Correcting pulse duration effects in the diffusional kurtosis of the multi-compartment Kärger model

To demonstrate a method of reducing pulse duration effects for the diffusional kurtosis of the multi-compartment Kärger model (KM) as estimated with a Stejskal-Tanner DWI sequence.

An effective diffusion time is introduced that corrects errors in the apparent diffusional kurtosis arising from a nonzero pulse duration δ for the multi-compartment KM. The correction is exact to first order in the diffusion time Δ, and numerical calculations are used to assess how well it reduces pulse duration effects. Specifically, for the two-compartment KM, the deviations of the apparent kurtosis obtained with the Stejskal-Tanner sequence from the exact kurtosis are calculated for the full range of δ and Δ, and similar calculations are performed for the deviation in the derivative of the kurtosis with respect to Δ. For the general multi-compartment KM, upper bounds on the maximum magnitude of the deviations are determined. Application of the correction to estimation of intercompartmental exchange rates is illustrated with several examples.

For the two-compartment KM, the correction reduces the deviation of the apparent kurtosis and its time derivative for most values of δ and Δ. For the general multi-compartment KM, the maximum deviation magnitude, relative to the initial kurtosis, is 2.26% for the uncorrected kurtosis and 0.57% after correction. The correction reduces the maximum deviation magnitude of the derivative from 46% to less than 1%.

Pulse duration effects for the kurtosis of the multi-compartment KM can be strongly suppressed by applying the effective diffusion time correction.