txt/2203.10517.txt

IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. XX, NO. XX, XXXX 2020 1
Learning Whole Heart Mesh Generation From
Patient Images For Computational Simulations
Fanwei Kong, Shawn C. Shadden
Abstract — Patient-specific cardiac modeling combines
geometries of the heart derived from medical images
and biophysical simulations to predict various aspects of
cardiac function. However, generating simulation-suitable
models of the heart from patient image data often requires
complicated procedures and significant human effort. We
present a fast and automated deep-learning method to
construct simulation-suitable models of the heart from
medical images. The approach constructs meshes from
3D patient images by learning to deform a small set of
deformation handles on a whole heart template. For both
3D CT and MR data, this method achieves promising ac-
curacy for whole heart reconstruction, consistently outper-
forming prior methods in constructing simulation-suitable
meshes of the heart. When evaluated on time-series CT
data, this method produced more anatomically and tempo-
rally consistent geometries than prior methods, and was
able to produce geometries that better satisfy modeling
requirements for cardiac flow simulations. Our source code
and pretrained networks are available at https://github.
com/fkong7/HeartDeformNets .
Index Terms — Geometric Deep Learning, Mesh Genera-
tion, Shape Deformation, Cardiac Simulations
I. INTRODUCTION
IMAGE-based cardiac modeling is used to simulate various
aspects of cardiac function, including electrophysiology
[1], hemodynamics [2] and tissue mechanics [3]. This method
derives geometries of the heart from patient image data and
numerically solves mathematical equations that describe var-
ious physiology on discretized computational domains. Such
“digital twin” modeling of a patient’s heart can provide infor-
mation that cannot be readily measured to facilitate diagnosis
and treatment planning [4]–[6], or to quantify biomechanical
underpinnings of diseases [7]. This paradigm has motivated
numerous research efforts on a wide range of clinical applica-
tions, such as, simulations of the stress and strain of cardiac
tissues when interacting with implantable cardiac devices [8],
the cardiac flow pattern after surgical corrections [4], [6], and
cardiac rhythm outcome after ablation surgery [5].
This work was supported by the NSF , Award No. 1663747. We
thank Drs. Shone Almeida, Amirhossein Arzani and Kashif Shaikh for
providing the time-series CT image data.
Fanwei Kong, is with the Department of Mechanical Engineering,
University of California at Berkeley, Berkeley, CA 94720 USA (e-mail:
fanwei [email protected]).
Shawn C. Shadden, is with the Department of Mechanical Engineer-
ing, University of California at Berkeley, Berkeley, CA 94720 USA (e-
mail: [email protected]).Generating simulation-suitable models of the heart from
image data has remained a time-consuming and labor-intensive
process. It is the major bottleneck limiting large-cohort val-
idations and clinical translations of functional computational
heart modeling [2], [9]. Indeed, prior studies have been limited
to only a few subjects [2], [4], [5]. The entwined nature of the
heart makes it difficult to differentiate individual cardiac struc-
tures, and typically a complicated series of steps are needed
to identify and label various structures for the assignment
of boundary conditions or modeling parameters. Deforming-
domain computational fluid dynamics (CFD) simulations of
the intracardiac hemodynamics, is particularly labor-intensive
since it requires reconstructing temporally-consistent deforma-
tions of the heart from a sequence of image snapshots.
Deep learning methods can train neural networks from
existing data to automatically process medical images and gen-
erate whole heart reconstructions. Most deep learning methods
have, however, focused on segmentation (pixel classification)
rather than construction of a computer model of the heart,
usually represented by tessellated meshes [10]. Prior studies
on automated cardiac mesh reconstruction thus adopted multi-
stage approaches, where segmentation of the heart was first
generated by convolutional neural networks (CNN) and surface
meshes of the heart were then created from the marching cube
algorithms and following surface post processing methods
[11]. However, the intermediate segmentation steps often intro-
duce extraneous regions containing topological anomalies that
are unphysical and unintelligible for simulation-based analyses
[11]. Direct mesh reconstruction using geometric deep learning
[12], [13] provides a recent avenue to address the end-to-end
learning between volumetric medical images and simulation-
ready surface meshes of the heart [14]–[16]. However, these
approaches often assumes the connectivity of the meshes.
That is, the shape and topology of the predicted meshes from
these approaches are pre-determined by the mesh template
and cannot be easily changed to accommodate various mesh
requirements for different cardiac simulations.
To overcome these short comings, we propose to learn to
deform the space enclosing a whole heart template mesh to
automatically and directly generate meshes that are suitable
for computational simulations of cardiac function. Here we
propose to leverage a control-handle-based shape deformation
method to parameterize smooth deformation of the template
with the displacements of a small set of control handles and
their biharmonic coordinates. Our approach learns to predict
the control handle displacements to fit the whole heart templatearXiv:2203.10517v2  [eess.IV]  8 Nov 20232 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. XX, NO. XX, XXXX 2020
to the target image data. We also introduce learning biases to
produce meshes that better satisfy the modeling requirements
for computational simulation of cardiac flow. The contributions
of this work are summarized as follows:
1) We propose a novel end-to-end learning method combin-
ing deformation handles to predict deformation of whole
heart mesh templates from volumetric patient image
data. We show that our approach achieves comparable
geometric accuracy for whole heart segmentation as
prior state-of-the-art segmentation methods.
2) We introduced novel mesh regularization losses on
vessel inlet and outlet structures to better satisfy the
meshing requirements for CFD simulations. Namely, our
method predicts meshes with coplanar vessel caps that
are orthogonal to vessel walls for CFD simulations.
3) We validated our method on creating 4D dynamic whole
heart and left ventricle meshes for CFD simulation
of cardiac flow. Our method can efficiently generate
simulation-ready meshes with minimal post-processing
to facilitate large-cohort computational simulations of
cardiac function.
A. Learning-Based Shape Deformation
Shape deformation using low-dimensional control of de-
formation fields has been extensively studied for decades in
computer graphics and has been ubiquitously used in anima-
tion. These methods usually interpolate the transformation of a
sparse set of control points to all points on the shape. Among
the most popular approaches were are free-form-deformation
that uses a regular control point lattice to deform the shape
enclosed within the lattice [17], cage-deformation that uses
a convex control cage that encloses the shape [18], as well
as control-handle-based approaches that directly place control
points on the surface of the shape [19]–[21]. Recent works
have shown success in integrating these shape deformation
methods in deep-learning frameworks for automated mesh
reconstruction from single-view camera images [22], gener-
ative shape modeling [23] as well as deformation transfer
[24]. However, these approaches were designed to take 2D
camera images or 3D meshes as input and used memory-
intensive CNNs or fully connected neural network to predict
the transformation of control points. They thus cannot be
directly applied to deform complicated whole heart structures
from high-resolution 3D medical image data. Therefore, we
herein propose to use graph convolutional networks (GCN)
and sparsely sampling of the volumetric image feature map to
predict control point translations and thus efficiently produce
meshes from 3D medical images.
B. Mesh Reconstruction From 3D Medical Images
Recent works on direct mesh reconstruction from volumet-
ric images aim to deform an initial mesh with pre-defined
topology to a target mesh [14], [15]. Our previous approach
leveraged a GCN to predict deformation on mesh vertices
from a pre-defined mesh template to fit multiple anatomical
structures in a 3D image [15]. However, different structures
were represented by decoupled mesh templates and thus stillrequired post-processing to merge different structures for com-
putational simulations involving multiple cardiac structures.
Similarly, [16] used deep neural networks and patient metadata
to predict cardiac shape parameters of a pre-built statistical
shape model of the heart. Our approach presented herein, in
contrast, deforms the space enclosing the mesh template. Once
being trained on the whole heart template, our network can
deform alternative template meshes that represent a subset
of the geometries in the template to accommodate different
modeling requirements.
A few studies have focused on learning space deformation
fields. [25] used a 3D UNet to predict a deformation field to
deform heart valve templates from CT images. Additionally,
our preliminary work combined free-form deformation (FFD)
with deep learning to predict the displacement of a control
point grid to deform the space enclosing a simulation-ready
whole heart template [26]. However, predicting the defor-
mation fields requires many degrees of freedom to produce
accurate results. For example, since FFD has limited capability
for complex shape deformation, our prior method required a
dense grid of thousands of control point to achieve acceptable
whole heart reconstruction accuracy. Herein we demonstrate
that using control-handle-based deformation with biharmonic
coordinates achieves higher reconstruction accuracy while
using far less control points than the FFD-based approach.
II. M ETHODS
A. Shape Deformation Using Biharmonic Coordinates
We parameterize deformations of whole heart meshes with
the translations of a small set of deformation handles sampled
from the mesh template. Given a set of mesh vertices V∈
Rn×3and a set of control points P∈Rc×3, we compute
the biharmonic coordinates W∈Rn×c, which is a linear
map, V=WP.nandcare the number of vertices and the
number of control points, respectively. Wis defined based on
biharmonic functions and can be pre-computed by minimizing
a quadratic deformation energy function while satisfying the
handle constraints with linear precision [21]. Namely, let
Q∈Rc×nbe the binary selector matrix that selects rows of X
corresponding to the control handles, and let T∈R(n−c)×n
be the complementary selector matrix of Qcorresponding to
the free vertices. W is computed by
V= arg min
X∈Rn×31
2trace(XTAX),subject to QX=P (1)
V= (QT−TT(TATT)−1TAQT)| {z }
WP (2)
where Ais a positive semi-definite quadratic form based on
the squared Laplacian energy to encourage smoothness [21].
Under this framework, displacements of the control handles
can smoothly deform the underlying mesh template.
B. Network Architecture
Figure 1 shows the overall architecture of our network. The
central architecture is the novel control-handle-based mesh de-
formation module, which learns to predict the displacements ofKONG et al. : LEARNING WHOLE HEART MESH GENERATION FROM PATIENT IMAGES FOR COMPUTATIONAL SIMULATIONS 3
Fig. 1. Diagram of the proposed automatic whole heart reconstruction approach. A total of three deformation blocks were used to progressively
deform the mesh templates, using 75, 75 and 600 control handles, respectively, for the 3 deformation blocks.
control handles based on image features, so that the underlying
mesh templates can be smoothly deformed to match the input
3D image data.
1) Image Encoding and Segmentation Modules: We applied
a residual 3D CNN backbone to extract and encode image
features at multiple resolutions [27]. The CNN backbone
involves 4 down-sampling operations so that image feature
volumes at 5 different resolution are obtained. These image
feature volumes are used as inputs to GCN layers to predict
the displacements of control handles. Similar to [15], we also
used a segmentation module that predicted a binary segmen-
tation map to enable additional supervision using ground truth
annotations. This module was only used during training.
2) Mesh Deformation Module: Biharmonic coordinates con-
strain the displaced control handles to be located on the
deformed mesh template. Therefore, regardless of which set
of control handles are sampled, these handles will be located
at the corresponding positions on the template mesh. We
used a neural network to update the coordinates of all points
(S∈Rn×3) on the mesh template and obtain the coordinates
of the selected control handles ( P∈Rc×3) from the updated
mesh vertex locations to deform the template using the pre-
computed biharmonic coordinates. This design allows picking
arbitrary sets of control handles to deform the template at
various resolutions after training. Furthermore, training to pre-
dict the coordinates of every mesh vertex provides additional
supervision that can speed up training.
Since the mesh template can be represented as a graph,
a GCN was used to predict the mesh vertex displacements.
We chose to approximate the graph convolutional kernel with
a first order Chebyshev polynomial of the normalized graph
Laplacian matrix [12]. At each mesh vertex, we extracted the
image feature vectors at the corresponding image coordinatesfrom multiple image feature volumes with various resolution.
These image feature vectors were then concatenated with the
mesh feature vectors following a GCN layer. The combined
vertex feature vectors were then processed by three graph
residual blocks. We then used an additional GCN layer to
predict displacements as 3D feature vectors on mesh vertices.
We used a total of three deformation blocks to progressively
deform the template mesh. The first and second deformation
blocks used 75 control handles to deform the mesh, whereas
the last deformation block used more control handles, 600, for
a more detailed prediction.
C. Network Training
Fig. 2. Graphical illustration of different loss functions. Y ellow and teal
on the right panel shows the caps and walls to apply the mesh regular-
ization losses, respectively, and arrows shows cap normal vectors.4 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. XX, NO. XX, XXXX 2020
The training of the networks was supervised by 3D ground
truth meshes of the whole heart as well as a binary segmenta-
tion indicating occupancy of the heart on the input image grid.
We used the following loss functions (illustrated in figure 2)
in training to produce accurate whole heart geometries while
ensuring the resulting mesh is suitable to support simulations.
1) Geometric Consistency Losses: The geometric consis-
tency loss Lgeois the geometric mean between the point
and normal consistency losses to supervise the geometric
consistency between the prediction and the ground truth [15].
We note that edge length and Laplacian regularization losses,
such as used in [15], are not necessary since the smoothness of
the mesh prediction is naturally constrained by the biharmonic
coordinates used to deform the template. Since only the
selected control points were used to deform the mesh template
while the displacements of all mesh points were predicted, we
needed to regularize the L2distances between the mapped
mesh points ( S∈Rn×3) and the corresponding mesh vertices
on the deformed mesh template ( V∈Rn×3). This consistency
loss between the points and the mesh ensures that coordinates
of other unselected control points also result in reasonable
deformations. In other words, the deformation results should
not be sensitive to the choice of pre-selected control points.
2) Mesh Regularization for CFD Simulations: Cardiac mod-
els generally includes portions of the great vessels connected
to the heart (e.g., pulmonary veins and arteries, venae cavae,
and aorta). For CFD simulation of cardiac flow, locations
where these vessels are truncated (so-called inflow and out-
flow boundaries, or “caps”) should be planar and nominally
orthogonal to the vessel. On our training template, we labeled
these caps, as well as the associated vessel walls. Figure 2
shows the identified cap and wall faces on left atrium (LA),
right atrium (RA) and aorta. We applied a co-planar loss
on each cap that penalizes the L2differences of the surface
normals on the cap. Namely, Lcoplanar =P
kP
j∈Ck||nj−
1
|Ck|P
j∈Cknj||2
2where Ckis the set of mesh faces for the
kth cap and njis the normal vector for the jth face on Ck.
For mesh vertices that are on the vessel walls near the caps,
we minimized the absolute value of the dot product between
the surface normal vectors and the surface normal vector of
the caps to encourage orthogonality. Namely, Lorthogonal =P
kP
j∈Wk|⟨nk,1
|Ck|P
p∈Cknp⟩|,where Wkis the set of
mesh faces on the vessel wall that corresponds to the kth cap.
3) Weighted Mesh Losses: Patient images may not always
contain the targeted cardiac structures. As shown in Figure
2 (left), cardiac structures such as pulmonary veins, pul-
monary arteries and the aorta are often not captured in full,
although the truncks of these structures can be necessary for
simulations. We thus aim to predict “complete” whole heart
structures from incomplete image data. Namely, we computed
the bounding box of the ground truth meshes and assigned zero
weights within the geometric consistency loss for predicted
mesh vertices that were located outside the bounding box.
Furthermore, as the geometry of inlet vessels are important
to the accuracy of CFD results, we applied a higher weight
for the geometric consistency loss on mesh vertices that are
located on vessel walls near the inlets.4) Total Losses: The total loss on a predicted mesh Mis
Lmesh(M,G, W ) =X
iLgeo(Mi, Gi,wi)
+αX
k(Lcoplanar (M) +βLorthogonal (M))(3)
where Girepresents the ground truth mesh for individual
cardiac structure, and wirepresents the weighting vector for
each mesh point. Mcan be both the deformed whole heart
mesh template Vand the mesh obtained from mapping all
mesh points S. The total loss for training is a weighted sum
of the mesh losses and the segmentation loss, which is the
sum of the binary cross-entropy and the dice losses between
the predicted occupancy probability map Ipand the ground
truth binary segmentation of the whole heart Ig.
Ltotal=λ1Lmesh(S, G, W ) +λ2Lmesh(V, G, W )+
λ3||S−V||2
F+Lseg(Ig, Ip)(4)
5) Image Augmentation for Shape Completion: Leveraging
the mesh template, we trained our method to predict the
geometries of the whole heart represented by the template
mesh when the images do not cover the complete cardiac
structures. Since CT images often do not cover the whole
heart, we selected CT images that did cover the whole heart
(n=10) from our training set and then generated 10 random
crops for each image while keeping the ground truth meshes
to be the same. Figure 3 visualizes example image crops
and the corresponding ground truth meshes. We also applied
Fig. 3. Visualization of augmented input image crops and the corre-
sponding ground truth meshes.
random shearing, rotations and elastic deformations, following
the same augmentation strategies described in our prior work
[15].
III. E XPERIMENTS
A. Datasets and Experiments
1) Task-1: Whole Heart Segmentation for 3D Images: We
applied our method to public datasets of contrast-enhanced
3D CT images and 3D MR images from both normal and
abnormal hearts. For training and validation, we used a total
of 102 CT images and 47 MR images from the multi-
modality whole heart segmentation challenge (MMWHS) [10],
orCalScore challenge [28], left atrial wall thickness challenge
[29] and left atrial segmentation challenge [30]. Among them,
we used 87 CT and 41 MR images for training, and we used 15
CT images and 6 MR images for validation, where we tuned
the hyper-parameters and selected the model trained with the
hyper-parameter set that performed best on the validation data.
We then evaluated the final performance of the selected modelKONG et al. : LEARNING WHOLE HEART MESH GENERATION FROM PATIENT IMAGES FOR COMPUTATIONAL SIMULATIONS 5
on a held out test dataset from the MMWHS challenge, which
contained 40 CT and 40 MR images. For CT images, the
in-plane resolutions vary from 0.4×0.4mm to 0.78×0.78
mm and the through-plane resolutions vary from 0.5mm to
1.6mm. For MR images, the in-plane resolutions vary from
1.25×1.25mm to 2×2.mm and the through-plane resolutions
vary from 2.mm to 2.3mm.
Fig. 4. Illustration of example CT and MR image data, the correspond-
ing surface meshes generated from manual segmentation using the
marching cube algorithm, and the resulting ground truth surface meshes
after post processing.
For each image in the dataset, we followed the MMWHS
challenge [10] and created ground truth segmentation of 7
cardiac structures to supervise the training and evaluate model
performance on validation and test datasets. The 7 cardiac
structures included the blood cavities of left ventricle (LV),
right ventricle (RV), left atrium (LA), right atrium (RA),
LV myocardium (Myo), aorta (Ao), and pulmonary artery
(PA), for all images. Figure 4 illustrates our pipeline to
generate smooth ground truth surface meshes from the manual
segmentations. We resampled the segmentation to a resolution
of1.×1.×1.mm, then used the marching cube algorithm
to generate the surface meshes for each cardiac structure. We
then applied a Windowed-Sinc smoothing filter [31] with a low
pass band of 0.01 and 20 iterations of smoothing to generate
smooth ground truth meshes. Furthermore, as visualized in the
example CT case in Figure 4, surface meshes were clipped at
the image bounding box to remove the fictitious surface at
the image boundaries for cardiac structures that exceeded the
coverage of the image data.
We compared the geometric accuracy of the reconstructed
whole heart surfaces against prior deep-learning methods that
demonstrated strong performance of segmenting whole heart
geometries from 3D medical images. Namely, we considered
HeartFFDNet [26], our prior work that generates simulation-
ready whole heart surface meshes from images by learning
free-form deformation from a template mesh, MeshDeformNet
[15] that predicts displacements on sphere mesh templates, as
well as 2D UNet [32] and a residual 3D UNet [27] that are
arguably the most successful neural network architecture for
image segmentation. We also implemented a SpatialConfigu-
ration Net (SCN) [33] that ranked first for CT and second for
MRI in the MMWHS challenge, using our residual 3D UNet
backbone. This segmentation-based approach incorporates rel-
ative positions among structures to focus on anatomically
feasible regions. All methods were trained on the same trainingand validation data splits, and used the same pre-processing
and augmentation procedures to ensure a fair comparison.
2) Task-2: Whole Heart Mesh Construction for 4D Images:
We applied our method on time-series CT images to evaluate
its performance on creating whole heart meshes for CFD
simulations. Since the MMWHS dataset does not include
pulmonary veins, LA appendage or venae cavae, we prepared
another set of ground truth segmentations to include these
structures. The geometric accuracy and the mesh quality of
the reconstructed meshes for CFD simulations were then
evaluated on 10 sets of time-series CT images against the
learning-based mesh reconstruction baselines, HeartFFDNet
and MeshDeformNet.
Fig. 5. Visualization of simulation-ready templates with trimmed
inlet/outlet geometries and tagged face IDs for prescribing boundary
conditions.
3) Task-3: CFD Simulations: We conducted CFD simula-
tions of cardiac flow using the predicted whole heart meshes
from time-series CT images. Since our predicted model does
not contain heart valves, only diastolic flow was simulated.
We also conducted CFD simulations for the LV and simulated
the LV flow for the entire cardiac cycle. Figure 5 visualizes
the simulation-ready templates of the 4 heart cambers and
the LV with trimmed inlet/outlet geometries and tagged face
IDs for prescribing boundary conditions. These simulation-
ready templates were manually created from the training whole
heart template in a surface processing software, SimVascular
[34].We linearly interpolated the pre-computed biharmonic
coordinates onto the new templates so that our trained mod-
els can readily deform these new templates. The simulation
results were compared against results obtained from time-
series ground truth meshes created manually in SimVascular
[34]. We also compared simulation results among our method,
HeartFFDNet, and a conventional semi-automatic model con-
struction pipeline based on image registration, where a manu-
ally created ground truth mesh was morphed based on trans-
formations obtained from registering images across different
time points.
B. Evaluation Metrics
We used Dice similarity coefficient (DSC) and Hausdorff
Distance (HD) to measure segmentation accuracy. The DSC
and HD values for the MMWHS test dataset were evalu-
ated with an executable provided by MMWHS organizers.
For mesh-based methods, we converted the predicted surface
meshes to segmentation prior to evaluation. Mesh quality was
compared in terms of the percentage self-intersection, which
measures the local topological correctness of the meshes,6 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. XX, NO. XX, XXXX 2020
orthogonality of the vessel caps with respect to the vessel
walls, as well as the coplanarity of the vessel caps. The
percentage mesh self-intersection was calculated as the per-
centage of intersected mesh facets detected by TetGen [35]
among all mesh facets. The orthogonality between vessel
caps and walls (Cap-Wall-Orthogonality) was measured by
the normal consistency between the mean cap normal vector
and the vector connecting the centroids of the mesh points
on the cap and on the wall, respectively. Namely, CWO =P
k1− ⟨1
|Wk|P
i∈Wk|ni,1
|Ck|P
j∈Ck|nj⟩where WkandCk
represent the sets containing the mesh vertices on a vessel wall
and the corresponding vessel cap. Vessel caps coplanarity was
measured by the projected distance between the mesh vertices
on the cap and the best fit plane over those mesh vertices. For
CFD simulations, we compared integrative measures during a
cardiac cycle, namely, LV volume and average kinetic energy
KE′=1
2VLVR R R
ρu2dV, where VLVis the volume of the
LV and uis the flow velocity. We also compared the mean
velocity near the mitral valve opening (MO) and aortic valve
opening (AO) during a cardiac cycle. Paired t-test was used
for statistical significance.
C. Deforming-Domain CFD simulations of Cardiac Flow
We applied the Arbitrary Lagrangian-Eulerian (ALE) for-
mulation of the incompressible Navier-Stokes equations to
simulate the intraventricular flow and account for deforming
volumetric mesh using the finite element method. Since time
resolution of image data is too coarse (about 0.1s) to be used
directly in time-stepping of the Navier–Stokes equations, cubic
spline interpolation was applied to interpolate the meshes
predicted at different imaging time points so that the time
resolution of the interpolated meshes was 0.001s, which cor-
responded to the simulation time step. For the fluid domain,
the mesh motions computed from these interpolated meshes
were imposed as Dirichlet boundary conditions on the chamber
walls. For simulations of LV flow, we imposed Dirichlet
boundary conditions on the mitral inlet during systole, and
on the aortic outlet during diastole. Neumann (prescribed
pressure) boundary conditions were applied to the mitral inlet
during diastole or to the aortic inlet during systole. Diastole
and systole phases were determined based on the increase and
decrease of the LV volume. For simulations of diastolic cardiac
flow within 4 heart chambers, we applied Neumann boundary
conditions to the pulmonary vein inlets, and imposed Dirichlet
boudary condition on the aortic outlet. Blood was assumed to
have a viscosity µof4.0×10−3Pa·sand a density ρof
1.06g/cm3. The volumetric mesh was created automatically
from our predicted surface mesh using TetGen [35], using a
maximum edge size of 1.5mm. The equations were solved with
the open-source svFSI solver from the SimVascular project
[36].
IV. R ESULTS
A. Comparative Studies of Whole Heart Segmentation
Performance on MMWHS Dataset
1) Comparison of Geometric Accuracy with Other Methods:
Table I compares the average Dice scores and Hausdorffdistances of the reconstruction results of both the whole heart
and the individual cardiac structures for the MMWHS test
dataset. We show the accuracy of deforming the template by
mapping all mesh points ( S) and by interpolating the mesh
deformation using only 600 uniformly-sampled control han-
dles ( V). Mapping all points consistently achieved higher dice
scores than using 600 selected control handles, but the HDs are
worse for some cardiac structures. For both CT and MR data,
in terms of Dice scores, our method consistently outperformed
HeartFFDNet and 3D UNet for all cardiac structures and
achieved comparable performance with MeshDeformNet, 2D
UNet, 3D SCNet for most cardiac structures. Our method
achieved the best HDs for LA, RA and RV for CT data and
for all cardiac structures except for aorta and PA for MR data.
Figure 6 presents the best, median, and worst segmentation
results of our method on CT and MRI test images and pro-
vides qualitative comparisons of the results from the different
methods. As shown, mesh-based approaches, ours, HeartFFD-
Net and MeshDeformNet produced smooth and anatomically
consistent cardiac geometries while segmentation-based ap-
proaches, 2D UNet, residual 3D UNet, 3D SCNet produced
segmentations with topological artifacts such as missing parts,
holes, and isolated islands. Although 3D SCNet produced
higher Dice scores than residual 3D UNet, it produced a
few misclassifications where the LA was incorrectly classified
into RV . Although MeshDeformNet produced smooth and
anatomically consistent cardiac geometries, it was prone to
gaps between adjacent cardiac structures by deforming un-
coupled spheres. Our method and the HeartFFDNet were able
to avoid this limitation by deforming the space enclosing
a whole heart template, preserving the connections among
cardiac structures.
2) Effect of Varying Control Handle Numbers: We investi-
gated the effect of various design choices on the whole heart
segmentation performance of our proposed method. Table II,
presents the effect of varying the number of control handles
used during training on the average Dice scores and Hausdorff
distances of the reconstruction results. Increasing the number
of control handles used in the last deformation block from
75 to 900 generally resulted in increased performance for
most cardiac structures. However, the resulting improvement
in terms of Dice scores was only around 1%, indicating
the robustness of our method towards using relatively fewer
numbers of control handles. Similarly, using more control
handles in the first and/or second deformation blocks did not
result in significant improvement for most cardiac structures.
Therefore, in our final network model, we chose to use a small
number of control handles (75) in the first and second blocks
to reduce the computational cost, and used 600 control handles
in the last deformation block for a slightly better performance.
3) Effect of Individual Loss Components on Whole Heart
Segmentation Performance: Since our training pipeline in-
volves a joint supervision of multiple objectives, we performed
an ablation study on the total training loss Ltotal to evaluate
the contribution of individual loss components. Namely, we
trained network models while removing the segmentation loss
Lseg, and the L2consistency loss ||S−V||2
Fto investigate
the effectiveness of supervising a segmentation branch, andKONG et al. : LEARNING WHOLE HEART MESH GENERATION FROM PATIENT IMAGES FOR COMPUTATIONAL SIMULATIONS 7
TABLE I
COMPARISON OF WHOLE -HEART SEGMENTATION PERFORMANCE , DSC ( ↑)AND HD ( MM) (↓),FROM DIFFERENT METHODS ON THE MMWHS
CT AND MR TEST DATASETS .* D ENOTES SIGNIFICANT DIFFERENCE OF"OURS (S)" F ROM THE OTHERS (P-VALUES <0.05)
CT MR
Method Myo LA LV RA RV Ao PA WH Myo LA LV RA RV Ao PA WH
DCSOurs (S) 90.07 93.18 93.47 89.48 91.48 93.33 85.60 91.76 80.45 86.98 91.61 88.08 88.09 85.76 78.14 87.41
Ours (V) 88.38* 92.53* 91.99* 88.76* 90.59* 91.25* 84.73* 90.53* 78.62* 86.27* 89.38* 87.79* 87.20* 83.30* 77.55 86.04*
HeartFFDNet 83.85* 90.55* 89.38* 86.33* 87.65* 90.65* 80.20* 87.82* 70.67* 83.27* 86.92* 84.47* 82.77* 79.71* 69.68* 81.33*
MeshDeformNet 89.94 93.23 93.98 * 89.18 91.00 94.98 * 85.22 91.80 79.71 88.13 92.23 88.82 89.24 *88.98 *81.65 *88.17 *
2DUNet 89.87 93.08 93.06 87.71* 90.49* 93.43 83.23* 91.09* 79.47 86.41 89.61* 85.21 86.48* 86.94 77.24 85.94*
3DUNet 86.34* 90.17* 92.28* 86.77* 87.58* 92.34* 81.29* 88.78* 76.11* 85.20* 87.90* 86.63* 82.77* 74.18* 76.38 84.04*
3DUNet+SCN 90.09 92.63* 93.43 89.01 90.49* 91.61 84.05 91.18* 78.36* 85.77* 89.84* 88.09 87.19 84.35 76.85 86.12*
HDOurs (S) 14.41 10.72 10.41 13.80 11.63 6.59 7.88 16.95 16.39 12.12 11.93 13.93 14.76 7.19 9.12 19.97
Ours (V) 14.40 8.18* 6.87* 12.46 *9.55* 5.54* 8.45 16.63* 15.96 *10.16 *8.97* 12.56 *12.46 * 7.39 9.14 18.91 *
HeartFFDNet 14.20 8.74* 7.66* 13.24 10.44* 6.17 8.35 16.57 18.21* 12.43 12.57 15.57 16.36 9.26* 11.36* 22.28*
MeshDeformNet 14.39 10.41 10.33 13.67 13.36 5.27* 9.16* 17.62 16.92 12.22 11.63 15.05 14.73 6.05* 7.79* 21.08
2DUNet 9.98* 9.34 6.10* 13.78 10.39 5.63 8.38 16.37 20.34 10.78* 10.62 17.43 16.32 6.98 8.09 27.54*
3DUNet 13.64 11.47 10.12 16.56* 16.17* 6.88 9.88* 19.91* 34.97* 33.81* 36.28* 24.36* 27.72* 15.52* 10.13 51.54*
3DUNet+SCN 13.78 12.80 9.86 17.02 17.70* 6.57 7.77 28.04* 39.30* 34.87* 21.06* 28.37* 28.20* 8.05 8.49 53.76*
Fig. 6. Example segmentation results for CT and MR images from different methods. The CT or MR images that our method had the best,
the median, and the worst Dice scores among the CT or MR test data were selected, thus illustrating best, typical, and worst segmentation
results, respectively. The gold arrows indicate locations of artifacts unsuitable for simulations, such as gaps between adjacent cardiac structures for
MeshDeformNet, missing structures, holes, noisy boundaries, and isolated islands for the segmentation-based methods.
the effectiveness of encouraging the consistency between
directly mapped mesh points ( S) and deformed mesh vertex
locations ( V), respectively. We trained two additional models
while removing supervision on Vor on S, respectively, to
validate the effectiveness of supervising both meshes together.
Table III presents the effect of removing individual loss
components on the whole heart segmentation performance
evaluated on the MMWHS test dataset. Removing any of theaforementioned objectives resulted in a significant decrease
in whole heart Dice scores for both CT and MR data, as
well as decreased Dice scores for most cardiac structures. The
Hausdorff distances increased significantly for most cardiac
structures when supervision on the smoothly deformed mesh
template Vwas removed. However, there were no significant
changes in Hausdorff distances for most cardiac structures
following the removal of other objectives.8 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. XX, NO. XX, XXXX 2020
TABLE II
ACOMPARISON OF WHOLE -HEART SEGMENTATION PERFORMANCE , DSC ( ↑)AND HD ( MM) (↓)ON THE MMWHS CT AND MR TEST DATASETS ,
WHEN USING DIFFERENT NUMBERS OF CONTROL HANDLES DURING TRAINING . B1/B2/B3 D ENOTES THE NUMBERS OF CONTROL HANDLES
USED IN THE THREE DEFORMATION BLOCKS . * D ENOTES SIGNIFICANT DIFFERENCE OFOURFINAL NETWORK MODEL USING "75/75/600"
CONTROL HANDLES FROM THE OTHERS (P-VALUES <0.05)
CT MR
B1/B2/B3 Myo LA LV RA RV Ao PA WH Myo LA LV RA RV Ao PA WH
DCS75/75/600 90.07 93.18 93.47 89.48 91.48 93.33 85.60 91.76 80.45 86.98 91.61 88.08 88.09 85.76 78.14 87.41
75/75/75 88.08* 92.48* 92.54* 88.42* 90.98* 92.76 84.77 90.77* 79.51 86.57 90.71* 87.42 87.55 83.21* 74.40* 86.33*
75/75/150 88.37* 92.59* 92.37* 88.26* 90.65* 92.78 84.20* 90.69* 78.40* 85.84* 90.64* 86.99* 86.84* 82.81* 74.67* 85.89*
75/75/300 88.31* 93.47 93.28 89.20 91.28 93.96 84.84 91.34* 80.23 87.98 92.39 * 87.08* 87.94 86.84 78.98 87.46
75/75/900 89.04* 93.20 93.36 89.54 91.64 93.97 *85.99 91.66 78.64* 87.07 91.54 86.91* 86.77 84.73 75.22 86.48*
75/300/600 89.91 93.22 93.27 89.17 90.73* 93.83 85.48 91.52 79.74 86.00* 91.18 88.26 87.61 83.94 73.17* 86.66*
600/600/600 89.53 93.01 93.07 88.43* 90.87* 93.32 84.95 91.25* 79.87 86.32 91.33 87.20* 87.34 83.42* 73.59* 86.55*
HD75/75/600 14.41 10.72 10.41 13.80 11.63 6.59 7.88 16.95 16.39 12.12 11.93 13.93 14.76 7.19 9.12 19.97
75/75/75 14.33 10.89 11.18 14.14 11.21 6.87 7.88 16.76 16.24 12.19 12.43 14.62 14.18 8.22 9.90 20.00
75/75/150 14.33 9.98 9.75 15.38* 12.33* 5.86* 9.40* 17.59 16.54 12.33 11.89 15.27* 15.31 8.48* 10.86* 20.53
75/75/300 14.29 10.88 10.67 14.70 11.64 6.35 7.80 17.74 16.95 12.45 12.78 15.44* 13.55* 7.03 8.77 21.45*
75/75/900 14.61 11.02 11.01 13.44 11.64 6.30 8.93* 16.84 17.93* 12.88 12.94 14.19 13.99 8.12 10.50* 21.37*
75/300/600 14.50 11.20 10.90 13.79 11.29 5.82* 8.32 17.36 16.63 12.00 12.03 13.53 12.30 * 8.17 10.46* 20.38
600/600/600 14.36 10.60 10.28 14.58 12.06 7.04 8.16 17.42 17.06 12.92* 13.60* 14.42 14.07 8.33 10.25* 20.70
TABLE III
IMPACT OF INDIVIDUAL LOSS COMPONENTS OF Ltotal ON THE PREDICTION ACCURACY ON MMWHS MR AND CT TEST DATASETS . * D ENOTES
SIGNIFICANT DIFFERENCE OF OUR FINAL NETWORK MODEL "OURS (S)" F ROM THE OTHERS (P-VALUES <0.05)
CT MR
Models Myo LA LV RA RV Ao PA WH Myo LA LV RA RV Ao PA WH
DCSOurs (S) 90.07 93.18 93.47 89.48 91.48 93.33 85.60 91.76 80.45 86.98 91.61 88.08 88.09 85.76 78.14 87.41
w/o segmentation 87.11* 93.32 92.32* 88.74 90.65* 92.90 85.09 90.68* 77.96* 86.31 90.81* 87.48 87.03* 85.47 77.28 86.28*
w/o L2 88.85* 92.94 92.57* 88.90* 90.96* 93.68 83.87* 91.10* 79.57* 85.96 90.56* 86.75* 87.01 84.46 75.00* 86.23*
w/o L2+V 85.89* 93.18 92.34* 89.11 90.83* 93.41 85.38 90.57* 79.08* 86.92 91.93 87.51* 87.01 85.02 75.30* 86.66*
w/o L2+S 86.12* 92.73* 90.84* 88.78* 90.41* 91.99* 83.81* 90.05* 78.11* 87.09 90.94* 87.63 87.34 85.04 76.77 86.58*
HDOurs (S) 14.41 10.72 10.41 13.80 11.63 6.59 7.88 16.95 16.39 12.12 11.93 13.93 14.76 7.19 9.12 19.97
w/o segmentation 14.41 9.98 10.44 15.04* 12.06 6.80 8.44 17.50 17.62 12.71 13.60* 14.57 15.70 7.89 8.91 20.73
w/o L2 14.32 10.86 10.49 14.63* 12.39 6.34 8.38 17.26 16.54 11.84 11.46 14.74 14.75 8.17* 9.86 20.52
w/o L2+V 14.42 10.41 10.27 14.43 12.34 6.30 6.78 * 17.55 17.09 12.47 11.79 14.40 14.39 7.51 9.93 21.19*
w/o L2+S 14.17 12.20* 12.58* 16.31* 13.54* 8.17* 9.46* 17.82 16.65 13.72* 14.35* 16.19* 16.07* 8.91* 10.37* 20.74
B. Construction of Cardiac Meshes for CFD Simulations
TABLE IV
ABLATION STUDY OF MESH REGULARIZATION LOSSES ON VESSEL INLET
AND OUTLET STRUCTURES ON CT TEST DATASET (N=20).
CoP+
Ortho+HWCoP+Ortho CoP None
Cap-Wall
Orthogonality ( ↓)LA 0.128 ±0.121 0.032±0.012 0.365 ±0.265 0.273 ±0.266
RA 0.023 ±0.008 0.012±0.008 0.105 ±0.038 0.066 ±0.026
Ao 0.019 ±0.023 0.005±0.006 0.467 ±0.117 0.127 ±0.024
Cap Coplanarity
(mm) (↓)LA 0.228 ±0.041 0.256 ±0.029 0.12±0.024 0.312 ±0.058
RA 0.34 ±0.073 0.339 ±0.055 0.185±0.043 0.466 ±0.114
Ao 0.447 ±0.115 0.429 ±0.063 0.263±0.068 0.852 ±0.16
Wall Chamfer
Distance (mm) ( ↓)LA 2.093 ±0.803 2.715 ±1.105 2.487 ±0.898 2.042±0.857
RA 2.021 ±1.176 2.66 ±1.301 2.231 ±0.983 1.899±0.952
1) Ablation Study of Individual Loss Components on Vessel
Inlet/Outlet Structures: CFD simulations of cardiac flow re-
quires well-defined inlet and outlet vessel structures to pre-
scribe boundary conditions for the inflow and outflow. Figure
7 and table IV demonstrate the effect of applying individual
regularization loss components on the predicted inlet and
outlet geometries (pulmonary veins, vena cava, and aorta).
Without any of the regularization losses, the predicted vessel
structure lacked well define caps. Indeed, our ground truth
meshes were generated from manual segmentations where
vessels were not truncated precisely orthogonal to the vessel
walls by the human observers, and the caps were not co-
planar due to necessary smoothing steps to filter out the
Fig. 7. Visualization of example whole heart surface predictions follow-
ing addition of regularization losses on vessel inlet/outlet structures. The
yellow regions highlight the ”caps” where the regularization losses were
applied.
staircase artifacts. The coplanar loss and the orthogonal loss
succeeded in producing more planar cap geometries that were
more orthogonal to vessel walls. Owning to the imperfect
ground truth vessel meshes, although adding regularization
losses to the training objective improved the structural quality
of inlet geometries, it slightly reduced the geometric accuracy
in terms of Chamfer distances compared with the ground truth.
Applying a higher weight on the inlet mesh vertices in the
geometric consistency loss was able to improve the geometricKONG et al. : LEARNING WHOLE HEART MESH GENERATION FROM PATIENT IMAGES FOR COMPUTATIONAL SIMULATIONS 9
TABLE V
COMPARISON OF DCS (↑)AND HDS(MM) (↓)OF PREDICTIONS
FROM DIFFERENT METHODS ON 4D CT TEST IMAGES (N=20). *
DENOTES SIGNIFICANT DIFFERENCE OF"OURS (S)" F ROM THE
OTHERS (P<0.05)
Myo LA LV RA RV Ao PA WH
DiceOurs (S) 89.53 93.30 94.48 92.91 94.32 96.20 85.31 93.14
Ours (V) 88.27* 91.60* 93.21* 92.18* 93.21* 95.62* 83.48* 91.97*
HeartFFDNet 84.37* 88.38* 91.41* 90.26* 90.19* 93.03* 70.44* 88.94*
MeshDeformNet 90.58 *95.18 *95.85 *93.50 94.63 *97.50 * 80.21* 93.94 *
HD (mm)Ours (S) 6.04 10.21 4.95 10.04 6.61 3.80 19.71 16.02
Ours (V) 5.91* 10.64 5.36 10.32 7.03* 4.16 19.14 15.69
HeartFFDNet 6.78* 12.01* 6.37 10.85* 8.77* 5.13* 23.20 16.46
MeshDeformNet 5.98 9.29 4.39 10.42 6.35*3.42 23.25 15.77
accuracy of vessel inlets while maintaining satisfactory mesh
quality for CFD simulations.
Fig. 8. Qualitative comparison of whole heart surfaces from different
methods at the end-diastolic phase and the end-systolic phase of a set
of time-series image data. The colormap for end-systolic surfaces shows
vertex displacement magnitude from end-systole to end-diastole.
2) Comparison with Other Methods on Time-Series CT Data:
Table V compares the reconstruction accuracy between our
method and the other baseline methods on end-diastolic and
end-systolic phases of a cardiac cycle. Overall, our method
demonstrated high accuracy comparable to the prior state-
of-the-art approach MeshDeformNet, both in terms of Dice
scores and Hausdorff distances. Figure 8 shows a qualitative
comparison of the reconstructed whole heart surfaces at end-
systolic and end-diastolic phases and the estimated surface
motion by computing the displacements of mesh vertices
over time. MeshDeformNet produced gaps between cardiac
structures as well as overly smoothed pulmonary veins and
vena cava geometries, since that method is biased by the
use of sphere templates rather than a more fitting template
of the whole heart. In contrast, our method produced high-
quality geometries of the vessel inlets and outlets as well
as whole heart geometries that better match with the ground
truth. Furthermore, our method demonstrated a more accurate
estimation of surface deformation over time, which is required
for prescribing boundary conditions for CFD simulations.
Figure 9 provides further qualitative comparisons between
using FFD and using biharmonic coordinates to deform the
template. Using biharmonic coordinates enables more flexible
Fig. 9. Comparison of whole heart surface predictions between using
control handles as in our approach and using FFD as in HeartFFDNet.
deformation and can thus more closely capture detailed ge-
ometries such as the left atrial appendage. In contrast, geome-
tries of left atrial appendage predicted from HeartFFDNet were
strongly biased by the geometries of the template, although it
used far more control points (4096) than our method (600).
Furthermore, our method was able to predict cardiac structures
that were not covered in the image data. Namely, thanks to
the augmentation pipeline, our method generated reasonable
geometries of the pulmonary arteries and pulmonary veins.
In contrast, manual segmentation can only produce surface
meshes of the cardiac structures captured in the images and
HeartFFDNet predicted flat and unphysiological geometries
despite starting from a realistic whole heart template.
We further quantified the accuracy of the predicted shape
of the heart outside the input image data. Since most images
from the time-series CT dataset did not cover the entire
heart, we selected 28 images that covered the entire heart
from the MMWHS CT test dataset, and cropped them above
various axial planes to evaluate the accuracy of the predicted
whole heart reconstruction when increasing portions of cardiac
structures were uncovered in the input images. Figure 10
(top) compares the average point-to-point distance errors for
each cardiac structures when the image volume was cropped
along the axial view before and after applying the proposed
random-cropping augmentation method and weighted losses
on the meshes. When the random-cropping augmentation
was applied, our method produced more accurate aorta and
pulmonary arteries. As expected, the distance errors increased
when more image data were removed. When as much as
30% of the image volume was removed, the average distance
errors of pulmonary arteries and aorta were around 1 cm with
the augmentation, whereas the average distance errors were
around 2.5 cm without the augmentation. Figure 10 (bottom)
visualizes three examples of the reconstruction results where
15%,22.5%, and 30% of the image data were removed. Our
method produced reasonable geometries of the pulmonary
arteries, pulmonary veins, and aorta in all cases. Although10 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. XX, NO. XX, XXXX 2020
our method tended to predict a shorter aorta when the image
data had limited coverage of the aorta, we note that the length
of aortic outlet is often arbitrary when creating meshes for
CFD simulations and thus does not significantly impact the
simulation results.
Fig. 10. Accuracy of shape completion of the heart when image data
has limited coverage for aorta, pulmonary arteries and veins. Top: A
comparison of point-to-point L2 distance between the meshes predicted
using uncropped input images and using cropped input images at varies
percentage, for network models trained without and with the random-
cropping augmentation. Bottom: Example prediction results for three
cases using uncropped input images and using cropped input images at
varies percentage. The color map on the meshes for uncropped images
indicates different cardiac structures whereas those for cropped images
indicates L2 distance in mm.
Table VI compares the quality of the predicted inlet and
outlet geometries as well as the percentage face intersection of
the whole heart meshes. Besides comparing with our baselines,
HeartFFDNet and MeshDeformNet, we also compared our
method with the surface meshes generated from applying the
Marching Cube algorithm on manual ground truth segmen-
tations, where the vessel inlet and outlet geometries were
manually trimmed by human experts. Our method produced
significantly better vessel inlet and outlet geometries than
HeartFFDNet and MeshDeformNet. Also, our method outper-
formed the manual segmentation in terms of Cap-Wall Or-
thogonality. When deforming the mesh template using control
handles, our method achieved the lowest percentage of face
intersection than other deep-learning methods, and the small
amount of face intersections that occurred could be readily
corrected by a few iterations of Laplacian smoothing.C. CFD Simulations of Cardiac Flow
We were able to successfully conduct CFD simulations
using the automatically constructed LV meshes for all 10
patients, as well as for 9 of 10 patients with the 4-chamber
meshes. The 1 failed case had structure penetrations between
two pulmonary veins, causing the simulation to diverge. Figure
11 displays the simulation results of the velocity streamlines
at multiple time steps during diastole for 2 different patients.
The simulation results demonstrate the formation of typical
vortex flow during ventricle filling.
Fig. 11. Velocity streamlines from CFD simulations of 2 different
patients using the predicted 4D meshes.
Fig. 12. Quantitative comparisons of the % errors in LV volume, volume
averaged KE density, mean velocity near the MO during diastole and
mean velocity near the AO during systole among different methods.
Lines show the mean values and shades show the 95% confidence
intervals.
Figure 12 provides quantitative comparisons of the ac-
curacy of CFD simulation results of LV flow. Both our
approach and HeartFFDNet significantly outperformed the
image-registration-based approach in terms of all metrics.
Namely, the image-registration-based method significantly un-
derestimated the LV volume during diastole since the recon-
structed meshes did not capture the large deformation of LV
from systole to diastole. Our proposed approach demonstrated
comparable or slightly better accuracy than HeartFFDNet in
general, with smaller volume errors throughout the cardiac
cycle and smaller errors in average kinetic energy and mean
aortic flow velocity during systole.KONG et al. : LEARNING WHOLE HEART MESH GENERATION FROM PATIENT IMAGES FOR COMPUTATIONAL SIMULATIONS 11
TABLE VI
ACOMPARISON OF THE QUALITY OF THE INLET /OUTLET GEOMETRIES AND WHOLE HEART SURFACE QUALITY FROM DIFFERENT METHODS .
Cap-Wall Orthogonality ( ↓) Cap Coplanarity (mm) ( ↓) % Face Intersection ( ↓)
LA RA Ao LA RA Ao WH
Ours (V) 0.038±0.046 0.013±0.007 0.013±0.012 0.22±0.024 0.284±0.044 0.292±0.088 0.018±0.022
HeartFFDNet 0.137 ±0.08 0.228 ±0.182 0.494 ±0.386 0.398 ±0.068 0.45 ±0.125 0.949 ±0.557 0.262 ±0.191
MeshDeformNet 0.106 ±0.104 0.044 ±0.038 0.209 ±0.117 1.145 ±0.165 0.917 ±0.379 0.36 ±0.216 0.034 ±0.068
Manual 0.04 ±0.04 0.034 ±0.054 0.025 ±0.023 0.037 ±0.009 0.035 ±0.007 0.02 ±0.003 0.0 ±0.0
Fig. 13. Qualitative comparisons of the simulated flow pattern from different methods at different time phases during a cardiac cycle for an example
case. Left: Streamlines within the left ventricle models. Right: Contours of the velocity magnitude at the same clipping plane. Color map shows the
velocity magnitude
Figure 13 qualitatively compares the simulated LV flow
pattern during both systole and diastole using meshes automat-
ically constructed by our proposed approach and HeartFFD-
Net, semi-automatically constructed by conventional image
registration and manually constructed by human observers.
Image registration underestimated the LV expansion from end
systole to diastole, leading to underestimated flow velocity
and disparate flow pattern compared with the ground truth.
Both of our approaches generally produced similar vortex
structures during diastole and converging flow during systole,
with moderate differences in flow velocity and vortex locations
compared with the ground truth.
V. D ISCUSSION
Automated image-based reconstruction of cardiac meshes is
important for computational simulation of cardiac physiology.
While deep-learning-based methods have demonstrated suc-
cess in tasks such as image segmentation and registration, fewstudies have addressed the end-to-end learning between images
and meshes for modeling applications. Furthermore, prior
learning-based mesh reconstruction approaches suffer from
a number of limitations such as using decoupled meshes of
individual cardiac structures and assumed mesh topology, thus
unable to directly support different cardiac simulations without
additional efforts [14], [15]. We addressed this challenge
herein using a novel approach that trains a neural network
to learn the translation of a small set of control handles to
deform the space enclosing a whole heart template to fit
the cardiac structures in volumetric patient image data. Our
method demonstrated promising whole-heart reconstruction
accuracy and was able to generate simulation-ready meshes
from time-series image data for CFD simulations of cardiac
flow.
Our approach achieved comparable geometric accuracy to
the prior state-of-the-art whole heart mesh reconstruction
method MeshDeformNet [15] while having the additional
advantage of directly enabling various cardiac simulations. We12 IEEE TRANSACTIONS ON MEDICAL IMAGING, VOL. XX, NO. XX, XXXX 2020
TABLE VII
COMPARISON OF MODEL SIZE ,TRAINING AND TESTING TIME .
Ours HeartFFDNet MeshDeformNet 2D UNet 3D UNet
# of Parameters 8.7M 8.5M 16.8M 31.1M 18.6M
Training Time 18 hrs 26 hrs 32 hrs 7 hrs 37 hrs
Test Time 0.230s 0.177s 0.425s 1.555s 0.367s
note that our approach used fewer parameters in the CNN
encoder compared to MeshDeformNet (Table VII) and the use
of biharmonic coordinates naturally ensures the smoothness of
deformation without using explicit mesh regularization (e.g.,
Laplacian and/or edge length loss constraints [15]). This is im-
portant since mesh regularization schemes can complicate the
optimization process [37], whereas we observed our approach
to converge significantly faster than MeshDeformNet (18 vs
32 hrs on a GTX2080Ti GPU).
For CFD simulations requiring the time-dependent mo-
tion of the heart over the cardiac cycle, our method has
the advantage of deforming the template mesh in a tem-
porally consistent manner, enabling automated construction
of dynamic cardiac meshes within minutes on a standard
desktop computer. Registration-based approaches, in contrast,
often require test time optimizations that are computationally
expensive and prone to local minimums, which often lead
to inaccurate registration results such as underestimation of
large deformation. Although deep-learning approaches have
been proposed to speed-up the registration process [38], [39],
large-deformation registration on cardiac images remains chal-
lenging for learning-based approaches. The establishment of
temporal feature correspondence of our method is due to
similar features of time-series images naturally being encoded
into similar feature vectors by the CNN encoders and does
not require explicit training. Nevertheless, ground truth data
of anatomical landmarks could be incorporated in the future
during training to further improve the accuracy of feature
correspondence across different time frames or patients.
Blood flow simulations developed from our automated mesh
generation process demonstrated circulatory flow patterns dur-
ing diastole and converging flow patterns during systole in the
ventricular cavity consistent with prior studies [2], [40]. How-
ever, we observed an average of 15-25% error in the simulated
mean velocity and kinetic energy, despite a promising mean
LV Dice scores of 93% and an mean volume error of 6%. Such
amount of volume error is consistent with the inter- and intra-
observer variations of manual LV segmentation [10], [15].
Indeed, simulation of blood flow is sensitive to uncertainties in
geometry, such as inflow directions and vessel and/or LV wall
smoothness [40], [41]. We plan to conduct intra- and inter-
observer studies on the ground truth meshes to further un-
derstand the relationship between prediction uncertainties and
the accuracy of CFD simulations. Nevertheless, our approach
is among the first to enable creation of simulation-suitable
meshes from patient images. And our design of using template
meshes and control handles could support shape editing and
analysis to study the effect of geometric variations on CFD
simulations.
Our proposed method has the following limitations. First,
the testing images we used from the benchmark MMWHStest dataset and the times-series CT dataset do not cover the
full variations of cardiac abnormalities observed clinically. For
example, our test datasets did not contain patients with con-
genital heart defects and thus the performance of our trained
network for those patients were not evaluated. Furthermore,
image data used to training and testing using relatively similar
imaging protocols and parameters, such as slice thickness,
field of view, and spatial orientation. The above limitations
can be addressed by retraining the model with data more
representative of particular use cases (e.g. particular abnor-
malities or scanner protocol). A related limitation is that the
whole-heart template used may need to be modified to capture
richer variations of cardiac malformations. For example, the
current template assumes four separate and distinct pulmonary
vein ostia and thus may not fully capture pulmonary veins
with alternate branching patterns, which can be important
for preoperative planning of pulmonary and cardiac surgery
[42]. Similarly, the template used would not be suitable for
cardiac malformations such as single-ventricle patients with
congenital heart diseases since the structures of the heart
are significantly different from our current training template.
Nonetheless, this framework could still be utilized if sufficient
training data of, say, single-ventricle patients were available
and a corresponding single-ventricle mesh template were used.
To better handle the above applications, in future work we aim
to add a template retrieval module to automatically select a
template that best suits the application. Furthermore, implicit
shape representation [43] can be combined with our learning-
based shape deformation approach to predict cardiac structures
with different anatomies.
VI. C ONCLUSION
We proposed a novel deep-learning approach that directly
constructs simulation-ready whole heart meshes from cardiac
image data and allows switching of template meshes to
accommodate different modeling requirements. Our method
leverages a graph convolutional network to predict the trans-
lations of a small set of control handles to smoothly deform
a whole heart template using biharmonic coordinates. Our
method consistently outperformed prior state-of-the-art meth-
ods in constructing simulation-ready meshes of the heart, and
was able to produce geometries that better satisfy modeling
requirements for cardiac flow simulations. We demonstrated
application of our method on constructing dynamic whole
heart meshes from time-series CT image data to simulate the
ventricular flow driven by the cardiac motion. The presented
approach is able to automatically construct whole heart meshes
within seconds on a modern desktop computer and has the
potential in facilitating high-throughput, large-cohort valida-
tion of patient-specific cardiac modeling, as well as its future
clinical applications.
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