The distortions of the free water model for diffusion MRI data when assuming single compartment relaxometry and proton density

Abstract

Objective. To document the bias of the simplified free water model of diffusion MRI (dMRI) signal vis-à-vis a specific model which, in addition to diffusion, incorporates compartment-specific proton density (PD), T1 recovery during repetition time (TR), and T2 decay during echo time (TE). Approach. Both models assume that volume fraction f of the total signal in any voxel arises from the free water compartment (fw) such as cerebrospinal fluid or edema, and the remainder (1-f) from hindered water (hw) which is constrained by cellular structures such as white matter (WM). The specific and simplified models are compared on a synthetic dataset, using a range of PD, T1 and T2 values. We then fit the models to an in vivo healthy brain dMRI dataset. For both synthetic and in vivo data we use experimentally feasible TR, TE, signal-to-noise ratio (SNR) and physiologically plausible diffusion profiles. Main results. From the simulations we see that the difference between the estimated simplified f and specific f is largest for mid-range ground-truth f, and it increases as SNR increases. The estimation of volume fraction f is sensitive to the choice of model, simplified or specific, but the estimated diffusion parameters are robust to small perturbations in the simulation. Specific f is more accurate and precise than simplified f. In the white matter (WM) regions of the in vivo images, specific f is lower than simplified f. Significance. In dMRI models for free water, accounting for compartment specific PD, T1 and T2, in addition to diffusion, improves the estimation of model parameters. This extra model specification attenuates the estimation bias of compartmental volume fraction without affecting the estimation of other diffusion parameters.