Purpose:

Increased incidence of kidney diseases is a substantial global concern and current biomarkers and existing treatment options are unsatisfactory. Change in renal tubule luminal volume fraction (TVF) is a potential rapid biomarker for kidney disease¹, and may also be valuable for gaining a better mechanistic understanding of renal (patho-)physiology^2,3,4. T₂ mapping is an established MRI technique that can be used for quantifying changes in the tissue water fraction in vivo, and may provide a tool to probe renal tissue properties noninvasively. The ultimate aim of this work is to determine the TVF in the rat kidney from MRI using T₂ mapping, by applying multiexponential analysis of the T₂ driven signal decay to examine the micro-morphological and physiological changes in renal tissue. In order to achieve this goal, we developed a protocol tailored for T₂ mapping of the rat kidney, and determined a suitable numerical solution for multi-exponential decomposition of the T₂-decay based on linformation from iterature and numerical algorithms. We evaluated and validated protocol and algorithms using synthetic data and measurements in purpose-built phantoms.

Methods:

Tubular fluid, which originates from ultrafiltration in the glomeruli, has a substantially longer T₂ compared to the renal parenchyma. Therefore, the tubular contribution to the signal should be separable from the tissue signal by nonlinear least squares regression. To improve the robustness of the regression, bisquare weights⁵ were applied, which minimizes a weighted sum of squares, such that the weight given to each data point depends on how far the point is from the fitted line. The numerical solution for multi-exponential decomposition was done using MATLAB functions. The algorithm was evaluated using synthetic data simulations and measurements in phantoms. We developed a 2-compartment-model based on Bloch-simulations toolkit (Brian.A. Hargreaves) to estimate the actual T₂ echo modulation curve in a multi-spin-echo experiment. Simulations were repeated for a range of T₂ and SNR, yielding a database of simulated T₂, which was then used to identify the T₂ value that most closely matched the experimentally measured data at each voxel (See example Figure1). Gaussian distributed white noise, was applied to the signal, such that the signal-to-noise ratio SNR =mean(s)/σ, is similar to the noise found in the magnitude images acquired during in vivo experiments. A full dictionary of simulated T₂ decay curves was acquired by repeating the simulations, each time with a different: T₂=[5:5:50,60,70:15:100,120,140:25:190,220,250:35:320,360,420,500];T₁=[1400,1500,1720,1850], TR =[400,500:200:1500,1800:300:3000],flipAng=(120°to180°,with2°increments),echo-spacing=[5:10,12,13,15,16,18:2:38,41:3:50],SNR=[5,10,20,30,50,80,120,180,270,400,600,900] tubule fraction scale (0% to 95%, with 5% increments). A novel phantom was designed to mimic realistic changes of TVF in the rat kidney. The housing was designed using Autodesk Fusion 360 and printed in a cylinder on a 3D-Printer (Dimension 1200es). Pure water was used for comparison. Water doped with MnCl₂ and CuSO₄ was used to achieve T₁ and T₂ times similar to the tubular fluid and the renal parenchyma. MRI data were acquired with a 2-channel volumetric transceiver RF coil on a 9.4T animal MR scanner (Biospec, Bruker BioSpin). T₂ mapping was performed with a MESE-technique: TE=6.4ms, TErange= 6.4,12.8,19.2,25.6,32,38.4,44.8,51.2,57.6,64,70.4,76.8,83.2ms, slice thickness=1mm, FOV=5x5cm, matrix=240x240, resolution 0.02mm, number of averages=1 and total acquisition time=4m 0 sec for each T₂ map.

Results:

Table1 provides an example of the Mean Absolute Error (MAE) measuring TVF acquired with a modified numerical solution for multi-exponential decomposition, using the dictionary of distributed T₂s with echo spacing. In addition, MAE was determined for varying volume fractions, number of echoes and flip angles. Our results demonstrate the mean error variation for (SNR=30,esp=15,T₂=50ms,frac=15%,T₁=500ms,flipAng=180°) was predicted to be 2.4%. An oscillation of about 2.6% was observed due to imperfect refocusing pulses. Figure2 shows a visualization of the reconstructed maps of the custom-built T₁-T₂ phantom; the histogram shows the T₂ distribution corresponding to the selected exemplary ROI. An accuracy of 95% and 98% (Table2) was achieved with modified Levenberg-Marquardt and Trust-Region on the phantom. Table3 shows the estimated TVF after the fitting procedure (Trust-Region) before and after removing the contribution of T₁.

Discussion:

Since in vivo experiments are limited by the constraints of acquisition time and resolution, we applied multi-exponential decomposition on simulations of several different conditions of simulated T₂ map acquisition, in order to determine the best protocol tailored for T₂ mapping of the rat kidney. Application of this approach on the mechanical phantom showed that the accuracy increased gradually with increasing TVF, but the average accuracy (83.6%) was still suboptimal. Upon correction of T₁ effects on signal intensity, the accuracy of our approached increased to 98.11%. Validation of initial results using a second independent measurement demonstrated excellent reproducibility.

Conclusion:

Our preliminary results demonstrate that modified Trust-Region is promising for research into quantitative assessment of renal TVF in in vivo applications. Future in vivo experiments with physiologically relevant interventions (e.g. increased pressure in the renal pelvis and tubules) for altering TVF is required to further study these methods. Future validation of this MR approach with intravital microscopy, i.e. for quantitative comparison of changes in the vascular and renal tubular compartments with those observed by T₂* and T₂, is also warranted. Ultimately, these investigations have the potential to help uncover the hidden patterns in acute renal injury that lead to chronic kidney disease, which will improve diagnosis, prognosis and treatment of renal disorders.

Acknowledgements

This work was funded in part (TN, ES, SW, TG, KC) by the German Research Foundation (Gefoerdert durch die Deutsche Forschungsgemeinschaft (DFG), Projektnummer 394046635, SFB 1365, RENOPROTECTION). We thank the MDC-Weizmann Helmholtz International Research School for Imaging and Data Science from the NAno to the MESo (iNAMES).