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.

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.

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.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.