Background and purpose: Intravoxel Incoherent Motion Imaging(IVIM) has shown the potential to separate pure diffusion and the contribution from microcirculation using diffusion-weighted imaging(DWI). Yet, the derived results of IVIM vary with the mathematical model and the selection of b-values. Which is the best model? Does the universal best model exist? So the aim of this study was to investigate different mathematical models for IVIM imaging in healthy human kidneys.

Methods: 21 healthy volunteers (9 male/ 12 female; median age 25.5 years; range 23-28 years) underwent MRI examination using 3T clinical MR scanner (Achieva, Philips Healthcare, Best, The Netherlands) with 8-channel abdomen coil. IVIM was acquired using a single-shot spin-echo echo-planar imaging (EPI) pulse sequence with respiration trigger. 10 b-values were used (0, 10, 25,40, 75, 100, 200, 300, 500, and 700s/mm²) on 3 gradient directions with following parameters: FOV=240×384×151（AP/RL/FH）mm³, matrix=80×128, slice thickness=3.0 mm with a gap of 1 mm, and TE/TR=78/1344 ms. Images were motion corrected in FSL, and processed in Matlab with home-developed program. Regions of interest (ROIs) were manually drawn on bilateral cortex and medulla of central section near the renal hilum using ImageJ. D_slow and perfusion fraction(f) were derived from fitted signal intensity using following 4 different IVIM models: (1) Model 1: ln(S_b/S₀)=f-b*D [1] for b=0, 200, 300, 500, 700 s/mm²; (2) Model 2: D_slow was calculated from mono-exponential fitting of b=0, 200, 300, 500, 700 s/mm². Using the obtained and fixed D_slow, signal intensity was fitted by S_b/S₀ = f*exp(-b*D_fast)+(1-f)*exp(-b*D_slow) for all b-values to get f and D_fast ;(3) Model 3: combine IVIM and DKI, S_b/S₀ = f*exp(-b*D_fast)+(1-f)*exp(-b*D_slow+b²*D_slow²*K/6)[2]; (4) Model 4: a typical multi-step ROI based approach was applied as Ref[3]. Different from the literature, instead of define the optimized threshold of b values, D_slow and f were selected from the fitting with minimum sum of the squared residual (SSE) individually. The difference of D_slow and f between cortex and medulla of kidney were compared using one-way analysis of variance (ANOVA) test and non-parametric test was used when the data distribution was skewed. Finally, Coefficient of Variance(CoV) was calculated. P<0.05 is considered for statistically significant.

Results: A representative D_slow and f mapping of kidneys from Model 1-3 are shown in Fig 1. The grayscale background is b=0 imaging. Derived D_slow and f values from four models are shown in Fig 2 and Table 1. All models can show significant differences in D_slow between cortex and medulla except for model 4, which can’t differentiate right cortex and right medulla. Yet, only model 3 shows significant difference in f value between cortex and medulla. As shown in Table 1, in general, D_slow is more consistent than f. The CoV of D_slow and f from model 1 show the best performance.

Discussion and Conclusion: Previously, Moritz C Wurnig et al suggested that the combined IVIM-DKI model is more accurately describes the behavior of tissue in diffusion experiments [2]. However, in our study its CoV is larger than others. From our study, model 1 and 2 are more reliable than other two models, while model 3 might be more sensitive to physiological alternation. Model 4, which is ROI based, showed moderate CoV while the sensitivity to tissue microstructure is decreased. MRI signal mainly originates from intra-, extra- and vascular water molecule, yet, the visibility of MR signal was dominated by relaxation times of individual components and the TE/TR settings. TE=78ms was used in our study, which might be long enough to vanish signal from extracellular water molecule at 3T. Different TE/TR settings are used in different study, and relaxation times changes with physiological state, the number of visible components in the MR signal is unknown. This might contribute to the controversy of optimized mathematical models of IVIM. Investigation of the relaxation times of individual water components might be compulsory before the searching of optimized mathematical model.