11institutetext: Biomedical Engineering Department, School of Biomedical
Engineering & Imaging Sciences, King’s College London, London,
UK22institutetext: Department of Informatics, Technical University of Munich,
Munich, Germany 33institutetext: Department of Computing, Imperial College
London, London, UK 44institutetext: Clinical Scientific Computing, Guy’s & St.
Thomas’ NHS Foundation Trust, London, UK 55institutetext: Child Health, King’s
College London, London, United Kingdom 66institutetext: Paediatric and Fetal
Cardiology, Evelina London Children’s Hospital, London, UK
66email<EMAIL_ADDRESS>
# The Challenge of Fetal Cardiac MRI Reconstruction Using Deep Learning

Denis Prokopenko 11 Kerstin Hammernik 2233 Thomas Roberts 1144 David F A Lloyd
5566 Daniel Rueckert 2233 Joseph V Hajnal 11

###### Abstract

Dynamic free-breathing fetal cardiac MRI is one of the most challenging
modalities, which requires high temporal and spatial resolution to depict
rapid changes in a small fetal heart. The ability of deep learning methods to
recover undersampled data could help to optimise the kt-SENSE acquisition
strategy and improve non-gated kt-SENSE reconstruction quality. In this work,
we explore supervised deep learning networks for reconstruction of kt-SENSE
style acquired data using an extensive in vivo dataset. Having access to
fully-sampled low-resolution multi-coil fetal cardiac MRI, we study the
performance of the networks to recover fully-sampled data from undersampled
data. We consider model architectures together with training strategies taking
into account their application in the real clinical setup used to collect the
dataset to enable networks to recover prospectively undersampled data. We
explore a set of modifications to form a baseline performance evaluation for
dynamic fetal cardiac MRI on real data. We systematically evaluate the models
on coil-combined data to reveal the effect of the suggested changes to the
architecture in the context of fetal heart properties. We show that the best-
performers recover a detailed depiction of the maternal anatomy on a large
scale, but the dynamic properties of the fetal heart are under-represented.
Training directly on multi-coil data improves the performance of the models,
allows their prospective application to undersampled data and makes them
outperform CTFNet introduced for adult cardiac cine MRI. However, these models
deliver similar qualitative performances recovering the maternal body very
well but underestimating the dynamic properties of fetal heart. This dynamic
feature of fast change of fetal heart that is highly localised suggests both
more targeted training and evaluation methods might be needed for fetal heart
application.

###### Keywords:

Image Reconstruction Fetal Cardiac MRI Deep Learning.

##  1 Introduction

Dynamic free-breathing fetal cardiac imaging is one of the most challenging
applications of magnetic resonance imaging (MRI). Fetal heart imaging requires
a large field of view to encompass the maternal anatomy combined with high
spatial and temporal resolutions to depict tiny dynamic structures of the
fetal heart. The imaging must accommodate uncontrolled fetal motion and
maternal respiration while capturing fetal cardiac beating, which could be
more than twice as fast as an adult heartbeat.

Conventional kt-SENSE [22] can deliver dynamic MRI of fetal heart across
multiple cardiac cycles using a prior-led reconstruction of highly
undersampled signals. While there are other reconstruction methods to deliver
dynamic fetal cardiac MRI using non-Cartesian or non-uniform sampling [6, 12]
or gating [5, 11], we focus on the kt-SENSE approach as it was used to acquire
the substantial dataset of fetal cardiac MRI. The kt-SENSE is simpler to use
to collect the data compared to non-uniform or non-Cartesian methods and
provides real-time fetal cardiac data over multiple cardiac cycles without
averaging in contrast to gated approaches. In case of kt-SENSE, the data is
usually acquired in two stages using sampling patterns, which have high
temporal resolution to freeze bulk fetal and fetal cardiac motion. One
acquisition pattern in Figure 1 samples high-resolution undersampled k-space
data in time (kt data). The other pattern in Figure 1 acquires low-resolution
(low k) fully-sampled kt data, which helps to disambiguate dynamic features in
undersampled data during reconstruction. However, the two-stage acquisition
approach is inefficient because the same anatomy is sampled twice, while
changes in fetal pose between the two samplings could introduce differences in
the collected data reducing the quality of the reconstruction.

(a)

(b)

Figure 1: The kt-SENSE acquisition patterns to sample high-resolution
undersampled (a) and low-resolution densely sampled (b) kt data.

Recent advances in deep learning (DL) for dynamic adult cardiac MRI
reconstruction [3, 16, 17, 18, 21] expanded the variety of methods that can be
used for the reconstruction. The ability to recover fully-sampled data
directly from undersampled information is a common aim of the proposed DL
reconstruction methods. In the case of fetal cardiac MRI, they have the
potential to replace the dense acquisition part (Figure 1) with a
reconstruction from data acquired with undersampling pattern (Figure 1). As a
result, it could reduce the acquisition time up to two times, using only one
part of the two-stage sampling approach, and increase the robustness of the
reconstruction to the spontaneous motion between the stages of acquisition.
However, the use of DL reconstruction methods for fetal cardiac MRI
reconstruction is limited due to additional constraints of the application
domain. The fully-sampled high-resolution fetal cardiac ground truth data is
currently unavailable. This is due to the limitations on the spatio-temporal
resolution required to freeze the motion and scanner acquisition rate. Also,
the lack of real high-resolution dynamic MRI data forces DL methods to employ
high-resolution reconstructions as ground truth. As a result, the models are
optimised to mimic the target reconstruction algorithms with their biases
rather than the true depiction of the anatomy. In addition, the networks
usually perform dynamic adult heart MRI reconstruction from retrospectively
undersampled gated cine modality, which differs from the fetal cardiac case,
where the recovery of the heartbeat over multiple cycles is desired. In the
absence of the ground truth data, emerged self-supervised versions showed
similar performance to supervised models according to the numerical
evaluations [1, 24]. However, the self-supervised models delivered a less
reliable depiction of the moving edges, which are the most sensitive anatomy
in the case of fetal cardiac MRI.

In this work, we study the performance of supervised DL baselines to recover
fully-sampled low-resolution dynamic fetal cardiac MRI from undersampled data
to make the kt-SENSE [22] algorithm more robust to motion and shorten the
acquisition time. First, we present and compare a set of U-Net-based
architectures trained on data combined over multiple coils (coil-combined) to
recover undersampled data, focusing on dynamic properties of fetal heart.
Next, we take the best-performing versions and present their performance being
trained on multi-coil data, which enables their prospective application to the
existing kt-SENSE acquisition and reconstruction pipelines and direct
comparison with the state-of-the-art Complementary Time-Frequency domain
Network (CTFNet) proposed for gated adult heart MRI reconstruction.

##  2 Methods

We investigate the reconstruction of free-breathing dynamic fetal heart MRI
volumes acquired with a multi-coil receiver array as a part of kt-SENSE [22]
algorithm. We use the fully-sampled low-resolution data acquired from scanner
to study DL methods to recover real depiction of anatomy rather than mimicking
conventional reconstruction algorithms with their biases. The data is sampled
in kt space, but it can be represented in temporal image space (xt) and
temporal frequency image space (xf) as well. First, we use the coil-combined
SENSE [15] data to study the reconstruction quality of dynamic features of
fetal heart using a set of modified U-Net models [20]. Next, we take the best-
performing models and train them directly on multi-coil data to use the
advantages of the diverse coil data. Training on coil data allows us to
optimise the models in a clinically relevant way to work with the undersampled
data acquired prospectively from the scanner. Finally, we compare the models
with an iterative Complementary Time-Frequency Domain Network (CTFNet) [16],
which was introduced as a state-of-the-art method for adult cine MRI
reconstruction.

Figure 2: The architecture with optional data consistency (DC) layer [21] and
skip connection propagating temporal average. The skip connection is used for
3D models trained on data in the xf domain.

The 2D version of the U-Net based model with optional data consistency (DC)
layer [21] in Figure 2 processes each complex-valued image frame in xt space
independently without explicitly exploiting the spatio-temporal correlations
available in fetal cardiac data. To enrich the input with temporal
information, we add a sliding window average or a temporal average to the
undersampled data as additional input channels. The sliding window average is
a sum of $R$ consecutive image frames, where $R=8$ is the acceleration factor
of undersampling. Temporal averaging delivers an average of all frames scaled
by acceleration factor $R$.

The 3D version of the U-Net based model with an optional DC layer [21] in
Figure 2 processes the volumes that contain all available temporal information
within the slice volume. In contrast to the 2D case, the 3D models can process
data in the temporal frequency (xf) domain, which is a sparser representation
than the xt representation and usually helps to improve the reconstruction
quality [13, 22]. Since the xf representation has most of the energy
concentrated in the temporal average frame, the optimisation of the loss
function is likely to favour reconstruction of the temporal average rather
than the lower energy dynamic temporal frequencies. To shift the focus to non-
zero frequency frames, we add the temporal average to the 3D U-Net output via
a skip connection shown in Figure 2.

Our fetal cardiac MRI dataset includes multi-planar stacks of multi-slice
multi-coil dynamic fetal cardiac MRI scans acquired from 56 subjects (3
healthy volunteers, 53 patients with congenital heart diseases, $55809$
dynamic 3D coil volumes). The bSSFP sequence [2] was used together with
regular Cartesian kt undersampling [23], voxel size $2.0\times 2.0\times 6.0$
mm, $8\times$ acceleration, and 28 coil receiver to acquire the data on a
Philips Ingenia 1.5T MR system. Ethical approvals were obtained (REC
14/LO/1806, REC 07/H0707/105), and each subject gave informed consent. A
subset of $20\%$ of cases chosen on a patient level is used for testing only.
The rest of the data is used for training the models with $20\%$ of it set
apart for validation. The low-resolution fully-sampled signal is sampled
across $19$ central k-space lines and zero-padded in the phase-encoding
direction producing images of resolution $152\times 400$ for $64$ frames, with
a temporal resolution of $72$ ms per frame, which is sufficient to capture
fetal cardiac motion [19]. In addition, coil sensitivity maps and coil noise
covariance matrix were acquired for each multi-coil volume, which we use to
normalise the data to the unit noise level. While the coil data forms our
multi-coil dataset, we create an additional coil-combined dataset by combining
coil data using SENSE reconstruction [15]. To mimic the kt-SENSE [22]
acquisition sampling used to collect the dataset, we retrospectively
undersample data with the uniform lattice pattern [23] and acceleration factor
$R=8$.

The U-Net architectures follow the original implementation [20] with
convolutional kernel size $3$ and $4$ downsampling steps with $2\times 2$ max
pooling. The optional data consistency (DC) layer has three modes: no DC,
forced DC and adjustable DC. The forced option replaces the output of the
model with available input data, while the adjustable option uses a merging
coefficient which is optimised as an additional model parameter. For both
datasets, the U-Net modifications were trained to optimise the
$\mathcal{L}_{1}$ loss function for $50$ epochs using Adam [9] with a learning
rate of $0.0001$ and exponential decay of $0.95$ using the PyTorch framework
[14]. The final set of model parameters is chosen based on the performance of
the models on the validation subset.

In the case of CTFNet, the architecture follows the original implementation
and training procedure [16]. The model was tuned over $150$ epochs optimising
the $\mathcal{L}_{1}$ loss function on the patches using Adam with the same
learning rate and decay as for U-Net-based architectures. In addition, we used
adjustable DC coefficient to merge the available input information into model
prediction.

The evaluation is performed for $14$ modifications of U-Net trained on the
coil-combined dataset and for the $3$ best-performing versions of U-Net
together with CTFNet trained on multi-coil data. The quantitative evaluation
compares coil-combined predicted volumes and ground truth data in the xt
domain per volume according to normalised mean squared error (NMSE), mean
squared error (MSE), mean absolute error (MAE), peak signal-to-noise ratio
(PSNR) and structural similarity (SSIM) over a masked body region. While the
NMSE, MSE and MAE compare tensors with complex intensities, magnitude tensors
are evaluated using PyTorch Image Quality (PIQ) [8] implementation of PSNR and
SSIM [7]. The presence of important dynamic features of fetal heart is
evaluated visually in temporal and frequency domains.

##  3 Results

Table 1: Comparison of the U-Net models trained on coil-combined dataset.  Model description | NMSE $\downarrow$ | MSE $\downarrow$ | MAE $\downarrow$ | PSNR $\uparrow$ | SSIM $\uparrow$
---|---|---|---|---|---
2D U-Net, no DC | $0.7976$ | $4102.3838$ | $49.3082$ | $12.2359$ | $0.6209$
2D U-Net, adjustable (adj.) DC | $0.7829$ | $4019.8306$ | $49.0102$ | $12.3327$ | $0.6324$
2D U-Net, forced DC | $0.7715$ | $3967.0254$ | $49.1194$ | $12.3991$ | $0.6393$
2D U-Net, sliding window | $0.0062$ | $32.0378$ | $4.1111$ | $33.7646$ | $0.9826$
2D U-Net, temporal average | $0.0176$ | $91.4503$ | $5.7255$ | $29.6221$ | $0.9658$
3D U-Net, xt, no DC | $0.0130$ | $67.1712$ | $5.7132$ | $30.2262$ | $0.9678$
3D U-Net, xt, adj. DC | $0.0108$ | $55.7603$ | $5.3444$ | $31.0387$ | $0.9710$
3D U-Net, xt, forced DC | $0.0107$ | $55.1941$ | $5.3293$ | $31.0834$ | $0.9713$
3D U-Net, xf, no DC | $0.0097$ | $50.7774$ | $4.8127$ | $31.6965$ | $0.9742$
3D U-Net, xf, adj. DC | $0.0091$ | $47.1734$ | $4.7795$ | $32.0303$ | $0.9772$
3D U-Net, xf, forced DC | $0.0087$ | $45.5490$ | $4.7054$ | $32.2168$ | $0.9774$
3D U-Net, xf, skip connect, no DC | $0.0053$ | $27.7157$ | $3.6231$ | $34.4853$ | $0.9854$
3D U-Net, xf, skip connect, adj. DC | $0.0049$ | $25.5143$ | $3.5402$ | $34.8319$ | $0.9863$
3D U-Net, xf, skip connect, forced DC | $0.0049$ | $25.3647$ | $3.5373$ | $34.8663$ | $0.9864$
Figure 3: Comparison of the models trained on coil-combined dataset. The
figure shows axial frame view and a slice through fetal heart (red line) in
temporal (xt) and frequency (xf) domains for ground truth volume and each
model prediction with the corresponding error maps.

In case of model optimisation using coil-combined data, the best results were
shown by 3D U-Nets with temporal average skip connection and data consistency
trained using the xf representation of data. The model managed to deliver the
best values according to evaluated metrics for both forced and adjustable
modes of data consistency layer (Table 1). The next best performance was
achieved using the same model without data consistency. Qualitatively, the
models were highly effective at recovering accurate image depictions of static
or slowly moving maternal and fetal anatomy as revealed by the subtraction
images in Figure 3. Even though the 3D U-Net with data consistency and skip
connection delivered the closest to ground truth results for rapid changes in
small regions such as fetal heart, there was still a clear under-
representation of the beating of a tiny heart seen in both temporal and
frequency domains.

Additional access to temporal information played a crucial role in improving
the performance of the trained models. In the simplest case of a 2D U-Net with
DC, the frame-wise training approach fails to deliver reliable results with
model overfitting on training data. Temporal average and sliding window
average information supplied with the input boosted the performance for all
evaluated metrics compared to 2D U-Net without access to an additional input
of temporal information. The additional inputs helped to improve the 2D U-Net
performance reducing the NMSE more than $100$ and almost $50$ times for
sliding window and temporal average injections respectively and improving the
SSIM to $0.9826$ and $0.9658$. The same trend can be seen in Figure 3 as the
models are able to recover the main features of a slice, while 2D U-Net with
sliding window resolved some slow dynamic features as well.

All variants of 3D U-Net showed improved performance compared to the 2D U-Net
with DC according to evaluated metrics. Qualitatively, 3D models recovered
more information about anatomy movements and resolved aliasing artefacts
slightly better. The 3D U-Net case showed positive changes in model
performance moving from a temporal representation of the data to a sparser xf
domain and additional propagation of temporal average via skip connection. The
combination of sparse data representation and skip connection helped to
outperform 2D U-Net with sliding window, recovering a more detailed depiction
of the fetal heart beating in both temporal and frequency domains (Figure 3).

Figure 4: Comparison of the models trained on multi-coil dataset. The figure shows axial frame view and a slice through fetal heart (red line) in temporal (xt) and frequency (xf) domains for ground truth volume and each model prediction with the corresponding error maps. Table 2: Comparison of the models trained on multi-coil dataset.  Model description | NMSE $\downarrow$ | MSE $\downarrow$ | MAE $\downarrow$ | PSNR $\uparrow$ | SSIM $\uparrow$
---|---|---|---|---|---
CTFNet, adj. DC | $0.0082$ | $52.2186$ | $3.5009$ | $34.6011$ | $0.9869$
3D U-Net, xf, skip connect, no DC | $0.0032$ | $16.5106$ | $2.7226$ | $36.9108$ | $0.9897$
3D U-Net, xf, skip connect, adj. DC | $0.0032$ | $16.3916$ | $2.7202$ | $36.9298$ | $0.9897$
3D U-Net, xf, skip connect, forced DC | $0.0032$ | $16.3363$ | $2.7088$ | $36.9645$ | $0.9898$

The introduction of a data consistency layer enhanced the performance of all
U-Net-based models and improved the evaluated metrics (Table 1). The forced
mode for DC enabled slightly better performance across the models than an
adjustable injection of the available input into output.

In the case of multi-coil data, three versions of 3D U-Net in xf domain with
skip connection and CTFNet were fine-tuned and compared. The 3D U-Net with
skip connection in xf space and forced DC delivered the best performance
(Table 2). The 3D U-Net with adjustable and no DC showed the second and the
third-best results, outperforming the state-of-the-art CTFNet model proposed
for a superficially similar task of adult heart reconstruction. The image
representation of prediction delivered by the best-performing 3D U-Net has
similar to the ground truth depiction of the anatomy in Figure 4. However, the
dynamic features of the recovered fetal heart remain underrepresented in both
temporal and frequency domains.

##  4 Discussion

In this work, we studied the reconstruction quality of kt-SENSE acquired fetal
heart MRIs introducing gradual improvements to the U-Net backbone model. Most
of the modifications delivered faithful reconstructions of the maternal
anatomy and some dynamic features of adult breathing and fetal motion. The
best performance was delivered by the 3D U-Net with forced DC and skip
connection optimised on xf data representations. The quantitative evaluation
reported excellent performance according to estimated global image measures.
The reconstruction results showed a clear depiction of the maternal and main
fetal features. However, there is a room for further improvements to recover
the highly-dynamic features of fetal heart.

The CTFNet performed less well than the best U-Net architectures by all
measures. It was able to recover the large-scale anatomy, but the periodic
dynamics and tiny fetal heart size limited the reconstruction of fetal
heartbeat.

Notable performance was shown by the 2D U-Net with sliding window, which
outperformed the basic 3D U-Net, even though the latter should have benefited
from access to all available frames. It is evident that the sliding window
average is highly effective at resolving the aliasing artefacts preserving
slower time variations. Still, the reconstructed details could not fully
represent the fetal heartbeat.

In this work, we considered training the models to recover real-time fully-
sampled low-resolution ground truth from data undersampled with uniform
Cartesian undersampling pattern and acceleration factor $8$. Such data
strategy allows us to incorporate the presented models trained on coil data
directly into existing fetal cardiac MRI pipelines based on kt-SENSE
acquisition used to sample the dataset. In addition, the use of fully-sampled
low-resolution data helps to avoid biases that models could grasp from
learning high-resolution reconstruction delivered by conventional methods.
While one could use other acquisition planning with non-uniform non-Cartesian
patterns, lower acceleration factor or data binning to deliver better
reconstruction quality [4, 10, 16, 18], the produced results would be out of
touch with the acquisition procedure used to collect the dataset used in our
study.

The presented results showed that the metrics helped to evaluate the global
reconstruction quality. However, they were less effective in describing the
errors that only occur in small spatial regions. Therefore, we believe that
more localised metrics together with more advanced backbone architectures
could push further the reconstruction quality of fetal heart delivered by the
DL models. While the local measures could help to address the unbalanced
dynamic features in data, a more complex backbone could include explicit
features focused on motion reconstruction.

##  5 Conclusion

In this work, we studied the challenge of fetal cardiac MRI reconstruction
using deep learning models. We progressively improved the performance of the
U-Net backbone by introducing a set of modifications, which resulted in a
systematic comparison of $14$ versions of the model and the cutting-edge
CTFNet, designed for adult cardiac imaging. The most effective model was 3D
U-Net with data consistency and temporal average skip connection trained in xf
domain according to both qualitative and quantitative assessments. The CTFNet
model designed for adult imaging data was not that effective for fetal cardiac
reconstruction, highlighting the more challenging nature of the fetal heart
compared to the adult heart. The best-performing networks were highly
effective at recovering the large-scale field of view. However, they were
unable to fully recover the detailed dynamic features of the fetal heart. This
feature of fast change that is highly localised suggests both more targeted
training and evaluation methods might be needed for fetal heart application.
Exploring these will be the subject of future work.

##  6 Acknowledgements

We appreciate the funding from EPSRC Centre for Doctoral Training in Smart
Medical Imaging EP/S022104/1, support from Philips Medical Systems and core
funding from the Wellcome/EPSRC Centre for Medical Engineering WT
203148/Z/16/Z and NIHR Biomedical Research Centre at Guy’s and St Thomas’ NHS
Trust.

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