Diffusion mapping is a promising method for studying medical anatomy in microstructure. However, diffusion mapping usually needs multiple scans with different b values. Therefore it requires long scanning time, which makes the sampling sequences more prone to motion artifacts,¹ thus impossible to detect the quick variation of diffusion coefficient under different physiological status, such as the diffusion in functional MRI.² Although many methods have been proposed to minimize the duration of diffusion mapping,^3-5 at least two measurements are still needed in the order of seconds. In the present work, we propose a new imaging method, single-shot diffusion mapping through overlapping-echo detachment (DM-OLED) planar imaging method, together with corresponding signal separation algorithm, to achieve reliable single-shot diffusion mapping in about 120 milliseconds. The resolution of the separated images from the overlapping-echo signal is comparable with the image obtained with single-shot EPI sequence under similar conditions.

The DM-OLED sequence is shown in Fig. 1. The flip angle of the two excitation pulses α = 45°, phase encoding number N_pe=64, G₁ and G₂ are echo-shifting gradients to shift the echoes from the k-space center. G_d is diffusion-weighting gradient, and only the first echo signal is diffusion weighted. Since the two echo signals have a same T₂ weighting, the effect of T₂ relaxation can be neglect in the signal expression:

$$\left\{ \begin{gathered} {S_1} = \int\limits_{\vec r} {\rho (r)} \frac{1}{2}\left| {\sin \alpha } \right|\left( {1 + \cos \alpha } \right){e^{ - b \cdot D\left( r \right)}}dr,{\text{ }}the\ first \ echo \\ {S_2} = \int\limits_{\vec r} {\rho (r)} \left| {\sin \alpha \cos \alpha } \right|dr,{\text{ }}the \ second \ echo \\ \end{gathered} \right.$$

where ρ(r) is proton density,$$$\small{b = {\gamma ^2}{G_d}^2{\delta _d}^2(\Delta - {\delta _d}/3)}$$$is the diffusion factor, γ is the gyromagnetic ratio, δ is the duration of G_d, Δ is the diffusion time, and D is the apparent diffusion coefficient (ADC).

Numerical simulations were performed. We used a phantom consisting of 8 circles, with ADC valuing from $$$\small {\text{0}}{\text{.67}} \times {\text{1}}{{\text{0}}^{{\text{ - 9}}}}$$$to $$$\small {\text{2}}{\text{.50}} \times {\text{1}}{{\text{0}}^{{\text{ - 9}}}}$$$ s/m², the ADC values were clockwise equivalently incremental from the leftmost circle. The relative spin densities was 0.5 in the leftmost circle and 1.0 in the others. The T₂ was 0.15s. The T₁ was 1.5 s. All above parameters were uniform in every circle. A matrix size of 4096 grids was used for the two-dimension model with a field of view of 60 × 60 mm². The acquisition matrix was 64 × 128, the total scanning time was about 120 ms,Δ=16 ms, and the acquisition bandwidth was 131.8 kHz.

After sampling, the following expressions were used to separate the two signals :

$$\left\{ {{{\mathbf{x}}_1},{{\mathbf{x}}_2}} \right\} = \mathop {\arg \min }\limits_{{{\mathbf{x}}_1},{{\mathbf{x}}_2}} \left[ {||{{\mathbf{x}}_1} - {{\mathbf{x}}_{10}}||_2^2 + {\lambda _1}||\nabla {{\mathbf{x}}_1}|{|_1} + {\lambda _2}||\nabla {{\mathbf{x}}_2}|{|_1} + {\lambda _3}||\nabla \left( {{{\mathbf{x}}_1} - \beta {{\mathbf{x}}_2}} \right)|{|_1}} \right]$$

$${{\mathbf{x}}_1}{e^{i{\varphi _1}({\mathbf{r}})}} + {{\mathbf{x}}_2}{e^{i{\varphi _2}({\mathbf{r}})}} = {{\mathbf{x}}_0}$$

where β = |x₁₀|₁/|x₂₀|₁, x₁₀, x₂₀, x₁ and x₂ are original and separated images respectively from each echo signal, φ₁(r) and φ₂(r) are linear phase ramps of x₁ and x₂. x₀ is the image from the overlapping-echo signal. The regularization parameters λ₁ = 0.7, λ₂ = 0.5, and λ₃ = 0.1 were used in the separation. Finally, we used the diffusion formula to calculate the ADC values.

The results are shown in Fig. 2. The two separated images (Fig. 2b and c) from the DM-OLED sequence have the same amplitude change tendency and profile as that from the conventional EPI (Fig. 2d). The diffusion mapping (Fig. 2f) from DM-OLED method is in good agreement with the diffusion model (Fig. 2e). But there still exists obvious amplitude jump at the edges of the circles. The fluctuation may be due to the violent variation of spin density and diffusion coefficient at the edges of the circles. The DM-OLED method and separation algorithm has a good performance in diffusion mapping. Although amplitude deviation still exists and the deviation is enhanced in the ADC calculation because of logarithmic operation, the results are acceptable. In general, we can obtain ADC map with a single shot and effectively reduce the scanning time by the proposed method. The SNR can be improved due to the low signal attenuation, and the ADC map can be insensitive to motion artifacts. The DM-OLED method can obtain overlapping echoes with different b values in a single shot, which helps us shorten the acquisition interval of two signals in real-time diffusion imaging. The validation of DM-OLED method as a reliable fast diffusion measurement tool will promise the use of this method for clinical vivo measurements.