Reply to: On the perils of multiexponential fitting of diffusion MR data.

Abstract

We would like to thank the authors of the letter for their interest and comments on our recent article.1 They have questioned our fitting procedure in which the fast-free diffusion coefficient (Df) was fixed to the diffusion coefficient of free water at 37°C (3.0 × 10−3 mm2/s). Moreover, they have interpreted that the fast and slow diffusion component fractions (Ff and Fs, respectively) correspond to the extracellular and intracellular water fractions, respectively, based on the results of previous studies2-5 and showed that their fractions depended on whether the diffusion analysis was performed with constrained or unconstrained fits. The primary purpose of our study was to noninvasively obtain information on brain perfusion and diffusion using a triexponential diffusion model assuming three diffusion components: perfusion-related, fast-free (unrestricted), and slow-restricted diffusion. In particular, Ff and Fs in our model are not assumed to correspond to the extracellular and intracellular water fractions, respectively. The slow-restricted diffusion in our model may mainly reflect both extracellular and intracellular diffusion. However, the interpretation of these diffusion fractions still remains unknown. A previous study has shown that the extracellular and intracellular diffusion separation based on the difference in diffusivity between the two compartments is ineffective because they have similar diffusion coefficients.6 Other studies have reported that intracellular water itself has multiple diffusion components7 and that apparent diffusion coefficient of the brain changes during the cardiac cycle.8, 9 To further complicate matters, the water exchange between the extracellular and intracellular compartments potentially affects the diffusion measurements of these compartments.10 Thus, the modeling of various diffusion components should be further discussed in future studies. In our study, a constrained fitting procedure was used to improve the accuracy and robustness of the analysis. As shown in table 1 of their letter, in comparison with the constrained fit, the unconstrained fit demonstrated substantially higher standard deviations for the diffusion parameters. Our preliminary study (data not shown) also indicated that the unconstrained fit led to considerable fitting error, perhaps because of the large number of variables in the triexponential model and the relatively small blood volume fraction in the brain. In contrast, the constrained fit for our model successfully showed a close correlation between the perfusion-related diffusion coefficient and regional cerebral blood flow obtained using arterial spin labeling in the caudate nucleus and putamen of healthy subjects, as demonstrated in our article.1 We therefore believe that the triexponential diffusion analysis with the constrained fitting procedure would be desirable to extract perfusion-related information for the brain from diffusion-weighted data.