On the Influence of the Temporal Gradient Profile on the Apparent Diffusion Coefficient in the Motional Narrowing Regime in Closed Geometries

Frederik Bernd Laun¹, Bram Stieltjes

In DWI, the apparent diffusion coefficient is determined by both, the diffusion process and the temporal profile of the diffusion gradients. In this work a technique to determine the influence of the temporal gradient profile on the measured ADC is developed for the motional narrowing regime in closed geometries. It yields a direct series expansion in powers on inverse time. It is shown that the discontinuities and integrals over the derivatives of the gradient profile determine the constants of this series expansion.