Introduction

Fully-sampled DW-TSE-PROPELLER is more robust to geometric distortion and motion artifacts than diffusion-weighted single-shot / multi-shot echo planar imaging (DW-ssEPI or DW-msEPI), but it requires longer acquisition time for IVIM mapping.^1,2 An advantage of DW-TSE-PROPELLER is the data redundancy in the k-space center, which makes it possible to accelerate data acquisition by under-sampling the k-space of each DW image with fewer blades.³ However, the effect of under-sampled artifacts during IVIM parameter fitting needs to be investigated. Therefore, we rotated blades along the b-value dimension to cover sufficient k-space information and developed a synthetic data-driven physics-informed network (SDDPI-Net) for rapid IVIM fitting. Compared with k-t SLR⁴ and subspace-LLR⁵, SDDPI-Net could directly estimate more accurate parameter maps without an extra voxel-wise fitting method by an end-to-end deep learning framework. Meanwhile, SDDPI-Net provides better-preserved tissue boundaries than other physical-informed deep learning methods DEEPIVIM⁶, IVIMNET⁷, and MANTIS⁸.

Methods

Pulse sequence, data preprocessing, and synthetic data generation: Figure 1(a) shows the sequence diagram of DW-TSE-PROPELLER acquisition. Figure 1(b) shows the twelve-blade and two-blade schemes used for fully-sampling and under-sampling the k-space of each DW image, respectively. The data preprocessing pipeline is shown in Figure 1(c). Figure 1(d) shows the procedure of generating input-label pairs (x₀, x) as training and validation data sets from realistic IVIM maps. According to the IVIM bi-exponential model, the signal intensity at a specific b-value, S_b, is defined by the following equation:
$$S_b(S_0,D,f,D^*)=S_0 \times [f \times e^{-b \times D^*}+(1-f) \times e^{-b \times D}]$$The input-label pairs were split into 3902/879 pairs for network training/validation.
Network: SDDPI-Net is based on DIDN (Deep Iterative Down-Up) network⁹. DIDN was used as de-aliasing network g(·;θ₁) to learn artifacts-free information from DW-TSE-PROPELLER images x₀. The parameter estimate network h(·;θ₂) consists of two fully connected layers with PReLU (parametric rectified linear unit). These fully connected layers can effectively map from learned information to four features m (m₁, m₂, m₃, m₄). Three modified sigmoid functions modulate feature values (m₂, m₃, m₄) to physically plausible IVIM parameters (D, D^*, and f). The modulation scalars of D, D^*, and f lay in [0, 3000] μm²/s, [0, 50000] μm²/s, and [0, 1.0], respectively. $$\begin{cases} S_0=m_1 \\ D=D_{min}+sigmoid(m_2)\times (D_{min}-D_{max}) \\ D^*=D_{min}^*+sigmoid(m_3)\times (D_{min}^*-D_{max}^*) \\ f=f_{min}+sigmoid(m_4)\times (f_{min}-f_{max}) \end{cases}$$ The estimated physically plausible values for S₀, D, f, and D^* were substituted into the IVIM bi-exponential model to generate artifacts-free DW-TSE-PROPELLER images x_rec.
An l₁-norm between the predicted signal x_rec from SDDPI-Net and fully-sampled DW-TSE-PROPELLER images x was used as a loss term. The overall architecture of SDDPI-Net is shown in Figure 3.
Experiments: In vivo data were acquired from two healthy volunteers on a Philips Ingenia CX 3.0T MRI scanner with a 16-channel head coil. Participants were instructed for four scans: (1) DW-ssEPI scan, (2) DW-msEPI scan, (3) fully-sampled DW-TSE-PROPELLER scan, and (4) under-sampled DW-TSE-PROPELLER scan. All scans were acquired with FOV = 220 mm × 220 mm, repetition time (TR) = 3000 ms, slice number = 8, slice thickness = 4 mm, 12 b-values. The other parameters for under-sampling DW-TSE-PROPELLER included: echo time (TE) = 106 ms, echo train length (ETL) per blade = 16, 2 blades per b-value, an effective matrix diameter of 128. DW-ssEPI (other parameters: TE = 145 ms, ETL = 128) / DW-msEPI (other parameters: TE = 69 ms, ETL = 32, 4 shots per b-value) and fully-sampling DW-TSE-PROPELLER (TE = 106 ms, 12 shots per b-value) scans were used as references to compare distortion resistance and quantitative accuracy, respectively.

Results

Figure 3 compares the zoomed-in results of DW-TSE-PROPELLER and EPI sequences in the forebrain region susceptible to geometric distortion. The anti-distortion ability of the DW-TSE-PROPELLER is based on the characteristic of TSE sequence. Therefore, the results of DW-TSE-PROPELLER were consistent with the reference TSE image. Whereas the results of DW-ssEPI and DW-msEPI had obvious geometric distortion. SDDPI-Net produced distortion-free IVIM parametric maps from the data acquired within similar acquisition time to DW-msEPI.
Figure 4 shows IVIM parametric maps of an in vivo human brain estimated from different reconstruction methods. Incoherent artifacts caused by inconsistent trajectory per b-value corrupted the structural information in the zero-filled fitted D and f maps. Subtle missing details and inhomogeneous appearance still exist in other methods. The results of SDDPI-Net have sharper contrast and homogeneous appearance.
Table 1 summarizes the mean normalized root mean square error (nRMSE) and structural similarity index(SSIM) between the reference maps and the estimated maps over all 16 testing slices. SDDPI-Net yielded the small reconstruction errors and the highest similarity to the reference at R = 6.

Discussion and conclusion

SDDPI-Net can provide distortion-free and artifacts-free IVIM parametric maps from under-sampled DW-TSE-PROPELLER data. It solves under-sampling reconstruction and IVIM parameter fitting in an end-to-end framework, so it outperforms other combination methods. Compared with MANTIS, the robustness of the reconstruction of SDDPI-Net is achieved by constraining the output of SDDPI-Net to physically plausible IVIM parameter ranges via modifying sigmoid function.

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