Intravoxel incoherent motion analysis of renal allograft diffusion with clinical and histopathological correlation in pediatric kidney transplant patients
Clare B Poynton1, Marsha Lee2, Yi Li1, Zoltan Laszik3, John D Mackenzie1, Pauline W Worters4, and Jesse Courtier1

1Department of Radiology and Biomedical Imaging, University of California, San Francisco, San Francisco, CA, United States, 2Department of Pediatrics, University of California, San Francisco, San Francisco, CA, United States, 3Department of Pathology, University of California, San Francisco, San Francisco, CA, United States, 4GE Healthcare, Menlo Park, CA, United States

### Synopsis

This study investigated the use of intravoxel incoherent motion (IVIM) analysis for characterizing diffusion in renal allografts of pediatric transplant recipients. Patients were separated into two groups according to whether or not a renal allograft biopsy resulted in a change in clinical management. Patients requiring a change in management (i.e., increase in immunosuppression) showed statistically significant differences in tissue diffusivity in the region of the biopsy relative to those that did not require any change. These results suggest IVIM analysis may be a useful non-invasive tool for guiding clinical management of pediatric kidney transplant patients.

### Introduction

Changes in the apparent diffusion coefficient (ADC) and fractional anisotropy (FA) obtained from diffusion-weighted imaging (DWI) and diffusion tensor imaging (DTI), respectively, have been found in patients with renal pathology [1-3], but may not distinguish well between flow effects and diffusion effects [4,5]. Intravoxel incoherent motion analysis (IVIM) of DWI data allows for estimation of the pseudo-diffusion (tubular/vascular flow) and passive structural diffusion in renal parenchyma [5]. We hypothesized that IVIM may be useful for characterizing diffusion differences in renal allografts of pediatric transplant recipients.

### Methods

This study was conducted after obtaining IRB approval and written informed consent from each subject. Between 10/2014 and 9/2015, 14 pediatric renal transplant recipients (mean age 15.7 $\pm$ 2.9) were prospectively scanned on a clinical 3T magnetic resonance (MR) scanner, prior to obtaining an ultrasound-guided renal transplant biopsy. An echo-planar DTI sequence was performed in the coronal plane using four b values (200, 400, 600, 800 $\textrm{s/mm}^{2}$), 20 diffusion directions, FOV=36cm, TE=90ms, TR=2500ms, matrix size= 192 x 192, and scan-time=90s . For each b-value, an accompanying T2-weighted (b=0) image was acquired. Data from 11 subjects was analyzed following inspection of the dicom data for image quality. The magnetization, M, at each voxel was modeled according to Eq 1:

$$M = M_{0} ( f_{p}\, \textrm{exp}(-b D_{p}) + (1 - f_{p})\, \textrm{exp}(-b D_{t}))$$

where $M_{0}$ is the total magnetization, $f_{p}$ is the perfusion fraction, $D_{p}$ is the pseudo-diffusivity, and $D_{t}$ is the tissue-diffusivity [4]. The IVIM parameters, $\mathbf{x} =\{ f_{p}, D_{p}, D_{t}\}$, were estimated for each voxel and each diffusion direction independently according to Eq 2:

$$\mathbf{x}^{*} = \underset{\mathbf{x}}{\arg \min} \displaystyle\sum_{b_{j}}\Big(M - M_{0}( f_{p} \, \textrm{exp}(-b_{j} D_{p}) + (1 - f_{p})\, \textrm{exp}(-b_{j} D_{t}))\Big)^{2} \qquad \textrm{s.t.} \qquad f_{p} \in [0,1], \; D_{p} > 0, \; \textrm{and} \; D_{t} > 0,$$

where $b_{j} \in \{200, 400, 600, 800 \}$ . Eq 2 was solved in Matlab using a standard constrained nonlinear optimization technique. For each subject, final IVIM maps of each parameter estimate were obtained by computing the mean across all diffusion directions. Regions of interest (ROIs) were defined for each subject on the cortex (n=1) and medulla (n=3), using the coronal plane of a single b0 image. Medullary ROIs of uniform size (5x5 voxels) were defined in the lower-polar, inter-polar, and upper-polar regions. For each subject, mean values of $D_{p}$, $D_{t}$, and $f_{p}$ were computed from the cortical ROI and the medually ROI that corresponded to the biopsy site. Subjects were grouped according to whether the biopsy resulted in a change in clinical management (change vs. no change). Group differences in cortical and medullary IVIM estimates and intra-group cortico-medullary differences in tissue-diffusivity were assessed using two-tailed t-tests.

### Results

For patients in the no change group, mean $\pm$ std (units) of IVIM parameters in the medullary ROI were: $f_{p} = 39 \pm 7 \, (\%)$, $D_{p} = 60.9 \pm 8.5 \, (\textrm{x}10^{-3} \textrm{mm}^{2}\textrm{/s})$, and $D_{t} = 1.2 \pm 0.008 \, (\textrm{x}10^{-3} \textrm{mm}^{2}\textrm{/s})$. For patients in the change group, $f_{p} = 37 \pm 10 \, (\%)$, $D_{p} = 64.7 \pm 12.2 \, (\textrm{x}10^{-3} \textrm{mm}^{2}\textrm{/s})$ , and $D_{t} = 1.0 \pm 0.013 \, (\textrm{x}10^{-3} \textrm{mm}^{2}\textrm{/s})$. The b0 image and $D_{t}$ map from a representative subject from each group is shown in Fig 1. Descriptive statistics of each parameter in the medullary ROIs are shown in Fig 2. All IVIM estimates were lower in the change group, with this difference being statistically significant for $D_{t}$ (p = 0.017). No statistically significant group differences in IVIM parameters were found in the cortex. Within both groups, the mean tissue-diffusivity in the cortical ROI (ctx) was higher than in the medullary ROI (med), and this difference was statistically significant for the change group: $D_{t, ctx} = 1.3 \, \textrm{x}\, 10^{-3} \textrm{mm}^{2}\textrm{/s}$, $D_{t, med} = 1.0 \, \textrm{x}\, 10^{-3} \textrm{mm}^{2}\textrm{/s}$ with p = 0.016. For the no change group, $D_{t, ctx} = 1.3 \, \textrm{x}\, 10^{-3} \textrm{mm}^{2}\textrm{/s}$, $D_{t, med} = 1.2 \, \textrm{x}\, 10^{-3} \textrm{mm}^{2}\textrm{/s}$ with p = 0.25.

### Conclusions

The main findings of this study include (1) lower tissue-diffusivity in the medulla of patients with a biopsy that resulted in a change in management and (2) within the change group, decreased tissue diffusivity in the medullary relative to the cortical ROIs. Although the number of subjects in this study was small, these results suggest that pathology, such as tubulitis and interstitial inflammation found on biopsy, may be associated with reductions in tissue-diffusivity. Thus, IVIM analysis may be a useful tool for non-invasive assessment of renal allografts in pediatric transplant recipients, potentially sparing unnecessary renal biopsies.

### Acknowledgements

No acknowledgement found.

### References

[1] Eisenberger U, Thoeny HC, Binser T, Gugger M, Frey FJ, Boesch C, Vermathen P. Evaluation of renal allograft function early after transplantation with diffusion-weighted MR imaging. Eur Radiol 2010;20: 1374–1383.

[2] Hueper K, Gutberlet M, Rodt T, Gwinner W, Lehner F, Wacker F, Galanski M, Hartung D. Diffusion tensor imaging and tractography for assessment of renal allograft dysfunction-initial results. Eur Radiol 2011;21:2427–2433.

[3] Lanzman RS, Ljimani A, Pentang G, Zgoura P, Zenginli H, Kropil P, Heusch P, Schek J, Miese FR, Blondin D, Antoch G, Wittsack HJ. Kidney transplant: functional assessment with diffusion-tensor MR imaging at 3T. Radiology 2013;266:218–225.

[4] Le Bihan D, Breton E, Lallemand D, Grenier P, Cabanis E, Laval-Jeantet M. MR imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders. Radiology 1986; 161:401–407.

[5] Notohamiprodjo M, Chandarana H, Mikheev A, Rusinek H, Grinstead J, Feiweier T, Raya JG, Lee VS, Sigmund EE. Combined intravoxel incoherent motion and diffusion tensor imaging of renal diffusion and flow anisotropy. Magn Reson Med. 2015 Apr;73(4):1526-32.

### Figures

Fig 1. b0 images (A,C) and mean Dt estimates (B,D) from a representative patient from the no change group (A,B) and the change group (C,D) are shown above. The yellow boxes show enlarged views of the inter-polar (A,B) and lower-polar (C,D) areas surrounding the medullary ROIs (red boxes).

Fig 2. Box plots showing the min, max, first and third quartile, and median of each IVIM parameter in medullary ROIS of both groups are shown above. The change group shows lower estimates in all three parameters and this difference is statistically significant for Dt (p=0.017).

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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