Estimation of multicomponent flow in the kidney with multi-b-value spectral diffusion

Examine the theory and potential clinical application of estimated intravoxel "flow" of separated perfusion, tubular flow, and tissue diffusion from multi-b-value DWI in kidney allografts.

Multi-b-value DWI (nine b-values; 0-800 s/mm²) from a kidney cortex is simulated with anisotropic and non-Gaussian (i.e., anomalous) vascular, tubular, and tissue components and analyzed with a Bayesian biexponential, least-squares triexponential, and spectral diffusion MRI. Comparison and application of biexponential, triexponential, and spectral diffusion flow proxies as the product of signal fraction $f$ and diffusion coefficient $D$ , $fD$ for each component, is demonstrated in a two-center study of 54 kidney allografts patients (21 females/33 males, 48.8 ± 10.5 years, NCT05058170) and compared to fibrosis (Banff 2017 interstitial fibrosis and tubular atrophy score 0-6 from clinical biopsies of the renal cortex), impaired kidney function (Chronic Kidney Disease Epidemiology Collaboration 2021 estimated glomerular filtration rate<45 mL/min/1.73 m²), and proteinuria (mg/24 h).

Spectral diffusion $\mathrm{fD}$ demonstrated strong correlation to input $\mathrm{fD}$ of the simulated anisotropic and anomalous components. It agreed with both three-component diffusion ( $y=1.10x-0.1$ , $R^2=0.74$ ) and two-component diffusion ( $y=1.01+0.2,R^2=0.88$ ). $\mathrm{fD}$  showed similar or improved agreement and correlation to input than the individual parameters $f$ and $D$ , and spectral diffusion showed similar or improved agreement than corresponding bi- and triexponential models. In kidney allografts, $\mathrm{fD}$ from spectral diffusion showed that allografts with higher fibrosis score had higher $f{D}_{\text{tissue}}$ (one-way analysis of variance F-statistic = 3.86, p = 0.02) and that allografts with impaired function had reduced $f{D}_{\text{tubule}}$ (Mann-Whitney U-test = -2.14, p = 0.04). Across diagnostic groups of function and fibrosis, $f{D}_{\text{vasc}}$ negatively correlated with proteinuria ( $y=-348x+1144,p=0.035R^2=0.82$ ).

Spectral diffusion MRI with multi-Gaussian $\mathrm{fD}$ as a flow proxy separated different anomalous and anisotropic diffusion components of perfusion, tubular flow, and tissue diffusion and may hold clinical value in diffusion MRI of kidney pathophysiology.