DeepEMC-T2 Mapping: Deep Learning-Enabled T2 Mapping Based on Echo Modulation Curve Modeling

Abstract

Purpose:

Echo modulation curve (EMC) modeling enables accurate quantification of T2 relaxation times in multi-echo spin-echo (MESE) imaging. The standard EMC-T2 mapping framework, however, requires sufficient echoes and cumbersome pixel-wise dictionary-matching steps. This work proposes a deep learning version of EMC-T2 mapping, called DeepEMC-T2 mapping, to efficiently estimate accurate T2 maps from fewer echoes.

Methods:

DeepEMC-T2 mapping was developed using a modified U-Net to estimate both T2 and Proton Density (PD) maps directly from MESE images. The network implements several new features to improve the accuracy of T2/PD estimation. 67 MESE datasets acquired in axial orientation were used for network training and evaluation. Additional 57 datasets acquired in coronal orientation with different scan parameters were used to evaluate the generalizability of the framework. The performance of DeepEMC-T2 mapping was evaluated in seven different experiments.

Results:

Compared to the reference, DeepEMC-T2 mapping achieved T2 estimation errors from 1%−11% and PD estimation errors from 0.4%−1.5% with 10/7/5/3 echoes, which are more accurate than standard EMC-T2 mapping. By incorporating datasets acquired with different imaging parameters and orientations for joint training, DeepEMC-T2 exhibits robust generalizability across varying imaging protocols. Increasing the echo spacing and including longer echoes improve the accuracy of parameter estimation. The new features proposed in DeepEMC-T2 mapping all enabled more accurate T2 estimation.

Conclusions:

DeepEMC-T2 mapping enables simplified, efficient, and accurate T2 quantification directly from MESE images without dictionary matching. Accurate T2 estimation from fewer echoes allows for increased volumetric coverage and/or higher slice resolution without affecting total scan times.

Introduction

Quantitative T2 mapping has great potential to provide additional information of clinical value to the current diagnostic MRI workflow for various applications (1), including the detection of brain lesions (2), assessment of myocardial edema (3, 4), diagnosis of biochemical changes in the knee cartilage (5, 6), detection, characterization, and grading of assorted lesions in the body (7–10), and muscle physiology research (11). Multi-echo spin-echo (MESE) imaging is a common MRI acquisition strategy for T2 mapping. However, accurate quantification of T2 relaxation times in MESE imaging presents significant challenges in clinical practice, including long scan times, limited volumetric coverage, high specific absorption rate (SAR), and the inherent bias of T2 estimation caused by B1+ inhomogeneity and imperfect slice profiles that create stimulated and indirect echoes in the MESE echo train (12).

To enable accurate T2 estimation, a T2 map can be estimated from MESE images using Bloch simulation-based signal matching (12). With this technique, stepwise Bloch simulations of the experimental pulse sequence are first performed to create a database or dictionary of underlying signal evolution, each corresponding to a specific combination of T2 and B1+ values. Due to B1+ inhomogeneity and imperfect slice profiles, each simulated T2-decaying signal in the dictionary follows a generalized echo-modulation curve (EMC) instead of a pure exponential decay. A T2 map is generated by matching the MESE images with the pre-generated dictionary. Specifically, the signal evolution of each pixel in the MESE images is compared to every entry in the dictionary to identify the best match. The T2 value corresponding to the best-matched dictionary entry is then allocated to the respective pixel location. Repeating this process for each pixel location generates a T2 parameter map. Based on the estimated T2 map, a proton density (PD) map can then be computed by back-projecting the first echo image using an exponential model (12). This EMC-T2 mapping technique enables accurate T2 mapping in clinically feasible scan times (13–18). It can be performed as a post-processing step using DICOM images directly reconstructed from the MESE acquisition on the scanner. Therefore, it does not require modification of the imaging sequence. To accelerate the dictionary matching process, EMC-T2 mapping was also optimized to incorporate a gradient-descent search algorithm, as described in reference (19).

While EMC-T2 mapping achieves improved accuracy compared to exponential model-based T2 fitting, it faces several significant challenges. First, pixel-wise parameter matching in EMC-T2 mapping requires postprocessing time and computational resources that may limit widespread clinical translation (12). Despite the significant acceleration of the mapping procedure achieved by the latest algorithm (19), it still demands a substantial computational cost. Second, robust T2 estimation requires an adequate number of echoes for dictionary matching, which necessitates a long echo train length (ETL) in MESE imaging. This results in increased SAR and also limits the number of slices or slice resolution that can be acquired within each TR. Reducing the number of echoes, as will be seen in our results presented below, can lead to significant T2 estimation error.

In this study, we propose a deep learning version of EMC-T2 mapping, referred to as DeepEMC-T2 mapping, to address these challenges. The training of the DeepEMC-T2 mapping model is based on a modified U-Net structure incorporating several novel components, including a data consistency loss, spatiotemporal filters, and the removal of the Pooling/Downsampling and Upsampling layers. After network training, DeepEMC-T2 mapping enables efficient and accurate estimation of both T2 and PD maps directly from a reduced number of echoes compared to standard EMC-T2 mapping without using a dictionary. We also assessed the performance and accuracy of DeepEMC-T2 mapping with different numbers of echoes. In the following sections, we first review the standard EMC-T2 mapping technique. The main framework of our proposed DeepEMC-T2 mapping technique is then described, followed by an evaluation of its performance in multiple in-vivo imaging experiments.

Methods

Recap of Standard EMC-T2 Mapping

In an ideal situation with a perfect RF slice and B1+ profile, the signal evolution along the echo train in MESE imaging follows an exponential decay based on the following equation:

$$M\left(t\right)=PD·e^{-\frac{t}{T_2}}$$ [1]

Here, $M$ represents the signal intensity at different echo times, $PD$ denotes the proton density and $t$ denotes the echo times. In practice, B1+ inhomogeneity, particularly at high field strengths, can lead to stimulated and indirect echoes, which cause substantial signal contamination in acquired images. This contamination occurs as a result of the separation of magnetization into three coherence pathways with each refocusing pulse (12). In this case, the resulting T2 decay of MESE no longer follows a standard exponential model as shown in Equation 1, although this model is commonly employed for T2 fitting in clinical practice.

The overall framework of EMC-T2 mapping to address these limitations is illustrated in Figure 1a. Based on the MESE imaging parameters used for data acquisition, stepwise Bloch simulation is performed to simulate all coherence pathways, including stimulated and indirect echoes, throughout the echo train. The simulation is repeated for a pre-defined range of T2 and B1+ values to create a dictionary of theoretical EMCs. Each entry in the dictionary represents a single echo-modulation curve that is associated with a unique combination of a T2 value and a B1+ value. For a fixed imaging protocol, the simulation needs to be performed only once as a preprocessing step.

Figure 1.

(a) Standard EMC-T2 framework: A T2 map is generated through pixel-wise T2 dictionary matching and a PD map is generated by back-projecting the first echo image with the estimated T2 map. (b) New DeepEMC-T2 framework: A spatiotemporal U-net is developed and trained on MESE images with variable echoes using a supervised scheme. The reference T2 and PD maps for training are calculated from images with 10 echoes using the standard EMC-T2 mapping approach. The original MESE images with 10 echoes were retrospectively cut to 7, 5, and 3 echoes for evaluation, which can potentially enable increased volumetric coverage and/or reduced SAR.

The estimation of a T2 map in EMC T2 mapping involves matching the signal evolution of each pixel in the acquired MESE images to the simulated EMC dictionary. Specifically, for each pixel location, the L2 norm of the difference between the signal evolution and each entry of the EMC dictionary is calculated. The T2 value associated with the dictionary entry that has the minimal L2 norm with the acquired signal is then assigned to the current pixel location. This matching process is repeated for all pixel locations in all acquired image slices to generate multi-slice T2 maps. Based on the estimated T2 map, a PD map can then be computed for each slice by back-projecting the first echo MESE image to time t=0 using the following equation:

$$P{D}_r=I_{r(t=TE1)}{/e}^{-\frac{TE1}{T{2}_r}}$$ [2]

Here, $I_{(t=TE1)}$ represents the first echo image, TE1 is the first echo time and T2 is the estimated T2 map. Note that an exponential model can be used to generate a PD map since the MESE signal undergoes pure exponential decay between the excitation and first acquisition event (23), and is thus not contaminated by stimulated and indirect echoes.

DeepEMC-T2 Mapping: The Network Design

DeepEMC-T2 mapping employs deep neural networks to achieve simplified, more efficient, and accurate T2 estimation directly from MESE images with a smaller number of echoes. The training of the DeepEMC-T2 network follows a supervised scheme, where reference T2 and PD maps are estimated from MESE images with 10 echoes using the standard EMC-T2 method, as shown in Figure 1.

The DeepEMC-T2 network is implemented using the U-Net with several modifications. First, the standard U-Net (24) employs spatial filters that may not be optimal for extracting the temporal features of T2 decay information. Instead, spatiotemporal filters with a 3×3×3 kernel size are implemented to explore image features along both the spatial and temporal dimensions in MESE images. The temporal branch of the filter plays a crucial role in exploring the relationship between the temporal dimension and can contribute to improved estimation accuracy. The modified U-Net structure (shown in Supporting Information Figure S6) consists of an encoder and a decoder with skip connections between them. The linear transforms are applied in the final layer to map features at each pixel to T2 and PD maps following all spatiotemporal encoder and decoder blocks. This is implemented using two 2D convolutional layers (Conv2D) with a kernel size of $1\times 1$. To estimate a consistent value range of the output T2 maps, the output activation function for predicting T2 maps was modified as a negative Log-Sigmoid to extend the output value range to [0,∞].

Second, the standard U-Net usually incorporates Pooling and Upsampling layers to enlarge the spatial receptive field while concurrently reducing computational costs (25). The spatial receptive field is defined as the area of the input image that a specific neuron in a convolutional layer considers or takes into consideration while making predictions or extracting features. A larger spatial receptive field proves beneficial for tasks requiring predictions based on large regions of input images, such as segmentation and object detection. For the EMC-T2 mapping, however, a larger spatial receptive field could potentially introduce irrelevant features to the prediction of T2 values at a specific pixel location because the estimation of T2 values at each pixel location in the conventional EMC-T2 relies solely on the temporal decay of a given spatial location in the MESE images. Accordingly, we propose to eliminate the standard Pooling and Upsampling layers in the modified U-Net used in DeepEMC-T2. This aims to reduce the spatial receptive field, ensuring that the prediction of the T2 value at a specific location relies on the temporal decay of the given spatial location and its nearby spatial locations in the MESE images. Note that there is not expected to be a conflict with the use of spatiotemporal filters, as the spatial receptive field (e.g., entire input image FOV), implemented with Pooling and Upsampling layers, is significantly larger than the neighboring regions explored using spatiotemporal filters (e.g., 3 × 3 pixels per filter).

Third, a data-consistency (DC) loss is incorporated into network training. Specifically, the training of the DeepEMC-T2 network enforces two types of loss functions, including (1) an L1 loss between the predicted T2 and PD maps (denoted as $\text{T}{2}_{\text{p}}$ and $\text{P}{\text{D}}_{\text{p}}$) and the reference T2 and PD maps (denoted as $\text{T}{2}_{\text{r}}$ and $\text{P}{\text{D}}_{\text{r}}$) and (2) two additional loss functions to minimize the L1 norm of the difference between the first-echo reference image (denoted as ${\text{I}}_{1\text{r}}$ from the reference MESE images) and a synthesized first-echo image that is computed through forward-projection according to the predicted T2 and PD maps and the reference T2 and PD maps, as shown in Figure 1b. The loss function is formulated as Equation 3 below.

$$\begin{gathered} {\text{L}}_{\theta }=\left|\right|\text{T}{2}_{\text{r}}-\text{T}{2}_{\text{p}}{\left|\right|}_1+\left|\right|{\text{PD}}_{\text{r}}-{\text{PD}}_{\text{p}}{\left|\right|}_1+ \\ {\lambda }_1\left|\right|{\text{PD}}_{\text{r}}{\text{e}}^{-\frac{\text{T}{\text{E}}_1}{{\text{T}2}_{\text{p}}}}-{\text{I}}_{1\text{r}}{\left|\right|}_1+{\lambda }_2\left|\right|{\text{PD}}_{\text{p}}{\text{e}}^{-\frac{\text{T}{\text{E}}_1}{{\text{T}2}_{\text{r}}}}-{\text{I}}_{1\text{r}}{\left|\right|}_1 \end{gathered}$$ [3]

Note that for data consistency, two synthesized first-echo images are generated by using $\text{T}{2}_{\text{p}}/\text{P}{\text{D}}_{\text{r}}$ and $\text{T}{2}_{\text{r}}/{\text{PD}}_{\text{p}}$, respectively, corresponding to the two loss functions for data consistency as shown in Equation 3 and Figure 1b. ${\lambda }_1$ and ${\lambda }_2$ are empirically set to 1 to balance the weights of each part of loss in this work.

The performance of our modified U-Net combining the three features above to improve DeepEMC-T2 mapping was demonstrated in different experiments as described below.

Datasets

Two MESE databases with different scan parameters were collected for our study. The first database (referred to as the axial-TE15ms dataset) includes a total of 67 axial brain datasets retrospectively collected from an early study (19), which were used in all experiments in our study. This database includes 37 datasets from healthy subjects (8 males, 6 females [mean age=43.5±11.2 years] and 23 datasets with anonymized subject information) and 30 datasets from patients with multiple sclerosis (MS) (8 males and 22 females, mean age=48.8±9.0 years). All datasets in this database were acquired on a 3T clinical MRI scanners (MAGNETOM Skyra, Siemens Healthineers, Erlangen, Germany) using a vendor-provided MESE sequence. All subjects provided written consent forms prior to the MRI scans. Each dataset includes 26 slices with 10 echoes each. Other imaging parameters included: FOV=220×206mm², matrix size=128×120, slice thickness=3mm, TR=4100ms, first TE=15ms, ΔTE=15ms.

The second database (referred to as the coroanl-TE12ms dataset) includes 57 coronal brain datasets that were collected from clinical patients with subjective or mild cognitive impairment (32 males and 25 females, mean age=73.5±6.0 years) and were retrospectively used in this study with Institutional Review Board approval. All datasets in this database were acquired on a 3T clinical MRI scanners (MAGNETOM Biograph mMR, Siemens Healthineers, Erlangen, Germany) using a vendor-provided MESE sequence. Each dataset includes 42 slices with 10 echoes each. Other imaging parameters included: FOV=220×171mm², matrix size=128×100, slice thickness=2mm, TR=8230ms, first TE=12ms, ΔTE=12ms. All the axial-TE15ms and coronal-TE12ms datasets in the two databases were accelerated using parallel imaging (GRAPPA: GeneRalized Auto-calibrating Partial Parallel Acquisition) with an acceleration rate of 2. All images were directly reconstructed on the scanners.

Two dictionaries were generated for the axial-TE15ms and coronal-TE12ms databases, respectively in our study. Simulations were repeated for a range of 440 T2 relaxation values (1–1000ms, with a step size of 1ms from 1–300ms and a step size of 5ms from 300–1000 ms) and 41 B1+ values (0.8–1.2 with a step size of 0.01).

Network Training

Three DeepEMC-T2 models were trained using the two databases. The first model was trained only on the axial-TE15ms database (referred to as the axial-TE15ms model), the second model was trained only on the coronal-TE12ms database (referred to as the coronal-TE12ms model), and the third model was trained on a combination of both axial-TE15ms and coronal-TE12ms datasets (referred to as the joint model). This approach was implemented to assess the generalizability of DeepEMC-T2 mapping.

For the axial-TE15ms model, 49 datasets acquired in 32 healthy controls and 17 MS patients were used for training, 6 datasets acquired in 5 healthy controls and 1 MS patient were used for validation, and evaluation was performed in the remaining 12 datasets that were all acquired in MS patients. For the coronal-TE12ms model, 40 datasets were used for training, 5 datasets were used for validation, and 12 datasets were used for evaluation. For the joint model, the training, validation, and evaluation datasets for the axial-TE15ms and coronal-TE12ms models were combined, resulting in a total of 89 datasets for training, 11 datasets for validation, and 24 datasets for evaluation.

The model weights in network training were updated using the adaptive gradient descent optimization (ADAM) algorithm (26) with a learning rate of 0.0003. A batch training strategy was implemented with a minibatch size of 4–16 depending on the number of echoes selected from MESE images for training. The total iteration steps were 200 epochs, and the best model was chosen when the smallest L1 loss between reference and estimated T2 maps was achieved in the validation datasets. The training was performed using PyTorch (version 2.0) on a server with an NVIDIA Tesla A100 GPU card. All experiments follow the above training configuration.

Evaluation

A total of seven experiments were designed to evaluate the proposed DeepEMC-T2 mapping technique. Experiment 1 compared DeepEMC-T2 mapping with standard EMC-T2 mapping (simply referred to as EMC-T2 mapping hereafter) for estimating T2 and PD maps. Experiment 2 evaluated the impact of the number of echoes and echo spacing in MESE images on the accuracy of parameter estimation for both EMC-T2 and DeepEMC-T2 mapping. Specifically, this was performed using MESE images with the first 3 echoes (echoes 1–3), the first 5 echoes (echoes 1–5), echoes 1,3,5, and echoes 1,5,10. Note that the echo spacing is increased when using echoes 1,3,5 and 1,5,10 in MESE imaging for parameter estimation. Experiment 3 evaluated the generalizability of DeepEMC-T2 mapping to different imaging orientations (e.g., axial and coronal) and acquisition parameters (e.g., ΔTE=15ms and ΔTE=12ms). Specifically, a joint network model was trained using both axial-TE15ms and coronal-TE12ms databases to test whether it can reconstruct T2/PD maps from images acquired in different orientations, compared to the standard axial-TE15ms or coronal-TE12ms model trained only on either the axial-TE15ms or coronal-TE12ms database. Experiments 4–6 evaluated whether the incorporation of a DC loss, removal of the Pooling and Upsampling layers in the U-Net, and the use of spatiotemporal filters could improve the accuracy of parameter estimation in DeepEMC-T2 mapping, respectively. Finally, Experiment 7 assessed if a B1+ map needs to be jointly estimated in DeepEMC-T2 mapping. For this evaluation, we modified the model to estimate a T2 map, a PD map, and a B1+ map simultaneously in DeepEMC-T2 mapping, incorporating an additional B1+ loss into the network training to investigate whether this affects the accuracy of T2 estimation compared to the model without the B1+ loss. The average computational cost (inference time per case) between DeepEMC-T2 and EMC-T2 mapping was summarized for all the test cases. The generation of T2 maps using traditional and deep learning EMC-T2 mapping was both conducted on a high-performance cluster. 40 CPUs, 256 GB of memory, and 1 GPU card with 80 GB of memory were requested for the tasks. The dictionary-based matching implemented in standard EMC-T2 mapping was executed in Matlab with built-in C++ functions on CPUs. The inference for DeepEMC-T2 mapping was carried out in Python and executed on GPU.

For all the experiments, the T2 and PD maps generated from all the 10 echoes using standard EMC-T2 mapping were treated as the ground truth reference for supervised training and for evaluation. For assessment of the accuracy of T2 quantification, the differences between the reconstructed T2 maps and the reference T2 maps were assessed by calculating the pixel-wise relative error in different T2 ranges from 40–160ms with an increment of 40ms. For example, 40–80ms was set as T2 range 1, 80–120ms was set as T2 range 2, etc. Different masks representing different T2 ranges were generated from the reference T2 maps, and the obtained masks were applied to the reconstructed T2 maps directly without adaption for calculating the pixel-wise relative error. For experiment 1, the differences between the reconstructed T2 maps and the reference T2 maps were also evaluated in the MS lesions by calculating the pixel-wise relative error. For each dataset, a mask was manually drawn to cover the boundary of a MS lesions following the guidance of Dr. Shepherd. This process was performed using the MatrixUser software (27) in Matlab. The pixel-wise relative error was defined as:

$$\text{Error}\left(\%\right)=\frac{|\text{pred}-\text{Ref}|}{\text{Ref}}\times 100\%$$ [4]

The differences between the predicted PD maps and the reference PD maps were assessed by calculating the pixel-wise relative error averaged over all pixel locations. Paired student t-test was used for statistical analysis, where a P value less than 0.05 was considered statistical significance.

Results

Experiment 1: Comparison Between EMC-T2 and DeepEMC-T2 Mapping

Figure 2a and Figure 3a show a representative case comparing T2 and PD maps estimated using EMC-T2 mapping and DeepEMC-T2 mapping from MESE images with different numbers of echoes. The T2 and PD maps estimated from standard EMC-T2 mapping using all 10 echoes were treated as the reference for calculating the error maps. DeepEMC-T2 mapping consistently yielded improved accuracy compared to EMC-T2 mapping across different numbers of reduced echoes.

Figure 2.

(a) A representative case comparing T2 maps estimated using EMC-T2 and DeepEMC-T2 from MESE images with varying numbers of echoes. The T2 maps estimated from standard EMC-T2 using all 10 echoes were treated as the reference standard for calculating the error maps. (b) Quantitative comparison of T2 estimation in all test cases with varying numbers of echoes based on averaged pixel-wise errors in different T2 ranges. The error map and quantitative comparison indicate that DeepEMC-T2 mapping enables more accurate T2 map estimation than EMC-T2 mapping, particularly as the number of echoes is reduced. (c) Quantitative comparison of T2 estimation in the selected lesion area averaged over all test cases. It indicates that DeepEMC-T2 mapping allows for more accurate T2 estimation in the lesion region.

Figure 3.

(a) A representative case comparing PD map estimated using EMC-T2 and DeepEMC-T2 from MESE images with varying numbers of echoes. The PD maps estimated from standard EMC-T2 using all 10 echoes were treated as the reference for calculating the error maps. (b) Quantitative comparison of PD estimation in all test cases with varying numbers of echoes with different numbers of echoes based on averaged pixel-wise errors. The error map and quantitative comparison indicate that DeepEMC-T2 mapping enables more accurate PD map estimation than EMC-T2 mapping, particularly as the number of echoes is reduced.

Figure 2b summarizes the quantitative comparison of T2 estimation averaged over all test cases (n=12). The improvement of DeepEMC-T2 mapping over EMC-T2 mapping reached statistical significance (P<0.05) for all the T2 ranges across different numbers of reduced echoes. Similarly, Figure 3b provides a quantitative overview of PD estimation averaged over all test datasets. The improvement of DeepEMC-T2 mapping over EMC-T2 mapping reached statistical significance (P<0.05) for 5 and 3 echoes. These results highlight that DeepEMC-T2 mapping enables more accurate parameter estimation than EMC-T2 mapping with a smaller number of echoes.

Figure 2c summarizes the quantitative comparison of T2 estimation in the selected lesions averaged over all test cases. The results indicate that DeepEMC-T2 mapping enables more accurate T2 estimation in the lesion region, especially when the number of echoes is reduced to 5 and 3.

Experiment 2: The Impact of Echo Spacing on DeepEMC-T2 Mapping

Figure 4a and Figure 5a show a representative example comparing T2 and PD maps estimated from MESE images with echoes 1,3,5 and echoes 1,5,10 with a larger echo spacing, and with 5 echoes (echoes 1–5) and 3 echoes (echoes 1–3) with the default echo spacing using both EMC-T2 and DeepEMC-T2 mapping. It can be seen that increasing the echo spacing while reducing the number of echoes has a neglectable impact on both T2 and PD estimation for both EMC-T2 and DeepEMC-T2 mapping. In addition, the results demonstrate that including longer echoes while maintaining the same number of echoes can improve the accuracy of parameter estimation for both EMC-T2 and DeepEMC-T2 mapping.

Figure 4.

(a) A representative example comparing T2 maps estimated from MESE images for echoes 1,5,10 and echoes 1,3,5 with a larger echo spacing, and for 5 echoes (echo 1–5) and 3 echoes (echo 1–3) with the default echo spacing using both EMC-T2 and DeepEMC-T2. (b) Quantitative comparison of T2 maps in test datasets based on averaged pixel-wise errors in different T2 ranges. The results suggest that increasing the echo spacing while reducing the number of echoes has little impact on the accuracy of T2 map estimation in DeepEMC-T2 mapping. This also shows that including the longer echoes while maintaining the same number of echoes can improve the accuracy of the estimated T2 map for DeepEMC-T2 mapping.

Figure 5.

(a) A representative example comparing PD maps estimated from MESE images for echoes 1,5,10 and echoes 1,3,5 with a larger echo spacing, and for 5 echoes (echo 1–5) and 3 echoes (echo 1–3) with the default echo spacing using both EMC-T2 and DeepEMC-T2. (b) Quantitative comparison of PD maps estimated in 15 test datasets based on averaged pixel-wise errors. The results demonstrated that increasing the echo space while reducing the number of echoes has little impact on the accuracy of PD map estimation in DeepEMC-T2 mapping. This also suggests that including the longer echoes while maintaining the same number of echoes can improve the accuracy of the estimated PD map for DeepEMC-T2 mapping.

Figure 4b and Figure 5b summarize the corresponding quantitative comparison for T2 and PD estimation in all test cases. For both EMC-T2 and DeepEMC-T2 mapping, there was no significant difference between echoes 1,3,5 (3 echoes) with a larger echo spacing and echoes 1–5 (5 echoes) with the default echo spacing for all ranges of T2 estimation (P>0.05). The errors for PD estimation from echo 1,3,5 (3 echoes) and echoes 1–5 (5 echoes) were all below 2% for both EMC-T2 and DeepEMC-T2 mapping. This confirms our visual observation that using a larger echo spacing with a reduced number of echoes can maintain the accuracy of parameter estimation. Besides, there is a significant improvement for both T2 and PD estimation (P<0.05) from 3 echoes (echoes 1–3) with the default echo spacing to echoes 1,3,5 (also 3 echoes) with a larger echo spacing. This suggests that increasing the echo spacing while maintaining the same number of echoes can improve the accuracy of parameter estimation. In addition, there is also a significant improvement for both T2 and PD estimation (P<0.05) from echoes 1,3,5 to echoes 1,5,10 with a larger echo spacing. This verifies that including longer echoes while maintaining the same number of echoes can improve the accuracy of parameter estimation.

Experiment 3: The generalizability of DeepEMC-T2 Mapping

Figure 6a and Figure 7a illustrate the use of the axial-TE15ms model, the coronal- TE12ms model, and the joint DeepEMC-T2 Mapping network model in reconstructing T2/PD maps from an axial-TE15ms dataset with varying numbers of echoes. Similarly, Figure 8a and Figure 9a showcase the application of these models in reconstructing T2/PD maps from a coronal-TE12ms dataset with different number of echoes. The results indicate that models trained solely on axial-TE15ms or coronal-TE12ms datasets lack generalizability to datasets from other imaging orientations. In contrast, the joint model demonstrates robust generalization across both imaging orientations without reducing accuracy. Figure 6b, Figure 7b, Figure 8b, and Figure 9b summarize the corresponding quantitative comparison for T2 and PD estimation across all test cases.

Figure 6.

(a) A representative case from the axial-TE15ms dataset comparing T2 maps reconstructed using the axial-TE15ms model, the coronal-TE12ms model, and the joint DeepEMC-T2 Mapping network model with varying numbers of echoes. (b) Quantitative comparison of T2 estimation error across all the test cases of the axial-TE15ms dataset reconstructed using the axial-TE15ms model, the coronal-TE12ms model, and the joint DeepEMC-T2 Mapping network model with varying numbers of echoes. The result indicates that the model trained solely on coronal-TE12ms datasets lacks generalizability to axial-TE15ms datasets in estimating T2 maps. However, the joint model demonstrates robust generalization on axial-TE15ms datasets without reducing accuracy in estimating T2 maps.

Figure 7.

(a) A representative case from the axial-TE15ms dataset comparing PD maps reconstructed using the axial-TE15ms model, the coronal-TE12ms model, and the joint DeepEMC-T2 Mapping network model with varying numbers of echoes. (b) Quantitative comparison of PD estimation error across all the test cases of the axial-TE15ms dataset reconstructed using the axial-TE15ms model, the coronal-TE12ms model, and the joint DeepEMC-T2 Mapping network model with varying numbers of echoes. The result indicates that the model trained solely on coronal-TE12ms datasets lacks generalizability to axial-TE15ms datasets in estimating PD maps. However, the joint model demonstrates robust generalization on axial-TE15ms datasets without reducing accuracy in estimating PD maps.

Figure 8.

(a) A representative case from the coronal-TE12ms dataset comparing T2 maps reconstructed using the axial-TE15ms model, the coronal-TE12ms model, and the joint DeepEMC-T2 Mapping network model with varying numbers of echoes. (b) Quantitative comparison of T2 estimation error across all the test cases of the coronal-TE12ms dataset reconstructed using the axial-TE15ms model, the coronal-TE12ms model, and the joint DeepEMC-T2 Mapping network model with varying numbers of echoes. The result indicates that the model trained solely on axial-TE15ms datasets lacks generalizability to coronal-TE12ms datasets in estimating T2 maps. However, the joint model demonstrates robust generalization on coronal-TE12ms datasets without reducing accuracy in estimating T2 maps.

Figure 9.

(a) A representative case from the coronal-TE12ms dataset comparing PD maps reconstructed using the axial-TE15ms model, the coronal-TE12ms model, and the joint DeepEMC-T2 Mapping network model with varying numbers of echoes. (b) Quantitative comparison of PD estimation error across all the test cases of the coronal-TE12ms dataset reconstructed using the axial-TE15ms model, the coronal-TE12ms model, and the joint DeepEMC-T2 Mapping network model with varying numbers of echoes. The result indicates that the model trained solely on axial-TE15ms datasets lacks generalizability to coronal-TE12ms datasets in estimating PD maps. However, the joint model demonstrates robust generalization on coronal-TE12ms datasets without reducing accuracy in estimating PD maps.

Experiments 4–6: The Impact of DC Loss, Removing Pooling and Upsampling layers, and Spatiotemporal Filters

Supporting Information Figure S1 shows a representative case comparing T2 and PD maps estimated using DeepEMC-T2 mapping with and without a DC loss. The error maps indicate that incorporating a DC loss into DeepEMC-T2 training can improve the estimation of both T2 and PD maps, as indicated by the red arrows. The quantitative comparison in all test cases is summarized in the first and second rows of Table 1. The improvement from incorporating a DC loss reached statistical significance (P<0.05) in all ranges of T2 estimation for 10, 7, and 5 echoes and in PD estimation for 7, 5, and 3 echoes as highlighted by the red stars in the second row of Table 1.

Table 1.

Quantitative comparison of T2 and PD maps estimated from MESE images using various new features across all test datasets based on averaged pixel-wise errors. The results confirm that incorporating DC loss, removing Pooling and Upsampling layers, and using spatiotemporal convolution kernels all lead to the improvement in the estimation of T2 and PD maps.

T2 ranges (ms) / PD	40- 80	80- 120	120- 160	PD	40- 80	80- 120	120- 160	PD	40- 80	80- 120	120–160	PD	40- 80	80- 120	120- 160	PD
Network Architecture	Error (%)
	10 Echoes				7 Echoes (1–7)				5 Echoes (1–5)				3 Echoes (1–3)
✓ DC Loss ✓ Spatiotemporal ✗ Pool&Up layers (Proposed)	1.05	1.04	1.17	0.43	1.43	1.60	1.96	0.53	2.81	3.67	4.34	0.83	5.75	8.32	10.75	1.46
✗ DC Loss ✓ Spatiotemporal ✗ Pool&Up layers	1.35*	1.32*	1.38*	0.57	2.54*	2.53*	2.61*	0.66*	3.51*	4.00*	4.65*	0.94*	6.06	8.15	10.61	1.55*
✓ DC Loss ✓ Spatiotemporal ✓ Pool&Up layers	2.21*	2.41*	2.72*	0.93*	2.49*	2.76*	3.39*	1.03*	3.48*	4.19*	5.25*	1.18*	8.89*	11.56*	15.20*	2.76*
✓ DC Loss ✓ Spatial ✗ Pool&Up layers	2.94*	2.98*	3.14*	0.92*	3.89*	4.09*	4.30*	1.11*	4.24*	5.10*	6.04*	1.25*	7.06*	9.63*	12.65*	2.09*

BOLD denotes the lowest error among all compared models, while * indicates whether our proposed DeepEMC-T2 framework achieves significant improvement compared to the model lacking specific proposed features, determined through a t-test conducted among all test cases.

Supporting Information Figure S2 presents a representative case comparing T2 and PD maps estimated using DeepEMC-T2 mapping with and without the Pooling and Upsampling layers. The error maps highlight a reduction of error in both T2 and PD estimation by removing the Pooling and Upsampling layers. The quantitative comparison in all test cases is summarized in the first and third rows of Table 1. The improvement of removing Pooling and Upsampling layers reached statistical significance (P<0.05) for all ranges of T2 estimation and PD estimation across different numbers of echoes.

Supporting Information Figure S3 compares T2 and PD maps estimated using DeepEMC-T2 mapping with spatial and spatiotemporal convolution kernels in one case. Error maps visually demonstrate that including spatiotemporal convolution filters in DeepEMC-T2 mapping improves the estimation of both T2 and PD. The quantitative analysis of pixel-wise relative error in different T2 ranges for all test cases, as shown in the first and fourth rows of Table 1. The improvement reached statistical significance (P<0.05) for all ranges of T2 estimation and PD estimation across different numbers of echoes.

Experiment 7: The Impact of B1+ on the DeepEMC-T2 Mapping

Supporting Information Figure S4a shows a representative case comparing T2 maps estimated using DeepEMC-T2 mapping with and without incorporating the reference B1+ map and a B1+ loss for different numbers of echoes. The error maps demonstrate that incorporating the B1+ map into DeepEMC-T2 mapping does not have an impact on the accuracy of T2 estimation. Supporting Information Figure S4b presents the estimated B1+ map using DeepEMC-T2 mapping when a B1+ loss is incorporated.

This observation is confirmed in the quantitative comparison between DeepEMC-T2 mapping with and without incorporating a B1+ loss across all test cases, as shown in Supporting Information Figure S4c. There was no significant difference between DeepEMC-T2 mapping with and without incorporating a B1+ loss for all ranges of T2 estimation (P>0.05). Supporting Information Figure S5 shows estimated T2 maps from two upper slices with highly inhomogeneous B1+ maps using DeepEMC-T2 mapping without incorporating a B1+ loss. The results indicate that DeepEMC-T2 mapping without incorporating a B1+ loss can estimate accurate T2 maps even in slices with highly inhomogeneous B1+. These results suggest that B1+ has a negligible impact on the accuracy of the estimated T2 map using DeepEMC-T2 mapping.

Comparison of Computational Cost

The average fitting time (for EMC-T2 mapping) / inference time (for DeepEMC-T2 mapping) across all test cases for the different numbers of echoes are: 8.47±0.53 / 0.16±0.01 seconds for all 10 echoes, 8.04±0.44 / 0.14±0.02 seconds for 7 echoes (echoes 1–7), 7.92±1.48 / 0.15±0.01 seconds for 5 echoes (echoes 1–5), 6.49±0.29 / 0.14±0.02 seconds for 3 echoes (echoes 1–3), 6.59±0.33 / 0.15±0.02 seconds for echoes 1,3,5, and 6.54±0.36 / 0.16±0.01 seconds for echoes 1,5,10. The computational costs reported were per dataset including all image slices. Our results indicate that DeepEMC-T2 mapping enables 45.7~52.1x faster computational times for each case compared to EMC-T2 mapping.

Discussion

Deep learning has shown great promise for improving quantitative MRI in general (28). It can be used to improve quantitative MRI reconstruction (28–31), to improve the estimation of the parameters from reconstructed images (32–35), and to accelerate more complex multicomponent analysis (18). In this work, we developed DeepEMC-T2 mapping, a deep learning framework for T2 quantification based on EMC modeling using the MESE sequence. After network training, DeepEMC-T2 mapping enables direct and efficient estimation of both T2 and PD maps without a dictionary matching step that is required in standard EMC-T2 mapping. More importantly, DeepEMC-T2 mapping allows for more accurate estimation of parameter maps from fewer echoes compared to EMC-T2 mapping. This can be leveraged to improve slice resolution and/or volumetric coverage, both of which are of significant clinical importance.

Our results have demonstrated that DeepEMC-T2 mapping enables accurate estimation of both T2 and PD from all 10 echoes compared to the reference, with an error below 1.2% for T2 estimation in different T2 ranges and below 0.5% for PD estimation. Meanwhile, when the number of echoes is reduced (e.g., from 10 echoes to 7, 5, and 3 echoes by truncating the late echoes), DeepEMC-T2 Mapping yielded more accurate parameter estimation than EMC-T2 mapping. This is because DeepEMC-T2 mapping can more effectively estimate the underlying T2 decay patterns with a reduced number of echoes, while conventional dictionary matching becomes less robust with fewer echoes. The TR of a MESE sequence is typically on the order of seconds, including the time required to acquire an echo train and some additional idle time to ensure signal recovery at the end of each echo train. To improve imaging efficiency, the idle time for a given image slice can usually be used to acquire other slices in an interleaved manner. As a result, reducing the number of echoes can help reduce the SAR of MESE acquisition and potentially increase the total number of image slices or slice resolution.

Our results have also shown that when the number of echoes is reduced, increasing the echo spacing improves the accuracy of T2 and PD estimation. Meanwhile, maintaining the same number of echoes while expanding the echo spacing proves beneficial in improving the accuracy of T2 and PD estimation. This is likely because of the increased T2 decay range that contributes to a more accurate estimation of the T2 and PD maps. This finding suggests that it is possible to acquire fewer echoes with a larger echo spacing, and this can be leveraged to reduce SAR without affecting the accuracy of the parameter estimation. In addition, including longer echoes while maintaining the same number of echoes can improve the accuracy of T2 and PD estimation. This is particularly beneficial for improving the accuracy of T2 estimation in the larger T2 ranges (e.g., 120–160 ms), as indicated by the height difference of the error bars between echoes 1,5,10 and echoes 1,3,5 as shown in Figure 4b.

Our results have indicated that the DeepEMC-T2 mapping model trained on an individual database (e.g., the axial-TE15ms model or the coronal-TE12ms model) with specific scan parameters cannot be directly applied to estimate parameter maps from datasets with different imaging orientations and acquisition parameters. This is expected because the underlying T2 decay of MESE images varies with different scan parameters, and different simulated dictionaries were employed to generate reference parameter maps. However, we have demonstrated that DeepEMC-T2 Mapping can be trained on multiple databases with varying scan protocols to enable improved generalizability.

Three new components have been incorporated into the DeepEMC-T2 mapping framework to improve the accuracy of parameter estimation, including a DC loss, removal of the Pooling and Upsampling layers that are typically implemented in the standard U-Net, and spatiotemporal convolution kernels. First, the incorporation of the DC loss increases the accuracy of parameter estimations, albeit with a minor improvement (Supporting Information Figure S2 and Table 1). Second, eliminating the Pooling and Upsampling layers in U-Net improves T2 and PD estimation. In our study, using spatiotemporal filters with a kernel size (e.g., 3×3 pixels) allows the network to exploit correlations among nearby small regions. In contrast, the Pooling and Upsampling layers in the standard U-Net are designed to expand the spatial receptive field while reducing computational costs, enabling the network to efficiently learn features across the entire image FOV. However, we have found that including excessive unrelated information from distant pixel locations (e.g., the entire FOV) in the MESE images can diminish the accuracy of T2/PD estimation. This is because the estimation of T2 and PD values at a specific pixel location (e.g., [x, y]) does not depend on the entire input MESE images. Therefore, we removed the Pooling and Upsampling layers from the U-Net to narrow the receptive field (25), thereby eliminating unrelated information from distant pixel locations in the input MESE images. Our experiments have demonstrated that this adjustment leads to more accurate parameter estimation. Third, the use of spatiotemporal convolution kernels helps extract additional temporal correlations along the echo dimension compared to spatial convolution kernels only, which contributes to the improvement in the accuracy of the estimated T2 and PD maps.

For standard EMC-T2 mapping, the B1+ constraint is crucial to ensure accurate T2 estimation due to B1+ inhomogeneity. However, our results suggest that DeepEMC-T2 mapping does not require the B1+ constraint to maintain accurate T2 and PD map estimation. This is likely because the B1+ information is already incorporated in the generation of reference T2 maps using standard EMC-T2 mapping. Therefore, by applying a T2 loss, DeepEMC-T2 mapping inherently integrates this information during network training, and the trained network is able to learn and adapt to the features of regions with inhomogeneous B1+ from the reference T2 maps generated with the B1+ constraint.

The DeepEMC-T2 mapping framework has the potential to be extended for additional applications, including the simultaneous estimation of multiple MR parameters. Recent innovations have enabled the estimation of multiple MR parameters from a single data acquisition. Notable examples include Magnetic Resonance Fingerprinting (MRF) (20), Z-location shuffling, Multiple Echoes, and B-interleaving for Relaxometry-diffusion Acquisitions (ZEBRA) (21), as well as MR-STAT (Magnetic Resonance Spin Tomography in Time-domain) (22). Typically, these techniques rely on traditional dictionary matching or fitting processes. By adapting the DeepEMC-T2 framework to enforce different loss functions tailored to specific parameters, it is expected that the reconstruction efficiency of these advanced quantitative MRI techniques can be significantly improved.

This study has several limitations that require discussion. First, the current implementation of DeepEMC-T2 mapping is based on DICOM images that are reconstructed directly on the scanner. As a result, it is a post-processing step after image reconstruction. It is expected that our DeepEMC-T2 mapping framework can also be implemented with accelerated MESE images, combining image reconstruction and parameter estimation as a single step. This can potentially reduce total scan times and/or improve spatial resolution. Second, DeepEMC-T2 mapping can be implemented with datasets acquired using a radial MESE sequence. In particular, radial MESE imaging with a golden-angle radial rotation scheme (36,37,38,39) could be particularly interesting for DeepEMC-T2 mapping. This may allow for a higher acceleration of data acquisition, leveraging the incoherent sampling behavior of radial sampling. It can also enable improved motion robustness for applications in the spinal cord or abdominopelvic organs. Third, while this study only focused on a single compartmental model, recent studies have shown that multicomponent analysis can improve myelin water imaging and the investigation of microstructural compartmentation in general (18). However, the challenges associated with multicomponent analysis include limitations in computational power, particularly as the size of the dictionary increases. These can also be addressed with an extension of DeepEMC-T2 mapping to a multi-compartmental model.

Conclusion

This work introduces a novel deep learning framework to implement EMC-T2 mapping. It addresses challenges associated with standard EMC-T2: the need for a time-consuming dictionary matching step and an adequate number of echoes in MESE imaging. DeepEMC-T2 mapping enables simple, efficient, and accurate T2 quantification directly from acquired MESE images with a reduced number of echoes. This allows one to reduce the number of 180° refocusing pulses, leading to an important increase in coverage to achieve whole brain imaging with more clinically feasible scan times. The new DeepEMC-T2 framework could facilitate more widespread clinical translation of the EMC-T2 mapping technique for various applications and also more efficient and robust multicomponent analysis (18).

Supplementary Material

Supinfo

Figure S1 A representative case comparing T2, and PD maps estimated from MESE images using DeepEMC-T2 with and without DC loss. The error maps indicate that incorporating a DC loss into the training of the DeepEMC-T2 can improve the estimation of both T2 and PD maps, as highlighted by the arrows in the error maps. However, the visual impact is relatively small.

Figure S2 A representative case comparing T2, and PD maps estimated using DeepEMC-T2 with and without the Pooling and Upsampling layers. The error maps indicate a significant reduction in error for both T2 and PD estimation by removing the Pooling and Upsampling layers.

Figure S3 A case comparing T2, and PD maps estimated using DeepEMC-T2 with spatial and spatiotemporal convolution kernels in one case. Error maps suggest that the use of spatiotemporal convolution filters in DeepEMC-T2 results in a significant improvement of T2 and PD estimation.

Figure S4 (a) A representative case comparing T2 maps estimated using DeepEMC-T2 mapping with and without incorporating the reference B1+ map and a B1+ loss for different numbers of echoes. (b) The estimated B1+ map using DeepEMC-T2 mapping when a B1+ loss is incorporated. (c) Quantitative comparison between DeepEMC-T2 mapping with and without incorporating a B1+ loss across all test cases. The result demonstrates that incorporating the B1+ map into DeepEMC-T2 mapping does not have an impact on the accuracy of T2 estimation.

Figure S5 Estimated T2 maps from two upper slices with highly inhomogeneous B1+ maps using DeepEMC-T2 mapping without incorporating a B1+ loss. The results indicate that DeepEMC-T2 mapping without incorporating a B1+ loss can estimate accurate T2 maps even in slices with highly inhomogeneous B1+.

Figure S6 The detailed architecture of the DeepEMC-T2 modified from a standard U-Net. First, the spatial convolution filters in the standard U-Net are replaced with spatiotemporal convolution filters to efficiently extract the image features along both the spatial and temporal dimensions in MESE images. Second, Pooling and Upsampling layers that are implemented in the standard U-net are removed to reduce the spatial receptive field, ensuring that the prediction of the T2 value at a specific location relies on the temporal decay of the given spatial location and its nearby spatial locations in the MESE images. The linear transforms are applied in the final layer to map features at each pixel to T2 and PD maps following all spatiotemporal encoder and decoder blocks, which was implemented using two 2D convolutional layers (Conv2D) with a kernel size of $1\times 1$.