Accelerated cardiac T1 mapping with recurrent networks and cyclic, model-based loss

Abstract

Background

Using the spin-lattice relaxation time (T1) as a biomarker, the myocardium can be quantitatively characterized using cardiac T1 mapping. The modified Look-Locker inversion recovery (MOLLI) sequences have become the standard clinical method for cardiac T1 mapping. However, the MOLLI sequences require an 11-heartbeat breath-hold that can be difficult for subjects, particularly during exercise or pharmacologically induced stress. Although shorter cardiac T1 mapping sequences have been proposed, these methods suffer from reduced precision. As such, there is an unmet need for accelerated cardiac T1 mapping.

Purpose

To accelerate cardiac T1 mapping MOLLI sequences by using neural networks to estimate T1 maps using a reduced number of T1-weighted images and their corresponding inversion times.

Materials and Methods

In this retrospective study, 911 pre-contrast T1 mapping datasets from 202 subjects (128 males, 56 ± 15 years; 74 females, 54 ± 17 years) and 574 T1 mapping post-contrast datasets from 193 subjects (122 males, 57 ± 15 years; 71 females, 54 ± 17 years) were acquired using the MOLLI-5(3)3 sequence and the MOLLI-4(1)3(1)2 sequence respectively. All acquisition protocols used similar scan parameters: TR = 2.2 ms, TE = 1.12 ms, and FA = 35°, gadoteridol (ProHance, Bracco Diagnostics) dose ~0.075 mmol/kg. A bidirectional multi-layered long short-term memory (LSTM) network with fully connected output and cyclic model-based loss was used to estimate T1 maps from the first three T1-weighted images and their corresponding inversion times for pre-contrast and post-contrast T1 mapping. The performance of the proposed architecture was compared to the three-parameter T1 recovery model using the same reduction of the number of T1-weighted images and inversion times. Reference T1 maps were generated from the scanner using the full MOLLI sequences and the three-parameter T1 recovery model. Correlation and Bland-Altman plots were used to evaluate network performance where each point represents averaged regions of interest in the myocardium corresponding to the standard American Heart Association 16-segment model. The precision of the network was examined using consecutively repeated scans. Stress and rest pre-contrast MOLLI studies as well as various disease test cases including amyloidosis, hypertrophic cardiomyopathy, and sarcoidosis were also examined. Paired t-tests were used to determine statistical significance with p < 0.05.

Results

Our proposed network demonstrated similar T1 estimations to the standard MOLLI sequences (pre-contrast: 1260 ± 94 ms vs. 1254 ± 91 ms with p = 0.13; post-contrast: 484 ± 92 ms vs. 493 ± 91 ms with p = 0.07). The precision of standard MOLLI sequences was well preserved with the proposed network architecture (24 ± 28 ms vs. 18 ± 13 ms). Network-generated T1 reactivities are similar to stress and rest pre-contrast MOLLI studies (5.1 ± 4.0 % vs. 4.9 ± 4.4 % with p = 0.84). Amyloidosis T1 maps generated using the proposed network are also similar to the reference T1 maps (pre-contrast: 1243 ± 140 ms vs. 1231 ± 137 ms with p = 0.60; post-contrast: 348 ± 26 ms vs. 346 ± 27 ms with p = 0.89).

Conclusions

A bidirectional multi-layered LSTM network with fully connected output and cyclic model-based loss was used to generate high-quality pre-contrast and post-contrast T1 maps using the first three T1-weighted images and their corresponding inversion times. This work demonstrates that combining deep learning with cardiac T1 mapping can potentially accelerate standard MOLLI sequences from 11 heartbeats to 3 heartbeats.

1. Introduction

Using the spin-lattice relaxation time (T1) as a biomarker, cardiac T1 mapping can be used to quantitatively characterize the myocardium. As such, cardiac T1 mapping has shown promise in differentiating various cardiomyopathies such as acute myocardial infarction¹, amyloidosis², and Anderson-Fabry disease³. The diagnostic value of T1 mapping can be increased with the acquisition of post-contrast T1 maps and hematocrit measurements. By combining pre-contrast and post-contrast T1 maps with hematocrit measurements, extracellular volume (ECV) maps can be generated. ECV maps have shown clinical utility in differentiating disease states that would be difficult to diagnose with native T1 mapping alone^4–6. In addition, cardiac T1 mapping has shown potential in differentiating ischemic and normal myocardium^7–10. For assessment of coronary artery disease (CAD), cardiac T1 mapping is acquired during stress and rest states where the increased myocardial blood volume during stress increases T1^7,11. This difference in stress and rest T1 values known as the T1 reactivity has been shown to be a promising biomarker for CAD assessment. Some studies have also found T1 differences between systolic and diastolic phases due to blood volume changes which could also have some diagnostic value^12–15.

The modified Look-Locker inversion recovery (MOLLI) sequences have become the standard clinical method for T1 mapping. The MOLLI-5(3)3 and MOLLI-4(1)3(1)2 sequences⁶ used for pre-contrast and post-contrast T1 mapping have reduced the breath-hold duration to 11 heartbeats in comparison to the original MOLLI-3(3)3(3)5 sequence¹⁶. Although the MOLLI-5(3)3 and the MOLLI-4(1)3(1)2 variants reduce breath-hold durations compared to the original sequence, an 11-heartbeat breath-hold is still often difficult for sick subjects, particularly during exercise or pharmacologically induced stress. These breath-holds can result in loss of coverage due to longer rest period requirements between the slice acquisitions and can lead to poor T1 maps from motion-related artifacts. Shorter sequences such as the shortened modified Lock-Locker sequence (shMOLLI)² and the saturation recovery single-shot acquisition (SASHA)¹⁷ have been proposed. Although shMOLLI and SASHA have shorter acquisitions, these sequences suffer from reduced precision compared to the standard MOLLI sequences^18–20. Because of this, there is an unmet need for accelerated cardiac T1 mapping sequences to reduce the breath-hold burden on subjects while still maintaining the high precision and accuracy of current sequences.

Recently, deep learning approaches have gained popularity in MRI due to their accuracy and speed in various tasks. In the context of cardiac T1 mapping, deep learning has led to the development of various automated quantitative analysis pipelines. Fahmy et al. have developed an automated quantification pipeline by using a fully connected network for myocardial segmentation with polar transformations for motion compensation before performing a pixel-wise curve fitting for T1 estimation²¹. Puyol-Anton et al. use a convolutional neural network with Bayesian Inference for uncertainty-based quality control of an automated T1 quantification pipeline²². Jeelani et al. have used a recurrent neural network for reconstructing sub-sampled time-series images and a U-Net architecture for T1 estimation²³. However, few works have demonstrated the application of deep learning to accelerate cardiac T1 mapping. Although Jeelani et al. perform in-plane acceleration of the time-series images; in-plane acceleration cannot lead to the acceleration of the T1 mapping sequence itself. This work aims to use neural networks to accelerate cardiac T1 mapping sequences without compromising the quality of current cardiac T1 mapping sequences. Previous work has demonstrated the use of a multi-layer perceptron (MLP) for accelerating cardiac T1 mapping²⁴. The MLP work demonstrates several notable differences from this work. First, our work utilizes a cyclic, model-based loss function that incorporates consistency to the acquired MRI signals. Second, our network utilizes a bidirectional long short-term memory (LSTM) network²⁵ to encode the T1-weighted images and inversion times prior to a fully connected output, a network which we call the T1NET, to accelerate the MOLLI-5(3)3 and the MOLLI-4(1)3(1)2 sequence to 3-heartbeat sequences.

2. Materials and Methods

2.1. Data Acquisition and Processing

In this retrospective study, 911 pre-contrast T1 mapping datasets from 202 subjects (128 males, 56 ± 15 years; 74 females, 54 ± 17 years) and 574 post-contrast datasets from 193 subjects (122 males, 57 ± 15 years; 71 females, 54 ± 17 years) were acquired using 3T Skyra and 3T Prisma Siemens scanners. All human data was acquired in accordance with the local institutional review board (IRB) policies and written informed content was obtained. Datasets consisted of healthy volunteers as well as subjects clinically referred for cardiac MRI scans. Datasets with banding artifacts across the heart or with poor motion compensation were excluded. All acquisition protocols used similar scan parameters: TR = 2.2 ms, TE = 1.12 ms, and FA = 35°, gadoteridol (ProHance, Bracco Diagnostics) dose ~0.075 mmol/kg. Pre-contrast and post-contrast networks were trained using the first three acquired T1-weighted images and their corresponding cumulative times from inversion (which we now refer to as inversion times) as shown in Equation 1.

$$t=TI+\left(n-1\right)RR$$ (1)

where TI = 100 ms, n = 1–3, and RR is the heartbeat interval. T1-weighted images were acquired and motion compensated through the Siemens MOLLI pipeline^26,27, cropped to the central 128 × 128, and vectorized giving dimensions of batch × T × 2. T corresponds to the number of T1-weighted images and their inversion times (T = 3) used as input to the networks. Reference T1 maps were generated from the scanner using the full MOLLI-5(3)3 and MOLLI-4(1)3(1)2 sequences and the three-parameter T1 recovery model¹⁶ shown in Equations 2–3

$$S\left(t\right)=A-B{e}^{-t/T{1}^{*}}$$ (2)

$$T1=T{1}^{*}\left(\frac{B}{A}-1\right)$$ (3)

where A, B, and T1 are the three fitting parameters, S(t) are the T1-weighted images and t are their inversion times. The T1 values were then compensated for inversion efficiency²⁸.

2.2. Network Architecture and Implementation Details

Recurrent neural networks (RNN) are a type of network architecture that demonstrate dynamic temporal capabilities by forming nodal connections along a temporal sequence while using hidden states to track time-series datasets to exhibit memory-like behavior. RNNs have shown excellent capabilities for problems involving time-series analysis making RNNs a natural extension for fitting T1-weighted images and their inversion times to the three-parameter T1 recovery model. As a particular type of RNN, LSTMs have shown powerful dynamic temporal and memory-like behavior by using hidden and cell states to track time-series datasets while information gates modulate the information flow^29,30. We used a multi-layer (N=7) bidirectional LSTM to generate an encoding of the input T1-weighted images and inversion times. We used learnable initial hidden and cell states to improve the learning procedure and a fully connected output to predict the A, B, and T1 parameters. Figure 1 demonstrates the architecture of the proposed T1NET network.

Figure 1.

Illustration of the proposed multi-layer bidirectional long short-term memory (LSTM) with fully connected output network architecture (T1NET) for cardiac T1 mapping. Inputs to the network have dimensions of B × T × 2. T corresponds to the number of T1-weighted images and inversion times used as network input (T = 3). B = 2¹⁵ is the batch size. Forward LSTM (fLSTM) and backward LSTM (bLSTM) modules generate a forward and backward hidden state output, $H_{t,n}^F$ and $H_{t,n}^B$, for a given time step, t, and network layer, n. The hidden state outputs then become input to the following LSTM modules. The final forward and backward LSTM encodings are vectorized, and a fully connected prediction layer was used to output A, B, and T1 from the three-parameter T1 recovery model. Reference T1 maps were generated using the full modified Look-Locker inversion recovery sequences (MOLLI-5(3)3 and MOLLI-4(1)3(1)2) and the three-parameter T1 recovery model.

Training was performed using a cyclic model-based loss function and the L1 loss function for 100 epochs using an NVIDIA P40 GPU on a Linux Fedora 26 operating system with the PyTorch framework³¹ and took approximately 18 hours. Training details for the T1NET are described in Supporting Information Appendix A1. The loss function is described by Equation 4 below

$$\mathcal{L}\left(A,B,T1,\widehat{T1}\right)={\Vert \widehat{S}\left(t\right)-S\left(t\right)\Vert }_1+{\Vert \widehat{T1}-T1\Vert }_1$$ (4)

where A, B, and T1 are the network-generated parameters and S(t) is the signal intensity generated from the network using the three-parameter model in Equation 2. $\widehat{S}\left(t\right)$ and $\widehat{T1}$ are the reference T1-weighted signal intensities and T1 maps respectively. The second term demonstrates a standard pixel-wise mean absolute error loss between the reference and network-generated T1 maps. The first term demonstrates a pixel-wise mean absolute error loss function between the reference and network-generated T1-weighted signal intensities, termed the cyclic model-based loss, where the network predicted A, B, and T1 parameters are used with the three-parameter recovery model to generate network predicted T1-weighted signal intensities. Supporting Information Appendix A2 demonstrates performance comparisons of the T1NET with and without the cyclic model-based loss function. The Adam optimizer was used with a learning rate of 0.0003 and a batch size of 2¹⁵ pixels or two 128 × 128 T1 maps. The T1NET architecture contains approximately 1.35 million parameters. For the pre-contrast network, training was performed on 657 datasets from 131 subjects consisting of 44 healthy volunteers and 87 clinically referred subjects. Validation was performed on 106 datasets from 32 subjects consisting of 11 healthy volunteers and 21 clinically referred subjects. Testing was performed on 146 datasets from 39 subjects consisting of 13 healthy volunteers and 26 clinically referred subjects. For the post-contrast network, training was performed on 427 datasets from 125 subjects consisting of 42 healthy subjects and 83 clinically referred subjects. Validation was performed on 63 datasets from 33 subjects consisting of 12 healthy volunteers and 21 clinically referred subjects. Testing was performed on 82 datasets from 35 subjects consisting of 10 healthy volunteers and 25 clinically referred subjects.

2.3. Performance Evaluation

To evaluate performance, we compared T1 maps generated using the T1NET architecture, T1 maps generated using the three-parameter model with the same reduction of the number of T1-weighted images and inversion times (now referred to as the reduced model), and the reference T1 maps generated by the scanner using the full MOLLI sequences and the three-parameter model. We quantitatively evaluated these methods using correlation and Bland-Altman plots where each point represents averaged regions of interest (ROIs) in the myocardium corresponding to the standard American Heart Association (AHA) 16-segment model³² or averaged ROIs in the left ventricular (LV) blood pool.

Furthermore, the T1NET was compared to other state-of-the-art architectures including the MLP²⁴ and the U-Net³³ architectures. We examined the performance of each of these networks where the training dataset reduction factor (TDRF) increases as 2ⁿ for n = 0, … , 5. For example, a TDRF of 2 corresponds to a 2-fold decrease in the training dataset. For all n, we use a 10-fold cross-validation approach where the number of training datasets that are randomly excluded is based on the TDRF. For each fold, we examined the correlation coefficient (R²), normalized root mean squared error (NRMSE), and peak signal-to-noise ratio (PSNR) calculated from averaged ROIs in the myocardium corresponding to the standard AHA 16-segment model. The structural similarity index (SSIM) values, calculated from 128 × 128 T1 maps, were also examined for each of the networks. Implementation details for the MLP and U-Net architectures are described in Supporting Information Appendix A3.

Because ECV maps have been shown to improve the diagnostic value of T1 mapping, we examined the quality of ECV maps produced by the T1NET. To produce network-generated ECV maps, pre-contrast and post-contrast T1 maps were predicted by the pre-contrast and post-contrast trained T1NET respectively. Manually segmented cardiac masks were then used to register the network-generated pre-contrast and post-contrast T1 maps using the Advanced Normalization Tools³⁴ (ANTs) to perform affine rigid registration followed by Demons deformable registration³⁵ with histogram matching. ECV maps were then calculated using the following Equation 5 below

$$ECV=\left(1-HCT\right)\frac{\frac{1}{T{1}_{\mathit{\text{myo}},\mathit{\text{post}}}}-\frac{1}{T{1}_{\mathit{\text{myo}},\mathit{\text{pre}}}}}{\frac{1}{T{1}_{\mathit{\text{blood}},\mathit{\text{post}}}}-\frac{1}{T{1}_{\mathit{\text{blood}},\mathit{\text{pre}}}}}$$ (5)

where HCT is the hematocrit measurement, T1_myo,post and T1_myo,pre are the post-contrast and pre-contrast T1 values of the myocardium, and T1_blood,post and T1_blood,pre are the post-contrast and pre-contrast T1 values of the LV blood pool. Hematocrit measurements were obtained from blood samples collected prior to MRI scans. ECV testing was performed on 10 pre-contrast and post-contrast T1 mapping datasets from 3 patients.

One of the main detriments of shorter T1 mapping sequences is the reduced precision in comparison to the MOLLI sequences^18–20. To evaluate the precision of the T1NET and the reduced model in comparison to the standard MOLLI sequences, we examine the difference in T1 values between consecutively repeated pre-contrast scans for three slices from one subject.

Because different sites with varying acquisition schemes and hardware will have different normative T1 ranges³⁶, we also tested the robustness of our network to these scanner variations by training pre-contrast networks on either Skyra (488 datasets from 87 subjects) or Prisma (169 datasets from 44 subjects) datasets and evaluating on either Skyra (116 datasets from 26 subjects) or Prisma (30 datasets from 13 subjects) test datasets.

One of the main concerns with deep learning neural networks is the ability of these networks to preserve the characteristics that distinguish healthy subjects from disease subjects. Therefore, testing was also performed on disease test cases including 9 pre-contrast datasets and 3 post-contrast datasets from 3 amyloidosis subjects, 3 pre-contrast datasets from 1 hypertrophic cardiomyopathy (HCM) subject, and 3 pre-contrast datasets from 1 sarcoidosis subject to determine how well our proposed network was able to preserve various disease states. Disease cases were diagnosed by a cardiologist with over 5 years of experience.

T1 reactivities between stress and rest have been shown to have the potential for CAD assessment. Because of this, we tested the performance of our network on stress and rest pre-contrast T1 test cases from 7 subjects as well as systolic and diastolic pre-contrast and post-contrast test cases from 1 subject.

Statistical significance was determined by comparing network or reduced model T1 estimations of myocardial and LV segments to reference T1 maps using paired t-tests with p < 0.05. All statistical analysis was performed using SciPy’s statistical packages³⁷.

3. Results

3.1. Cardiac T1 mapping using the multi-layer LSTMs

Figures 2 and 3 demonstrate the performance of the T1NET in comparison to the reduced model for generating pre-contrast and post-contrast T1 mapping test datasets respectively.

Figure 2.

Myocardial pre-contrast T1 mapping results of T1NET and the reduced model fitting (T = 3). (A) Correlation and Bland-Altman plots of the T1NET. Each dot corresponds to the average of a myocardial AHA segment. (B) Correlation and Bland-Altman plots of the reduced model fitting. The network produces similar T1 maps compared to reference T1 maps (1260 ± 94 ms vs. 1254 ± 91 ms with p = 0.13). The reduced model also produces similar T1 maps compared to the reference T1 maps (1262 ± 125 ms vs. 1254 ± 91 ms with p = 0.06). However, T1NET demonstrates a higher correlation coefficient, lower NRMSE, and lower inter-subject variance compared to the reduced model. (C) Network-generated pre-contrast short-axis cardiac T1 maps in comparison to reference T1 maps and their corresponding difference images. (D) Reduced model-generated pre-contrast short-axis cardiac T1 maps in comparison to reference T1 maps and their corresponding difference images.

Figure 3.

Myocardial post-contrast T1 mapping results of the T1NET and reduced model fitting (T = 3). (A) Correlation and Bland-Altman plots of the T1NET. Each dot corresponds to the average of a myocardial AHA segment. The network produces similar T1 maps compared to the reference T1 maps (484 ± 92 ms vs. 493 ± 91 ms with p = 0.07). (B) Correlation and Bland-Altman plots of the reduced model fitting. The reduced model also produces similar T1 maps compared to the reference T1 maps (490 ± 95 ms vs. 493 ± 91 ms with p = 0.64). However, T1NET demonstrates a higher correlation coefficient, lower NRMSE, and lower inter-subject variance compared to the reduced model. (C) Network-generated post-contrast short-axis cardiac T1 maps in comparison to reference T1 maps and their corresponding difference images. (D) Reduced model-generated post-contrast short-axis cardiac T1 maps in comparison to reference T1 maps and their corresponding difference images.

The T1NET demonstrated similar myocardial T1 estimations to the standard MOLLI sequences (pre-contrast: 1260 ± 94 ms vs. 1254 ± 91 ms with p = 0.13; post-contrast: 484 ± 92 ms vs. 493 ± 91 ms with p = 0.07). Similarly, the reduced model demonstrates myocardial T1 estimations that are comparable to the standard MOLLI sequences (pre-contrast: 1262 ± 125 ms vs. 1254 ± 91 ms with p = 0.06; post-contrast: 490 ± 95 ms vs. 493 ± 91 ms with p = 0.64). However, network-generated pre-contrast and post-contrast T1 maps show reduced inter-subject variance compared to the reduced model.

Supporting Information Figure S1 and Supporting Information Figure S2 demonstrate accurate T1 estimation of the T1NET for regions of interest in the LV blood pool for pre-contrast and post-contrast test datasets respectively.

LV blood pool T1 values are accurately generated for pre-contrast and post-contrast datasets using the T1NET in comparison to the reference method (pre-contrast:1908 ± 140 ms vs. 1892 ± 115 ms with p = 0.18; post-contrast: 332 ± 87 ms vs. 327 ± 89 ms with p = 0.62) whereas the reduced model shows significance deviations from the reference pre-contrast T1 mapping datasets (pre-contrast: 1633 ± 701 ms vs. 1892 ± 115 ms with p = 8.34 × 10⁻⁸; post-contrast: 339 ± 89 ms vs. 327 ± 89 ms with p = 0.29). Although the T1NET performs similarly to the reduced model for post-contrast T1 mapping test datasets, the T1NET performs the T1 estimation much faster than the reduced model T1 estimation. T1 estimation of 2¹⁵ pixels or two 128 × 128 T1 maps requires less than half a second whereas reduced model T1 estimation for the same batch size requires approximately 62 seconds. Furthermore, Supporting Information Appendix A4 demonstrates that the T1NET produces similar results to reference T1 maps for a wide range of inversion time variations described by mean(Δt). Δ represent the finite differences operator. t is given by Equation 1 and describes the inversion times for corresponding pre-contrast T1-weighted images. mean(Δt) is a metric used to describe the variation in heart rate and inversion times, where larger values of mean(Δt) signify lower heart rates and longer inversion times. This suggests that the T1NET is fairly robust against variations of the inversion times.

Figure 4 shows the results of the T1NET and the reduced model for generating ECV maps.

Figure 4.

Myocardial ECV results of T1NET and the reduced model fitting (T = 3). (A) Correlation and Bland-Altman plots of the T1NET. Each dot corresponds to the average of a myocardial AHA segment. (B) Correlation and Bland-Altman plots of the reduced model fitting. The network produces similar ECV maps compared to reference ECV maps (30.0 ± 2.7 % vs. 29.6 ± 3.1 % with p = 0.51). The reduced model also produces similar ECV maps compared to the reference ECV maps (29.4 ± 5.0 % vs. 29.6 ± 3.1 % with p = 0.78). However, T1NET demonstrates a higher correlation coefficient, lower NRMSE, and lower inter-subject variance. (C) Network-generated short-axis cardiac ECV maps in comparison to reference ECV maps and their corresponding difference images. (D) Reduced model-generated short-axis cardiac ECV maps in comparison to reference ECV maps and their corresponding difference images.

Network-generated ECV maps are similar to reference ECV maps with myocardial ECV values of 30.0 ± 2.7 % vs. 29.6 ± 3.1 % and p = 0.51. ECV maps generated using the reduced model are also similar to reference ECV maps with myocardial ECV values of 29.4 ± 5.0 % vs. 29.6 ± 3.1 % and p = 0.78. Although ECV maps generated using the reduced model show slightly more accurate mean myocardial ECV values compared to the T1NET, the T1NET demonstrates reduced inter-subject variance as well as lower NRMSE and higher PSNR myocardial ECV estimations.

3.2. Comparison with existing state-of-the-art networks

Figure 5 demonstrates the quantitative metrics of the MLP network, U-Net, and the T1NET using 10-fold cross-validation for each TDRF.

Figure 5.

Myocardial pre-contrast T1 mapping results for the (A) correlation coefficient (R²), (B) normalized root mean squared error (NRMSE), (C) peak signal-to-noise ratio (PSNR), and (D) structural similarity index (SSIM) of the multi-layer perceptron (MLP) network, the U-Net, and the T1NET using 10-fold cross-validation for each training dataset reduction factor. Error bars show ±1 standard deviation of error.

The T1NET demonstrates a higher R², lower NRMSE, higher PSNR, and higher SSIM for all TDRFs compared to both the MLP network and the U-Net. Furthermore, it can be seen that the superior performance of the T1NET becomes more pronounced as the training dataset is reduced and the T1NET has reduced inter-network variance compared to the MLP and U-Net architectures. Supporting Information Figure S3 and Supporting Information Figure S4 demonstrate correlation and Bland-Altman plots of pre-contrast and post-contrast T1 maps for the MLP network, U-Net, and the T1NET.

Table 1 demonstrates T1 estimations for ROIs in the myocardial and LV blood pool for all test datasets generated using the reduced model, the MLP network, the U-Net, the T1NET, and the reference T1 maps.

Table 1.

Performance comparisons for T1 map generation using the reduced model, a multi-layer perceptron (MLP), U-Net, the T1NET, and reference T1 maps. Numbers correspond to averages for AHA regions of interest in the myocardium (MYO) and the left ventricular blood pool (LVB) with their corresponding standard deviations, mean ± SD. P-values indicate the statistical significance of network and reduced three-parameter model T1 maps in comparison to the reference T1 maps with p < 0.05.

	Pre-contrast (p-value)		Post-contrast (p-value)
Region	LVB	MYO	LVB	MYO
Reduced Model	1633 ± 701 (8.34 × 10−8)	1262 ± 125 (0.06)	339 ± 89 (0.29)	490 ± 95 (0.64)
MLP	1940 ± 164 (3.89 × 10−4)	1288 ± 94 (1.23 × 10−19)	322 ± 88 (0.72)	473 ± 91 (8.90 × 10−5)
U-Net	1811 ± 115 (4.90 × 10−13)	1213 ± 114 (2.77 × 10−22)	321 ± 80 (0.61)	450 ± 83 (7.75 × 10−15)
T1NET	1908 ± 140 (0.18)	1260 ± 94 (0.13)	332 ± 87 (0.62)	484 ± 92 (0.07)
Reference	1892 ± 115	1254 ± 91	327 ± 89	327 ± 89

Although the U-Net and the MLP networks are similar to the reference post-contrast T1 maps for ROIs in the LV blood pool, these networks show significant deviations from the reference pre-contrast T1 maps for ROIs in the LV blood pool and the myocardium as well. These results further suggest that the proposed T1NET outperforms the U-Net and MLP architectures. It is notable that although the reduced model demonstrates closer average T1 for post-contrast test datasets for ROIs in the myocardium compared to the T1NET, both networks show non-significant deviations from reference post-contrast T1 maps. Given the inter-subject variance demonstrated in Table 1, the difference in the performance of the reduced model and the T1NET for ROIs in the myocardium for post-contrast test datasets is likely negligible.

3.3. Preservation of MOLLI precision

Figure 6 demonstrates a precision box plot for T1NET generated T1 maps and reduced model T1 maps in comparison to the reference T1 maps using regions of interest in the myocardium and LV blood pool for consecutively repeated pre-contrast T1 mapping test datasets.

Figure 6.

Precision box plots for network-generated pre-contrast T1 maps and reduced model-generated T1 maps in comparison to reference T1 maps. Network-generated T1 maps show similar precision results compared to reference T1 maps (24 ± 28 ms vs. 18 ± 13 ms) whereas reduced model T1 maps have much higher variance in comparison to reference T1 maps (33 ± 48 ms vs. 18 ± 13 ms).

T1 maps generated using the T1NET show similar precision compared to the reference T1 maps (24 ± 28 ms vs. 18 ± 13 ms). This suggests that the precision of the MOLLI sequence is not compromised by using reduced T1-weighted images and inversion times as input to the T1NET. In contrast, the reduced model has a much higher variance in comparison to the reference T1 maps (33 ± 48 ms vs. 18 ± 13 ms).

3.4. Network robustness to scanner variations

Table 2 illustrates that when the T1NET network is trained on Skyra datasets, the network retains the ability to generate Prisma T1 maps with comparable quality to networks trained on Prisma T1 mapping datasets with 1201 ± 66 ms vs. 1190 ± 85 ms and p = 0.33.

Table 2.

Performance comparisons of the T1NET trained using either Prisma or Skyra pre-contrast training datasets and evaluated on either Prisma or Skyra pre-contrast test datasets. Numbers correspond to averages for AHA regions of interest in the myocardium with their corresponding standard deviations, mean ± SD. Networks trained on Skyra datasets demonstrate similar T1 maps to reference Prisma datasets with 1201 ± 66 ms vs. 1190 ± 85 ms and p = 0.33. Networks trained on Prisma datasets demonstrate similar Skyra T1 maps to networks trained on Skyra datasets with 1258 ± 104 ms vs. 1259 ± 97 ms and p = 0.51.

		Test Data
		Prisma	Skyra
Training Data	Prisma	1190 ± 85	1258 ± 104
	Skyra	1201 ± 66	1259 ± 97

When the T1NET network is trained with Prisma datasets, the network retains the ability to generate Skyra T1 maps with comparable quality to networks trained on Skyra T1 mapping datasets with 1258 ± 104 ms vs. 1259 ± 97 ms and p = 0.51. These results suggest that our network demonstrates robustness across different scanner models from a single vendor.

3.5. Network robustness for disease test cases

Figure 7 demonstrates the performance of the T1NET on amyloidosis pre-contrast and post-contrast test datasets.

Figure 7.

Myocardial pre-contrast and post-contrast T1 mapping results of the T1NET for amyloidosis test datasets. (A) Pre-contrast correlation and Bland-Altman plots of the T1NET. Each dot corresponds to the average of a myocardial AHA segment. Pre-contrast amyloidosis T1 maps generated using the T1NET are similar to the reference T1 maps (1243 ± 140 ms vs. 1231 ± 137 ms with p = 0.60). (B) Post-contrast correlation and Bland-Altman plots of the T1NET. Post-contrast amyloidosis T1 maps generated using the T1NET are similar to the reference T1 maps (348 ± 26 ms vs. 346 ± 27 ms with p = 0.89). (C) Network-generated pre-contrast short-axis amyloidosis T1 maps in comparison to reference T1 maps and their corresponding difference images. (D) Network-generated post-contrast short-axis amyloidosis T1 maps in comparison to reference T1 maps and their corresponding difference images.

Accurate T1 estimation with minimal bias can be seen for amyloidosis test cases when using the T1NET. Amyloidosis T1 maps generated using the proposed network are similar to the reference T1 maps (pre-contrast: 1243 ± 140 ms vs. 1231 ± 137 ms with p = 0.60; post-contrast: 348 ± 26 ms vs. 346 ± 27 ms with p = 0.89). Figure 8 demonstrates the performance of the T1NET on hypertrophic cardiomyopathy and sarcoidosis test datasets.

Figure 8.

Myocardial pre-contrast T1 mapping results of the T1NET for hypertrophic cardiomyopathy (HCM) and sarcoidosis test datasets. (A) Pre-contrast correlation and Bland-Altman plots of the T1NET for HCM test datasets. Each dot corresponds to the average of a myocardial AHA segment. Pre-contrast HCM T1 maps generated using the T1NET are similar to the reference T1 maps (1267 ± 38 ms vs. 1263 ± 41 ms with p = 0.74). (B) Pre-contrast correlation and Bland-Altman plots of the T1NET for sarcoidosis test datasets. Pre-contrast sarcoidosis T1 maps generated using the T1NET are similar to the reference T1 maps (1241 ± 53 ms vs. 1220 ± 57 ms with p = 0.30). (C) Network-generated pre-contrast short-axis HCM T1 maps in comparison to reference T1 maps and their corresponding difference images. (D) Network-generated pre-contrast short-axis sarcoidosis T1 maps in comparison to reference T1 maps and their corresponding difference images.

Hypertrophic cardiomyopathy and sarcoidosis test datasets are also well preserved with the T1NET (pre-contrast HCM: 1267 ± 38 ms vs. 1263 ± 41 ms with p = 0.74; pre-contrast sarcoidosis: 1241 ± 53 ms vs. 1220 ± 57 ms with p = 0.30). This suggests good robustness to diseased datasets that the network has not seen and demonstrates promise for clinical use.

3.6. Network-generated stress and rest pre-contrast T1 maps

Figure 9 demonstrates the results of T1NET for generating stress and rest pre-contrast T1 maps on test datasets.

Figure 9.

Pre-contrast T1 mapping results of the T1NET for stress and rest T1 mapping studies. (A) Correlation and Bland-Altman plots of the T1NET for stress T1 mapping. Each dot corresponds to the average of a myocardial AHA segment. (B) Correlation and Bland-Altman plots of the T1NET for rest T1 mapping. The network T1 reactivity was 5.1 ± 4.0 % and the scanner T1 reactivity was 4.9 ± 4.4 % with p = 0.84. (C) Network-generated pre-contrast short-axis cardiac stress T1 maps in comparison to reference T1 maps and their corresponding difference images. (D) Network-generated pre-contrast short-axis cardiac rest T1 maps in comparison to reference T1 maps and their corresponding difference images.

Network-generated rest T1 maps demonstrate good consistency with reference T1 maps. Network-generated stress T1 maps show improved results compared to reduced model T1 maps, however, fidelity to reference T1 maps is reduced compared to network-generated rest T1 maps. The network T1 reactivity was 5.1 ± 4.0 % and the scanner T1 reactivity was 4.9 ± 4.4 % with p = 0.84. While different T1 reactivity values have been reported based on the type of sequence and analyses methods used, the T1 reactivities found here are similar to reported literature T1 reactivities of 4.79 ± 3.14 %¹⁴ and 7.1 ± 3.8 %¹⁵ at 3T that use a MOLLI sequence.

3.7. Network-generated systolic and diastolic pre-contrast T1 maps

Figure 10 shows the pre-contrast and post-contrast T1 differences between T1NET generated systolic and diastolic T1 maps in comparison to reference T1 maps.

Figure 10.

Pre-contrast and post-contrast T1 differences between T1NET generated systolic and diastolic T1 maps in comparison to reference T1 maps. (a) The pre-contrast network T1 difference was 19±19 ms and the pre-contrast reference T1 difference was 23±16 ms with p=0.64. (b) The post-contrast network T1 difference was 41±11 ms and the post-contrast reference T1 difference was 40±13 ms with p=0.79.

The pre-contrast network T1 difference was 19 ± 19 ms and the pre-contrast reference T1 difference was 23 ± 16 ms with p = 0.64. The post-contrast network T1 difference was 41 ± 11 ms and the post-contrast reference T1 difference was 40 ± 13 ms with p = 0.79. This suggests that the T1NET is able to preserve the differences in T1 due to blood volume changes between systolic and diastolic phases.

4. Discussion

The main purpose of this work was to develop a deep learning architecture for generating T1 maps using a reduced number of T1-weighted images and inversion times in order to accelerate the pre- and post-contrast MOLLI T1 mapping sequences. Such acceleration could decrease the breath-hold burden and lead to fewer motion-related artifacts. Using a multi-layer bidirectional LSTM with a fully connected output network, we demonstrated high-quality network-generated T1 maps using a reduced number of T1-weighted images and inversion times. Network-generated pre-contrast and post-contrast T1 maps demonstrate good myocardial T1 consistency to reference MOLLI T1 maps while also showing reduced inter-subject variance in comparison to the reduced model T1 maps. Furthermore, significant improvements in LV blood pool T1 values were seen with the T1NET in comparison to the reduced model. This suggests that the T1NET mainly allows for reduced inter-subject variance and improved LV blood pool T1 estimation as well as faster T1 estimation in comparison to the reduced model. The reduction in variance afforded by our network also leads to the preservation of the precision of the MOLLI sequences that is reduced from the high inter-subject variance of the reduced model. Furthermore, our network has shown improved performance in comparison to other network architectures including the MLP network and U-Net. The bidirectional LSTM modules and fully connected prediction performed by our network provides temporal information encoding that improves T1 estimation compared to these networks while the cyclic model-based loss function incorporates the physics of the T1 mapping procedure into the network training process which reduces the amount of training data necessary to achieve good performance.

Stress pre-contrast T1 maps generated using the T1NET showed worse T1 estimation in comparison to the rest pre-contrast T1 maps. Although this can be explained by the increased heart rate and motion from inducing stress, our training dataset also did not contain any stress pre-contrast T1 maps. Incorporating stress pre-contrast T1 mapping datasets into the training procedure would likely improve the performance of network-generated stress pre-contrast T1 mapping test cases. Although stress pre-contrast T1 maps demonstrated worse quality compared to rest pre-contrast T1 maps, network-generated T1 reactivities were similar to reference T1 reactivities. Our network was also able to generate high-quality T1 maps for amyloidosis, hypertrophic cardiomyopathy, and sarcoidosis test cases while also accurately predicting T1 differences between systolic and diastolic pre-contrast and post-contrast T1 maps. This suggests that the cyclic model-based loss function affords the network sufficient variability in the training dataset for our network to be fairly robust for various clinical T1 mapping studies.

Our datasets contained T1 maps from multiple scanners including a 3T Prisma and 3T Skyra scanner. Although T1 maps vary across different scanners and sites due to differences in acquisition schemes and hardware, such a training scheme did not appear to negatively impact network performance. Our experiments with Skyra-trained networks and Prisma-trained networks showed accurate T1 estimation of test cases from either scanner and similar performance to networks trained using both Skyra and Prisma datasets. Driven by the cyclic model-based loss function, these networks mainly learned the T1 fitting procedure which seems to provide the network robustness to scanner T1 variations.

4.1. Limitations

The T1NET was trained using motion-compensated T1-weighted images directly provided by the scanner. The Siemens built-in MOLLI pipeline performs motion compensation using all acquired T1-weighted images^26,27. Therefore, the results of the scanner motion compensation and registration method may change using reduced T1-weighted images. However, given that fewer T1-weighted images would need to be acquired with this deep learning approach, motion and breath-hold requirements would be reduced from the accelerated sequence which would likely improve motion compensation methods.

Our network has demonstrated some robustness to scanner variations by generating accurate Prisma and Skyra T1 maps when only trained on data from the other scanner. However, it is possible that these scanners are similar enough that the network has minimal issues. Differences in acquisition schemes and hardware directly affect the range of normal and abnormal T1. Therefore, different sites with varying acquisition schemes and hardware will have different normative T1 ranges³⁶.When greater differences in T1 maps from our training set are expected, the performance of our network may decrease. Further experimentation with T1 maps from different scanners at different sites would be necessary to better understand the extent of the robustness of the T1NET to scanner variations.

We have shown that our network performs well for various disease states such as amyloidosis (n = 3), hypertrophic cardiomyopathy (n = 1), and sarcoidosis (n = 1), while also accurately predicting ECV maps (n = 3), T1 reactivities between stress and rest T1 maps (n = 7), and T1 differences between systolic and diastolic T1 maps (n = 1). Although our network performed well for these small number of disease and ECV cases, testing on larger sample sizes would be necessary to fully understand the capabilities of the T1NET in a clinical setting.

4.2. Conclusions

By combining a multi-layered LSTM with fully connected output and a cyclic model-based loss function, we demonstrated a deep learning approach for generating high-quality pre-contrast and post-contrast T1 maps from a reduced number of T1-weighted images and inversion times. We have shown that the T1NET demonstrates robustness to diseased test datasets and provides accurate T1 reactivity for stress and rest T1 mapping studies while also maintaining the precision of MOLLI sequences. This work demonstrates that combining deep learning with cardiac T1 mapping sequences can potentially accelerate standard MOLLI sequences from 11 heartbeats to 3 heartbeats which could lead to reduced breathing related motion artifacts and reduced breath-hold durations.

Supplementary Material

fS1

Supporting Information Figure S1. Left ventricular blood pool pre-contrast T1 mapping results of the T1NET and reduced model fitting (T = 3). (A) Correlation and Bland-Altman plots of the T1NET. Each dot corresponds to the average of a region of interest in the left ventricular blood pool. The network produces similar T1 maps compared to reference T1 maps (1908 ± 140 ms vs. 1892 ± 115 ms with p = 0.18). (B) Correlation and Bland-Altman plots of the reduced model fitting. The reduced model exhibits significant deviations from the reference T1 maps (1633 ± 701 ms vs. 1892 ± 115 ms with p = 8.34 × 10⁻⁸).

fS2

Supporting Information Figure S2. Left ventricular blood pool post-contrast T1 mapping results of T1NET and reduced model fitting (T = 3). (A) Correlation and Bland-Altman plots of the T1NET. Each dot corresponds to the average of a region of interest in the left ventricular blood pool. The network produces similar T1 maps compared to reference T1 maps (332 ± 87 ms vs. 327 ± 89 ms with p = 0.62). (B) Correlation and Bland-Altman plots of the reduced model fitting. The reduced model also produces similar T1 maps to the reference T1 maps (339 ± 89 ms vs. 327 ± 89 ms with p = 0.29). However, T1NET demonstrates a higher correlation coefficient, lower NRMSE, and lower inter-subject variance.

fS3

Supporting Information Figure S3. Myocardial pre-contrast T1 mapping results of T1NET, U-Net, and a multi-layer perceptron (MLP) with T = 3. (A) Correlation and Bland-Altman plots of the T1NET (1260 ± 94 vs. 1254 ± 91 with p = 0.13). Each dot corresponds to the average of a myocardial AHA segment. (B) T1NET generated pre-contrast short-axis cardiac T1 maps in comparison to reference T1 maps and their corresponding difference images. (C) Correlation and Bland-Altman plots of the U-Net (1213 ± 114 vs. 1254 ± 91 with p = 2.77 × 10⁻²²). (D) U-Net generated pre-contrast short-axis cardiac T1 maps in comparison to reference T1 maps and their corresponding difference images. (E) Correlation and Bland-Altman plots of the MLP (1288 ± 94 vs. 1254 ± 91 with p = 1.23 × 10⁻¹⁹). (F) MLP generated pre-contrast short-axis cardiac T1 maps in comparison to reference T1 maps and their corresponding difference images.

fS4

Supporting Information Figure S4. Myocardial post-contrast T1 mapping results of T1NET, U-Net, and a multi-layer perceptron (MLP) with T = 3. (A) Correlation and Bland-Altman plots of the T1NET (484 ± 92 vs. 493 ± 91 with p = 0.07). Each dot corresponds to the average of a myocardial AHA segment. (B) T1NET generated post-contrast short-axis cardiac T1 maps in comparison to reference T1 maps and their corresponding difference images. (C) Correlation and Bland-Altman plots of the U-Net (450 ± 83 vs. 493 ± 91 with p = 7.75 × 10⁻¹⁵). (D) U-Net generated post-contrast short-axis cardiac T1 maps in comparison to reference T1 maps and their corresponding difference images. (E) Correlation and Bland-Altman plots of the MLP (473 ± 91 vs. 493 ± 91 with p = 8.90 × 10⁻⁵). (F) MLP generated post-contrast short-axis cardiac T1 maps in comparison to reference T1 maps and their corresponding difference images.

Data Availability Statement

The code for the T1NET and example datasets will be provided publicly at https://github.com/gadluru/T1NET-rapid-T1mapping.