Jianbo Shao^{1}, Zhiyao Tian^{1}, Xiaowen Wang^{2}, Zujun Hou^{3}, and Xuehua Peng^{1}

GFR would fail to tell the functional status of each kidney for CKD cases,so we try to use machine learning methods to predict GFR of pediatric kidneys based on the IVIM diffusion parameters. The results is that,With account of kidney compensation, averaged correlation between predicted and measured GFR up to 0.9 (*p < 0.05*) was obtained for the combination of perfusion-fraction f and pseudo-flow fD*. For comparison, if not taking into account kidney compensation, the best predictor attained the correlation of 0.3. We conclude that a noninvasive method can predict well the GFR of children with kidney diseases using multiple b values DWI. The best predictions involved the use of perfusion-fraction f and pseudo-flow fD* which are closely related to renal blood perfusion.

Figure 1. MRI images and ADC/IVIM parameter maps from a 11-year old boy. (a) T1-weighted image, (b) diffusion-weighted image at b-value of 50 s/mm2, (c) color-coded ADC map, (d-f) colored coded D, D* and f maps from IVIM model. MRI images taken from slice near central section of kidneys, with left kidney hydronephronetic due to PUJO. Median ADC values within ROI of each kidney are 1.76 (right) and 1.50 (left).

Figure 2. Pearson’s correlation coefficient (averages from 10 trials each) between predicted and estimated GFR values for K-NN methods without taking into account kidney compensation. Median values of DWI parameters from both kidneys are used, i.e. no search performed for the optimal list of kidneys. All correlation coefficients are below 0.3, with the highest being from the {f,fD*} and 3-NN combination

Figure 3. Pearson’s correlation coefficient (averages from 10 trials each) between predicted and estimated GFR values for K-NN methods with search algorithm for optimal list of kidney selections. Median values of DWI parameters from left, right or both kidneys indicated on the optimal lists returned by search algorithm (temperature parameter=0.5 and 400 iterations) are used. All correlation coefficients are above 0.45, with the highest values approaching 0.7.

Figure 4. Examples of plots of predicted vs estimated GFR for (a,b) {f,fD*} and (c,d) {D,fD*} from SVR method. (a,c) Overlay of predicted (circles) and estimated (squares) GFR values. (b,d) Correlation plots between eGFR and predicted GFRs (pGFR). Least-squares-fit line (long-dashed) with y = x line (dotted) are shown for reference. RMSE and correlation coefficient r are indicated. Search algorithm used 2000 iterations per trial and step-wise ‘temperature’ reduction.

Figure 5. Best results of GFR prediction (with lowest RMSE) using stochastic search algorithm and machine learning method 1-NN for parameters {f, fD*} for (a) fixed ‘temperature’ parameter T and (b) step-wise reducing T. (a,c) Overlay of predicted (circles, dashed line) and estimated (squares, solid line) GFR (eGFR) values. (b,d) Correlation plots between eGFRs and predicted GFRs. Least-squares-fit line (long-dashed) with y = x line (dotted) are shown for reference. Correlation coefficients r are indicated.