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Evaluation of reliability and self-consistency of compartment size-distribution estimations by oscillating gradient spin-echo sequences
Melisa L. Gimenez1,2, Leonardo A. Pedraza Pérez1,2, and Gonzalo A. Álvarez1,2,3
1Instituto Balseiro, CNEA, Universidad Nacional de Cuyo, San Carlos de Bariloche, Argentina, 2Centro Atómico Bariloche, CNEA, CONICET, San Carlos de Bariloche, Argentina, 3Instituto de Nanociencia y Nanotecnologia, CNEA, CONICET, San Carlos de Bariloche, Argentina

Synopsis

Keywords: Microstructure, Quantitative Imaging

Changes in tissue microstructure are promising biomarkers of neurological diseases. However, achieving robust and reliable, non-invasive diagnostic tools to estimate microstructural features is a major challenge. We perform a systematic analysis using Non-uniform Oscillating Gradient Spin Echo (NOGSE) sequences to estimate size distributions of white-matter phantoms. We evaluate the reliability and self-consistency of the inference method. We find that estimation of the distribution’s mode is very robust and reliable for sharp and smooth gradient modulations. These results contribute to developing reliable diagnostic tools based on quantitative images of tissue microstructure.

INTRODUCTION

Observing changes in tissue microstructure by non-invasive Diffusion-Weighted Imaging (DWI) is a promising biomarker of neurological pathologies1-5. Achieving robust and reliable diagnostic tools for estimating compartment size distributions is challenging due to the complexity of validating these techniques2,6,7. Most of the validation methods are via invasive techniques, with surgical interventions when performing biopsies and histology. The tissue microstructure is modified during these manipulations8. Acquiring such microstructure details and even its validation non-invasively would provide valuable tools for diagnostics and neuroscientific research.

As a step towards achieving this goal, we here evaluate the reliability and self-consistency of estimating compartment size-distribution using Non-uniform Oscillating Gradient Spin-Echo (NOGSE) sequences9-12. NOGSE factors out experimental imperfections and other relaxation weightings. It exploits a “decay-shift” rather than the “decay-rate” of the magnetization signal, often used in conventional methods. The “decay-shift” provides higher parametric sensitivity to compartments sizes, but occurs when gradient modulations are sharp. We thus evaluate the inference of estimating compartment size distributions with fast and smooth gradient modulations, where the latter is more feasible to be implemented in the clinic. We use white-matter phantoms that mimic extra-axonal compartments13 to address the reliability and self-consistency of the estimated restriction-size distributions.

METHODS

White-matter phantom. We used home-made phantoms containing aramid fibers immersed in water to emulate restriction-size distributions similar to those found in the extra-axonal space of the white matter in the human brain13. Figure 1a shows a SEM image of the aramid fibers and Figure 1b a transverse plane magnetic resonance image (MRI) of the phantoms with the fibers arranged parallelly in packages of different compaction (Region of Interest (ROI) 1 to 4). ROI5 contains only water. We assume that the underlying restriction-size distribution is represented by a single log-normal probability density with mean size lc and standard deviation σc.

NOGSE MRI acquisition. MRI scans were performed at 9.4T on a Bruker Avance III HD WB NMR spectrometer with a Micro 2.5 probe. Images were acquired with the NOGSE sequences based on the implementation described by Capiglioni et al.12 (Fig. 2). We use TR=2000 ms; TE=70.5 ms; in-plane resolution of 83×83μm2; slice thickness of 1 mm; 10 averages; EPI encoding and an acquisition time ~4 minutes; NOGSE gradients G were 20 mT/m - 600 mT/m and applied perpendicular to the main axis of the fiber bundles, with sinusoidal (smooth) or trapezoidal (sharp) NOGSE modulations.

RESULTS AND DISCUSSION

Comparison between modulating gradient shapes. We first evaluate the reconstructed restriction-size distributions determined from the NOGSE sequences with sharp or smooth gradient modulations. Figure 3 shows the mean size lc and standard deviation σc obtained from fits to the averaged signal of ROI1, for different gradient strengths G, diffusion times T and number of refocusing periods N. Similar log-normal size distributions are estimated, although smooth modulations give slightly smaller mean sizes and distribution widths. This is consistent with the observation of tortuous diffusion between the interstitial compartments of the phantoms16. Higher parametric fluctuations are observed at the lower and higher ends of the gradient strengths and at the lower and higher ends of the diffusion times on the explored dynamic range. This behavior is expected from predictions of optimal setting parameters for size-distribution inferences17.

Self-consistency analysis. We compare the resulting restriction-size distributions of Fig. 3 with the ones obtained from single-restriction size fits of pixel-by-pixel data. Figures 4a,b show a map of the determined single-restriction sizes for each pixel. The observed different fiber densities are consistent with the preparation compaction degree. The fitted parameters are also consistent among sharp and smooth modulation. Single-size histograms from the pixel-by-pixel fits of ROI1 are shown in Fig. 4c. They provide very similar size-distribution between the smooth and sharp modulations. In this case, we use the same NOGSE parameters determined from the region with lower dispersion of the estimated values in Fig. 3a.
We also compare the histograms with the restriction-size distribution that arise from the averaged-signal fits of ROI1 with the smooth or sharp modulation. Both sequences estimate quite comparable restriction-size distributions. However, the distribution from the pixel-by-pixel differs from the one obtained via the averaged-signal. The distribution size mode is very robust as both approaches give indistinguishable values. Nevertheless, there is an inconsistency in the distribution-width determination. We found that the single size assumption for the pixel fitting does not provide the complete information. By an inversion procedure, we then extract the averaged restriction-size per pixel and per diffusion time x of NOGSE (Fig. 5a). Figure 5b shows now a better agreement of the size-mode and width of the distribution, without assuming a distribution model for the pixel-by-pixel analysis.

CONCLUSION

By a systematic analysis of the estimated microstructural properties of the white-matter phantoms, we evaluate the reliability and self-consistency of obtaining compartment-size distributions with the NOGSE sequence. The estimation of the distribution’s mode is very robust, and thus reliable for both, sharp and smooth gradient modulations. We found that both types of modulation give comparable microstructural information, but the sharp modulation is more prone to be affected by Rician noise. These results thus help pave the way towards implementing new diagnostic methods based on quantitative images of tissue microstructure features.

Acknowledgements

This work was supported by CNEA; CONICET, ANPCyT-FONCyT PICT-2017-3156, PICT-2017-3699, PICT-2018-4333; PIP-CONICET (11220170100486CO); UNCUYO SIIP Tipo I 2019-C028, 2022-C002, 2022-C030; Instituto Balseiro; A collaboration program from MINCyT (Argentina) and MAECI (Italy) and Erasmus+ Higher Education program from the European Commision.

References

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Figures

Figure 1. Home-made white-matter phantoms. (a) SEM image of aramid fibers of mean diameter ~12 μm that emulate axons similar to those found in white matter of the human brain13. (b) Transverse plane MRI of the phantoms with the aramid fibers immersed in water in a plastic tube. The numbered regions represent the different ROIs analyzed in this work. ROIs 1 to 4 correspond to each aramid fiber package that emulates restriction-size distributions and ROI5 only contains water.

Figure 2. (a) Sharp (squared) and (b) smooth (sinusoidal) modulations of the NOGSE sequence. The NOGSE sequence starts with a π/2-pulse excitation followed by a modulated gradient G(t) that comprises the concatenation of two gradient modulations with different frequencies (CPMG14 and Hahn15). NOGSE consists of N refocusing periods during a total diffusion time T, with (N-1) refocusing periods of duration 2x corresponding to the CPMG-like modulation. The signal is acquired using an MRI acquisition encoding (ACQ).

Figure 3. Inferred mean size lc and standard deviation σc. Experimental data was fitted from ROI1 for several values of (a) the gradient strength G (at a fixed diffusion time T=21.5 ms), (b) the diffusion time T and (c) the number of refocusing periods N (at a fixed T=21.5 ms), using the smooth or sharp modulation.

Figure 4. Restriction-size maps obtained for NOGSE (a) sharp and (b) smooth modulations. (c) Histograms of single restriction-size estimation in ROI1 from the maps in (a) and (b), and their log-normal fit (for a sharp modulation: mode=4.40 μm, σc=0.36 μm, and for a smooth modulation mode=4.53 μm, σc=0.36 μm), compared to the corresponding reconstructed lognormal restriction-size distribution by analyzing the mean signal of ROI1 (for a sharp modulation: mode=4.30 μm, σc=4.40 μm, and for a smooth modulation mode=4.40 μm, σc=2 μm). We considered D0=2.3 μm2/ms for all fits.

Figure 5. Reliability and self-consistency of the reconstructed size-distributions. (a) Inversion procedure to extract the averaged restriction size per pixel and NOGSE diffusion time x from the magnetization signal, without including a restriction-size distribution model. (b) Histograms of single restriction-size estimation for every pixel and diffusion time x, compared to the corresponding reconstructed lognormal restriction-size distribution from the average signal.

Proc. Intl. Soc. Mag. Reson. Med. 31 (2023)
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DOI: https://doi.org/10.58530/2023/4308