Darya Morozov^{1}, Alexander L. Sukstanskii^{1}, and Scott C. Beeman^{1}

It has been suggested that adipocyte hypertrophy plays a key role in the pathogenesis of systemic insulin resistance and type 2 diabetes. A method for quantifying adipocyte size/hypertrophy in-vivo would be a major advance towards understanding the pathogenesis of type 2 diabetes. In-vivo quantification of adipocyte size might be achievable using short time regime diffusion MR, which carries information about size of the system. Herein, we explore the feasibility of measuring adipocyte size based on the diffusion of triglyceride within adipocytes and the principles of the short diffusion time regime.

Obesity
is assumed to be a primary cause of type 2 diabetes, but the pathogenesis of
the disease is still not well understood. It has been suggested that adipose
tissue hypoxia - a condition induced by adipocyte hypertrophy - initiates
adipose tissue inflammation and leads to systemic insulin resistance^{1}.
A method for quantifying adipocyte size/hypertrophy in-vivo would be a major advance
towards understanding the pathogenesis of type 2 diabetes, yet no such method
exists.
In-vivo quantification of adipocyte
size might be achievable using short time regime diffusion MR, which carries
information about size of the system and is defined as a regime in which the
displacement of the particle is significantly smaller than the actual
compartment size and b·D_{0}<<1 ^{2,3,4 }(Eq. 1):

$$$D(t)=D_{0}\cdot(1-\frac{4}{3\sqrt{\pi}}\frac{1}{R}\sqrt{Δ\cdot D_{0}}) $$$

Where D(t) is the measured
diffusivity of the system (calculated from a mono-exponential representation of
the diffusion signal decay), D_{0} is the free diffusivity of the diffusing
molecule of interest, and R is the radius of the system and Δ is the diffusion time. In the context of adipocyte size, the
“system” is defined as a single spherical oil droplet that typically comprises
>99% of the adipocyte volume (a common surrogate for adipocyte size), and
the “diffusing molecules of interest” are the triglyceride molecules within the
oil droplet.

Based on the short time regime theory, our objective is to develop a direct, non-invasive, and quantitative measure of adipocyte size using diffusion MR. We use Monte Carlo simulations, microcapillary phantoms and ex-vivo adipose tissue to explore this possibility.

Simulations: Monte Carlo simulations of particle random-walk
were performed on M (10^{5}-10^{6}) random particles with
random starting positions inside of infinitely long cylinders with diameters of
50, 100 and 150 μm (roughly the size of adipocytes)^{4}. Diffusion of
water (D_{0}=2 μm^{2}/msec) and lipids (D_{0}=0.0175 μm^{2}/msec)
inside the three different size cylinders was simulated at diffusion times ranging
from 30 to 100 ms or 200 to 600 ms for water or lipids, respectively. These
values fall into the short diffusion time regime.

Experimental samples: Ground-truth phantoms constructed from water-filled microcapillaries having inner diameters of 50±5, 100±5 and 150±5 μm and formalin-fixed mice epididymal white adipose tissue (eWAT).

Short-time regime diffusion MR: Diffusion MR experiments were conducted at 11.7T MRI scanner using stimulated echo imaging sequence modified with diffusion encoding gradients. Experimental parameters for imaging of microcapillaries: TR/TE=8000/11 ms, ∆=30 ms (chosen based on simulations), 10 gradient steps, max b-value of 0.5 ms/μm2, NS=1. Experimental parameters for imaging of eWAT: TR/TE=3000/34.6 ms, ∆=400 ms (chosen based on simulations), 10 gradient steps, max b-value of 20 ms/μm2, NS=1.

Simulations: This simulation was used to interrogate the limitations of
the model. Sizes estimated from the simulation data are in good agreement with the
input sizes (Figure 1B,D). For example, in case of cylinders filled with lipids (Figure
1D), sizes of 45.6, 82.7, 139.7 μm are estimated for true input sizes of 50, 100 and 150 μm at ∆ of 400 ms and b-value of 14 ms/μm^{2}. Importantly, the
uncertainly of the diameter estimates increases with the true diameter. This
can be explained by the inverse relationship between the term which carries the
size information (rightmost term of Eq. 1) and the true radius of the system.
Restated, as the radius increases, D(t) and D_{0} converge and the size
information about the system diminishes. In practical terms, the results of
this simulation imply that, to experimentally resolve large diameters, one must
be aware of the relationship between the SNR, the true diameter, and the
precision of the estimated diameter. A quantitative in-silico interrogation of
this relationship is the subject of ongoing investigation.

Microcapillary phantoms: The
calculated diameters of microcapillaries appear to be in good agreement
with the ground-truth sizes obtained from manufacturer (dashed black lines in
Figure 2C).
For example, sizes of 48.0, 115.6 and 150.1 μm are estimated for true capillary sizes of 50, 100 and 150 μm at b-value of 0.2 ms/μm^{2}. Rigorously quantification
of the experimental uncertainty in the diameter measurements is ongoing.

Ex vivo tissue: As a proof-of-principle, diffusion
experiments were conducted on two eWAT samples from lean mice using a diffusion
time of 400 ms. Here, the mean adipocyte sizes were found to be 49.8±6.8 μm and 43.2±5.0 μm, for the two samples respectively. These adipocyte
size estimates are in good agreement with those measured by histology^{6}.