Sanjay Kumar Verma^{1}, Jadegoud Yaligar^{1}, Navin Michael^{2}, Tian Xianfeng^{1}, Venkatesh Gopalan^{1}, Suresh Anand Sadananthan^{2}, Rengaraj Ananthraj^{1}, and S. Sendhil Velan^{1,2}

Non-Invasive Imaging of Brown Adipose Tissue is of significant interest due to its potential to combat obesity and diabetes. In this study, we have utilized diffusion spectroscopy to estimate the droplet size distribution in chow and high-fat diet fed brown adipose tissues obtained from rodents. The high-fat diet BAT exhibited

All animal protocols
were approved by the local institutional committee. Twelve male Wister rats at seven weeks of age
were randomized into control and high-fat
diet. Tissue samples (150–200 mg)
were obtained at 15 weeks of age from the interscapular
BAT. Samples
were placed between susceptibility-matching plugs in a NMR tube and experiments
were performed with an AVANCE III 9.4T NMR
spectrometer using a 5-mm indirect detection broadband probehead with an actively shielded z-gradient coil. The diffusion experiments were performed with
varying diffusion times (Δ = 0.25, 0.5, 1 and 2 s) with gradient pulse duration (δ = 10 ms), and gradient switching interval (τ = 0.5 ms). The
spectral area under the most prominent fat peak at ~1.3 ppm was integrated and fitted to Stejskal–Tanner equation $$S = S_{0}e^{-\gamma^{2}g^{2}\delta^{2}\left(\triangle-\frac{\delta}{2}-\frac{\tau}{3}\right)D}$$ to calculate the apparent diffusion coefficient
(ADC). The distribution of lipid
droplet size with radius *R* and diffusion *D*, can be
assessed by modelling the
restricted diffusion behavior, as described by Murday
and Cotts^{3} and simplified by Garasanin et al.^{4} assuming
the rapid convergence of the Bessel function:

$$S(R)= S_{0}(R) exp\left[\frac{-54 g^2 R^2 γ^2 \left[3\left\{exp \left(\frac{-13D(∆-δ)}{3R^2}\right)-2 exp\left(\frac{-13Dδ}{3R^2}\right)-2 exp \left(\frac{-13D∆}{3R^2} \right)+exp \left(\frac{-13D\left(∆+δ\right)}{3R^2} \right)+2\right\} R^2-26Dδ\right]}{15379D^2}\right]$$

The observed NMR signal is the volume weighted average and described
by the log normal probability distribution function *P*(*r*) expressed as:

$$ S_{0bs} = \frac{\int_{}^{}S(r)r^{3} P(r)dr} {\int_{}^{}r^{3} P(r)dr}=\frac{\sum_{R_{min}}^{R_{max}}S(r)r^{3}P(r)}{\sum_{R_{min}}^{R_{max}}r^{3}P(r)}$$

where the denominator is
a normalization constant, and *R*_{min
}and* R*_{max} are the minimum
and maximum droplet radii, respectively. We assume here that almost all of the
fat molecules within a droplet in BAT hit the boundary during 2 s at least
once. The NMR signal attenuation at diffusion time Δ = 2 s
was fitted to above equation with a nonlinear least squares fit to obtain the
mean radius and variance of the distribution.

Results & Discussion

A significant reduction in ADC values is observed with increased diffusion time. With varying diffusion time from 0.5 to 2 s the ADC values for control group changed from 0.94 × 101. Cinti, S. 2006. The role of brown adipose tissue in human obesity. Nutr. Metab. Cardiovasc. Dis. 16: 569–574.

2. Dorfman, S. E., D. Laurent, J. S. Gounarides, X. Li, T. L. Mullarkey, E. C. Rocheford, F. Sari-Sarraf, E. A. Hirsch, T. E. Hughes, and S. R. Commerford. 2009. Metabolic implications of dietary trans-fatty acids. Obesity (Silver Spring). 17: 1200–1207.

3. Murday, J. S., and R. M. Cotts. 1968. Self-diffusion coefficient of liquid lithium. J. Chem. Phys. 48: 4938.

4. Garasanin, T., T. Cosgrove, L. Marteaux, A. Kretschmer, A. Goodwin, and K. Zick. 2002. NMR self-diffusion studies on PDMS oil in water emulsion. Langmuir. 18: 10298–10304.

5. Cao, P., S. J. Fan, A. M. Wang, V. B. Xie, Z. Qiao, G. M. Brittenham, and E. X. Wu. 2015. Diffusion magnetic resonance monitors intramyocellular lipid droplet size in vivo. Magn. Reson. Med. 73: 59–69.

6. Fieber, W., V. Hafner, and V. Normand. 2011. Oil droplet size determination in complex flavor delivery systems by diffusion NMR spectroscopy. J. Colloid Interface Sci. 356: 422–428.

Figure 1. Modelling of diffusional decay with Murday-Cotts equation. The dotted lines (control diet) and full lines (high-fat diet) show the nonlinear least square fitted signal decay for Δ = 2 s.

Figure 2. Log-normal distributions
of the droplet size estimated in control and high-fat diet fed tissues. The
distribution curves were discretized to 64 intervals within the radius range of
0.1 to 5 μm.

Figure 3. H&E-stained optical images of control diet (A) and high-fat diet BAT (B).