# FaBiAN: A Fetal Brain magnetic resonance Acquisition Numerical phantom

Hélène Lajous  Department of Radiology, Lausanne University Hospital (CHUV)
and University of Lausanne (UNIL), Lausanne, Switzerland  CIBM Center for
Biomedical Imaging, Switzerland<EMAIL_ADDRESS>Christopher W. Roy
Department of Radiology, Lausanne University Hospital (CHUV) and University of
Lausanne (UNIL), Lausanne, Switzerland  Tom Hilbert  Department of Radiology,
Lausanne University Hospital (CHUV) and University of Lausanne (UNIL),
Lausanne, Switzerland  Advanced Clinical Imaging Technology (ACIT), Siemens
Healthcare, Lausanne, Switzerland  Signal Processing Laboratory 5 (LTS5),
Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
Priscille de Dumast  Department of Radiology, Lausanne University Hospital
(CHUV) and University of Lausanne (UNIL), Lausanne, Switzerland  CIBM Center
for Biomedical Imaging, Switzerland  Sébastien Tourbier  Department of
Radiology, Lausanne University Hospital (CHUV) and University of Lausanne
(UNIL), Lausanne, Switzerland  Yasser Alemán-Gómez  Department of Radiology,
Lausanne University Hospital (CHUV) and University of Lausanne (UNIL),
Lausanne, Switzerland  Jérôme Yerly  Department of Radiology, Lausanne
University Hospital (CHUV) and University of Lausanne (UNIL), Lausanne,
Switzerland  CIBM Center for Biomedical Imaging, Switzerland  Thomas Yu
Signal Processing Laboratory 5 (LTS5), Ecole Polytechnique Fédérale de
Lausanne (EPFL), Lausanne, Switzerland  Hamza Kebiri  Department of Radiology,
Lausanne University Hospital (CHUV) and University of Lausanne (UNIL),
Lausanne, Switzerland  CIBM Center for Biomedical Imaging, Switzerland  Kelly
Payette  Center for MR Research, University Children’s Hospital Zurich,
University of Zurich, Zurich, Switzerland  Neuroscience Center Zurich,
University of Zurich, Zurich, Switzerland  Jean-Baptiste Ledoux  Department of
Radiology, Lausanne University Hospital (CHUV) and University of Lausanne
(UNIL), Lausanne, Switzerland  CIBM Center for Biomedical Imaging, Switzerland
Reto Meuli  Department of Radiology, Lausanne University Hospital (CHUV) and
University of Lausanne (UNIL), Lausanne, Switzerland  Patric Hagmann
Department of Radiology, Lausanne University Hospital (CHUV) and University of
Lausanne (UNIL), Lausanne, Switzerland  Andras Jakab  Center for MR Research,
University Children’s Hospital Zurich, University of Zurich, Zurich,
Switzerland  Neuroscience Center Zurich, University of Zurich, Zurich,
Switzerland  Vincent Dunet  Department of Radiology, Lausanne University
Hospital (CHUV) and University of Lausanne (UNIL), Lausanne, Switzerland
Mériam Koob  Department of Radiology, Lausanne University Hospital (CHUV) and
University of Lausanne (UNIL), Lausanne, Switzerland  Tobias Kober  Department
of Radiology, Lausanne University Hospital (CHUV) and University of Lausanne
(UNIL), Lausanne, Switzerland  Advanced Clinical Imaging Technology (ACIT),
Siemens Healthcare, Lausanne, Switzerland  Signal Processing Laboratory 5
(LTS5), Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland
Matthias Stuber  Department of Radiology, Lausanne University Hospital (CHUV)
and University of Lausanne (UNIL), Lausanne, Switzerland  CIBM Center for
Biomedical Imaging, Switzerland  Meritxell Bach Cuadra  CIBM Center for
Biomedical Imaging, Switzerland  Department of Radiology, Lausanne University
Hospital (CHUV) and University of Lausanne (UNIL), Lausanne, Switzerland

###### Abstract

Accurate characterization of _in utero_ human brain maturation is critical as
it involves complex and interconnected structural and functional processes
that may influence health later in life. Magnetic resonance imaging is a
powerful tool to investigate equivocal neurological patterns during fetal
development. However, the number of acquisitions of satisfactory quality
available in this cohort of sensitive subjects remains scarce, thus hindering
the validation of advanced image processing techniques. Numerical phantoms can
mitigate these limitations by providing a controlled environment with a known
ground truth. In this work, we present FaBiAN, an open-source Fetal Brain
magnetic resonance Acquisition Numerical phantom that simulates clinical
T2-weighted fast spin echo sequences of the fetal brain. This unique tool is
based on a general, flexible and realistic setup that includes stochastic
fetal movements, thus providing images of the fetal brain throughout
maturation comparable to clinical acquisitions. We demonstrate its value to
evaluate the robustness and optimize the accuracy of an algorithm for super-
resolution fetal brain magnetic resonance imaging from simulated motion-
corrupted 2D low-resolution series as compared to a synthetic high-resolution
reference volume. We also show that the images generated can complement
clinical datasets to support data-intensive deep learning methods for fetal
brain tissue segmentation.

###### keywords:

Fetal brain magnetic resonance imaging (MRI); Numerical phantom; Extended
phase graph (EPG) simulations; Fast spin echo (FSE) sequence; Half-Fourier
Acquisition Single-shot Turbo spin Echo (HASTE) sequence; Single-Shot Fast
Spin Echo (SS-FSE) sequence; Super-Resolution (SR) reconstruction; Data
augmentation; Fetal brain tissue segmentation

## Introduction

Today, there is a growing awareness of the importance of early brain
development on health later in life[1, 2, 3, 4, 5, 6, 7, 8, 9] as brain
maturation involves complex and interconnected structural and functional
processes that can be altered by various genetic and environmental factors.
Magnetic resonance imaging (MRI) may be required during pregnancy to
investigate equivocal situations as a support for diagnosis and prognosis, but
also for postnatal management planning[10]. In clinical routine, T2-weighted
(T2w) fast spin echo (FSE) sequences are used to scan multiple 2D thick slices
that provide information on the whole brain volume with a good signal-to-noise
ratio (SNR) while minimizing the effects of random fetal motion during
acquisition[11]. However, stochastic movements of the fetus in the womb cause
various artefacts in the images, including drops in signal intensity. Post-
processing approaches built on motion estimation and correction can compensate
for such artefacts. Especially, super-resolution (SR) reconstruction
techniques take advantage of the redundancy between low-resolution (LR) series
acquired in orthogonal orientations to reconstruct an isotropic high-
resolution (HR) volume of the fetal brain with reduced intensity artefacts and
motion sensitivity[12, 13, 14, 15, 16, 17]. Navigating through the resulting
SR volume provides valuable information on the developing brain anatomy,
including consistent biometric measurements[18, 19, 20]. Besides, fetal brain
tissue segmentation is critical for further investigation of brain
development, especially for volumetric evaluation[21, 22, 23, 24, 25]. Manual
segmentation is a cumbersome and time-consuming task. Therefore, supervised
deep learning approaches that rely on annotated data have emerged as accurate
techniques for automated delineation of the fetal brain[22, 23, 24, 26]. The
development and validation of such advanced image processing and analysis
methods require access to large-scale data to account for the subject
variability, but the number of good quality, exploitable MR acquisitions
available in this sensitive cohort remains relatively scarce.

Numerical simulations can mitigate these limitations by providing a controlled
environment with a known ground truth for accurate, robust and reproducible
research[27, 28]. MR developments often rely on computer simulations that
enable pulse sequence design, accurate prototyping and evaluation of new
advanced acquisition schemes as well as validation of reconstruction
techniques in a controlled setting[29, 27, 30, 31, 28]. Such platforms are
also valuable educational tools for physicists and technologists[29, 30]. In
this sense, MR simulations can efficiently complement or even substitute the
design and use of sophisticated experimental phantoms, as well as experiments
on animal models or even on human volunteers[30]. MR simulators can be
designed to address multiple challenges, such as system imperfections,
multichannel transmission, correction/suppression of image artefacts, and
optimization of specific absorption rate (SAR)[32, 31]. Motion is a major
hurdle in various MRI applications, from cardiovascular MR to functional MRI
analysis and fetal imaging, as it is responsible for artefacts in the images
and can lead to erroneous data analysis and interpretation[32, 27, 30, 28].
Whereas periodic movements can be directly related to physiological processes
such as breathing or a heartbeat, and may therefore be compensated during
post-processing, stochastic fetal motion impedes the repeatability of
measurements[28] and thus hinders retrospective motion correction. The
difficulty of estimating such unpredictable movements results in the lack of
any ground truth, yet necessary for the validation of new methods[32].
Numerical phantoms are an interesting alternative that offers a fully scalable
and flexible environment where any image-acquisition, -reconstruction, or
-processing technique can be evaluated, optimized, and validated from a
collection of synthetic, yet realistic data that simulate multiple controlled
conditions. Furthermore, the results obtained by these various strategies can
be quantitatively compared to each other through simulated reference data
based on full-reference image quality assessment metrics such as the mean
squared error (MSE), the peak signal-to-noise ratio (PSNR), or even the more
perceptual structural similarity index (SSIM)[33, 12, 34].

In contrast to a simplified analytical description of the MR signal arising
from proton isochromats, advanced developments in the field of MRI require
more realistic numerical simulations[31]. Two main approaches have been
investigated: on one hand, (i) the analytical numerical formalism is based on
a mathematical description of both the anatomy and the MR experiment as in the
Shepp-Logan head phantom[35], and on the other hand, (ii) voxel-based phantoms
are usually derived from segmented clinical acquisitions relevant to the
targeted application[27]. The correspondence between the image and the
corresponding k-space is governed by the continuous Fourier transform in
analytical numerical models which enables an accurate representation of
k-space, whereas it is approximated by its discrete version in their voxel-
based equivalents. Analytical numerical phantoms are powerful tools to study
k-space truncation artefacts while voxel-based simulations can be used to also
model physiological processes and motion that may alter the acquisitions[27,
28]. However, spatial and temporal resolutions depend on the original images
from which voxel-based phantoms are derived, which may limit their use in
reproducibility studies. Hybrid phantoms have been developed to leverage both
approaches and overcome their respective limitations, resulting in versatile
and realistic models as in the Mathematical Cardiac-Torso (MCAT), the extended
Cardiac-Torso (XCAT) and the MRXCAT phantoms[27, 28]. Depending on the
targeted application, advanced phantoms can be built on these models to
include more features as in the case of the fetal extended Cardiac-Torso
cardiovascular magnetic resonance imaging (Fetal XCMR) phantom that combines
two independent XCAT models of both the anatomy and physiology of a mother and
her baby with a simulation framework for 2D cardiovascular magnetic resonance
(CMR) acquisitions[28]. Paradoxically, the diversity of MRI simulators makes
it difficult to compare one setup to another[27]. Examples of advanced MRI
simulation platforms based on numerical solutions of the Bloch equations
include the Jülich Extensible MRI Simulator (JEMRIS)[36] which makes it
possible to simulate motion during acquisition, the MRiLab[31] that is built
on the generalized multi-pool exchange model, a more biologically relevant
tissue model, and the Magnetic Resonance Imaging SIMULator (MRISIMUL)[37]
which uses Graphics Processing Units (GPU) resources of a computer to enable
complex large-scale analysis without any simplifications of the underlying MRI
model. Indeed, it is worth noticing that realistic MRI simulations are
hampered by the high computational burden associated with the 3D
representation of the simulated object and the introduction of motion during
acquisition[30, 31]. Although the parallelization of calculations on computer
clusters allows to speed up the simulations, such advanced infrastructures are
not always available.

To our knowledge, there is no simulation framework for fetal brain MRI. In
this work, we present FaBiAN, an open-source Fetal Brain magnetic resonance
Acquisition Numerical phantom that simulates T2w images of the _in utero_
developing brain built on segmented HR anatomical images from a normative
spatiotemporal MRI atlas of the fetal brain[10]. It relies on the extended
phase graph (EPG) formalism[38, 39, 40] of the signal formation, a surrogate
for Bloch equations to describe the magnetization response to various MR pulse
sequences, including complex acquisition schemes that involve multiple
radiofrequency pulses and gradients. Modeling the evolution of spin
magnetization depending on tissue properties allows to gain insight into the
obtained MR signal and to evaluate its behavior. Originally suggested to
assess signal intensities in multi-echo experiments with variable flip
angles[41], the EPG algorithm has aroused growing interest in recent years,
especially for precise characterization of echoes[42, 43, 44] and diffusion
effects[45], evaluation of physics-constrained reconstruction methods[46],
sequence pulse design[38, 47, 48] and quantitative MRI techniques[49, 50, 51].
The EPG formalism relies on the Fourier representation of the evolution of
spin magnetization within a voxel after application of various RF pulses and
gradients. It assumes that a single set of relaxation parameters can
characterize a given tissue[40]. The Fourier series are used to account for
the multiple resonant frequencies that may arise from local magnetic field
inhomogeneities within a voxel. The EPG algorithm provides fast and accurate
simulations where the resolution of Bloch equations may be demanding due to
the need to compute a numerical solution for each resonant frequency within a
single voxel.

Simulations of FSE acquisitions of the fetal brain by FaBiAN are based on a
flexible and realistic setup that accounts for intensity non-uniformity fields
and stochastic fetal motion. We investigate the capabilities of the developed
framework and provide a proof of concept of its practical value in two key
application examples. First, we generate LR images with multiple levels of
motion to fine-tune a SR reconstruction algorithm[16, 52]. Then, we explore
the potential of using multiple fetal brain images simulated at different
gestational ages (GA) with several motion amplitudes and a variety of
acquisition parameters for data augmentation in fetal brain tissue
segmentation.

## Methods

### Numerical implementation of FSE sequences

Figure 1 provides an overview of the workflow implemented in MATLAB
(MathWorks, R2019a) to simulate T2w fetal brain images acquired using clinical
FSE sequences. i) High-resolution anatomical images from a normative
spatiotemporal MRI atlas[10] are used as a model of normal fetal brain. ii)
Segmented brain tissues are organized into gray matter, white matter and
cerebrospinal fluid as shown in Table 1, and iii) are assigned relaxometry
properties from the literature at 1.5 T[53, 54, 55, 56, 57] or 3 T[58, 59, 60,
61, 62] accordingly. iv) The T2 decay over time is computed in every voxel of
the HR anatomical images from the sequence parameters using the EPG
formalism[39, 63]. v) The Fourier domain, or k-space, of the simulated images
is sampled from the T2 decay matrix to reflect the process of FSE acquisition
in the presence of random rigid motion. vi) The final simulated images are
recovered by a 2D inverse Fourier transform. As highlighted by Table 2, we
have developed this open-source numerical phantom with the idea of keeping the
framework as general as possible to enable users a large flexibility in the
type of images simulated. As such, multiple acquisition parameters can be set
up with respect to the MR contrast (effective echo time, excitation/refocusing
pulse flip angles, echo spacing, echo train length), the geometry (number of
2D slices, slice orientation, slice thickness, slice gap, slice position,
phase oversampling), the resolution (field-of-view, matrix size), the resort
to any acceleration technique (acceleration factor, number of reference lines)
or to scanner interpolation, as well as other settings related to the age of
the fetus, the radiofrequency transmit field inhomogeneities, the amplitude of
random fetal motion in the three main directions, and the SNR. The entire
simulation pipeline is described in detail in the following.
Code availability - FaBiAN source code is distributed under the open source
BSD 3-Clause License to support its use for research purposes. It can be
downloaded from the following Zenodo repository[64].

Figure 1: Workflow for simulating images of the fetal brain acquired by a FSE sequence (i) from segmented HR anatomical MR images[10], illustrated for a fetus of 30 weeks of GA. (ii) Brain tissues are organized into gray matter, white matter and cerebrospinal fluid. (iii) Anatomical structures are converted to the corresponding MR contrast to obtain reference T1 and T2 maps of the fetal brain at either 1.5 or 3 T. (iv) The EPG algorithm[39, 63] allows to accurately simulate the T2 decay over time in every brain voxel by accounting for the effects of the stimulated echoes, as highlighted by the enlargement of the beginning of the curve. This spatiotemporal information is subsequently used (v) to sample the Fourier domain of the simulated images of the moving fetus. After the addition of noise to match the SNR of real clinical acquisitions, (vi) synthetic FSE images of the fetal brain are eventually recovered by 2D inverse Fourier transform ($2D$ $FT^{-1}$). Gray matter | White matter | Cerebrospinal fluid
---|---|---
Amygdala | Cerebellum | Cerebrospinal fluid
Caudate | Corpus callosum | Lateral ventricle
Cortical plate | Fornix |
Hippocampus | Hippocampal commissure |
Putamen | Intermediate zone |
Subthalamic nuclei | Internal capsule |
Thalamus | Midbrain |
| Miscellaneous |
| Subplate |
| Ventricular zone |
Table 1: Classification of segmented brain tissues[10] as gray matter, white matter and cerebrospinal fluid. GA (weeks) | 30 (from 21 to 38)
---|---
Magnetic field strength (T) | 1.5
Field inhomogeneities | from BrainWeb[65, 66]
Acquisition parameters |
Contrast |
Effective echo time ($ms$) | 90
Echo spacing ($ms$) | 4.08
Echo train length | 224
Excitation flip angle (˚) | 90
Refocusing pulse flip angle (˚) | 180
Geometry |
Slice orientation | sagittal, coronal or transverse
Slice thickness ($mm$) | 3.00
Slice gap ($mm$) | 0.3
Number of slices | 46
Phase oversampling ($\%$) | 80.3571
Shift of the field-of-view ($mm$) | $\pm 1.6$
Resolution |
Field-of-view ($mm^{2}$) | $360\times 360$
Base resolution ($voxels$) | 320
Phase resolution ($\%$) | 70
Reconstruction matrix | 320 x 404
Zero-interpolation filling | None
Acceleration technique |
Reference lines | 42
Acceleration factor | 2
Amplitude of 3D rigid motion |
Little motion |
Translation ($mm$) in x | $\pm 1$
Translation ($mm$) in y | $\pm 1$
Translation ($mm$) in z | $\pm 1$
3D rotation (˚) | $\pm 2$
Moderate motion |
Translation ($mm$) in x | $\pm 3$
Translation ($mm$) in y | $\pm 3$
Translation ($mm$) in z | $\pm 3$
3D rotation (˚) | $\pm 5$
Strong motion |
Translation ($mm$) in x | $\pm 4$
Translation ($mm$) in y | $\pm 4$
Translation ($mm$) in z | $\pm 4$
3D rotation (˚) | $\pm 8$
Noise |
Mean | 0
Standard deviation | 0.15
Table 2: The flexibility of FaBiAN is illustrated by the number of sequence
parameters and settings available to the user. Default values are given for a
fetus of 30 weeks of GA and for the clinical HASTE protocol dedicated to fetal
brain examination at CHUV (see Datasets).

#### Fetal brain model and MR properties

Our numerical phantom is based on segmented 0.8-mm-isotropic anatomical images
(Fig.1-i) from the normative spatiotemporal MRI atlas of the developing brain
built by Gholipour and colleagues from normal fetuses scanned between 19 and
39 weeks of gestation[10]. Due to the lack for ground truth relaxometry
measurements in the fetal brain, all thirty-four segmented tissues are merged
into three classes according to medical experts: gray matter, white matter and
cerebrospinal fluid (Fig.1-ii and Table 1). Corresponding T1 and T2 relaxation
times at 1.5 T[53, 54, 55, 56, 57] are assigned to these anatomical structures
to obtain reference T1 and T2 maps, respectively (Fig.1-iii). The value of
these relaxometry properties at 3 T is estimated from the literature[58, 59,
60, 61, 62], assuming that doubling the magnetic field strength from 1.5 T to
3 T increases the T1 relaxation time by approximately 25% in gray matter and
10% in both white matter and cerebrospinal fluid, while the T2 properties
remain unchanged.

#### Intensity non-uniformity (INU) fields

Non-linear slowly-varying INU fields due to transmit field inhomogeneities
(B1+) are based on BrainWeb estimations from real scans to simulate T2w
images[66, 67, 65, 68, 69]. The available 20% INU version is resized to fit
the dimensions of the atlas images and normalized by 1.2 to provide
multiplicative fields in the range of 0.8 to 1.2 over the brain area. It is
subsampled to a 0.1-mm resolution with linear interpolation in the slice
thickness orientation in order to account for B1 bias field variations across
the slice profile.

#### EPG formalism

The EPG algorithm[39, 63] simulates the T2 decay in every voxel of the
anatomical images over each echo train (Fig.1-iv) based on the FSE sequence
pulse design. The T1 and T2 maps of the fetal brain are fed into the EPG
estimation, as well as the realistic INU fields described above that results
in a spatially varying flip angle. The resulting 4D matrix that combines
information about both the anatomy and the magnetic relaxation properties of
the fetal brain is hereafter referred to as the T2 decay matrix.

#### K-space sampling and image formation

The T2 decay matrix is Fourier-transformed and subsequently used for k-space
sampling of the simulated images. For a given echo time (TE), at most one line
from the associated Fourier domain of the T2 decay matrix is used, with the
central line corresponding to the effective TE. If resorting to any
acceleration technique such as GRAPPA interpolation, multiple reference lines
are consecutively sampled around the center of k-space. Beyond, one line out
of two is actually needed to simulate an acceleration factor of two. As a
first approximation, these sampled lines are copied to substitute the missing
lines. According to partial Fourier imaging techniques, the properties of
Hermitian symmetry in the frequency domain are used to fill the entire
k-space. While intra-slice motion can be neglected in FSE sequences, inter-
slice random 3D translation and rotation of the fetal brain are implemented
during k-space sampling (Fig. 1-v). If needed, zero-interpolation filling
(ZIP) is implemented by filling the edges of the simulated k-space with zeros
to reach the desired reconstruction matrix size. Data in k-space are
previously processed using a Fermi low-pass filter with a radius of 0.85 and a
width of 1/23 to avoid Gibbs ringing artefacts[70, 71]. Complex Gaussian noise
(mean, 0; standard deviation, 0.15 for Half-Fourier Acquisition Single-shot
Turbo spin Echo (HASTE) implementation, 0.01 for Single-Shot Fast Spin Echo
(SS-FSE) implementation respectively) is added to simulate thermal noise
generated during the acquisition process and qualitatively match the SNR of
clinical data. The simulated images are eventually recovered by 2D inverse
Fourier transform (Fig.1-vi).

With the aim of replicating the clinical protocol for fetal brain MRI, FSE
acquisitions are simulated in the three orthogonal orientations. Besides, the
position of the field-of-view is slightly shifted by $\pm 1.6mm$ in the slice
thickness orientation to produce additional partially-overlapping datasets in
each orientation.

#### Fetal motion

The amplitude of typical fetal movements is estimated from clinical data[72].
Three levels are defined accordingly for little, moderate and strong motion of
the fetus, with a maximum of $5\%$ corrupted slices over the fetal brain
volume. They are characterized by a uniform distribution of respectively
$[-1,1]mm$, $[-3,3]mm$ and $[-4,4]mm$ for independent translation in every
direction and $[-2,2]$˚, $[-5,5]$˚ and $[-8,8]$˚ for 3D rotation (Fig.1-v).

#### Computational specifications

Since the addition of 3D motion during k-space sampling is expensive in
computing memory, the simulations are run on 16 CPU workers in parallel with
20 GB of RAM each.

### Simulating data from clinical MR acquisitions

#### Clinical datasets

Data were acquired in accordance with the relevant guidelines and regulations,
under the supervision of Ethics Boards composed of representatives at
different levels (hospitals, cantons, and federal state). Mothers of all
fetuses included in the current work provided written informed consent for the
re-use of their data for research purposes. Clinical cases are used as typical
acquisition examples to generate realistic synthetic images of the fetal brain
throughout development and to visually compare the quality of the simulated
images.

Thirteen healthy subjects in the GA range of 21 to 33 weeks were scanned at
Lausanne University Hospital (CHUV) as part of a larger institutional research
protocol approved by the ethical committee of the Canton of Vaud, Switzerland
(CER-VD, decision number: 2021-00124). In particular, these clinical cases are
used to showcase the implemented pipeline and the realistic appearance of the
corresponding synthetic HASTE images, as well as to explore the potential of
FaBiAN in optimizing SR fetal brain MRI.

Fifteen subjects (thirteen neurotypical subjects and two subjects with light
ventriculomegaly) from the Fetal Tissue Annotation Dataset (FeTA)[25] in the
GA range of 21 to 34.6 weeks were scanned at University Children’s Hospital
Zurich (Kispi). Their inclusion in research studies was approved by the
ethical committee of the Canton of Zurich, Switzerland (KEK, decision number:
2016-01019). The original LR series were reconstructed using a simplified
version of the Image Registration Toolkit (SIMPLE IRTK)[14] under Licence from
Ixico Ltd, including rigid registration to template[73]. Preprocessing steps
included the manual creation of a mask for the reference image series,
denoising using the Baby Brain Toolkit module[74] and bias field correction by
3D Slicer[75, 76]. The resulting SR reconstructions were manually segmented
according to the FeTA annotation guidelines[25]. In particular, the clinical
cases from Kispi allow to extend FaBiAN to generate multiple SS-FSE images of
the fetal brain with various settings. We investigate if these simulated
images are realistic enough to replace part of the original data in the
training phase of a deep learning network for fetal brain tissue segmentation,
and to complement a clinical dataset to improve the performance of the
segmentation algorithm.

#### Clinical MRI protocol

Typical fetal brain HASTE images are acquired on patients at 1.5 T (MAGNETOM
Aera, Siemens Healthcare, Erlangen, Germany) with an 18-channel body coil and
a 32-channel spine coil at CHUV. At least three T2w series of 2D thick slices
are acquired in three orthogonal orientations using an ultra-fast multi-slice
HASTE sequence (TR/TE, $1200ms$/$90ms$; flip angle, $90$˚; echo train length,
$224$; echo spacing, $4.08ms$; field-of-view, $360\times 360mm^{2}$; voxel
size, $1.13\times 1.13\times 3.00mm^{3}$; inter-slice gap, $10\%$)[20, 77].
Twenty-two to thirty slices are needed to cover the whole fetal brain
depending on the GA (between 21 and 33 weeks) and size of the fetus, which
corresponds to an acquisition time of between 26 to 36 seconds.

Fetal brain SS-FSE images are acquired on patients on either a 1.5-T or 3-T
clinical GE whole-body scanner (Signa Discovery MR450 or MR750), either using
an 8-channel cardiac coil or body coil, at Kispi. At least three series of 2D
thick slices are acquired in three orthogonal orientations using a T2w SS-FSE
sequence (TR/TE, $3000-3200ms$/$116.032-124.08ms$; flip angle, $90$˚; echo
train length, $224$; echo spacing, $3-3.2ms$; field-of-view, from $240\times
240mm^{2}$ to $300\times 300mm^{2}$; isotropic in-plane resolution, from
$0.47\times 0.47mm^{2}$ to $0.59\times 0.59mm^{2}$; slice thickness,
$3.00-4.00mm$)[25]. Twenty-four to forty-three slices are needed to cover the
whole fetal brain depending on the GA (between 21 and 34.6 weeks) and size of
the fetus, which corresponds to an acquisition time of between one to two
minutes.

The position of the field-of-view is slightly shifted in the slice thickness
orientation to acquire additional data with some redundancy. In clinical
practice, a total of six partially-overlapping LR series are commonly acquired
in the three orthogonal orientations for subsequent SR reconstruction of the
fetal brain.

#### Simulated datasets

The general framework presented in this paper makes it possible to simulate
the clinical acquisition schemes described above for different MR vendors, at
various magnetic field strengths, and with realistic SNR and amplitude of
fetal movements.

The clinical cases from CHUV are used as representative examples of fetal
brain HASTE acquisitions: the corresponding sequence parameters are replicated
to simulate HASTE images of the fetal brain at various GA. The amplitude of
fetal movements in clinical acquisitions is assessed by an engineer expert in
MR image analysis to ensure a similar level of motion in the simulated images.
Besides, a 3D HR 1.1-mm-isotropic HASTE image of the fetal brain is simulated
without noise or motion to serve as a reference for the quantitative
evaluation of SR reconstructions from simulated LR 1.1-mm-in-plane HASTE
images.

SS-FSE images of the fetal brain are simulated for fifteen subjects in the GA
range of 21 to 35 weeks at either 1.5 T or 3 T. We reproduce the same
acquisition parameters and geometry as in the clinical dataset from Kispi. For
every subject, three partially-overlapping series are simulated in each of the
three orthogonal orientations, two with little motion and one with moderate
motion.

Figure 2 displays the histograms of the distribution of GA across the original
clinical cases and the simulated subjects according to the MR vendor and the
main magnetic field strength, and of the in-plane isotropic resolution in the
corresponding LR images of the fetal brain.

Figure 2: Distribution of (a) GA across all clinical cases and simulated
subjects involved in this work and (b) in-plane isotropic resolution in the
corresponding LR FSE images of the fetal brain.

#### Motion index

A motion index is defined to support the assessment of the level of fetal
movements in acquisitions and simulations based on binary masks that are drawn
on each LR series to cover the whole fetal brain volume[78]. This index is
estimated from tracking the slice-to-slice displacement of the 2D brain mask
centroids. It is computed as the sum of distances between the centroids of the
2D brain masks of adjacent slices over the central third of the slices of the
3D brain mask normalized by the number of slices considered. This index was
correlated with the assessment of the motion level in multiple clinical
acquisitions by an engineer expert in MR image analysis. An index less than
0.5 mm stands for little motion, in the range of [0.5,1]mm for moderate
motion, and larger than 1 mm for strong motion. This motion index correlates
well with the assessment of motion by an engineer expert in MR image analysis
and is used in the following to estimate the amplitude of fetal movements in
clinical acquisitions and ensure a similar level of motion in the simulated
images.

### Qualitative assessment

Two medical doctors specialized in neuroradiology and pediatric
(neuro)radiology respectively, provided qualitative assessment of the HASTE
images of the fetal brain simulated in the GA range of 21 to 33 weeks, in the
three orthogonal orientations and with various levels of motion. Special
attention was paid to the MR contrast between brain tissues, to the SNR, to
the delineation and sharpness of the structures of diagnostic interest that
are analyzed in clinical routine, as well as to characteristic motion
artefacts. To facilitate visualization and qualitative comparison of images
throughout this manuscript, simulated brain images are co-registered with
clinical acquisitions of fetuses at the same GA and with equivalent level of
motion, using the landmark registration of 3D Slicer[79].

### Application 1: SR reconstruction

#### Implementation of SR reconstruction

Orthogonal T2w LR HASTE series contain redundant information that enables the
subsequent reconstruction of a 3D HR volume. Clinical acquisitions,
respectively simulated images, are combined into a motion-free 3D image
$\mathbf{\hat{X}}$ using the Total Variation (TV) SR reconstruction
algorithm[16, 52] which solves:

$\displaystyle\mathbf{\hat{X}}=\arg\min_{\mathbf{X}}\
\frac{\lambda}{2}\sum_{kl}\|\underbrace{\mathbf{D}_{kl}\mathbf{B}_{kl}\mathbf{M}_{kl}}_{\mathbf{H}_{kl}}\mathbf{X}-\mathbf{X}_{kl}^{LR}\|^{2}+\|\mathbf{X}\|_{TV},$
(1)

where the first term relates to data fidelity with $k$ being the $k$-th LR
series $\mathbf{X}^{LR}$ and $l$ the $l$-th slice, $\|\mathbf{X}\|_{TV}$ is a
TV prior introduced to regularize the solution, and $\lambda$ balances the
trade-off between data fidelity and regularization terms (default setting,
$\lambda$=0.75). $\mathbf{D}$ and $\mathbf{B}$ are linear downsampling and
Gaussian blurring operators given by the acquisition characteristics.
$\mathbf{M}$ encodes the rigid motion of slices.

Clinical acquisitions from CHUV and the corresponding simulated images are
reconstructed using the docker version of the MIAL Super-Resolution Toolkit
reconstruction pipeline[16, 52].

#### Regularization setting

LR HASTE images of the fetal brain are simulated to mimic clinical MR
acquisitions of three subjects of 26, 30 and 33 weeks of GA respectively, with
particular attention to ensuring that the motion level is respected. For each
subject, a SR volume of the fetal brain is reconstructed from the various
orthogonal acquisitions, either real or simulated (six, respectively seven and
eight series were acquired and are further simulated in the subject of 26,
respectively 30 and 33 weeks of GA), with different values of $\lambda$ (0.1,
0.3, 0.75, 1.5, 3) to study the potential of FaBiAN in optimizing the quality
of the SR reconstruction in a clinical setup. Indeed, the weight $\lambda$ is
a sensitive hyper-parameter in SR methods that are based on solving an inverse
problem. A quantitative analysis is conducted on the resulting SR
reconstructions to determine the value of $\lambda$ that provides the sharpest
reconstruction of the fetal brain with high SNR, namely the smallest
normalized root mean squared error (NRMSE) with respect to the corresponding
synthetic 3D HR ground truth.

#### Number of LR series: an SNR and motion case study

Static LR HASTE images of the fetal brain (GA of 30 weeks) are recovered after
the addition of various levels of complex Gaussian noise (mean, 0; standard
deviation, 0.07, 0.15 or 0.3) to k-space. A standard deviation of 0.15 results
in synthetic images that closely resemble clinical acquisitions. Six
independent realizations of the 2D series are generated for each SNR. A SR
volume of the fetal brain is reconstructed from three, six and nine orthogonal
LR HASTE series using the different realizations. In total, fifty-four SR
volumes are reconstructed.

Additional LR HASTE acquisitions of the fetal brain (GA of 30 weeks, standard
deviation of the noise of 0.15) are simulated with inter-slice motion. The
impact of little and moderate movements of the fetus on SR reconstructions
from various numbers of LR series is studied using a reference series without
motion and with little amplitude of fetal motion respectively.

The different configurations are compared to each other by computing the
NRMSE, the local SSIM and its mean (MSSIM) over the image with respect to the
3D isotropic ground truth. The latter are computed using Matlab _ssim_
function with the standard deviation of the isotropic Gaussian function that
determines the weights of the pixels in a neighborhood to estimate local
statistics set to its default value (1.5), and the dynamic range of the
normalized input images to 255.

### Application 2: Data augmentation for automated fetal brain tissue
segmentation

LR SS-FSE images of the fetal brain are simulated based on the MR sequence
parameters and acquisition settings extracted from the clinical cases scanned
at Kispi to mimic typical MR acquisitions, thus minimizing confounding
factors. The synthetic images are interpolated to $0.8594mm\times 0.8594mm$ in
the in-plane direction to match the resolution of the clinical SR
reconstructions. Label maps are automatically generated from the simulation
framework using a nearest-neighbour interpolation. Two different labels are
assigned to the ventricular system (lateral, third and fourth ventricles) and
to the extra-axial cerebrospinal fluid spaces in the SR reconstructions from
Kispi subjects[25], whereas the segmented HR anatomical images[10] from which
our simulations are derived distinguish the lateral ventricles from the
cerebrospinal fluid[10]. For consistency between brain annotations, we merge
the labels that correspond to structures from the ventricular system and the
cerebrospinal fluid spaces in both models.

#### Network architecture

We designed a convolutional neural network based on the well established U-Net
architecture[80] for biomedical semantic image segmentation, as it recently
proved its ability to perform well for 2D fetal brain MRI tissue
segmentation[22]. The baseline 2D U-Net is trained using an hybrid loss
function $\mathcal{L}_{hybrid}$.

$\displaystyle\mathcal{L}_{hybrid}=(1-\lambda)\mathcal{L}_{cce}+\lambda\mathcal{L}_{dice}$
(2)

where $\mathcal{L}_{cce}$ is the categorical cross-entropy loss function,
$\mathcal{L}_{dice}$ the Dice loss layer that maximizes the Dice coefficient
between network output and manual segmentation[22, 81] to mitigate any
imbalance in the samples from the different classes. $\lambda$ balances the
contribution of the two terms of the loss.

Our 2D U-Net model consists of an encoding and a decoding paths. Each layer in
the encoding path is composed of a cascade of double 3x3 convolutions,
followed by a rectified linear unit (ReLu) activation function and a 2x2 max-
pooling downsampling layer. The number of feature maps is doubled after each
layer, from 32 to 512. In the decoding path, 2x2 upsampled encoded features
concatenated with the corresponding encoding path are 3x3 convolved and passed
through the ReLu activation function. All convolutional layer outputs are
batch normalized. The network prediction is computed with a final 1x1
convolution. The implementation is performed in the framework of TensorFlow
2.5[82] and an Nvidia GeForce RTX 2080 GPU is deployed for training.

#### Experimental design

As indicated in Table 3, we compare four configurations that combine different
proportions of subjects with SR volumes from clinical MR acquisitions and
subjects with simulated LR images: a baseline (_A_) that consists of real data
only (fifteen subjects), a configuration (_B_) that gathers ten original
subjects and five simulated ones, a configuration (_C_) with eight original
subjects and seven simulated ones, and a configuration (_D_) that complements
the fifteen original subjects from the baseline (_A_) with fifteen simulated
ones. Since we could not automatically propagate the annotations on the
simulated images to the corresponding SR reconstruction, and conversely the
labels in the SR reconstruction from clinical acquisitions to the original LR
2D series, three LR series are needed to replace one SR volume. The
segmentation is computed on skull-stripped images to process only the voxels
within the intracranial volume.

Configuration | Number of clinical subjects | Number of simulated subjects | Total number of subjects
---|---|---|---
(_A_) | 15 | 0 | 15
(_B_) | 10 | 5 | 15
(_C_) | 8 | 7 | 15
(_D_) | 15 | 15 | 30
Table 3: Configurations studied to compare the performance of an algorithm for
automated fetal brain tissue segmentation. For each configuration, the
respective number of clinical cases and simulated subjects, as well as the
total number of subjects involved in the cross-validation are reported.

#### Training strategy

Networks are fed with 64-by-64 overlapping patches in the axial orientation.
To avoid any bias, we ensure an equivalent number of 2D patches between an SR-
reconstructed clinical case and three orthogonal LR images simulated for a
given subject. Intensities of all image patches are standardized and each
patch is repeated once using conventional data augmentation operations, namely
by random flip and rotation of the patches ($n$ times, by $n\times 90$˚,
$n\in\llbracket 0,3\rrbracket$).

Five-fold cross-validation approaches (training sets: 12 subjects, validation
sets: 3 subjects) are used to determine the epochs for the learning rate decay
in each configuration.

All networks are trained with an initial learning rate of $0.001$ and a decay
factor of $0.1$. (_A_) networks, respectively (_B_), (_C_), and (_D_)
networks, are trained for $115$ epochs, respectively $138$, $158$, and $190$
epochs, with a learning rate decay scheduled at epochs $[55,75]$, respectively
$[77,109]$, $[95,130]$, and $[94,160]$.

#### Analysis

The performance of the fetal brain tissue segmentation networks is evaluated
based on the Dice similarity coefficient (DSC)[83] that quantifies the overlap
between the predicted segmentation and the manually-annotated ground truth.
The performance metrics are assessed on the validation sets. We report the
average over all folds. _P_ -values of Wilcoxon rank sum test between each
configuration and the baseline (_A_) for individual fetal brain tissue
segmentation are adjusted for multiple comparisons using Bonferroni
correction. _p_ $<0.05$ is considered statistically significant.

## Results

### Computational performance

As highlighted in Figure 1 for a fetus of 30 weeks of GA whose brain is
covered by twenty-five slices, the computation time to convert segmented HR
anatomical images of the fetal brain to MR contrast is in the order of one
second. EPG simulations[39, 63] are run in every voxel of the 3D HR anatomical
images in less than four minutes. For one axial series with either little,
moderate or strong motion, k-space sampling takes less than seven minutes for
HASTE images simulated with an acceleration factor of two, respectively less
than eight minutes for SS-FSE images simulated without using any acceleration
technique.

### Qualitative assessment

Figure 3 illustrates the close resemblance between simulated HASTE images of
the fetal brain and clinical MR acquisitions in terms of MR contrast between
tissues, SNR, brain anatomy and relative proportions across development for
representative subjects in the GA range of 23 to 32 weeks, as well as typical
out-of-plane motion patterns related to the interleaved slice acquisition
scheme. Experts in neuroradiology and in pediatric (neuro)radiology report a
good contrast between gray and white matter, which is important to investigate
the cortex continuity and identify the deep gray nuclei as well as any
neuronal migration defect. They also notice good SNR in the different series
and report proper visualization of the main anatomical structures: the four
ventricles, the corpus callosum, the vermis, the cerebellum, even sometimes
the fornix. Besides, they are able to monitor the evolution of normal gyration
throughout gestation. However, they point out that small structures such as
the hypophyse, the chiasma, the recesses of the third ventricle, and the
vermis folds that look part of the cerebellum, are more difficult to observe.
The cortical ribbon is clearly visible but quite pixelated, which is likely to
complicate the diagnosis of polymicrogyria. White matter appears too
homogeneous, which makes its multilayer aspect barely distinguishable, with an
MR signal that is constant across GA, thus preventing physicians from
exploring the myelination process throughout brain maturation.

Figure 3: Visual inspection and comparison between clinical MR acquisitions
and representative simulated HASTE images of the fetal brain in the three
orthogonal orientations at four different GA (23, 26, 30 and 32 weeks). The
amplitude of movement of the fetus is indicated from the motion index
computation. Red arrows point out typical out-of-plane motion patterns.

### Application 1: SR reconstruction

#### Regularization setting

Thanks to its controlled environment, FaBiAN makes it possible to adjust the
parameter $\lambda$ for optimal SR reconstruction with respect to a simulated
3D isotropic HR ground truth of the fetal brain. Figure 4 explores the quality
of SR fetal brain MRI from LR HASTE images corrupted by motion depending on
the weight of TV regularization in two subjects of 26 and 30 weeks of GA
respectively. Based on the simulations, a high level of regularization
($\lambda=0.1$) provides a blurry SR reconstruction with poor contrast between
the various structures of the fetal brain, especially in the deep gray nuclei
and the cortical plate. In addition, the cerebrospinal fluid appears brighter
than in the reference image. A low level of regularization ($\lambda=3$) leads
to a better tissue contrast but increases the overall amount of noise in the
resulting SR reconstruction. A fine-tuned regularization ($\lambda=0.75$)
provides a sharp reconstruction of the fetal brain with a high SNR and a
tissue contrast close to the one displayed in the reference image. In the SR
images reconstructed from clinical LR HASTE series altered by a little-to-
moderate level of motion, as in the simulations, the structure of the corpus
callosum and the delineation of the cortex are especially well defined for
appropriate TV regularization ($\lambda=0.75$), leading to high-SNR HR images
of the fetal brain. Although the NRMSE between SR reconstructions from
simulated HASTE images and the corresponding ground truth are close to each
other for a given GA across the various weights studied, Figure 5 shows that
the error is systematically minimal for $\lambda=0.75$, which further supports
this parameter setting for optimal SR reconstruction of the fetal brain from
this type of MR images.

Figure 4: Appreciation of the quality of SR reconstruction depending on the
weight $\lambda$ that controls the strength of the TV regularization. The
potential of our framework FaBiAN for optimizing the reconstruction quality
through parameter fine-tuning in the presence of motion is illustrated at two
GA: 26 and 30 weeks. Two representative clinical cases are provided for
comparison. The results for three values of $\lambda$ are presented. For
$\lambda=0.1$, the SR reconstruction looks blurry with poor tissue contrast.
Using $\lambda=3$ improves the contrast but the images look noisy. For
$\lambda=0.75$, the SR reconstruction is sharp with a contrast between
different brain tissues similar to that observed in the 3D isotropic ground
truth. Clinical cases from which the simulated HASTE images are derived
highlight the accuracy of a SR reconstruction for this intermediate value of
$\lambda$, especially with regards to the definition of the corpus callosum
and the delineation of the cortex. Figure 5: NRMSE between SR reconstructions
from simulated data at a GA of 26, 30 and 33 weeks respectively and the
corresponding 3D HR ground truth depending on the weight $\lambda$ of the TV
regularization. Six values of $\lambda$ are tested: 0.1, 0.3, 0.5, 0.75, 1.5
and 3. The NRMSE is minimal for $\lambda$ = 0.75.

#### Number of LR series: an SNR and motion case study

Figure 6 shows the NRMSE and the MSSIM between SR reconstructions from
different numbers of orthogonal LR HASTE series simulated with various SNR or
variable amplitude of movements and a 3D HR reference[84].

Figure 6: (a) NRMSE and (b) MSSIM between SR reconstructions from different
numbers of orthogonal LR HASTE series simulated at a GA of 30 weeks and the
corresponding static 3D HR ground truth. The left panel shows results for
motion-free data with various noise levels, a standard deviation of 0.15
leading to a similar appearance as in clinical acquisitions. The right panel
illustrates how the algorithm performs depending on the amplitude of fetal
movements in the input series.

In the case of static data (Figure 6-left panel), the NRMSE decreases when
increasing the number of series used in the SR reconstruction. According to
both the NRMSE and the MSSIM, the quality of the SR reconstructions resulting
from simulated images with an SNR close to that observed in clinical
acquisitions and from synthetic images with a distribution of complex Gaussian
noise of twice less standard deviation is similar. Noisier images lead to a
slight decrease in the NRMSE, but also in the MSSIM which in turn increases
with the number of series.

The stronger the movements in the LR series, the higher the NRMSE of the
resulting SR reconstruction. The addition of motion-corrupted LR series to
reconstruct a SR volume of the fetal brain does not increase the MSSIM. Data
with slight motion are well handled by the SR algorithm as the MSSIM is
equivalent for SR reconstructions from static images and series with little
motion. In the case of moderate motion, the MSSIM is lower than in the case of
little motion.

Figure 7 highlights the benefit of increasing the number of orthogonal LR
series on the rendering of the SR reconstruction. The higher the number of LR
series combined in the SR reconstruction, even altered by motion, the smoother
the frontal cortex and the sharper the putamen area in the resulting SR
volume[84].

Figure 7: Appreciation of sharpness and tissue contrast enhancement in SR
reconstructions from higher numbers of simulated orthogonal LR HASTE images
corrupted by little motion at a GA of 30 weeks in comparison with the
corresponding static 3D HR ground truth. The frontal cortex looks smoother and
the putamen area sharper in the SR reconstruction from nine series compared to
the SR reconstruction from three series. The mapping of local SSIM values and
the computation of the MSSIM over the corresponding region-of-interest further
support these observations.

### Application 2: Data augmentation for automated fetal brain tissue
segmentation

We aim at proving the realistic appearance of the simulated images
(representative SS-FSE images of two subjects scanned / simulated at 1.5 T and
3 T respectively are provided as Supplementary Material) and demonstrating the
practical value of the developed environment to complement clinical datasets
for data augmentation strategies in deep learning, here with the example of
fetal brain tissue segmentation.

Table 4 shows the mean DSC $\pm$ standard deviation computed for every
segmented brain tissue in each configuration. Overall, the performance of the
segmentation algorithm is maintained when replacing original subjects by
synthetic images obtained from an SS-FSE sequence simulated with the same
acquisition parameters as in the clinical protocol. This trend is also
observed for each individual structure studied. In the configuration (_C_),
the overall DSC for brain tissue segmentation is slightly increased as
compared to the baseline with statistical significance.

| (_A_) C15/S0 | (_B_) C10/S5 | (_C_) C8/S7 | (_D_) C15/S15
---|---|---|---|---
CSF & Ventricles | 0.93 $\pm$ 0.01 | 0.94 $\pm$ 0.01 | 0.94 $\pm$ 0.02 (*) |  0.95 $\pm$ 0.02 (*)
Cortical GM | 0.77 $\pm$ 0.02 | 0.80 $\pm$ 0.04 | 0.81 $\pm$ 0.05 (*) |  0.84 $\pm$ 0.05 (*)
WM | 0.92 $\pm$ 0.01 | 0.92 $\pm$ 0.02 | 0.92 $\pm$ 0.02 |  0.93 $\pm$ 0.02
Cerebellum | 0.88 $\pm$ 0.04 | 0.87 $\pm$ 0.10 | 0.87 $\pm$ 0.09 |  0.92 $\pm$ 0.04 (*)
Deep GM | 0.85 $\pm$ 0.03 | 0.84 $\pm$ 0.10 | 0.87 $\pm$ 0.04 |  0.90 $\pm$ 0.04 (*)
Brain stem | 0.84 $\pm$ 0.03 | 0.85 $\pm$ 0.04 | 0.86 $\pm$ 0.04 |  0.88 $\pm$ 0.03 (*)
Overall | 0.87 $\pm$ 0.06 | 0.87 $\pm$ 0.08 | 0.88 $\pm$ 0.06 (*) |  0.90 $\pm$ 0.05 (*)
Table 4:  DSC (mean $\pm$ standard deviation) in the different configurations
studied for all segmented brain tissues: cerebrospinal fluid (CSF) and
ventricles, cortical gray matter (GM), white matter (WM), cerebellum, deep
gray matter and brain stem, and on average. The number of clinical cases (Cxx)
and the number of simulated subjects (Sxx) are recalled. The segmentation
algorithm performs better (score in bold) in every structure when
complementing the baseline dataset (configuration _A_) with simulated subjects
(configuration _D_). _P_ -values of Wilcoxon rank sum test between each
configuration and the baseline (_A_) for individual fetal brain tissue
segmentation are adjusted for multiple comparisons using Bonferroni
correction. _p_ $<0.05$ (*) is considered statistically significant.

Since the simulated images look realistic enough to substitute for original
clinical acquisitions, we further investigate if they can be used to
complement real data in a data augmentation strategy. As expected, increasing
the training data by a combination of fifteen original cases and fifteen
simulated subjects (configuration _D_) results in a significantly improved
mean DSC of 0.90 $\pm$ 0.05 over the six segmented brain tissues as compared
to the baseline (_A_) (see Table 4). In more detail, the DSC is higher for all
segmented brain structures when complementing clinical acquisitions with close
simulated data, with statistical significance ($\emph{p}<0.05$) for the
cerebrospinal fluid and ventricles, the cortical gray matter, the cerebellum,
the deep gray matter and the brain stem.

Figure 8 illustrates on an axial view the accuracy of fetal brain tissue
segmentation in a subject of 30.6 weeks of GA. The results obtained in the
configuration (_D_) where real clinical data are complemented with simulated
subjects look close to the manually-annotated ground truth. In particular, the
segmentation seems to be more accurate in the cortex with an enhanced
sensitivity to folding as compared to the segmentation obtained in the
baseline (_A_) where the network is solely trained on clinical data.

Figure 8: Illustration of the accuracy of fetal brain tissue segmentation in a
subject of 30.6 weeks of GA on (a) an axial slice from the SR reconstruction.
Comparison of (b) the reference manual annotations, (c) the segmentation
results obtained by the baseline (_A_) where the network is trained on
clinical SR reconstructions only (C15/S0), (d) the segmentation results
obtained by the configuration (_D_) that complements this original dataset
with fifteen additional simulated subjects (C15/S15), overlaid on the SR
image. The segmentation of the cortex especially looks more accurate in (d),
with an increased sensitivity to folding as highlighted by the white arrows.

## Discussion & Conclusion

In this work, we present FaBiAN, a novel Fetal Brain magnetic resonance
Acquisition Numerical phantom, and illustrate some of its potential uses. Our
tool relies on EPG simulations[39, 63] to account for stimulated echoes in the
computation of the T2 decay in every voxel of the HR anatomical images from
which the simulated images are derived. The developed framework remains
general and highly flexible in the choice of the sequence parameters and
anatomical settings available to the user. It simulates as closely as possible
the physical principles involved in FSE sequences on several MR systems,
namely from various MR vendors and at different magnetic field strengths,
resulting in highly realistic T2w images of the developing brain throughout
gestation.

The limitations in the resemblance of the simulated HASTE images as compared
to typical clinical MR acquisitions may be explained by the origin of the
simulated images and the lack of T1 and T2 ground truth measurements, both in
the multiple fetal brain tissues and throughout maturation. HASTE images are
simulated from a normative spatiotemporal MRI atlas of the fetal brain[10]
where representative images at each GA correspond to an average of fetal brain
scans across several subjects, thus resulting in smoothing of subtle inter-
individual heterogeneities, especially in the multilayer aspect of the white
matter. As a first approximation, we consider average T1 and T2 values of the
various fetal brain structures labeled as gray matter, white matter or
cerebrospinal fluid throughout development. As a result, our simulated images
may fail to capture the fine details of the fetal brain anatomy as well as
maturation processes that imply changes in T1 and T2 relaxation times during
gestation. In this sense, experts report that they would feel confident in
performing standard biometric measurements on the simulated images and in
evaluating the volume of white matter, but not its fine structure. It is worth
noticing that in-plane motion artefacts like signal drops are not accounted
for at this stage, as slices severely corrupted by such artefacts will be
removed from the analysis. Furthermore, we restricted our simulations to
images of the fetal brain without the remaining fetal anatomy or the
surrounding maternal uterine cavity, as most image analysis and post-
processing techniques intended for fetal brain MRI, including SR
reconstruction, first perform an automated fetal brain
extraction/segmentation. Unlike other models that represent fetal subjects by
scaled pediatric data and oversimplify the complexity of the fetal brain
anatomy by reducing it to white matter alone or to a single brain tissue
label[85, 86, 87], we wanted our numerical simulations to be based on a
comprehensive model of the fetal brain consistent with the underlying clinical
application. In this sense, the normative spatiotemporal MRI atlas of the
fetal brain[10] from which the simulated FSE images are built captures the
details of the fetal brain anatomy throughout maturation. Thanks to the
flexibility of FaBiAN, the surrounding fetal and maternal anatomy, as well as
any other structures, could easily be included as long as we have access to
segmented HR images, for instance by resorting to more complex anatomical
models such as the XCAT phantoms[88, 89, 90]. Several models can also be
combined.

We have designed this open-source simulator to aid in the development and
validation of advanced image processing techniques dedicated to improving
fetal brain MRI. Despite SR reconstruction has already demonstrated its
potential for accurate biometric measurements in the fetal brain[18, 19, 20],
some parameters still need to be adjusted to the nature of the input LR images
to provide optimal evaluation and support computer-assisted diagnosis. In
fetal MRI, the level of regularization is commonly set empirically based on
visual perception[12, 13, 14, 17]. Intuitively, the level of regularization
depends on the amount of data available to solve the ill-posed inverse
problem. Thanks to its controlled environment, the presented framework makes
it possible to explore the optimal settings for SR fetal brain MRI according
to the quality of the input motion-corrupted LR series with respect to a
synthetic 3D HR ground truth. It is worth noticing that in-plane motion
artefacts like signal drops are not accounted for in the simulation workflow
at this stage, as heavily corrupted slices are commonly removed from the
reconstruction. Besides, FaBiAN also enables quantitative assessment of the
robustness of any SR reconstruction algorithm depending on various parameters
that can be intrinsic to the system like noise, or related to the clinical
application such as the amplitude of fetal motion in the womb and the number
of series used for SR reconstruction[84]. For instance, a decrease in the
MSSIM when adding motion-corrupted series to reconstruct a SR volume of the
fetal brain as compared to the SR reconstruction from static series can be
caused by an inappropriate slice-to-volume registration (SVR). Therefore, our
numerical phantom provides a valuable framework for reproducibility studies
and validation of image processing methods. Additional examples among its wide
variety of applications include the simulation of a static reference volume at
a given GA on which to align the clinical orthogonal LR series acquired in a
subject at the same GA in order to perform SVR and subsequent SR
reconstruction of the fetal brain, especially in the presence of heavily
motion-corrupted acquisitions. Besides, the performance of the SVR can be
quantitatively assessed by comparing the motion transform estimated by the
algorithm to the controlled 3D rigid movements actually simulated in the
images. Synthetic HR images can also be used as a reference for more general
motion compensation techniques.

As raised by Wissmann and colleagues, the lack of comparability between
simulation setups hinders the evaluation of image reconstruction methods in
relation to each other[27]. With this first MR acquisition simulation
framework of the developing fetal brain, we aim at providing the community
with a unified environment for the evaluation and validation of various post-
processing techniques to improve the analysis of fetal brain MR images and
support accurate diagnosis.

Furthermore, the developed simulator generates T2w images of the fetal brain
realistic enough to complement real clinical acquisitions for data
augmentation strategies, as shown here with a proof of concept for fetal brain
tissue segmentation. It especially makes it possible to exploit the whole
range of GA in the simulated data when clinical cases are scarce and not
necessarily uniformly distributed across development. Thus, we can take
advantage of larger and more diverse datasets at no cost.

In the configuration (_C_) that combines eight original cases and seven
simulated subjects, the mean DSC over all segmented fetal brain tissues is
slightly increased as compared to the baseline. This can be explained by the
higher number of synthetic images contained in the validation sets. Although
the resort to an atlas restricts the inter-subject variability at a given GA,
the great flexibility of FaBiAN also lies in the possibility of simulating
images from various sources, either atlases or clinical segmented HR
anatomical images of the fetal brain like SR reconstructions. Thus, it becomes
possible to simulate several subjects at a given GA from various fetal brain
models to increase the inter-subject anatomical heterogeneity in the synthetic
images.

In line with the demonstration of the added value of our numerical framework
FaBiAN for diverse applications that revolve around improving diagnosis and
prognosis from MR images of the developing fetal brain, future work aims at
investigating the ability of such a simulator to generalize post-processing
tools like fetal brain tissue segmentation to datasets acquired on other MR
systems and with other sequence parameters using a collection of various
synthetic images for domain adaptation techniques.

Data availability - All the simulated datasets that support the various proof-
of-concept studies documented in this manuscript will be made publicly
available on a Zenodo repository upon acceptance of the present work.

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## Acknowledgements

This work was supported by the Swiss National Science Foundation through
grants 182602, 141283 and 173129, by the European Union’s Horizon 2020
research and innovation program under the Marie Sklodowska-Curie project
TRABIT (agreement No 765148), by the Forschungszentrum für das Kind (FZK), the
Hasler Foundation, the Anna Muller-Grocholski Foundation, and the Zurich
Neuroscience Center PhD Grant. We acknowledge access to the facilities and
expertise of the CIBM Center for Biomedical Imaging, a Swiss research center
of excellence founded and supported by Lausanne University Hospital (CHUV),
University of Lausanne (UNIL), Ecole polytechnique fédérale de Lausanne
(EPFL), University of Geneva (UNIGE) and Geneva University Hospitals (HUG). We
would like to thank Dr. Ruth Tuura from the Center for MR Research of
University Children’s Hospital Zurich (Zurich, Switzerland) for her support in
answering questions about acquisition parameters specific to the
implementation of the SS-FSE sequence by GE. We would also like to thank Ji
Hui from the Center for MR Research of University Children’s Hospital Zurich
(Zurich, Switzerland) for the annotation of the SR fetal brain MR images in
subjects scanned at Kispi.

## Author contributions statement

H.L. investigated the HASTE sequence pulse design using the IDEA sequence
programming interface provided by Siemens Healthineers, built on the initial
simulation framework to develop FaBiAN, implemented additional features such
as the inclusion of intensity non-uniformity fields and stochastic motion, and
extended this numerical phantom, originally thought to simulate HASTE
acquisitions of the fetal brain, to FSE sequences from other MR vendors. H.L.
suggested a classification of segmented brain tissues as gray matter, white
matter or cerebrospinal fluid, reviewed the state of the art in order to find
out T1, T2 and T2* values reported in the developing fetal brain as well as in
premature and full-term newborns at 1.5 T, and extrapolated from the more
general literature the corresponding T1 and T2 values at 3 T. H.L.
automatically generated the brain masks of the simulated images and manually
refined them, reconstructed the super-resolution fetal brain volumes from
clinical, respectively synthetic, 2D motion-corrupted series, participated in
the design of the different case studies, analyzed all the results, prepared
the tables and figures, and wrote the article. C.W.R. implemented the skeleton
of the original simulator, helped H.L in optimizing it, and suggested
complementary case studies. T.H. helped H.L. to understand the design of the
HASTE sequence and to improve the simulation process. C.W.R. and T.H. equally
contributed to this work. P.d.D. provided clinical cases acquired at CHUV from
the fetal MRI database whose SR reconstructions were previously evaluated as
excellent. P.d.D and H.K. participated in the design of the data augmentation
experiments using simulated images in the context of fetal brain tissue
segmentation. P.d.D. implemented the deep learning network for fetal brain
tissue segmentation and evaluated its performance in the different
configurations studied. P.d.D. and S.T. assisted H.L. in using the SR
reconstruction pipeline[52]. S.T. especially helped with the installation
procedure. Y.A.G. provided a script that saves matlab matrices to nifti images
with the right orientation matrix. J.Y. provided a script that preprocesses
the data in k-space using a Fermi low-pass filter before zero-interpolation
filling. T.Y. provided a script that computes a motion index from the brain
masks. K.P. shared the data from fifteen subjects scanned at Kispi, including
clinical LR SS-FSE images of the fetal brain and corresponding SR
reconstructions together with their manual annotations. K.P. performed the SR
reconstructions of the data from Kispi. K.P. also provided information about
the protocol for fetal brain examination as it is conducted in clinical
routine at Kispi. J.B.L. provided information on the clinical protocol for
fetal brain MRI as it is performed at CHUV. R.M. assessed the clinical cases.
A.J. supported the use of detailed clinical cases from Kispi to extend our
simulation framework to FSE sequences from other MR vendors and demonstrate
its added value in providing multiple synthetic data at no cost for data
augmentation strategies. M.K. and V.D. validated and complemented the labels
of the various anatomical structures in the developing fetal brain. V.D.
provided approximate relaxometric T1 and T2 values in the cerebrospinal fluid
in pediatric patients. M.K. detailed the features radiologists routinely
analyze in clinical images of the fetal brain to determine the neurotypical or
pathological status of the fetus, as well as the various artefacts they
typically encounter in LR HASTE images. M.K. and V.D. provided qualitative
assessment of the simulated HASTE images. P.H., T.K. and M.S. supported the
writing of this manuscript and provided regular feedback during the project.
M.B.C. regularly assessed the realistic appearance of the simulated HASTE
images as compared to typical clinical acquisitions of the fetal brain at CHUV
throughout the implementation of the simulation pipeline, qualitatively
estimated the level of motion in clinical series, suggested some application
examples where the simulator could be particularly valuable, participated in
the design of the various experiments presented in this manuscript, and
supported the analysis of the results as well as the writing of the
manuscript. M.B.C. is the recipient of the FNS grant that supports the whole
project. All authors reviewed the manuscript.

## Additional information

Competing interests The authors declare no competing interests.

## Supplementary Material

Figure 9: Visual inspection and comparison between clinical MR acquisitions
(GE Healthcare) and representative simulated SS-FSE images of the fetal brain
in the three orthogonal orientations, at 1.5 T and 3 T respectively, and at
two GA (21 and 28 weeks).