Introduction

$T_{1\rho}$ relaxation, known as the spin‐lattice relaxation time in the rotating frame, is sensitive to molecular interactions including dipolar interactions, chemical exchange, and diffusion. In the head and neck, $T_{1\rho}$ relaxation has been used to evaluate the early irradiated change in the parotid gland ¹ and differentiate the inflammatory and normal tissue ². In these studies, $T_{1\rho}$ is measured by using a mono-exponential relaxation model. However, the compartmentation of tissues may lead to bi- or multi-exponential $T_{1\rho}$ relaxation. Preliminary studies showed that $T_{1\rho}$ relaxation in muscle ³, cartilage ⁴, menisci ⁵ and brain ⁶ follows a bi-exponential decay. In this work, we report our observation of bi-exponential $T_{1\rho}$ relaxation in parotid glands on human subjects.

Method

Nine healthy volunteers (age $25.5\pm 3.5$, $3$ females and $6$ males) were scanned on a Philips Achieva 3.0T scanner (Philips Healthcare, Best, the Netherlands) under the approval of the institutional review board. The body RF coil was used as the transmitter and a 16-channel Philips neurovascular phased-array coil which covers the entire parotid glands was used as the receiver. Imaging parameters include: resolution 1.2 mm × 1.2 mm, slice thickness 5 mm with total 9 slices, TE/TR 4.9 ms/2500 ms, 12 TSLs for [0 5 8 12 15 25 35 45 60 70 80 90] ms, spin-lock frequency 400 Hz.
The data sets at 12 TSLs were fit to a mono-exponential model, $S_{mono}=S_{0}\cdot e^{-TSL/T_{1\rho, mono}}$ and a bi-exponential model based on Levenberg-Marquardt algorithm, $S_{bi}=S_{01}\cdot e^{-TSL/T_{1\rho, long}}+S_{02}\cdot e^{-TSL/T_{1\rho, short}}$, where $S_{0}$ and $S_{01}+S_{02}$ are scaling constants; $T_{1\rho, mono}$ is the $T_{1\rho}$ value fitted by the mono-exponential model; $T_{1\rho, long}$ and $T_{1\rho, short}$ represent the long and short component of the $T_{1\rho}$ in the bi-exponential model, respectively. The fractions of the pools with long and short $T_{1\rho}$ are defined as $f_{long} = S_{01}/(S_{01}+S_{02})$ and $f_{long} = S_{02}/(S_{01}+S_{02})$, respectively. Six ROIs for each subjects were contoured manually on the left parotid gland. The $T_{1\rho, mono}$, $T_{1\rho, long}$ and $T_{1\rho, short}$ and $f_{long}$ of six ROIs were calculated.
The residual sum of squares (RSS) of mono-exponential fitting and bi-exponential fitting were calculated to compare the goodness of fit. To quantitatively evaluate the significance of their difference, F test was performed. The F-ratio is defined as $$F=\frac{(RSS_{1}-RSS_{2})/(NV_{2}-NV_{1})}{RSS_{2}/(N-NV_{2}))},$$ where $RSS_{1}$ and $RSS_{2}$ correspond to the mono-exponential and bi-exponential models, respectively; N represents the data points acquired (N=12); and $NV_{1}$ and $NV_{2}$ are the numbers of variables in each model.

Results

In parotid glands, the long and short $T_{1\rho}$ were of ~59-70 msec with a fraction of ~0.73-0.91 and ~10-25 msec with a fraction of ~0.09-0.27 respectively, while mono $T_{1\rho}$ ~50-61 msec. The F ratios of 9 subjects range from 10 to 174 with a P value of 0.01. There is a significantly improvement of fitting by using bi-exponential model compared to mono-exponential model. Figure 1 displays typical raw-images at different TSLs for $T_{1\rho}$ quantification. Figure 2a illustrates 6 ROIs drawn on the left parotid gland. Figure 2b plots the $T_{1\rho}$ fitting curves of mono- and bi-exponential models from the 6th ROI. Figure 3 lists the measured parameters from two models and the corresponding F ratios. Figure 4 shows adjusted R-squared maps of mono- and bi-exponential fitting models. Figure 5 shows $T_{1\rho, mono}$,$T_{1\rho, short}$, $T_{1\rho, long}$ maps and the fraction map of long $T_{1\rho}$ component.

Discussion and Conclusion

The fitting results show that bi-exponential fitting curve matches to raw data better than the mono-exponential fitting curve. Note that there are regions in the bi-exponential fitting maps (e.g. long and short $T_{1\rho}$ maps, fraction map) with extreme values. This may due to blood vessels and gland ducts in the parotid area. When drawing ROIs, we carefully avoid these regions by selecting areas which are homogeneous and with values satisfying certain criteria ( $T_{1\rho, short}$<$T_{1\rho, mono}$, $T_{1\rho, long}$>$T_{1\rho, mono}$, $T_{1\rho, short}$>0, $T_{1\rho, long}$<100 ms). Bi-exponential fitting appears to be more susceptible to the presence of noise compared to mono-exponential fitting. Higher SNR of images is required to achieve reliable fitting results. It is worthy of further investigation how much SNR is needed to achieve reliable bi-exponential fitting in our application.
Bi-exponential $T_{1\rho}$ relaxation observed in parotid glands may be caused by combination of free water and constrained water. The long and short $T_{1\rho}$ values and their fraction in the tissue may have high sensitivity to the structural changes of parotid gland and have potential clinical use. Further study is needed to explain the reasons causing bi-exponential relaxation at a cellular level and demonstrate its possible clinical applications.

Acknowledgements

This study is supported by a grant from the Research Grants Council of the Hong Kong SAR (Project SEG CUHK02).