# High-efficient Bloch simulation of magnetic resonance imaging sequences
based on deep learning

Haitao Huang111Haitao Huang and Qinqin Yang contributed equally to this work.
Qinqin Yang222Haitao Huang and Qinqin Yang contributed equally to this work.
Jiechao Wang  Pujie Zhang
Shuhui Cai  Congbo Cai<EMAIL_ADDRESS>
###### Abstract

Bloch simulation constitutes an essential part of magnetic resonance imaging
(MRI) development. However, even with the graphics processing units (GPU)
acceleration, the heavy computational load remains a major challenge,
especially in large-scale, high-accuracy simulation scenarios. Here we present
a framework based on convolutional neural networks to build a high-efficient
2D Bloch simulator, termed Simu-Net. Compared to the mainstream GPU-based MRI
simulation software, Simu-Net successfully accelerates simulations by over
hundreds of times in three MRI pulse sequences. The accuracy and robustness of
the proposed framework were also verified qualitatively and quantitatively.
The trained Simu-Net was applied to generate sufficient customized training
samples for deep learning-based $\rm T_{2}$ mapping and comparable results to
conventional methods were obtained in the human brain. As a proof-of-concept
work, Simu-Net shows the potential to apply deep learning for rapidly
approximating the Bloch equation as a forward physical process.

###### keywords:

Bloch simulation , magnetic resonance imaging , deep learning , dynamic
convolution , synthetic data generation

††journal: Arxiv

[inst1]organization=Department of Electronic Science,addressline=Fujian
Provincial Key Laboratory of Plasma and Magnetic Resonance, Xiamen University,
city=Xiamen, postcode=361005, country=China

##  1 Introduction

The non-invasive nature of magnetic resonance imaging (MRI) makes it an
outstanding clinical tool in disease diagnosis and research. However, the slow
imaging speed and heavy financial burden hinder the development of novel MRI
pulse sequences and reconstruction algorithms. Following the underlying
physics, MRI simulations allow for rapid iteration of MRI techniques using
simple analytical signal expressions or complex numerical modeling. Thus, it
becomes an indispensable part of pulse sequence optimization, evaluation and
artifact tracing [1, 2, 3, 4]. In the era of deep learning (DL), MRI
simulation is widely used for training data generation [5, 6, 7], which has
spawned a series of novel techniques, including ultra-fast parametric mapping
[8, 9, 10, 11, 12], signal separation [13] and cardiac motion tracking [14].

One of the main challenges of Bloch simulation is its slow simulation speed.
To make the simulation closer to the real situation, many factors need to be
considered, such as the shape of the radio frequency (RF) profile, the maximum
slew rate of gradient and non-ideal imaging conditions. On the one hand,
simulating these factors involves a series of discrete execution intervals,
and the computational cost will increase with the complexity of the pulse
sequence. On the other hand, two-/three-dimensional Bloch simulations require
parallel computation of a large number of evolution-specific spins, which
further increases the computation load. To address this, graphics processing
unit (GPU) acceleration was introduced and has become the mainstream of
complex large-scale MRI simulations [15, 16, 17]. In addition to this, several
well-designed software (e.g., SPROM [2], MRISIMUL [16], MRiLab [15])
consisting of graphical user interfaces (GUI) were released. The high-
performance scientific computing software improves accessibility and allows
for more realistic simulation (e.g., multi-pool exchange models) in a personal
computer. Despite the great development, traditional MRI simulation is still
limited by the computing hardware and has a non-negligible time consumption.

A recent promising and generic approach to speed up simulations is to use
machine learning models to approximate the slow forward process. Related
applications include but are not limited to modeling molecular energies [18],
climate science [19], and even emulating cosmological power spectra [20]. A
powerful tool is physics-informed neural networks (PINN) [21, 22], which is
designed to efficiently solve general nonlinear partial differential
equations. By combining the data-driven solution with physical constraints,
PINN can represent the continuous solution space within the boundary
conditions under the small samples training. With this tool, rapid modeling
and prediction of myocardial and cerebral hemodynamics can be achieved in
medical imaging [23, 24]. However, among the proposed DL-based simulation
methods, only a few works involve MRI and are all limited to accelerate
magnetic resonance fingerprinting (MRF) [25, 26, 27]. An example in Ref [26]
uses a four-layer neural network for rapid MRF dictionary generation from
patient-specific heart rates, which enables online $\rm T_{1}$ and $\rm T_{2}$
mapping in the fast-paced clinical workflow. Although the preliminary results
are encouraging, the current schemes only consider the evolution of a single
voxel, making it difficult to generalize to other MRI techniques, especially
pulse sequences with complex spatial encoding [28].

In this study, a proof-of-concept is presented for the application of deep
learning for fast MRI pulse sequence simulation. Although most of the current
work is dedicated to using deep learning in solving inverse problems [29, 30],
we still try to explore its possibilities in forward physical process
approximation. For this purpose, we constructed a two-dimensional fast Bloch
simulator based on a convolutional neural network (CNN), called Simu-Net. A
dynamic convolution layer [31, 32] was introduced to encode sequence-specific
imaging parameters for physics-modulated simulation. The accuracy of the
proposed framework was investigated in one advanced and two classical pulse
sequences. The speed of simulation was also compared with that of the
mainstream MRI simulation software. Finally, we apply the trained Simu-Net to
generate a large number of customized training samples for DL-based $\rm
T_{2}$ mapping and validate it with in vivo human brain.

##  2 Methods

###  2.1 Traditional Bloch Simulation

To make this paper self-contained, we briefly review the traditional Bloch
simulation. Specifically, the spin magnetization vector
$\rm\boldsymbol{M}=[M_{x},M_{y},M_{z}]^{T}$ of isochromatic can be expressed
by Bloch equation [33]:

$\displaystyle{d\boldsymbol{M}\over
dt}={\gamma}\boldsymbol{M}\times\boldsymbol{B}-\begin{bmatrix}M_{x}\over
T_{2}\\\ M_{y}\over T_{2}\\\ M_{z}-M_{0}\over T_{1}\end{bmatrix}$ (1)

where $\gamma$ is gyromagnetic ratio, $\rm M_{0}$ is the thermal equilibrium
magnetization vector depending on the proton density. The regrowth of the
longitudinal magnetization ($\rm M_{z}$) is characterized by relaxation time
constant $\rm T_{1}$, and the decay of the transverse magnetization ($\rm
M_{x,y}$) is governed by constant $\rm T_{2}$. $\boldsymbol{B}$ denotes the
overall field, including the main static field $\rm B_{0}$ with field
inhomogeneity $\Delta{\rm B_{0}}$, RF field $\boldsymbol{B_{1}}$ and linear
gradient field $\boldsymbol{G}$ at location $\boldsymbol{r}$. It can be
modeled in the rotating frame as follows:

$\displaystyle\boldsymbol{B}(\boldsymbol{r},t)=(B_{0}+\Delta{B}_{0}(\boldsymbol{r})+\boldsymbol{G}(t)\cdot\boldsymbol{r})\hat{z}+\boldsymbol{B_{1}}(t)$
(2)

In general, the acquired MR signals are driven by specific pulse sequences and
then reconstructed to images through discrete Fourier transform. Under
reasonable assumptions and approximations, the numerical simulation of Bloch
equation can be described as successive applications of operators to the
magnetization vector, where the initial magnetization vector is given by
parametric objects. Despite the complexity of pulse sequences, they can all be
represented as linear combinations of three operators, i.e., RF operator,
gradient operator and evolution operator. Therefore, transient magnetization
vectors
$\boldsymbol{M}(\boldsymbol{r},t^{+})$/$\boldsymbol{M}(\boldsymbol{r},t^{-})$
can be used to record the spin history effect as [2]:

$\displaystyle\boldsymbol{M}(\boldsymbol{r},t^{+})=\boldsymbol{R}_{\alpha}\boldsymbol{M}(\boldsymbol{r},t^{-})$
(3)
$\displaystyle\boldsymbol{M}(\boldsymbol{r},t^{+})=\boldsymbol{G}_{t}\boldsymbol{M}(\boldsymbol{r},t^{-})$
$\displaystyle\boldsymbol{M}(\boldsymbol{r},t^{+})=\boldsymbol{E}_{T_{1},T_{2},t}\boldsymbol{M}(\boldsymbol{r},t^{-})$

here, for RF operator $\boldsymbol{R}_{\alpha}$, a simple rotation operation
with flip angle $\alpha$ is applied to represent the effect of RF pulse, and
the transmitting RF coil inhomogeneity ($\rm B_{1}^{+}$) impacts the strength
of the flip angle. The gradient operator $\boldsymbol{G}_{t}$ is the time-
varying linear gradient field for spatial encoding. Exponential decay terms of
$\rm T_{1}$ and $\rm T_{2}$ relaxations (respectively, $1-e^{-t/T_{1}}$ and
$e^{-t/T_{2}}$) are performed using the operator
$\boldsymbol{E}_{T_{1},T_{2},t}$. The effects of susceptibility-induced $\rm
B_{0}$ inhomogeneities are present throughout the pulse sequence, resulting in
additional phase accumulation in spins. At the signal acquisition stage, the
integrals of all magnetization vectors are assigned to each voxel in k-space
according to the desired sampling trajectory.

###  2.2 Bloch Simu-Net

A deep learning framework with non-linear activation units, termed Bloch Simu-
Net, is used to approximate the forward physical process of 2D Bloch
simulation. A schematic demonstration of the proposed framework is shown in
Figure 1. Briefly, parametric templates ($\rm T_{1}$, $\rm T_{2}$, $\rm
M_{0}$, $\rm B_{0}$ and $\rm B_{1}$), $\textit{P}_{\textit{j}}$, and position
encoding template (PET), $\textit{P}_{\textit{e}}$, were first created to
initialize the spatial distribution of various properties of virtual objects.
The scan-specific pulse sequence parameters, $\textit{P}_{\textit{s}}$, were
used to generate dynamic convolution kernels through a multilayer perceptron,
$\mathcal{F}$, for sequence-informed encoding. Finally, a simulated MR image,
$\textit{I}_{\textit{w}}$, can be obtained from an encoder-decoder network,
$\mathcal{N}$, by feed with encoded feature maps, f. Thus, the nonlinear
forward physical process can be simplified as:

$\displaystyle\textit{I}_{w}=\mathcal{N}(f_{\mathcal{F}(P;\theta_{\mathcal{F}})};\theta_{\mathcal{N}})$
(4)

where, P denotes the combination of $\textit{P}_{\textit{j}}$,
$\textit{P}_{\textit{e}}$ and $\textit{P}_{\textit{s}}$.
$\theta_{\mathcal{N}}$ and $\theta_{\mathcal{F}}$ are the trainable parameters
of the encoder-decoder network and the multilayer perceptron, respectively. In
practice, the encoder-decoder network is a five-level U-Net [34]. The details
of parametric templates, PET and dynamic convolution module are described in
the following sections.

Figure 1: Schematic illustration of Simu-Net for fast simulation of MRI
sequences. The complex-valued position encoding template and parametric
templates ($\rm T_{1}$, $\rm T_{2}$, $\rm M_{0}$, $\rm B_{0}$ and $\rm B_{1}$)
were encoded to sequence-informed feature maps by dynamic convolution. The
filters of dynamic convolution were generated by pulse sequence parameters and
learnable multi-layer perceptron. The encoder-decoder is a five-level U-Net.

####  2.2.1 Parametric Templates

For 2D spatial encoding in Bloch simulations, the spatial distribution of
tissue parameters ($\rm T_{1}$, $\rm T_{2}$, $\rm M_{0}$) and field
inhomogeneity ($\Delta{\rm B_{0}}$, $\rm B_{1}$) should be constructed as
parametric templates. In this work, the tissue parameters were synthesized
using multi-contrast MRI data from the IXI database (http://brain-
development.org/ixi-dataset/) following the MOST-DL method [6]. In brief, the
registered $\rm PD$-weighted and $\rm T_{2}$-weighted images were firstly
transformed to pseudo parametric maps and then upsampled to $512\times 512$
grids, in which $\rm T_{2}\in[0,650]$ ms, $\rm M_{0}\in[0,1]$. The field
inhomogeneity can be modeled as a random surface through 2D low-order
polynomial functions and Gaussian functions. Finally, the $\Delta{\rm B_{0}}$
field is bounded within $\pm 150$ Hz and the $\rm B_{1}^{+}$ field is scaled
to the range of $0.7\thicksim 1.3$.

####  2.2.2 Position Encoding Template

Some advanced MRI sequences, such as the spatiotemporal encoding imaging
method [35] or MOLED acquisition [8, 36], involve special spatial encoding,
which results in nonlocal signal modulation patterns in the image domain.
However, the translation invariance nature of CNN makes it impossible to
accurately learn the mapping relationship between parametric templates and MRI
signals at different spatial positions. To adapt this, PET is introduced to
Simu-Net. Specifically, a zero-filled complex matrix of the same size as the
target image is firstly created, then $1+1j$ is assigned to the symmetric
position of the four quadrants. After the inverse Fourier transform, a
complex-valued PET is obtained. A representative example of PET is shown in
Figure 1 (top left), where there is a high-frequency periodic signal
modulation along the horizontal and vertical directions.

####  2.2.3 Sequence-informed Dynamic Convolution

How to encode one-dimensional sequence information into network training is
the main challenge of Simu-Net. Inspired by dynamic filter learning [32], a
dynamic filter generation module was introduced to generate the dynamic
convolution kernels by feeding pulse sequence parameters (e.g., flip angles,
echo spacing, echo time), as shown in Figure 1. The subsequent encoder-decoder
network will be uncertain if the series of varying imaging parameters are
unknown. Hence, the dynamic convolutional module should be placed before the
encoder-decoder network to fusion the inputs and sequence parameters, termed
sequence-informed dynamic convolution. Specifically, a 3-layer perceptron is
used as a non-linear encoder $\mathcal{F}(\cdot)$ with trainable parameters
$\theta_{\mathcal{F}}$. The $P_{s,i}$ is the i-th vector consisting of a set
of normalized sequence parameters as the input of $\mathcal{F}(\cdot)$. Then,
the weights of dynamic convolution kernels, $\omega_{i}$, are obtained as
follows:

$\displaystyle\omega_{i}$ $\displaystyle=\mathcal{F}(P_{s,i};\theta_{F})$ (5)

After dynamic filter generation, two dynamic convolutional layers with
$1\times 1$ kernel can be constructed using the weights, $\omega_{i}$, and be
applied to combined parametric templates and PET as:

$\displaystyle f_{1}$ $\displaystyle=Conv_{1}(concat(P_{e},P_{j});\omega_{1})$
(6) $\displaystyle f_{2}$ $\displaystyle=Conv_{2}(ReLU(f_{1});\omega_{2})$

Finally, a total of 16 parameters-encoded feature maps were obtained as the
inputs of a further encoder-decoder network. Note that the number of nodes in
the hidden layer is 1448, and the output size is 362 for the multilayer
perceptron in this work.

###  2.3 Experiments

The traditional Bloch simulations were performed on MRiLab [15]
(https://leoliuf.github.io/MRiLab/) and SPROM [2]
(https://doi.org/10.6084/m9.figshare.19754836.v2) software. Three different
MRI pulse sequences were selected as examples to validate our proposed method,
including fast spin echo (FSE), gradient-echo echo-planar imaging (GRE-EPI)
and multiple overlapping-echo detachment planar imaging (MOLED). Figure 2
gives the sequence diagrams of these three pulse sequences. In this work, we
only considered the following parameters that most govern the signal: echo
time (TE), echo spacing (ESP), echo train length (ETL), flip angles of
excitation (FA) and refocusing RF pulse (Re-FA) and echo-shifting gradients
(SG). Detailed variable imaging parameters considered in Simu-Net training are
listed in Table 1. The spatial resolution of all experiments is fixed at
$1.7\times 1.7$ mm2 ($\rm FOV=220\times 220$ mm2, matrix size = $128\times
128$), and the magnetization is set to recover instantaneously after signal
sampling (i.e., the repetition time, $\rm TR$, can be ignored).

Figure 2: The sequence diagrams of (A) fast spin echo (FSE), (B) gradient-echo
echo planar imaging (GRE-EPI) and (C) multiple overlapping-echo detachment
(MOLED). In MOLED, four excitation pulses and a refocusing pulse are used to
prepare spin echoes with different echo times followed by an EPI readout
module. The positions of different echoes in k-space are determined by four
echo-shifting gradients ($\rm G_{1}$, $\rm G_{2}$, $\rm G_{3}$ and $\rm
G_{4}$). ESP: echo spacing; ETL: echo train length; EPI: echo planar imaging.
Table 1: Parametric templates, non-ideal conditions, imaging parameters for
three MRI sequences. Re-FA is the flip angle of refocusing pulse. SG is the
applied shift gradient.

| Parametric Template | Non-ideal Condition | Imaging Parameter
---|---|---|---
| $\rm T_{2}$ | $\rm M_{0}$ | $\Delta{\rm B_{0}}$ | $\rm B_{1}^{+}$ | TE | ESP | ETL | FA | Re-FA | SG
FSE | $\checkmark$ | $\checkmark$ | $\backslash$ | $0.7\thicksim 1.3$ | $\backslash$ |  $8\thicksim 15$ ms | 16 | $20\thicksim 70^{\circ}$ | $180^{\circ}$ | $\backslash$
GRE-EPI | $\checkmark$ | $\checkmark$ |  $-150\thicksim+150$ Hz | $\backslash$ | 40-80 ms |  $0.375\thicksim 0.55$ ms | $\backslash$ | $90^{\circ}$ | $\backslash$ | $\pm{5}\%$
MOLED | $\checkmark$ | $\checkmark$ | $\backslash$ | $0.7\thicksim 1.3$ | $\backslash$ |  $0.375\thicksim 0.54$ ms | $\backslash$ | $30^{\circ}$ | $180^{\circ}$ | $\pm{5}\%$

####  2.3.1 Fast Spin Echo Simulation

FSE sequence has been commonly used in clinical practice to obtain high-
resolution $\rm T_{2}$-weighted MR images [37]. Figure 2(A) illustrates a
typical multi-shot FSE sequence, where one shot is composed of one excitation
RF pulse followed by multiple refocusing pulses. In this sequence, $\rm
B_{1}^{+}$ field inhomogeneity, ESP and FA are considered to significantly
affect the contrast of final MR images; thus, these parameters were randomly
sampled from the empirical ranges (Table 1). Besides, the fixed parameters are
as follows: shot number = 8, ETL = 16, Re-FA = $180^{\circ}$. The TE of the
FSE sequence is governed by the varying ESP.

####  2.3.2 Gradient-echo Echo-planar Imaging Simulation

Single-shot GRE-EPI sequence plays a vital role in BOLD functional MRI [38]
and perfusion MRI [39]. However, its sensitivity to $\rm B_{0}$ field
inhomogeneity can distort the resulting images. A typical GRE-EPI sequence is
shown in Figure 2(B). $\rm G_{pre}$ represents the prephase gradient, which is
typically set to $1/2$ the area of phase-encoding gradients to ensure that the
echo is centered in k-space. For GRE-EPI simulation, TE and ESP were selected
in dynamic filter generation since those parameters affect the distortion, and
FA was fixed to $90^{\circ}$.

####  2.3.3 Multiple Overlapping-echo Imaging Simulation and $\rm T_{2}$
mapping

Single-shot MOLED sequence is a recently proposed technique for ultra-fast
$\rm T_{2}$ mapping [36]. As shown in Figure 2(C), MOLED uses four excitation
pulses and a refocusing pulse to prepare multiple spin echoes with different
TEs. The echo-shifting gradients $\rm G_{1}-G_{4}$ shift the position of spin
echoes in k-space. Through the EPI readout module, a whole image containing
multiple echoes can be obtained within a few hundred milliseconds. In this
sequence, ESP and SG will affect the range of TEs, FA = $30^{\circ}$ and Re-FA
= $180^{\circ}$.

Due to the complexity of overlapping-echo signals, high-fidelity quantitative
parametric mapping is highly dependent on deep learning-based decoding. We
followed the workflow of MOST-DL [6] for MOLED $\rm T_{2}$ mapping, where the
Bloch simulation was replaced by the proposed Simu-Net for generating training
samples. A five-level U-Net [34] was trained by synthetic data to learn the
end-to-end mapping from complex-valued MOLED images to $\rm T_{2}$ maps.
During the testing phase, the $128\times 128$ overlapping-echo image was zero-
padded to $256\times 256$ in k-space and then normalized in the image domain.

For validating the Simu-Net on synthetic data generation for MOLED $\rm T_{2}$
mapping, in vivo MOLED data were acquired from one healthy volunteer on a
whole-body MRI system at 3T (MAGNETOM Prisma TIM, Siemens Healthcare,
Erlangen, Germany) with a 20-channel head coil. The study protocol was
approved by the institutional research ethics committees, and written informed
consent was obtained from the volunteer. The imaging parameters were as
follows: TE = 22.0, 52.0. 82.0, 110.0 ms, TR = 8000 ms, FOV = $220\times 220$
mm2, matrix size = $128\times 128$, GRAPPA = 2, FA = $30^{\circ}$, slice
number = 21, slice thickness = 4.0 mm. For comparison, we collected MOLED data
with three different ESP (i.e., 1.08, 0.93 and 0.75 ms). Noted that the ESP of
the readout gradient is 2 times that of the simulation to maintain the
consistency of the ETL. The reference $\rm T_{2}$ maps were obtained from the
SE sequence using the TEs = 35, 50, 70, 90 ms, TR = 2500 ms.

###  2.4 Implementation and validation

In this work, three pulse sequences are treated as different non-linear
functions. Thus, we trained the neural networks separately for different pulse
sequences. The training data of Simu-Net was generated by SPROM software [2],
and the sample size is 2000 for each task. Additional 100 samples were
generated for network evaluation. The learning rate was initially set as
$1.2\times 10^{-4}$ and decayed every 25 epochs, and $\rm L_{1}$ norm was
chosen as the loss function in all experiments. The network training and
testing pipelines were coded using PyTorch library. All processes were
performed on a machine with an NVIDIA 2080Ti GPU.

To quantitatively evaluate the results, peak signal-to-noise ratio (PSNR) and
structural similarity index (SSIM) were calculated between simulated results
of the Simu-Net and Bloch equation. In addition, we qualitatively and
quantitatively evaluated the results of MOLED $\rm T_{2}$ mapping with
different imaging parameters, where linear regression analysis was performed
on the in vivo experiments at the region-of-interest (ROI) level. These ROIs
were manually selected from gray/white matter and then were used to calculate
the mean $\rm T_{2}$ values.

##  3 RESULTS

The results of Bloch equation and deep learning-based Simu-Net for FSE, GRE-
EPI and MOLED are shown in Figure 3. For FSE and GRE-EPI, the quality of
simulated images from Simu-Net agrees well with those from Bloch simulation,
even with the effect of $\rm B_{1}$/$\rm B_{0}$ inhomogeneity (Figure 3A and
B). The errors maps show the precision of FSE (PSNR = 52.38 dB, SSIM = 0.997)
simulation is higher than that of GRE-EPI (PSNR = 38.36 dB, SSIM = 0.950). As
for MOLED, high-fidelity magnitude (PSNR = 37.51 dB, SSIM = 0.970) and phase
can be simultaneously obtained by Simu-Net, as shown in Figure (C). The
zoomed-in views demonstrate that the Simu-Net can achieve high-accuracy
simulation even with complex signal modulation.

Figure 3: The simulation results of Bloch equation and deep learning-based
Simu-Net. (A) The results of FSE simulation with $\rm B_{1}$ inhomogeneity,
case 1: FA = $55.72^{\circ}$, ESP = 12.0 ms; case 2: FA = $56.16^{\circ}$, ESP
= 11.6 ms. (B) The results of GRE-EPI simulation with $\Delta{\rm B_{0}}$
inhomogeneity, case 1: TE = 45.6 ms, ESP = 0.544 ms; case 2: TE = 51.2 ms, ESP
= 0.446 ms. (C) The results of MOLED simulation, case 1: ESP = 0.54 ms; case
2: ESP = 0.375 ms.

Table 2 compares the speed of MRI simulation between Bloch simulation and
Simu-Net. Two mainstream software (MRiLab and SPROM) are used to perform Bloch
simulations under GPU acceleration. It can be seen that the time required to
simulate an MRI image is specific to the pulse sequence, where the GRE-EPI
takes about 12 seconds, MOLED about 30 seconds, and FSE about 500 or 1300
seconds. Surprisingly, Simu-Net enables millisecond-level simulation of
different pulse sequences and increases the simulation speed of FSE sequences
by 8728 times.

Table 2: The comparison of speed for synthesizing one data. Sequence | MRiLab | SPROM | Simu-Net
---|---|---|---
FSE | 497.53 s | 1320.20 s | 0.057 s
GRE-EPI | 11.44 s | 29.81 s | 0.064 s
MOLED | 12.16 s | 32.42 s | 0.073 s

Figure 4 shows the results of GRE-EPI simulation from Bloch equation and Simu-
Net for investigating the $\rm B_{0}$-introduced image distortion and TE-
dependent signal attenuation. The spatial distribution of the $\Delta{\rm
B_{0}}$ field used in simulations is shown in Figure 4(A). In Figure 4(B),
GRE-EPI images with different geometric distortions can be obtained by Simu-
Net at an increased $\Delta{\rm B_{0}}$ field, even the severe distortions
(white arrows) due to $\pm 150$ Hz inhomogeneous field. In addition, the
simulated signal attenuation of Simu-Net from 5 ROIs (marked by red) agrees
well with that of Bloch simulation, where the signal intensity decreases with
increasing echo time (Figure 4C).

Figure 4: The results of GRE-EPI simulation from Bloch equation and Simu-Net.
The $\Delta{\rm B_{0}}$ with the same spatial distribution (A) but different
intensities were used in Bloch simulation and Simu-Net (B). The line chart (C)
shows the changes of signal intensity over echo times from 5 ROIs on the $\pm
150$ Hz case (marked by red).

Figure 5 examines the effects of spin numbers on the MOLED simulation. Here,
all experiments take into account the effect of $\rm B_{1}$ inhomogeneity and
use the same imaging parameters. For traditional Bloch simulation, the
insufficient number of spins (e.g., $256\times 256$ or $128\times 128$) leads
to signal corruption in the final $128\times 128$ MOLED images, and additional
echoes can also be observed in k-space (marked by white arrows). In contrast,
Simu-Net achieves high-accuracy simulations with a limited number of spins,
delivering high-fidelity strip patterns in the image domain and almost
lossless signal quality in k-space.

Figure 5: The effects of template size (the number of spins) on MOLED
simulation. An insufficient number of spins ($256\times 256$ or $128\times
128$) result in image degradation and additional echoes in k-space (white
arrows) for Bloch simulation. For Simu-Net, high-accuracy MOLED simulation can
be achieved by using templates with a size of $256\times 256$.

Figure 6 shows the in vivo results of MOLED $\rm T_{2}$ mapping, where the
training samples were generated by Bloch simulation and Simu-Net. To
reconstruct MOLED images with different acquisition parameters (ESP = 1.08,
0.93 and 0.75 ms), three independent training sets (4000 samples each) were
obtained, which took 40 hours for Bloch simulation and 15 minutes for Simu-
Net. It can be seen that Simu-Net enables MOLED $\rm T_{2}$ mapping with image
quality close to that of Bloch simulation and significantly reduces the time
of data generation.

Figure 6: Comparison of MOLED $\rm T_{2}$ mapping for in vivo human brain with
different acquisition parameters (ESP = 1.08, 0.93 and 0.75 ms) from Bloch
simulation samples and Simu-Net samples. The reference $\rm T_{2}$ maps were
obtained by SE sequence with TE = 35, 50, 70, 90 ms. It took 40 hours for
Bloch simulation to generate 12000 training samples and about 15 minutes for
Simu-Net.

Linear regression plots quantitatively compare the $\rm T_{2}$ values derived
from the Bloch simulation and Simu-Net, as shown in Figure 7. A total of 72
ROIs covering the whole brain were manually selected from grey matter and
white matter to calculate the mean $\rm T_{2}$ values. The quantitative values
of both methods in these ROIs are relatively consistent with the reference
method, with $\rm R^{2}$ greater than 0.9. However, the results of Simu-Net
for different imaging parameters are slightly less consistent than those of
Bloch simulation, with $\rm R^{2}$ decreasing from 0.947, 0.933, and 0.942 to
0.934, 0.924, and 0.919, respectively.

Figure 7: Linear regression analysis of $\rm T_{2}$ maps obtained by using
MOLED and reference method in different echo spacing (1.08, 0.93 and 0.75 ms).
The training samples were generated by Bloch simulation (top row) and Simu-Net
(bottom row), respectively.

##  4 DISCUSSION

In this work, we proposed a deep learning-based framework, Simu-Net, for
ultra-fast MRI simulation. To the best of our knowledge, Simu-Net is the first
method for approximating the 2D Bloch equation using convolutional neural
networks. As the core component of this framework, sequence-informed dynamic
convolution is designed to encode scan-specific parameters to generate
physically constrained MRI images. The framework was demonstrated in an
advanced and two classical pulse sequences, where Simu-Net was shown to
efficiently and accurately simulate complex-valued signals even with field
inhomogeneity. The application of Simu-Net for fast training data generation
was also demonstrated through MOLED simulation for in vivo $\rm T_{2}$ mapping
under various imaging parameters. The preliminary results show that Simu-Net
can significantly facilitate the application of synthetic-data-driven deep
learning and achieve MRI simulations close to Bloch equation with a speedup of
hundreds of times.

Dynamic convolution was firstly proposed by Jia et al. to improve the
performance of ImageNet classification by introducing attention mechanisms
[32] without increasing the depth and width of the network. However, in Simu-
Net, dynamic convolution was used to transform pulse sequence parameters into
learnable convolution kernels and enable simultaneous encoding of 2D
(parametric templates) and 1D (imaging parameters) information to high-
dimensional feature maps. This strategy improves the flexibility of physics-
informed network training rather than simple end-to-end mapping. On the other
hand, Simu-Net is trained by a few randomly sampled synthetic data similar to
classical PINN. Although these data are discrete points in a high-dimensional
solution space, Simu-Net achieves continuous data-driven solutions to Bloch
equations. From the results of Figure 4, we see that TE-dependent signal
attenuation and $\rm B_{0}$-introduced geometric distortion of GRE-EPI can be
successfully simulated, closing to Bloch equations, which shows the
generalizability of Simu-Net on unseen imaging parameters following the
physical laws.

Due to the fast forward inference of convolutional neural networks, Simu-Net
can significantly speed up Bloch simulations and surpass the GPU-accelerated
high-performance scientific computing software. The results in Table 2 show
that accelerations of more than 8000 times can be achieved for FSE simulation.
Compared to GRE-EPI and MOLED, FSE with hundreds of pulses needs to simulate
much more discrete spin evolution at a small-time interval, dramatically
increases the required computational time. In contrast, Simu-Net performs MRI
simulations in the form of domain transformation, ignoring the spin history
effects and avoiding complex signal encoding. Based on this, synthetic-data-
driven deep learning may no longer be limited by the computational burden of
data generation. Although Simu-Net also uses synthetic data for network
training, it is essentially a function approximation of the forward physical
process and thus requires a much smaller sample size than the inverse problem.
Figure 8 shows the effects of different sample sizes on MRI simulation for
Simu-Net. It can be seen that less than 2000 samples is enough to train Simu-
Net for high-accuracy MRI simulation, even for MOLED with complex spatial
encoding.

Figure 8: The effects of the number of training samples on FSE (blue), GRE-EPI
(red) and MOLED (green) simulation for Simu-Net.

In Simu-Net, CNN priors and PET are believed to jointly contribute to high-
accuracy MOLED simulation. Unlike FSE and GRE-EPI, multiple echoes prepared by
independent RF pulses result in strip patterns in the image domain of MOLED
signal, which means that it is modulated by a special point spread function.
To characterize the inverse Fourier transform of unconventional frequency
domain signals, PET was concatenated with parametric templates to achieve
complex-space localization. Our experiments show that the training of MOLED
simulation is difficult to converge without the input of position encoding.
Although classical sequences are not affected by this, the introduction of
position encoding is still considered as a generalized extension of Simu-Net.

As a proof-of-concept, Simu-Net has demonstrated the possibility of
accelerating Bloch simulation using deep learning. Its applications may not be
limited to synthetic data generation but also include large-scale high-
accuracy simulation, model-driven self-supervised learning [40], pulse
sequence optimization [41], or reinforcement learning [42]. However, its
limitations cannot be ignored, for example, variable spatial resolution (i.e.,
FOV and matrix size) and generalized models (adaptable to different pulse
sequences) still remain challenges. Due to the relatively fixed number of
nodes in a neural network, achieving variable output sizes may benefit from
natural languages processing methods, such as recurrent neural network (RNN)
or long short-term memory (LSTM) [43, 44]. Future work will explore broader
applications of Simu-Net, and we believe these ideas can be extended to other
areas to accelerate the computation of forward physical model.

##  5 CONCLUSION

A novel deep learning framework called Simu-Net was proposed to greatly speed
up Bloch simulations and verified on three different sequences. The simulation
and in vivo results show the flexibility, reliability and efficiency of this
framework. This work firstly demonstrates the possibility of deep learning for
2D forward physical process approximation and may play an important role in
promoting the development and optimization of MRI pulse sequences, the
analysis and research of imaging experimental results, and the DL-based MRI
methods.

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SF2A 2021

# Well-being in French astrophysics

N. A. Webb  IRAP, Université de Toulouse, CNRS, CNES, Toulouse, France  C. Bot
CDS, Université de Strasbourg, CNRS, Observatoire astronomique de Strasbourg,
UMR 7550, 67000 Strasbourg, France  S. Charpinet1 T. Contini1 L. Jouve1 F.
Koliopanos1 A. Lamberts  Université Côte d’Azur, Observatoire de la Côte
d’Azur, CNRS, Laboratoire Lagrange, Laboratoire Artḿis, France  H. Meheut3 S.
Mei  Université de Paris, CNRS, Astroparticule et Cosmologie, F-75013 Paris,
France  I. Ristorcelli1 G. Soucail1

###### Abstract

It has become clear that early career astrophysics researchers (doctoral
researchers, post-docs, etc) have a very diverse appreciation of their career,
with some declaring it the best job that you can have and others suffering
from overwork, harrassment and stress from the precarity of their job, and
associated difficulties. In order to establish how astrophysics researchers,
primarily in France, experience their career, we sent out a survey to
understand the impact that their job has on their well-being. 276 people
responded to the survey. Whilst around half of the respondents expressed
pleasure derived from their career, it is clear that many (early career)
researchers are suffering due to overwork, with more than a quarter saying
that they work in excess of 50 hours per week and 2% in excess of 90 h per
week. Almost 30% professed to having suffered harrassment or discrimination in
the course of their work. Further, whilst only 20% had suffered mental health
issues before starting their career in astrophysics, $\sim$45% said that they
suffered with mental health problems since starting in astrophysics. Here we
provide results from the survey as well as possible avenues to explore and a
list of recommendations to improve (early) careers in astrophysics.

###### keywords:

careers, well-being

##  1 Introduction

Astrophysics is an exciting subject that attracts many young people, as there
are many rewards to be had in research in this field, such as enjoying
intellectual challenges, interacting with knowledgeable and fascinating
colleagues, the possibility to be creative and discover new things and
travelling, to name but a few. However, in recent years a general feeling of
discouragement has been observed in a significant fraction of doctoral
researchers and post-docs (e.g. Woolston 2019; Auerbach et al. 2018). In some,
the feelings are tending towards distress, which can lead to terrible
consequences.

To understand the situation in France, we put in place an anonymous survey
using the platform Framaforms. The survey was open from 29th March - 3rd May
2021 and the questions were provided in English and French. It was announced
via the French national astronomy and astrophysics society (SF2A) newsletter,
in French astrophysics laboratories, as well as a couple of Swiss/Canadian
institutes and some French nuclear and particle physics institutes with groups
working on astrophysics. The questionnaire covered five main areas, namely
general questions about work, such as favourite aspects of astrophysics
research, the number of hours worked, perceived external constraints and
future plans for remaining in the field. We also asked about relationships
with colleagues, notably any issues concerning harassment or discrimination.
We questioned about mental health issues, both before and since working in
astrophysics. We requested suggestions for improvements that could be made as
well as positive feedback and finally we inquired about some demographics,
such as the respondents age, position, country where they are working,
nationality and gender. None of the questions were obligatory. The results and
a discussion are presented in the following sections, taking into account the
small number statistics and eventual bias. Our aim was to identify reasons for
any suffering, identify improvements that can be made, propose solutions to
laboratories, doctoral schools and gouverning bodies and ultimately improve
the PhD, post-doc and career experience.

##  2 Results from the survey

276 people responded to the survey, but as none of the questions were
obligatory, not everyone responded to each question. 57.8% of respondents
identified as male, 40.6% as female and 1.6% identified as other. The survey
was open to anyone from planetary science/astrophysics or connecting areas,
but targeted doctoral researchers and post-docs. As a result, the majority of
the respondents were doctoral researchers (108 respondents) and post-docs (99
respondents). 9 respondents were undergraduates and 62 in a permanent position
(27 with (teaching) duties and 35 with no formal duties). The large majority
of respondents (232) worked in France, with only 46 working outside of the
France. Two thirds (190 people) were French and one third (86 people) were of
a different nationality.

When asked about what was the best aspect of the job, almost all respondents
replied that they enjoyed the intellectual challenge (243 people), discovering
new things (209), the independence they had in their work (192) and
interacting with colleagues (188). About half of the respondents enjoyed the
creativity of their work (147 respondents), travelling (119) and sharing their
discoveries (114 people). Less people cited the University/academic
environment as their preferred aspect of their job (97 people), 54 appreciated
the fact that their acquired skills will be useful for a future position, 39
cited the social life and just 6 evoked their salary as one of their favourite
things. Other things that were occasionally cited were the prestige of the
position, the international environment and supervising students.

Figure 1 shows the number of hours worked per week estimated by the
respondents. In France, the working week is 35 hours and doctoral researchers
sign a contract stipulating this volume. 44% of respondents felt external
pressure to work outside legal hours, whilst 49% did not feel that pressure
(7% did not know whether they felt external pressure). 55% felt that they
should work outside of legal hours (37% that they shouldn’t and 8% did not
know). The reasons cited as to why long hours were worked were to be
competitive/obtain a permanent position, because they enjoyed working more
hours, because they can’t achieve the work required without working longer
hours, they are unable to switch off, they felt that more work is expected
from post-doc/PhDs than permanent staff and some felt that as others work
outside legal hours, so should they.

Figure 1: The number of hours worked per week by the respondents.

With regards to job satisfaction, more than half agreed with the statement
Research is the best job that you can have and almost three quarters felt that
their work gave them a sense of purpose and just over a half agreed that they
looked forward to going to work every day. 61% felt well integrated in their
institute.

With regards to work-life balance, 62% said that they got sufficient sleep
most nights. 35% felt that their life was balanced with respect to work,
outside activities and sleep. 55% were satisfied with their living conditions
and 48% were satisfied with their financial situation. 54% felt that the
environment in which they work inspires them, 61% agreed that senior
colleagues are there for them when needed and 48% agreed that they handle
setbacks and disappointments in their work well. Just 36% agreed that they
were satisfied with their career progression. 64% planned to stay in academia,
with 11% planning to leave and 25% unsure. However, when asked if they would
stay in academia if they were guaranteed a permanent position, 81% said they
would stay, 5% said that they would leave and 14% were unsure. Difficulties
cited were precarity (most highly cited), the geographical instability due
short term contracts, the pressure felt to publish both frequently and high
impact papers, feeling undervalued, the general disregard for well-being in
the domain, supervisors with (very) poor management skills, difficulties in
competing with child-free colleagues, a perception that people in positions of
power may misuse their privilege, a lack of information provided for non-
academic areas of research (how to access resources, etc) and the large amount
of bureaucracy, especially when entering a new institute.

With regards to people’s living situations, 13 people said that they had taken
on a second job to supplement their salary and 30 people were struggling with
debt. 23 post-docs had children or family members to care for, while 6
doctoral researchers had family members to care for. 20 doctoral researchers
and 35 postdocs were living apart from their partners and/or children. 10
permanent staff were also living apart from their partners and/or children.
30% of the women were living apart from their partners and/or children but
only 18% of men.

29% of the people responding to the survey had experienced harassment or
discrimination since working in the domain. A further 4% were unsure whether
they had experienced harassment or discrimination. Only 26% of those that had
experienced harassment or discrimination reported the incident(s). Reasons why
the incidents were not reported were because the respondents were embarrassed
by the situation (20%), they didn’t feel that someone would listen (37%), they
felt that other people have worse problems (25%), they didn’t know where to go
for help (16%) or due to a language barrier (2%). The types of harassment or
discrimination encountered are shown in Figure 2. Respondents who chose other
cited discrimination based on nationality, discrimination based on hierarchy,
discrimination due to having kids (or not), language discrimination and
discrimination due to research subject. Whilst the data is incomplete for the
gender of respondents having experienced gender discrimination, 32 were
female, 2 male and 0 other.

Figure 2: The nature of the different types of harassment/discrimination
encountered by respondents and the number of people experiencing the different
types of incidents. Respondents who chose other cited discrimination based on
nationality, hierarchy, due to having kids (or not), language discrimination
and discrimination due to research subject.

We asked how often people felt overwhelmed by their situation at work over the
course of the last year. 10% felt overwhelmed all of the time and 34% had
often felt overwhelmed. Just 6% had not felt overwhelmed at all over the last
year. Of those that felt overwhelmed all of the time, none of them were
permanent staff. 43% of all respondents agreed that they were happy with their
health and well-being.

Concerning mental health, 20% of respondents stated that they suffered from
depression or other mental health problems before starting in research,
however since starting their career, 44% of respondents suffer from depression
or other mental health problems. The types of health issues suffered by the
respondents both before starting research in astrophysics and since starting
are given in Figure 3 . 41% have sought help for these issues. The other 59%
have not sought help because they were embarrassed by the situation (15%),
they didn’t feel that someone would listen (13%), they felt that other people
have worse problems (51%), they didn’t know where to go for help (12%) or due
to a language barrier (not speaking the local language, 9%). The problems
experienced since starting astrophysics have caused some of the respondents to
turn to alcohol abuse (23 people), drug abuse (8 people), other substance
abuse (2 people), disordered eating (32 people), self-harm (9 people) and one
suicide attempt in an aim to deal with their problems.

Figure 3: The nature of the different mental health issues suffered by
respondents and the number of people experiencing them, before starting in
astrophysics research (blue) and since starting in the domain (red).
Respondents who chose other cited post-traumatic stress syndrome, burnout,
gender dysphoria, sleep disorder and imposter syndrome.

We also questioned about possible solutions. 81% of respondents agreed that
PhD and post-doc supervisors should get training in supervision and 73% agreed
that academic staff in general should get training in mental health issues,
while 76% felt that more discussion of well-being should take place. Other
suggestions from respondents included, longer temporary contracts ($>$ 3
years), mentoring or general help to construct a future either in or out of
research, improving relations between permanent and temporary staff, improving
communication by having more open discussion on working hours, racism, sexism,
etc, providing a realistic outlook about research jobs etc before the PhD,
improving the welcome and provision of information for new hires, providing
information on how to access psychological support (in English), improving
transparency in decisions made and minimising (or helping with) administrative
tasks.

Finally, we also asked about the most positive experiences in astrophysics
research. These were plentiful and included: publishing work, international
connections, international recognition, launching satellites/instruments,
making new discoveries, attending international conferences, working abroad,
getting a PhD, doing outreach, teaching, collaborating, interdisciplinary
work, meeting people, learning, supervising, receiving constructive feedback,
having scientific discussions, observing, changing domains, having great
ideas, having proposals accepted, promotions, press releases and sharing
success and contributing to big projects.

##  3 Discussion

Whilst the majority of respondents were male, the percentage of female
respondents (see Section 2) was far in excess of the number of female
astrophysicists in France ($\sim$25%). This is a well known phenomenon, where
more women than men respond to online surveys e.g. Cull et al. (2005). Women
may also feel more concerned by the topics discussed, enhancing the percentage
of respondents, as more women than men have suffered from gender
discrimination (see Section 2) and more of the women stated that they suffered
from depression and/or mental health issues (54% of the women that responded)
compared to 34% of men that responded, similar to numbers found by Evans et
al. (2018). 100% of those who replied to the gender question as ’other’ also
stated that they suffered from depression and/or mental health issues.

68% of respondents worked significantly in excess of the legal number of hours
per week prescribed in France, primarily due to external pressure. These were
almost all non-permanent staff, the same group that felt that they were either
often or constantly overwhelmed. The proportion of men and women working more
than the number of legal hours was similar. It is clear that working in excess
of 90 hours per week leaves no time for any other activity during the week
outside of work, sleeping and eating, which is clearly unhealthy. However,
only a third of those working long hours were the same people that felt that
they did not get enough sleep, indicating that it was often not long working
hours that reduced sleep. Stress could be a factor preventing people from
sleeping. The pressure felt to publish and/or be competitive/obtain a
permanent position were frequently cited in the reasons for working long
hours. The figures indicate that temporary staff are working longer hours than
permanent staff, putting them more at risk of poor (mental) health.

One of the major sources of stress is the precarity in astrophysics research,
as seen from the number of people that plan to leave academia, but would stay,
if they could be guaranteed a job. Precarity was also the most highly cited
difficulty encountered in astrophysics, along with related issues such as
geographical instability. However, a fifth of respondents would not definitely
stay in academia even if they were guaranteed a permanent job. Of those that
are definitely planning to leave, one third had experienced harassment or
discrimination in astrophysics or had experienced mental health issues since
starting, which could explain part of their motivation. A further third is due
to precarity issues, leaving a final third who are leaving for other reasons.

The number of people suffering with mental health issues since starting their
career in astrophysics has more than doubled compared to prior to starting
their career. This is a startling rise, but numbers recorded are commensurate
with the study of graduate students in biosciences at the University of
Berkeley (Evans et al. 2018) only slightly higher than in other studies e.g.
Woolston (2019) who polled $>$6000 doctoral researchers from all subjects in
various countries around the world or the study by Auerbach et al. (2018)
carried out by the World Health Organisation that revealed that 31% of
students showed signs of major depression, general anxiety disorder or panic
disorder etc, in the previous 12 months. It is clear that there is a major
problem, not just in France, but all over the world and this needs to be
resolved to restore people’s mental health and well-being. The problem needs
to be tackled at the source and many of the suggestions proposed or agreed on
by the respondents could go someway to help, namely training PhD and post-doc
supervisors in supervision and training academic staff in mental health
issues, along with more open discussion on well-being, working hours, racism,
sexism, sexual harrassment, bullying, etc. Lengthening temporary contracts and
providing mentoring or general help to construct a future either in or out of
research could also help (see Section 4).

Finally, this survey was planned for release on March 30th 2020, but was
delayed for a year because of the outbreak of the COVID-19 pandemic. It is
clear that the unprecedented situation over the year before releasing the
survey has added stress to everyone’s lives and thus had an impact on well-
being and mental health. It is difficult to fully decorrelate the impact of
the COVID-19 pandemic on the long-term well-being. However, has evident from
other publications (e.g. Woolston 2019; Auerbach et al. 2018) and our own
observations, suffering in (early career) research has been prevalent for many
years before the COVID-19 pandemic outbreak and the pandemic appears to have
simply exacerbated existing problems.

##  4 Recommendations

Following the survey and numerous discussions amongst the authors of this
paper, a dedicated workshop on the issue at the 2021 French National Astronomy
meeting, along with further discussions with other groups which aim to improve
well-being in astrophysics, we have drawn up a list of recommendations for
institutes, masters programmes/doctoral schools and gouverning bodies. Some of
the points may seem minor, but implementing the recommendations would go a
long way to helping people feel included, accepted and happy in their job. We
are aware that some of these recommendations have been put into place in some
institutes, or some specific areas, but applying them across the board could
help significantly to improve the day to day life of our colleagues.

During our discussions, it became clear that there is a lot of help and
information already available, but it is often dispersed, making access
complicated. We propose a single, highly visible webpage (e.g. as a part of
the SF2A webpages) which regroups all of the relevant information (well-being,
support for harassment, mental health support, etc) so colleagues and
organisations know where to locate it. In addition, a working group is being
put into place to help maintain the webpage and help implement current and
future recommendations.

###  4.1 Recommendations at the institute level

A common source of stress for younger colleagues on short term contracts is
that they are frequently required to move institutes, often in different
countries where they don’t necessarily speak the local language, and this
requires a lot of administrative activities with many papers to fill out,
often available in the local language only. This makes a short and simple job,
long and complicated. Providing paperwork in English would facilitate this
aspect. Further, a lot of new recruits find that no provision for an office
space, a computer or other basics have been organised at their arrival.
Putting these things into place in advance and introducing the new arrivals to
key people immediately, can make new arrivals feel welcome and appreciated.
Further, providing information booklets (with information on opening a bank
account, finding an appartment, organisation within the institute, how to
access the intranet, mailing lists, etc) along with introductory meetings
(introducing key people, key structures, etc) will also help their
integration. Up to date information on the local website (in English) and
mailing lists (with specific mailing lists for students and post-docs) would
also facilitate integration. More (non-)scientific events should be organised
to facilitate colleagues meeting and creating a team spirit. This would also
help bridge the perceived gap between permanent and temporary staff. Institute
messages should ideally be written in the local language as well as English to
be inclusive, as part of an effort to reinforce inclusivity.

Many (international) mentor programmes exist, but institutes should also
provide a mentoring programme to be able to provide local information
(recruitment possibilities in the area, specificities for applying for local
jobs, applying for funding etc). Whilst finding mentors in an institute with a
broad knowledge of working in astrophysics within France and abroad as well as
working in industry, for example, will be difficult to find, having a pool of
mentors identified (and their expertise) would mean that colleagues will know
who to consult about which issue. Regular or occasional mentoring should be
provided. Open discussion of common problems encountered (e.g. imposter
syndrome, well-being, hours worked, racism, sexism, etc) are recommended. This
could be through a weekly or bimonthly coffee or dedicated seminars, for
example.

Not all students and post-docs will stay in academia. More information should
be provided to younger colleagues on moving to other domains and to remove the
perceived stigma that leaving academia is shameful. Institutes should aim to
keep contact with previous researchers that have moved into industry. They
could be invited once a year, perhaps during the PhD day, to provide
information on finding jobs outside of academia.

###  4.2 Recommendations for masters programmes and doctoral schools

Several respondents to the survey felt that they did not have a clear picture
about their chances of getting a permanent job in astrophysics before deciding
to start a PhD and as a result felt that they wouldn’t have chosen such a
career path if they had had a proper understanding of the requirements.
Masters programme should therefore provide information to all students
spelling out the difficulties, to allow students to take an informed decision,
however, labouring the point can be a source of stress to others. Doctoral
schools should also try to form alumni associations, if one does not already
exist at that particular University, so that current students can contact
previous students to get feedback and tips on staying in research or moving
into industry. More talks/information should also be provided about bad
practice (supervisors requiring replies to emails late at night or at the
weekend, long working hours, etc). In general, we recommend that the training
during Masters and PhD programmes should take into account the fact that the
majority of the students will not work in academia over the long term.

###  4.3 Recommendations for gouverning bodies

To avoid the stress of frequently changing jobs, and losing friends, support
networks, etc, post-doc positions could be increased in length (ideally beyond
three years). Where possible, post-doc salaries should be harmonised and
provide for an evolution of the salary over the time the post-doc is employed.
This could be done for example through salary recommendations when applying
for national funding, if it is not yet implemented.

Everyone working in astrophysics should be trained in well-being, harassment,
discrimination etc. This will enable them to be aware of problems and be
familiar with the language associated with these issues. This training should
be obligatory and done using online courses with tests, which need to be
passed every few years. A proto-type demonstrator is currently being drawn up,
to provide a basis for a nationally deployed platform. Every institute should
have a clearly identified person that is properly trained to deal with
harassment. This person should not be the direct superior of anyone within the
institute to avoid a conflict of interest.

##  5 Conclusions

Through this short paper, we aimed to share results from our survey and
provide some discussion and recommendations that could help improve the day to
day lives of colleagues. By being aware of the problems and implementing
solutions, we can all help to improve our colleagues lives and make our
environment a better place to work in and above all preserve the (mental)
health of all.

###### Acknowledgements.

We thank the people that answered the survey, those who will take on board
what has been said and those that will help improve research careers in the
future. We are grateful to Benoît Mosser for insightful discussion and helpful
comments on this paper. We acknowledge Framaforms, Topcat and Excel in the
production of this work. We remember our colleagues that departed too soon,
your memory will help us strive towards a better tomorrow.

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