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

Abstract

The short-time surface-to-volume ratio (S/V) limit [Mitra et al., Phys. Rev. Lett. 68, 3555 (1992)] 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 interpret 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 ( ρ0.2em≥0.99). Furthermore, there was a smoother transition between OGSE frequency f and PGSE diffusion time when using tefffalse(S/Vfalse)=9/false(64ffalse), rather than the commonly used teff=1/false(4ffalse), 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.

On modeling

“…A scaling law derived from the Bloch‐Torrey equation helped to simplify the parametric dependence of transverse relaxation rate caused by blood pool contrast agents, and to explain the increased sensitivity to the microvasculature for increasing contrast concentration Observation of the decrease of at short diffusion times in porous media (Figure A), in a fiber phantom, in cell suspensions, and in vivo in breast and in brain tumors Effect of structural disorder on the time‐dependent diffusion, relating structural fluctuations in heterogeneous media to the diffusive dynamics.…”

“…Observation of the decrease of at short diffusion times in porous media (Figure A), in a fiber phantom, in cell suspensions, and in vivo in breast and in brain tumors …”

Characterization of Prostate Microstructure Using Water Diffusion and NMR Relaxation

“…The range of times over which the S/V limit (2) is applicable is t≪lpore2/(2dD0), where l pore is the pore characteristic length scale; this estimate was recently validated in a phantom on the same clinical scanner used in this study [28]. Assuming that glandular lumen has D 0 ≈ 3 μm 2 /ms (free water at body temperature), and diameter l pore ~100 μm, the S/V limit will apply for t ≪ 500 ms.…”

Physical and numerical phantoms for the validation of brain microstructural MRI: A cookbook

“…Plain fiber bundles serve as a phantom to model the extra-axonal space, and have been used to study the effect of axonal packing geometry on the (time-dependent) diffusion coefficient (Burcaw et al, 2015), as well as to validate the short-time limit (Latour et al, 1994; Mitra et al, 1993) using oscillating gradients diffusion weighting schemes (Lemberskiy et al, 2017).…”