Introduction

It is thought that reduced nephron number is the primary cause of reduced kidney function¹. Cationic ferritin (CF) enhanced MRI (CFE-MRI) measures glomerular number and individual glomerular volume (IGV) in the excised and perfused kidneys^2-4 The IGV distribution may be useful in detecting the early signs of disease. Currently, IGV calculated from MR images is validated with measurements of glomerulus size from histology sections of the same kidney. A physical model of the susceptibility-induced artifact by CF accumulation on the glomerulus will enable accurate quantitative measurement of IGV without the need for stereology. In this work, we use spin echo (SE) and gradient recalled echo (GRE) measurements of glomerular profiles along with a classical model of static susceptibility^5-8 to correct IGV measurements in CFE-MRI.

Methods

Contrast Enhancement of Glomeruli – A rat received CF (5.75mg/100g) as described in previous publication² and prepped for high resolution imaging. Imaging – All imaging was performed on a Bruker 7T/30 Clinscan MRI. Excised kidneys were first imaged with a 2D GRE pulse sequence (TE/TR = 20/80; resolution = 58.0 x 58.0 x 200 um3; α = 30°; bandwidth = 80 Hz/pixel). A 2D SE pulse sequence was applied using the same parameters. Image Processing – MIPAR software was used to identify glomeruli in each SE and GRE images. Line profiles of signal magnitude were measured on all glomeruli in orthogonal directions to B0 (Profile width = 17 voxels), FIG 1. Orthogonal profiles were averaged together to obtain a mean profile for each glomerulus. A threshold on the minimum value was applied in each glomerulus profile to isolate glomeruli believed to be located in the 2D image plane (SE-Threshold = 1159; GE-Threshold = 180). Finally, only glomeruli that overlapped in both SE and GRE images were used for analysis. Local inhomogeneities such as CF labeled glomeruli produce a geometric distortion in MR following, $$$x' = x+\frac{\Delta B}{G_{x}}$$$ (ΔB=Magnetic field from inhomogeneity, Gx = Gradient Strength in x-direction). Distortion occurs via geometric distortion (GRE and SE) and reduction in signal magnitude (GRE only). The amount of geometric distortion is calculated using $$$\frac{\Delta x}{\lambda_{x}}=\lambda$$$, where λx is the factor of geometric distortion simulated for CF labeled glomeruli in GRE images. Signal magnitude is reduced by a factor λ, $$$\lambda = \frac{G_{x}}{G_{x}+G'_{x}}$$$, where G’x is the added background gradient arising from the inhomogeneity. Here, we simplify the problem and average G’x over the voxel length, $$$G'_{x} = \frac{\Delta B}{\Delta x}$$$. Fom the modified spin density (ρ’), we calculate the corrected image, ρ(λx’), with the assumptions above using $$$\rho(\lambda x') = \frac{\rho '(x')}{\lambda}$$$. We applied the relation for correcting images to each mean profile measured in GRE images to produce a corrected profile as would be seen in the SE image. Individual glomerulus volume (IGV) was calculated using a spherical model equation and the full width at half-minimum (FWHM) of the profile as the glomerulus diameter.

Results

We used a classical model of static susceptibility to correct IGV measurements from GRE images. IGV measurements from SE images (IGV_SE) matched literature values that were also validated with stereology². The factor of geometric distortion for GRE images was found to be λ_x=~1.1. The reduction in signal magnitude was found to be λ=~ 0.22. We used λ and λ_x to correct the mean profiles measured from GRE images. A correlation coefficient of 0.9951 was measured between the mean GRE profile and the mean SE profile (FIG 1). IGV distribution was re-calculated using corrected profiles. The number of significantly different bins between IGV_SE and IGV_GRE changed from >1/5 of all bins for uncorrected GRE profiles to <1/20 of all bins using corrected GRE profiles (FIG 2).

Discussion

In this work, we were able to obtain accurate IGV measurements from CFE-MRI. A regression of corrected GRE values compared to values measured in SE images had an R² value of 0.88. These measurements were made using high-resolution MR images and within healthy glomeruli. Future work will need to account for the use of lower resolutions used in in vivo CFE-MRI to accurately adjust IGV values. Also, further work will be focused in accounting for the non-healthy glomeruli where leakage of macromolecules, such as CF, occur and results in a stretched profile of the glomerulus in MR images as seen previously⁹. This work will be a useful foundation in any application where negative contrast agents are used to quantify tissue microstructure.

Acknowledgements

The authors gratefully thank the molecular imaging core at the University of Virginia and Jack Roy for his great input and help with this project. Many thanks to Jeremy Gatesman, Kimberly A. deRonde, and the UVa veterinary staff for all their help.