise mono-exponential fitting algorithm. All T1rho values greater than 120ms were discarded as not physiological for cartilage.

We estimated the angular orientation of the cartilage similarly to previously reported methods [5,11]. For each slice, the x and y values of each cartilage pixel were fitted using a least-squares circle fitting algorithm. The center point of the circle was used to calculate the angular orientation of each cartilage pixel as shown in Figure 2. We used only slices with a wide range of angular orientations and relatively smooth T1rho maps to maximize the accuracy of the angular estimates and decrease the effect of partial voluming. For better visualization, we combined the results from three or four neighboring slices and averaged T1rho values over angular bins of 5°.

To account for the approximate nature of the angle measures we used the location of peak values of T2 to identify the magic angle. T1rho dispersion curves were calculated at these and other angles by averaging all T1rho values from the combined data from neighboring slices found within 3 degrees of the angle of interest for each of the FSLs.

This analysis did not take into account the variation in structural organization between the different regions of articular cartilage meaning that within each angular bin there are collagen fibers with a wide range of orientations. We did not acquire images with sufficient resolution to perform a laminar evaluation of AD. This laminar variation in cartilage collagen orientation may account for the somewhat linear increase seen in the T1rho dispersion curves (Figure 5) instead of the sharp increases we expect. This steady increase could also be due to the noisy nature of the dispersion data. Figure 4 shows that for FSL above 550Hz there is less of a change in T1rho values measured with different FSL than there is for FSL below 550Hz. Indicating that there may be diminishing benefits for FSL above 550Hz.

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Figure 1: Image acquisition parameters for the three pulse
sequences used. Each participant was scanned using the qDESS sequence and one
of the other two.

Figure 2: A circle with the least-squares best fit to
the femoral cartilage was identified and the angular orientation of each
cartilage pixel was then determined as the angle between radial line from the
center of the circle to that point and the vertical line through the center of
the circle. The T1rho values were then averaged over bins of 5° (shown here)
or 6°.

Figure 3: T1rho maps with different spin-lock
frequencies (100 Hz (d), 250 Hz (a), 550 Hz (b and e), and 1000 Hz (c and f)). Note
how all three maps show the same regional variations although the magnitude
T1rho values are different.

Figure 4: T1rho
as a function of angular orientation relative to B0 for four representative regions
of cartilage. Estimated locations for magic angles are shown with dotted lines.
Note that all T1rho curves vary with angle in the same way that the T2 curves
do.

Figure 5: T1rho dispersion for various orientations
for four representative regions of cartilage. Although the curves are noisy it
is still clear that there is T1rho dispersion at the magic angle.