894 the number of parameters p and the number of data points n: 2 Radj ¼ 1 ð1 R2Þ ð n n p 1Þ where n = 7 for seven b-values and p = 2 or 3 for mono- and bi-exponential models respectively. F-tests were performed to evaluate whether the bi-exponential model was justified over a mono-exponential model: F ¼ ðSSEmono SSEbiÞ=ðDFmono SSEbi=DFbi DFbiÞ where SSEmono and SSEbi are the sum-of-squared errors (SSE) of the mono- and bi-exponential fits respectively, and DFmono and DFbi are the degrees of freedom of both analyses (DF = n – p). All statistical analyses had a significance level of 5%. 4 ð Þ 5 ð Þ Results The mono-exponentially fitted ADCs were significantly different (P < 0.001) among the five regions and normally distributed (Tables 2 and 3). The left lobe showed the highest ADC (1.423 × 10−3 mm2/s) and the lowest ADC was found centrally in the medial right lobe (1.107 × 10−3 mm2/s). The bi-exponentially fitted Dslow was not shown to be significantly different (P= 0.140) among the five regions and were normally distributed (Tables 2 and 3). The median of the Dslow components varied between 0.923 and 1.062× 10−3 mm2/s for each of the five regions. The bi-exponentially fitted Dfast was significantly differ- ent (P<0.001) between the five regions and non-normally distributed (Tables 2 and 3). The median of the Dfast components varied between 17.8 and 46.8 ×10−3 mm2/s for the five regions. The left lobe showed the highest fraction of micro- perfusion ffast (47%) and the lowest fraction of diffusion fslow (53%). The dorso-lateral right lobe showed the lowest Table 2 Tests of normality Region Segment 1 2 3 4 5 5/8 6/7 2/3 7 5 ADC 0.798 0.895 0.814 0.208 0.230 Dslow 0.929 0.708 0.309 0.523 0.735 Dfast 0.022* 0.086 0.007* 0.563 0.167 fslow/fast 0.761 0.005* 0.900 0.023* 0.663 P values (Shapiro–Wilk tests) indicate deviations from normal distribution (P<0.05). Measurements of Dfast and f fractions were non-normally distributed, Dslow values were normally distributed Eur Radiol (2012) 22:891–899 fraction of microperfusion ffast (24%) and the highest fraction of molecular diffusion fslow (76%). The fslow and ffast fractions were significantly different among the five regions (P< 0.001) (Table 3). The adjusted R2 showed that the bi-exponential model fitted better to the diffusion data than the mono-exponential model for each liver region (Radj, bi2>Radj, mono2). Further- more, the F-tests showed that the diffusion data fitted significantly better to the bi-exponential model (F>21.4, P < 0.010) than to the mono-exponential model in all individual fitting procedures. Parametric maps Diffusion weighted imaging data of the medial liver of one subject were used to calculate ADC and Dslow maps (Fig. 2). The Dslow map showed a more homogeneous distribution of the bi-exponential fitted slow diffusion throughout the liver. The ADC map showed more differing values between different regions of the liver, especially near blood vessels and in the left lobe. Influence of blood vessels In one subject, the effects of microperfusion on the mono- and bi-exponential models were illustrated by including blood vessels in the ROI; this showed a large influence of microperfusion on the ADC (Fig. 3). When the blood vessels were excluded from the ROI a decreased ADC was observed. However, Dslow was similar to when blood vessels were included in the ROI. Simulation study The systematic literature search resulted in six multi-region DWI studies of the liver in which a minimal of 20 patients were included and in which between two and four different regions of healthy liver parenchyma were analysed [13, 19, 21, 25, 26, 30]. Studies in which mono-exponential analyses were performed showed ADCs between 1.00 and 2.69 × 10−3 mm2/s using sets of two, three or five b-value combinations between 0 and 1300 s/mm2 (Table 4). We found ADCs between 0.94 and 2.39 × 10−3 mm2/s when using the same b-value combinations. All mono- exponential studies reported significantly (P< 0.05) differ- ent ADCs between the different liver regions, this was confirmed by our simulation study (P< 0.001). In one study a bi-exponential analysis of two different regions of liver parenchyma was performed using a series of ten b-values between 0 and 800 s/mm2 (Table 5) [13]. They did not find significantly different Dslow components among different liver regions (P= 0.5); this was confirmed by our simulation study (P= 0.105).