Anomalous diffusion of brain metabolites evidenced by diffusion-weighted magnetic resonance spectroscopy in vivo

Abstract

Translational displacement of molecules within cells is a key process in cellular biology. Molecular motion potentially depends on many factors, including active transport, cytosol viscosity and molecular crowding, tortuosity resulting from cytoskeleton and organelles, and restriction barriers. However, the relative contribution of these factors to molecular motion in the cytoplasm remains poorly understood. In this work, we designed an original diffusion-weighted magnetic resonance spectroscopy strategy to probe molecular motion at subcellular scales in vivo. This led to the first observation of anomalous diffusion, that is, dependence of the apparent diffusion coefficient (ADC) on the diffusion time, for endogenous intracellular metabolites in the brain. The observed increase of the ADC at short diffusion time yields evidence that metabolite motion is characteristic of hindered random diffusion rather than active transport, for time scales up to the dozen milliseconds. Armed with this knowledge, data modeling based on geometrically constrained diffusion was performed. Results suggest that metabolite diffusion occurs in a low-viscosity cytosol hindered by ∼2-μm structures, which is consistent with known intracellular organization.

Figure 1

Modified asymmetric LASER spectroscopy sequence with diffusion-weighting oscillating gradients inserted around the first adiabatic full passage pulse. Slice selection gradients are in gray, and spoiler gradients are in black.

Figure 2

Diffusion-weighted NMR spectra acquired in the rat brain during a single scanning session, for different diffusion times t_d and diffusion-weighting b=1 millisecond/μm². The tendency of metabolite signal to decrease as t_d decreases can be visually assessed on data, as exemplified for N-acetylaspartate (NAA) (dotted horizontal line represents the NAA peak height for the longest t_d). This is a direct experimental manifestation of anomalous diffusion.

Figure 3

(A) The apparent diffusion coefficient (ADC) measured for N-acetylaspartate (NAA), total creatine tCr, and choline compounds tCho, over 20 sessions, as a function of t_d (represented in log-scale). The increase of ADC at shorter t_d is a characteristic signature of subdiffusion, and evidence that hindered random diffusion is the dominant transport mechanism for the metabolites. Statistical significance of the ADC variation between two consecutive t_d, averaged over the three metabolites, was assessed using Student's paired t-test (the star symbol stands for P<0.01). (B) The ADC averaged for the three metabolites, and the best fit using the ‘neurite' and the ‘cell body' geometrically constrained diffusion models (see text for details). Both models yield a free diffusion coefficient D_free=0.55 μm²/millisecond, slightly lower than in free water, and typical 1.8-μm distance between obstacles, which is consistent with known cellular architecture. Although best fits are represented in the time domain, modeling was actually performed in the frequency domain.

Figure 4

A compilation of apparent diffusion coefficient (ADC) averaged for N-acetylaspartate (NAA), tCr, and tCho, as reported in the past published studies when data are available, illustrating the relative stability of metabolite diffusion at long t_d. Extending the ‘neurite' and the ‘cell body' models at long t_d using parameters derived on our own data allows accounting very well for ADC stability as reported in the literature. Note that averaged ADC as measured in the present study are also presented in the time domain (black diamonds at very short t_d), for comparison only. Numbers next to diamonds stand for the referenced published articles: 1 (ref. 21); 2 (ref. 26); 3 (ref. 27); 4 (ref. 28); 5 (ref. 20); 6 (ref. 23); 7 (ref. 22); 8 (ref. 29); 9 (ref. 30); 10 (ref. 31); 11 (ref. 32); 12 (ref. 33); 13 (ref. 34); 14 (ref. 35); 15 (ref. 36); 16 (ref. 25).