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 $fD$ (ml/100g/min) is presented and simulated. Multi-compartment anisotropic DWI signal is simulated with Rician noise and SNR=50 and analyzed with a rigid bi-exponential, a rigid tri-exponential and diffusion spectrum imaging model of intravoxel incoherent motion (spectral diffusion) to study extraction of multi-compartment flow. The regularization parameter for spectral diffusion is varied to study the impact on the resulting spectrum and computation speed. 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) to demonstrate multi-compartment flow of various kidney pathologies.

Results: Simulation of anisotropic multi-compartment flow from spectral diffusion demonstrated strong correlation to truth for both three-compartment anisotropic diffusion ( $y=1.08x+0.1,R^2=0.71$ ) and two-compartment anisotropic diffusion ( $y=0.91+0.6,R^2=0.74$ ), 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 decreasing trend of tubular and vascular flow with higher levels of fibrosis, and significant increase in tissue parenchyma flow (f-stat=3.86, p=0.02). Tubular $fD$ was significantly decreased in allografts with impaired function (eGFR<45ml/min/1.73m²)(Mann-Whitney U 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 with water transport time, even with moderate anisotropy such as in kidneys. The use of spectral diffusion with a multi-Gaussian model and a fixed regularization parameter is particularly promising in organs such as the kidney with variable numbers of physiologic compartments.