Comparison of different mathematical models for IVIM in healthy human kidneys

Zhongwei Chen^{1}, Youfan Zhao^{1}, Zhenhua Zhang^{1}, Haiwei Miu^{1}, and Qiong Ye^{1}

**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/mm^{2}) on 3 gradient directions with following parameters: FOV=240×384×151（AP/RL/FH）mm^{3},
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}/S_{0})=f-b*D [1] for
b=0, 200, 300, 500, 700 s/mm^{2}; (2) Model 2: D_{slow} was calculated
from mono-exponential fitting of b=0, 200, 300, 500, 700 s/mm^{2}. Using
the obtained and fixed D_{slow}, signal intensity was fitted by S_{b}/S_{0}
= 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}/S_{0} = f*exp(-b*D_{fast})+(1-f)*exp(-b*D_{slow}+b^{2}*D_{slow}^{2}*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.

Figure
1 : (A),(C),(E) show the D_{slow} mapping from model1-3, (B),(D),(F)
show the f mapping from corresponding model.

Figure 2. Differences of D_{slow} and f between four
models.
*:p<.05, LC=Left
Cortex,
LM=Left
Medulla, RC=Right Cortex, RM=Right Medulla

Table 1. The CoV and (mean±STD) of D_{slow} and f from these four models. LC=Left
Cortex,
LM=Left
Medulla, RC=Right Cortex, RM=Right Medulla

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

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