Statistical assessment of a model combining IVIM and T2 decay for multi-b-value, multi-echo-time DW-MRI in abdominal organs
Matthew R Orton1, Neil P Jerome1, Thorsten Feiweier2, Dow-Mu Koh3, Martin O Leach4, and David J Collins4

1Radiotherapy and Imaging, Institute of Cancer Research, London, United Kingdom, 2Siemens Healthcare, Erlangen, Germany, 3Department of Radiology, Royal Marsden NHS Foundation Trust, London, United Kingdom, 4CRUK Cancer Imaging Centre, Division of Radiotherapy and Imaging, Institute of Cancer Research, London, United Kingdom

### Synopsis

The IVIM model is essentially a two-compartment model, and it has previously been noted that the T2 relaxation times in each compartment may not be equal. This work uses the Akaike Information Criterion to compare two combined IVIM-T2 models using data acquired in various abdominal organs with all combinations of five echo-times and six b-values. The first model has the same T2 in each compartment, the second has different T2s, and we show that the second model has greater statistical support in the liver (but not spleen or kidney), implying that both T2 values can be measured in this organ.

### Introduction

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.

### Methods

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.

### Results

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.

### Discussion

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.

### Acknowledgements

CRUK and EPSRC support to the Cancer Imaging Centre at ICR and RMH in association with MRC and Department of Health C1060/A10334, C1060/A16464 and NHS funding to the NIHR Biomedical Research Centre and the Clinical Research Facility in Imaging.

### References

1. Koh DM, Collins DJ, Orton MR. Intravoxel incoherent motion in body diffusion-weighted MRI: reality and challenges. AJR Am J Roentgenol. 2011 Jun;196(6):1351-61.

2. Lemke A, Laun FB, Simon D, Stieltjes B, Schad LR. An in vivo verification of the intravoxel incoherent motion effect in diffusion-weighted imaging of the abdomen. Magn Reson Med. 2010 Dec;64(6):1580-5.

3. Jerome NP, d'Arcy JA, Orton MR, Feiweier T, Koh D-M, Leach MO, and Collins DJ. Proc Intl Soc Mag Reson Med, 21 (2013), #2201.

4. Jerome NP, Orton MR, d'Arcy JA, Collins DJ, Koh DM, Leach MO. Comparison of free-breathing with navigator-controlled acquisition regimes in abdominal diffusion-weighted magnetic resonance images: Effect on ADC and IVIM statistics. J Magn Reson Imaging. 2014 Jan;39(1):235-40.

5. de Bazelaire CM, Duhamel GD, Rofsky NM, Alsop DC. MR imaging relaxation times of abdominal and pelvic tissues measured in vivo at 3.0 T: preliminary results. Radiology. 2004 Mar;230(3):652-9.

6. Barth M, Moser E. Proton NMR relaxation times of human blood samples at 1.5 T and implications for functional MRI. Cell Mol Biol. 1997 Jul;43(5):783-91.

### Figures

Figure 1. Example for liver (first case in fig. 2) showing the data and the fit with the extended model shown as a surface (top), and as a collection of attenuation curves for each TE (middle). Bottom plot shows fapp as a function of TE (solid purple line), f from the standard model (dashed green line) and independent estimates of f for each TE (with one standard error).

Figure 2. Results for all organs from all volunteers. Blue dots/red circles show the extended and standard model estimates, and corresponding lines indicate one standard error. Plot for T2p also indicates the AIC preference for the extended or standard models.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
2014