Extraction of Tissue-Specific ADC Based on Multi-Exponential T2 Analysis
Qiqi Tong1, Mu Lin1, Hongjian He1, Xu Yan2, Thorsten Feiweier3, Hui Liu2, and Jianhui Zhong1

1Center for Brain Imaging Science and Technology, Department of Biomedical Engineering, Zhejiang University, Hangzhou, China, People's Republic of, 2MR Collaboration NE Asia, Siemens Healthcare, Shanghai, China, People's Republic of, 3Siemens Healthcare, Erlangen, Germany

### Synopsis

Multi-component diffusion models with each component of its own T2 value have been studied previously. When the diffusion signal is decomposed into three compartments (short, intermediate and long T2), the respective ADC values can be obtained. Our results from simulations and in vivo measurements show that the model successfully separates signal from different tissue types, allows extraction of tissue-specific ADC, and results are mostly free of partial volume problem. Moreover, an ADC without T2 effect can also be generated by combining the ADCs of all components.

### Introduction

Conventionally, the diffusion signal is assumed to originate from tissue containing multiple compartments with different characteristics [1]. The bi-exponential model based on this assumption decomposes signal into fast/slow diffusion, but the fitted fractions are inconsistent with histology. This may be due to the existence of multiple T2 components within each voxel. Previous work has found that at least three exponential T2 components exist in neural tissue [2]. Some studies correlated T2 and diffusion and showed that these T2 components exhibited different diffusion characteristics [3], or reported TE dependency of ADC in white matter [4], indicating a multi-T2 and multi-diffusion nature of biological tissue. We propose a multi-component diffusion model to decompose diffusion-weighted signal into three compartments (short, intermediate and long T2), thereby obtaining the respective ADC values of these compartments as well as an ADC without T2 effect.

### Methods

A multicomponent diffusion model is combined with T2 analysis. A T2 spectrum was calculated voxel-by-voxel using the regularized non-negative least-squares (rNNLS) approach [5], three T2 segments can be recognized separately. The signal evolution of each component can be reorganized as $S_{0}(TE)=\sum_{j=M}^Nx(T_{2j})e^{-TE/T_{2}}$, where $x(T_{2j})$ is the T2 distribution and $[M,N]$ is the range of the corresponding T2 segment. Each of the components is supposed to have a respective ADC as well, so the diffusion signal $y$ with a b-value can also be written as a sum of these components in the matrix form:$$\begin{bmatrix}y(TE_{1},b)\\y(TE_{2},b)\\...\\y(TE_{n},b)\end{bmatrix}_{n\times1}=\begin{bmatrix}S_{0s}(TE_{1})&S_{0m}(TE_{1})&S_{0l}(TE_{1})\\S_{0s}(TE_{2})&S_{0m}(TE_{2})&S_{0l}(TE_{2})\\...&...&...\\S_{0s}(TE_{n})&S_{0m}(TE_{n})&S_{0l}(TE_{n})\end{bmatrix}_{n\times3}\times\begin{bmatrix}e^{-bADC_{s}}\\e^{-bADC_{m}}\\e^{-bADC_{l}} \end{bmatrix}_{3\times1},$$ where $S_{0s,m,l}(TE_{n})$ denotes the signal of short, medium and long T2 components without diffusion weighting at the echo time $TE_{n}$, and $ADC_{s,m,l}$ are their diffusion coefficients, respectively. The ADC for each component was calculated using linear fitting. These ADCs can either be analyzed separately, or combined to obtain a single ADC using: $$ADC=\ln(\frac{S_{0s}(0)e^{-bADC_{s}}+S_{0m}(0)e^{-bADC_{m}}+S_{0l}(0)e^{-bADC_{l}}}{S_{0s}(0)+S_{0m}(0)+S_{0l}(0)})/(-b).$$

For the purpose of a time efficient acquisition and in order to enable the separation of T2 mapping and diffusion imaging, a prototype SE-EPI sequence was used for all acquisitions. The non-diffusion images were acquired with 30 logarithmically equally spaced TEs between 28ms and 230ms. The diffusion images were acquired with 13 TEs varying from the minimum 55ms to 136ms.

All scans were performed in a healthy subject on a 3T system (MAGNETOM Prisma, Siemens Healthcare, Erlangen, Germany). Other scan parameters were: FOV=220*220*3 mm3, matrix size=110*110, mono-polar diffusion gradient parallel to the readout direction, b=1000 s/mm2, δ=11.5 ms and Δ=25.9 ms, TR=4 s, 6/8 Fourier acquisition, parallel acceleration factor=2, bandwidth=2065 Hz/px. The total scan time was about 9 minutes, which is tolerable to the subject.

### Results & Discussion

In the T2 distribution spectrum (Fig. 1a) for one image slice, three peaks can be assigned to the three components, corresponding to intra-cellular water, extra-cellular water, and CSF [6]. However, in most of the voxels only one or two components can be extracted, as shown in Fig. 1b.

The combined ADC map and three separate ADC maps are represented in Fig. 2. The ADC map of short T2 component (<35 ms) is noisy (Fig. 2b), most likely due to the fact that the minimum TE (28 ms) of non-diffusion sequence is too long comparing to this short T2. The medium T2 component gives an ADC map of brain tissue eliminating CSF (Fig. 2c). The long T2 component (>200 ms) has a larger ADC value than that of the other two components. Its distribution is clearly consistent with CSF (Fig. 2d). It is noticeable that the corpus callosum overlaps with CSF in the combined ADC map (Fig. 2a) but is fully separated in the separate ADC maps.

We also observed a TE dependence of ADC acquired in conventional way, as shown in Fig. 3. The measured ADC decreased over TE in the white matter regions such as major forceps, and increased in the grey matter regions such as the cingulate gyrus. These changes are in agreement with the result in [4]. The combined ADCs and their simulated trends considering T2 effect over TE are according to the measured ADCs (Fig. 3f), illustrating that the TE dependence of ADC may due to the T2 differences of multiple ADC components. As the TE increases, the relative fraction of two ADC components changes accordingly and results in change of their mean ADC. Furthermore, it is impossible to measure an ADC without T2 effect unless zero TE is used.

### Conclusion

Based on multi-exponential T2 analysis, the proposed method is able to obtain the respective ADC values of different tissues. Moreover, it has the capability of supplying an ADC without T2 effect.

### Acknowledgements

No acknowledgement found.

### References

[1] Assaf Y, et al., JMRI, 1998, 131(1): 69-85.

[2] Does M D, MRM, 1996, 35(2): 207-213.

[3] Peled S, et al., MRM 1999, 42(5): 911-918.

[4] Qin W, et al. MRM, 2009, 61(4): 755-760.

[5] Whittall K P, et al., JMRI 1989, 84(1): 134-152.

[6] Harkins K D, et al., MRM 2012, 67(3): 793-800.

### Figures

Figure 1: a The distribution of T2 of all voxels in one typical axial slice illustrated in Figure 2. There exist three peaks of the T2 values at 32, 67 and 1100 ms, respectively. b T2 distributions of three typical voxels, where only one or two components can be assigned.

Figure 2: ADC maps using the proposed method. a is the combined ADC map, and b-d are the respective ADC maps of short T2 (<35 ms), medium T2, and long T2 (>200 ms) components, respectively. The corpus callosum and CSF overlapped region is outlined in the blue dotted lines.

Figure 3: a Combined ADC map, b-e Conventional ADC maps at different TEs, with the regions of major forceps and cingulate gyrus indicated with red and blue solid outlines, respectively. Their corresponding mean measured ADCs and mean combined ADCs with trends over TE are shown with standard deviation error bar in f.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
2024