Frederik Bernd Laun1, Wolfhard Semmler1, Bram Stieltjes2
1Medical Physics in Radiology, German Cancer Research Center, Heidelberg, Baden-Wrttemberg, Germany; 2Quantitative Imaging-based Disease Characterization, German Cancer Research Center, Heidelberg, Baden-Wrttemberg, Germany
We study the link between apparent kurtosis and eigensystem of the confining domain. It is shown that the fourth cumulant of the phase distribution for closed domains in the motional narrowing regime is properly described by a series expansion in inverse powers of the diffusion time. The coefficients are proportional to the product of two constants. One of them is solely determined by the eigensystem, while the other is solely determined by the temporal profile of the diffusion gradients. In conclusion, a clear relation between the apparent kurtosis and the eigensystem is established.