It is estimated that each year around 2 million people die of Acute Kidney Injury (AKI)[1,2]. Development of non-invasive MR methods is essential to diagnose AKI as early as possible. Parametric mapping of renal T₂^* gives access to the blood oxygenation level dependent contrast. We previously monitored renal T₂^* changes continuously during ischemia-reperfusion (I/R) in rats[3]. Absolute T₂^* values are hard to compare due to factors such as magnetic field strength, B₀ homogeneity, voxel size etc. Minkowski Functionals (MFs) allow a quantitative analysis of tissue heterogeneity – independent of absolute signal intensities (if applied to images) or parameter values (if applied to parametric maps). This approach was recently used to characterize changes in tumor tissue heterogeneity on T₂-weighted images, independent of tumor size[4]. The principles behind MFs are illustrated in Fig.1. We previously analysed total renal T₂^* heterogeneity to distinguish between healthy, ischemic and reperfused kidneys independent of absolute T₂^*[5]. In this study we developed this approach further to capture heterogeneity within renal layers, specifically the cortex and outer medulla, to provide an even more detailed and selective insight into these pathophysiologically different layers.

Animal model: Seven anesthetized Lewis rats (male, 2-3 months, 250–300g) underwent renal I/R inside a 9.4T MR system (Bruker Biospin, Germany)[3]. T₂^* was monitored with a temporal resolution of ~3min. Ischemia was induced by closing a remotely-controlled hydraulic occluder around the renal artery and vein for 45 minutes, subsequent release of the occlusion led to reperfusion. Interruption and restoration of renal blood flow was confirmed by time-of-flight MR angiography.
MR imaging: Experiments were conducted with a birdcage RF resonator for transmission in conjunction with a four channel receive RF coil array (Bruker Biospin, Germany) customized for rats. T₂-weighted pilot scans and local B₀ shimming that uses a voxel tailored to the kidney were performed first. For T₂^* mapping a respiratory-gated multi gradient echo (MGE) sequence (TR=50ms, number of echoes=10, first TE=1.43ms, echo spacing=2.14ms, averages=4) was employed with a total acquisition time of ~1min 20sec. A coronal oblique image slice was acquired (spatial in plane resolution=(226×445)μm², slice thickness=1.4mm. T₂^* maps (Fig.2) were calculated using MATLAB (The MathWorks, Inc., Natwick, USA).
Layer segmentation model: An established renal segmentation model[3,6], which defines three regions of interest (ROIs) within each renal layer based on histological data and photographs of freshly excised rat kidneys was extended in order to provide one large ROI for each layer. By connecting the three ROIs within each layer a large section of cortex and outer medulla could be captured with the ROIs. T₂^* maps were manually registered to this segmentation model (Fig.2).
Heterogeneity analysis: The bias of differences in the absolute T₂^* was removed by re-scaling 0.01 to 0.99 percent of the intensities in each ROI to the range[0,1]. The ROIs were then thresholded in 10 steps to create binary images. Minkowski Functionals were calculated for visible pixels using MATLAB[7]; both the total number of pixels and number of pixels at the edges were counted to yield the area and perimeter (Fig.1), respectively, as a function of the threshold. Comparisons between time points were performed by choosing threshold values showing the largest differences between ischaemia / reperfusion and baseline and performing a t-test at this threshold.

When Minkowski Functionals were plotted as a function of the 10 grayscale threshold levels, each of the MF had a unique shape for each dataset (Fig.3). Significant differences were observed in the cortical area when comparing baseline with ischemia (at threshold level 6, t=1.84, *p=0.049). No significant differences in cortical area were observed between baseline and reperfusion (at threshold level 6, t=0.56, **p=0.29). Within the outer medulla, the area calculated as a function of grayscale threshold showed significant differences between baseline and ischaemia (at threshold level 3, t=3.44, *p<0.01). At threshold level 5 a significant difference was observed between baseline and reperfusion (t=2.41, **p=0.02). While the perimeter showed no significant differences in the cortex, in the outer medulla, however, significant differences were found between baseline and ischemia (at threshold level 3, t=4.53, *p<0.01) and between baseline and reperfusion (at threshold level 7, t=3.32, **p<0.01).Our preliminary results demonstrate the feasibility and utility of Minkowski Functionals for detecting changes in renal cortical and medullary T₂^* heterogeneity during renal ischemia and reperfusion. T₂^* heterogeneity analysis using MF is thus an encouraging novel technique for identifying changes in (for making distinctions between) healthy and injured kidneys. MF analysis holds the potential for implementation as a diagnostic method in renal pathophysiological scenarios and requires further investigation, even in other organs and pathologic situations.