To better characterize chemical structures of the fatty acid (saturated vs. unsaturated) in brown adipose tissue (BAT), a Multi-Varying-Peaks MR Spectroscopic (MVP-MRS) model is proposed and compared to the traditional Dixon model of single fat- and water- peak or fixed multi-fat-peaks model.

Identification of the BAT volume and distribution by in vivo imaging is clinically important. Studies were first reported by using PET-CT scans ¹. However, the need for using ionizing radiation (18F-FDG) limits applications of PET for longitudinal studies in humans. Previous MRI studies have used chemical shift between muscles and fat to differentiate the two tissues ^2-5 or water fat imaging (WFI) using IDEAL algorithm ⁶. However, these WFI methods assume a fixed multi-peak spectroscopic model for both WAT and BAT and depend on fat fraction ratio and differences of relaxation time to differentiate BAT from WAT⁷. There have been studies showing that this model is inaccurate when trying to identify BAT using only fat fraction. Representative MR spectra of BAT and WAT showed that, though majority of the spectrum lies in the main peak (-(CH₂)_n- at 1.3-ppm), there is a substantial amount of spectrum contained with the other fat peaks (e.g. 2.1- and 5.3-ppm, while water peak at 4.7-ppm)^7-8. The BAT and WAT spectra show significantly more differences, e.g. relative peak magnitudes and chemical shift (location on the spectrum chart), at a higher magnet field⁸. Therefore, to differentiate the BAT from WAT, a spectroscopic signal model is needed that approximates the major fat resonances. Here we propose a MVP-MRS model as follows

$$s(t)=(\rho_{w}+\sum_{n=1}^N\beta_{n}e^{j2\pi f_{n}t})e^{j2\pi \phi t} $$

where ρ_w is the water proton density, f_n and β_n are the resonant frequency and proton density of the n^th fat peak (n=1,…,N) relative to water. Five (N=5) fat peaks, located at 0.9, 1.3, 2.1, 4.3, and 5.3 ppm, were selected, corresponding to different structures of the fatty acid (saturated vs. unsaturated), which are more representative of compositions of the fatty acid⁸. It is noted that ρ_w and β_n are complex numbers. In order to solve for the (N+1) unknowns (ρ_w and β_n), a total of 2(N+1) measurements of MR signals are needed.

MR experiments were conducted on a 7 T Varian Magnex small animal scanner. MR data was acquired from an oil/butter phantom (a water cylinder embedded with vials of soybean oil, butter, and water) and a 2-month old C57BL6 mouse, approved by IAUCC (University of Georgia), using a 2D gradient-echo sequence with 12 echoes (first TE=5.70 ms, with incremental spacing of 0.525 ms).MR data was analyzed with a modified Matlab water-fat analysis toolbox (http://ismrm.org/workshops/FatWater12/data.htm) using the proposed MVP-MRS model. All components of ρ_w and β_n are normalized to the main/highest fat peak (-(CH₂)_n- at 1.3 ppm). Figure 1 presents MRI images of the butter/oil and mouse intercapsular water/fat distribution. BAT and WAT areas were identified by their fat fraction (BAT: 50.69% ±6.61%, WAT: 85.10% ±6.84%.)

Figure 2 presents the averages and standard deviations of the 5 fat peaks for the oil/butter data and mouse BAT/WAT data. It was seen that the butter and oil have similar fatty acid structures and homogenous distributions (small standard deviations), while the BAT and WAT have different compositions and inhomogeneous distributions (large standard deviations). To differentiate BAT from WAT, a machine learning algorithm, AdaBoost, is adopted for classification. We randomly selected 80% of the data for classifier training, and the rest (20%) for testing. The train-test procedure was repeated 100 times. Figure 3 presents the classification rates. Since butter and oil have similar fatty acid structures, a classification rate of only 90% was achieved; while the BAT and WAT have different compositions, resulting in a classification rate of 98%.

Traditional Dixon or multipeak IDEAL methods requires accurate knowledge of the fat spectrum, including the frequency shifts and the relative amplitudes of the peaks. However, the fat spectrum may likely change from subject to subject and sequence to sequence with different T₁ and T₂ weightings^9-10. Additionally, due to inhomogeneous distribution of the BAT and WAT, and partial volume effect resulting from limited spatial resolution, a fixed-peaks signal model can no longer unbiasedly represent the fat spectrum. Our MR imaging-based MVP spectral model is built upon high spatial resolution MR images, so it is therefore capable of providing high resolution spatial distribution of BAT in the tissues of interest. This will also allow for a longitudinal monitoring of WAT beiging, which is induced by either a pharmaceutical or physical approach, e.g. exposure to cold environment or exercising.