Fig 1.
Characterizing size distributions from NOGSE data.
(A) NOGSE MRI sequence used, encompassing an initial block probing the confinements over a time TNOGSE, and a single-shot spin-echo Echo-Planar-Imaging readout (NOGSE gradients are shown along the RO direction, but can be applied in arbitrary orientations). (B) x time-dependence of the NOGSE signal attenuation E(TNOGSE) for different size distributions. Note that as the lognormal distribution width increases the E(TNOGSE) changes both in curvature and in overall amplitude; the inset highlights this by normalizing the curves to their first point (Min(x)). (C) Probability distributions P(l) extracted from fitting the simulations in (B) for a given restricting length l in a noise-less reconstruction. The extracted distributions overlap perfectly with the simulated ones. (D) Effects of adding noise to the NOGSE signal for the widest distribution considered in (C): notice that even when fluctuations reach 10% of the signal, the fits remain robust and the distributions are well reconstructed (inset). Throughout this Fig symbols represent the synthetic data whereas solid curves represent fits to these data. For all distributions lc = 2 μm, G = 40 G/cm, N = 8, TNOGSE = 30ms.
Fig 2.
Validating NOGSE’s size distribution predictions in yeast cells.
(A) A representative image of the examined yeast ensemble; note that objects larger than ~8 μm are not observed in these images, suggesting that the wide right shoulder of the microscopy-derived distribution in (B) arises from unresolved, adjacent cells. (B) Size distribution reconstructed from a NOGSE experiment on the yeast ensemble (red curve, with symbols in the inset presenting the experimental data and the solid line their best fit), overlaid on the cellular size distribution obtained from optical microscopy (bin size = ~ 0.05 μm). NOGSE parameters: TNOGSE = 30 ms, G = 87.3 G/cm, N = 8. D0 was assumed 1x10-5 cm2/sec, as this gave the best fits to the data.
Fig 3.
Raw NOGSE MRI data arising from sagittal images of a mouse brain, masked for the corpus callosum and plotted as a function of increasing x-values.
Notice the clear increase in signal intensity with increasing x-values, as the weighting gradient transitions from a mostly long bipolar block to an OGSE-like sequence–while always retaining a constant-time fashion. Notice as well the different profiles evidenced by the various corpus callosum sub-sections. The diffusion gradients were along the phase-encoding direction, i.e. along the vertical axis of the image.
Fig 4.
Mapping histological size distributions in a mouse corpus callosum.
(A) Definitions of the various ROIs placed in different anatomical regions, superimposed on a reference MRI image. (B) Ensuing curves (symbols) and best fits (solid lines) arising from a NOGSE MRI experiment. (C) Size distributions P(l) extracted from (B), under a D0 = 0.7x10-5 cm2/sec assumption. (D-F) Maps of the mean, the peak and the width values extracted from pixel-by-pixel fits of the NOGSE response, highlighting the contrast between the corpus callosum different anatomical regions. NOGSE parameters: TNOGSE = 30 ms, N = 8, GNOGSE = 57.6 G/cm applied perpendicular to the main axis of the fibers in the corpus callosum (i.e., the vertical axis of the images). The extracted values describe the correlation lengths lc. See Materials and Methods for further parameters.
Fig 5.
Idem as in Fig 3, but showing raw NOGSE MRI data from coronal images of a mouse brain.
Different brain regions manifest different NOGSE signal increases with increasing x-values, even within the gray matter. These features allow for the microstructural segmentations shown in the main text. The asterisk in the top-leftmost image represents a tissue area damaged upon preparation.
Fig 6.
Mapping size distributions of a mouse’s gray matter.
(A) ROI definitions of various GM regions. (B) NOGSE curves from these ROIs (symbols) along with the size distribution fittings in each ROI (solid lines). Note the stronger amplitude modulation in the gray matter compared with the WM shown in Fig 3. (C) Size distributions extracted from the data in (B). (D-F) Maps of mean sizes, peak values and distribution widths obtained by fitting the NOGSE data retrieved from a mouse brain, reflecting the correlation lengths lc. Cortical layering can be observed, and are marked with Roman numbers on the Mean size map. NOGSE parameters: TNOGSE = 30 ms, G = 57.6 G/cm, N = 8; the gradient was oriented along the left-right axis of the image, and D0 was assumed 0.7x10-5 cm2/sec.
Fig 7.
On the need for distributions to describe the NOGSE response arising in brain tissues.
(A) Simulation for NOGSE data arising from a distribution characterized by lc = 2 μm and σ = 0.5 at G = 57.6 G/cm, N = 8, and TNOGSE = 30 ms along with fits to the distribution (red curve) and an attempt to fit just a single size to the data (black curve). Residuals of the fits are shown in the inset. (B) Idem but for experimental data arising from ROI #4 of the corpus callosum (see Fig 4A for the ROI’s definition). The residuals clearly demonstrate the need for distributions to fit the data in a robust way.
Fig 8.
NOGSE’s size-resolving potential in human- and materials-oriented setting.
(A-B) Simulations predicting NOGSE’s ability to extract cellular size distributions in clinically-relevant settings, involving G = 6 G/cm, N = 64, and TNOGSE = 120 ms, D0 = 3.0E-5 (cm)2/sec. Notice that even when assuming the relatively weak gradients available in whole body MRIs, cell-sized distributions can be resolved and characterized. The inset in panel B analyzes the effect of 0.1 and 3% noise added to the third distribution, showing that with some noise levels, distribution can still be reconstructed. All definitions are akin to those in Fig 1B and 1C. (C-D) Simulations demonstrating NOGSE’s ability to extract pore distributions in mesoporous materials (10–1000 nm range), using the stronger diffusion gradients available in NMR scanners (G = 200 G/cm, N = 160, and TNOGSE = 150 ms, D0 = 0.41E-5 (cm)2/sec). Notice the strong differences in signals arising when pores are distributed around lc = 300nm.