Background

Cardiovascular magnetic resonance parametric mapping is routinely used for examining fibrosis and edema[1], where myocardial T₁ is mostly measured by Modified-Look-Locker-Inversion-recovery (MOLLI) and saturation-recovery-single-shot-acquisition (SASHA), and T₂ is assessed by T₂-prepared balanced-Steady-State-Free-Precession (T₂-prep bSSFP)[2-4]. The curve-fitting algorithm is used for reconstructing the pixel-wise map, which is sensitive to the initial conditions, time-consuming, and not robust[5].
In this study, we hypothesize that a deep-learning approach could perform the fitting task for all these most used sequences and improve the robustness. We developed a 1D neural network (DeepFittingNet) and trained it using the simulations of MOLLI, SASHA, and T₂-prep SSFP. DeepFittingNet was tested by in-vivo data and compared with the curve-fitting method.

Methods

DeepFittingNet is designed to predict the A, B, and Tx for inversion-/saturation-recovery T₁ mapping and T₂ mapping methods (Figure 1A). A, B, and Tx, and the measured signal time courses ($$$M(t)$$$ and $$$t$$$) of these sequences could be expressed as the following model:
$$M(t)=A+B\cdot{e^{-\frac{t}{Tx}}}$$ [1]
Here, Tx represents T₁ or T₂. t is inversion-/saturation-recovery time or echo time of T₂-prep pulse.
DeepFittingNet first adopts a bidirectional recurrent neural network (RNN) to allow inputting of different numbers of signals from various sequences and then uses a fully connected neural network (FCNN) to predict A, B and T_x. RNN includes eight hide layers. The hide size for each layer was 32. The neurons of each layer of FCNN were designed as 400, 400, 200, 200, 100, 50, 30, and 3. Each hider layer of both RNN and FCNN is followed by a leaky rectified linear unit activation function. Specifically, the last two layers of FCNN are repeated three times. For each iteration, the mean squared error between measured signals and ones generated using Equation 1 with predictions from the previous iteration are input.
Dataset: MOLLI3(3)3(3)5, MOLLI5(3)3, SASHA, and T₂-prep bSSFP were simulated 5000000 times using the Bloch equation. For each simulation of each sequence, T₁ (from 100ms to 2500ms), T₂ (from 20ms to 250ms), heart rate (from 30bpm to 130bpm), off-resonance frequency (0Hz ±30Hz), flip angle (Normalized B₁:1 ± 0.2), signal-to-noise ratio (from 20 to 120), inversion efficiency (80% ± 20%), and saturation efficiency (100% ± 20%) were randomly changed. Each signal time course of each sequence with and without noise was fitted to Equation 1 using the curve-fitting method with specified initial conditions for obtaining reference A, B, and Tx. For the T₂, A was defined as the fitting residual [6].
Thirty-two subjects (20 male; 28±9 yrs) were imaged by MOLLI3(3)3(3)5, MOLLI5(3)3, SASHA, and T₂-prep bSSFP on a Philips 3T scanner (Achieva TX) using typical imaging parameters, which was approved by the Institutional Review Board. All participants provided written informed consent. Fourteen (9 male; 28±10 yrs) of them were scanned twice in two separate scans. For each subject, only the mid-ventricular slice in the short-axis view was scanned. The curve-fitting method was used for building T₁ and T₂ maps for all scans.
Training, Validation, and Testing: DeepFittingNet was implemented using the Pytorch library and trained using all simulated signals with 500 epochs. The learning rate was 0.001 and an ADAM optimizer was used. In every iteration of training, each sequence fed 6400 signal time courses. The MAE calculated as the following equation was used to update DeepFittingNet.
$$$MAE=\frac{1}{M}\sum_{}^{}|A-\hat{A}|+|B-\hat{B}|+|T_{x}-\hat{T_{x}}|$$$ [2]
Where $$$A$$$, $$$B$$$, and $$$T_{x}$$$ are references, and $$$\hat{A}$$$, $$$\hat{B}$$$, and $$$\hat{T_{x}}$$$ are corresponding predictions. M is batch size.
Validation dataset included 10 MOLLI3(3)3(3)5 T₁ maps, 7 MOLLI5(3)3 T₁ maps, 10 SASHA T₁ maps, and 10 T₂ maps by T_2­-prep bSSFP from 14 subjects. Rest in-vivo images were used in the testing. Left-ventricle and septal myocardium, and blood were segmented. Mean and standard deviation (SD) were calculated for each region of interest. Analysis was performed using linear regression, Bland-Altman, and paired Student’s t-test method.

Results

The model with the lowest MAE for the left-ventricle myocardium and septum of the validation dataset was selected. Figure 2 indicates that the fitting tasks of these mapping sequences could be simplified by one neural network. Compared to curve-fitting, DeepFittingNet improved the robustness for inversion-recovery T₁ (Figure 3). There was no difference in the either LV or septal T₁ for MOLLI5(3)3 and SASHA between curve-fitting and DeepFittingNet (all P>0.05, Figure 4). The mean difference in LV and septal T₁ between two methods were 3.58ms and 3.95ms for MOLLI3(3)3(3)5, and 0.42ms for T₂-prep bSSFP (all P<0.05). Except for the difference of 19.86ms in MOLLI3(3)3(3)5 blood T₁ between the two methods, for the rest three sequences, the mean blood T₁/T₂ difference was negligible (all p<0.05). In Table 1, DeepFittinNet had comparable T₁ precision to the curve-fitting method.

Discussion and Conclusion

Our study demonstrated that a single deep neural network could complete T₁ and T₂ calculations for the most clinically used MR relaxometry mapping sequences. Compared to the curve-fitting algorithm, the deep-learning approach had comparable performance while improving the robustness for inversion-recovery T₁ estimation.

References

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