The present study first proposed the non-Gaussian DKI model as a potential non-invasive method for evaluating of CAI.
Jensen et al. first proposed DKI in 2005, as an extension of conventional DWI, which requires ultrahigh b-values (> 1000 s/mm2) and a modified image post-processing procedure. The traditional model of DWI was established based on the assumption that water diffusion exhibits Gaussian behavior without any restriction and that the diffusion-weighted MRI signal mono-exponentially decreases with increasing b-values; however, a deviation from simple mono-exponential decay is readily identified in the kidney, under either healthy or pathological conditions. DKI could be utilized to analyze non-Gaussian water diffusion with a polynomial model and has been used to identify the heterogeneity of cellularity and microstructural complexity.
DKI can yield two characteristic variables: D and K. D is the diffusion coefficient corrected by a non-Gaussian bias, and K quantifies the deviation of tissue diffusion from a Gaussian pattern . Recently, in animal models, DKI has been used to assess liver fibrosis, which demonstrated additional meaningful information different from that of conventional DWI. There were only two studies focused on DKI in healthy kidneys, which showed conflicting results. And the results showed that whether the maximal b- values (600 and 1000s/mm) are sufficiently high remains controversial. Huang et al.  showed that in a normally functioning kidney, the MK value of the cortex is lower than that of the medulla. Among these diffusion kurtosis indicators, the difference between cortex and medulla is reliable with the presence of radially-oriented vessels, tubules, and collecting ducts in the medulla . Interestingly, Pentang et al.  showed that the cortical MK is larger than the medullary MK.
As a particular metric of the DKI model, K has been hypothesized to represent the direct interaction of water molecules with the cell membrane intracellular compounds and expanded K recommends that the tissue has increasingly irregular and heterogeneous environments with numerous great interfaces. In tumor cells, an increased nuclear-cytoplasmic ratio and microstructural were revealed by K value . The accurate underlying meaning of the diffusional kurtosis metrics is not yet mastered, and DKI acquisition still needs improvement.
Liu et al. found that in the pathogenesis of IgAN, the progressive loss of glomerular capillary structures and the disappearance of glomerular cellular elements with replacement by an expanding extracellular matrix and fibrous tissue could result in more complex microstructure and marked variation in cell size and shape than in healthy kidneys, leading to increased K.
In our study, we found that the MK increased gradually with the deterioration of kidney function, which indicates the increase of a much more irregular and heterogeneous environment in renal allograft with the worsening of renal function. As we know, the primary pathology change of CAI is the glomerulosclerosis and tubular atrophy/interstitial fibrosis, which means a tendency of the more irregular and heterogeneous environment in the renal allograft.
Liu et al. also demonstrated that K showed better performance than ADC in glomerulosclerosis in terms of the diagnostic efficacy, with a relatively larger AUC and stronger correlation. However, the level of statistical significance was not achieved. These results indicate that the K in the DKI model showed clinical potential for assessing the severity of renal sclerosis in the glomeruli and can provide more information compared with ADC.
In our study, we found that ADC and the Mean D value of cortex in patients with severely decreased eGFR were significantly lower than those in patients with higher eGFR. In comparison, the Mean K value in patients with higher eGFR was lower than in patients with severely reduced eGFR.
According to our research, although all the six parameters showed significant differences except cortical ADC and medullary Mean D between Group 1 and Group 2, the ROC's considerable differences were only found in ADC of Medulla and MK of cortex and medulla. But the ADC demonstrated an extremely low specificity, and the MK of the cortex showed the largest AUC. Meanwhile, we performed a random autopsy to confirm the histography change of renal allograft. We found that there were glomerulosclerosis and tubular atrophy/interstitial fibrosis of the randomly selected patients, which confirmed that K increased with the deterioration of renal function and renal fibrosis progression. So, we suggested that Mean K showed excellent CAI prediction for the identification of both glomerulosclerosis and tubular atrophy/interstitial fibrosis.
At the same time, the higher Mean K value of patients with decreased renal function may be partially due to interstitial fibrosis. The higher cell density and collagen deposition may result in lower ADC values in renal allografts . This showed that DKI parameters have broad clinical application prospects in the non-invasive screening of the function of renal allografts at various stages. When 0.491 was set as the cutoff value, the Mean K in the cortex demonstrated a sensitivity of 87% and specificity of 100% for predicting impaired allograft function.
There are limitations to this study. First, the number of patients with normal eGFR was little. And it limits the accuracy of ROC curves. Second, not all the patients were performed biopsy in this study to analyze the quantitative correlation between histopathologic results and DKI parameters.
So, although we confirmed that the DKI model was associated with the changes of eGFR and can assess CAI to some extent if the DKI model can evaluate the evolution of CAI more accurately before the change of eGFR still needs to be studied. In the future, we aim to perform a more extensive sample size research to explore if the micro-changes detected by the DKI model can stand for the change of CAI more accurately even earlier than eGFR.