Quantification of Multi-Compartment Flow with Spectral Diffusion MRI

Purpose: Estimation of multi-compartment intravoxel flow in fD in ml/100g/min with multi-b-value diffusion weighted imaging and a multi-Gaussian model in the kidneys. Theory and Methods: A multi-Gaussian model of intravoxel flow using water transport time to quantify fD is presented and simulated. Multi-compartment anisotropic DWI signal is simulated analyzed with (1) a rigid bi-exponential, (2) a rigid tri-exponential, and (3) diffusion spectrum imaging model of intravoxel incoherent motion (spectral diffusion). The application is demonstrated in a two-center study of 54 kidney allografts with 9 b-value advanced DWI that were split by function (CKD-EPI 2021 eGFR<45ml/min/1.73m2) and fibrosis (Banff 2017 interstitial fibrosis and tubular atrophy score 0-6). Results: Spectral diffusion demonstrated strong correlation to truth for simulated three-compartment anisotropic diffusion (y=1.08x+0.1, R2=0.71) and two-compartment anisotropic diffusion (y=0.91x+0.6, R2=0.74), outperforming rigid models in cases of variable compartment number. Use of a fixed regularization parameter set to {\lambda}=0.1 increased computation up to 208-fold and agreed with voxel-wise cross-validated regularization (concordance correlation coefficient=0.99). Spectral diffusion of renal allografts showed significant increase in tissue parenchyma compartment fD (f-stat=3.86, p=0.02). Tubular fD was significantly decreased in allografts with impaired function (Mann-Whitney Utest t-stat=-2.14, p=0.04). Conclusions: Quantitative multi-compartment intravoxel flow can be estimated in ml/100g/min with fD from multi-Gaussian diffusion, even with moderate anisotropy such as in kidneys. The use of spectral diffusion with a multi-Gaussian model and a fixed regularization parameter shows promise in organs such as the kidney with variable numbers of physiologic compartments.