Extraction of Tissue-Specific ADC Based on Multi-Exponential T2 Analysis

Qiqi Tong^{1}, Mu Lin^{1}, Hongjian He^{1}, Xu Yan^{2}, Thorsten Feiweier^{3}, Hui Liu^{2}, and Jianhui Zhong^{1}

A multicomponent diffusion model is combined with T_{2} analysis. A T_{2} spectrum was calculated voxel-by-voxel using the regularized non-negative least-squares (rNNLS) approach [5], three T_{2} 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 T_{2} distribution and $$$[M,N]$$$ is the range of the corresponding T_{2} 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 T_{2} 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 T_{2} 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 mm^{3}, matrix size=110*110, mono-polar diffusion gradient parallel to the readout direction, b=1000 s/mm^{2}, 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.

In the T_{2} 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 T_{2} 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 T_{2}. The medium T_{2} component gives an ADC map of brain tissue eliminating
CSF (Fig. 2c). The long T_{2} 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 T_{2} effect over TE are according to the
measured ADCs (Fig. 3f), illustrating that the TE dependence of ADC may due to
the T_{2} 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 T_{2}
effect unless zero TE is used.

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[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.

Figure 1:** a** The
distribution of T_{2} of all voxels in one typical axial slice illustrated in
Figure 2. There exist three peaks of the T_{2} values at 32, 67 and 1100 ms, respectively. **b**
T_{2}
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 T_{2} (<35 ms), medium T_{2}, and long T_{2}
(>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