Introduction

Saturation transfer MRF (ST-MRF) enables simultaneous acquisition of free water, semisolid magnetization transfer (MT), and CEST parameter maps^1,2. A pseudo-randomized MRF schedule can be used to create unique saturation signal profiles for different tissue properties. Previous studies utilized deep-learning networks to optimize the acquisition schedule to improve scan efficiency and reconstruction accuracy^3,4. However, the complexity of the networks could not allow us to gain insight into how specific acquisition parameters influence the performance of tissue parameter quantification. Recently, the linear projection-based L1-regularization (LASSO) method was successfully applied to reduce the number of frequency offsets in the Z-spectra⁵, which relies on linear modeling at the expense of lower prediction accuracy in comparison to non-linear deep-learning models. Herein, we developed an interpretable importance-ranking network (IRnet) to optimize MRF acquisition with a minimal number of sequence parameter settings for tissue parameter determination.

Methods

IRnet was trained with ST-MRF signals simulated by Bloch-McConnell equations with a three-pool exchange model, free bulk water (w), semisolid macromolecule (m), and amide protons (s). A pre-defined reference MRF schedule (N =103) and tissue parameters, such as relaxation times (T₁ⁱ and T₂ⁱ), pool size ratios (Fⁱ) for each pool (i), exchange rate from i- to j- pool (k_ij), and B₀ inhomogeneity were used for the simulation. IRnet consisted of (i) an encoder network for feature extraction and (ii) a replicator network with a single middle layer for interpretation (Fig. 1). The IRnet is defined as follows:
$$\widetilde{\theta}_1=arg \min_{\theta_1}(E_{S_{MRF}\sim P(S_{MRF})}[\parallel reconN(S_{MRF}\mid\theta_1)-P_t\parallel_2])\quad{[1]}$$
$$\widetilde{\theta}_2=arg \min_{\theta_2}(E_{S_{MRF}\sim P(S_{MRF})}[\parallel repN(S_{MRF}\mid\theta_2)-encN(S_{MRF}\mid\widetilde{\theta}_1)\parallel_2])\quad{[2]}$$
where $$$reconN(S_{MRF}\mid\theta_1):S_{MRF}\rightarrow\widehat{P}_t$$$ is a reconstruction network with trainable parameters θ₁ and trained parameter $$$\widetilde{\theta}_1$$$ is used in the encoder network (encN) in Eq. [2], P_t denotes ground-truth tissue parameters, S_MRF =[s₁,s₂,…s_k,…s_N] denotes input ST-MRF signals, and $$$E_{S_{MRF}\sim P(S_{MRF})}[.]$$$ denotes the expectation operator, given that S_MRF belongs to P(S_MRF) distribution. $$$repN(S_{MRF}\mid\theta_2):S_{MRF}\rightarrow{\widehat{P}_{en}}$$$ is a replicator network estimating encoded tissue parameters $$$\widehat{P}_{en}$$$ which is used to calculate a loss function with encoded tissue parameters P_en from an encoder network, $$$encN(S_{MRF}\mid\widetilde{\theta}_1):S_{MRF}\rightarrow{{P}_{en}}$$$. As the replicator network has a single middle layer, weights (w^np, n = the number of dynamic scans for ST-MRF and p = the number of encoded tissue parameters or nodes in the single middle layer) assigned to each input node (S_MRF) represent the importance of the corresponding sequence parameters for tissue parameter quantification. The importance can be ranked as follows:
$${Importance}\ {ranking} = arg sort (\sum_{P=1}^L{W^{np}})\quad{[3]}$$
where weight matrix $$$W^{np}\in\widetilde{\theta}_2$$$, L denotes the number of encoded tissue parameters; weight matrix W^np=[w¹¹,w¹²,…w^np]. For in-vivo studies, nine healthy subjects participated after informed consent was obtained in accordance with IRB requirements. ST-MRF images were obtained from a multi-shot 3D TSE pulse sequence with varied frequency offsets (Ω), RF saturation powers (B₁), RF saturation times (Ts), and relaxation delay times (Td).

Results and Discussion

The IRnet ranked the importance of each dynamic scan and then important scans were selected. In the simulation study (Fig. 2A), the reference schedule (Ref, N = 103) had the lowest normalized root mean square error (nRMSE) against ground-truth tissue parameters. Reducing the number of scans from #103 to #60 resulted in a marginal increase in the nRMSE. To ensure high reconstruction accuracy, the dynamic scan number of #60 was selected for in vivo studies. Individual tissue parameter accuracies obtained with the optimal schedule (IRnet) were comparable with the reference schedule (Ref), as shown in Fig. 2B. The MRF schedules for the four scan parameters optimized by IRnet are shown in Fig. 3, which reduced a total scan time by ~42%. In vivo brain tissue parameter maps were reconstructed from the reference schedule with 103 dynamic scans, as well as pseudo-random, LASSO, and IRnet-based optimized schedules with 60 dynamic scans (Fig. 4). All tissue parameters from IRnet were in good agreement with reference, despite the ~2-fold scan time reduction. Their SSIM outperformed the tissue parameters obtained from pseudo-random and LASSO, particularly for the exchange rates (k_mw and k_sw), In Fig. 5A, compared with the average tissue parameters obtained from the reference schedule (#103), tissue parameter quantification with #60 dynamic scans was accurate, which is in line with the simulation result. The tissue quantification accuracy was evaluated by calculating nRMSE between the reference and tissue parameters estimated with the different MRF schedules (Fig. 5B). The lowest nRMSE values for all tissue parameters were obtained with the IRnet method.

Conclusions

The importance-ranking network could optimize MRF acquisition with a minimal number of scan parameters for tissue parameter determination. The interpretable IRnet framework could significantly reduce data acquisition time for ST-MRF without compromising the fidelity of the tissue parameter quantification.

Acknowledgements

This work was supported in part by grants from the National Institutes of Health.

References

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