Deep blind arterial input function: signal correction in perfusion cardiac magnetic resonance

Authors: habib  rebbah
magalie  viallon
pierre  croisille
timothé  boutelier
Venue: MIDL_io_2024_Conference
Published: 2024-01-29 15:40:51

Abstract: Objectives: The non-linear relationship between gadolinium concentration and the signal in perfusion cardiac magnetic resonance (CMR) poses a significant challenge for accurate quantification of pharmacokinetic parameters. This phenomenon primarily impacts the arterial input function (AIF), causing it to appear saturated in comparison to the temporal concentration profile. This study aims to leverage a blind deconvolution strategy through a deep-learning approach to address the saturation in the AIF.

Methods: We propose the utilization of a convolutional neural network (CNN) architecture with the saturated AIF and a set of myocardial tissue signals as inputs, generating the corrected AIF as the output. To train the network, a dataset comprising over 3×10^6 simulated AIFs with associated signals from five simulated tissues response for each instance was employed. To assess the effectiveness of the approach, the trained network was evaluated using a dual-saturation sequence to compare the corrected AIF with the unsaturated version. The clinical dataset encompassed scans from 43 patients.

Results: The mean square error (MSE) for the testing subset of the simulated database was 0.69% of the peak. In the in vivo dataset, the coefficient of determination R2 was 0.26 and 0.86 for the saturated and corrected AIF, respectively, in comparison to the unsaturated AIF.

Conclusion: The proposed network successfully corrects the acquisition-induced effects on the AIF. Moreover, the extensive simulated database, featuring diverse acquisition parameters, facilitates the robust generalization of the network's application.

Main paper: 
 introduction: 
 The intravenous administration of gadolinium-based contrast agent (CA) in cardiovascular magnetic resonance (CMR) during its initial vascular transit has become a clinical standard for assessing myocardial perfusion states (Jerosch-Herold et al., 2006) . Specifically, dynamic contrast enhanced (DCE) imaging in the cardiac domain has demonstrated its efficacy in evaluating various diseases (Montalescot et al., 2013; Nagel et al., 2019) . Perfusion quantification typically involves employing a deconvolution approach based on a parametric tracer-kinetic model and an arterial input function (AIF) (Sourbron and Buckley, 2011;  Other research has focused on estimating the correct AIF directly from acquired images using a blind deconvolution approach (Schabel et al., 2010) . This assumes a shared AIF among various tissues with different tissular responses, with the redundancy of information allowing simultaneous estimation of tissular pharmacokinetic parameters and the corresponding AIF. However, the practical application of such a method requires a sufficiently diverse range of tissue responses to ensure stability. One frequently suggested approach is to constrain the AIF to a specific parametric time-course model, such as Parker's AIF. Bayesian approaches have shown also promising results (Schmid et al., 2007) . Despite the stability limits, these methods can be computationally intensive due to the conventional iterative resolution of the deconvolution problem for tissue response and AIF.To overcome these limitations, recent studies propose using a deep learning approach to correctly estimate the AIF from the acquisition. One approach involves using unsaturated AIFs from dynamic susceptibility contrast (DSC) acquisitions and their corresponding DCE profiles to train a conditional generative adversarial network for correcting DCE saturated AIFs (Choi et al., 2020) . Another approach uses a similar method based on unsaturated AIFs obtained using the dual-saturation sequence to train a 1D U-Net for correcting input DCE AIFs (Scannell et al., 2023) . Although both methods present promising results, their generalization is limited by the variability in their databases, primarily due to differences in magnetic field strength (1.5 vs. 3T) and MRI machine characteristics.To the best of our knowledge, the latest proposition introduces a form of blind deconvolution into a physics-informed neural network (PINN) to constrain AIF estimation (van Herten et al., 2022) . Despite the extensive dataset and the absence of the need for labeled data, the main limitation is the considerable computation time required for this approach (1 hour per slice for a standard personal computer).In this study, we propose a deep learning solution to estimate the AIF while maximizing generalization, based on simulations and blind deconvolution principle, taking saturated AIF and tissue signals as inputs to return the estimation of the unsaturated AIF. The objective is to develop a user-friendly and efficient solution that circumvents the need for complex modeling of acquisition sequences and can be extended to diverse acquisition parameter settings. 
simulated database: 
 A large simulated database of AIFs and their corresponding tissue responses of over 3 × 10 6 cases is used to train the network. We adopted Parker's simplified form to generate the unsaturated AIFs, as described in (Parker et al., 2006) .EQUATIONFive different tissue responses were generated for each AIF using the Toft-Kety model (Tofts and Kermode, 1991; Tofts et al., 1999) . The concentration observed for each case can be computed as follows:EQUATIONA uniform, independent, and identically distributed random sampling of the parameters in Equation (1) and Equation (2) enabled the generation of 3,906,250 unique cases, with the upper and lower bounds described in Annex A. Eventually, the simulated AIF is converted into a saturated signal using a simplified set of Bloch equations tailored for cardiac perfusion acquisition, involving perfect saturation followed by SPGR pulses (equation 1.2.7 in (Rebbah, 2019) ). Annex B provides details on the conversion process. Tissue concentrations were converted by assuming a linear approximation with their corresponding signals, employing a proportionality coefficient set arbitrarily to 1.Due to the simulation aspect, time step units were used rather than absolute time length, employing a signal length of 40 steps for both AIF and tissue responses. Additionally, to avoid any scaling issues, we normalized all inputs and outputs-accurate AIF, saturated AIF, and tissue signals-to the [0, 1] range.The evaluation of the network was conducted using in vivo data obtained from a set of 43 patients/volunteers with dual-saturation acquisitions extracted from the in vivo database described in (Daviller et al., 2021) . The perfusion sequences were acquired on a 3T MAG-NETOM Prisma (Siemens Healthineers, Erlangen, Germany) at 3 to 5 short-axis locations for every heartbeat with a bolus injection (6 ml/s) of gadoterate meglumine (0.2 mmol/kg) (Dotarem, Guerbet, Paris, France).The unsaturated AIF was computed by avering blood time curves derived from ROIs positionned in the cavity on the short recovery time acquisition series of the dual perfusion sequence acquisition. For the saturated acquisitions, an automatic registration was provided by the manufacturer (MOCO series, Siemens Healthcare). LV blood pool time curves, and myocardial time curves were obtained from ROIs manually delineated at the optimal contrast perfusion image to obtain the saturated AIF for correction and a set of myocardial signals. A linear interpolation is used if necessary to match inputs length of the proposed model. A K-means algorithm was employed to select 5 main signals, computed as the average signal of each cluster. To match the simulated signal length, all time profiles were linearly interpolated to obtain signals with a length of 40 time steps.The proposed network is illustrated in Figure 1 . It consists of a two-branch Convolutional Neural Network (CNN): a 1D branch for the saturated Arterial Input Function (AIF) and a 2D branch for the 5 tissue signals. The outputs of the two branches are flattened, combined, and processed through dense layers. The final output is a correction of the input saturated AIF. Annex D provides a comparison with a fully blind deconvolution model (without saturated AIF input).The randomly allocated subdivision of the simulated dataset between training and validation follows an 80/20% ratio, corresponding to 3,198,093/781,250 cases. Training was conducted using the ADAM optimizer with a learning rate of 0.001 and Mean Squared Error (MSE) loss between the proposed corrected AIF and the unsaturated simulated one. This training process spanned 30 epochs, with each epoch consisting of 20,000 cases per batch.The study was implemented using Python and the TensorFlow 2 framework. The model is completed with a scale correction process. The output of blind deconvolution typically yields an estimate of the AIF that is scalefree, as all multiples of the proposed AIF satisfy the deconvolution problem, allowing the flow or K trans to absorb the variation. To estimate the correct scale factor, we followed recommendations in the literature and chose to match the area under the curve (AUC) of the tail of the correct AIF with the AUC of the tail of the saturated one (Schabel et al., 2010) . Specifically, we selected the last 10 time points to represent the tail of the AIF. 
training results: 
 After 30 epochs, the model converged with a MSE of 0.69 × 10 -2 for both the training and validation subsets. Figure 2 showcases a few randomly selected results from the validation dataset. The unsaturated AIF (green line) is barely discernible, hidden by the prediction of the proposed algorithm (blue line).However, we observed a peculiar phenomenon where, in each training iteration, certain temporal positions of the corrected AIF consistently exhibited values of zero. These specific temporal positions varied with each new training process but remained constant within the same iteration, independent of the input conditions. The cause of this behavior is unclear, but a straightforward solution was implemented. Following a successful training, the temporal positions where the corrected AIF exhibited zeros were identified and a postprocessing step to interpolate the values at those time points was added. In the algorithm presented here, there were two instances of zero values. Refer to Annex E for further details. The green line representing the unsaturated AIF when it is not apparent, is under the blue line, representing an accurate prediction. The orange arrows highlight the zeros points.The comprehensive evaluation of the entire algorithm (comprising the network and the post-processing correction for scale and zero values) using dual-saturation sequences was conducted by comparing discrepancies in the unsaturated AIF (AIF unsat ) with the saturated one (AIF sat ) and the discrepancies of the AIF unsat and the corrected AIF estimated by our algorithm (AIF db for deep blind). The discrepancies were evaluated as MSE and coefficient of determination R2. Moreover, myocardial blood flow (MBF) was estimated using a deconvolution algorithm with a free-form residue function (Olea Medical), for each AIF along with the extracted main myocardial signals. The results presented in Figure 3 and Figure 4 showcase some selected cases. The median MSE for the AIF sat was 0.15 +/-0.05 compared to 0.07 +/-0.03 for the AIF db . The median R2 was 0.27 +/-0.12 for the AIF sat compared to 0.86 +/-0.45 (+/-0.10 with outlier exclusion for two cases) of the AIF db . The median relative error of MBF estimations was 3.78 +/-1.99 for the AIF sat compared to the AIF db was 0.34 +/-0.57. More in vivo results are gathered in Annex C.  
discussion: 
 The proposed approach demonstrated its capability to estimate the unsaturated version of the AIF accurately. Training the model with simulated data allows to easily explore perfusion parameters, enhancing its robustness and generalizability compared to strategies using limited number of in vivo data to train the network (Annex D). Figure 2 highlights that some simulated AIFs differ from real acquired AIFs. However, this variability promotes learning the underlying convolution operation between the AIF and tissue responses to derive tissue signals.While the principle of deconvolution in perfusion imaging traditionally involves only tissue signals, our approach deviates from this by incorporating the saturated AIF, thereby constraining the deconvolution. In conventional literature (Schabel et al., 2010) , this is achieved by choosing a parametric time-course model; however, our approach constrains the solution through the effect of the acquisition. The challenge then becomes finding an AIF that can explain both the tissue signals and the transformation induced by the acquisition leading to the observed saturated AIF. Previous research suggested that ignoring tissue signals and using only the saturated AIF could accurately predict its unsaturated version (Choi et al., 2020; Scannell et al., 2023) . However, we argue that such results primarily reflect the low variability of the datasets used for training in those studies, as they utilized perfusion acquisitions from very few centers with limited variations in acquisition parameters. Incorporating both the saturated AIF and tissue signals in our approach allows for better constraint of the solution. Moreover, choosing simulation with high parameter variations supports the validity of the results.The solution presented here is preliminary work intended to demonstrate the network's ability to correct acquisition effects. However, the model proposed generates fixed zeros whose origin cannot be currently explained. Preliminary tests with the addition of multiple dropouts seem to address this issue effectively (Annex E), warranting further investigation. Nevertheless, the proposed post-processing successfully passed the evaluation test with real acquisition data. Notably, we did not introduce noise to the training data. This choice is derived from the practical pipeline induced by our method. Indeed, all inputs are averaged from a group of signals, using ROIs of the LV blood pool for the saturated AIF and myocardial signal classification for the five main tissue signals. This process significantly enhances the signal-to-noise ratio. Future work will focus on refining this aspect to enable the use of direct signals. However, the successful evaluation on real acquired data supports our initial intuition.An intriguing open question concerns the performance dependency on input tissue signals. Specifically, the decision to solely utilize myocardial signals for deriving the five principal signals warrants consideration. Notably, a homogeneous myocardium may likely decrease the algorithm's performances, as evidenced by the outlier results observed in vivo. Furthermore, the adoption of K-means clustering to extract the main signals as cluster centroids is noteworthy. If the chosen number of clusters is restricted relative to the variability of the acquired signals, erroneous main signals may be generated through the averaging of disparate signals within the same cluster. Subsequent efforts will predominantly concentrate on precisely quantifying thus constraints and exercising greater discretion in selecting inputs. proach. However, these results are likely influenced by the limited dataset variability, as these studies utilized perfusion acquisitions from a few centers with restricted protocol parameter variations. Additional inputs such as the main signals or the AIF sat can provide constraints to enhance the solution. One could also experiment with fewer primary signals, theoretically achieving accurate AIF unsat estimation. Nevertheless, such approaches will expose the process to a higher risk of error.In this section, we compare the same proposed model (with dropout rate of 0.2) trained with:The simulated database as described in the main textThe dual saturation acquisitions from the in vivo databaseThe dual saturation acquisitions from the in vivo database to fine tune the model trained with the simulated databaseThe performances of the models were evaluated using 10 cases from in vivo database and 10,000 cases of the simulation training dataset. To train with in vivo data, we split them in two sets: 26 for training and 7 for testing and managing the training process. The performances were evaluated in terms of MSE and R2. The results are presented in Figure 8 .The results highlight the advantage of the models trained with the simulated database. The fine-tuned model exhibits a slight improvement in terms of MSE and R2 compared to the model trained solely with the in vivo database. However, the model trained with the simulated database outperforms the fine-tuned model for in vivo and simulation dataset. These results lend support to the proposed strategy and its ability to generalize.  
 
 Appendix:  


Decision: The authors proposed a deep learning method trained on simulated data to correct the saturated arterial input function (AIF) signal in perfusion cardiac MR.  This is a real and clinically significant problem. Given the saturated AIF and a set of myocardial tissue signals, the network predict the unsaturated AIF. The trained network was evaluated using a dual-saturated sequence to compare the corrected AIF with the unsaturated version. The results show some improvement and the proposed network generated corrected AIF with better R2 scores than the saturated AIF.

Reviews: review: paper_summary: paper_summary: The authors proposed to use a CNN with the saturated AIF and a set of myocardial tissue signals as inputs, to generate the
corrected AIF as the output. A simulated datasets was created to train the network, and a real clinical dataset was used for testing. The results show that the proposed network can correct the acquisition-induced effects on the AIF and also displays the ability for generalization.
main_review: main_review: The current version may need more clarifications. It would be more clear to the readers if the motivation of the proposed method and the major findings can be further clarified. For example, at the end of the introduction, it would be helpful to highlight the difference between the proposed method and the previous methods.
strength_weakness: strength_weakness: - It seems not clear to me why 2 branches of the CNN are 1D and 2D for different inputs. It would be helpful to explain the motivation/reason for this design.

- The zero point issues in Figure 2 may need more discussion. During training, do the targets in the simulated database have the patterns of such zero points? If not, this issue is likely to be caused by the implementation.
questions: questions: It would be more clear to the readers if the motivation of the proposed method and the major findings can be further clarified. For example, at the end of the introduction, it would be helpful to highlight the difference between the proposed method and the previous methods.
paper_summary: paper_summary: The authors proposed a deep learning methods to get corrected AIF from saturated AIF and a set of myocardial tissue signals, using a large of synthetic dataset for network training. The trained network was evaluated using a dual-saturated sequence to compare the corrected AIF with the unsaturated version. The result showed that the proposed network generated corrected AIF with better R2 scores than the saturated AIF.
main_review: main_review: Thanks for the authors addressing my questions. The authors provided more experiments in the revision which makes the paper more solid. Based on the revision provided, I would like to increase my final rating.
strength_weakness: strength_weakness: The proposed methods utilized simulated data for training, then the trained network was applied on in-vivo data. The difference between the simulated data and in-vivo data could cause performance degradation. The authors failed to take into this consideration. Therefore, the authors's claiming that "Training the model with simulated data allows to easily explore perfusion parameters, enhancing its robustness and generalizability compared to strategies using limited number of in-vivo data to train the network." is not convincing. The author should compare the proposed methods with 1) simulated data for pre-training, then apply transfer learning on in-vivo data. 2) in-vivo data only for network training. In addition, the authors should compare the proposed methods with conventional non-deep learning methods and existing deep learning methods, to have a comprehensive performance evaluation. Regarding to the network architecture, since the inputs include acquired saturated AIF and 5 main signals from perfused tissues, it is better to have an ablation study to compare several networks with different inputs, such as 1) only saturated AIF. 2) saturated AIF and 1-5 main signals from perfused tissues. Since the AIF is time series signal, it is better to compare the the proposed network architecture with some other network architectures such as RNNs. Last one, the authors observed that certain temporal positions of the corrected AIF consistently exhibited values of zero, while the cause is unclear. Therefore, it is better to double-check the simulation procedure. It is better to exclude these outliers in the training data to affect the training even though it might be tiny.
questions: questions: 1. The author adopted Parkers' simplified from to generate simulated database. Is there sophisticated model to do simulation and how do you think it might affect the result?
2.  The authors mentioned that time step units rather than absolute time length in generating simulated data for training. Did the authors do data interpolations when applied to the in-vivo data which could be acquired with different time resolution?
3. Does the corrected AIF is used for quantitative evaluation of perfusion imaging? If so, could the author evaluate it the estimated corrected AIF besides MSE and R2?
paper_summary: paper_summary: The authors propose a CNN model trained on simulated data to correct the arterial input function signal in perfusion cardiac MR.
main_review: main_review: Based on the authors' responses, I decided to raise my evaluation to borderline reject. However, I still think the work is not ready for publication. Understanding why  AIF in the experiments consistently exhibited values of zero is important. Is this a finding or a bug/mistake in their code?
strength_weakness: strength_weakness: In my opinion, the main weaknesses of the paper are the lack of comparisons against other methods in the literature and the fact that the corrected AIF in the experiments consistently exhibited values of zero. Still, the authors were not able to explain why this happened.

I believe the authors also missed the opportunity to compare their proposed model against a fine-tuned version of their model using in vivo data, which would increase our understanding of the discrepancy between training in simulated data and in vivo data.
questions: questions: - Why the corrected AIF in the experiments consistently exhibited values of zero?
- How does the proposed model compare against others in the literarture?
- How does the proposed model compare against training using in vivo data and training on simulated data and fine-tuning on in vivo data?

Comments: title: Response
Response
Response
comment: We thank the reviewer for its insightful feedback. We hope that the new version of the article addresses all its questions.


•	Why the MSE arrow is entering the CNN block in Figure 1?

To represents the gradient backpropagation (based on MSE).

•	Was training on nearly 4M simulated data points necessary for the proposed model to achieve its performance?

Indeed, the actual number itself may not be as crucial as the coverage of the possibility space. Testing a broader sampling (thus fewer cases) but ensuring at least the same coverage of the space (or even greater coverage) could be an interesting point to investigate.

•	Why the corrected AIF in the experiments consistently exhibited values of zero?

For the moment, the reason is not clear. However, we have added an appendix (E) to discuss this point in more detail. It appears that certain nodes are not "used", and dropout forces them to be involved. We hope to gain insights and potential avenues for further investigation during the conference.

•	How does the proposed model compare against others in the literarture?

The comparison with deep learning methods is in Appendix D.2. Comparing with other non-deep learning methods seems more complex to implement. We chose the "dual saturation" method as the gold standard. This leaves: the population AIF method and direct signal correction. Testing the former seems unviable as its limitations have long been documented. Comparing with the latter is more debatable: either the sequence modeling is near-perfect and the approach result is almost error-free, or the modeling is inadequate and claiming our approach is better would be of little interest. We prefer to emphasize one of the primary benefit of our approach: the "user-friendly" aspect. No modeling is required, and no information other than image intensities is used.

•	How does the proposed model compare against training using in vivo data and training on simulated data and fine-tuning on in vivo data?

This point is added in annexe D.
The authors thank the reviewer for the numerous suggestions for improvement that we have incorporated into the new version of the article.

1.	Ablation study about the training data. 1) simulated data only for network training. 2) simulated data for pre-training, then apply transfer learning on in-vivo data. 3) in-vivo data only for network training.

Added in Appendix D.2.

2.	Ablation study about the network input. 1) only saturated AIF. 2) saturated AIF and 1-5 main signals from perfused tissues.

Added in Appendix D.1. Additionally, we mention that direct comparison may not cover all scenarios. Blind deconvolution, for instance, theoretically could lead to correct estimations with only 2 signals. However, even if tests with our data had shown this, the obtained model would have been highly sensitive to errors. Having 5 signals + an initial AIF estimation helps guard against potential errors.

3.	Compare the proposed method with conventional methods and other existing deep learning methods.

The comparison with deep learning methods is in Appendix D.2. Comparing with other non-deep learning methods seems more complex to implement. We chose the "dual saturation" method as the gold standard. This leaves: the population AIF method and direct signal correction. Testing the former seems unviable as its limitations have long been documented. Comparing with the latter is more debatable: either the sequence modeling is near-perfect and the approach result is almost error-free, or the modeling is inadequate and claiming our approach is better would be of little interest. We prefer to emphasize one of the primary benefit of our approach: the "user-friendly" aspect. No modeling is required, and no information other than image intensities is used.

4.	About corrected AIF consistently exhibited values of zero, the authors should find out the reason.

Appendix E is added to detail this point.

1.	The author adopted Parkers' simplified from to generate simulated database. Is there sophisticated model to do simulation and how do you think it might affect the result?

Yes, we could have used gamma functions instead of Gaussians, often described as closer to reality. Additionally, we modeled two passages of the contrast agent; more passages could have been added. But more importantly, we could have also modeled dual-bolus profiles. It seems that the gains from the former approaches may be limited. However, simulating dual-bolus profiles could indeed greatly improve the generalization of the model.

2.	The authors mentioned that time step units rather than absolute time length in generating simulated data for training. Did the authors do data interpolations when applied to the in-vivo data which could be acquired with different time resolution?

Thank you for pointing out this omission. Yes, linear interpolation is used if necessary. A sentence has been added to the methodology section.

3.	Does the corrected AIF is used for quantitative evaluation of perfusion imaging? If so, could the author evaluate it the estimated corrected AIF besides MSE and R2?

The overall clinical evaluation is ongoing. However, we have added the MBF calculated with the 5 main myocardial signals extracted. A comparison is proposed in addition to R2 and MSE in the main text, and a more detailed version is in Appendix C. Additionally, mapping results for one volunteer have also been added in Appendix C.
Firstly, the authors express their gratitude to the reviewer for its interest in this work. We have submitted a revised version of the article, which we hope addresses all of the requests.

- "It seems not clear to me why 2 branches of the CNN are 1D and 2D for different inputs. It would be helpful to explain the motivation/reason for this design."

The reason lies in the shape of the two inputs: 1D for the AIF and 2D for the signals (5 main signals).

- "The zero point issues in Figure 2 may need more discussion. During training, do the targets in the simulated database have the patterns of such zero points? If not, this issue is likely to be caused by the implementation."

Indeed, we have added an appendix (E) dedicated to this issue. As you will notice, the pattern of zeros is not present in the database. Furthermore, the same implementation leads to their appearance at different points depending on the training performed. Finally, the same implementation can entirely remove them by adding dropout layers. It seems that dropout layers 'force' the network to involve all nodes. Why this is not the case without them is currently unclear. This is one of the reasons motivating us to submit to a conference dedicated to medical AI topics. We hope that this point will raise the interest of participants as it did for all the reviewers.

- "It would be clearer to the readers if the motivation of the proposed method and the major findings can be further clarified. For example, at the end of the introduction, it would be helpful to highlight the difference between the proposed method and the previous methods."

Indeed, thank you for pointing it out. A sentence has been added at the end of the introduction for this purpose.