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

Joāo S Periquito; Thomas Gladytz; Jason M Millward; Paula Ramos Delgado; Kathleen Cantow; Dirk Grosenick; Luis Hummel; Ariane Anger; Kaixuan Zhao; Erdmann Seeliger; Andreas Pohlmann; Sonia Waiczies; Thoralf Niendorf

doi:10.21037/qims-20-1360

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

Quant Imaging Med Surg. 2021 Jul;11(7):3098-3119. doi: 10.21037/qims-20-1360.

Authors

Affiliations

¹ Berlin Ultrahigh Field Facility (B.U.F.F.), Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany.
² Institute of Physiology, Charité - Universitätsmedizin Berlin, Campus Mitte, Berlin, Germany.
³ Experimental and Clinical Research Center, a Joint Cooperation between the Charité Medical Faculty and the Max Delbrück Center for Molecular Medicine in the Helmholtz Association, Berlin, Germany.
⁴ Physikalisch-Technische Bundesanstalt (PTB), Berlin, Germany.

Abstract

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/mm²), 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-range_large led to a decrease in MAPE _ftubules compared to b-range_small. The use of a medium b-value range of b=0-1,380 s/mm² improved f_tubules precision, and further b_max increases beyond this range yielded diminishing improvements. Fixing D_blood and D_tissue significantly reduced MAPE _ftubules 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.

Keywords: Kidney; MRI; diffusion-weighted imaging; non-negative least squares (NNLS); tubular volume fraction.