Statistical evaluation of bi-exponential IVIM effect in healthy human liver and its dependence on the cut-off b-value for segmented biexponemtial fit
Oi Lei Wong1, Jing Yuan1, Gladys Goh Lo2, Thomas W. T. Leung3, Wai Ki Chung2, and Benny W. H. Ho2

1Medical Physics and Research Department, Hong Kong Sanatorium & Hospital, Hong Kong, Hong Kong, 2Department of diagnostic & interventional radiology, Hong Kong Sanatorium & Hospital, Hong Kong, Hong Kong, 3Comprehensive Oncology Center, Hong Kong Sanatorium & Hospital, Hong Kong, Hong Kong


The use of IVIM in assessing the microcapillary perfusion and true diffusion has attracted elevating attention. The segmented bi-exponential fitting has been widely adopted to calculate IVIM metrics, in which a cut-off b-value is pre-defined for perfusion and diffusion region separation. This study calculated the corrected Akaike Information Criterion (AICc) for bi-exponential IVIM model in the healthy human liver with varying cut-off b-values and then compared to the AICc for the mono-exponential model. The statistical preference of the bi-exponential model to mono-exponential model was demonstrated based on the lowest AICc. This bi-exponential model preference was independent of the choice of cut-off b-value and ROI location.


Apparent diffusion coefficient (ADC) has widely been applied in the clinic. However, the micro-capillary perfusion effect is not considered in mono-exponential model. Contrariwise, this effect is included in the bi-exponential intravoxel incoherent motion (IVIM). Despite the best fitting method for the bi-exponential IVIM model is yet to determine, the segmented bi-exponential fit has been suggested to be more robust than the simultaneous full bi-exponential fit [1]. Indeed, the estimate of true diffusion (D) and perfusion fraction (f), using segmented bi-exponential fit, is dependent on the pre-defined cut-off b-value to separate the perfusion and diffusion region on DW signal decay curve. Such cut-off b-value, however, is often heuristically chosen from a low b-value range (50 – 200 s/mm2) without a standardized value. For example, Koh et al. defined the cut-off b-value to be 100 s/mm2 [2] while Cohen et al. used 50 s/mm2 in the liver [3]. Also, the behaviour of the DW signal decay curve may be regional dependent where different IVIM metrics between the left and right liver lobe has been previously identified [4]. We, thus, hypothesize that the model preference (bi-exponential and mono-exponential) may be affected by the choice of cut-off b-value and the selection of ROI. We evaluated the model perference due to both effects using the corrected Akaike Information Criterion (AICc).


Liver imaging was performed on 7 healthy volunteers using a 1.5T MRI (Optima MR450w, General Electric Healthcare, Milwaukee) and a dedicated 32-channel phase array. A non-elastic belt was used to minimize respiratory motion during free breathing. Coronal diffusion scans (TE/TR=77/2200ms, 5 x 10mm slices, 35cm FOV, diffusion encoding direction =LR, 6 NSA) were performed with the b-values of 0, 10, 20, 30, 40, 50, 100, 200, 300, 400, 500 s/mm2. The bulk respiratory motion was first corrected with a rigid body transformation using MCFLIRT (FSL, FMRIB, Oxford, UK). Voxel-based IVIM analysis was then performed using a custom Matlab script (Mathworks Natick, MA) based on a two-step segmented unconstrained analysis: (1) nine D were obtained from a monoexponential fit with b-values no smaller than 10, 20, 30, 40, 50, 100, 200, 300 and 400 s/mm2, and the corresponding f values were subsequently obtained using the intercept; (2) nine D* were determined from the bi-exponential IVIM model with each set of f and D values calculated in step one. Afterwards, AICc value for the bi-exponential IVIM model was calculated using each set of IVIM metrics. A mono-exponential fit using all b-values was also performed to calculate ADC and the mono-exponential AICc value. The model preference between bi-exponential and mono-exponential model was then determined based on the lowest AICc value. The voxel map of the cut-off b-value corresponding to the set of IVIM metrics with the lowest AICc value (bcut) was also obtained. A circular ROI (diameter = 10mm) was selected on the left and the right liver lobe separately on the same slice (Figure1). A ranksum test was performed to compare the IVIM metrics and bcut.


When comparing with AICc using mono-exponential model, all voxels within both left and right liver ROI presented with lower AICc using bi-exponential model for all choices of cut-off b-value. As illustrated in Figure 2, significant difference between left and right liver lobe were observed in D (4.33±1.16 x 10-3 mm2/s vs. 1.63±0.27 x 10-3 mm2/s, p<0.01) and bcut (93.6±27.7 s/mm2 vs. 170.1±34.2 s/mm2, p<0.05). Larger f was also observed in the left liver lobe (0.16±0.02) when compared to the right (0.12±0.03) (p=0.05).


When compared with the mono-exponential model, the bi-exponential model was noted to be the preferred model based on our results, which was independent of the choice on the cut-off b-value. The model preference was also observed to be independent of the ROI location though a significant difference between left and right liver lobe was obtained using D. Moreover, our calculated bcut range for both liver lobe agreed with the typical value used in the literature. However, a significant difference in the bcut value has been observed in regional basis (Figure 3). The smaller bcut value and the larger f value in the left liver lobe may indicate a more prominent perfusion effect. Our voxel-wise IVIM metrics were calculated based on these varying bcut, which could be different from the traditional approach with a single fixed bcut. Whether this approach could improve the accuracy of IVIM quantification needs to be further investigated.


No acknowledgement found.


[1] Cho G. et al. Comparison of fitting methods and b-value sampling strategies for intravoxel incoherent motion in breast cancer. MRM 2015; 74(4):1077-85

[2] Koh DM. Et al. Intravoxel incoherent motion in body diffusion-weighted MRI: reality and challenges. 2011 American Journal of Roentgenology 196(6): 1351-61.

[3] Cohen AD et al. The effect of low b-values on the intravoxel incoherent motion derived pseudodiffusion parameter in liver 2015 MRM, 73: 306-311

[4] Wong OL et al. Evaluation of Pseudo-hepatic anisotropy artifact in liver intravoxel incoherent motion (IVIM) based on clustering technique. 2015 The proceeding of 23rd ISMRM, Toronto, Canada.


The ROI selections (red: left liver lobe, green: right liver lobe) overlaying on the b=0s/mm2 image. Location of the ROIs was carefully chosen to avoid major vessels.

The calculated bcut value (mean±SD) of the left and right liver lobe (p< 0.05)

The calculated bopt map is overlaying on the b=0s/mm2 image.

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