# Shape-aware Segmentation of the Placenta in BOLD Fetal MRI Time Series

S. Mazdak Abulnaga<EMAIL_ADDRESS>
CSAIL/EECS, Massachusetts Institute of Technology, Cambridge, MA, USA
MGH/HST Martinos Center for Biomedical Imaging, Harvard Medical School,
Boston, MA, USA Neel Dey<EMAIL_ADDRESS>
CSAIL, Massachusetts Institute of Technology, Cambridge, MA, USA Sean I. Young
<EMAIL_ADDRESS>
MGH/HST Martinos Center for Biomedical Imaging, Harvard Medical School,
Boston, MA, USA
CSAIL, Massachusetts Institute of Technology, Cambridge, MA, USA Eileen Pan
<EMAIL_ADDRESS>
CSAIL/EECS, Massachusetts Institute of Technology, Cambridge, MA, USA
Katherine I. Hobgood<EMAIL_ADDRESS>
CSAIL, Massachusetts Institute of Technology, Cambridge, MA, USA Clinton J.
Wang<EMAIL_ADDRESS>
CSAIL/EECS, Massachusetts Institute of Technology, Cambridge, MA, USA P. Ellen
Grant<EMAIL_ADDRESS>
Fetal-Neonatal Neuroimaging and Developmental Science Center, Boston
Children’s Hospital, Harvard Medical School, Boston, MA, USA Esra Abaci Turk
<EMAIL_ADDRESS>
Fetal-Neonatal Neuroimaging and Developmental Science Center, Boston
Children’s Hospital, Harvard Medical School, Boston, MA, USA Polina Golland
<EMAIL_ADDRESS>
CSAIL/EECS, Massachusetts Institute of Technology, Cambridge, MA, USA

###### Abstract

Blood oxygen level dependent (BOLD) MRI time series with maternal hyperoxia
can assess placental oxygenation and function. Measuring precise BOLD changes
in the placenta requires accurate temporal placental segmentation and is
confounded by fetal and maternal motion, contractions, and hyperoxia-induced
intensity changes. Current BOLD placenta segmentation methods warp a manually
annotated subject-specific template to the entire time series. However, as the
placenta is a thin, elongated, and highly non-rigid organ subject to large
deformations and obfuscated edges, existing work cannot accurately segment the
placental shape, especially near boundaries. In this work, we propose a
machine learning segmentation framework for placental BOLD MRI and apply it to
segmenting each volume in a time series. We use a placental-boundary weighted
loss formulation and perform a comprehensive evaluation across several popular
segmentation objectives. Our model is trained and tested on a cohort of $91$
subjects containing healthy fetuses, fetuses with fetal growth restriction,
and mothers with high BMI. Biomedically, our model performs reliably in
segmenting volumes in both normoxic and hyperoxic points in the BOLD time
series. We further find that boundary-weighting increases placental
segmentation performance by $8.3$% and $6.0$% Dice coefficient for the cross-
entropy and signed distance transform objectives, respectively.

Keywords: Placenta, Fetus, Segmentation, BOLD MRI, Shape

##  1 Introduction

#### Biomedical motivation.

The placenta delivers oxygen and nutrients to support fetal growth. Placental
dysfunction causes pregnancy complications that affect fetal development,
leading to a critical need to assess placental function in vivo. Blood oxygen
level dependent (BOLD) MRI images oxygen transport within the placenta
(Sørensen et al., 2013; Abaci Turk et al., 2019) and has emerged as a
promising tool to non-invasively study placental function. Temporal analysis
of BOLD MRI with maternal oxygen administration can identify contractions
(Abaci Turk et al., 2020; Sinding et al., 2016), biomarkers of fetal growth
restriction (Luo et al., 2017; Sørensen et al., 2015), predict placental age
(Pietsch et al., 2021), and can study congenital heart disease (You et al.,
2020; Steinweg et al., 2021).

#### Challenges and current approaches.

Despite its importance for many downstream clinical research tasks, placental
segmentation is often performed manually and can take a significant amount of
time, even for a trained expert. For temporal BOLD MRI studies, manual
segmentation is rendered more challenging due to the sheer number of MRI scans
acquired and rapid signal changes due to common experimental designs. For
example, maternal oxygenation experiments acquire several hundred whole-uterus
MRI scans to observe signal changes in three stages: normoxia (baseline),
hyperoxia, and return to normoxia. During the hyperoxic stage, BOLD signals
increase rapidly, giving the placenta a hyperintense appearance. Further,
placental shape undergoes large deformation caused by maternal breathing,
contractions, and fetal movements which are typically stronger during
hyperoxia (You et al., 2015), as illustrated in Figure 1.

Current practice analyzes BOLD signals with respect to a template volume.
Deformable registration of all volumes in the time series to the template is
performed to enable spatiotemporal analysis (Abaci Turk et al., 2017; You et
al., 2015; Chi et al., 2023). However, template-to-volume registration within
the uterus can lead to large errors, necessitating outlier detection and
possibly rejecting a significant number of volumes (Abaci Turk et al., 2017;
You et al., 2015). These registration difficulties arise from the placenta,
fetus, and mother being subject to highly disparate deformation models along
the temporal sequence. For example, the fetus undergoes piecewise-rigid motion
whereas the placenta deforms highly non-rigidly, thus precluding the direct
use of standard registration frameworks such as ANTs (Tustison et al., 2020)
and VoxelMorph (Balakrishnan et al., 2019) on temporal whole-uterus images.

#### Contributions.

To address these challenges, we propose a deep network framework to
automatically segment the placenta in BOLD MRI time series. Our model is
trained on volumes obtained during the normoxic and hyperoxic phases from each
patient so as to capture placental shape and appearance variability during
maternal oxygenation. As the placenta is a thin and elongated organ, we use a
boundary-weighted formulation (parameterized by thresholded signed distance
function approximations) of several popular region and/or shape-based
segmentation objectives which yield significant gains in both placental
segmentation accuracy and surface overlap over their non-boundary-weighted
equivalents. Our model demonstrates consistency in the predicted segmentation
label maps on a large dataset of unseen BOLD MRI and generalizes to a broad
range of gestational ages and pregnancy conditions, thus enabling improved
non-invasive pregnancy studies via maternal oxygenation. Finally, to
demonstrate the feasibility of our method for clinical research, we illustrate
an application based on relative BOLD signal increases.

This paper extends our preliminary analysis of placental segmentation
(Abulnaga et al., 2022b) first presented at the International Workshop on
Perinatal, Preterm and Paediatric Image Analysis held in conjunction with the
International Conference on Medical Image Computing and Computer-Assisted
Intervention (MICCAI) in 2022. We expand on it by providing more motivation
for the work in Section 1 and relevant context for boundary-weighted and
shape-aware segmentation losses in Section 2. In our methods in Section 3, we
provide additional details, illustrations, and justification for the chosen
additive boundary-weighted loss formulation. We then experiment with several
additional shape-aware and boundary-weighted loss functions in our experiments
(Section 4) alongside introducing qualitative measures of temporal
segmentation performance and providing failure cases. Lastly, we provide a
substantially expanded discussion of our work in Section 5 which overviews its
place in the shape-aware segmentation literature and its utility for clinical
research.

Figure 1: During maternal oxygen administration, the placenta undergoes large
shape deformation caused by fetal motion (left) and strong BOLD signal changes
caused by maternal hyperoxia (right). Placental boundaries are marked in red.
Signal normalization is based on averaging all MRI intensities in the first
normoxic period.

##  2 Related Work

#### Placenta segmentation in structural MRI.

Machine learning segmentation models for the placenta have been previously
proposed and include both semi-automatic (Wang et al., 2015) and automatic
(Alansary et al., 2016; Torrents-Barrena et al., 2019a; Pietsch et al., 2021;
Specktor-Fadida et al., 2021) approaches. While semi-automatic methods have
achieved success in predicting segmentation label maps with high accuracy,
these approaches are infeasible for segmenting BOLD MRI time series due to the
large number of volumes that would require manual annotation. The majority of
automatic methods focus on segmentation in structural images as opposed to
BOLD MRI as in this work. For example, Alansary et al. (2016) proposed a model
for segmenting T2-weighted (T2w) images based on a 3D CNN followed by a dense
CRF for segmentation refinement and validated it on a singleton cohort that
included patients with fetal growth restriction (FGR). Torrents-Barrena et al.
(2019a) developed a segmentation framework based on super-resolution and a
support vector machine and validated it using a singleton and twin cohort of
T2w MRI. Specktor-Fadida et al. (2021) focused on transferring segmentation
networks across MRI sequences using a self-training model yielding successful
segmentation of steady-state precession MRI sequences. For a detailed
treatment of fetal MRI segmentation, we refer the reader to the survey by
Torrents-Barrena et al. (2019b).

#### Placenta segmentation in BOLD MRI.

BOLD MR images of the placenta differ greatly from anatomical images, as BOLD
images have lower in-plane resolution and the contrast between the placental
boundary and surrounding anatomy is less pronounced. Anatomical images may
also benefit from super-resolution approaches to increase SNR in the acquired
image (Uus et al., 2020). Pietsch et al. (2021) are the first to consider
placental segmentation in functional MRI. They proposed a 2D patch-based U-Net
model for functional image segmentation and demonstrated a successful
application of age prediction using the estimated T2* values. They focused on
a cohort of singleton subjects and demonstrated successful applications to
abnormal pregnancy conditions including preeclampsia. In contrast to their
approach that segments derived T2* maps, we evaluate our segmentation model on
BOLD MRI time series. Furthermore, our 3D model operates on the entire volume
rather than patches, thereby helping to better resolve the boundaries of the
placenta.

#### Boundary-weighted segmentation objectives.

Popular supervised segmentation losses such as cross-entropy underperform in
the presence of highly imbalanced classes common in radiology volumes. As the
interface between organs can be obfuscated by motion-related artifacts and/or
isointense appearance, strongly penalizing incorrect predictions near the
boundary has been demonstrated to improve segmentation performance across
several biomedical applications (Ma et al., 2021). For example, Kervadec et
al. (2021) and Zhang et al. (2020) implemented distance metrics on organ
contour predictions in addition to region-based losses such as soft Dice to
improve performance. In parallel, several works regress ground truth distance
transforms which are strongly weighted near the organ boundary (Hoopes et al.,
2022). As illustrative examples, Huang et al. (2021) regressed ground truth
distance maps that are normalized using the Heaviside function to penalize
near-boundary misclassifications, while Karimi and Salcudean (2019) proposed a
soft-Hausdorff distance loss parameterized by distance transforms. Lastly, the
boundary weighting formulation we use is most similar to that of Caliva et al.
(2019), wherein a thresholded signed distance transform is used to upweigh
boundary neighborhoods in region-based losses.

##  3 Methods

We train a model $F_{\theta}:\mathbf{X}\rightarrow\mathbf{Y}$ parameterized by
$\theta$ that takes volumes from a BOLD MRI time series
$\mathbf{X}\in\mathbb{R}^{H\times W\times D\times T}$ and independently
predicts a placental segmentation label map $\mathbf{Y}\in\\{0,1\\}^{H\times
W\times D\times T}$ for each time point $t\in\\{1,\dots T\\}$, where $T$ is
the total number of time points at which MRI scans were acquired. For a given
BOLD time series, we have a small number $N_{l}$ of frames with ground truth
labels $(\mathbf{x},\mathbf{y})$, where $\mathbf{x}\in\mathbb{R}^{H\times
W\times D}$ is an MRI scan and $\mathbf{y}\in\\{0,1\\}^{H\times W\times D}$ is
the ground truth placenta label map. The model predicts segmentation label
maps on each $3$D volume in the time series independently.

###  3.1 Architecture and data considerations

We use a standard 3D U-Net (Ronneberger et al., 2015) with $4$ blocks in the
contracting and expanding paths each. Each block consists of two consecutive
Conv-BatchNorm-ReLU blocks using filters of size $3\times 3\times 3$. Each
block is followed by max pooling (contraction path) or transpose convolution
(expansion path). We employ batch normalization before ReLU activation. We
augment the images using random affine transforms, flips, whole-image
brightness shifts, contrast changes, random noise, and elastic deformations,
all using TorchIO (Pérez-García et al., 2021). Specific to segmentation with
maternal oxygenation, we simulate the effects of maternal normoxia and
hyperoxia with a constant intensity shift in the placenta. All augmentation
decisions were made based on cross-validation performance.

To capture the MRI signal and placental shape changes resulting from maternal
hyperoxia and fetal motion, we specifically train on several manually
segmented volumes in the normoxic or hyperoxic phase. This allows the model to
learn from the realistic variations that arise during maternal oxygenation.

###  3.2 Additive Boundary Loss

To emphasize placental boundary details during training, we construct an
additive boundary-weighting $w_{\delta}$ which is compatible with any per-
voxel segmentation loss function $L\left(\cdot\right)$. Given a ground truth
placental label map $\mathbf{y}$, we denote its boundary as
$\partial\mathbf{y}$. We use a signed distance function $f_{\mathbf{y}}(x)$
that measures the signed distance, $d(x,\partial\mathbf{y})$, of voxel
$x\in\mathbb{R}^{3}$ to the boundary, where $f_{\mathbf{y}}(x)>0$ when inside
of the placenta and $f_{\mathbf{y}}(x)<0$ when outside. The boundary weighting
is additive for voxels within $\delta$-distance of $\partial\mathbf{y}$,

$w_{\delta}(x)=\begin{cases}w_{1}&\text{if }\quad 0\leq
f_{\mathbf{y}}(x)<\delta,\\\ w_{2}&\text{if }-\delta<f_{\mathbf{y}}(x)<0,\\\
0&\text{otherwise}.\end{cases}$ (1)

The weighted loss $L_{w}$ is then,

$L_{w}\left(x\right)=L\left(x\right)\left[w_{c}\left(x\right)+w_{\delta}\left(x\right)\right],$
(2)

where $w_{c}(x)$ is a per-voxel class weighting. In practice, we set
$w_{2}>w_{1}$, to account for class weighting and to penalize outside voxels
more heavily and learn to distinguish the placenta from its surrounding
anatomy.

We note that several forms of boundary-weighted losses exist in the literature
(Ma et al., 2021) with ours being most similar to Caliva et al. (2019). Many
of these use a decaying weight for voxels further from the boundary, while we
use a constant weighting. For computational efficiency, rather than computing
$f_{\mathbf{y}}(x)$ for all voxels $x$ as in Caliva et al. (2019), we
approximate the region of distance $\pm\delta$ from $\partial\mathbf{y}$ using
convolutional kernels. To find voxels $x$ with $|f_{\mathbf{y}}(x)|<\delta$,
we estimate a $2\delta$-wide boundary by an average pooling filter on
$\mathbf{y}$ with kernel size $K$ and take the smoothed outputs to lie in the
boundary. A larger $K$ produces a wider boundary, penalizing more
misclassified voxels. See Figure 2 for an illustration. Computing the boundary
using a convolution operator is advantageous as it does not require computing
the signed distance transform directly, which is computationally expensive and
bottlenecks deep network training.

Figure 2: Illustration of inner and outer boundaries used in the additive
boundary loss. Right image is zoomed in from the top left corner of the
placenta (green box) to closely illustrate boundaries. Placenta segmentation
outline is shown in red and inner and outer boundaries $\delta$-distance away
are shown in blue.

###  3.3 Implementation Details

We train using a learning rate $\eta=10^{-4}$ with linear decay for $5500$
epochs and select the model with the best Dice score on the validation set.
For the additive boundary loss, we set $w_{1}=1$, $w_{2}=40$, and $K=11$. For
training, we use a simple preprocessing pipeline. All images are normalized by
scaling the 90 percentile intensity value to $1$ without thresholding or
clipping any values. We crop or pad all volumes in the dataset to have
dimension $112\times 112\times 80$ and train on the entire 3D volume. We use a
batch size of $8$ MRI volumes in training. We augment our data with random
translations of up to 10 voxels, rotations up to 22∘, Gaussian noise sampled
with $\mu=0,\sigma=0.25$, elastic deformations with $5$ control points and a
maximum displacement of $10$ voxels, whole volume intensity shifts up to $\pm
25\%$, and whole-placenta intensity shifts of $\pm 0.15$ normalized intensity
values. These values were determined by cross-validation on the training set.
When evaluating the model on our test set, we post-processed produced label
maps by taking the largest connected component to eliminate islands. Our
segmentation code and trained model are available at
https://github.com/mabulnaga/automatic-placenta-segmentation.

##  4 Experiments

###  4.1 Data

Our dataset consists of BOLD MRI scans taken from two clinical research
studies. Data were collected from $91$ subjects of which $78$ were singleton
pregnancies (gestational age (GA) at MRI scan of $23$ weeks (wk), $5$ days (d)
to $37$wk$6$d), and $13$ were monochorionic-diamniotic (Mo-Di) twins (GA at
MRI scan of $27$wk$5$d – $34$wk$5$d). Of these, $63$ pregnancies were
controls, $16$ had fetal growth restriction (FGR), and $12$ had high maternal
body mass index (BMI, BMI $>30$). Obstetrical ultrasound was used to classify
subjects with FGR. For singleton subjects, FGR classification was done based
on having fetuses with estimated weight less than the 10 percentile. For twin
subjects, FGR classification was determined by monochorionicity and
discordance in the estimated fetal weight by growth restriction ($<$10
percentile) in one or both fetuses; and/or ii) growth discordance ($\geq
20\%$) between fetuses. Table 1 shows patient demographics and GA ranges per
group.

Table 1: Demographic information for subjects in our analysis. GA is gestational age. Group | Criteria | Control | FGR | High BMI
---|---|---|---|---
Singleton | # subjects | $60$ | $6$ | $12$
| GA at MRI |  $23$wk$5$d – $37$wk$6$d |  $26$wk$6$d – $34$wk$5$d |  $26$wk$4$d – $36$wk$6$d
Twin | # subjects | $3$ | $10$ | $0$
| GA at MRI |  $31$wk$2$d – $34$wk$5$d |  $27$wk$5$d – $34$wk$5$d | N/A

MRI BOLD scans were acquired on a $3$T Siemens Skyra scanner (GRE-EPI,
interleaved with $3$mm isotropic voxels, TR $=5.8$–$8$s, TE $=32-47$ ms, FA =
$90^{\circ})$. To eliminate intra-volume motion artifacts, we split the
acquired interleaved volumes into two separate volumes with spacing $3\times
3\times 6$mm, then linearly interpolate to $3\times 3\times 3$mm. In our
analysis, we only consider one of two split volumes, as the signals are
redundant between pairs. Maternal oxygen supply was alternated during the BOLD
acquisition via a nonrebreathing facial mask to have three 10-minute or
5-minute consecutive episodes: 1. normoxia (21% $O_{2}$), 2. hyperoxia (100%
$O_{2}$, 15L/min), and 3. a return to normoxia (21% $O_{2}$).

To generate training data, the placenta was manually segmented by a trained
observer. Each BOLD MRI time series had $1$ to $6$ manual segmentations,
yielding a total of $176$ ground truth labels. The data was then split into
training, validation, and test sets: ($65\%/15\%/20\%$: $63/11/17$ subjects).
Data was stratified to have proportional distributions of subjects with
singleton and twin pregnancies, then to proportionally distribute healthy
controls, subjects with FGR, and subjects with high BMI. Our test set had $15$
singleton pregnancies and $2$ twins. Of the singleton pregnancies, $12$ were
healthy controls, $1$ had FGR, and $2$ had high BMI. Both twin subjects had
FGR. Our test set had a total of $31$ labeled images, none of which were used
before final evaluation.

Each subject in the training set had up to $N_{l}=6$ ground truth
segmentations in the BOLD time series. To prevent bias in sampling images, we
train by randomly sampling $1$ of $N_{l}$ ground truth segmentations for each
subject. The length of one epoch is the number of subjects rather than the
number of images. Subject-wise random sampling was used to reduce bias from
subjects with more ground truth labels.

###  4.2 Evaluation

#### Performance measures.

We first compare the predicted segmentation label maps to ground truth
segmentations. We measure similarity using the Dice score (Dice), the
95-percentile Hausdorff distance (HD95), and the Average Symmetric Surface
Distance (ASSD). To evaluate the feasibility of the produced segmentations for
clinical research studying whole-organ signal changes, we evaluate the
percentage error in the mean BOLD values between our prediction and the ground
truth (BOLD error), defined as $100\times|\hat{b}-b|/{b}$, where $b$ and
$\hat{b}$ denote the mean BOLD signal in the ground truth and in the predicted
segmentation, respectively. As estimating whole-organ BOLD signal changes is
an important clinical research task, this metric quantifies the appropriate
error caused by using automatic placental segmentations.

#### Benchmarked segmentation loss functions.

We benchmark several popular loss functions and their boundary-weighted
extensions to assess their performance on placental segmentation. We quantify
improved performance using the boundary-weighting approach (Eq. 1) by
comparing performance of the cross-entropy loss ($\mathcal{L}_{\mathrm{CE}}$)
and the signed distance transform (SDT) loss ($\mathcal{L}_{\mathrm{SDT}}$)
with their boundary-weighted counterparts ($\mathcal{L}_{\mathrm{BW-CE}}$,
$\mathcal{L}_{\mathrm{BW-SDT}}$). The SDT loss poses segmentation as a
regression problem and predicts the signed distance transformation to the
placenta boundary. The loss $\mathcal{L}_{\mathrm{SDT}}$ computes the mean-
squared error of the predicted SDT from ground truth (Hoopes et al., 2022). We
also benchmark performance on the widely used soft Dice loss
($\mathcal{L}_{\mathrm{Dice}}$) (Milletari et al., 2016) and a boundary-
weighted Focal loss ($\mathcal{L}_{\mathrm{BW-Focal}}$) with $\alpha=0.5$,
$\gamma=2$ (Lin et al., 2017). As segmentation often benefits from hybrid loss
functions (Ma et al., 2021), we also evaluate various combinations of losses.
Lastly, we evaluate two boundary-focused signed distance-based loss functions
from Huang et al. (2021) ($\mathcal{L}_{\mathrm{Shape}}$) and from Karimi and
Salcudean (2019) ($\mathcal{L}_{\mathrm{HD}}$).

#### Consistency with hyperoxia.

We evaluate our model’s sensitivity to oxygenation by comparing the accuracy
of predictions in normoxia and hyperoxia for subjects with multiple ground
truth annotations. We compute segmentation performance using metric $m$ in
normoxia ($m_{\mathrm{normoxia}}(\mathbf{y}_{i},\hat{\mathbf{y}_{i}})$), and
in hyperoxia ($m_{\mathrm{hyperoxia}}(\mathbf{y}_{i},\hat{\mathbf{y}_{i}})$),
where $m_{\mathrm{normoxia}}(\mathbf{y}_{i},\hat{\mathbf{y}_{i}})$ denotes the
similarity using metric $m$ of our predicted segmentation
$\hat{\mathbf{y}_{i}}$ to the ground truth $\mathbf{y}_{i}$ for subject $i$ in
normoxia. For the evaluation metric $m$, we use the Dice score, HD$95$, ASSD,
and percentage BOLD error. To evaluate consistency with oxygenation, we
compute the mean absolute error between segmentation performance in both
oxygenation phases
$\left|m_{\mathrm{normoxia}}\left(\mathbf{y}_{i},\hat{\mathbf{y}_{i}}\right)-m_{\mathrm{hyperoxia}}\left(\mathbf{y}_{i},\hat{\mathbf{y}_{i}}\right)\right|$.
A low error indicates predicted segmentations are consistent with oxygenation
changes in the placenta.

#### Temporal consistency.

We assess the consistency of our predictions by applying our model to all
volumes in the BOLD time series of the test set. Since our volumes are
acquired interleaved and split into two separate volumes, we apply our model
to every second volume in the time series, yielding a mean of $111.7\pm 45.3$
volumes per subject. We measure consistency by comparing the Dice score
between consecutive volumes. We qualitatively evaluate segmentation
performance across the time series and visualize robustness to fetal motion
and oxygenation change.

###  4.3 Results

Table 2 reports the performance of several segmentation losses on the test
set. Figure 3 presents box-and-whisker plots of each model’s performance. Both
our best performing models trained using $\mathcal{L}_{BW-CE}$ and
$\mathcal{L}_{\mathrm{BW-Focal}}$ achieve a mean Dice score of $82.80$, though
$\mathcal{L}_{BW-CE}$ produces slightly lower variance. This model also
achieves low relative BOLD error ($4.11\pm 3.0\%$), indicating that our
model’s segmentations are suitable for clinical research studies assessing
whole-organ signal changes. Similar performance is achieved for the other loss
functions. Our model also outperforms the two shape-based baselines
$\mathcal{L}_{\mathrm{Shape}}+\mathcal{L}_{\mathrm{Dice}}$ and
$\mathcal{L}_{\mathrm{HD}}+\mathcal{L}_{\mathrm{Dice}}$ on all metrics, though
performance improvements are not statistically significant. These shape-based
baselines demonstrate less consistent performance as they have higher variance
with outliers (Figure 3).

Table 2: Test results produced by our 3D U-Net model trained using different loss functions. Numbers in bold indicate the best result in each column. We evaluate commonly used loss functions and the shape-based loss ($\mathcal{L}_{\mathrm{Shape}}$) of (Huang et al., 2021) and the soft-Hausdorff distance loss ($\mathcal{L}_{\mathrm{HD}}$) of Karimi and Salcudean (2019). Loss | Dice | HD$95$ (mm) | ASSD (mm) | BOLD error $(\%)$
---|---|---|---|---
$\mathcal{L}_{\mathrm{BW-CE}}$ | $\mathbf{82.80\pm 3.25}$ | $13.31\pm 6.4$ | $\mathbf{4.01\pm 1.0}$ | $4.11\pm 3.0$
$\mathcal{L}_{\mathrm{BW-CE}}(N_{l}=1)$ | $81.98\pm 5.3$ | $\mathbf{12.61\pm 4.66}$ | $4.08\pm 1.02$ | $4.30\pm 4.52$
$\mathcal{L}_{\mathrm{CE}}$ | $76.47\pm 7.43$ | $17.92\pm 11.02$ | $5.96\pm 2.1$ | $5.22\pm 2.53$
$\mathcal{L}_{\mathrm{Dice}}$ | $77.13\pm 9.74$ | $22.51\pm 18.02$ | $6.14\pm 3.95$ | $8.95\pm 11.37$
$\mathcal{L}_{\mathrm{BW-CE}}+\mathcal{L}_{\mathrm{Dice}}$ | $79.82\pm 6.57$ | $15.91\pm 7.93$ | $4.44\pm 1.3$ | $4.61\pm 2.59$
${\mathcal{L}_{\mathrm{CE}}+\mathcal{L}_{\mathrm{Dice}}}$ | ${81.44\pm 6.42}$ | ${12.87\pm 8.9}$ | ${4.14\pm 1.42}$ | ${5.84\pm 8.28}$
$\mathcal{L}_{\mathrm{BW-Focal}}$ | $81.82\pm 4.71$ | $12.88\pm 5.04$ | $4.10\pm 0.97$ | $4.44\pm 3.4$
$\mathcal{L}_{\mathrm{BW-Focal}}+\mathcal{L}_{\mathrm{Dice}}$ | $82.80\pm 3.91$ | $12.75\pm 5.58$ | $4.02\pm 0.92$ | $\mathbf{4.06\pm 1.75}$
${\mathcal{L}_{\mathrm{Focal}}+\mathcal{L}_{\mathrm{Dice}}}$ | ${81.96\pm 6.19}$ | ${14.02\pm 8.99}$ | ${4.27\pm 1.62}$ | ${6.32\pm 7.25}$
$\mathcal{L}_{\mathrm{BW-SDT}}$ | $80.63\pm 5.96$ | $16.63\pm 12.4$ | $4.68\pm 1.92$ | $5.64\pm 6.35$
$\mathcal{L}_{\mathrm{SDT}}$ | $76.06\pm 8.67$ | $20.14\pm 14.25$ | $6.01\pm 2.51$ | $7.09\pm 8.86$
$\mathcal{L}_{\mathrm{HD}}+\mathcal{L}_{\mathrm{Dice}}$ | $80.39\pm 7.16$ | $16.16\pm 12.17$ | $4.62\pm 1.98$ | $6.35\pm 9.52$
$\mathcal{L}_{\mathrm{Shape}}+\mathcal{L}_{\mathrm{Dice}}$ | $81.54\pm 6.30$ | $16.06\pm 13.28$ | $4.65\pm 2.26$ | $5.25\pm 4.59$

The boundary weighting improves the performance of several loss functions
compared to their non-boundary weighted counterparts. Training the model with
our boundary weighting results in a statistically significant increase in
performance. When trained using $\mathcal{L}_{\mathrm{CE}}$, we achieve a mean
Dice of $82.5$ with boundary weighting in the loss compared to $76.5$ without.
Similarly, for $\mathcal{L}_{\mathrm{SDT}}$ we achieve a mean Dice of $80.6$
with boundary weighting compared to $76.1$ without. However, training with an
additive Dice loss improves this performance gap:
$\mathcal{L}_{\mathrm{CE}}+\mathcal{L}_{\mathrm{Dice}}$ achieves a Dice of
$81.4$ compared to $82.8$ for $\mathcal{L}_{\mathrm{BW-CE}}$, and
$\mathcal{L}_{\mathrm{Focal}}+\mathcal{L}_{\mathrm{Dice}}$ achieves a Dice of
$82.0$ compared to $82.8$ for $\mathcal{L}_{\mathrm{BW-
Focal}}+\mathcal{L}_{\mathrm{Dice}}$. The boundary-weighting also improves
mean performance of ASSD and BOLD error and demonstrates more narrow
distributions of distortion with fewer outliers (see Figure 3.) Using only the
first segmented volume of the BOLD MRI series in normoxia also results in a
small drop in performance ($\mathcal{L_{\mathrm{BW-CE}}}$ ($N_{l}=1$)). Adding
labeled examples from the hyperoxic phase helps generalization, as the
placental shape and intensity patterns can change greatly.

Our performance is consistent across pregnancy conditions, as we achieve Dice
scores of ($77.4$, $88.1$) on the two subjects with twin pregnancies, $82.8\pm
3.0$ on the singletons (N$=15$), $83.0\pm 5.4$ on the FGR cohort (N=$3$),
$82.6\pm 3.0$ on the controls (N=$12$) and $(80.6,86.5)$ on the two BMI cases.

|
---|---
Dice | HD$95$
|
ASSD | BOLD error
Figure 3: Box-and-whisker plots of Dice (top left), HD$95$ (top right), ASSD (bottom left), and BOLD error (bottom right) on the test set across all models. We evaluate several commonly used loss functions with and without our boundary weighting and evaluate the baseline shape-based loss ($\mathcal{L}_{\mathrm{Shape}}$) of Huang et al. (2021) and the soft-Hausdorff distance loss ($\mathcal{L}_{\mathrm{HD}}$) of Karimi and Salcudean (2019). Black horizontal lines inside the box indicate the median. The boxes extend to the 25 and 75 percentiles and the whiskers reach to the most extreme values not considered outliers (black bars). The outliers, shown as crosses, are points farther than 1.5 times the interquartile range. Mean values are indicated on the top horizontal axis. Boundary weighting results in higher mean values with more narrow distributions of distortion compared to their non-boundary weighted counterparts. We further observe improved performance compared with baseline losses in terms of mean, variance, and number of outliers.  |  |  |  |
---|---|---|---|---
|  |  |  |
$74.6$ | $84.4$ | $85.6$ | $86.5$ | $88.0$
Figure 4: Example predictions on $5$ subjects from the test set. Ground truth
segmentations are shown in yellow and predictions in red. Dice scores are
indicated below each column. Two slices are shown for each subject, spaced
$18$mm apart.

Our model performs consistently well in the normoxic and hyperoxic phases. For
the $5$ subjects with ground truth segmentations in both the normoxia and
hyperoxia, we achieve a mean absolute difference between predictions in
normoxia and hyperoxia of $3.78\pm 1.17$ Dice, $3.15\pm 1.90$mm HD95, $0.77\pm
0.16$mm ASSD, and $3.21\pm 1.36\%$ relative BOLD error. These results suggest
that our model is robust to contrast changes in the placenta resulting from
maternal hyperoxia, and can be used in studies quantifying oxygen transport in
the organ. A larger number of subjects are needed to assess statistical
significance.

Figure 4 compares the predicted label maps with ground truth on $5$ subjects
with increasing Dice scores using the BW-CE model. The model accurately
identifies the location of the placenta, but in the worst cases misses
boundary details.

#### BOLD Time Series Evaluation

Figure 5 presents example predicted segmentations at multiple points in the
BOLD MRI time series for $3$ subjects. The predicted segmentations are robust
to large fetal deformations and placental signal changes. Figure 6 (top)
presents distributions of Dice score between predicted label maps of
consecutive frames in the BOLD time series for all subjects in the test set.
Distributions have high medians (Dice $>90$) for all but one case, with high
density at high Dice scores (Dice $>90$). Dice differences are highly affected
by fetal and maternal motion that cause placental deformation. We visually
verified that modest drops in Dice ($<90$) were mainly due to fetal motion,
but $3$ subjects had a small number of frames with large drops (Dice $<70$)
that were caused by errors in the produced label maps. Figure 6 (bottom) shows
$3$D models of failed segmentations from two subjects from frames with Dice
$<70$. Our model omitted parts of the placenta for Subject $9$ and added a
large region for Subject $15$. In practice, these failures ocurred in a small
number of frames, $6.8\%$ of frames for Subject $9$ and $0.45\%$ of frames for
Subject $15$. Overall, predicted label maps are consistent between consecutive
volumes of the MRI time series, achieving a Dice of $92.0\pm 1.7$ and a BOLD
difference of $2.1\pm 0.60\%$. The small differences between the relative
mean-BOLD values suggest these produced segmentations may be suitable for
research studies assessing placental function.

Figure 5: Consistency of predictions throughout the time series on $3$
subjects from the test set. Each row corresponds to a subject. The leftmost
column shows the ground truth segmentation outlined in yellow, and temporal-
predicted segmentations in columns $2$–$5$ are shown in red. The same axial
slice is shown for each subject, and images span the time series.
Segmentations are consistent across time series, achieving consecutive BOLD
differences of ($2.6\pm 2.0\%$, $1.1\pm 1.4\%$, and $2.6\pm 2.1\%$) and Dice
scores of $90.7\pm 0.4$, $95.5\pm 0.3$, and $89.7\pm 8.8$ (top, middle, and
bottom). Variations in these metrics are expected due to fetal motion and
changes in oxygenation due to the BOLD protocol.

Automatic segmentation of each volume in BOLD MRI time series is advantageous
as it can enable whole-organ spatiotemporal analysis without requiring inter-
volume registration, which may fail under the presence of large motion. We
illustrate a possible application of automatic placenta segmentation by
investigating the percentage increase in BOLD signal in response to maternal
hyperoxia. We calculate the percentage increase over the baseline period:
$\Delta b=|b_{H}-b_{N}|/b_{N}$, where $b_{N}$ denotes the mean BOLD signal
over the baseline period, and $b_{H}$ denotes the mean of the signal in the
last $10$ frames of the hyperoxic period. Figure 7 shows a scatter plot of the
hyperoxia response for all subjects in the test set and two examples of the
BOLD signal time course in the produced placenta segmentation label maps. In
the control subjects (N=$12$), we observe an increase of $10.2\pm 11.1\%$. The
observed increase for the healthy controls is consistent with previous studies
that demonstrated an increase of $12.6\pm 5.4\%$ (N=$21$) (Sørensen et al.,
2015) and from $5\%$ to $20\%$ throughout gestation (N=$49$) (Sinding et al.,
2018).

Figure 6: Top: Per-subject density distributions of Dice scores between
consecutive predictions in BOLD MRI time series. Dots inside distributions
indicate the median. Bottom: Example failure cases at frames with Dice $<70$.
$3$D models of placentae predicted at two consecutive time points are shown
for two subjects. Left: The region in black is distorted in the predicted
segmentation of subject $9$. Right: A large portion of the placenta
(encircled) is wrongfully predicted in the placenta of subject $15$. Failure
cases are likely to occur with large drops in consecutive Dice (Dice $<70$).

##  5 Discussion

We proposed a model to automatically segment the placenta in BOLD MRI time
series and achieved close matching to ground truth labels with consistent
performance in predicting segmentations in both the normoxic and hyperoxic
phases. Our solution was developed to be resilient to the variability caused
by large signal changes in the BOLD experiment protocol.

#### Shape-aware segmentation.

Identification of the placental boundary is challenging as the organ is a thin
and elongated structure with limited contrast with surrounding anatomy. In
this work, we emphasized these challenging aspects of placental shape during
network training by using a simple additive boundary-weighted loss function.
As hypothesized, boundary weighting significantly improved placenta
segmentation performance when integrated with the popular cross-entropy and
signed distance transform (SDT) losses as compared with their non-boundary
weighted counterparts. We then performed an extensive evaluation over shape-
based losses including our chosen formulation and the losses of Karimi and
Salcudean (2019), and Huang et al. (2021) and found that our adopted loss
outperforms others in several key aspects of placenta segmentation. Lastly, we
broadly find that shape-based losses outperform losses without shape
information (cross-entropy, Dice, and SDT losses), demonstrating that
including shape information can aid in the identification of the placenta.

#### Utility for clinical research.

The main objective of this work was to develop a segmentation model to assess
whole-organ signal changes in BOLD MRI time series. We achieve low BOLD error
(4%) compared to ground truth with performance that is consistent across
oxygenation period. Segmenting each volume in the BOLD MRI time series can be
advantageous for clinical research assessing whole-organ temporal changes. We
illustrated one possible study in assessing placental response during
hyperoxia and observed an increase in signal intensity consistent with prior
work. However, our cohort is limited, and several factors, including maternal
position, gestational age, and contractions are covariates not considered.
Producing segmentations that are resilient to placental oxygenation can also
enable essential post-processing such as motion correction (Abaci Turk et al.,
2017), reconstruction (Uus et al., 2020), and mapping to a standardized
representation (Miao et al., 2017; Abulnaga et al., 2019, 2022a; Chi et al.,
2023). These tasks are often essential in clinical research studies assessing
placental function.

We provide access to our code and trained model for use in future clinical
research studies. Our model is robust to gestational age, pregnancy condition,
and oxygenation. Further, the model requires simple preprocessing and can be
used with a variety of EPI scans. In this work however, we only trained and
tested on isotropic MRI with TE=$32-47$ ms. It is unclear how well the model
would work on scans with earlier GA, nonistropic images, or different imaging
protocols.

A limitation of relying only on segmentations is that they can only be used to
quantify whole-organ signal changes, such as mean T2$\star$ or mean BOLD
increase. One is often interested in assessing functional differences within
subregions of the placenta, for example across twins in Mo-Di pregnancies (Luo
et al., 2017; Shnitzer et al., 2022), within vessels (Torrents-Barrena et al.,
2019a), or across cotyledons (Dey et al., 2023). Localized analysis requires
deformable registration (Abaci Turk et al., 2017) to track changes within
these regions. Having reliable segmentations for each point in the BOLD MRI
time series can be used to improve registration, for example by treating
segmentations as spatial priors. One may also consider methods that jointly
learn registration and segmentation such as that of Xu and Niethammer (2019).

|
---|---
Figure 7: Example application using our model’s produced placenta
segmentations in BOLD time series to characterize oxygenation response from
maternal hyperoxia. Left: Observed increase relative to normoxic baseline for
the test set. Right: Example time series for one singleton control (GA=33wk2d,
Dice=$85.5$, $\Delta b=14.1\%$) and one singleton FGR subject (GA=34wk5d,
Dice=$83.5$, $\Delta b=2.5\%$).

#### Comparison to prior work.

The closest work to ours is that of Pietsch et al. (2021) that proposes a 2D
U-Net based model to automatically segment the placenta in functional MRI
(BOLD, T2$\star$). They achieve a Dice of $58$ on a cohort of $108$ subjects
of low- and high-risk singleton subjects of a wide GA range. Their performance
was comparable to the inter-rater variability of two radiologists (Dice=$68$),
which represents an upper limit. In contrast, we achieve a Dice of $82.8$ on a
cohort of singleton and twin subjects from healthy pregnancies, subjects with
FGR, and subjects with high BMI. While comparing our work with that of Pietsch
et al. (2021) provides context for our performance, direct comparison with
this work is not feasible due to differences in data set size and patient
demographics, imaging protocols, and MRI study design. An interesting
direction of future work is to quantify the improvement in performance due to
model design versus dataset composition.

#### Limitations and Future Work.

The main limitation of this work is the inability to quantify segmentation
performance across the entire BOLD MRI study. While we demonstrated low
absolute differences in predictions between normoxia and hyperoxia, we only
had $5$ subjects with ground truth images in multiple time points. We measured
the consistency of consecutive predictions via Dice overlap and percentage
BOLD differences. However, without correction for inter-frame placental
deformation, the reported scores are subject to noise caused by motion. We
performed visual quality control and found that for many subjects, modest
drops in Dice ($<90$), were often due to fetal motion displacing the placenta.
In a small number of cases, we observed large drops (Dice $<70$) that were
caused by segmentation error (Figure 6 bottom). Since we apply the model to
each volume in the time series independently, imaging artifacts, such as
intensity and geometric artifacts, can affect the predicted segmentations.

We performed a comprehensive evaluation of several commonly used loss
functions with and without our boundary weighting approach, and compared with
shape-based baselines of two previous works: $\mathcal{L}_{\mathrm{Shape}}$ of
Huang et al. (2021) and $\mathcal{L}_{\mathrm{HD}}$ of Karimi and Salcudean
(2019). While our boundary-weighting outperformed these loss functions, we
observed that any shape-based loss improved performance over conventional loss
functions (e.g. $\mathcal{L}_{\mathrm{CE}}$, $\mathcal{L}_{\mathrm{Dice}}$),
demonstrating the benefit in capturing the placenta boundary accurately.
Additional loss functions exist that we did not compare with, such as the
distance transform-based boundary loss of Kervadec et al. (2021), and the
boundary contour-based loss functions of Specktor-Fadida et al. (2021) and
Jurdi et al. (2021). Similar to our baselines, these loss functions are
additive and aim to improve boundary capture and reduce the Hausdorff
distance. Consequently, we do not expect significant differences over our
proposed model, though future work should compare with additional baselines.
Since our proposed loss is a boundary-based weighting rather than a separate
loss function, it is versatile to be used with any existing loss.

Future work can investigate semi-supervised learning approaches to incorporate
all unlabeled volumes in the BOLD MRI time series, increasing the variety of
available data to potentially improve temporally consistent segmentation. As
there are often a few hundred unlabeled volumes in each BOLD time series,
these approaches can more accurately capture the rapid signal changes
resulting from fetal motion and maternal oxygenation. The unlabeled data can
be incorporated using non-rigid registration as in (Xu and Niethammer, 2019;
Zhao et al., 2019; Chartsias et al., 2020) or by using unsupervised shape-
regularization losses (Mirikharaji and Hamarneh, 2018; Young et al., 2023).

##  6 Conclusion

We developed a model to automatically segment the placenta in BOLD MRI time
series. Our model performed consistently well at different oxygenation phases
of the BOLD protocol, and across a variety of pregnancy conditions and
gestational ages. We demonstrated one potential clinical research application
of this work in quantifying BOLD increase due to hyperoxia that matched
reported values from the literature. Automatic segmentation in BOLD MRI time
series can be used to investigate oxygenation dynamics in the placenta. For
example, temporal segmentations can be used to derive T$2\star$ maps to
perform whole-organ signal comparisons across population groups, enabling
quantitative analysis of placental function with the ultimate goal of
developing biomarkers of placental and fetal health.

##  7 Acknowledgments

This work was supported in part by NIH NIBIB NAC P41EB015902, NIH NICHD
R01HD100009, R01EB032708, R21HD106553, MIT-IBM Watson AI Lab, NSERC PGS D, NSF
GRFP, and a MathWorks Fellowship.

Ethical Standards

Written informed consent was obtained from all subjects. The data used in this
work came from two clinical resarch studies. The study protocols were reviewed
and approved by Boston Children’s Hospital institutional review board (IRB),
from IRB protocol #P00012416 and #P00012586. All methods were carried out in
accordance with institutional guidelines and regulations.

Conflicts of Interest

The authors declare no conflicts of interest.

Data availability

The data is currently not approved for public release. The data is being de-
anonymized with plans for a future public release. The code and model weights
are available at https://github.com/mabulnaga/automatic-placenta-segmentation.

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