High-frequency asymptotic behaviour of the apparent diffusion coefficient 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): The purpose of this work was to investigate how the high-frequency asymptotic behaviour of the ADC is affected when an approximate cosinusoidal waveform is used for OGSE-DWI measurements. Approach: A theoretical study was performed that derived the asymptotic behaviour of the ADC from first principles for three MPG waveforms. Results: The difference in predicted behaviour between an approximate cosinusoidal waveform and an ideal waveform may be important when making precise measurements of the surface-to-volume ratio. Impact: The microstructure of a complex medium can be characterised by measuring the high-frequency limit of the ADC with OGSE-DWI. However, it is important to understand how the limitations of the gradient hardware affect the interpretation of the data.