11institutetext: Centre for Computational Imaging and Simulation Technologies
in Biomedicine, School of Mechanical Engineering, University of Leeds, Leeds,
UK 22institutetext: Institute of Medical and Biological Engineering, School of
Mechanical Engineering, University of Leeds, Leeds, UK 33institutetext:
Department of Medical Physics and Engineering, St James’s University Hospital,
Leeds Teaching Hospitals NHS Trust, Leeds, UK 44institutetext: Division of
Informatics, Imaging, and Data Sciences, Faculty of Biology, Medicine and
Health, University of Manchester, Manchester, UK 55institutetext: School of
Medicine and Population Health, University of Sheffield, Sheffield, UK
66institutetext: School of Computing Science, University of Glasgow, Glasgow,
UK

# Deep-Motion-Net: GNN-based volumetric organ shape reconstruction from
single-view 2D projections

Isuru Wijesinghe 1122 Michael Nix 33 Arezoo Zakeri 44 Alireza Hokmabadi 55
Bashar Al-Qaisieh Ali Gooya 3366 Zeike A. Taylor 1122

###### Abstract

We propose Deep-Motion-Net: an end-to-end graph neural network (GNN)
architecture that enables 3D (volumetric) organ shape reconstruction from a
single in-treatment kV planar X-ray image acquired at any arbitrary projection
angle. Estimating and compensating for true anatomical motion during
radiotherapy is essential for improving the delivery of planned radiation dose
to target volumes while sparing organs-at-risk, and thereby improving the
therapeutic ratio. Achieving this using only limited imaging available during
irradiation and without the use of surrogate signals or invasive fiducial
markers is attractive. The proposed model learns the mesh regression from a
patient-specific template and deep features extracted from kV images at
arbitrary projection angles. A 2D-CNN encoder extracts image features, and
four feature pooling networks fuse these features to the 3D template organ
mesh. A ResNet-based graph attention network then deforms the feature-encoded
mesh. The model is trained using synthetically generated organ motion
instances and corresponding kV images. The latter is generated by deforming a
reference CT volume aligned with the template mesh, creating digitally
reconstructed radiographs (DRRs) at required projection angles, and DRR-to-kV
style transferring with a conditional CycleGAN model. The overall framework
was tested quantitatively on synthetic respiratory motion scenarios and
qualitatively on in-treatment images acquired over full scan series for liver
cancer patients. Overall mean prediction errors for synthetic motion test
datasets were 0.16$\pm$0.13 mm, 0.18$\pm$0.19 mm, 0.22$\pm$0.34 mm, and
0.12$\pm$0.11 mm. Mean peak prediction errors were 1.39 mm, 1.99 mm, 3.29 mm,
and 1.16 mm.

###### Keywords:

Motion Modelling Adaptive Radiotherapy Graph Neural Network Graph Attention
X-ray image Synthetic Data.

##  1 Introduction

In this paper, we present a method, labelled Deep-Motion-Net, for estimating
3D volumetric organ deformation from a single in-treatment kV planar X-ray
image acquired at any arbitrary gantry (projection) angle. Internal anatomical
motion confounds the precise delivery of radiation to target volumes during
external beam radiotherapy. Precision is critical for achieving tumour
coverage while preserving surrounding sensitive healthy tissues( [1]) since
normal tissue damage prevents dose escalation to the gross target volume (GTV)
to the desired therapeutic level. In hypo-fractionated treatments (i.e.
Stereotactic Ablative Body Radiotherapy), wherein higher, but more precisely
targeted doses are used, unaccounted motion is yet more critical and sometimes
prohibitive. Hence, to fully exploit the potential of external beam radiation,
tumour and organ movements must be addressed during irradiation such that more
radiation is delivered to the target tumour while sparing organs-at-risk
(OARs).

Typically, a cone beam CT image is acquired at the start of treatment and used
to ensure the patient is correctly positioned with respect to the linear
accelerator (linac). However, this static single-timepoint representation
ignores anatomical motion that subsequently occurs during radiation delivery,
which may cause overdosing of OARs, or underdosing of tumour, leading to
poorer outcomes for survival and post-treatment morbidity ([1]). To deal with
respiratory-induced tumour/organ motions, numerous mitigation strategies have
been developed, broadly categorised as either passive or active ([1, 2]).
Defining an internal-target-volume (ITV) that includes a motion-encompassing
margin is an example of a passive mitigation technique( [2]). The motion-
encompassing margin is normally estimated based on 4D-CT data acquired at
treatment planning and hence reflects an average estimate of the motion that
corresponds with in-treatment motion with uncertain accuracy. While these
margins allow for inaccuracies during treatment, they also result in greater
irradiation of normal tissues( [3]), meaning overall radiation intensity must
be reduced, and treating the target tumour becomes more difficult.

To minimise, or even eliminate the ITV, effective active motion management is
critical. Respiratory-gating is a popular method since it is relatively easy
to implement, but it implies a longer time to deliver the specified dose
because radiation is only delivered for a segment of the respiratory cycle(
[1]). In contrast, real-time tracking, which repositions and/or reshapes the
radiation beam as the target moves, implies no prolongation of treatment
sessions but is more technically challenging to realise. Moreover, its
effectiveness can be limited by the time delay between detecting a change in
target position and the system adjustment, resulting in a persistent lag in
the system’s response to the target position.

All such active methods critically rely on real-time information on the tumour
position during treatment. Gating and tracking techniques often rely on
implanted markers to track the target mobility in real-time. These markers are
invasive, and in any case, only provide information on specific locations
(i.e., marker positions) inside tissues, rather than the target/OARs as a
whole( [4]). Techniques based on non-invasive imaging are preferred. Treatment
systems integrating magnetic resonance imaging (MR-linac) arguably provide an
excellent basis for this( [5]) in the form of real-time in-treatment images
that are radiation-free and have good soft tissue contrast and resolution(
[6]). However, current MR-linacs provide only orthogonal pairs of 2D slices
rather than true 3D images and hence do not directly enable visualisation of
the whole 3D geometry of a target tumour region and surrounding OARs. More
importantly, such systems are expensive and rare, meaning very few patients
currently can access them.

In contrast, most conventional linacs are equipped with on-board kV X-ray
imaging, and such systems will inevitably be used to treat most patients;
techniques that can recover anatomical motion from such images are therefore
attractive. The key challenges, however, are poor soft tissue contrast and
compression of volumetric information along projection directions.
Reconstructing high-quality 3D organ shapes from such images is, therefore,
difficult. We hypothesise nonetheless that when combined with suitable prior
information in the form of learned models of motion patterns and corresponding
image appearance, such images do provide sufficient information to recover
accurate 3D anatomical information.

We propose a deep graph neural network (GNN) model for this purpose. The model
learns a mapping from kV image-derived features to displacements of nodes in a
patient-specific template organ mesh. Features are extracted by a
convolutional neural network (CNN) image encoder, while regression of the
features with node displacements is learned by a graph attention (GAT)
network. Importantly, the complete model is end-to-end trainable by virtue of
a series of feature pooling networks (FPNs) that fuse image features with the
3D graph nodes, eliminating non-trainable components (i.e. vertex projection
onto the 2D image space) that would otherwise be required. Finally, the model
also learns projection angle-dependent features by encoding the angle in an
additional channel to the input image. By this means, the model can
reconstruct the 3D anatomy from kV images acquired at any projection angle. To
the best of our knowledge, this is the first framework capable of
reconstructing 3D anatomy from such inputs. While the method is general, we
focus in this work on respiratory motion, and evaluate the method using
synthetic and real images from liver cancer patients.

##  2 Previous work: 3D shape reconstruction from single-view projections

We here review existing techniques for recovering 3D geometry from 2D images,
comparable to our approach. Another major class of techniques are so-called
surrogate-driven models, which estimate internal anatomical motion using some
surrogate signal under the assumption the two are well correlated. For further
information on such approaches, interested readers are referred to [7].

###  2.1 RGB image-based reconstruction

Several reports have described techniques for reconstruction from RGB images.
For example, [8] proposed the GNN-based Pixel2Mesh algorithm, which deforms an
ellipsoidal surface mesh using CNN-derived semantic characteristics from an
input image, and applies it to the analysis of natural shapes (aeroplanes,
chairs, cars, etc.). The ellipsoidal starting mesh limits the approach to
genus-0 shapes, though in principle it could be adapted to other topologies.
[9] extended the method to better capture local surface geometry, though the
topological constraints remained. Similar ideas were used in [10, 11] to
reconstruct 3D human body shapes from single RGB images. In the medical
domain, [12] proposed a CNN architecture for reconstructing 3D lung shapes, in
the form of point clouds, from a single-view 2D laparoscopic image.

###  2.2 Projection image-based reconstruction

While clearly sharing elements of our target problem, reconstruction from RGB
images rather than 2D projections is nonetheless a substantially different
one. Various approaches addressing the latter scenario have appeared recently.
[13] proposed X2CT-GAN to reconstruct 3D-CT volumes from bi-planar 2D X-ray
images using generative adversarial networks. Reconstruction of full CT
volumes is impressive, however, in our scenario only single-view projections
are available, making the problem significantly more challenging.

[14] proposed a CNN-based approach for reconstructing lung surface shapes from
single-view 2D projections. Their method employs free-form deformation to
learn the optimal smooth deformation from multiple templates to match the
query 2D image. [15] proposed X-ray2Shape to reconstruct 3D liver surface
meshes by combining GNN and CNN networks (the latter to encode image
features). A mean shape derived from 124 patients was used as prior (i.e.
initial template) and deformed by the GNN to match the individual organ shape.
Later, the same authors [16, 17] extended the approach to reconstruct multiple
abdominal organ shapes from a single projection image. These approaches [14,
15, 16, 17] are designed to operate on images acquired at fixed projection
angles—front view projections, equivalent to gantry angle 0 in our case—and
therefore cannot directly accommodate images from arbitrary angles, as
required here.

This limitation was addressed by [18], who proposed a CNN architecture to
predict principal component analysis (PCA) coefficients in a 4D-CT-based
breathing motion model. The authors used an angle-dependent region of interest
(ROI) 2D projection mask to remove pixels unrelated to respiration and an
angle-dependent fully-connected (FC) layer. This layer was designed to handle
discrete (integer-valued) angles ranging from 0 to 360, and only a single
group of weights and biases were used to generate its output for each degree
of the projection angle. For real, continuously varying angles, binary
projection masks at the nearest integer were chosen. However, challenges
appeared in cases with significant intensity variations between DRRs and CBCT
projections, affecting localization accuracy due to intensity shift issues.
Additionally, reconstruction artefacts in 4D-CT images, such as structural
blurriness or duplications, influenced localization accuracy. The study
suggests potential limitations in handling variations in breathing amplitude
and patient setup during treatment, recommending retraining PCA and CNN models
with repeated 4D-CT data acquisition for validation. Furthermore, tumour
localization using binary projection masks proved challenging for certain
cases and projection angles, when the corresponding images contained little
information related to breathing motion [18].

A further limitation of the foregoing approaches is their prediction only of
organ surface shapes, rather than their full volumes. A true volumetric
approach for estimating liver deformations was recently proposed by [19].
Their method first used a GNN to predict the deformed liver surface. These
deformations were then passed as boundary conditions to a finite element model
of the liver, which computed the corresponding volumetric deformations. In
this way, some level of biomechanical constraint was also introduced. The
approach was evaluated for several projection angles (specifically:
$0^{\circ}$, $45^{\circ}$, and $90^{\circ}$). However, the model required
retraining for each angle; that is, each new angle effectively required a
separate model. The model also required a very high number (3840) of image
features to be encoded on graph nodes; in our approach, we use only 20.
Finally, while biomechanical constraints can, in principle, be attractive for
enforcing physical plausibility, the finite element solutions were, in
practice time consuming, which may be significant for clinical use, especially
in-treatment adaption of therapy.

All of these 3D geometry reconstructions using single-view projection-based
approaches utilized DRR images with a wide field-of-view (FOV) to encompass
the entire liver anatomy for their experiments. However, in clinical settings,
projection images are usually acquired with a limited FOV. This discrepancy
poses challenges for prior methods [14, 15, 16, 17, 19] when extracting
features by projecting vertices onto the DRR/kV plane, as the projected mesh
nodes may extend beyond the boundaries of the projection FOV, thereby
hindering effective feature extraction [19].

###  2.3 Recapitulation

Several approaches to reconstructing organ geometry from single-view
projection images have been proposed. Their main shortcomings, addressed by
our proposed method, are as follows:

  * •

_Fixed projection angle_ : Most existing approaches [14, 15, 16, 17, 19] are
designed to operate on images acquired at fixed projection angles rather than
the varying angles used during RT.

  * •

_Surface reconstruction only_ : Most existing approaches [14, 15, 16, 17, 18]
reconstruct only surface representations of the involved organs and do not,
therefore, describe deformations within those organs.

  * •

_Wide field of view_ : Most existing approaches [14, 15, 16, 17, 19] depend on
DRR images with a wide FOV, not reflective of the usual clinical situation.

##  3 Methodology

Building on several of the works cited above, the core of our approach is a
GNN that learns mappings from kV image features to nodal displacements of a
patient-specific organ mesh. The model is trained individually for each
patient. This section provides a comprehensive description of the components
of the approach, including the 3D organ representation, model architecture,
and loss functions.

Figure 1: Illustration of the Deep-Motion-Net architecture. A 2D-CNN image
encoder extracts projection angle-dependent semantic features from an input kV
X-ray image. A feature pooling layer comprising four learnable feature pooling
networks attaches these features to the appropriate vertices in the patient-
specific template mesh. Finally, a graph-attention-based network predicts the
corresponding mesh deformation.

###  3.1 3D organ shape representation

We use a 3D unstructured tetrahedral mesh to describe the volumetric organ
shape, rather than its surface only. The mesh can be described as an
undirected graph $G=\\{V,E,F\\}$, where $V$ is the set of $N$ vertices in the
mesh, $E$ represents the set of edges between connected vertices, and $F$ are
feature vectors attached to vertices. Patient-specific organ template meshes,
derived from reference CT volumes, are constructed for each patient. In our
experiments we used meshes with $N=785$, $827$, $803$, and $756$,
respectively, for livers in four patients.

###  3.2 Model architecture

The proposed architecture (shown in Figure 1) consists of two components: a
2D-CNN encoder with four learnable feature pooling networks (FPNs), which
extract perceptual features from the kV image and attach them to mesh nodes
and a GAT-based mesh deformation network.

####  3.2.1 Incorporating projection angle

Inputs to the 2D-CNN encoder are a single-view kV image and its corresponding
projection angle. We first normalise the projection angle by dividing it by
360 since the gantry rotation varies from 0 to 360 degrees. Before sending the
input image to the image encoder, we concatenate the projection angle
information as an extra channel. This concatenation part is accomplished by
expanding and reshaping the projection angle to align with the spatial
resolution of the input image (i.e. 256$\times$256).

####  3.2.2 2D-CNN configuration

The projection angle-dependant perceptual features of the image are then
extracted using four convolutional layers in the image encoder, containing 16,
32, 64, and 128 filters, respectively. For all convolutional layers, the
kernel size was set to 3$\times$3, and stride and padding were both set to 1.
Exponential Linear Units (ELUs) were applied for non-linearity after every
convolutional operation. Hidden layer outputs were normalised using group
normalisation ([20]) since this helps reduce the internal covariate shift,
which regularly alters the distribution of the hidden-layer activations during
model training. Output feature maps of each convolutional layer were then
down-sampled using 2$\times$2 max-pooling layers with stride two before
passing into the next layer.

####  3.2.3 Feature pooling networks

We integrated learnable feature pooling networks (FPNs) to efficiently learn
optimal associations between image features and mesh nodes in our
architecture. This utilization of FPNs allows the network to maximise the
predictive performance through end-to-end training, eliminating non-trainable
components and enabling full optimization of feature learning capabilities for
the downstream graph network. We use four FPNs, each coupled with its
respective CNN convolutional layer (Figure 1). Each FPN has two layers: an
adaptive average pooling layer (AAP) and a FC layer. The AAP, with output size
7$\times$7, is applied over the output of the corresponding convolutional
layer to reduce the dimension so that an input feature map with dimensions
$H\times W\times C$ is reduced to $7\times 7\times C$. The output is flattened
before sending it into the FC layer, which contains $5N$ neurons. We reshaped
the output feature vector of each FPN into ($N$, 5). These outputs were then
concatenated with 3D coordinates of the template mesh before feeding into the
graph network. Each mesh vertex thereby acquires a total of 23 features: five
from each of the four FPNs, and three representing the 3D vertex position.

####  3.2.4 Mesh deformation network

The objective of this network is to estimate the 3D coordinates for each
vertex in the deformed mesh configuration. We developed a GNN architecture
which relies on a series of GAT-based blocks with residual connections (i.e.
skip/shortcut connections). We applied residual connections to increase the
impact of earlier layers on the final node embeddings. These connections
substantially speed up training and produce better quality output shapes. The
fundamental building block is identical to the Bottleneck residual block
([21]), with 1$\times$1 convolution and 3$\times$3 convolution layers replaced
by per vertex FC layers and GAT layers ([22]), respectively. Further, group
normalization layers are used instead of batch normalization ([23]) since
small batch sizes result in incorrect estimates of batch statistics, which
substantially increases model error. We employed ELUs to impart non-linearity.

This deformation network is similar to the graph-CNN architecture described in
[10], but with two differences: graph convolutional network (GCN) layers are
replaced by GAT layers and ReLU is replaced by ELU activation. GAT layers
incorporate attention mechanisms which allow the assignment of different
weights for different neighboring node feature vectors depending on how they
interact. GCNs ([24]), by contrast, use isotropic filtering and thereby assign
similar weight to all feature vectors around the current node. ELU activation
avoids the dying ReLU problem and may generate negative non-linear outputs.

###  3.3 Loss functions

The overall objective function $\mathcal{L}$ is defined as:

$\mathcal{L}=\mathcal{L}_{Shape}+\lambda\mathcal{L}_{Laplacian},$ (1)

with weighting term $\lambda$. $\mathcal{L}_{Shape}$ quantifies the difference
between the predicted and ground-truth 3D meshes. The template mesh starting
shape is defined by its vertices $V$ (Sect. 3.1). We define $Y$ and $\hat{Y}$
to be the ground-truth and predicted deformed positions of these vertices. An
intuitive objective is then to minimize the per vertex $L_{1}$ loss between
$Y$ and $\hat{Y}$:

$\mathcal{L}_{Shape}=\sum_{i=1}^{N}\mathinner{\\!\left\lVert\hat{Y}_{i}-Y_{i}\right\rVert}_{1},$
(2)

where $Y_{i}$ and $\hat{Y}_{i}$ are the $i^{\rm{th}}$ vertices in the
respective sets.

Using $\mathcal{L}_{Shape}$ alone the vertices were found to move too freely.
We introduced a discrete Laplacian ([8]) loss $\mathcal{L}_{Laplacian}$ as a
regularization term to limit this freedom by ensuring vertices do not move too
far in relation to their neighbours. The additional constraint ensures that
the mesh has a smooth surface. The discrete Laplacian of a vertex
$\hat{Y}_{i}$ is denoted as:

$\delta_{\hat{Y}_{i}}=\frac{1}{|S(\hat{Y}_{i})|}\sum_{j\in
S(\hat{Y}_{i})}(\hat{Y}_{i}-\hat{Y}_{j}),$ (3)

where $\hat{Y}_{j}$ is a neighbouring vertex of $\hat{Y}_{i}$ and
$S(\hat{Y}_{i})$ denotes the set of all such neighbours. The discrete
Laplacian loss is then given by:

$\mathcal{L}_{Laplacian}=\frac{1}{N}\sum_{i=1}^{N}\mathinner{\\!\left\lVert\delta_{V_{i}}-\delta_{\hat{Y}_{i}}\right\rVert}_{2}^{2},$
(4)

where $\delta_{V_{i}}$ and $\delta_{\hat{Y}_{i}}$ are the discrete Laplacian
before and after the deformation, respectively.

In our experiments, we used $\lambda=0.1$ to balance the weights of the two
losses.

###  3.4 Implementation and training details

The complete network was implemented using PyTorch and PyTorch-geometric
([25]). The model was trained using the Adam optimizer, with a learning rate
of 0.0002 and weight decay of 0.001. The batch size for both training and
validation datasets was set to 16. Group normalization was used to normalize
the hidden layer outputs of both 2D-CNN and GNN. We used single-headed
attention in the GAT layers due to memory restrictions. Early stopping was
employed to monitor the validation loss with a patience of 30 consecutive
epochs, and if the loss did not improve, the optimizer itself stopped the
training. However, if there was no progress after eight consecutive epochs,
the learning rate was decreased by a factor of 0.8. All weights were
initialized using the scheme in [26]. The gradient descent converged after 400
epochs to the optimal solution. As described in 0.A, we conducted a series of
experiments to determine the optimal network components. The training lasted
approximately 36 hours with 256$\times$256 image resolution on a Nvidia Quadro
RTX 4000 GPU using a Precision 7820 Tower XCTO Base workstation.

##  4 Synthetic dataset generation

Model training requires paired sets of organ motion instances and
corresponding kV images. However, to the best of our knowledge, there are no
means of directly measuring such motions while also acquiring the requisite
images. Hence, we use synthetically generated data to train and, in this work,
to evaluate the model. Plausible patient-specific motion patterns are
extracted from 4D-CT images, and new synthetic instances are produced by
interpolating and, within reasonable bounds, extrapolating from these. The
process is as follows: 1) 4D-CT images are analysed using the SuPReMo toolkit
(Surrogate Parameterized Respiratory Motion Model - [27, 28]), which produces,
among other things, a model of the motion present in the images, linked with
appropriate surrogate signals; 2) new, yet plausible motion instances are
generated from this model by randomly perturbing the surrogate signal; 3) the
resulting motion fields are used to deform the reference (phase 0) CT volume;
4) Digitally Reconstructed Radiographs (DRRs) are generated from these
deformed volumes for all required projection angles, and 5) the DRRs are style
transferred to match kV image intensity and noise distributions. The result is
a set of realistic ‘kV’ images of the deformed anatomy acquired at various
projection angles, for which ground-truth 3D motion states are known. Finally,
the target organ is segmented from the reference CT volume, and an organ
template mesh is constructed. Full details are presented in the following
sections.

###  4.1 Generation of synthetic motion states from 4D-CT data

SuPReMo is a toolkit for simultaneously estimating a motion model and
constructing motion-compensated images from a 4D-CT dataset. The resulting
model describes the anatomical motion present in the raw data over a single
(averaged) breath cycle and is linked with corresponding scalar surrogate
signals derived, for example, from breathing traces or image features. For
formulation reasons (see [27, 28]), two surrogate signals are required;
however, these needn’t be independent, and as a practical measure in each case
we constructed the second signals as temporal derivatives of the first,
computed for example using finite differences. Example surrogate signals are
plotted in Fig. 2. Our 4D-CT datasets each decompose the breath cycle into 10
bins (phases).

(a)

(b)

Figure 2: Example surrogate signals: original signals associated with the
input 4D-CT data (red) and randomly generated variations from these (grey),
used in turn to synthesise new motion states. The first and second signals are
plotted at the left and right, respectively.

First, we fit SuPreMo’s motion model for each individual case with input
surrogate signal and 4D-CT data. This returns the motion-compensated
reconstructed 3D-CT (MCR) image volume and the fitted motion model, which are
then utilised to simulate new motion states by varying the input surrogate
signal. Each point $s_{i},\,i\in[0,9]$ on the curve is randomly perturbed by a
value in the range $\pm 0.4s_{i}$. Extrapolating beyond this range is more
likely to cause unrealistic motion and even folding in the resulting images. A
new surrogate signal is then created by fitting a $3^{\rm rd}$ order
polynomial to the new points. The latter ensures the new signal remains smooth
over the full breath cycle. Examples of such generated signals are shown in
Fig. 2. Using this new signal, and MCR as a reference volume, SuPReMo’s motion
model generates corresponding deformed 3D-CT volumes and their related
deformation vector fields.

For each test case (Sect. 5), we created 11 separate surrogate signals, each
comprising ten deformed configurations, resulting in 110 synthetic deformation
states in total. To introduce more diversity into the synthetic motion
instances and substantially deviate from the original 4D-CT data, we
incorporated rigid motions by applying random translations/shifts along the
left-right (LR), anterior-posterior (AP), and superior-inferior (SI)
directions and produced a total of 550 deformed states. This is also
advantageous during testing on real in-treatment kV images, as it reflects the
variations in onboard patient setup across different scan series or fractions,
potentially leading to shifts in the in-treatment kV images.

###  4.2 Generation of synthetic kV X-ray images

For each deformation state, DRRs were obtained from the deformed 3D-CT volumes
using the Siddon-Jacobs ray tracing technique ([29, 30]). The latter, given a
source position and projection direction, computes the line integral of
Hounsfield unit densities along ray lines to a prescribed 2D plane. In
radiotherapy, in-treatment kV images are acquired perpendicularly to the
anatomical axial direction.

The resulting DRRs lack scatter properties and noise characteristics of
genuine kV X-ray images, making them appear sharper and higher in contrast.
We, therefore, used a CycleGAN ([31]) by conditioning on projection angle to
effect DRR-to-kV style transformation. The conditional CycleGAN was trained on
an unpaired set of DRRs and real in-treatment kV images for each case
separately since the FOV acquisition varies from patient to patient. Histogram
equalization was first applied on the kV images to stretch the intensity
histograms concentrated on a narrow interval to a broader range and increase
contrast. All DRRs were then passed to the conditional CycleGAN to create the
final synthetic kV X-ray images.

###  4.3 Creation of template meshes

Binary masks of the relevant organs were extracted from reference 3D-CT
volumes using 3D Slicer’s Segment Editor. These masks were then used to
generate tetrahedral meshes using the Iso2Mesh( [32]) tool in MATLAB. The
resulting meshes were scaled and translated to reflect image voxel sizes and
correct image origins. By these means, the meshes are physically aligned with
the relevant anatomical regions in the 3D-CT volumes. Ground-truth positions
of the mesh nodes for each of the generated deformation states are produced by
interpolating the displacement vector field at the node positions.

##  5 Model evaluation and results

###  5.1 Clinical datasets

We evaluated the Deep-Motion-Net framework using data from four liver cancer
patients, with focus on liver motion. Each patient dataset comprised: 1) a
4D-CT with 10 phases (i.e. 10 $\times$ 3D-CT volumes), spatial resolutions of
$0.98\times 0.98\times 2.0$ mm3, and image dimensions of $512\times 512\times
105$; and 2) two kV scan series, each covering approx. 4-5 mins of free
breathing and a full rotation of the treatment gantry, acquired at the start
of treatment sessions on different days. As per clinical practice, the kV
scans were centered on the liver region and used a constrained FOV. As a
result, for some projection angles, the images include only a segment of the
liver.

###  5.2 Experiments on synthetic data

We first evaluated the framework’s ability to recover motion states
synthetically generated from the clinical data, and for which ground-truth
deformations were correspondingly available. For each patient, synthetic
motion and image data were generated as per Sect. 4. Each patient’s 550
deformation states were then split into training, validation, and test sets in
the proportions 350, 100, and 100, respectively. For training and validation
deformation states, 100 uniformly sampled (i.e. at projection angle intervals
of $3.6^{\circ}$) synthetic kV images were generated (giving 35,000 training
and 10,000 validation images). For test states, 50 kV images were generated at
_randomly_ sampled projection angles (giving 5,000 test images). To ensure
good FOV alignment of the synthetic and real kV images for each patient, each
synthetic image was generated using FOV origin header information from a
corresponding (i.e. acquired at a comparable projection angle) real image
within one of the scan series. To avoid doubt, the real kV images subsequently
played no further role in the experiment. Model-predicted and ground-truth 3D
liver shapes were compared for all synthetic kV images in the test sets.

Summary results are presented in Table 1. The study employed Euclidean
distance as the metric to evaluate the distance errors between ground-truth
and estimated shapes. Distributions of mean and peak errors for each test set,
and for each projection angle (divided into bins), are shown in Figure 3.
Finally, surface renderings of the ground-truth, reference, and predicted mesh
shapes, overlaid on deformed 3D-CT volumes, are presented in Figure 4.

Table 1: Summary statistics for all test sets with synthetic kV images. Patient case numbers are indicated in column 1. $E_{pred}$ and $U_{GT}$ refer to prediction errors and underlying ground-truth nodal deformation magnitudes, respectively. _Mean (std)_ : means (and standard deviations) of values across all nodes, all deformation states, and all projection angles. _Mean peak_ : means of the peak values for each deformation state across all projection angles. _Max peak_ : overall maximum values from all nodes, deformation states and angles. _99 th Percentile_: $99^{\rm th}$ percentile values from all nodes, deformation states and angles. All values reported in mm. Case |  | Mean (std) | Mean peak | Max peak |  $99^{\rm th}$ Percentile
---|---|---|---|---|---
1 | $E_{Pred}$ | 0.16$\pm$0.13 | 1.39 | 6.75 | 0.75
$U_{GT}$ | 10.18$\pm$1.33 | 14.71 | 28.12 | 13.85
2 | $E_{Pred}$ | 0.18$\pm$0.19 | 1.99 | 7.97 | 0.97
$U_{GT}$ | 11.65$\pm$1.76 | 15.76 | 34.91 | 14.38
3 | $E_{Pred}$ | 0.22$\pm$0.34 | 3.29 | 14.66 | 1.81
$U_{GT}$ | 14.89$\pm$2.54 | 19.36 | 49.63 | 17.65
4 | $E_{Pred}$ | 0.12$\pm$0.11 | 1.16 | 4.36 | 0.51
$U_{GT}$ | 10.07$\pm$1.13 | 12.86 | 25.64 | 11.97

(a)

(b)

Figure 3: Effect of projection angle on prediction accuracy: box and whisker
plots of mean (top) and peak (bottom) prediction errors grouped according to
image projection angle (degrees). Each box and whisker shows the distribution
of errors for the indicated projection angle using all deformation states in
the test set. For clarity of visualisation, angles are further grouped into 10
equal bins covering a full revolution. Results for patients 1 (blue), 2
(yellow), 3 (green), and 4 (red) are shown for each bin.

Figure 4: Visualisations of ground-truth deformed (left column), template
(middle column), and estimated deformed (right column) 3D liver shapes. Meshes
are overlaid on the deformed 3D-CT volume. Rows 1-3 show, respectively, axial,
coronal, and sagittal views. Results are shown for the _worst_ performing test
case for patient 1: image projection angle $80.849^{\circ}$, and deformation
state producing highest errors. Contours in the right column indicate the
spatial distribution of errors on the surface. Similar results for patients
2-4 are presented in the supplementary material.

For each of the four test sets the overall mean error was low: $\leq 0.22$ mm.
Within each test set, the maximum peak errors (i.e. overall max error found in
any of the deformation states and at any node) were rather higher, ranging
from 4.36 mm for patient 4 to 14.66 mm for patient 3. These peak values
occurred for the deformation states with the highest ground-truth displacement
(namely: 28.12, 34.91, 49.63, and 25.64 mm for patients 1, 2, 3, and 4,
respectively) for each test set. Higher underlying ground-truth displacements
corresponded, _in general_ , with higher peak errors, although mean errors
were consistently low. As indicated by Figure 3, the displacement prediction
accuracy was almost independent of the image projection angle: box-and-whisker
plots of both mean and peak errors are very similar across the range of
angles.

Finally, it is important to note that the higher peak errors in all cases were
extremely localised within the meshes. This is indicated firstly by the low
overall mean values and more so by the $99^{\rm th}$ percentile errors (Table
1), which were below 1 mm for 3/4 test sets and below 2 mm for the fourth.
That is, the errors were low, even sub-millimetres, for the vast majority of
the mesh nodes. The point is further illustrated by the renderings of
predicted mesh shapes colour-mapped by displacement error in the right columns
of Figure 4. For liver meshes, the error was close to zero over most of the
surface, and had only very localised regions of higher values.

###  5.3 Evaluation on real kV images

Our second set of experiments used real in-treatment kV images from each
patients’ second scan series (i.e. the series _not_ used during training data
creation). These series contained 1378, 1310, 1320, and 1292 images for
patients 1, 2, 3, and 4, respectively. In the absence of ground-truth
deformations, direct assessment of prediction errors is impossible. Therefore,
two approaches were adopted: 1) semi-quantitative assessment based on an image
similarity metric between input real kV images and model-generated DRRs; and
2) qualitative assessment based on overlaying model-predicted liver boundaries
on input kV images. For the qualitative assessment, all images in the scan
series were used. To reduce computation time (associated, in particular, with
spline deformation of the image volumes), only 100 images, uniformly sampled,
were used from each patients’ series in the similarity-based assessment.

####  5.3.1 Mutual Information-based assessment:

3D organ deformations predicted for a given input kV image can be used to
deform the patient’s reference CT volume. The correspondence between the input
image and a DRR generated from this deformed CT volume should then improve
with the accuracy of the model prediction. With this in mind, we used kV-to-
DRR image similarity, quantified using mutual information (MI), as a surrogate
measure of the model’s deformation prediction accuracy. In particular, we
assessed the improvement in MI when using the model-deformed CT volume
compared with using the undeformed volume.

The process is summarised in Figure 5. The input kV image is passed to the
model, which predicts the corresponding 3D organ mesh deformation. A thin-
plate-spline (TPS) transformation is initialised using the reference and
deformed mesh, and used to deform the reference 3D-CT volume. A DRR is then
generated using the input kV image’s projection angle. Separately, the
deformed mesh is used to generate a 3D binary mask, covering the liver-
predicted shape, from which a 2D ‘mask DRR’ is produced. The latter is used to
create regions of interest (ROIs) in both the DRR described above and the
input kV image. MI is then computed between these two ROIs. The ROI masking
process ensures the similarity computation is restricted to the image regions
to which the model predictions apply; deformations in the remainder of the
3D-CT volume, derived from the TPS transformation, are merely extrapolated
rather than directly predicted. Finally, a comparable process is followed to
produce a reference DRR (i.e. without accounting for the motion) for
comparison: the DRR is generated from the undeformed (reference) 3D-CT volume,
a ROI mask is created from the reference organ mesh, and MI is computed
between the masked DRR and input kV image.

Figure 5: Illustration of the process of MI-based assessment of model
prediction accuracy.

Table 2 summarizes the results of these experiments. The similarity score
values using the reference 3D-CTs are lower than for the motion-corrected
(deformed) volumes, suggesting our model is making sensible predictions of the
liver motion. Moreover, the marginal disparities in average MI values led us
to conduct a one-way ANOVA test for each patient case. For this purpose, we
generated two groups. In the first group, MI scores were computed by comparing
masked DRRs generated using predicted deformed 3D-CT image volumes with
corresponding masked real kV images. The mask was produced using the mask DRR
projection derived from the predicted deformed 3D binary mask volume. In the
second group, MI scores were recalculated, this time by comparing the DRR
generated from the undeformed (reference) 3D-CT volume with the input kV
image. Here, the ROI mask was created from the reference organ mesh.
Subsequently, we conducted a one-way ANOVA test based on these two groups for
each test dataset. The resulting p-values for MI differences between the
reference and deformed versions were 0.0449, 0.0283, 0.0453, and 0.0423 for
patients 1, 2, 3, and 4, respectively, suggesting statistically significant
(assuming alpha value of 0.05) differences.

Table 2: MI similarity scores (mean $\pm$ standard deviation, computed from the 100 images sampled from each scan series) between real kV images and DRRs generated at the same projection angles for each patient case. Column 2 presents values when the reference (i.e. undeformed) CT volume is used. Column 3 presents values when the CT volume is deformed using the model-predicted deformation fields. All values were computed on the liver region. Case | Reference | Deformed
---|---|---
1 | 1.16$\pm$0.31 | 1.33$\pm$0.23
2 | 1.14$\pm$0.21 | 1.39$\pm$0.14
3 | 1.13$\pm$0.27 | 1.28$\pm$0.23
4 | 1.31$\pm$0.25 | 1.47$\pm$0.15

####  5.3.2 Qualitative assessment by boundary overlay:

Histogram-equalised kV images from the mentioned scan series were fed into the
trained models to obtain 3D mesh shape predictions. As mentioned, all images
in the scan series were used. From each predicted mesh, a corresponding binary
image volume was generated. Finally, the projected liver surface boundaries
were obtained through ray-tracing on these binary image volumes, and
superimposed on the respective input kV images. Samples from each patient are
shown in Figure 6. Supplementary materials, moreover, include animated
versions based on the full scan series of each patient case for further
reference. These latter most effectively show (qualitatively) the consistent
alignment of the model predictions with the input images across many breathing
cycles and the full rotation of the treatment gantry.

(a)

(b)

(c)

(d)

Figure 6: Samples of overlaid predicted liver boundary projections on
corresponding real kV images for the four patients. Rows 1-4 show,
respectively, results for patients 1-4. Results for images acquired at four
projection angles (degrees, indicated below the images) are shown.

###  5.4 Comparison model

We compared the performance of our approach with that of the recently
presented IGCN model ([16, 17]). As described, like our approach, IGCN
predicts 3D organ shapes from single-view X-ray images. It is, however,
limited to images with a constant projection angle (e.g. 0∘, corresponding to
anterior-posterior projection), and predicts only 3D surface geometries rather
than 3D volumetric configuration. To ensure fairness, we therefore conducted
the comparison on this basis.

We trained our model as previously described, and using the data described in
sect. 5.2. To train the IGCN model, we first extracted surface meshes from the
ground-truth volumetric meshes in the training, validation, and test sets. We
then trained the model using the deformed surface meshes and associated
synthetic kV images for projection angle of zero. Image dimensions were
256$\times$256\. Initial batch size, learning rate, and total number of epochs
were as specified in [16]: 1, 0.0001 and 1000, respectively.

Images with projection angle zero from the test set were passed to the IGCN
model, which predicted corresponding deformed surface meshes. To facilitate a
meaningful comparison with our model, therefore, we derived corresponding
surface meshes from the latter’s predicted volumetric meshes for the same
images. The outcomes presented in Table 3 for the test set show that our
method achieved overall higher accuracy in liver surface deformation across
all patient cases. Further, we conducted one-way ANOVA tests for each test set
to check for statistically significant differences in mean errors between our
approach and IGCN. Two groups were produced by calculating the mean of the
Euclidean distances between ground-truth and predicted surface meshes
independently for each test dataset, one for our model and the other for the
IGCN model. Each list comprises 100 mean error values, reflecting the 100
deformed states in the test set, where each deformed state corresponds to a
single kV (front-view) projection. Subsequently, we performed a one-way ANOVA
test based on these two groups for each test dataset. The resulting p-values
of 0.0419, 0.0088, 0.0074, and 0.0485 for patients 1, 2, 3, and 4,
respectively, confirmed this significance (assuming 0.05 alpha value).

Table 3: Summary prediction error statistics from performance comparison between our model and IGCN. All errors are computed with respect to predicted organ surface meshes. Patient case numbers are indicated in column 1. $E_{Pred}^{Ours}$ and $E_{Pred}^{IGCN}$ refer to prediction errors for our method and IGCN, respectively. $U_{GT}$ refer to underlying ground-truth deformation magnitudes. _Mean (std)_ : means (and standard deviations) of values across all nodes, all deformation states, and all projection angles. _Mean peak_ : means of the peak values for each deformation state across all projection angles. _Max peak_ : overall maximum values from all nodes, deformation states and angles. _99 th Percentile_: $99^{\rm th}$ percentile values from all nodes, deformation states and angles. All values reported in mm. Case |  | Mean (std) | Mean peak | Max peak |  $99^{\rm th}$ Percentile
---|---|---|---|---|---
1 | $E_{Pred}^{Ours}$ | 0.17$\pm$0.11 | 0.89 | 4.91 | 0.47
$E_{Pred}^{IGCN}$ | 0.18$\pm$0.25 | 1.13 | 6.37 | 0.93
$U_{GT}$ | 10.11$\pm$1.24 | 13.94 | 28.12 | 13.53
2 | $E_{Pred}^{Ours}$ | 0.14$\pm$0.15 | 1.53 | 7.13 | 0.67
$E_{Pred}^{IGCN}$ | 0.17$\pm$0.21 | 2.81 | 8.79 | 1.18
$U_{GT}$ | 11.37$\pm$1.55 | 15.41 | 34.91 | 14.09
3 | $E_{Pred}^{Ours}$ | 0.15$\pm$0.13 | 1.46 | 13.83 | 0.77
$E_{Pred}^{IGCN}$ | 0.19$\pm$0.23 | 2.05 | 14.31 | 1.23
$U_{GT}$ | 14.52$\pm$2.39 | 18.71 | 49.63 | 16.74
4 | $E_{Pred}^{Ours}$ | 0.12$\pm$0.09 | 0.78 | 3.98 | 0.44
$E_{Pred}^{IGCN}$ | 0.14$\pm$0.17 | 0.97 | 5.31 | 0.77
$U_{GT}$ | 10.01$\pm$1.05 | 12.17 | 25.64 | 11.33

##  6 Discussion and conclusions

We presented a GNN-based model for recovering 3D volumetric organ mesh
deformation from a single in-treatment kV planar X-ray image acquired at
arbitrary projection angles. This approach has several attractive features: it
uses only readily accessible in-treatment imaging capabilities, rather than
expensive and rare systems like MRI; it requires no extra sensing to provide
surrogate signals; and no invasive fiducial marker implantation. Moreover, the
model is end-to-end trainable, ensuring all components, and especially the
image feature encoder, are optimised with respect to the overall prediction
accuracy. To the best of our knowledge, this is the first example of a deep
learning framework able to reconstruct volumetric 3D organ models accurately
from arbitrary-angled single-view images, and thereby to enable such
reconstructions across complete in-treatment scan series. We demonstrated the
feasibility and accuracy of the technique using data from four liver cancer
patients.

The model was trained with synthetic data constructed using the SuPReMo
toolkit. Training in this way is essential in the absence of ground-truth
deformations corresponding to real kV images; that is, there appears to be no
other way of acquiring paired deformation/image sets for this scenario. For
similar reasons, in this first study, direct quantitative evaluation of the
model performance was also carried out using synthetic data. Naturally, the
performance of the model will depend on the fidelity with which real patient
motions are reproduced in the synthetic data. While SuPReMo appears to do a
reasonable job of characterising the motion present in the input 4D-CT data,
these data represent only averaged breathing cycles and do not by themselves
provide information about the variability of this motion. Pragmatically,
therefore, in the present work, we assumed some bounds on the variations from
this average, and randomly generated motion states within these (Sect. 4.1).
We are exploring more rigorous approaches to characterising the patient motion
variability (and incorporating this in model training data) based on kV image
sequences acquired over several minutes during treatment.

While we focused here on respiratory motion estimation, our approach can in
principle be used to predict any motion patterns, e.g. peristaltic motion of
the gut or longer-term structural changes, given appropriate training data. As
mentioned, the model involves no assumptions of periodicity or other specific
motion characteristics. Clearly, the generation of training data is more
challenging in some scenarios than in others, but this presents a practical
difficulty rather than a theoretical one.

As mentioned, our approach has been developed specifically to accommodate
input kV images acquired at arbitrary projection angles. We demonstrated this
by training and evaluating the models with images generated at different
projection angles. As shown in Figure 3, the prediction accuracy was indeed
virtually independent of the projection angle.

We observed that the model prediction accuracy can be influenced by the
quality and characteristics of the CT volumes from which training data are
constructed. The higher peak errors found for patients 2 and 3 appear to be at
least partly attributable to this. The CT volumes of these two patient cases
exhibited certain reconstruction artefacts related to motion. For patient 3,
in large amplitude deformed cases, these resulted in some mesh-image
misalignment problems even in the ground-truth data (specifically, with the
deformed states at initial and final time points) produced from SuPReMo. The
deformed images for Patients 1 and 4, by contrast, contained no obvious
artefacts or ambiguous anatomy, and peak errors were correspondingly smaller
(Table 1). As emphasised, however, the regions of higher peak errors, even in
patients 2 and 3, were nonetheless very localised, and mean errors remained
low.

In the absence of ground-truth motion states for real in-treatment kV images,
the evaluation was conducted through qualitative and semi-quantitative methods
as described in Section 5.3. Qualitative assessment involved visualizing
overlaid organ contours on the input kV images, while semi-quantitative
evaluation employed deforming reference CT volumes using predicted motions and
calculating resulting image similarities. In the former experiment, the model
appeared (again, qualitatively) to make sensible predictions. The animations
included as supplementary material showed consistent and smoothly
transitioning organ contours from one image to the next without noticeable
jumps between frames, despite the prediction for each frame being independent
of its neighbours (the model contains no recurrence mechanism, for example,
and makes predictions based on single input images). This suggests the model
is not greatly affected by noise or other irregularities present in the real
images. In the latter experiment, compensating for the patient motion using
the predicted deformation fields improved the similarity between the input
images and corresponding model-derived DRRs, again indicating the model makes
sensible predictions for the real images.

A limitation of our method, as currently implemented, is that we only estimate
the deformation of the target organ; nearby OARs and other anatomy are
ignored. However, the model itself imposes no restrictions in this respect. If
suitable training data covering the relevant anatomy, and meshes of the
relevant anatomical structures can be generated, the model can in principle
estimate motions for these in the same way. SuPReMo, for example, provides
deformation vector fields for the whole image volume, which could be used for
this purpose. OAR and other meshes can normally be created similarly to the
liver meshes used here. Potentially, the prediction of deformations for
multiple disconnected meshes could result in anomalous overlapping regions.
However, such instances would hopefully be rare when the training data include
no such behaviour. If needed, separate non-overlap constraints in the
formulation could also be conceived, which penalise mesh interpenetration in a
way analogous to some contact formulations in computational mechanics. Albeit,
this would increase the complexity of the approach. A simpler alternative
could be deploying a single mesh covering all relevant anatomy. In all
scenarios, it is possible that both model and training data size requirements
would increase, though the overall approach would remain the same.

A key part of the synthetic data creation was the development of a method for
generating realistic synthetic kV X-ray images. While DRRs produced from ray
tracing through CT volumes ultimately are also X-ray-based images, they do not
suffer from the same scatter and noise phenomena of in-treatment kV X-ray
images. Their appearance, consequently, is noticeably different. Therefore we
first trained a CycleGAN [31] for each patient by conditioning on projection
angle to learn the genuine kV X-ray style that can be transferred to the DRRs.
CycleGANs are particularly well-suited to this task since they require only
unpaired sets of DRRs and kV images. We initially used transposed convolution
layers for the decoder part of the generators, however, we encountered
checkerboard-like artefacts in several cases. These were eliminated by instead
using convolution layers followed by pixel shuffle layers ([33]).

The purpose of this research is to enhance the probability of curing cancer by
maximising tumour control probability (TCP) while minimising normal tissue
complication probability (NTCP). Conformal RT techniques, such as SABR, prove
valuable in this context by enhancing TCP while keeping NTCP low, thereby
increasing the Therapeutic Index. However, when there is motion, the healthy
tissue located in the low-dose zone may migrate into the treatment field,
leading to the delivery of a higher radiation dose to the healthy tissue.
This, in turn, leads to patients enduring intolerable levels of toxicity.
Another scenario arises when the tumour moves away from the radiation field,
resulting in a reduced radiation dose to the tumour. Despite the consistent
toxicity status, with the healthy tissue remaining stationary while the tumour
moves, the tumour receives a suboptimal radiation dose, resulting in a lower
TCP value. This necessitates a reduction in the prescribed dose to bring the
NTCP back to an acceptable level. Hence, patients may not fully benefit from
conformal radiation treatments like SABR due to challenges associated with
motion. This, in turn, poses challenges for clinicians in delivering an
optimal radiation dosage to patients, ultimately influencing the overall
outcomes for patients. Therefore, with this research, we aim to ameliorate
patient motion effects and improve the Therapeutic Index without the use of
surrogate signals or invasive fiducial markers, enabling clinicians to reduce
the NTCP to acceptable levels, thus allowing for larger prescription doses
that will result in better outcomes for the patient. This will then enable
clinicians to adapt therapies for diverse patient cohorts.

As mentioned, two general approaches to adapting RT treatments could be
considered using motion estimates generated by our technique: inter- and
intra-fraction adaption. Inter-fraction plan adaption could be achieved by
retrospectively estimating the motion that occurred during a treatment
fraction and computing motion-compensated spatial distributions of delivered
dose (dose accumulation); the treatment plan could then be adapted accordingly
for subsequent fractions. No new technology seems to be needed for this,
beyond the requirement to image throughout the fraction, rather than during
initial patient positioning only. We are currently developing a workflow for
this process which, in outline, is as follows: 1) Deep-Motion-Net is trained
using patient planning or treatment simulation 4D-CT data; 2) kV images are
acquired throughout treatment delivery; 3) Deep-Motion-Net predicts organ
motion states for all input kV images; 4) organ (mesh) motion predictions are
used to deform patient reference 3D-CT volumes via thin plate spline
transformation (with organ nodes as driving control points); 5) positions of
the gantry/MLCs at the start and end of each time period are determined
(interpolation in between); 6) dose for the predicted anatomy is computed; 7)
dose is mapped to a common reference anatomy (corresponding to reference 3D-CT
volume) 8) cumulative delivered dose (sum of contributions from individual
motion states) is computed and compared with planned dose.

Intra-fraction adaption requires prediction of target motion, and adjustment
of radiation delivery in response, in real-time during the treatment. While
our model computes motions quickly (inference time for each input image is
$\sim$27 msec), the inevitable response lag of the treatment system, due both
to data processing following a motion input and the physical inertia of the
delivery apparatus, means motion predictions must in practice be computed
somewhat _ahead of time_. In principle, our approach could be extended to
enable this using ideas from sequence-to-sequence learning, e.g. by
incorporating RNN (recurrent neural networks) or LSTM (long-short-term memory)
components in the model to capture sequences of organ motions, given dynamic
sequences of input kV images. Our recent work on generative modelling of
cardiac MR image sequences ([34]) can provide further inspiration here.

## CRediT authorship contribution statement

Isuru Wijesinghe: Conceptualization, Methodology, Investigation, Software,
Formal analysis, Writing – original draft. Arezoo Zakari: Software, Writing -
review & editing. Alireza Hokmabadi: Software. Michael G. Nix:
Conceptualization, Resources, Writing – review & editing, Supervision. Bashar
Al-Qaisieh: Resources. Ali Gooya: Conceptualization, Writing – review &
editing, Supervision. Zeike A. Taylor: Conceptualization, Resources, Funding
acquisition, Writing – review & editing, Supervision.

## Acknowledgements

This work was supported by Cancer Research UK funding for the Leeds
Radiotherapy Research Centre of Excellence (RadNet - C19942/A28832) and a
Royal Academy of Engineering / Leverhulme Trust Research Fellowship (DIADEM-
ART LTRF2021-17115). The authors gratefully acknowledge the support and advice
of Dr Jamie McClelland on using SuPReMo.

##  Appendix 0.A Ablation study

Table 4: Impact of reducing the number of image encoder MLPs. All values reported in mm. Experiment | Mean (std) | Mean peak | Max peak |  $99^{\rm th}$ Percentile
---|---|---|---|---
1 | 0.21$\pm$0.18 | 1.92 | 7.53 | 1.19
2 | 0.23$\pm$0.22 | 2.88 | 8.47 | 1.45

This section describes the experiments we performed to determine the impact of
each model component on the overall model performance. All experiments were
conducted by training the model for 400 epochs. The synthetic data generated
for patient 1 were used; hence all results should be compared with patient 1
values in Table 1).

We first assessed the impact of the four MLPs in the image encoder. As
described, our incorporated an MLP for each convolutional layer, with each MLP
responsible for five features per vertex, for a total of 20 features. Two
experiments were conducted: 1) we removed MLPs associated with the first two
convolutional layers, resulting in only ten image features per vertex; 2) we
removed all MLPs except the final one, associated with the final convolutional
layer, resulting in five features per vertex. In each of these cases,
projection angle information was integrated into the input layer. Results are
shown in Table 4, which demonstrate the importance of all four MLPs.

Table 5: Impact of removing gantry (projection angle) information from the image encoder. All values reported in mm. Mean (std) | Mean peak | Max peak |  $99^{\rm th}$ Percentile
---|---|---|---
0.23$\pm$0.21 | 2.81 | 9.33 | 1.27

We next explored the impact of projection angle information in the image
encoder by omitting this information from the input layer. For this
experiment, the number (i.e. four) of MLPs remained constant. The results in
Table 5 show that feeding angle information to the input layer is more
successful.

Table 6: Impact of removing skip connections from the mesh deformation network. All values reported in mm. Mean (std) | Mean peak | Max peak error |  $99^{\rm th}$ Percentile
---|---|---|---
0.20$\pm$0.19 | 2.04 | 7.69 | 1.31

In the next experiment, we focused on the effect of residual connections used
in the mesh deformation network by simply removing them. Results in Table 6
indicate our approach with residual connections was superior.

Table 7: Impact of replacing graph-attention layers with graph convolutional network layers. All values reported in mm. Mean (std) | Mean peak | Max peak |  $99^{\rm th}$ Percentile
---|---|---|---
0.18$\pm$0.16 | 1.51 | 7.05 | 0.83

Finally, we explored the impact of the graph attention layers in the mesh
deformation network by replacing them with GCN layers. The architecture was
otherwise unchanged. Results in Table 7 demonstrate that utilizing GAT layers
is more effective.

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rightsretained

# EMMI: Empathic Human-Machine Interaction for Establishing Trust in Automated
Driving

Tobias Oetermann1, Pia Dautzenberg1, Gudrun Voß1, Christopher Brockmeier1,
Stefan Ladwig1, Patrick Gebhard2, Tanja Schneeberger2, Markus Funk3, Raymond
Brueckner3, Felix Schäfer4, Norbert Helff5, Andreas Gomer6, Lutz Eckstein1

Institute for Automotive Engineering (ika) RWTH Aachen University1, German
Research Center for Artificial Intelligence (DFKI)2, Cerence GmbH3,
CanControls GmbH4, Charamel GmbH5, Saint-Gobain Research Germany6

(2022)

###### Abstract

Highly automated vehicles represent one of the most crucial development
efforts in the automotive industry. In addition to the use of research
vehicles, production vehicles for the general public are realistic in the near
future. However, to fully exploit the benefits of these systems, it is
fundamental that users have an appropriate level of trust in automation.
Recent studies indicate that more research is needed in this area.
Furthermore, beyond the management of user trust, the system should also
convey a perceptible added value to realize not only trust, but also
acceptance and thus use. The EMMI project pushes both, the management of user
trust while conveying added value to the user. Therefore, an advanced socio-
emotional user model for estimating user trust and various user-centered HMI
systems with unique UX are being developed. Together, the systems are employed
to induce changes in the users’ trust in automated vehicles.

###### keywords:

trust in automation; trust detection; gaze detection; automated driving; HMI;
UX

††conference: arXiv, April 2022

<ccs2012> <concept> <concept_id>10003120.10003121</concept_id>
<concept_desc>Human-centered computing Human computer interaction
(HCI)</concept_desc> <concept_significance>500</concept_significance>
</concept> <concept> <concept_id>10003120.10003121.10003126</concept_id>
<concept_desc>Human-centered computing HCI theory, concepts and
models</concept_desc> <concept_significance>100</concept_significance>
</concept> </ccs2012>

[500]Human-centered computing Human computer interaction (HCI) [100]Human-
centered computing HCI theory, concepts and models

##  1 Trust in Automation

One of the key challenges of current research and development projects is the
automation of the primary driving task. The technology for automated driving
is known to be an essential instrument to achieve the goals related to the
improvement of road safety [5]. But what about user acceptance? A low level of
technology acceptance is likely to cause an equivalent level of usage and may
thus negatively impact the level of market penetration. Beyond technology
development, the goal of current research projects therefore is to better
understand user acceptance and relevant influencing factors to derive measures
that have the potential to contribute to an increase in acceptance. Current
studies suggest that potential users both, in Germany [26] and internationally
[23] are critical towards highly automated driving. A representative survey
conducted by TÜV e.V. [18] on the assessment and acceptance of autonomous
vehicles revealed that 60% of the respondents foresee increasing safety
through use of self-driving vehicles. Nevertheless, 89% expressed reservations
about the new technology. Almost 70% fear technical problems that are likely
to lead to malfunctions or even accidents. 32% of the respondents trust
technology to handle difficult situations less sovereign than a human driver.
There is evidence that the listed concerns of the respondents regarding
technology acceptance are related to the influencing factor trust in
automation (TiA) [16].

A definition of Lee and See [12] describes TiA as _“[…] the attitude that an
agent will help achieve an individual’s goals in a situation characterized by
uncertainty and vulnerability”_. We likewise understand TiA to be a subjective
construct of users that an automated system will act in a desirable manner in
situations characterized by uncertainty for and/or vulnerability of the user.
TiA not only influences overall acceptance of automated vehicles, but also
whether the technology is (in)properly used or even disused [11]. An
appropriate level of trust therefore seems to be crucial both, in terms of
system acceptance and safe system use [11]. Due to the relevance of TiA in the
context of automated driving, the EMMI project focuses on this construct in
particular. First, possibilities for objective detection of users’ TiA are
aimed at, to recognize the users’ socio-emotional behavior during automated
driving. An estimation of the users’ TiA is discussed to be the central
prerequisite for enabling an empathic reaction of the vehicle, which is
triggered by fluctuations in the user trust level. The empathic reaction could
positively increase the credibility and thus the users’ trust in the system in
the long term [20]. Overall, multimodal emotion recognition and the associated
empathic system response are promising to bear a high unexplored potential to
have a lasting impact on trust in automated systems [8] (see Fig. 1).

(a) Gaze tracking as part of a driver monitoring system

(b) Emotion expression recognition as key elements for trust recognition

Figure 1: Development of objective detection of user TiA

Summarizing, the project is pursuing three distinct subsystems that pursue
specific goals and approaches to regulate users’ TiA to an appropriate level.
The different subsystems comprise an interactive empathic agent, a situational
visualization of vehicle status and environment information as well as an
indirect vehicle guidance for automated vehicles. The approach and relevance
of these goals are described in more detail in the following chapter.

##  2 Project Goals

The three subsystems of the EMMI project follow individual research
approaches, all of which can be expected to have an effect on the users’ TiA.
By integrating them into a comprehensive system, the potentials of the
subsystems are combined, and hypothetical synergy effects can arise. The
individual research approach and the connected project goals are briefly
presented below.

###  2.1 Goal 1: Increase trust through an empathic interactive agent that is
aware of users’ socio-emotional behavior

Since their recent success in smart home technologies, voice-based assistants
are now also state of the art in automotive technology. According to
forecasts, by 2028 they will be installed in around 90% of newly registered
vehicles worldwide 111https://www.automotiveworld.com/special-reports/special-
report-the-rise-of-the-in-car-digital-assistant/ \- last access April 12th,
2022. The goal of this technology is to realize a natural speech input and
output in order to imitate human communication. Adding humanoid aspects and
providing the interface with an embodiment can enhance this natural
interaction [17]. Empathic interactive agents enable human users to interact
through communication channels that are natural to them [3]. Several studies
indicate that interactive agents can elicit similar emotions like humans (e.g.
[21]) and increase trust in automated intelligent systems [25]. Also, the use
of embodied virtual agents to increase trust in automated driving has been
considered [7]. Therefore, one goal of the project is to examine the
integration of an empathic interactive agent in the context of highly
automated driving for user trust management (see Fig. 2).

Figure 2: Vision: An empathic interactive agent that supports the user to
trust the vehicle automation Figure 3: The EMMI Roadmap: Starting with
different concepts of three subsystems, these are condensed with use of the
multi-stage evaluation process and synthesized into a comprehensive system

###  2.2 Goal 2: Convey understanding for the vehicle behavior with
situational visualization of vehicle state and environmental information

The number of automated research and concept vehicles has been steadily
increasing in recent years [15]. The increased involvement of novice users
raises the question what information the automation has to display and respond
to from the users’ perspective. The majority of systems currently in use
answer this question similarly. To increase the understanding about the
automation function, environmental factors, travel trajectories, and detected
obstacles in the real environment are specifically presented (see Fig. 4)
222https://design.google/library/trusting-driverless-cars/ \- last access
April 12th, 2022333https://www.tesla.com/support/full-self-driving-computer \-
last access April 12th, 2022. The underlying research approach is to build
trust and acceptance through understanding [4, 14]. However, some questions do
not seem to have been finally answered yet: What is the main information that
can be used to influence the users’ level of trust? Is the information able to
generate an equal benefit for a broad user population? To what extent should
individual user specifics be taken into account with regard to the information
to be displayed? If these, and the research questions beyond, remain
insufficiently answered with regard to the visualization concepts of highly
automated vehicles, in the worst case too much or wrong information might lead
to a lack of understanding and thus to uncertainty that might lead to a loss
of trust [24, 10]. Thus, a systematic investigation of the type, the density
and the timing of information, as well as the user group to be considered and
its interindividual needs is required to enable a targeted use of display
concepts to manage user trust.

(a) Example: AR visualization of advanced navigation

(b) Example: Concept drawing of trust calibrating visualizations

Figure 4: Vision: Convey understanding of the vehicle automation by presenting
adaptive information

###  2.3 Goal 3: Provide the feeling of control by enabling an indirect
vehicle guidance for highly automated vehicles

Various studies have shown that users of automated systems generally trust
these systems more if they are given the opportunity to overrule the
automation [9, 13]. This increased level of trust is detached from the users’
perceived need to override automation. Even in cases where users do not
override the automation at any time, a higher basic trust can be found due to
the provided possibility of overriding [19]. Further research has shown that
users of automated systems are generally influenced in their manual driving
skills [2, 22]. Due to the lack of situation awareness or calibration of the
user as a controller in the driver-vehicle control loop, overriding the
automation by the user mostly poses a cognitive challenge and thus a potential
threat to road safety [6]. Nevertheless, to realize an appropriate level of
trust in automation and to give the user the possibility to influence the
automation, an indirect vehicle guidance is needed. The goal is to realize
trust by taking into account individual user wishes with regard to automated
vehicle control and to return the feeling of control over the vehicle. In
addition, an innovative and well-designed interaction can also contribute
strongly to the joy of use.

##  3 The EMMI Roadmap

The presented subsystems will subsequently be combined into a comprehensive
system and finally evaluated for their effectiveness and UX with respect to
trust calibration in the context of highly automated driving. The final
investigation will take place in a highly dynamic driving simulator to obtain
robust conclusions by providing the greatest possible immersion. The tool
makes it possible to examine scenarios that are subjectively perceived as
critical without the risk of user intervention that could endanger security.

The project plan envisions that relevant insights into the effectiveness of
the individual subsystems will be gained based on the iterative and user-
centered development approach even before the final investigation. The
evaluation process of the project follows a three stages approach (Fig. 3):
Initial insights will be gained within a virtual development environment.
Thus, the developed concepts will be evaluated in VR close to the later
potential user (see Fig. 5). The insights gained will be iteratively
incorporated into the development process. The second stage is the prototype
evaluation with functional samples, which will be tested on a new developed
HMI test bench. Final findings and approaches for industrialization will be
obtained in the concluding user study.

Figure 5: VR environment for early evaluation by the later potential user

##  4 Acknowledgments

This work is funded by the German Ministry for Economic Affairs and Energy in
the project EMMI, grant no. 19A20008F.

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