Analysis of the distribution of diffusion coefficients in cat brain at 9.4 T using the inverse Laplace transformation

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.