# CaRe-CNN: Cascading Refinement CNN for Myocardial Infarct Segmentation with
Microvascular Obstructions

Franz Thaler1,2 , Matthias A.F. Gsell1 , Gernot Plank1 and Martin Urschler3
1Gottfried Schatz Research Center: Medical Physics and Biophysics, Medical
University of Graz, Graz, Austria
2Institute of Computer Graphics and Vision, Graz University of Technology,
Graz, Austria
3Institute for Medical Informatics, Statistics and Documentation, Medical
University of Graz, Graz, Austria
https://orcid.org/0000-0002-6589-6560 https://orcid.org/0000-0001-7742-8193
https://orcid.org/0000-0002-7380-6908 https://orcid.org/0000-0001-5792-3971

###### Abstract

Late gadolinium enhanced (LGE) magnetic resonance (MR) imaging is widely
established to assess the viability of myocardial tissue of patients after
acute myocardial infarction (MI). We propose the Cascading Refinement CNN
(CaRe-CNN), which is a fully 3D, end-to-end trained, 3-stage CNN cascade that
exploits the hierarchical structure of such labeled cardiac data. Throughout
the three stages of the cascade, the label definition changes and CaRe-CNN
learns to gradually refine its intermediate predictions accordingly.
Furthermore, to obtain more consistent qualitative predictions, we propose a
series of post-processing steps that take anatomical constraints into account.
Our CaRe-CNN was submitted to the FIMH 2023 MYOSAIQ challenge, where it ranked
second out of 18 participating teams. CaRe-CNN showed great improvements most
notably when segmenting the difficult but clinically most relevant myocardial
infarct tissue (MIT) as well as microvascular obstructions (MVO). When
computing the average scores over all labels, our method obtained the best
score in eight out of ten metrics. Thus, accurate cardiac segmentation after
acute MI via our CaRe-CNN allows generating patient-specific models of the
heart serving as an important step towards personalized medicine.

##  1 INTRODUCTION

Figure 1:  Overview of the proposed CaRe-CNN architecture for segmenting
cardiac LGE MR images after MI. CaRe-CNN is a 3-stage CNN cascade that
exploits the hierarchical label definition of the data and refines
intermediate predictions in consecutive stages. The whole architecture is
trained end-to-end and all data is processed in 3D. As MVO can only be present
for data of the D8 subgroup, we consider Stage 2 predictions as final
predictions for data of the M1 and M12 subgroups.

Cardiovascular diseases are the leading cause of death worldwide among which
myocardial infarction (MI) is one of the most prevalent
diseases111https://www.who.int/health-topics/cardiovascular-diseases, last
accessed on October 8, 2023. MI is caused by a decrease or complete cessation
of blood flow in the coronary arteries which reduces perfusion in the supplied
myocardial tissue, leading to a metabolic undersupply that impairs cardiac
function and, ultimately, may result in myocardial necrosis. The accurate
assessment of tissue damage after acute MI is highly relevant as the extension
of myocardial necrosis is an important risk factor for developing heart
failure. On one hand, viable myocardial tissue with a potential for functional
recovery on restoration of normal blood supply by revascularization might
recover [Wroblewski et al., 1990, Perin et al., 2002], which may improve the
functional capacity and survival [Van der Wall et al., 1996, Kim and Manning,
2004]. On the other hand, precise delineation of infarcted myocardial tissue
is crucial to determine the risk of further adverse cardiovascular events like
ventricular tachycardia which may lead to sudden death [Rosenthal et al.,
1985, Hellermann et al., 2002]. For example, the presence of microvascular
obstructions, characterized by a damaged microvasculature resulting in a ’no-
reflow’ phenomenon preventing blood flow from penetrating beyond the
myocardial capillary bed, is linked to adverse ventricular remodeling and an
increased risk of future cardiovascular events [Hamirani et al., 2014, Rios-
Navarro et al., 2019]. Thus, the accurate assessment of post-MI tissue damage
is of pivotal importance. In clinical practice magnetic resonance (MR) imaging
is used to quantify areas of impaired myocardial function e.g. by estimating
the end-diastolic wall thickness of the left ventricle, or by evaluating the
contractile reserve, i.e. the myocardial stress-to-rest ratio [Kim et al.,
1999, Schinkel et al., 2007]. One of the most accurate methods is late
gadolinium enhanced (LGE) MR imaging, where the contrast agent accumulates in
impaired tissue areas, thus allowing to visualize the transmural extent of
tissues affected by MI [Selvanayagam et al., 2004].

However, analyzing LGE MR images to characterize tissue viability in an
accurate and efficient manner remains a significant challenge. Nowadays, deep
learning-based Convolutional Neural Networks (CNN) are widely adopted to
medical image analysis tasks like the detection of diseases in medical images
[Esteva et al., 2017, Feng et al., 2022], or image segmentation of the brain
[Akkus et al., 2017], the vertebrae [Payer et al., 2020], or the heart [Chen
et al., 2020]. From cardiac LGE MR data, healthy and necrotic myocardial
tissue can be assessed by CNN-based medical image segmentation, where each
voxel of an LGE MR image is assigned the respective label. Accurate cardiac
segmentation of patients after MI can provide a foundation for generating
anatomically accurate patient-specific models of the heart, which, in turn,
can be used e.g., to create cardiac digital twin models of human
electrophysiology [Gillette et al., 2021] to identify potential patient-
specific causes for arrhythmia improving personalized therapy planing [Campos
et al., 2022].

Due to the challenging nature of fully automated infarct segmentation, some
approaches in the literature rely on manual segmentations of the full
myocardium such that a distinction between healthy and infarcted tissue only
needs to be learned within that region [Zabihollahy et al., 2018, Moccia et
al., 2019]. Instead of using LGE MR data, [Xu et al., 2018] uses cine MR data
without contrast agents and a Long Short-Term Memory-based Recurrent Neural
Network [Graves et al., 2013] to predict myocardial infarct tissue from
motion. In contrast to that, [Fahmy et al., 2018] automatically segment both,
healthy and infarcted tissue from LGE MR images by employing a 2D CNN based on
the U-Net [Ronneberger et al., 2015] architecture. In another fully-automated
segmentation approach, [Chen et al., 2022] employed two consecutive 2D U-Net-
like CNNs as a cascade, where the first network learns to segment the full
myocardium, while the second is trained to refine the prediction to obtain the
infarct region. The authors show that the consecutive setup achieves better
Dice and Jaccard scores, but worse volume estimation compared to a parallel
setup of two CNNs. The semi-supervised myocardial infarction segmentation
approach in [Xu et al., 2022] proposes to use attention mechanisms to obtain
the coarse location of the myocardial infarction before refining the
prediction step-by-step. In order to allow training from unlabeled data, they
use an adversarial learning model that provides a training objective even when
ground truth labels are not available. The EMIDEC challenge held in
conjunction with the International Conference on Medical Image Computing and
Computer-Assisted Intervention (MICCAI) in 2020 aimed to automatically segment
myocardial infarct regions from LGE MR images in their segmentation track
[Lalande et al., 2022]. Different one- and two-stage approaches mostly based
on U-Net-like architectures were submitted by the challenge participants. The
highest scores in the segmentation track were achieved by [Zhang, 2021] who
employed a coarse to fine two-stage approach, where initial predictions are
obtained from a 2D U-Net variant before all 2D predictions are stacked to a 3D
volume. The stacked prediction in combination with the LGE MR image is then
refined by a 3D U-Net variant to obtain the final prediction.

In this work, we propose the Cascading Refinement CNN (CaRe-CNN), which –
differently to related work – is a fully 3D, end-to-end trained 3-stage CNN
cascade that exploits the hierarchical structure of cardiac LGE MR images
after MI and sequentially refines the predicted segmentations. Further, we
propose a series of post-processing steps that take anatomical constraints
into account to obtain more consistent qualitative predictions. Our CaRe-CNN
was submitted to the Myocardial Segmentation with Automated Infarct
Quantification (MYOSAIQ) challenge which was held in conjunction with the
International Conference on Functional Imaging and Modeling of the Heart
(FIMH) 2023\. We evaluate our method by comparing to state-of-the-art methods
submitted to the MYOSAIQ challenge where our CaRe-CNN ranked second out of 18
participating teams.

##  2 METHOD

In this work we propose CaRe-CNN, a cascading refinement CNN to semantically
segment different cardiac structures after MI from LGE MR images in 3D. An
overview of CaRe-CNN is provided in Fig. 1.

###  2.1 Notation and Definitions

Throughout this work, we will refer to the labels as left ventricle cavity
(LV), healthy myocardium (MYO), myocardial infarct tissue (MIT) and
microvascular obstruction (MVO). For further disambiguation of intermediate
results at the different stages of our method, we additionally define the full
myocardium (f-MYO) as MYO $\cup$ MIT $\cup$ MVO and the full myocardial
infarct tissue (f-MIT) as MIT $\cup$ MVO. A visualization of the label
definitions at different stages is provided in Fig. 2. While all scans in the
dataset are LGE MR images after MI, the dataset can be split into three
subgroups (D8, M1, M12) depending on how much time has passed since the MI,
see Section 3.1. Importantly, MVO is exclusive to the D8 subgroup and the
subgroup information is well-known for every image in the training and test
set.

Figure 2:  Visualization of the hierarchical label definitions per stage as
used by CaRe-CNN. While LV remains unchanged, f-MYO can be separated into MYO
and f-MIT of which the latter can be separated into MIT and MVO.

###  2.2 Cascading Refinement CNN

Our CaRe-CNN architecture exploits the hierarchical structure of the semantic
labels and is set up as a cascade of three consecutive 3D U-Net-like
architectures [Ronneberger et al., 2015] which are trained end-to-end.
Throughout this work, we will refer to each of these consecutive parts of the
processing pipeline as stages numbered from 1 to 3. By design, any subsequent
stage of CaRe-CNN receives the prediction of the preceding stage as additional
input, such that the prediction is gradually refined, see Fig. 1.

After randomly choosing and preprocessing a 3D image $\mathbf{x}$ with ground
truth $\mathbf{y}$ from the training set, the image $\mathbf{x}$ is provided
as input to CaRe-CNN. Stage 1 of CaRe-CNN aims to distinguish between the LV,
the f-MYO and the background based on the image information. By denoting the
Stage 1 model as ${\mathcal{M}}_{1}(\cdot)$ with trainable parameters
${\theta}_{1}$, the output prediction $\mathbf{\hat{p}}_{1}$ of Stage 1 for
image $\mathbf{x}$ can be expressed as:

$\mathbf{\hat{p}}_{1}={\mathcal{M}}_{1}(\mathbf{x};{\theta}_{1}).$ (1)

Please note that the output prediction $\mathbf{\hat{p}}$ refers to the model
output without activation function. In Stage 2, CaRe-CNN learns to predict the
LV, the healthy MYO, the f-MIT and the background by refining the Stage 1
prediction. To allow consecutive refinement of $\mathbf{\hat{p}}_{1}$ in Stage
2, we provide $\mathbf{\hat{p}}_{1}$ concatenated with the original image
$\mathbf{x}$ in the channel dimension as input to the Stage 2 model. This way,
$\mathbf{\hat{p}}_{1}$ can be refined based on the original image information
which is crucial for our cascading CNN as the label definition of the
individual stages is not the same. The Stage 2 model
${\mathcal{M}}_{2}(\cdot)$ with trainable parameters ${\theta}_{2}$ is defined
as:

$\mathbf{\hat{p}}_{2}={\mathcal{M}}_{2}(\mathbf{\hat{p}}_{1}\oplus\mathbf{x};{\theta}_{2}),$
(2)

where $\oplus$ refers to a concatenation in the channel dimension and
$\mathbf{\hat{p}}_{2}$ refers to the output prediction of Stage 2, again
without any activation function. Lastly, Stage 3 aims to distinguish all
labels, i.e., the LV, MYO, MIT, MVO as well as the background. To continue our
CNN cascade, we concatenate the prediction $\mathbf{\hat{p}}_{2}$ and the
image $\mathbf{x}$ in the channel dimension to provide both as input to the
Stage 3 model ${\mathcal{M}}_{3}(\cdot)$ of our cascading CNN. Formally, the
output prediction $\mathbf{\hat{p}}_{3}$ of Stage 3 can be expressed as:

$\mathbf{\hat{p}}_{3}={\mathcal{M}}_{3}(\mathbf{\hat{p}}_{2}\oplus\mathbf{x};{\theta}_{3}),$
(3)

where ${\theta}_{3}$ refers to the trainable parameters of Stage 3 and
$\oplus$ defines the concatenation operator.

###  2.3 Training Objective

In our training pipeline the segmentation loss is computed for each stage
individually and backpropagation through all stages is allowed to update model
weights in an end-to-end manner for the whole cascade. As the label definition
varies from stage to stage, we adapt the ground truth labels such that they
follow the label definition of the respective stage as defined in Fig. 2. For
every stage, we compute the generalized Dice loss between the ground truth
$\mathbf{y}$ and the label prediction
$\mathbf{\hat{y}}=\text{softmax}(\mathbf{\hat{p}})$ of that stage. Formally,
the generalized Dice loss $L_{\text{GD}}(\cdot)$ is expressed as:

$L_{\text{GD}}(\mathbf{y},\mathbf{\hat{y}})=1-2\frac{\sum_{k=1}^{K}w_{k}\cdot\sum_{m=1}^{M}\mathbf{\hat{y}}_{m}\cdot\mathbf{y}_{m}}{\sum_{k=1}^{K}w_{k}\cdot\sum_{m=1}^{M}\mathbf{\hat{y}}_{m}^{2}+\mathbf{y}_{m}},$
(4)

where $K$ represents the number of all labels and $M$ is the number of voxels.
The label weight $w_{k}$ for label $k$ is computed as the ratio of voxels
$M_{k}$ with label $k$ in the ground truth compared to the number of all
voxels, i.e. $w_{k}=\frac{M_{k}}{M}$. The square term
$\mathbf{\hat{y}}_{m}^{2}$ is used to account for class imbalance.

During training only images that actually contain the MVO label are forwarded
through Stage 3 as images with missing labels might lead to unstable training
which can greatly impact the performance at that stage. In order to provide a
loss at every stage for every iteration while also allowing all training
images to be selected at some point, we always randomly pick two training
images per iteration: One image with and one without the MVO label. The
overall training objective of CaRe-CNN for all stages and a single image can
then be expressed as:

$\begin{split}L(\mathbf{y},\mathbf{\hat{y}})&={\lambda}_{1}\underbrace{L_{\text{GD}}(\mathbf{y}_{1},\mathbf{\hat{y}}_{1};{\theta}_{1})}_{\text{update
${\mathcal{M}}_{1}$}}+{\lambda}_{2}\underbrace{L_{\text{GD}}(\mathbf{y}_{2},\mathbf{\hat{y}}_{2};{\theta}_{1},{\theta}_{2})}_{\text{update
${\mathcal{M}}_{1}$ and ${\mathcal{M}}_{2}$}}\\\
&+\delta_{\text{MVO}}\cdot{\lambda}_{3}\underbrace{L_{\text{GD}}(\mathbf{y}_{3},\mathbf{\hat{y}}_{3};{\theta}_{1},{\theta}_{2},{\theta}_{3})}_{\text{update
${\mathcal{M}}_{1}$, ${\mathcal{M}}_{2}$ and
${\mathcal{M}}_{3}$}},\end{split}$ (5)

where the stage weights ${\lambda}_{1}$, ${\lambda}_{2}$ and ${\lambda}_{3}$
serve as weights between the individual loss terms and are set to 1. The term
$\delta_{\text{MVO}}$ is set to $1$ if ground truth $\mathbf{y}$ contains MVO
anywhere and is $0$ otherwise. Finally, we provide the mean loss over the
batch to the optimizer.

Figure 3:  Predictions of CaRe-CNN (row 1) are in some cases incomplete for
the top-most slice towards the base of the left ventricle (col. 4). The
model’s uncertainty is computed as the entropy of the softmax prediction (row
3), where bright values indicate a higher uncertainty. The highest uncertainty
occurs in the incompletely labeled slice (col. 4). This motivates our post-
processing (PP) where, in this case, the incomplete prediction is removed (row
2).

###  2.4 Inference

As the subgroup (D8, M1, M12) for every image in the test set is known as
well, we utilize the subgroup information for test set data to determine the
final prediction as encouraged by the MYOSAIQ challenge organizers.
Specifically, we consider the label prediction $\mathbf{\hat{y}}_{3}$ of Stage
3 as the final label prediction $\mathbf{\hat{y}}_{f}$ only for D8 data, while
we use the Stage 2 label prediction $\mathbf{\hat{y}}_{2}$ as the final label
prediction $\mathbf{\hat{y}}_{f}$ for M1 and M12 data. The final label
prediction $\mathbf{\hat{y}}_{f}$ is defined as:

$\mathbf{\hat{y}}_{f}=\begin{cases}\mathbf{\hat{y}}_{2}&\text{if
}\mathbf{x}\in\text{\\{M1, M12\\}}\\\ \mathbf{\hat{y}}_{3}&\text{if
}\mathbf{x}\in\text{\\{D8\\}}.\end{cases}$ (6)

To further improve the final prediction of our method, we independently
trained $N=10$ CaRe-CNNs with random weight initialization and random data
augmentation. These $N$ models were used as an ensemble for which the final
label prediction is obtained by averaging the final label predictions of the
individual models. The average inference time per image for the whole ensemble
with post-processing takes roughly 8 seconds using an NVIDIA GeForce RTX 3090.

###  2.5 Post-Processing

Figure 4:  CaRe-CNN predictions before (row 1) and after (row 2) post-
processing. Images refer to the proposed disconnected component removal (col.
1), the top-most slice removal (col. 2-4) and the outlier region replacement
(col. 5-6). Red arrows indicate regions of interest.

As can be observed in Fig. 3 (bottom row), after training on the data our
CaRe-CNN remains ’uncertain’ about how far the heart should be segmented
towards the base which may result in a top-most slice that is incompletely
labeled. Even though such incomplete model predictions in themselves are not
incorrect, we decided to implement a series of post-processing steps to obtain
more consistent predictions that take anatomical constraints into account.

As a first step of our post-processing pipeline, we employ a disconnected
component removal strategy, where any components that are disconnected from
the largest component in 3D as well as in-plane in 2D are removed. In 3D, a
connected component analysis is performed where all foreground labels are
treated as one label and a 3D 6-connected kernel is applied. Any independent
region that is disconnected from the largest connected component is removed.
Due to the large slice thickness of the data, we also perform a connected
component analysis for every in-plane 2D slice independently, following the
same steps as described for the 3D variant and using a 2D 4-connected kernel
in-plane. The 2D strategy mostly affects the topmost slice that still contains
foreground predictions and removes some smaller in-plane disconnected regions
from that slice, see Fig. 4 (col. 1).

Next, we propose a top-most slice removal strategy, where we compare the
remaining foreground volume of the topmost slice that contains foreground
predictions to the foreground volume of its neighboring slice towards the
hearts’ apex (i.e. the slice ’below’ the top-most slice). In case that the
volume of the topmost slice is less than half the neighboring slice’s volume,
the topmost slice is removed completely. An example is shown in Fig. 4 (col.
4).

Lastly, an outlier region replacement strategy is applied, where very small
regions of a single label are treated as outliers and are replaced if they are
isolated from larger regions of the same label. In the first step of this
strategy, isolated regions are identified by performing a connected component
analysis per label using a 3D 6-connected kernel. Any region with a volume
smaller than 0.1 ml is considered to be an outlier and undergoes a correction
step, where the local neighborhood of each outlier voxel is observed to select
a new label for that voxel, see Fig. 4 (col. 5-6). Specifically, we obtain
label votes from all voxels within a 3D kernel of size $9\times 9$ in-plane
and $5$ out-of-plane, due to the large slice thickness. This anisotropic
kernel is sufficient as we perform a weighting based on a 3D Gaussian with
sigma value 2 that considers the actual physical distance of any candidate.
Importantly, votes from voxels marked as outliers are not considered. Finally,
the maximum of the weighted votes indicates the most likely label for that
voxel, which is then used as the label for that voxel.

##  3 EXPERIMENTAL SETUP

###  3.1 Dataset

In this work, we used the publicly available dataset from the MYOSAIQ
challenge222https://www.creatis.insa-lyon.fr/Challenge/myosaiq/, last accessed
on October 8, 2023, which was held in conjunction with FIMH 2023\. The aim of
the MYOSAIQ challenge is to automatically segment four different cardiac
structures from LGE MR images of patients after myocardial infarction. These
structures encompass the LV, MYO, MIT and MVO if present. The dataset consists
of 467 LGE MR images which are split into 376 training and 93 test images. All
images belong to one of three subgroups. The first subgroup (D8) encompasses
LGE images of 123 patients with acute myocardial infarction up to eight days
after the infarction and originates from the MIMI-cohort [Belle et al., 2016].
The second subgroup (M1) consists of LGE images of 204 patients, while the
third subgroup (M12) contains LGE images of 140 patients, which were
respectively obtained one and 12 months after coronary intervention and are
part of the HIBISCUS-cohort. For every image in the training dataset, a
corresponding ground truth segmentation is available. As the whole dataset
consists of images after myocardial infarction, all ground truth segmentations
in the dataset contain the LV, MYO and MIT label. However, the MVO label is
exclusive to the D8 subgroup and only present in roughly 66% of the D8 data.
The in-plane physical resolution of the dataset varies from 0.9 to 2.2 mm and
averages at 1.57 mm. Out-of-plane, the physical resolution varies from 5 to 8
mm.

###  3.2 Data Augmentation

We augment training data using the training framework from [Payer et al.,
2017, Payer et al., 2019] in 3D using random spatial and intensity
transformations. Spatially, we perform translation ($\pm 20$ voxels), rotation
($\pm 0.35$ radians), scaling (first isotropically with a factor between
$[0.8,1.2]$, then per dimension with a factor between $[0.9,1.1]$) and elastic
deformation (eight grid nodes per dimension, deformation values are sampled
from $\pm 15$ voxels). For robust intensity normalization of the MR images,
the 10 and 90 percentile are linearly normalized to $-1$ and $1$,
respectively. After normalization, a random intensity shift ($\pm 0.2$) as
well as an intensity scaling with a factor between $[0.6,1.4]$ is applied to
the training image before modulating intensity values per label by an
additional shift of ($\pm 0.2$) and scaling with a factor of $[0.9,1.1]$. All
augmentation parameters are sampled uniformly from the respective value range.
Images of the test set are not augmented, however, they are robustly
normalized identically to the training data to ensure similar intensity
ranges. To ensure consistency of the physical dimensions across the dataset,
all training and test images are trilinearly resampled to an isotropic spacing
of $1\times 1\times 1$ mm and an image size of $128\times 128\times 128$ voxel
before being provided to the CaRe-CNN model.

###  3.3 Implementation Details

At each stage of CaRe-CNN, a U-Net-like [Ronneberger et al., 2015] network
architecture is employed in 3D which follows the same structure, see Fig. 1.
Similar to an encoder-decoder, the architecture can be separated into a
contracting and an expanding path. Importantly, by using skip-connections, the
output of each level of the contracting path is concatenated to the input of
the same level of the expanding path in the channel dimension. At each of the
five levels of the contracting and the expanding path, we use a single block
consisting of two convolutions with an intermediate dropout layer [Srivastava
et al., 2014], after which a pooling or an upsampling layer is employed,
respectively. Two respectively three additional convolution layers are
employed before and after the U-Net-like network of each stage. All
intermediate convolution layers use a $3\times 3\times 3$ kernel and $64$
filters, while the last convolution layer of each stage uses a $1\times
1\times 1$ kernel and as many filters as there are labels at the respective
stage. He initialization [He et al., 2015] is used to initialize all weights
and the dropout rate is $0.1$. We employ max pooling layers and tri-linear
upsampling layers with a kernel size of $2\times 2\times 2$. Leaky ReLU [Maas
et al., 2013] with a slope of $0.1$ is used after intermediate convolution
layers, while a softmax activation is used after the last layer of each stage
to compute the loss. As optimizer, we employ Adam [Kingma and Ba, 2015] with a
learning rate of $0.001$, use an Exponential Moving Average strategy [Laine
and Aila, 2016] with a decay of $0.999$ and train for $200,000$ iterations.
For each training iteration, we select one image with and one without the MVO
label which corresponds to a batch size of $2$ for the Stage 1 and Stage 2
models. To ensure stable training, only images with the MVO label are
processed by the Stage 3 model, which results in an effective batch size of
$1$ for that model. During the development of our method, we trained our model
only on $2/3$ of the training data and used the remaining $1/3$ of the data as
a validation set. For our submission to the challenge, we trained CaRe-CNN on
all training data and evaluation was performed on the hidden test set. Final
results were obtained by averaging the prediction of a CaRe-CNN ensemble of
$10$ models on the test set and $5$ models on the validation set.

Mean over Labels
---
Team | DSC (%) | HD (mm) | ASSD (mm) |  CC ($\uparrow$) |  MAE ($\downarrow$) |  LOA ($\downarrow$) |  CRPS ($\downarrow$)
mean | std | mean | std | mean | std
($\uparrow$) | ($\downarrow$) | ($\downarrow$) | ($\downarrow$) | ($\downarrow$) | ($\downarrow$)
gemr22 | 74.9 | 10.3 | 13.452 | 7.545 | 0.711 | 0.607 | 0.931 | 6.044 | 18.228 | 0.011
(proposed)† | 78.9 | 8.5 | 13.200 | 9.244 | 0.574 | 0.560 | 0.938 | 5.500 | 16.140 | 0.010
akaroui | 75.4 | 10.0 | 13.779 | 8.392 | 0.697 | 0.689 | 0.929 | 5.827 | 17.644 | 0.035
Hairuiwang | 75.6 | 9.8 | 14.538 | 9.965 | 0.711 | 0.673 | 0.936 | 5.810 | 18.219 | 0.038
azanella | 75.1 | 10.6 | 13.483 | 7.195 | 0.724 | 0.685 | 0.905 | 5.842 | 18.337 | 0.010
KiwiYyy | 74.6 | 12.3 | 13.771 | 7.626 | 0.734 | 0.702 | 0.930 | 5.754 | 17.247 | 0.010
hoanguyen93 | 74.3 | 11.0 | 13.905 | 9.009 | 0.744 | 0.758 | 0.904 | 5.924 | 19.297 | 0.010
nicoco | 73.7 | 9.4 | 14.839 | 9.290 | 0.737 | 0.630 | 0.938 | 6.169 | 18.044 | 0.130
hang_jung | 73.7 | 9.9 | 15.063 | 8.752 | 0.835 | 0.766 | 0.907 | 6.415 | 19.802 | 0.014
Dolphins | 73.4 | 11.9 | 15.711 | 10.061 | 0.754 | 0.675 | 0.911 | 6.578 | 20.556 | 0.042
rrosales | 73.0 | 11.0 | 15.045 | 8.217 | 0.856 | 0.728 | 0.940 | 6.788 | 19.442 | 0.020
luiskabongo‡ | 72.3 | 10.6 | 15.584 | 9.561 | 0.804 | 0.718 | 0.917 | 7.099 | 21.622 | 0.105
calderds | 72.0 | 11.7 | 17.321 | 11.853 | 0.849 | 0.767 | 0.909 | 6.628 | 20.820 | 0.039
marwanabb | 69.8 | 12.9 | 15.667 | 9.499 | 1.131 | 1.183 | 0.883 | 7.534 | 22.477 | 0.071
agaldran | 69.3 | 19.6 | 15.947 | 10.926 | - | - | 0.722 | 11.712 | 54.175 | -
Erwan | 65.5 | 12.3 | 20.502 | 8.416 | 1.200 | 1.022 | 0.853 | 7.204 | 22.358 | 0.012
farheenramzan | 55.3 | 10.6 | 20.594 | 9.051 | 1.641 | 1.233 | 0.720 | 9.349 | 26.389 | 0.016
MYOSCANS | - | - | - | - | - | - | - | - | - | -
Table 1:  Quantitative evaluation showing the mean score over all labels for
ten metrics. The proposed CaRe-CNN is compared to the other MYOSAIQ challenge
participants. Invalid mean scores due to non-numeric results for at least one
label are indicated by -. The best, second and third best scores are
highlighted. †Our teamname on the evaluation platform is ’ominous_ocelot’.
‡Abbreviation for ’luiskabongo-inheart’.  Best 3 Methods per Label
---
| Team | DSC (%) | HD (mm) | ASSD (mm) |  CC ($\uparrow$) |  MAE ($\downarrow$) |  LOA ($\downarrow$) |  CRPS ($\downarrow$)
| mean | std | mean | std | mean | std
| ($\uparrow$) | ($\downarrow$) | ($\downarrow$) | ($\downarrow$) | ($\downarrow$) | ($\downarrow$)
LV | Overall Best | 93.7 | 2.8 | 6.406 | 2.013 | 0.392 | 0.233 | 0.980 | 6.881 | 17.121 | 0.012
gemr22 | 93.5 | 3.1 | 6.471 | 2.145 | 0.408 | 0.259 | 0.980 | 7.308 | 18.533 | 0.012
(proposed)† | 93.4 | 3.4 | 6.666 | 2.155 | 0.419 | 0.290 | 0.980 | 6.881 | 17.121 | 0.012
akaroui | 93.7 | 3.0 | 6.406 | 2.013 | 0.392 | 0.264 | 0.978 | 7.313 | 18.768 | 0.012
MYO | Overall Best | 82.2 | 4.1 | 11.753 | 5.712 | 0.390 | 0.211 | 0.967 | 7.891 | 22.251 | 0.013
gemr22 | 81.7 | 4.7 | 11.794 | 6.365 | 0.395 | 0.246 | 0.958 | 9.013 | 26.664 | 0.015
(proposed)† | 81.6 | 5.0 | 12.839 | 7.144 | 0.405 | 0.253 | 0.954 | 9.845 | 25.686 | 0.016
akaroui | 82.2 | 4.7 | 12.214 | 6.711 | 0.390 | 0.259 | 0.964 | 8.463 | 24.263 | 0.014
MIT | Overall Best | 68.4 | 16.1 | 16.746 | 12.482 | 0.924 | 1.310 | 0.855 | 4.044 | 17.866 | 0.007
gemr22 | 66.0 | 17.1 | 18.201 | 12.482 | 1.005 | 1.431 | 0.799 | 4.510 | 20.197 | 0.008
(proposed)† | 68.4 | 16.1 | 16.746 | 13.414 | 0.924 | 1.377 | 0.833 | 4.044 | 18.647 | 0.007
akaroui | 65.8 | 17.4 | 19.790 | 14.751 | 1.092 | 1.666 | 0.789 | 4.582 | 20.873 | 0.008
MVO | Overall Best | 72.0 | 9.5 | 14.539 | 5.682 | 0.547 | 0.321 | 0.995 | 1.231 | 3.106 | 0.003
gemr22 | 58.5 | 16.4 | 17.343 | 9.187 | 1.037 | 0.492 | 0.987 | 3.343 | 7.516 | 0.008
(proposed)† | 72.0 | 9.5 | 16.548 | 14.261 | 0.547 | 0.321 | 0.985 | 1.231 | 3.106 | 0.003
akaroui | 59.9 | 15.0 | 16.705 | 10.092 | 0.913 | 0.566 | 0.984 | 2.950 | 6.671 | 0.106
Table 2:  Quantitative evaluation showing the individual label scores of the
three best MYOSAIQ challenge participants for ten metrics. ’Overall Best’
refers to the best score obtained by any participant and is used as an upper
baseline for each label and metric. The best score for each metric considering
all 18 participants is highlighted in bold. †Our teamname on the evaluation
platform is ’ominous_ocelot’.  Ablation of Proposed CaRe-CNN Ensemble
---
PP | Label | DSC (%) | HD (mm) | ASSD (mm) |  CC ($\uparrow$) |  MAE ($\downarrow$) |  LOA ($\downarrow$) |  CRPS ($\downarrow$)
mean | std | mean | std | mean | std
($\uparrow$) | ($\downarrow$) | ($\downarrow$) | ($\downarrow$) | ($\downarrow$) | ($\downarrow$)
× | LV | 93.4 | 3.3 | 6.892 | 2.157 | 0.422 | 0.294 | 0.980 | 6.837 | 17.215 | 0.011
MYO | 81.6 | 4.8 | 12.088 | 6.611 | 0.400 | 0.238 | 0.957 | 9.944 | 25.271 | 0.016
MIT | 68.5 | 15.9 | 16.892 | 13.46 | 0.901 | 1.346 | 0.837 | 4.000 | 18.491 | 0.007
MVO | 71.7 | 10.0 | 17.569 | 13.853 | 0.576 | 0.329 | 0.985 | 1.210 | 3.104 | 0.003
✓ | LV | 93.4 | 3.4 | 6.666 | 2.155 | 0.419 | 0.290 | 0.980 | 6.881 | 17.121 | 0.012
MYO | 81.6 | 5.0 | 12.839 | 7.144 | 0.405 | 0.253 | 0.954 | 9.845 | 25.686 | 0.016
MIT | 68.4 | 16.1 | 16.746 | 13.414 | 0.924 | 1.377 | 0.833 | 4.044 | 18.647 | 0.007
MVO | 72.0 | 9.5 | 16.548 | 14.261 | 0.547 | 0.321 | 0.985 | 1.231 | 3.106 | 0.003
Mean Diff. | +0.1 | 0 | -0.161 | +0.223 | -0.001 | +0.009 | -0.002 | +0.003 | +0.120 | +0.000
Table 3:  Ablation of the proposed post-processing (PP) when applied to our
CaRe-CNN ensemble predictions. Scores before (×) and after (✓) post-processing
are shown for each label and ten metrics. The last row refers to the mean
difference, where improvements when using post-processing are highlighted in
green, while declines are highlighted in red.  Figure 5:  Qualitative results
of CaRe-CNN on the validation set. Columns refer to three consecutive slices
of LGE MR scans of patients after MI for the three subgroups: D8 (col. 1-3),
M1 (col. 4-6) and M12 (7-9). Rows refer to scans of two separate patients and
show the image (rows 1, 4), ground truth (rows 2, 5) and prediction of CaRe-
CNN (rows 3, 6).  Figure 6:  Qualitative results of CaRe-CNN on the test set.
Columns refer to three consecutive slices of LGE MR scans of patients after MI
for each subgroup: D8 (col. 1-3), M1 (col. 4-6) and M12 (7-9). Rows refer to
scans of two separate patients and show the image (rows 1, 3) and prediction
of CaRe-CNN (rows 2, 4). Ground truth is not available for the test set.

##  4 RESULTS

The quantitative evaluation is performed by comparing our CaRe-CNN method to
the other 17 participants of the MYOSAIQ challenge on the hidden test set. For
each participant, we obtained ten metric scores for each label individually
from the official evaluation
platform333https://codalab.lisn.upsaclay.fr/competitions/13631, last accessed
on October 8, 2023, which is publicly available. The used metrics respectively
encompass the mean and standard deviation of the Dice score (DSC) in percent
as well as the Hausdorff distance (HD) and average symmetric surface distance
(ASSD) in mm. Furthermore, the list of metrics includes the mean correlation
coefficient score (CC), mean absolute error (MAE), limits of agreement (LOA)
and the continuous ranked probability score (CRPS).

In order to summarize the results, we computed the mean score over the four
labels for each metric and present them in Table 1 for each participant. This
is also true for the standard deviation of DSC, HD and ASSD, where we also
computed the mean score over the labels. The best score for each metric is
given in bold, while the second and third best metric scores are shown in
underlined blue and italicized orange, respectively.

Table 2 presents quantitative results per label for each metric to give some
insight into the individual scores. In the interest of space, we only provide
the scores for the three best performing methods in the challenge as announced
at the FIMH 2023 conference. Nevertheless, to indicate the overall best score
over all teams for each metric and label, we additionally show the best score
obtained by any participant as an upper bound baseline. The best score for
each metric when considering all 18 challenge participants is given in bold.

Table 3 shows an ablation of the proposed CaRe-CNN ensemble with and without
post-processing. Again, the scores were obtained from the evaluation platform
of the challenge, where we submitted our prediction results from the exact
same models with and without post-processing. We show the score for each label
and all metrics evaluated in the challenge. The last row represents the mean
difference between the scores obtained with and without post-processing.
Underlined green numbers indicate an improvement and red numbers refer to a
decline in performance when post-processing is applied compared to when it is
not.

The qualitative evaluation of our CaRe-CNN is performed by visually inspecting
the predictions. As ground truth segmentations for the test set data are
hidden, we also present qualitative results of CaRe-CNN trained on $2/3$ and
validated on $1/3$ of the actual training data for the MYOSAIQ challenge in
Fig. 5 to allow a comparison of our predictions to the ground truth.
Additionally, we provide qualitative results of our final method submitted to
the challenge on the test set in Fig. 6, however, without publicly available
ground truth segmentations, the predictions are only compared to the
respective input images. Both figures show three consecutive slices of two MR
scans of patients after acute MI per subgroup (D8, M1, M12).

##  5 DISCUSSION

#### Quantitative Evaluation

The mean score over the four labels presented in Table 1 shows, that on
average our method achieved the best score for eight out of ten metrics. Other
participants only outperformed our method on the mean standard deviation of
the HD as well as the CC, where CaRe-CNN obtained a tied second best score.
Most notably, our method shows great improvements compared to the other
methods on the DSC and ASSD scores. Specifically, with a mean DSC of $78.9\%$,
CaRe-CNN achieved an improvement of $3.3\%$ compared to the second best method
with $75.6\%$. The same $3.3\%$ window applied to the range $[75.6\%,72.3\%]$
encompasses the second up to the 12 best mean DSC score. Similarly, with a
result of $0.574\text{ mm}$ on the ASSD score our method achieved an
improvement of $0.123\text{ mm}$ over the second best ASSD score with
$0.697\text{ mm}$. The second up to the 10 best score lie within the same
$0.123\text{ mm}$ window of $[0.697\text{ mm},0.820\text{ mm}]$.

More details are provided in Table 2, where the per label scores and the
overall best score of any method are shown. For the LV results, it can be
observed that our method obtained the best scores for MAE and LOA, and
obtained tied best scores with other methods for the CC and CRPS. Moreover,
the shown DSC, HD and ASSD scores are all very close to one another with our
method achieving $93.4\%$ (best: $93.7\%$) DSC, $6.67\text{ mm}$ (best:
$6.41\text{ mm}$) HD and $0.42\text{ mm}$ (best: $0.39\text{ mm}$) ASSD. On
MYO, our method did not obtain the best score on any metric and underperformed
compared to the overall best score most notably with $12.839\text{ mm}$ (best:
$11.753\text{ mm}$) HD, $9.845$ (best: $7.891$) MAE and $25.686$ (best:
$22.251$) LOA. Nevertheless, on other metrics like DSC and ASSD our method
remains competitive to the other methods achieving $81.6\%$ (best: $82.2\%$)
DSC and $0.405\text{ mm}$ (best: $0.390\text{ mm}$) ASSD.

Compared to the other challenge participants, our CaRe-CNN excelled when
segmenting the difficult but clinically most relevant MIT and MVO labels,
where our method obtained the best score for six and seven out of the ten
metrics, respectively. Among the three challenge winners, our method achieved
good improvements on the MIT label with $68.4\%$ ($+2.4\%$) DSC, $16.746\text{
mm}$ ($-1.455\text{ mm}$) HD, $0.924\text{ mm}$ ($-0.081\text{ mm}$) ASSD and
$4.044$ ($-0.466$) MAE. Interestingly, our method underperformed on the HD of
the MVO label achieving a mean of $16.548\text{ mm}$ (best: $14.539\text{
mm}$) and a standard deviation of $14.261\text{ mm}$ (best: $5.682\text{
mm}$). On other metrics, however, CaRe-CNN achieved great improvements for the
MVO label compared to the other two challenge winners, namely $72.0\%$
($+12.1\%$) DSC, $0.547\text{ mm}$ ($-0.366\text{ mm}$) ASSD, $1.231$
($-1.719$) MAE and $3.106$ ($-3.565$) LOA.

#### Post-processing

When observing the training data more closely, we noticed that the ground
truth annotations of the heart labels towards the base of the heart are not
always complete. Most notably, how far slices are labeled towards the base
varies from image to image, which is likely an artifact from the annotation
protocol. While such incomplete annotations are not incorrect, they introduce
a bias to the dataset which is reflected by a machine learning model and leads
to some expected inconsistencies in the model predictions. We mitigate these
inconsistencies using a series of post-processing steps to obtain more
consistent predictions and show that quantitative scores for all metrics are
almost unchanged in Table 3. The most affected metric is the HD resulting in a
mean of $13.200\text{ mm}$ (mean difference: $-0.161\text{ mm}$) and a
standard deviation of $9.243\text{ mm}$ (mean difference: $+0.223\text{ mm}$)
after post-processing. This confirms our expectation, that the top-most slice
removal strategy paired with the large slice thickness of $5.6\text{ mm}$ on
average leads to the HD being the most affected metric as it is defined as the
maximum distance of any voxel-pair of the same label between ground truth and
prediction. Nevertheless, the relative change over all metrics averages to
$0.6\%$ when using post-processing, which confirms that it can be safely
applied in order to improve the qualitative consistency of the predictions.

#### Qualitative Evaluation

The qualitative results on the validation set in Fig. 5 confirm that most
label predictions are very close to the ground truth. On closer inspection,
however, some differences can be spotted. For example, one of the two MVO
regions is predicted in one additional consecutive slice in contrast to the
ground truth (D8, top), while the MIT label is overpredicted close to the apex
(M1, bottom). Also, an MVO label prediction for a patient without MVO is
visible (D8, bottom). Nevertheless, many regions are predicted correctly, most
notably even for data where the wall is in parts only two to three voxels
thick (M12, bottom). On the test set in Fig. 5, qualitative results can only
be compared to the LGE MR image. Overall, the label predictions appear to be
realistic which is supported by our quantitative evaluation, however, further
confirmation needs to be performed by an expert.

#### Challenges and Limitations

One major challenge of correctly segmenting the structures of interest arises
from the limited resolution of the LGE MR data in combination with the shape
and small physical size of the structures, most notably the MIT and MVO label.
While the LV is comparatively easy to segment due to its size and blob-like
shape in 3D, the f-MYO label that surrounds the LV averages to a mid-diastolic
thickness of $6.47\pm 1.07\text{ mm}$ in women and $7.90\pm 1.24\text{ mm}$ in
men [Walpot et al., 2019] without considering infarction. In a small cohort,
[Khalid et al., 2019] showed that during ejection, healthy wall segments are
roughly three times as thick ($8.73\text{ mm}$) compared with infarcted wall
segments ($2.86\text{ mm}$). Furthermore, infarction might only affect some
part of the myocardial tissue in transmural direction such that two or even
all three of the f-MYO sublabels (MYO, MIT and MVO) might be present across
the already thin wall. The in-plane resolution of the LGE MR data with
$1.57\text{ mm}$ on average paired with the small physical size of some of the
structures of interest leads to a potential transmural thickness of only a few
voxels for these labels. Moreover, segmentation models are inherently
uncertain near the label borders and thus, prone to single voxel errors, which
can strongly affect the scores for small structures like the MIT and MVO
labels. The combination of these effects explains the disparity of the LV to
the MIT and MVO label scores for which CaRe-CNN achieved the best score in six
(MIT) and seven (MVO) out of ten metrics among 18 challenge participants.

A remaining challenge arises from the MVO label predictions for some patients
of the D8 subgroup, where the label was not predicted when it should be
present or vice versa. Since the presence of MVO is linked to an increased
risk of adverse cardiovascular events [Hamirani et al., 2014, Rios-Navarro et
al., 2019], incorrect predictions of MVO might impact clinical decision making
if trusted blindly. While manual verification by an expert is necessary, our
state-of-the-art predictions can alleviate the manual workload to obtain
correct segmentations of patient-specific anatomy.

##  6 CONCLUSION

In this work we presented CaRe-CNN, a 3-stage cascading refinement CNN, which
segments cardiac LGE MR images after MI. The cascading architecture is
designed to exploit the hierarchical label definition of the data and is
trained end-to-end fully in 3D. Furthermore, we employed a series of post-
processing steps that improve the consistency of the predictions by taking
anatomical constraints into account. The proposed CaRe-CNN was submitted to
the MYOSAIQ challenge, where it ranked second out of 18 participating teams
and achieved state-of-the-art segmentation results, most notably when
segmenting the difficult MIT and MVO labels. Due to great improvements over
related work on the difficult but clinically very relevant MVO label, our
method obtained the best score in eight out of ten metrics when computing the
mean over all labels. Precise segmentations of healthy and infarcted
myocardial tissue after MI allow patient-specific therapy planning and are an
important step towards personalized medicine. In our future work, we plan to
investigate uncertainty quantification strategies to further improve CaRe-CNN
for future rounds of the MYOSAIQ challenge.

## ACKNOWLEDGEMENTS

This research was funded by the InstaTwin grant FO999891133 from the Austrian
Research Promotion Agency (FFG).

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