The apparent diffusion coefficient (ADC) is analyzed for the case of oscillating diffusion sensitizing gradients. Exact analytical expressions are obtained in the high-frequency expansion of the ADC for an arbitrary number of oscillations N. These expressions are universal and valid for arbitrary system geometry. The validity conditions of the high-frequency expansion of ADC are obtained in the framework of a simple 1D model of restricted diffusion. These conditions are shown to be substantially different for cos- and sin-type gradients: for the cos-type gradients, the high-frequency expansion is valid when the period of a single oscillation is smaller than the characteristic diffusion time, the frequency dependence of ADC being practically the same for any N. In contrast, for the sin-type gradients, the high-frequency regime can be achieved only when the total diffusion time is smaller than the characteristic diffusion time, the frequency dependence of ADC being different for different N.
- Oscillating gradients