Use of the intravoxel incoherent motion (IVIM) model in abdominal regions is becoming more widespread [1], and so a deeper understanding of the underlying physical processes is of great interest. Where the tissue has a compartmental structure, the IVIM model may be associated with two compartments, typically vascular and tissue. A natural extension is to allow distinct T₂ values in each compartment. When multiple b-value data are acquired with a constant TE, T₂ differences between the compartments will bias the compartmental volume fraction to an extent that depends on TE [2]. Conversely, a T₂ measurement with multiple TEs will be influenced by the T₂ in both compartments, although the tissue compartment can easily be isolated by including a small diffusion gradient [3]. This abstract presents a statistical assessment in various abdominal organs comparing a two-compartment model that has different T₂ values in each compartment with a simplified model that assumes equal T₂ values.Data Acqusition: Five volunteers were recruited and a single coronal abdominal slice was obtained in free-breathing on a 1.5T MAGNETOM Avanto (Siemens Healthcare, Erlangen, Germany) using a prototype single-shot diffusion-weighted EPI sequence. Five echo times were acquired (62,72,82,92,102ms) for each of six b-values (0,50,100,150,200,250s/mm²) giving 30 combinations. Three orthogonal diffusion gradients were acquired with NSA=5 giving 400 images. TR=4500ms and δ/Δ=17.6/30ms. ROIs were drawn for liver, kidney and spleen, and a local head-foot alignment was applied in each case to reduce motion.

Model: Two models were used to fit the data. An IVIM model including simple T₂ dependency $${\sf{}Standard\;Model:}\quad{}S(b,\mathrm{TE})=S_0\mathrm{e}^{-\mathrm{TE}/T_2}\!\left(\,f\mathrm{e}^{-bD_p}+(1-f\,)\mathrm{e}^{-bD_t}\!\right),$$ and an extended IVIM model [3] that includes distinct T₂ terms in each compartment $${\sf{}Extended\;Model:}\quad{}\;S(b,\mathrm{TE})=S_0\!\left(\,f\mathrm{e}^{-\mathrm{TE}/T_{2p}}\mathrm{e}^{-bD_p}+(1-f\,) \mathrm{e}^{-\mathrm{TE}/T_{2t}}\mathrm{e}^{-bD_t}\!\right),$$ where the subscripts $$$\small{}p$$$ and $$$\small{}t$$$ refer to the pseudo-diffusion and tissue compartments. These equations were fitted using a non-linear least-squares algorithm, from which the Akaike information criterion (AIC) was computed to guide model comparison. By considering the T₂ scaling of the two diffusion terms in the extended model, an apparent $$$\small{}f$$$ can be defined as $$f_\mathrm{app}(\mathrm{TE}) = \frac{f \mathrm{e}^{-\mathrm{TE}/T_{2p}}}{f \mathrm{e}^{-\mathrm{TE}/T_{2p}} + (1-f\,) \mathrm{e}^{-\mathrm{TE}/T_{2t}}}$$ which is equal to the $$$\small{}f$$$ that would be estimated using the standard model. Thus,$$$\small{}\;f$$$ for the standard model is dependent on TE, but $$$\small{}f$$$ for the extended model is independent of TE.

An example liver data set with the fitted model is shown in figure 1, showing that the model accounts for all the signal variation in the data. The curves in the middle plot have visibly different (relative) heights of the fast component of this curve, which is what is captured by $$$\small{}f_\mathrm{app}$$$, as shown in the right-hand plot. This variability is not described by the standard model, and hence the AIC indicates a preference for the extended model in this example. Figure 2 shows the parameter estimates (and standard errors) for all organs and all volunteers, and these values are consistent with previous estimates [4,5]. Estimates for$$$\small{}\,D_p$$$, $$$\small{}D_t$$$ and $$$\small{}T_{2t}$$$ are very similar between the two models, whilst $$$\small{}f$$$ is similar for the kidney and spleen, but there are significant differences for $$$\small{}f$$$ in the liver. The$$$\small{}\,T_{2p}$$$ plot shows that the extended model was preferred in 4/5 liver cases, and all but one of the kidney and spleen cases prefer the standard model. Acquisitions of this kind are experimentally feasible, but the long scan time (~35 mins) makes clinical use impractical. However, these data indicate that in liver, standard estimates of $$$\small{}f$$$ depend on TE, which should be bourne in mind when interpreting clinical data. In liver it is likely that the two components correspond to vascular and tissue compartments, and while these $$$\small{}T_{2t}$$$ estimates are close to previous values for liver [5], the corresponding $$$\small{}T_{2p}$$$ estimates are lower than for ex-vivo blood (arterial ~181 ms, venous ~254 ms [6]). A direct comparison between our results and these ex-vivo values is challenging since blood entering the liver contains both arterial and venous contributions, and other effects (such as Haematocrit and even water exchange) may be relevant. Estimates of $$$\small{}T_{2p}$$$ and $$$\small{}T_{2t}$$$ in the kidney and spleen are similar (with large error bars on $$$\small{}T_{2p}$$$), which, as expected, shows the simpler model is preferred when T₂ differences are not significant. These data were acquired with constant values of the diffusion time parameters δ and Δ, which is important in this context to limit any effects to the echo time. The limited range of echo times used here was constrained by the interplay between the diffusion time parameters and TE, and it is of future interest to explore the effect of different diffusion times on such acquisitions.