Exact Analytical Results for ADC for Oscillating Diffusion Sensitizing Gradients

Alexander L. Sukstanskii¹

Apparent diffusion coefficient (ADC) is analyzed for the case of oscillating diffusion sensitizing gradients. The exact analytical expressions are obtained for the high-frequency expansion of ADC for an arbitrary number of oscillations. The validity conditions of the high-frequency expansion of ADC are analyzed. It is shown that these conditions are substantially different for cos- and sin-type gradients. For the cos-type gradients, the high-frequency regime is reached when T<<t_D (T is the period of oscillations, t_D is the characteristic diffusion time), whereas for the sin-type gradients, this regime is achieved when the total diffusion time t is smaller t_D.