TY - JOUR

T1 - Concise derivation of oscillating-gradient-derived ADC

AU - Sukstanskii, A. L.

AU - Ackerman, J. J.H.

PY - 2018/11

Y1 - 2018/11

N2 - The apparent diffusion coefficient (ADC) is analyzed for the case of oscillating diffusion-sensitizing gradients in the high-frequency regime. We provide a concise derivation of the analytical expression for the ADC for an arbitrary number of gradient oscillations N and initial phase φ. It is demonstrated that an ultimate goal – to determine the surface-to-volume ratio (S/V) from MR measurements by using oscillating gradients – can be achieved with cosine-type gradients (φ = 0) for an arbitrary N. However, to determine S/V employing gradients with φ ≠ 0 (including the sine-type gradients) and arbitrary N additionally requires prior knowledge of the time-dependent diffusion coefficient D(t). The latter is rarely known a priori but can be estimated under certain limiting conditions: (i) in the short time regime, when the total diffusion time of the measurements, t, is smaller than the characteristic diffusion time of the microstructural system of interest, an analytical expression for D(t) is available (Mitra's expression) and this allows S/V to be determined in the short time regime with sine-type gradients; (ii) in the important case of purely restricted diffusion, D(t) → 0 at sufficiently long time, the signal becomes independent of φ and behaves as for the cosine-type gradients, thus, allowing determination of S/V.

AB - The apparent diffusion coefficient (ADC) is analyzed for the case of oscillating diffusion-sensitizing gradients in the high-frequency regime. We provide a concise derivation of the analytical expression for the ADC for an arbitrary number of gradient oscillations N and initial phase φ. It is demonstrated that an ultimate goal – to determine the surface-to-volume ratio (S/V) from MR measurements by using oscillating gradients – can be achieved with cosine-type gradients (φ = 0) for an arbitrary N. However, to determine S/V employing gradients with φ ≠ 0 (including the sine-type gradients) and arbitrary N additionally requires prior knowledge of the time-dependent diffusion coefficient D(t). The latter is rarely known a priori but can be estimated under certain limiting conditions: (i) in the short time regime, when the total diffusion time of the measurements, t, is smaller than the characteristic diffusion time of the microstructural system of interest, an analytical expression for D(t) is available (Mitra's expression) and this allows S/V to be determined in the short time regime with sine-type gradients; (ii) in the important case of purely restricted diffusion, D(t) → 0 at sufficiently long time, the signal becomes independent of φ and behaves as for the cosine-type gradients, thus, allowing determination of S/V.

KW - ADC

KW - Diffusion

KW - MRI

KW - Oscillating gradients

UR - http://www.scopus.com/inward/record.url?scp=85053823487&partnerID=8YFLogxK

U2 - 10.1016/j.jmr.2018.09.010

DO - 10.1016/j.jmr.2018.09.010

M3 - Article

C2 - 30268941

AN - SCOPUS:85053823487

VL - 296

SP - 165

EP - 168

JO - Journal of Magnetic Resonance

JF - Journal of Magnetic Resonance

SN - 1090-7807

ER -