In this work, the usefulness of the inverse Laplace transformation (ILT) in the characterization of diffusion processes in the brain has been investigated. The method has been implemented on both phantom and in vivo cat brain data acquired at high resolution at 9.4 T. The results were compared with monoexponential and biexponential analyses of the same data. It is shown that in the case of diffusion restricted by white matter axonal tracts, the resulting diffusograms are in good agreement with the biexponential model. In gray matter, however, the non-monoexponential decay does not lead to a bimodal distribution in the ILT, even though the data can be fitted to a biexponential. This finding suggests the possibility of a distribution of diffusion coefficients rather than a discrete biexponential behavior. It is shown that this distribution is sensitive, for example, to experimental parameters such as the diffusion time. Thus, the ILT offers the possibility of implementing a unique tool for the analysis of heterogeneous diffusion, that is, the analysis of the diffusion coefficient distribution, which has the yet unexplored potential of being a valuable parameter in the characterization of tissue structure.
Bibliographical noteFunding Information:
This work was supported by NIH grant P41 RR08079, by the Keck foundation grant and by the Human Frontiers Science Program. We would like to thank Jaekeun Park for his help with the animal experiments.
- Cat brain
- Laplace transformation