Continuous diffusion spectrum computation for diffusion-weighted magnetic resonance imaging of the kidney tubule system

Background: The use of rigid multi-exponential models (with a priori predefined numbers of components) is common practice for diffusion-weighted MRI (DWI) analysis of the kidney. This approach may not accurately reflect renal microstructure, as the data are forced to conform to the a priori assumptions of simplified models. This work examines the feasibility of less constrained, data-driven non-negative least squares (NNLS) continuum modelling for DWI of the kidney tubule system in simulations that include emulations of pathophysiological conditions. Methods: Non-linear least squares (LS) fitting was used as reference for the simulations. For performance assessment, a threshold of 5% or 10% for the mean absolute percentage error (MAPE) of NNLS and LS results was used. As ground truth, a tri-exponential model using defined volume fractions and diffusion coefficients for each renal compartment (tubule system: D-tubules, f(tubules); renal tissue: D-tissue, f(tissue); renal blood: D-blood, f(blood);) was applied. The impact of: (I) signal-to-noise ratio (SNR) =40-1,000, (II) number of b-values (n=10-50), (III) diffusion weighting (b-range(small) =0-800 up to b-range(large) = 0-2,180 s/mm(2)), and (IV) fixation of the diffusion coefficients D-tissue and D-blood was examined. NNLS was evaluated for baseline and pathophysiological conditions, namely increased tubular volume fraction (ITV) and renal fibrosis (10%: grade I, mild) and 30% (grade II, moderate). Results: NNLS showed the same high degree of reliability as the non-linear LS. MAPE of the tubular volume fraction (f(tubules)) decreased with increasing SNR. Increasing the number of b-values was beneficial for f(tubules) precision. Using the b-rangelarge led to a decrease in MAPEf(tubules) compared to b-range(small). The use of a medium b-value range of b=0-1,380 s/mm(2) improved f(tubules) precision, and further b(max) increases beyond this range yielded diminishing improvements. Fixing D-blood and D-tissue significantly reduced MAPEf(tubules) and provided near perfect distinction between baseline and ITV conditions. Without constraining the number of renal compartments in advance, NNLS was able to detect the (fourth) fibrotic compartment, to differentiate it from the other three diffusion components, and to distinguish between 10% vs. 30% fibrosis. Conclusions: This work demonstrates the feasibility of NNLS modelling for DWI of the kidney tubule system and shows its potential for examining diffusion compartments associated with renal pathophysiology including ITV fraction and different degrees of fibrosis.