A Search for Wavelike Dark Matter with Dielectrically-loaded Multimode
Cavities Raphael Cervantes 2021 Physics

Gray RybkaAssociate ProfessorPhysics Leslie Rosenberg Masha Baryakhtar


# Anatomically Constrained Tractography of the Fetal Brain

Camilo Calixto, Camilo Jaimes, Matheus D. Soldatelli, Simon K. Warfield,
Ali Gholipour, and Davood Karimi

Computational Radiology Laboratory (CRL), Department of Radiology,
Boston Children’s Hospital, and Harvard Medical School, USA

###### Abstract

Diffusion-weighted Magnetic Resonance Imaging (dMRI) is increasingly used to
study the fetal brain in utero. An important computation enabled by dMRI is
streamline tractography, which has unique applications such as tract-specific
analysis of the brain white matter and structural connectivity assessment.
However, due to the low fetal dMRI data quality and the challenging nature of
tractography, existing methods tend to produce highly inaccurate results. They
generate many false streamlines while failing to reconstruct streamlines that
constitute the major white matter tracts. In this paper, we advocate for
anatomically constrained tractography based on an accurate segmentation of the
fetal brain tissue directly in the dMRI space. We develop a deep learning
method to compute the segmentation automatically. Experiments on independent
test data show that this method can accurately segment the fetal brain tissue
and drastically improve tractography results. It enables the reconstruction of
highly curved tracts such as optic radiations. Importantly, our method infers
the tissue segmentation and streamline propagation direction from a diffusion
tensor fit to the dMRI data, making it applicable to routine fetal dMRI scans.
The proposed method can lead to significant improvements in the accuracy and
reproducibility of quantitative assessment of the fetal brain with dMRI.

##  1 Introduction

###  1.1 Background and motivation

The human brain undergoes dramatic microstructural and macrostructural
developments in utero [1, 2]. It can be argued that the fetal period is the
most dynamic and critical stage in brain development [3, 4]. Processes such as
neurogenesis, synapse formation, neural migration, and axonal growth all begin
before birth. These processes form the brain microstructure and lay the
foundations for the formation and development of the structural brain
connectome [5, 6], which will continue its rapid development in the first few
months and years after birth. Various diseases and insults can interrupt
normal fetal brain development and result in lifelong neurodevelopmental and
psychiatric disorders [7, 8, 9]. Therefore, quantitative assessment of normal
and abnormal fetal brain development is very useful. Not only can it enhance
our understanding of the development of the brain’s cognitive capabilities,
but it can also facilitate the diagnosis, management, and treatment of
neurological disorders at their earliest stage [10, 11, 12, 13, 14].

Diffusion-weighted magnetic resonance imaging (dMRI) has played an
increasingly prominent role in studying the development of fetal brain [15,
16, 11, 17]. Although it lacks the spatial resolution of postmortem
histological analysis, dMRI is non-invasive, significantly faster and cheaper,
enables assessment of the whole brain in utero in 3D, and allows studying
large populations. In addition to assessing local tissue microstructure, fetal
dMRI can also be used to trace virtual streamlines with tractography
techniques. The streamlines provide a visual and quantitative representation
of the nerve fibers connecting different areas of the central nervous system.
Two important practical applications of tractography include tract-specific
analysis of the brain white matter and quantitative structural connectivity
assessment.

  * •

Tractography-generated streamlines can be used to identify and study specific
white matter tracts. Accurate delineation of these tracts is needed in
clinical studies and medical research. For example, changes in the micro-
structural properties of specific tracts are commonly used in studying brain
development and disorders. The majority of manual and automatic methods for
segmenting these tracts depend on tractography [18, 19, 20].

  * •

Tractography is also the main computation in structural connectivity analysis.
Structural connectivity is widely used in neuroscience and medicine to study
normal and abnormal brain development [3, 21]. The accuracy and
reproducibility of quantitative structural connectivity depend greatly on the
accuracy of tractography.

Although dMRI-based tractography suffers from significant challenges, constant
technical advancements have improved its accuracy and reproducibility [22,
23]. Moreover, our understanding of the capabilities and limitations of
tractography have improved [24, 25]. As a result, tractography has been
increasingly employed in medical applications and neuroscience research [26,
27, 28, 29]. However, most recent technical developments and medical
applications have focused on post-natal and adult brains. Comparatively, fetal
tractography has received far less attention. Fetal brain dMRI suffers from
persistent challenges such as low signal-to-noise ratio, imaging artifacts,
short scan times, unpredictable motion, and rapid brain development [30, 31,
32]. These factors have made it challenging to analyze fetal dMRI data and to
compute the desired results with the same level of accuracy, detail, and
reproducibility as in adult brains. Consequently, compared with post-natal and
adult brain imaging, fetal dMRI has remained at a primitive stage [4, 33, 34].
In particular, in-utero fetal brain tractography has been much less utilized.

Most prior works on fetal tractography have focused on one or a few selected
tract bundles and have shown low success rates and limited accuracy in
reconstructing the full extent of the tracts [10, 35, 36, 37, 38, 39, 15, 16,
11, 17, 33]. They have mostly applied standard tractography methods with
streamline propagation and stopping criteria based on ad-hoc rules such as
turning angles or thresholds on fractional anisotropy (FA). This approach can
be especially suboptimal for the developing brain, where white matter tracts
mature at different rates. The shape and microstructural makeup (hence
diffusivity values and FA) of white matter tracts change over time and at
different rates for different tracts [40, 39, 41, 5]. To cope with this
difficulty, it has been common to empirically adjust FA and angle thresholds
in ad-hoc ways to reconstruct different tracts [14, 36]. Many studies have
resorted to painstaking manual placement of multiple regions of interest
(ROIs) to ensure the desired tracts are reconstructed and reduce false
positive streamlines [41, 14, 42, 35]. High-quality anatomical images and/or
diffusion parameters maps are needed for precise ROI placement [36, 37, 43].
However, even for postmortem fetal brain tissue, where higher quality dMRI
data can be acquired, existing tractography methods tend to produce incomplete
and noisy results and often fail to reconstruct the full extent of even the
major white matter tracts [38, 41, 5, 39, 44].

Despite their limitations, prior works have demonstrated that tractography has
a unique potential for studying normal and abnormal brain development in utero
[11, 32, 35, 36, 37, 45, 13]. Past studies have successfully used tractography
of the fetal brain to (1) chart the normal maturation of different white
matter tracts and to gain new insights into the timing and speed of tract-
specific microstructural changes in utero [37, 46, 47]; (2) to analyze
structural connectivity of the fetal brain [48, 49]; and (3) to characterize,
classify, and understand the clinical heterogeneity of various brain
malformations that begin in the fetal period such as agenesis of corpus
callosum [17, 50, 12, 14]. Hence, there is a critical and urgent need for
methods and resources to enable accurate and reproducible tractography of the
fetal brain. Accurate tractography can advance the field of fetal brain
imaging in multiple ways by facilitating qualitative and quantitative
assessment of the development of white matter tracts and of the structural
connectome.

###  1.2 Contributions of this work

This paper introduces a new method for fetal brain tractography that leverages
tissue segmentation to ensure reconstruction of anatomically valid
streamlines. Accurate tissue segmentation enables the implementation of
precise streamline seeding and stopping rules that effectively remove spurious
streamlines. A deep learning method is developed to compute accurate tissue
segmentations. Streamline tracking is performed based on local fiber
orientations computed with a diffusion tensor model, which makes the method
applicable to single-shell dMRI scans. We tested our method on a set of
independent scans and found that it produced significantly more accurate
results than a standard tractography technique. Unlike recent studies that
rely on unique, high-quality data from the Human Connectome Project [51, 32],
our method can be applied to more typical dMRI scans. We release our software
to enable other research groups to use this method as a benchmark for future
studies.

##  2 Methods

###  2.1 Imaging data acquisition and preprocessing

In-utero fetal MRI scans for this work were acquired as part of a prospective
research study at Boston Children’s Hospital in Boston, MA, between 2013 and
2019. The research was approved by the Institutional Review Board (IRB) and
adhered to the Health Insurance Portability and Accountability Act (HIPAA).
Participants were recruited in advance and provided written consent before
each fetal MRI examination. Only pregnancies between 23 and 36 weeks of
gestational age (GA) with mothers between 18 and 45 years were included in
this work. The exclusion criteria included contraindications to MRI, any form
of high-risk pregnancy, fetal brain anomalies, and maternal comorbidities such
as diabetes, hypertension, or substance abuse.

Three-Tesla (3T) MRI scanners (Skyra and Prisma, Siemens Medical Solutions)
with 16-channel body matrix and spine coils were used to obtain the images.
The field of view and number of slices varied based on maternal and fetal
dimensions. T2-weighted Half-Fourier Single Shot Turbo Spin Echo (HASTE) fetal
brain images were obtained for structural sequences. We acquired multiple
images in orthogonal planes with the following acquisition parameters: TR of
1400-2000 ms, TE of 100-120 ms, in-plane resolution of 0.9-1.1 mm, 2 mm slice
thickness with no inter-slice space, and 2- or 4-slice interleaved
acquisition. For diffusion-weighted images, we obtained 2-8 echo-planar
diffusion-weighted images, each along orthogonal planes with respect to the
fetal head. Each of these acquisitions included one or two b=0 s/mm2 images
and 12-24 diffusion-sensitized images at b=500 s/mm2. The acquisition
parameters for diffusion-weighted images were TR of 3000-4000 ms, TE of 60 ms,
in-plane resolution of 2 mm, and slice thickness of 2-4 mm.

All studies were assessed for the availability of at least two diffusion-
weighted scans without excessive motion-induced artifacts, distortion, and
signal loss that could hinder successful motion correction and registration
between diffusion-weighted and structural T2-weighted scans. We used a
previously validated pipeline [31] to process each subject’s diffusion and
structural MRI data. This pipeline includes the reconstruction of structural
and diffusion-weighted volumes with a Kalman filtering-based motion tracking
and slice-to-volume registration algorithm [52]. It registers the dMRI
measurements for each subject into a standard atlas space and produces
consistent measurements that consist of scattered q-space data in each voxel.
We chose an isotropic voxel size of 1.2 mm for the reconstructed dMRI data.
These motion-corrected dMRI volumes were used in the subsequent analysis steps
described below.

We excluded subjects that were reconstructed with significant errors or
unusually low data quality. This decision was made by an expert via visual
inspection of mean diffusivity (MD), color fractional anisotropy maps, and
diffusion tensor glyphs to ensure adequate direction of the principal
eigenvectors. As a result, 85 fetuses were used to develop and validate the
new methods. Data from 74 subjects were used to develop the methods, for
hyper-parameter tuning of the deep learning method, and for preliminary
evaluations. A total of 11 fetuses were kept separate for independent final
validation of the method.

Figure 1 shows a schematic representation of the data processing and
computational steps that are applied to compute a whole-brain tractogram in
this work. The main steps include local fiber orientation estimation, tissue
segmentation, and anatomically constrained tractography, which are described
in the following sections.

Figure 1: A schematic representation of the data processing steps to compute a
whole-brain tractogram in this work. Super-resolved reconstruction of dMRI
data volumes is performed using the method described in [52].

###  2.2 Estimation of local fiber orientation

Streamline tractography builds upon a voxel-wise estimation of local fiber
orientations. It is well known that the accuracy of fiber orientation
estimation is one of the main factors influencing the accuracy of tractography
[53, 54]. For post-natal and adult brains, this need has given rise to
advanced methods to compute complex fiber configurations in each voxel, such
as crossing fibers and asymmetric fiber orientation distributions [55, 56].
For fetal dMRI, because of the far lower measurement quality, the application
of these methods is challenging and rarely attempted. Recently, dense multi-
shell data from the Human Connectome Project have been used by a few works to
estimate the fiber orientations in the fetal brain using more complex models
that the diffusion tensor [57, 58]. However, with standard fetal dMRI scans,
the diffusion tensor is the most complex model that can be reliably estimated
[4, 31, 33]. Therefore, we used the tensor model to estimate local fiber
orientations in this work.

Given the diffusion signal in a voxel, we estimate the diffusion tensor in
that voxel using a weighted linear least squares method [59]. We then computed
the diffusion orientation distribution function (dODF) from the diffusion
tensor ($D$) using the following equation [60, 61].

$\text{dODF}(u)=\frac{1}{4\pi|D|^{1/2}\big{(}u^{T}Du\big{)}^{3/2}}$ (1)

In this equation, $u$ is the unit vector denoting the orientation along which
the dODF is computed, and $|D|$ denotes the determinant of $D$.

Low diffusion anisotropy in fetal white matter leads to a high prevalence of
spurious streamlines with standard tractography techniques. To alleviate this
problem, we introduce an ad-hoc but simple and effective method to sharpen the
estimated dODF. Specifically, we compute the streamline propagation
probability as $p(u)=\text{dODF}^{k}(u)$, i.e., by raising the dODF to power
$k>1$. This operation increases the relative magnitude of $p$ along the
directions where dODF is larger and reduces its relative magnitude along the
directions where dODF is smaller, thereby effectively increasing the
anisotropy of $p$. Figure 2 shows example diffusion tensors and streamline
propagation probability maps computed with this approach. We compute $p(u)$
for unit vectors $u$ on a discrete sphere with 724 uniformly-spaced points.

Figure 2: Example diffusion tensors and the corresponding streamline
propagation probability maps ($p(u)$) for three different fetuses at three
different gestational ages (GA).

###  2.3 Segmentation of the brain tissue

Anatomically constrained tractography requires accurate brain tissue
segmentation in the dMRI space [62]. Given the lower spatial resolution and
contrast of dMRI, this segmentation is usually obtained via segmenting the
anatomical MRI and registering the segmentation to the dMRI space. However,
the registration is challenging because the contrast, spatial resolution, and
image distortions can differ greatly between the two modalities. Registration
errors can significantly impact the accuracy of tractography. Therefore,
direct tissue segmentation based on the dMRI data is highly desirable.
However, this task is challenging due to the varying contrast of dMRI
acquisitions, low SNR, and low spatial resolution. To tackle these challenges,
classical machine learning methods such as fuzzy c-means clustering with
spatial constraints [63], sparse representation of the dMRI signal in
dictionaries [64], and support vector machines [65] have been used in prior
works to address this task. More recently, deep learning methods have been
attempted by several studies and have shown better results [66, 67, 68, 69].
However, all these prior works have been reported for post-natal and adult
brains.

Due to the inferior image quality, rapid brain development, and paucity of
training data, segmentation of the fetal brain tissue is significantly more
challenging [70]. Existing works have focused on the segmentation of
anatomical MRI images. Several research groups have performed segmentation of
the cortical gray matter on T2 images [71, 72]. Segmentation of other tissue
types and structures, such as the white matter, ventricles, and cerebellum,
has also been addressed by a few recent studies [73, 74, 75]. However,
segmentation within the dMRI space remains unexplored in the literature. To
address this technology gap, we developed and validated a deep learning method
for fast, accurate, and reproducible segmentation of fetal brain tissue
directly in dMRI.

####  2.3.1 Generation of training and test labels

To create a training dataset, we adopted a multi-atlas segmentation strategy.
Our methodology entailed leveraging pre-existing segmentations on high-quality
diffusion tensor atlases of fetal brains [76]. These atlases have been
computed at one-week intervals between 23 and 35 gestational weeks and
comprise 12 structures/labels for fetuses under 31 gestational weeks and 11
labels for fetuses aged 31 weeks and above, as shown in Figure 3. This
difference stems from the presence of two transient zones in younger fetuses,
namely the subplate and intermediate zones. Note that due to spatial
resolution constraints, in our labels, the intermediate zone also contains the
ventricular zone and the subventricular zone. Using these atlases, for each
fetus, we generated the segmentations by following these steps:

  1. 1.

The three closest atlases, in terms of gestational weeks (that is, atlases at
weeks $t-1$, $t$, and $t+1$, for a fetus that is closest to age $t$) were
registered to the subject’s brain. This was performed using a deformable
diffusion tensor-based registration technique [77].

  2. 2.

The computed registration transformations were used to align the atlas tissue
segmentations to the subject fetal brain using a generic interpolator for
labeled images [78]. The probabilistic STAPLE algorithm [79] was then applied
to fuse these segmentations into a final tissue segmentation prediction for
the fetus.

  3. 3.

Automatic segmentations were reviewed and revised as needed by a board-
certified neuroradiologist with fellowship training in pediatric
neuroradiology. We excluded automatic segmentations with significant errors,
and we ensured the accuracy of the remaining segmentations by having two
research fellows with medical training carry out manual refinements where
needed.

  4. 4.

The resulting tissue segmentation map is then converted to the five-tissue-
type (5TT) maps that include five labels: white matter, cortical gray matter,
sub-cortical gray matter, CSF, and any pathological tissue. Example tissue
segmentation maps and 5TT maps are shown in Figure 3. The 5TT maps are used
for anatomically constrained tractography.

Figure 3: Depiction of two diffusion tensor atlases at two different
gestational weeks, namely 30 and 35 weeks. The left panel shows manually
annotated labels, while the right panel shows the converted labels to the
five-tissue-type (5TT) format. The 5TT image is used for anatomically
constrained tractography. Please note that the bottom part of the brainstem is
converted to a “gray matter” to ensure adequate termination of the streamlines
in tractography computation.

The above four-step procedure was used to generate segmentation labels for the
74 fetuses in the training set. For the 11 fetuses in the independent test
set, on the other hand, an expert manually generated the tissue segmentations
by following the same approach as that used for the atlases [76]. This ensured
optimal ground truth labels for validation of the new methods.

####  2.3.2 Deep learning model development

An important first decision in developing the automatic tissue segmentation
model is the choice of the model input. For this application, we decided to
compute the model input from the diffusion tensor, $D$, as
$u=v_{1}(D)\text{FA}(D)$. In this equation, $v_{1}$ is the eigenvector
associated with the largest eigenvalue and FA is fractional anisotropy. Hence,
the input is a three-channel image where each voxel shows the orientation of
the highest diffusion, modulated by fractional anisotropy. This representation
nicely summarizes the diffusion tensor. The decision to compute the model
input from the diffusion tensor has the advantage that it improves the
method’s generalizability to scans with varying numbers of measurements and
different data preprocessing pipelines. Given the fact that the diffusion
tensor can be reliably estimated with typical fetal scans, this choice
maximizes the method’s applicability.

Figure 4: Schematic representation of the deep learning model used for
automatic fetal brain tissue segmentation.

Figure 4 shows our proposed segmentation method. It works on image cubes that
are partitioned into patches of size $s^{3}$ voxels. The prediction target is
the tissue classification map for the center patch, shown in red in the
figure. As input, the network uses the 3-patch and 5-patch neighborhood of the
target patch location. Note that the target (center) patch itself is not
included in the input context. Therefore, $3^{3}-1$ and $5^{3}-1$ patches are
used as input to the network.

We can interpret our approach as providing two separate “views” of the input
image to the network for performing the desired prediction task. From this
viewpoint, our approach is similar to the standard approaches in self-
supervised learning methods. However, while the common approach in self-
supervised learning is to use data augmentation to generate two views of the
same data sample, we use input contexts of different sizes. As described
below, our method encourages the network to learn similar representations from
both input contexts (one larger than the other) for predicting tissue
classification.

The network itself consists of encoder and decoder sections. The encoder
includes five standard vision transformer (ViT) encoder modules [80]. The two
decoder sections are 3-layer MLPs of fully-connected layers with ReLU
activations. We denote the $3^{3}-1$\- and $5^{3}-1$-patch inputs as $x_{1}$
and $x_{2}$, respectively. As shown in Figure 4, each input patch is first
projected into ${\rm I\\!R}^{m}$, followed by fixed sinusoidal positional
encodings similar to [81]. This creates two input sequences $S_{1}$ and
$S_{2}$ that are passed through the encoder $f_{\theta}$ to compute the
representations $z_{1}$ and $z_{2}$. The representation $z_{1}$ is passed to
the two decoders: (1) ${f_{\phi}}_{1}$ computes the input image content (i.e.,
the FA-weighted direction of the major eigenvector) for the center patch; (2)
${f_{\phi}}_{2}$ computes the tissue classification for that patch.

##### Supervised training.

The supervised objective is to achieve accurate tissue classification. We use
the cross-entropy loss for this purpose:

$\mathcal{L}_{\text{S}}(x_{1},x_{2},y|\theta,\phi_{2})=\text{X}_{\text{ent}}(\hat{y}_{c},y_{c}).$
(2)

where $\hat{y}_{c}$ and $y_{c}$ represent the predicted and ground truth
tissue classification maps for the center patch. In both Equations (4) and
(2), the total loss for each patch is the voxel-wise sum for all voxels in the
patch.

##### Self-supervised training.

The self-supervised objective that we propose encourages: (1) the
representations ($z_{1}$ and $z_{2}$) computed by the encoder for the two
input contexts ($x_{1}$ and $x_{2}$) to be similar; and (2) the learned
representations are useful for predicting the masked input. We achieve this
using the following loss functions:

$\mathcal{L}_{\text{SS}_{1}}(x_{1},x_{2}|\theta)=\Big{(}1-\cos(z_{1}^{*},z_{2}^{*})\Big{)}+\alpha\sum_{i}\sum_{j\neq
i}C_{i,j}^{2}$ (3)

$\mathcal{L}_{\text{SS}_{2}}(x_{1},x_{2}|\theta,\phi_{1})=\|\hat{x}_{c}-x_{c}\|.$
(4)

The first term in $\mathcal{L}_{\text{SS}_{1}}$, based on cosine distance,
encourages high similarity between the representations, where $z_{1}^{*}$ and
$z_{2}^{*}$ are $\ell_{2}$-normalized $z_{1}$ and $z_{2}$. The second term is
similar to loss functions proposed by canonical correlation analysis-based
techniques such as Barlow Twins [82] and VICReg [83]. In this term, $C$ is the
cross-correlation of the representations, computed along the batch dimension:

$C_{i,j}=\frac{\sum_{k=1:K}{z_{1}^{*}}^{k}_{i}{z_{2}^{*}}^{k}_{j}}{\sqrt{\sum_{k=1:K}\big{(}{z_{1}^{*}}^{k}_{i}\big{)}^{2}}\sqrt{\sum_{k=1:K}\big{(}{z_{2}^{*}}^{k}_{j}\big{)}^{2}}},$
(5)

where $k$ denotes the data sample index within a batch and $K$ is the batch
size. This term encourages decorrelation of different elements of the
representations computed from the two input contexts. It helps avoid
dimensional collapse, which is a common pitfall in self-supervised learning.
As in [82], we normalize the representations such that they have a mean of
zero across the batch size and a unit norm for each data sample.

The second self-supervised loss, $\mathcal{L}_{\text{SS}_{2}}$, encourages
accurate prediction of the center image patch. In this equation, $\hat{x}_{c}$
and $x_{c}$ represent, respectively, the predicted and true image content for
the center patch.

The combined loss function used to train the model is a weighted sum of the
supervised and self-supervised loss terms:

$\mathcal{L}_{\text{total}}(x_{1},x_{2},y|\theta,\phi_{1},\phi_{2})=\mathcal{L}_{\text{S}}+\lambda_{1}\mathcal{L}_{\text{SS}_{1}}+\lambda_{2}\mathcal{L}_{\text{SS}_{2}}.$
(6)

The inclusion of self-supervised training objectives has several advantages.
First, based on the results of recent works in computer vision, they are
expected to improve the performance on the main task, i.e., tissue
classification. Second, self-supervised learning has been shown to be an
effective technique for reducing the impact of label noise [84, 85]. This is
an especially important consideration in this work because the inherently low
contrast in fetal dMRI results in inevitable label noise, even in manual
annotations. Moreover, self-supervised learning enables us to use additional
unlabeled data. In this work, we used 129 preterm newborn subjects scanned
between 26 and 36 gestational weeks from the developing Human Connectome
Project (dHCP) dataset [86]. For training with these unlabeled data, we
dropped the supervised loss term $\mathcal{L}_{\text{S}}$ from the combined
loss $\mathcal{L}_{\text{total}}$.

We empirically set the hyper-parameters as follows: $\alpha=0.05$,
$\lambda_{1}=\lambda_{2}=0.1$, and patch side length $s=5$ voxels. To train
the network using the combined loss, we used the Adam optimization method [87]
with an initial learning rate of $0.001$. We reduced the learning rate by a
factor of 0.90 after a training epoch if the validation loss did not decrease.
Training with the labeled and unlabeled data was performed in tandem and
alternately. Specifically, odd training iterations used a batch of unlabeled
data from the dHCP, and even training iterations used a batch of labeled
training data from our fetal scans. We used a batch size of 50. The network
was implemented in TensorFlow 1.4 and run on an NVIDIA RTX A6000 GPU on a
Linux machine with 128 GB of memory and 20 CPU cores.

###  2.4 Streamline tracing

The method developed in this work was based on the anatomically-constrained
tractography framework [62]. For streamline propagation, we use the 2nd-order
integration over fibre orientation distributions (iFOD2) algorithm [88]
implemented in MRtrix3 [89]. Streamlines are launched at the boundary of white
matter and (cortical and sub-cortical) gray matter. Any streamline that
violates the rules of anatomically-constrained tractography is discarded. The
main steps of the algorithm are summarized in Algorithm 1.

Input: dMRI data $x$ & the desired number of streamlines $M$.

Output: set of streamlines $\\{y_{i}\\}_{i\in 1,M}$.

Compute the diffusion tensor map $D$ from $x$.

Compute the streamline propagation probability $p(u)=\text{dODF}^{k}(u)$ using
Equation (1).

Compute the five-tissue-type image with the deep learning method.

Derive a map of the gray matter-white matter interface from the five-tissue-
type image.

Set minimum and maximum streamline lengths using Equation (7).

set $y=\\{\\}$ and $\textit{valid\textunderscore streamline\textunderscore
count}=0$

while  _$\text{valid\textunderscore streamline\textunderscore count} <M$_ do

Select a random seed point on the gray matter / white matter boundary.

Trace a streamline using iFOD2 until an endpoint is reached.

if  _streamline is valid_ then

Append the new streamline to $y$.

Increment valid_streamline_count by 1.

Algorithm 1 The proposed method for anatomically constrained fetal
tractography.

For streamline propagation with iFOD2 we used a step size of 0.6mm and angle
threshold of $20^{\circ}$. We aimed to reconstruct various projection,
association, and commissural fibers while minimizing the number of U-fibers.
As the range of valid streamline lengths varies depending on the brain size,
we set the maximum streamline length based on the total brain volume (in
$mm^{3}$) to reduce overly long erroneous streamlines. This strategy was
helpful in avoiding unrealistic but anatomically valid streamlines (e.g., a
streamline that starts at the brainstem, traverses the internal capsule,
crosses over to the contralateral hemisphere via the corpus callosum, and then
loops back to the brainstem through the contralateral internal capsule). On
the other hand, setting a proper minimum length effectively reduced short
association fibers, which typically do not contribute to major fiber bundles.
The lower and upper thresholds were determined by initially performing global
tractography on a few selected subjects and examining the results. Initially,
the minimum streamline length was set at 15mm and the maximum at 190mm. After
extracting 11 tracts, as listed below, we recorded the shortest streamline
length of each tract for every subject. The lowest value among all tracts for
every subject was then chosen as the minimum length threshold. Following that,
we recorded the 95th percentile of streamline lengths for every tract. The
highest value among all tracts for every subject was then selected as the
upper limit. These values were utilized in combination with the subject’s
brain volume to derive the equations presented below.

$\text{Length}_{min}=\frac{\sqrt[3]{Volume}}{1.6},\hskip
14.22636pt\text{Length}_{max}=\frac{\sqrt[3]{Volume}}{0.55}$ (7)

###  2.5 Evaluation

We evaluated the accuracy of the automatic tissue segmentation method in terms
of Dice similarity coefficient (DSC), 95th percentile of the Hausdorff
distance (HD95), and average symmetric surface distance (ASSD). An expert also
visually inspected the segmentation maps computed by the automatic method.

To assess the performance of the new anatomically constrained tractography
method, we applied it to compute whole-brain tractograms for the 11
independent test subjects. For each brain, we generated a total of 5 million
streamlines. Two neuroradiologists with specialized training in pediatric
neuroradiology and six years of experience in fetal imaging visually inspected
the whole brain tractograms. An expert manually extracted 11 tracts in
TrackVis [90] using the parcellation segmentation labels as ROIs and following
the definitions provided by Wassermann et al. [91]. This method required gray
matter parcellations. We used an atlas-based procedure to generate
parcellation labels using parcellations designed to reflect the ENA33 atlas
[92]. To achieve this, we utilized ANTs’ symmetric deformable registration
[93] to register a previously parcellated T2 atlas of the fetal brain (which
can be found at: http://www.crl.med.harvard.edu/research/fetal_brain_atlas/)
to the MD map of the age-corresponding atlas. The extracted tracks were:
Anterior Thalamic Radiation (ATR), Genu and Isthmus of the Corpus Callosum (CC
2 and CC 6, respectively), Cortico-Spinal Tract (CST), Frontal Aslant Tract
(FAT), Fronto-Pontine Tract (FPT), Inferior Occipito-Frontal fascicle (IFO),
Inferior Longitudinal Fascicle (ILF), Middle Longitudinal Fascicle (MLF),
Optic Radiations (OR), and Uncinate Fascicle (UF).

To compare our findings with previously established techniques, we employed
the Fiber Assignment by Continuous Tracking (FACT) algorithm [94] to compute
whole brain tractography for the same 11 test subjects using the computed
diffusion tensor map. We set a whole brain mask based on the segmentation
generated by the deep neural network and a step size of 0.6mm for streamline
propagation. We manually extracted the tracts from the FACT-computed whole-
brain tractograms by following the approach described above and maintaining
consistency with the ROIs.

Subsequently, two neuroradiologists independently assessed each tract
generated by our proposed method and FACT using TrackVis. The analysis was
conducted in a head-to-head comparative manner, and the radiologists were
blinded to which method corresponded to each visualization. However, the
visual appearance of the streamlines may have enabled them to distinguish
between the methods. The readers were provided with mean diffusivity and
fractional anisotropy maps, and no limitations were imposed on window-level
setting adjustments. We asked the raters to indicate which visualization was
better, significantly better, or if they were of equal quality. We then
converted their ratings to a 5-point scale, where 0 indicated no difference
between the methods, $\pm 1$ indicated that one method was slightly better
than the other, and $\pm 2$ indicated that one method was significantly
better. In our conversion, positive values favor our method, and negative
values favor FACT.

We also compared our proposed method with FACT in terms of sensitivity to the
angle threshold, which is one of the main settings in every tractography
algorithm. Tractography results, especially for the fetal brain, can be highly
sensitive to angle threshold setting, requiring careful adjustment to ensure
reconstruction of the tracts of interest. Therefore, a method that is less
sensitive to this setting is highly desirable as it can improve the
tractography accuracy and reduce the need for manual adjustment of the angle
setting for every subject/tract. In order to perform this comparison, we
applied our method with three angle thresholds of $15^{\circ}$, $20^{\circ}$,
and $25^{\circ}$, and we applied FACT with three angle thresholds of
$25^{\circ}$, $30^{\circ}$, and $35^{\circ}$. These angles were selected to
ensure the best overall tractography accuracy for the two methods. We
converted the tracts to binary masks by following these steps: (1) Compute
tract density maps, where each voxel shows the number of streamlines crossing
that voxel; (2) Compute a density threshold as the 1% percentile of the non-
zero densities; (3) Exclude voxels where the tract density is below the
threshold. Other non-zero voxels represent the binary mask of the extracted
tract. After computing the binary masks, we computed pair-wise DSC, HD95,
ASSD, and relative volume difference (VolDiff) between the three tracts
reconstructed with the three angle thresholds to quantify the sensitivity of
the method to angle threshold. We define VolDiff between two binary masks
$M_{1}$ and $M_{2}$ as
$\big{|}\text{vol}(M_{1})-\text{vol}(M_{1})\big{|}/\big{(}\big{|}\text{vol}(M_{1})+\text{vol}(M_{1})\big{|}/2\big{)}$.

##  3 Results

###  3.1 Assessment of automatic brain tissue segmentation

Figure 5 shows example fetal brain tissue segmentation results computed by the
deep learning method compared with the manually-generated ground truth. They
show that the automatic method can accurately segment all four tissue types.
Visual assessments by an expert confirmed that the computed segmentations were
free of any major errors. Table 1 presents quantitative segmentation
performance metrics for the four tissue types. The average DSC for white
matter, cortical gray matter, sub-cortical gray matter, and CSF was,
respectively, 0.898, 0.830, 0.837, and 0.841. These values are in the range of
performance metrics reported for the state-of-the-art segmentation methods
applied on fetal T2 MRI in recently-published studies [74, 73, 71, 72]. For
white matter, for example, the DSC values achieved by several deep learning
methods in a recent study [74] were in the range 0.85-0.90, while for our
method in this work it was $0.898\pm 0.024$. Similarly, surface distance error
quantified in terms of HD95 and ASSD are comparable with the results of recent
deep learning methods for T2 segmentation [74], including our own work [75].
These results indicate that the proposed method is able to segment the fetal
brain tissue with satisfactory accuracy in dMRI, which has an inherently lower
signal quality than T2.

Figure 5: Examples of segmentations predicted by our proposed method in three subjects at three different gestational ages (GA). Each panel shows the manual segmentation and the segmentation computed by the proposed method for four tissue types used in the five-tissue-type image. Please note that the last tissue type, reserved for pathological tissue [62], is omitted from this figure and excluded from this study, as it is absent in our cohort of healthy fetuses. GM stands for gray matter, and CSF stands for corticospinal fluid. Table 1: Segmentation performance metrics for the proposed method. Note that higher values of DSC and lower values of HD95 and ASSD are desirable. |  cortical gray matter |  sub-cortical gray matter |  white matter |  cerebrospinal fluid
---|---|---|---|---
DSC |  $0.830\pm 0.034$ |  $0.837\pm 0.045$ |  $0.898\pm 0.024$ |  $0.841\pm 0.030$
HD95 (mm) |  $1.049\pm 0.022$ |  $1.051\pm 0.030$ |  $0.955\pm 0.028$ |  $1.047\pm 0.025$
ASSD (mm) |  $0.240\pm 0.110$ |  $0.235\pm 0.120$ |  $0.209\pm 0.126$ |  $0.246\pm 0.133$
|  |  |  |

###  3.2 Assessment of extracted tracts

All 11 tracts were successfully extracted from the whole-brain tractograms
generated with our proposed method and 10 with FACT. It was observed that the
FAT tract was consistently present in the tractograms generated with our
proposed method but was absent in the tractograms generated with FACT.
Therefore, this tract was excluded for further analysis. Figure 6 displays
seven selected tracts for a visual comparison of the two methods. As shown in
this figure, FACT failed to reconstruct all tracts consistently, while our
method successfully reconstructed all of them. Figure 6 summarizes the results
of a head-to-head comparison of our proposed method and FACT by two experts.
It shows that the new anatomically constrained tractography method was
consistently superior to FACT in terms of the tract reconstruction success
rate and the scores provided by the experts.

Figure 6: A visual comparison of seven different tracts reconstructed using
the fiber assignment by continuous tracking (FACT) algorithm and our proposed
method for three fetal brains at different gestational ages (GA). The
following tracts are shown: Genu of the Corpus Callosum (CC_2), Cortico-Spinal
Tract (CST), Frontal Aslant Tract (FAT), Fronto-Pontine Tract (FPT), Inferior
Occipito-Frontal fascicle (IFO), Inferior Longitudinal Fascicle (ILF), and
Optic Radiations (OR). A white asterisk on top of the image means the tract
was not reconstructed by that method.

Table 2 summarizes the results of the experiment to quantify the impact of
angle threshold setting on the reconstruction of the tracts for the proposed
method and FACT. In this experiment, the tracts were converted to binary
masks, as described in Section 2.5 and several metrics of
agreement/disagreement between pairs of tracts reconstructed with different
angle thresholds were computed. The values in Table 2 represent the summary
for all 11 tracts considered. These results show that the new method is highly
robust to the setting. Changing the angle threshold between $15^{\circ}$ and
$25^{\circ}$ had a small impact on the tract reconstruction results, with a
mean pair-wise DSC of 0.941 for all tracts. For all four evaluation criteria
shown in Table 2, the results for our method were significantly ($p<0.001$)
better compared with FACT.

Table 2: Results of the experiment to assess the robustness of tractography methods to angle threshold setting. The values shown are computed pair-wise between the tracts reconstructed with different angle thresholds. Note that higher values of DSC and VolDiff and lower values of HD95 and ASSD are desirable. |  DSC |  HD95 (mm) |  ASSD (mm) |  VolDiff
---|---|---|---|---
Proposed method |  $0.941\pm 0.042$ |  $0.815\pm 0.027$ |  $0.208\pm 0.103$ |  $0.083\pm 0.032$
FACT |  $0.605\pm 0.119$ |  $1.664\pm 0.157$ |  $0.751\pm 0.195$ |  $0.279\pm 0.122$
|  |  |  |
Figure 7: Head-to-head comparison of different tracts reconstructed with our
proposed method and FACT, depicted using a balloon plot. The tracts were
extracted by following the same procedure for both our anatomically
constrained tractography method and FACT. Each circle’s size indicates the
percentage of cases assigned a given score. These results were computed from
11 fetuses (one per gestational week between 23 and 35 weeks) and two raters.
Negative scores (left side of the plot) favor FACT, and positive scores (right
side) favor the proposed method. Brown balloons indicate tracts scored when
both FACT and our proposed method could reconstruct the tracts, while green
balloons represent tracts reconstructed exclusively by our proposed method.
The following tracts were used for the evaluation: Anterior Thalamic Radiation
(ATR), Genu (CC_2) and Isthmus (CC_6) of the Corpus Callosum, Cortico-Spinal
Tract (CST), Fronto-Pontine Tract (FPT), Inferior Occipito-Frontal fascicle
(IFO), Inferior Longitudinal Fascicle (ILF), Middle Longitudinal Fascicle
(MLF), Optic Radiation (OR), and Uncinate Fascicle (UF).

##  4 Discussion

This paper introduces the development and validation of an anatomically
constrained fetal brain tractography method. Our method relies on the
classification/segmentation of brain tissue into white matter, cortical and
subcortical gray matter, and cerebrospinal fluid. These segmentations are
automatically computed by a deep learning method directly in the dMRI space, a
valuable capability that has not been reported in prior works. The
segmentation method only requires the diffusion tensor map as the input. The
same diffusion tensor map is used to infer the streamline propagation
direction for computing the tractogram. We convert the diffusion tensor into a
sharpened diffusion orientation distribution function that helps minimize the
probability of computing spurious streamlines and enables advanced
probabilistic tractography methods such as iFOD2.

Our automatic segmentation method outperforms multi-atlas-based approaches. In
our previous work, we achieved a DSC of $0.75\pm 0.17$ for cortical gray
matter, $0.69\text{--}0.86\pm 0.14$ for sub-cortical gray matter structures,
and $0.70\text{--}0.87\pm 0.15$ for white matter structures [76]. The new deep
learning method far surpasses this method, with higher average DSC values and
narrower standard deviations for all tissue types. Moreover, multi-atlas-based
automatic segmentation for this data typically takes 15-25 minutes per
subject, while our deep learning approach usually has an inference time of 3-5
seconds. Surface distance errors presented in Table 1 show that HD95
(representing large surface distance errors) for white matter, cortical gray
matter, and sub-cortical gray matter are all approximately 1mm, while the ASSD
(representing average surface distance errors) are approximately 0.20-0.25 mm.
These numbers suggest that our method can be used for accurate seeding and
stopping operations that are essential for anatomically constrained
tractography.

Accurate tissue classification enables us to: (1) Launch the streamlines at
seed points on the boundary between white matter and gray matter, and (2)
Effectively remove the spurious and anatomically invalid streamlines and only
preserve valid streamlines based on their paths and endpoints. Effective use
of anatomical information enables us to avoid premature termination of valid
streamlines or generate implausible streamlines that are prevalent in fetal
tractography, as observed in this study with FACT. Standard tractography
methods rely purely on the local diffusion tensor information for streamline
propagation and termination (e.g., based on FA). This can lead to high false
positive and false negative rates because of the low fetal dMRI data quality
that can give rise to noisy and inaccurate diffusion tensor estimates.

We evaluated the new method on a set of independent test subjects and compared
the results to tractography generated using FACT. Our manual extraction of the
tracts followed established criteria outlined by Wassermann et al. [91]
regarding where streamlines should start and pass through and which structures
to avoid. We followed the same tract definitions and extraction procedures for
both tractography methods. Expert evaluations showed that our method
consistently outperformed FACT in terms of expert scores. Our method was
consistently successful in reconstructing prominent white matter tracts. A
visual comparison of the tracts reconstructed by our method and the results
produced from the Human Connectome Project data [95] show that our results on
fetal brains are qualitatively comparable with adult brains.

While FACT was able to reconstruct most tracts (except for the FAT) as
evidenced in Figure 7, the tractography results generated by FACT were often
limited in their ability to reconstruct a sufficient number of streamlines.
While some cases in our method (like the FPT track of the GA30 fetus in Figure
6) exhibited less dense frontal fibers than anticipated, our approach utilizes
a probabilistic algorithm that can be remedied by increasing the number of
streamlines. Conversely, increasing the number of streamlines in FACT would
have no impact, as the pathways of the streamlines are already predetermined
by the principal eigenvector of the tensor and, thus, would not improve the
reconstruction of empty areas. Furthermore, our approach successfully
reconstructed tracts with highly curved areas like the optic radiations and
obtained the lateral projections of the CST.

A comparison of our results with the results of prior works on in-utero fetal
tractography exhibits significant advancements in the anatomical accuracy and
completeness of neural tracts, addressing limitations observed in earlier
research. Here, we detail these comparisons for specific tracts, underscoring
the enhancements our method provides. It’s worth noting that comparisons for
the ATR, FAT, and MLF are absent, as no previous group has extracted them on
fetuses.

  * •

Corpus Callosum: Prior investigations have focused on various segments of the
corpus callosum [42, 47, 32, 35, 37, 36]. Our approach stands out in its
ability to consistently generate tracts connecting both the medial and lateral
surfaces of the frontal lobes within the forceps minor. Furthermore, our
streamlines terminate accurately at the gray-white matter interface without
prematurely ending or crossing the cortical plate and ending into the CSF.

  * •

CST: Earlier studies have encountered difficulties in fully extracting the
CST, often resulting in premature termination of streamlines [35, 37] or
failure to capture lateral projections [42, 47]. Unlike these studies, our
approach consistently captures the complete intracranial CST, avoiding
inaccuracies such as streamline termination in the CSF or inappropriate
crossing through deep gray matter structures [32].

  * •

FPT: Limited research has depicted the FPT in fetuses. Our findings show more
extensive tract delineation, reaching all intended frontal targets without the
premature termination observed in previous work [36].

  * •

IFO: Unlike other works, our tracts reach all expected cortical targets [41,
42, 47], terminate at the junction of gray and white matter[36] and most
importantly, traverse the expected path through the external capsule.

  * •

ILF: Our work surpasses previous works [41, 42] on generating a fuller tract
that reaches all cortical targets and has results comparable to those of
Machado et al. [47] and Wilson et al. [32] However, it is worth noting that in
the two works above, only some branches of the ILF are visualized—e.g.,
missing one connecting the cuneus to the anterior mesial temporal gyri.

  * •

OR: Unlike previous attempts, our method ensures that optic radiation
streamlines do not prematurely terminate [37] and exclusively traverse white
matter to reach the occipital lobe, avoiding aberrant terminations [32] or
ventricular crossings [96] noted in earlier studies.

  * •

UF: While our findings align with the trajectory observed in previous studies
for the UF [42, 36], we additionally note that our tracts achieve expected
orbital targets, indicating a refinement over prior work.

Our study has some limitations. Firstly, the sample size of 84 fetuses is
relatively small due to the challenges of subject recruitment, fetal imaging,
and the moderate success rate of the dMRI reconstruction pipeline. Moreover,
generating manual segmentation labels on 3D images is very time-consuming. We
evaluated our tissue segmentation method and the complete tractography
technique on 11 independent test subjects and found statistically significant
improvements compared with FACT. Nonetheless, increasing the data size for
method development and validation will be useful. Secondly, our data was
obtained from a single center, and we employed an in-house pipeline for
preprocessing of the dMRI data. Validation of data from other centers helps
assess the generalizability of our method. Additionally, evaluating our method
with higher quality or multi-shell dMRI data can also be interesting. As we
have pointed out above, unlike some recent works that have used unique, high-
quality data from the Human Connectome Project [51, 32], our method has been
designed to work with more typical dMRI scans. We think this is a significant
advantage of our method because HCP-style data are very rare in fetal studies.
Nonetheless, applying our method to higher-quality data will be useful in
highlighting the potential advantages and limitations of our method compared
with existing techniques. Another limitation of our evaluations was that our
data included healthy subjects only. Future works can study the performance of
our method on abnormal fetal brains. Lastly, we anticipate that our method can
lead to significant improvements in the accuracy and reproducibility of
structural connectivity analysis, which is a main application of tractography.
We aim to pursue this line of investigation in our future work.

##  5 Conclusions

Our study has demonstrated the feasibility of anatomically-constrained
tractography of the fetal brain. The new method proposed in this work presents
a significant stride toward improving the accuracy of fetal brain
tractography. The higher tract reconstruction success rate and accuracy
offered by our method can enhance the accuracy of dMRI-based studies of the
fetal brain white matter in utero. It can also enable reliable quantitative
assessment of the structural connectivity of the fetal brain. Ultimately,
these new capabilities can enable important scientific and clinical
applications and lead to a better understanding of brain development at its
earliest stage.

## Acknowledgements

This research was supported in part by the National Institute of Neurological
Disorders and Stroke under award numbers R01NS128281 and R01 NS106030; the
Eunice Kennedy Shriver National Institute of Child Health and Human
Development under award numbers R01HD110772 and R01 HD109395; the National
Institute of Biomedical Imaging and Bioengineering under award numbers R01
EB031849, R01 EB032366, R01 EB018988, and R01 EB013248; the Office of the
Director of the NIH under award number S10 OD0250111; the Rosamund Stone
Zander Translational Neuroscience Center, Boston Children’s Hospital; the
Office of Faculty Development at Boston Children’s Hospital; and a scholarship
from the American Roentgen Ray Society. The content of this publication is
solely the responsibility of the authors and does not necessarily represent
the official views of the NIH.

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