Low-frequency asymptotic behaviour of the apparent diffusion coefficient when measured with approximate cosinusoidal gradient waveforms

Motivation: Existing theory for OGSE-DWI has been developed under the assumption of an ideal cosinusoidal gradient waveform, but it is impossible to implement such a waveform in practice. Goal(s): Investigate how the low-frequency asymptotic behaviour of the ADC is affected when OGSE-DWI measurements are performed with an approximate cosinusoidal waveform. Approach: A theoretical study was performed to derive the asymptotic behaviour of the ADC from first principles for three MPG waveforms. Results: The predicted low-frequency behaviour of the ADC for the CPHS and DS waveforms can clearly differ from that for the ideal cos waveform. Impact: The microstructure of a complex medium can be characterised by measuring the low-frequency limit of the ADC with OGSE-DWI. However, it is important to understand how the limitations of the gradient hardware affect interpretation of the data.