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.

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.

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.

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.