Ground-truth-free deep learning approach for accelerated quantitative parameter mapping with memory efficient learning

Naoto Fujita; Suguru Yokosawa; Toru Shirai; Yasuhiko Terada

doi:10.1371/journal.pone.0324496

Peer Review History

Original SubmissionNovember 26, 2024
26 Nov 2024 Author Response https://doi.org/10.1371/journal.pone.0324496.r001
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(Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: Reviewer recommendation: Accept with minor revisions. Detailed review: - Provide an abbreviation glossary and ensure each term is clearly defined when introduced. - Include discussion points on how this work might influence clinical workflows and address any potential biases or risks in real-world applications. - The reconstruction time (over 3 hours per volume for ZSSSL) is a significant limitation for clinical use. Expand the discussion of strategies to mitigate this issue, such as transfer learning or parameter reduction, in future work. - Ensure figures and tables are fully interpretable with detailed captions and legible text. - Strengthen the discussion around plans for prospective validation and explain how the method may perform under real-world imaging conditions. Reviewer #2: • The manuscript includes many technical terms and acronyms (e.g., CS, PI, SL, SSL, ZSSSL, MEL, GT, AF) without always defining them. This could make the text difficult to follow for readers outside the field. • The manuscript is highly technical, and some sections (e.g., network architecture, training strategies) are difficult to follow for readers who are not experts in MRI reconstruction or deep learning. • Add a background section to explain key terms, concepts, and MRI sequences. The paper would benefit from the addition of a background section to improve accessibility and readability. Many key concepts such as Self-Supervised Learning (SSL), Zero-Shot Self-Supervised Learning (ZSSSL), Memory Efficient Learning (MEL), and the qMRI sequences (MSME, VFA-SPGR, DESS) are central to the study but are not explained in sufficient detail for readers who may not be familiar with these techniques. • The network architecture section, as currently written, is highly technical and assumes a deep familiarity with deep learning concepts and MRI reconstruction. Terms like "unrolled network," "conjugate gradient method," and "residual blocks" are used without sufficient explanation. The section does not explain why the specific network architecture was chosen or how it addresses the challenges of qMRI reconstruction. • The mention of "Equation (S8)" and "Problem formulation" in the supplementary file (S1 File) is problematic because readers cannot access this information without switching to another document. 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Revision 1
5 Apr 2025 Author Response This document (reply_to_reviewer.docx) contains the text of the response to the reviewer and the revised text of the manuscript. Here, the referee’s comments were marked in light blue, the responses were in black, and the revisions were recorded using the track changes in Word. The page and line numbers are those in the highlighted version of the revised manuscript (manuscript_rev_highlighted.docx). In addition, to correct grammatical errors and improve overall readability, we used a professional English proofreading service by a native speaker. Please note that these corrections are not individually mentioned in the manuscript. We have included three newly created figures (Fig7.tif, Fig9.tif, and Fig11.tif) to improve the visual presentation of the quantitative results. As a result of adding these figures, the numbering of the subsequent figures has shifted: the original Fig 7 is now Fig 8, Fig 8 is now Fig 10, and Fig 9 is now Fig 12 in the revised manuscript. Reviewer #1: Reviewer recommendation: Accept with minor revisions. Detailed review: [R1-1] Provide an abbreviation glossary and ensure each term is clearly defined when introduced. Thank you for pointing this out. In response to your comment, we have reviewed the manuscript to ensure that all abbreviations are clearly defined upon their first appearance. Specifically, we have revised the following sentences: Introduction: page 3, line 2 Compressed sensing (CS)[7], which leverages the inherent sparsity of MR images and parallel imaging (PI)[8–11], which uses multiple receiver coils are also used to accelerate qMRI by reducing the number of data points acquired. Introduction: page 3, line 6 The DL framework commonly used in image reconstruction is supervised learning (SL), where many fully sampled (FS) data that satisfy the Nyquist condition are used to train the model parameters for reconstruction from undersampled (US) data that do not satisfy the Nyquist condition. Reconstruction models using SL have also been applied to accelerate qMRI. Material and Methods: page 8, line 22 The US k-space data used for training and testing were generated by retrospective sampling from the FS data under different acceleration factors (AFs), which represent the degree of acceleration relative to the acquisition time of the FS data (e.g., AF = 2 corresponds to a two-fold acceleration). Additionally, to further improve clarity and address a similar concern raised by Reviewer 2 (please see [R2-3]), we have added a “Background” section. This new section introduces and explains the technical terms in this study, thereby enhancing the overall accessibility of the manuscript. [R1-2] Include discussion points on how this work might influence clinical workflows and address any potential biases or risks in real-world applications. Thank you for the comment. We have added a brief discussion on the clinical impact of our method, the need for standardization, and potential real-world biases. The revised text is as follows: Discussion: page 19, line 20 The GT-free learning method and memory-efficient strategy used in this study are expected to shorten the total examination time of protocols incorporating conventional qMRI and enable the integration of qMRI sequences that were previously challenging due to long scan durations. SSL technology allows for the construction of DL models using only undersampled (US) data, even for qMRI sequences where acquiring fully sampled (FS) data is time-consuming. Additionally, ZSSSL facilitates the application of DL models to emerging qMRI sequences that are not yet widely adopted and lack large-scale training datasets. When incorporated into clinical workflows, these methods are expected to enhance objective diagnosis by utilizing qMRI as an imaging biomarker. However, to ensure the clinical relevance of observed quantitative values, a standardized workflow from image acquisition to quantitative analysis, including diagnosis and treatment planning, must be established. Such standardization will be essential alongside advancements in accelerated qMRI techniques. [R1-3] The reconstruction time (over 3 hours per volume for ZSSSL) is a significant limitation for clinical use. Expand the discussion of strategies to mitigate this issue, such as transfer learning or parameter reduction, in future work. Thank you for pointing out this important limitation. We have expanded the Discussion (page 20, line 17) to address potential strategies to reduce reconstruction time, such as transfer learning with SSL-pretrained weights, use of natural image or simulation-based pretraining, and model simplification via Neural Architecture Search. The revised text is as follows: Material and Methods: page 8, line 22 Although ZSSSL is highly effective because it does not require a training dataset, it has the drawback of lengthy reconstruction time. In this study, the reconstruction time per volume exceeded three hours, which may be acceptable in preclinical settings but is not feasible for clinical use. One potential solution to reduce the reconstruction time is to employ transfer learning (TL) using weights pretrained with SSL. Yaman et al. [37] reported that this TL approach effectively improves performance and reduces reconstruction time to less than one-tenth. Alternatively, TL using weights pretrained with natural images [44,45] or simulation-based training datasets [46] may also be effective. Another approach is to decrease the number of model parameters, which can be achieved through Neural Architecture Search (NAS)[47]. NAS is an automated technique for finding optimal neural network architectures by exploring a predefined search space, potentially reducing the model size while maintaining or improving the performance. Because the network used in this study has not yet undergone sufficient tuning of the hyperparameters such as the number of filters and layers, optimizing the model architecture remains a topic for future work. [R1-4] Ensure figures and tables are fully interpretable with detailed captions and legible text. Thank you for your comment. We have revised the figure captions to include more detailed explanations and ensured that all abbreviations are defined. In addition, we have checked label clarity to improve readability. The updated captions can be found in the revised manuscript as follows: Material and Methods: page 10, line 18 Fig 2. Architecture of the image reconstruction model used in this study. D_w corresponds to denoising in Equation (12) and DC corresponds to data consistency in Equation (13). The multi-contrast US k-space is the input and the multi-contrast reconstruction k-space is the output. Because MRI images are complex-valued, the input and output of the denoising unit are concatenated in real and imaginary parts in the channel dimension direction. US: Undersampled, CNN: Convolutional neural network. Material and Methods: page 10, line 30 Fig 3. Training strategy in this study. The figure illustrates the training, validation, and testing procedures for supervised learning, self-supervised learning, and zero-shot SSL. Ω is the original US k-space. Θ, Λ, Ξ, and Γ are subsets of the k-spaces. US: Undersampled. Material and Methods: page 14, line 27 Fig 4. Simulation procedures for Experiment 1 and Experiment 2. The blue box represents the simulation process of multi-contrast data. The yellow box illustrates the procedure for generating the fully sampled (FS) and undersampled (US) k-space data and coil sensitivity maps for training and testing in this study. US: Undersampled, FS: Fully sampled, GT: ground truth. Material and Methods: page 14, line 31 Fig 5. coil arrangement used to simulate multi-coil signals. (Left) The red cube represents the field of view (FOV), showing the spatial arrangement of the receiver coils. Different colors indicate the wiring patterns of each coil. (Right) A 2D projection of the coil arrangement. Each coil is modeled as a loop coil with a radius of 100 mm. Material and Methods: page 19, line 7 Fig 12. Memory consumption and training time per minibatch in each network parameter settings. (a) Maximum memory usage as a function of the number of filters, layers, and iterations. The solid blue line represents results with memory-efficient learning (w/ MEL), while the dashed orange line represents results without memory-efficient learning (w/o MEL). (b) Training time per minibatch. [R1-5] Strengthen the discussion around plans for prospective validation and explain how the method may perform under real-world imaging conditions. Thank you for the helpful comment. We have expanded the Discussion (page 21, line 22) to clarify the limitations of retrospective design and to describe plans for prospective validation. The revised text is as follows: Discussion: page 21, line 22 Second, the design of this study was retrospective, and its performance has not been verified using prospective data. In actual scans, imperfect imaging conditions, such as inaccurate sampling patterns due to eddy current effects, may degrade the reconstruction performance. For example, the B0 magnetic field inhomogeneity and eddy currents can cause geometric distortion and signal loss [55]. Therefore, when planning a prospective study, it may be necessary, for example to assess the impact of eddy currents on image distortion and trajectory deviation through spatiotemporal measurement of k-space trajectories using a field camera [56], and to evaluate the distortion itself through phantom study [57]. Validation with prospectively acquired US k-space data is a future issue, particularly in a study design such as the present study, which used only US k-space data. Reviewer #2: [R2-1] The manuscript includes many technical terms and acronyms (e.g., CS, PI, SL, SSL, ZSSSL, MEL, GT, AF) without always defining them. This could make the text difficult to follow for readers outside the field. Thank you for the comment. As noted in our response to [R1-1], we have revised the manuscript to define all technical terms and acronyms upon first use. In addition, we have added a Background section to improve clarity, as also explained in our response to [R2-3]. [R2-2] The manuscript is highly technical, and some sections (e.g., network architecture, training strategies) are difficult to follow for readers who are not experts in MRI reconstruction or deep learning. Thank you for the comment. We have added explanations to improve clarity where possible. For specific revisions addressing this point, please refer to our responses to [R2-3], [R2-4], and [R2-8]. [R2-3] Add a background section to explain key terms, concepts, and MRI sequences. The paper would benefit from the addition of a background section to improve accessibility and readability. Many key concepts such as Self-Supervised Learning (SSL), Zero-Shot Self-Supervised Learning (ZSSSL), Memory Efficient Learning (MEL), and the qMRI sequences (MSME, VFA-SPGR, DESS) are central to the study but are not explained in sufficient detail for readers who may not be familiar with these techniques. Thank you for the helpful suggestion. To improve accessibility and readability, we have added a new Background section. This section introduces key concepts, technical terms, and MRI sequences used in the study, including Self-Supervised Learning (SSL), Zero-Shot SSL (ZSSSL), and the qMRI sequences (MSME, VFA-SPGR, qDESS). The added section is located at the beginning of the manuscript and provides the necessary context for readers who may not be familiar with MRI reconstruction or deep learning. For a detailed explanation of Memory-Efficient Learning (MEL), please refer to our response to [R2-8]. Background Problem formulation In this section, we formulize the MRI sampling process. Under multi-coil conditions, the sampling process can be formalized as follows: █(y_Ω=E_Ω x#(1) ) where x∈R^(H×W×2) is the target image, and y_Ω∈R^(C×H×W×2) represents the US multi-coil k-space data. Ω is the sampling region, C is the number of receiving coils, and H×W is the image matrix size. The encoding operator E_Ω:R^(H×W×2)↦R^(C×H×W×2) in PI is defined as: █(E_Ω=[█(M_Ω FC_1@M_Ω FC_2@⋮@M_Ω FC_C )]#(2) ) where C_i is the sensitivity of the receiving coil, F is the discrete Fourier operator, and M_Ω is the sampling operator that fills unmeasured k-space points (outside Ω) with zeros. In this study, we extended the encoding operator in Equation (2) to the sampling process for multicontrast data. In multicoil/multicontrast data acquisition, different sampling regions are often employed for each contrast; thus, the multicontrast extension of the encoding operator in Equation (2) is defined as: █(E_Ω=[█(E_(Ω_1 )@E_(Ω_2 )@⋮@E_(Ω_P ) )]#(3) ) Thus, the operator E_Ω:R^(P×C×H×W×2)↦R^(P×H×W×2) is the encoding operator for multi-contrast k-space data, where P is the number of input contrast images, and Ω_i is the sampling region in k-space for the i-th contrast. Here, Ω={Ω_1,Ω_2,…,Ω_P} represents the sampling regions for all contrasts. Using this operator, the sampling operation for multi-coil / multi-contrast data can be expressed similarly to Equation (1). Henceforth, unless otherwise specified, the encoding operator in this paper refers to the multicontrast extended encoding operator defined in this section. Quantitative MRI sequences in this study This section provides an overview of the qMRI sequences used in the present study. In this study, MSME, VFA-SPGR, and qDESS were adopted as standard methods for 2D T2, 3D T1, and fast 3D T2 mapping, respectively. MSME is a pulse sequence used for T2 mapping that combines multi-slice imaging that excites multiple slices in parallel with the spin-echo technique, where a 90-degree RF pulse excites nuclear magnetization and a 180-degree RF pulse refocuses it to generate echo signals. MSME acquires multiple spin echoes at different echo times (TE) from a single excitation, thus enabling efficient T2 mapping. The signal model is expressed as follows: █(S_i (I_0,T_2 )=I_0 e^(-TE_i/T_2 )#(4) ) where I_0 and T_2 represent the proton density image and T2 map, respectively. 〖TE〗_i represents the echo time of the ith echo. Using the signal model in (4), the T2 map can be estimated using least-squares fitting (LSF). VFA-SPGR is a widely used method for T1 mapping, particularly for acquiring 3D T1 maps [29]. This method uses SPGR sequences acquired multiple times with multiple FA and constant TR and TE. The signal model for the SPGR sequence is as follows: █(S_i (I_0,T_1 )=I_0 ((1-e^(-TR/T_1 )))/(1-e^(-TR/T_1 ) cosα_i )#(5) ) where α_i is the flip angle of the ith measurement. If there are at least two measurements with different flip angles, T1 mapping is possible using Equation (5). qDESS is a 3D T2 mapping method based on the DESS sequence, a well-known, undistorted SNR-efficient 3D imaging technique [30]. In DESS, two contrast images, free induction decay (FID) signals, S_fid, and ECHO signals, S_echo, are obtained simultaneously per TR. T2 mapping is performed by utilizing the relationship between the FID signal and ECHO signal ratio as follows [31]: █(S_echo/S_fid =e^(-2(TR-TE)/T_2 )#(6) ) In a study by Sveinsson et al. [32], T1 and diffusion effects were considered, particularly when focusing on the knee. █(S_echo/S_fid =e^(-2(TR-TE)/T_2-(TR-τ/3)Δk^2 D ) sin^2⁡〖(α/2)〗 ((1+e^(-TR/T_1-TRΔk^2 D))/(1-cosαe^(-TR/T_1-TRΔk^2 D) ))#(7) ) where TR and TE represent the repetition and echo time, respectively. α is the flip angle, D is the diffusivity, and the dephasing per unit length induced by the unbalanced gradient is denoted by Δk =γGτ, where G and τ are the spoiler amplitude and duration, respectively. In this study, following Sveinsson et al.[32], we focused on knee imaging and assumed T1 to be 1000 ms, with other sequence parameters based on the SKM-TEA dataset [33]. Training strategy of deep learning MRI reconstruction In this section, the DL training method used in this study is described. In recent years, research on learning methods has been actively conducted with the development of DL networks. The datasets required differed depending on the learning method, and some datasets did not require a ground truth (GT). The represe Attachments Attachment Submitted filename: reply_to_reviewers.docx https://doi.org/10.1371/journal.pone.0324496.r003
28 Apr 2025 Decision Letter - Ibrahim Sadek, Editor Ground-truth-free deep learning approach for accelerated quantitative parameter mapping with memory efficient learning PONE-D-24-54559R1 Dear Dr. Terada, We’re pleased to inform you that your manuscript has been judged scientifically suitable for publication and will be formally accepted for publication once it meets all outstanding technical requirements. Within one week, you’ll receive an e-mail detailing the required amendments. When these have been addressed, you’ll receive a formal acceptance letter and your manuscript will be scheduled for publication. An invoice will be generated when your article is formally accepted. Please note, if your institution has a publishing partnership with PLOS and your article meets the relevant criteria, all or part of your publication costs will be covered. 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PLOS ONE does not copyedit accepted manuscripts, so the language in submitted articles must be clear, correct, and unambiguous. Any typographical or grammatical errors should be corrected at revision, so please note any specific errors here. Reviewer #1: Yes Reviewer #2: No ****** 6. Review Comments to the Author Please use the space provided to explain your answers to the questions above. You may also include additional comments for the author, including concerns about dual publication, research ethics, or publication ethics. (Please upload your review as an attachment if it exceeds 20,000 characters) Reviewer #1: There are no further comments. The authors have addressed properly the comments that are sent to them. Reviewer #2: Please improve the resolution of the figures to ensure clear visualization. Please consider revising the manuscript for improved clarity and smoother flow, as some sections are difficult to follow and may benefit from enhanced organization ****** 7. 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Formally Accepted
Acceptance Letter - Ibrahim Sadek, Editor PONE-D-24-54559R1 PLOS ONE Dear Dr. Terada, I'm pleased to inform you that your manuscript has been deemed suitable for publication in PLOS ONE. Congratulations! Your manuscript is now being handed over to our production team. At this stage, our production department will prepare your paper for publication. This includes ensuring the following: * All references, tables, and figures are properly cited * All relevant supporting information is included in the manuscript submission, * There are no issues that prevent the paper from being properly typeset You will receive further instructions from the production team, including instructions on how to review your proof when it is ready. Please keep in mind that we are working through a large volume of accepted articles, so please give us a few days to review your paper and let you know the next and final steps. Lastly, if your institution or institutions have a press office, please let them know about your upcoming paper now to help maximize its impact. If they'll be preparing press materials, please inform our press team within the next 48 hours. Your manuscript will remain under strict press embargo until 2 pm Eastern Time on the date of publication. For more information, please contact onepress@plos.org. If we can help with anything else, please email us at customercare@plos.org. Thank you for submitting your work to PLOS ONE and supporting open access. Kind regards, PLOS ONE Editorial Office Staff on behalf of Dr. Ibrahim Sadek Academic Editor PLOS ONE https://doi.org/10.1371/journal.pone.0324496.r005

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