Validation of surface-to-volume ratio measurements derived from oscillating gradient spin echo on a clinical scanner using anisotropic fiber phantoms

Abstract

A diffusion measurement in the short-time surface-to-volume ratio (S/V) limit (Mitra et al., Phys Rev Lett. 1992;68:3555) can disentangle the free diffusion coefficient from geometric restrictions to diffusion. Biophysical parameters, such as the S/V of tissue membranes, can be used to estimate microscopic length scales non-invasively. However, due to gradient strength limitations on clinical MRI scanners, pulsed gradient spin echo (PGSE) measurements are impractical for probing the S/V limit. To achieve this limit on clinical systems, an oscillating gradient spin echo (OGSE) sequence was developed. Two phantoms containing 10 fiber bundles, each consisting of impermeable aligned fibers with different packing densities, were constructed to achieve a range of S/V values. The frequency-dependent diffusion coefficient, D(ω), was measured in each fiber bundle using OGSE with different gradient waveforms (cosine, stretched cosine, and trapezoidal), while D(t) was measured from PGSE and stimulated-echo measurements. The S/V values derived from the universal high-frequency behavior of D(ω) were compared against those derived from quantitative proton density measurements using single spin echo (SE) with varying echo times, and from magnetic resonance fingerprinting (MRF). S/V estimates derived from different OGSE waveforms were similar and demonstrated excellent correlation with both SE- and MRF-derived S/V measures (ρ ≥ 0.99). Furthermore, there was a smoother transition between OGSE frequency f and PGSE diffusion time when using teffS/V=9/64f, rather than the commonly used t_eff = 1/(4f), validating the specific frequency/diffusion time conversion for this regime. Our well-characterized fiber phantom can be used for the calibration of OGSE and diffusion modeling techniques, as the S/V ratio can be measured independently using other MR modalities. Moreover, our calibration experiment offers an exciting perspective of mapping tissue S/V on clinical systems.

Keywords: OGSE diffusion; STEAM diffusion; anisotropic diffusion phantom; magnetic resonance fingerprinting; surface to volume ratio.

Figure 1

OGSE diffusion gradient waveform for 40 Hz with 10 periods and EPI train during one TR and the corresponding gradient modulation power spectra, |F(f)|², for (A) trapezoid, (B) cosine, and (C) stretched cosine gradients.

Figure 2

Demonstration of the post-processing steps on an EPI b = 0-image (A) from phantom 1 (top) and phantom 2 (bottom) derived from the trapezoidal gradient waveform first denoising using Marchenko-Pastur Principle Component Analysis (B) followed by Gibbs Ringing correction via local subvoxel shifts (C).

Figure 3

Time dependence of the diffusivity D in the 4 fiber bundles of Phantom 2 measured using different OGSE waveforms with f converted to time, t, according to (A) t_eff = 1/(4f) and (B) $t_{\mathrm{eff}}^{(S/V)}=9/(64f)$, as well as using PGSE and STEAM measurements from Phantom 2. The black points represent the mean diffusivity of surrounding water. The colored dots are the radial diffusivities within the fiber bundles. The colored dashed lines connect OGSE and PGSE. Axial cross section of both fiber phantoms showing (C) SE and (D) MRF derived PD, illustrating the difference in water fraction between fiber bundles. The labels on (C) correspond to the ROIs used for D(t) shown on (A) and (B). (E) FA map at long t illustrating the difference in anisotropy between fiber bundles, with higher FA corresponding to lower water fraction.

Figure 4

(A) Asymptotically linear dependence of D(ω) on $1/\sqrt{\omega }$ as the signature of the S/V limit is visible for all gradient waveforms, showing fits with c = 1.2. The points to the left of vertical dashed line are included in the fit. The horizontal dashed line is the value of D₀ that is fixed to the mean value of λ₁ (B) Sketch of fiber bundle cross-section for estimating typical distance between fibers, assuming strong short-range order (a triangular lattice).

Figure 5

(A) Correlation plots comparing OGSE-derived S/V, Eq (1), to S/V derived from PD measurements, Eq (2), using either MRF (x) or SE (+). OGSE derived S/V as a function of c, a multiplicative factor that defines the number of points used per fit, cf. the text around Eq. (8). (B) Bland-Altman plot showing no systematic difference in S/V estimation.