Impact of Deep Learning Architectures on Accelerated Cardiac T₁ Mapping using MyoMapNet

Abstract

Objective:

To investigate the performance of various deep learning (DL) architectures for MyoMapNet, a DL model for T₁ estimation using accelerated cardiac T₁ mapping from four T₁-weighted images collected after a single inversion pulse (Look-Locker, LL4).

Methods:

We implemented and tested three DL architectures for MyoMapNet: (a) a fully connected neural network (FC), (b) convolutional neural networks (VGG19, ResNet50), and (c) encoder-decoder networks with skip connections (ResUNet, U-Net). Modified Look-Locker Inversion Recovery (MOLLI) images from 749 patients at 3T were used for training, validation, and testing. The first four T₁-weighted images from MOLLI5(3)3 and/or MOLLI4(1)3(1)2 protocols were extracted to create accelerated cardiac T₁ mapping data. We also prospectively collected data from 28 subjects using MOLLI and LL4 to further evaluate model performance.

Results:

Despite rigorous training, conventional VGG19 and ResNet50 models failed to produce anatomically correct T₁ maps, and T₁ values had significant errors. While ResUNet yielded good quality maps, it significantly under-estimated T₁. Both FC and U-Net, however, yielded excellent image quality with good T₁ accuracy for both native (FC/U-Net/MOLLI= 1217 ± 64/ 1208 ± 61/ 1199 ± 61 ms, all P<0.05) and post-contrast myocardial T₁ (FC/U-Net/MOLLI= 578 ± 57/ 567 ± 54/ 574 ± 55 ms, all P<0.05). In terms of precision, the U-Net model yielded better T₁ precision compared to the FC architecture (standard deviation of 61 ms vs. 67 ms for the myocardium for native (P<0.05), and 31 ms vs. 38 ms (P<0.05), for post-contrast). Similar findings were observed in prospectively collected LL4 data.

Conclusion:

U-Net and FC DL models in MyoMapNet enable fast myocardial T₁ mapping using only four T₁-weighted images collected from a single Lock-Locker sequence with comparable accuracy. U-Net also provides slight improvement in precision.

Graphical Abstract

Introduction

Over the past decade, there has been increasing interest in myocardial T₁ mapping as a quantitative technique for assessing interstitial diffuse fibrosis (1,2). Various T₁ mapping pulse sequences have been proposed for pixel-wise measurement of myocardial T₁ relaxation times with several recent attempts aimed at improving accuracy, precision, coverage, and imaging efficiency (3–5). Among these T₁ mapping sequences, Modified Look-Locker Inversion Recovery (MOLLI) remains a commonly used part of the myocardial tissue characterization clinical protocol due to its excellent image quality and availability (6). However, technical improvements are still needed to overcome limitations such as lengthy scan times that require long breath-holds.

With advances in artificial intelligence (AI), particularly deep learning (DL), several studies have sought AI-based methods for improving cardiac T₁ mapping during data acquisition, reconstruction, or automatic analysis. Shao et al. developed a DL model for rapid calculation of myocardial T₁/T₂ values based on Bloch equation simulation with improvement in accuracy (7). Our group has previously shown how DL-based reconstruction networks can reduce the window of a single-shot acquisition and alleviate cardiac motion-induced artifacts in the T₁ map (8). DL-based reconstruction networks have also been used in MR fingerprinting to reduce the time required to calculate MR relaxation times from undersampled spiral data (9). Several other DL-based techniques have also been presented to automate analysis, motion correction, and quality control (10–12). Recently, we proposed MyoMapNet, a fully connected neural network (FC) for building a T₁ map from only four T₁-weighted images and thus shorten the imaging time of MOLLI with minimal loss in T₁ precision (13). The MyoMapNet reduces the scan time of standard MOLLI from 11 second to 4 seconds. In addition, the map reconstruction time remains very fast with near instantaneous inline map estimation. However, we did not rigorously study the optimal DL architecture for this model.

When estimating T₁, the input to the neural network can be pixel-wise, image-patch, or whole image, depending on the type of neural network and training strategy. A pixel-wise neural network, such as FC, is similar to the conventional curve-fitting method for performing T₁ calculation at a single pixel (7,9,13). However, this approach does not incorporate neighboring pixels. In contrast, two-dimensional (2D) convolutional neural networks such as VGG19 (14), ResNet50 (15), ResUnet (16), and U-Net (17) can be advantageous for extracting deep features and have successfully been used in various image classification and segmentation problems (18,19). Such convolutional or encoder-decoder methods utilize neighboring pixels within the same tissue to improve T₁ map quality, albeit potentially reducing sensitivity. The impact of alternate DL architectures on MyoMapNet performance has not been rigorously investigated.

In this study, we sought to investigate the performance (i.e., accuracy and precision) of different DL architectures on MyoMapNet by implementing pixel-wise (i.e., FC) and convolutional-based neural networks. MOLLI T₁ data were used for training, validation, and testing of each model. Model performance was further studied using a Look-Locker 4 (LL4) sequence collected from four T₁-weighted images after a single inversion pulse.

Methods

Figure 1 shows the study overview. Existing MOLLI data was used for training, validation, and testing (Figure 1A). Additional independent testing was done in a prospectively collected LL4 imaging dataset (Figure 1D). Specifically, the first four images from MOLLI were used for network training (Figure 1B-C) followed by testing using (a) the first four T₁-weighed images of MOLLI, and (b) prospectively collected LL4 images from phantom and in-vivo scans (Figure 1E-F).

Figure 1:

Study overview. (A) The retrospectively collected dataset is divided into three subsets: training, validation, and testing. (B-C) The input to the neural network is 4 T₁-weighted images and four inversion times. FC uses pixel-wise values as the input, while convolutional neural networks use the whole image. (D-F) Study design for evaluation of MyoMapNet in the retrospective dataset and the prospectively accelerated LL4 myocardial T₁ mapping sequence in four heartbeats.

To investigate DL architecture performance, we studied five state-of-the-art models: FC, VGG19, ResNet50, ResUnet, and U-Net. Each architecture and their hyper-parameters were selected based on their reported DL performance (20). The input to the FC network consisted of four T₁-weighted signals and their corresponding inversion-recovery times. The input for other networks consisted of four T₁-weighted images and their corresponding inversion-recovery times. To use inversion times as input to the neural network, the T₁-weighted images and inversion times were combined into eight channels: the first four channels consisted of the T₁-weighted images, and the last four channels comprised the inversion times (Supplementary Figures 1, 2, and 3).

The FC consisted of 6 layers with 400 neurons in the first two layers, 100 neurons in the 3^rd and 4^th layers, 50 neurons in the 5^th layer, and one in the output. The activation function was Leaky ReLU. VGG19 (14) consisted of 19 layers with small convolutional filters size 3×3 and an ReLU activation function, and the number of feature maps was doubled after each max-pooling operation. The last fully connected layer contained 1000 neurons adjusted to 160×160 neurons to output the T₁ map.

ResNet50 (15) is a very deep neural network consisting of 50 layers and a residual block designed to tackle the vanishing/exploding gradient problem of deep convolutional neural networks (CNN) (21). A residual block consists of 2 convolutional layers, with each followed by an activation function ReLU and a batch normalization. Identity mapping of the input to the block is created and concatenated to the output of the second convolutional layer allowing for skip connections. ResUnet (16) uses a U-Net encoder/decoder as its backbone in combination with residual connections. There are no fully connected layers in the network, and the output is a 2D matrix directly representing the T₁ map of size of 160×160 (Supplementary Figure 3).

The last architecture we investigated is U-Net (17), an encoder-decoder neural network with skip connections. The encoder is used to obtain the disentangled feature representation. The encoder consists of eight convolutional layers with convolution filters of 3×3 and a max-pooling of 2×2 after every two convolutional layers. After the first convolutional operation, the resulted feature map has 64 channels, which will be combined later with the latest convolutional layers with the same number of channels (64). This is followed by the last convolutional operation with a kernel size of 1×1 to output the T₁ map (Supplementary Figure 2). The number of feature maps increases from 64 for the two first layers to 512 for the last two layers. We opted for ReLU activation function. Each decoder level began with an up-sampling layer followed by a convolution to reduce the number of features by a factor of 2. Then, the up-sampled features were combined with features from the corresponding level of the encoder part using concatenation. All the neural networks were trained from scratch and optimized for T₁ estimation.

DL Models and Training

Our local Institutional Review Board (IRB) approved use of a consent waiver for retrospective data and written informed consent was prospectively collected from subjects prior to scanning. Patient information was handled in compliance with the Health Insurance Portability and Accountability Act. We retrospectively identified 749 subjects (407 male, 56±16 years) who underwent clinical scans at Beth Israel Deaconess Medical Center (BIDMC) from January 2019 to October 2020, in whom native and/or post-contrast T₁ images were collected. All patients were imaged on a 3T MRI scanner (MAGNETOM Vida Siemens Healthcare, Erlangen, Germany). Native and post-contrast T₁ mapping in three short-axis views of the left ventricle were imaged using MOLLI5(3)3 and MOLLI4(1)3(1)2 with the following imaging parameters: balanced steady-state free-precession readout, field-of-view = 360×325 mm², spatial resolution = 1.7×1.7×8 mm³, TR/TE/flip angle= 2.5 ms/1.02ms/35°, receiver bandwidth= 1093 Hz/pixel, GRAPPA acceleration rate = 2, readout lines per shot = 75, and slice gap = 16 mm. T₁-weighted images were motion-corrected using vendor-provided inline motion correction. Pixel-wise MOLLI T₁ maps were reconstructed off-line by fitting T₁-weighted signals at each pixel to a three-parameters conventional fitting model (22). T₁ maps were not scaled to account for inversion pulse inefficiency. The database was divided into training (~80%), validation (~10%) and testing (~10%). To create T₁ mapping using only four T₁-weighted images collected after a single inversion pulse, we used the first four images collected after the first inversion pulse of MOLLI5(3)3 and MOLLI4(1)3(1)2 and discarded the remaining T₁-weighted images.

All models were implemented using PyTorch and trained on an NVIDIA DGX-1 system equipped with 8 Tesla V100 graphics processing units (GPUs; each with 32 GB memory and 5120 cores) and a central processing unit (CPU) of 88 cores: Intel Xeon 2.20 GHz each, and 504 GB RAM.

Images from 607 patients and 78 patients were used for training and validation, respectively. Each model was trained by minimizing the mean absolute error (MAE) between the ground truth and the estimated T₁. All networks were trained with a mini-batch of 64, an Adam optimizer with a learning rate of 0.01, and a weight decay of 0.0001. To avoid overfitting or underfitting, T₁ estimation errors of the training and validation dataset were monitored during training. Error monitoring in the blood pool and myocardium also ensured that the model learned a good representation of these two regions of interest. For the training dataset, the T₁ estimation error across the entire image was calculated. For validation, the T₁ estimation error of the myocardium and blood were used to select the best model.

Evaluation

We first evaluated all trained models using existing MOLLI images from 64 patients (36 male, 56±17 years), 47 of which had post-contrast T₁ images. T₁ maps for MyoMapNet were estimated from the first four images collected after the first inversion pulse of MOLLI5(3)3 or MOLLI4(1)3(1)2 and compared to original MOLLI T₁ values, estimated from all T₁-weighted images. In addition, we prospectively collected phantom and in-vivo data to further evaluate the performance of all trained models (Figure 1D). An LL4 sequence was implemented in which four T₁-weighted images were collected after the first inversion time. All imaging parameters and inversion times were matched with MOLLI. To assess accuracy and precision, a phantom experiment was performed with an agarose gel-based phantom using nickel chloride as the paramagnetic relaxation modifier with twelve vials (23). Reference T₁ and T₂ times of each vial were measured by inversion-recovery spin-echo (IR-SE) and Carr-Purcell-Meiboom-Gill spin-echo (CPMG-SE) sequences, respectively, as previously reported (24). MOLLI5(3)3 and LL4 were performed at a simulated heart rate of 60 bpm. Each sequence was repeated 10 times, and repetitions of all sequences were performed in a random order.

Prospective in-vivo T₁ mapping data were collected in 28 subjects, consisting of eight healthy subjects (5 male; 27±14 years) and 20 patients (12 male, 61±12 years) undergoing a clinically-indicated cardiac MRI. Native T₁ mapping with MOLLI5(3)3 and post-contrast T₁ mapping by MOLLI4(1)3(1)2 (if applicable) were included in their clinical protocols. LL4 images were collected at one mid-cavity short axis slice before and after contrast in patients with clinically indicated use of gadolinium. For patients who received contrast, MOLLI4(1)3(1)2 and LL4 were scanned ~15 min after administration of 0.1 mmol/kg Gd-DTPA (Gadavist, Bayer Healthcare, Berlin, Germany).

Data Analysis

T₁ values in each vial were manually measured by drawing a region of interest (ROI) to calculate the mean and standard deviation (SD). The mean and SD of T₁ of each vial were averaged across all measurements. SD was used to compare T₁ precision among different methods. For each in-vivo T₁ map, the endocardium, epicardium, and blood pool were manually delineated to measure the mean and SD of T₁ of the left ventricle (LV) myocardium and blood pool.

The paired two-tailed Student’s t-test was used to assess statistical significance, and a p-value less than 0.05 was considered statistically significant. Bland-Altman was used to investigate agreement in T₁ measurements between MOLLI and the different MyoMapNet DL models. All data analysis was performed using MATLAB R2009b and R2018b (MathWorks, Natick, MA, USA). Statistical analyses were performed using GraphPad Prism version 9.2.0 (GraphPad Software, San Diego, CA, USA), and python library scikit-learn (0.19.1).

Results

All models converged before reaching the 3000 maximum iterations. U-Net was the fastest model during learning with less than 500 iterations, while FC continued learning to more than 1000 iterations. CNN based models converged at approximately 500 iterations. Learning was stopped if the model did not improve after 70 iterations to avoid overfitting. The loss curves and trained models are publicly available (https://github.com/HMS-CardiacMR/MyoMapUnet).

In-Vivo Evaluation using Existing MOLLI Data

Figures 2 and 3 show representative native and post-contrast T₁ maps for one subject. VGG19 and ResNet50 could not correctly predict T₁. ResUnet yielded a map that preserves anatomical regions without visual artifacts; however, there were substantial errors in the estimated T₁ in both the blood and myocardium. Visually, FC and U-Net provided excellent T₁ maps with similar image quality as MOLLI5(3)3. Similar results were achieved for post-contrast T₁ maps.

Figure 2:

Native and post-contrast T₁ maps generated using MOLLI and MyoMapNet for three different DL architectures calculated from the first four T₁-weighted images, extracted from corresponding MOLLI sequence and their differences. ResUNet created anatomically correct images but with significant T₁ errors. Both U-Net and FC resulted in similar image quality as MOLLI.

Figure 3:

Native and post-contrast T₁ maps generated using MOLLI and MyoMapNet using two different DL architectures calculated from the first four T₁-weighted images, extracted from the corresponding MOLLI sequence and their differences. The VGG19 and ResNet50 failed to estimate T₁ maps and resulted in blurry images.

Table 1 summarizes mean and SD values of myocardial and blood native post-contrast T₁ values across all subjects. For native myocardial and blood T₁, good agreement was achieved between (1) FC and MOLLI5(3)3 and (2) U-Net and MOLLI5(3)3. FC had a mean T₁ difference of 18 ms and 15 ms, and U-Net had a mean T₁ difference of 9 ms and −12 ms (all P<0.05). Bland-Altman plots (Figure 4) confirmed this agreement. The 95% confidence interval (CI) of T₁ differences between FC and MOLLI5(3)3 ranged from −1.8 ms to 39.3 ms for myocardial T₁ and from −45.6 ms to 75.5 ms for blood T₁. The 95% CI of T₁ differences between U-Net and MOLLI5(3)3 ranged from −10.8 ms to 29.6 ms for myocardial T₁ and from −54.1 ms to 30.2 ms for blood T₁. Bland-Altman analysis (Figure 4C-D) demonstrated FC and U-Net were in excellent agreement with MOLLI4(1)3(1)2 for post-contrast T₁. Mean myocardial and blood T₁ differences between them were 4.2 ms and 3.7 ms (FC vs. MOLLI4(1)3(1)2) and −6.2 ms and 0.1 ms (U-Net vs MOLLI4(1)3(1)2), all P<0.05 except for U-Net vs. MOLLI for blood T₁ (P=0.91). Due to large estimation errors from the other MyoMapNet models, the Bland-Altman analysis is not shown.

Table 1.

Myocardium and blood T₁ at 3T as measured by MOLLI and retrospectively estimated by MyoMapNet for existing dataset (N=64)

	Native T1				Post-Contrast T1
	Myocardium		Blood		Myocardium		Blood
	Accuracy	Precision	Accuracy	Precision	Accuracy	Precision	Accuracy	Precision
FC	1217 ± 64	67 ± 15	1866 ± 85	51 ± 22	578 ± 57	38 ± 12	432 ± 69	17 ± 5
VGG19	1259 ± 192	132 ± 33	1365 ± 202	69 ± 19	450 ± 56	48 ± 16	447 ± 64	27 ± 8
ResNet50	1057 ± 47	110 ± 32	1177 ± 66	54 ± 21	1052 ± 48	107 ± 25	1155 ± 49	54 ± 15
ResUnet	1033 ± 104	57 ± 12	1702 ± 120	37 ± 11	736 ± 85	66 ± 23	502 ± 77	28 ± 12
U-Net	1208 ± 61	61 ± 13	1839 ± 87	27 ± 7	567 ± 54	31 ± 13	428 ± 68	12 ± 5
MOLLI	1199 ± 61	60 ± 13	1851 ± 94	30 ± 9	574 ± 55	30 ± 9	428 ± 70	9 ± 3

Figure 4:

Bland-Altman plots demonstrating agreement between MOLLI and MyoMapNet for myocardial and blood T₁ values as calculated by FC and U-Net models using the existing in-vivo dataset (N=64). Mean differences and 95% limits of agreement are indicated in red and dotted lines, respectively. Each data point is averaged across three left-ventricular slices for each subject.

Box-and-whisker plots show T₁ precision (SD) of different DL models for native and post-contrast myocardium and blood pool (Figure 5). In native T₁ images, the U-Net model yielded better T₁ precision than the FC architecture (61 ms vs. 67 ms for the myocardium (P<0.05) and 27 ms vs. 51 ms for the blood pool for native T₁ (P<0.05)). Similar results were observed for post-contrast T₁ values (31 ms vs. 38 ms (P<0.05) for the myocardium and 12 ms vs. 17 ms for the blood pool (P<0.05)) (Table 1 and Figure 5).

Figure 5:

Box-and-whisker plots showing T₁ standard deviation of the myocardium and blood for existing MOLLI data from two MOLLI sequences (MOLLI5(3)3 for native T₁ and MOLLI4(1)3(1)2 for post-contrast T₁) and MyoMapNet via different DL architectures.

Phantom Experiments

Figures 6 and 7 show the accuracy and precision of T₁ values in different phantom vials with various T₁ and T₂ values across different DL models. Table 2 shows the measured T₁ values. Consistent with in-vivo findings in the existing dataset, MyoMapNet with VGG19, ResNet50, and ResUnet had large T₁ estimation errors compared to MOLLI. Both FC and U-Net yielded excellent maps (Supplementary Figure 4) with a T₁ mean difference of 10.6 ms and −5.57 ms, respectively (all P<0.05).

Figure 6:

T₁ accuracy and precision across phantom vials for MOLLI and MyoMapNet with FC, ResUnet, and U-Net models. FC and U-Net showed good precision, while ResUnet resulted in substantial measurement errors for different vials.

Figure 7:

T₁ accuracy and precision across phantom vials for MOLLI and MyoMapNet with VCG19 and ResNet50 models. Both VCG19 and ResNet50 resulted in large errors for different vials.

Table 2.

Mean and standard deviation of T₁ for each phantom vial measured by MOLLI and LL4 with MyoMapNet across different DL models

	Phantom Vials T1
	#1	#2	#3	#4	#5	#6	#7	#8	#9	#10	#11	#12
FC	300 ±4	307 ±5	405 ±9	455 ±5	516 ± 8	567 ±14	625 ±13	728 ±7	831 ±4	1004 ±6	1377 ±17	1604 ±16
VGG19	502±46	486 ±38	526 ±33	485±37	460±42	454±42	560±48	494±34	546±44	599 ±48	602±50	571 ±58
ResNet50	884±52	1168±45	1157±48	824±61	777±47	900±68	805±26	1128±40	1065±51	919 ±26	933±26	924 ±35
ResUnet	363±11	365 ±10	373 ±11	383 ±6	401 ± 8	407±7	428±10	525±9	661±7	878±19	1623 ±24	1859±22
U-Net	303 ±4	312 ±8	393 ±11	442 ±6	498 ±4	548±3	619±7	695±4	799 ±6	974±8	1374±11	1567±10
MOLLI	304 ±4	313 ±15	403 ±7	453 ±3	502±4	552 ±4	620 ±6	714 ±5	814 ±4	986 ±6	1367 ±10	1563±12

In-Vivo Evaluation using Prospectively Collected LL4

In the prospective LL4 study, the models exhibited similar performance as in the retrospective dataset (Figure 8). VGG19 and ResNet50 failed to generate anatomically correct images and had significant artifacts. ResUnet provided anatomically correct T₁ maps; however, T₁ values were significantly lower than those by MOLLI (Table 3). FC and U-Net yielded excellent image quality compared to MOLLI (Figure 8). Bland-Altman plots showed very good agreement between MOLLI and FC (mean-difference: 29.5 ms, 36.5 ms, 7.4 ms, 10.8 ms for native and post-contrast myocardium and blood pool) and between MOLLI and U-Net (mean-difference: 26.5 ms, 30.6 ms, 7.9 ms, 3.6 ms for native and post-contrast myocardium and blood pool) (Figure 9).

Figure 8:

Native (A) and post-contrast (B) T₁ maps generated using MOLLI and MyoMapNet with different DL architectures calculated from the prospectively collected LL4 sequence. VGG19 and ResNet50 failed to correctly estimate T₁ maps and resulted in blurry images. ResUNet was able to create anatomically correct images but with significant T₁ errors. Both U-Net and FC resulted in similar image quality as MOLLI.

Table 3.

Myocardium and blood T₁ at 3T as measured by original MOLLI and estimated by MyoMapNet using four T₁-weighted images collected in a separate LL4 sequence (not MOLLI) (N= 28).

	Native T1				Post-Contrast T1
	Myocardium		Blood		Myocardium		Blood
	Accuracy	Precision	Accuracy	Precision	Accuracy	Precision	Accuracy	Precision
FC	1199 ± 42	63 ± 20	1856 ± 96	50 ± 24	639 ± 48	31 ± 11	517 ± 69	20 ± 9
VGG19	1269 ± 189	133 ± 41	1387 ± 187	63 ± 20	458 ± 61	47 ± 17	452 ± 72	26 ± 9
ResNet50	1055 ± 40	96 ± 29	1187 ± 57	47 ± 17	1030 ± 42	88 ± 33	1158 ± 65	51 ± 16
ResUnet	997 ± 138	51 ± 11	1657 ± 156	35 ± 13	811 ± 98	63 ± 20	615 ± 74	25 ± 12
U-Net	1196 ± 47	57 ± 12	1850 ± 88	25 ± 10	624 ± 42	25 ± 8	510 ± 66	12 ± 4
MOLLI	1170 ± 34	55 ± 12	1819 ± 85	28 ± 13	632 ± 44	26 ± 10	506 ± 63	10 ± 8

Figure 9:

Bland-Altman plots demonstrating agreement between MOLLI and MyoMapNet for myocardium and blood T₁ values as calculated by FC and U-Net in patients imaged using the prospectively collected LL4 sequence (N=28). Mean differences and 95% limits of agreement are shown in red and dotted lines, respectively.

Similar to the retrospective dataset, LL4 box-and-whisker plots show good T₁ precision for FC and U-Net for native and post-contrast myocardium and blood pool (Figure 10). In native T₁ images, the U-Net model yielded better T₁ precision than the FC architecture (57 ms vs. 63 ms for the myocardium (P<0.05) and 25 ms vs. 50 ms for the blood pool for native T₁ (P<0.05)). There was no difference in precision between MOLLI and U-Net for native T₁ of blood or post-contrast T₁ of myocardium or blood (all P>0.05) (Figure 10).

Figure 10:

Box-and-whisker plots for the prospective LL4 dataset showing T₁ standard deviation of the myocardium and blood using MyoMapNet via different DL models.

Discussion

In this study, we evaluated the performance of several DL architectures for estimating T₁ values using MyoMapNet, an accelerated T₁ mapping sequence, in four heartbeats. Our results show that both FC and U-Net can successfully create T₁ maps from only four images with similar accuracy and precision as MOLLI. Furthermore, other DL convolutional networks such as VGG19 and ResNet50 failed to reliably estimate T₁ values. While the accuracy was similar between U-Net and FC, our finding shows a statistically significant improvement in T₁ precision with U-Net. Despite higher precision, the difference between the two methods yielded values that would likely not change clinical interpretation. Therefore, both ML models are potentially interchangeable.

ResUnet has shown promising results generating visually correct maps; however, it significantly underestimated T₁. ResUnet uses both U-Net and residual learning (ResNet). Since ResNet failed with respect to T₁ estimation, we hypothesize that its combination with U-Net degraded its performance instead of improving it, as usually expected when adding residual blocks to U-Net. Further studies are needed to investigate what caused this failure.

The FC network does not consider the information available in neighboring pixels since each pixel is treated independently. With the use of a convolutional-based network, we hypothesized that an improvement in precision could potentially be achieved even if accuracy did not improve. Nonetheless, in our study, well-established CNNs, such as VGG19 and ResNet50, performed poorly. The presence of max-pooling layers and fully connected layers after convolutions could be the main reason for this low performance. In a pilot study, we investigated the performance of the modified architectures based on VGG19 (mVGG) and ResNet50 (mResNet) without max pooling or fully connected layers after convolution and reported our preliminary findings (Supplementary Materials). The mVGG yielded improved map estimation and the mResNet exhibited better results; however, there was significant T₁ estimation error. We further investigated the cause of the failure and found that it was due to batch normalization in the residual blocks. We also modified the original ResUnet (mResUnet) which showed underestimation of T₁ values by updating the residual blocks containing batch normalization (the source of the issue). Next, the identity map was replaced by a convolutional layer followed by an activation function ReLU before concatenation, which resulted in a significant improvement. Further investigation is needed to rigorously study the impact of such architectures on MyoMapNet. Jun et al. (25) recently demonstrated that reasonably accurate brain T₁ values can be achieved by removing max pooling and fully connected layers. Another solution, albeit expensive in terms of calculation, could be the use of small patches as input and estimates the T₁ value of the central pixel of each patch (26,27).

Our choice of the various architectures was based on their previously reported performance (20). It is well known that the basic choice for image processing is CNN and rarely FC. Unlike U-Net, CNN uses FC after the last convolutional layer. As a result, CNN uses global information where the spatial arrangement of the input disappears. Thus, CNNs do not take into account spatial relationships between underlying objects. While this is an advantage for image classification and prediction, spatial relationship is important for T₁ estimation. Without the ability to preserve the structural integrity of images, the CNN was not able to generate anatomically correct T₁ maps. Indeed, in classification, learning feature mapping of an image allows conversion of it into a vector with high-level features that can be used with an FC to learn a non-linear combination of these features and generate an output. The use of pixel-wise based information with FC, or whole image information with an encoder-decoder U-Net, results in better representation learning and thus improved estimation.

To further facilitate clinical adoption of MyoMapNet, we integrated the two top-performing models for inline reconstruction of T₁ mapping such that MyoMapNet T₁ maps could be readily available upon completion at the scanner. This allows visualization of the maps on the scanner console without the need for off-line processing. While U-net has more significant computational burden, we did not notice any differences in computation time for map processing.

One of the major challenges of DL is its generalizability and robustness. Due to limited data access and widespread challenges due to the COVID-19 pandemic at the time of this study, we were unable to test the performance of our models on different MRI systems or field strengths. It is difficult to speculate how the performance of the models could be impacted by acquiring data from different scanners. We have previously reported rigorous analysis of various training schemes and their required number of T₁-weighted images for MyoMapNet with the FC model (13). In this study, we did not perform a similar analysis, as we expect the result to be similar. In an ad-hoc study, we evaluated whether we could measure T₁ values using only three T₁-weighted images with U-Net; however, we found significant errors in T₁ values (data not shown). The imaging parameters could potentially impact accuracy of T₁ estimates using MyoMapNet. All images were also collected at 3T. Further studies are needed to evaluate the performance of the model for different field strengths and vendors. Further transfer learning-based training may be necessary to further develop this approach for different systems.

In our training, we used the MOLLI sequence for the training of the model. However, MOLLI underestimates actual T₁ values (3,4). It also suffers from many confounders such as T₂, inflow, and B₀ and B₁ inhomogeneity (3,4). Other sequences, such as SASHA or SAPPHIRE (28,29) with improved accuracy could potentially be used to train MyoMapNet; however, since we did not have a large dataset for training using these sequences, MOLLI data was used. Numerical simulation can also potentially further improve accuracy by simulating T₁ recovery using the Bloch equation. There are several potential solutions for improving MyoMapNet accuracy using different training schemes, but further investigation is warranted.

Conclusion

U-Net and FC DL models in MyoMapNet enable fast myocardial T₁ mapping from only four T₁-weighted images collected by a single Lock-Locker sequence with comparable accuracy and precision.

Abbreviations

DL

Deep learning

AI

Artificial Intelligence

FC

Fully connected neural networks

CNN

Convolutional neural network

LL

Look-Locker

CI

Confidence interval

CPU

Central processing unit

GPU

Graphics processing units

MOLLI

Modified look-locker inversion recovery

MAE

Mean-absolute error

IR-SE

Inversion-recovery spin-echo

CPMG-SE

Carr-Purcell-Meiboom-Gill spin-echo

ROI

Region of interest

LV

Left ventricle

SD

Standard deviation

RAM

Random access memory