A comprehensive stroke risk assessment by combining atrial computational fluid dynamics simulations and functional patient data

Abstract

Stroke, a major global health concern often rooted in cardiac dynamics, demands precise risk evaluation for targeted intervention. Current risk models, like the CHA2DS2-VASc score, often lack the granularity required for personalized predictions. In this study, we present a nuanced and thorough stroke risk assessment by integrating functional insights from cardiac magnetic resonance (CMR) with patient-specific computational fluid dynamics (CFD) simulations. Our cohort, evenly split between control and stroke groups, comprises eight patients. Utilizing CINE CMR, we compute kinematic features, revealing smaller left atrial volumes for stroke patients. The incorporation of patient-specific atrial displacement into our hemodynamic simulations unveils the influence of atrial compliance on the flow fields, emphasizing the importance of LA motion in CFD simulations and challenging the conventional rigid wall assumption in hemodynamics models. Standardizing hemodynamic features with functional metrics enhances the differentiation between stroke and control cases. While standalone assessments provide limited clarity, the synergistic fusion of CMR-derived functional data and patient-informed CFD simulations offers a personalized and mechanistic understanding, distinctly segregating stroke from control cases. Specifically, our investigation reveals a crucial clinical insight: normalizing hemodynamic features based on ejection fraction fails to differentiate between stroke and control patients. Differently, when normalized with stroke volume, a clear and clinically significant distinction emerges and this holds true for both the left atrium and its appendage, providing valuable implications for precise stroke risk assessment in clinical settings. This work introduces a novel framework for seamlessly integrating hemodynamic and functional metrics, laying the groundwork for improved predictive models, and highlighting the significance of motion-informed, personalized risk assessments.

Full text

A comprehensive stroke risk assessment by
combining atrial computational fluid dynamics
simulations and functional patient data
Alberto Zingaro1,2,3,*, Zan Ahmad1,4, Eugene Kholmovski1, 5, Kensuke Sakata1, Luca
Dede’2, Alan K. Morris6, Alfio Quarteroni2,7, and Natalia A. Trayanova1
1ADVANCE, Alliance for Cardiovascular Diagnostic and Treatment Innovation, Johns Hopkins University, 3400 N.
Charles St., 21218, Baltimore, MD, USA
2
MOX, Laboratory of Modeling and Scientific Computing, Dipartimento di Matematica, Politecnico di Milano, Piazza
Leonardo da Vinci 32, 20133, Milano, Italy
3ELEM Biotech S.L., Pier07, Via Laietana, 26, 08003, Barcelona, Spain
4Department of Applied Mathematics and Statistics, Johns Hopkins University, 100 Wyman Park Dr, 21211,
Baltimore, MD, USA
5Department of Radiology, University of Utah, 30 N Mario Capecchi Dr., 84112, Salt Lake City, UT, USA
6
Scientific Computing and Imaging Institute, University of Utah, 72 Central Campus Dr., 84112, Salt Lake City, UT,
USA
7
Institute of Mathematics,
´
Ecole Polytechnique F
´
ed
´
erale de Lausanne, Station 8, Av. Piccard, CH-1015 Lausanne,
Switzerland (Professor Emeritus).
*alberto.zingaro@polimi.it
ABSTRACT
Stroke, a major global health concern often rooted in cardiac dynamics, demands precise risk evaluation for targeted intervention.
Current risk models, like the
CHA2DS2-VASc
score, often lack the granularity required for personalized predictions. In this
study, we present a nuanced and thorough stroke risk assessment by integrating functional insights from cardiac magnetic
resonance (CMR) with patient-specific computational fluid dynamics (CFD) simulations. Our cohort, evenly split between
control and stroke groups, comprises eight patients. Utilizing CINE CMR, we compute kinematic features, revealing smaller left
atrial volumes for stroke patients. The incorporation of patient-specific atrial displacement into our hemodynamic simulations
unveils the influence of atrial compliance on the flow fields, emphasizing the importance of LA motion in CFD simulations
and challenging the conventional rigid wall assumption in hemodynamics models. Standardizing hemodynamic features with
functional metrics enhances the differentiation between stroke and control cases. While standalone assessments provide
limited clarity, the synergistic fusion of CMR-derived functional data and patient-informed CFD simulations offers a personalized
and mechanistic understanding, distinctly segregating stroke from control cases. Specifically, our investigation reveals a
crucial clinical insight: normalizing hemodynamic features based on ejection fraction fails to differentiate between stroke and
control patients. Differently, when normalized with stroke volume, a clear and clinically significant distinction emerges and
this holds true for both the left atrium and its appendage, providing valuable implications for precise stroke risk assessment
in clinical settings. This work introduces a novel framework for seamlessly integrating hemodynamic and functional metrics,
laying the groundwork for improved predictive models, and highlighting the significance of motion-informed, personalized risk
assessments.
Introduction
Stroke remains a formidable medical challenge worldwide, posing a significant threat to both life and quality of life. According
to the World Stroke Organization, 13 million people experience stroke per year and, of those, 5.5 million die as a result
1
.
Characterized by a sudden interruption of blood flow to a part of the brain, stroke often results in long-lasting neurological
impairments
2
. The left atrium (LA) and left atrial appendage (LAA) are known to be pivotal in the multifaceted etiology of
stroke
3
. Thrombi, or clots, in this chamber, once formed, can embolize and travel to the cerebral circulation, precipitating an
ischemic stroke. Anomalies in the LA/LAA shape and function have been increasingly recognized as a potential precursor of
cerebrovascular events such as ischemic stroke
4,5
, necessitating a closer examination of the intricate morphological, functional,
and hemodynamic characteristics of this cardiac chamber. Atrial fibrillation (AF), a common arrhythmia, is often associated
with alterations in LA structure and biomechanics, contributing to stasis of blood flow and fostering a pro-thrombotic state
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patient ID sex age other pathologies BPM Period [s]
Control
C1 M 44 none 57.1 1.05
C2 M 56 none 50.3 1.19
C3 M 45 none 57.7 1.04
C4 M 49 none 51.5 1.17
Stroke
S1 F 29 none 76 0.79
S2 M 65 hypertension 67 0.90
S3 F 69 hypertension 51.5 1.17
S4 F 60 diabetes mellitus 69 0.87
Table 1. Information of the eight patients considered in the study.
within the atrium
6,7
. Congestive heart failure and hypertension are also linked with increased stroke risk
8–10
. Thus, it is clear
that a deeper understanding of LA hemodynamics can pave the way to the development of predictive models for stroke risk in
susceptible populations.
Contemporary risk assessment tools, such as the
CHA2DS2-VASc
score, while ubiquitously used, predominantly focus
on patient-centric risk factors, such as age, sex, and comorbidities, and do not consider factors pertaining to LA morphology
and function
11
. Oral anticoagulant (OAC) therapy is prescribed for AF patients based on this score
12
. However, OACs have
the potential to cause severe internal bleeding including intracerebral hemorrhage and are associated with higher mortality
rates
11,13
, necessitating an accurate assessment of OAC need. Unfortunately, the
CHA2DS2-VASc
score has severe limitations
in its predictive capabilities of stroke. This one-size-fits-all approach has been shown to be inaccurate and inconsistent over
various patient cohorts
14,15
. Several studies showed that patients might be administered too many OACs and exposed to its
side effects without deriving any benefit from it, or are incorrectly classified as low risk and thus are not protected
11,16,17
. In
addition, for patients who do not have AF, or in patients that exhibit asymptomatic arrhythmias and atrial high-rate episodes, it
is difficult to accurately assess stroke risk, since the
CHA2DS2-VASc
is not directly applicable
18,19
. Therefore, it is crucial
to precisely identify the patients who truly require these treatments, ensuring that high-risk individuals are not misclassified
as low risk, while also avoiding unnecessary exposure to the side effects of the medications and procedures administered for
those at lower risk. This gap in current risk stratification models underscores an urgent need for a more nuanced, individualized
approach that encapsulates the hemodynamic intricacies and geometric variabilities inherent within the LA. This need can be
addressed by the use of in-silico methodologies as a noninvasive tool to predict the likelihood of thrombus formation and stroke
risk in an individual subject20–32.
The use of computational fluid dynamics (CFD) models to assess hemodynamics in the LA/LAA has gained significant
attention in recent years for the purposes of thrombosis and stroke risk assessment, specifically in cohorts of AF patients. For
this purpose, Garcia et al. used rigid wall assumptions for CFD simulations on idealized ellipsoidal geometries synthetically
created to resemble the atrium
33
. Many studies utilized patient-specific 3D computed tomography (CT) images to simulate
flow dynamics across distinct LAA morphologies in AF and stroke patients. However, the majority of these studies ignore the
contractility of the atrial chamber by carrying out simulations under the assumption of a rigid LA wall
34–40
. In contrast, recent
studies have demonstrated that considering the contractility motion of the atrial walls, as opposed to rigid assumptions, yields
distinct flow fields in the atrium
22,26,27,41
. As a matter of fact, the rigid wall assumption tends to overestimate thrombosis risk
37
and is representative of a very specific and extreme case of AF (chronic AF)
42
. In order to account for endocardial motion in
CFD simulations, some researchers have developed methods for artificially computing the wall LA displacement to study stroke
risk stratification. Musotto et al.’s work utilized idealized assumptions for LAA mechanical properties in CFD simulations
43
.
Masci et al. introduced a definition of wall motion by applying a random displacement function to AF patient-specific 3D
geometries
44
. Zingaro et al. leveraged an idealized displacement model with a 0D closed-loop circulation model to compute
an LA boundary motion
45
. The method was then extended by Corti et al. to study the impact of AF on hemodynamics
21
.
However, in the absence of clinical data, all these displacements remained idealized and non-patient-specific. Differently,
with the use of dynamic patient-specific data such as CINE MRI or 4D CT scans, hemodynamic models can be more realistic
and patient-specific. Few examples of patient-specific displacement-informed CFD simulations are available in the literature;
however, they all focus on a small cohort of patients. Garcia-Villalba et al. perform CFD simulations in a cohort of six patients
and use 4D CT scans for boundary displacement in AF patients with and without thrombus formation
26
. Otani et al. carried
out CFD simulations with displacement from CINE MRI in two AF patients
46
. A 3D interpolation algorithm was applied
by Qureshi et al. for smoothing and minimization of discontinuities between slices to form a single patient-specific surface
mesh of the LA with CINE MRI
39,47
. Dueñas-Pamplona et al. used dynamic 4D CT data to simulate an LA CFD model in
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Figure 1. Biomarkers computed from dynamic meshes. In blue (
■
), control cases; in red (
■
), stroke cases. From the top left
to bottom right: maximum (circle) and minimum (cross) LA volume, LA stroke volume, LA ejection fraction, ostium area of
LAA, maximum (circle) and minimum (circle) LAA volume, LAA stroke volume, LAA ejection fraction, tortuosity of the
LAA.
two AF patients for the purpose of model verification and proof of concept of using patient-specific boundary conditions. The
insufficiency of these approaches – both in terms of wall modeling and size of the patient cohort – highlights the urgent need for
more comprehensive studies accounting for atrial contractility and a larger number of patients to achieve a more personalized
and mechanistic assessment of stroke risk.
In this paper, we assess stroke risk through atrial CFD simulations, incorporating patient-specific wall displacement
derived from image data. We consider a cohort of eight patients, evenly divided into stroke and control cases. We do
not restrict the patient cohort to AF patients as many of the aforementioned works do, allowing for generalizable insights
into the correlation between LA hemodynamics and stroke, independently of the precurring pathology. To run personalized
hemodynamic simulations, we merge CINE cardiac magnetic resonance (CMR) and contrast-enhanced (CE) magnetic resonance
angiography (MRA) to obtain accurate time-deforming volumetric meshes. To begin, we analyzed functional and morphological
characteristics of the LA and LAA directly from the CMR to identify distinguishing biomarkers between the two patient groups.
Then, we performed CFD simulations driven by the patient-specific displacements. We found that hemodynamic features from
the LA chamber alone do not separate well between the stroke and control groups of our cohort. Differently, when we plot our
hemodynamic computations against the functional and morphological features, we find several fluid dynamics features to be in
a separate range for the stroke group. Specifically, we provide a comprehensive merging of all our computed hemodynamic
features with the functional data and morphological characteristics of the LA and LAA. We report that several of these new
quantities provide clear distinctions between the stroke patients and control patients in our cohort, especially when normalized
with maximum volume, stroke volume, and beats per minute. This study presents an innovative framework that seamlessly
integrates hemodynamic and functional metrics, establishing a foundation for enhanced predictive models. It underscores
the vital role of motion-informed, personalized risk assessments. Importantly, no other study has explored the integration of
hemodynamic features with functional or morphological computations to achieve a personalized and comprehensive stroke risk
assessment.
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Figure 2. LA volumes and MV flowrate versus time for the control and stroke cases. In blue (■), control cases; in red (■),
stroke cases.
Control Stroke
C1 C2 C3 C4 S1 S2 S3 S4
E-wave [mL/s] 433.0 799.8 568.7 717.0 430.8 432.1 484.7 475.5
A-wave [mL/s] 336.9 817.4 512.9 632.7 298.1 492.5 469.4 401.1
EA ratio [–] 1.29 0.98 1.11 1.13 1.45 0.88 1.03 1.18
Table 2. MV flowrate peaks at E-wave and A-wave; EA ratio.
Results
To unravel the biomarkers associated with the risk of stroke development, we systematically compute and analyze various
features related to the LA/LAA geometry, its functioning, and hemodynamics. Starting with patient-specific data, we introduce
a set of biomarkers encoding information on the geometry and functioning of the LA and its appendage. Subsequently, our focus
shifts to the hemodynamics of both the LA and LAA, exploring the outcomes derived from the personalized CFD simulations.
In conclusion, in a cohesive approach aimed at providing a more personalized and mechanistic understanding of each patient,
we integrate these insights by combining functional data with fluid dynamics features.
Functional data
Our patient cohort consists of eight patients: four control, and four stroke cases. Patient characteristics are shown in Table 1.
Stroke patients presented higher beats per minute (BPM), hence a lower heartbeat period. To assess geometry and functioning
of the LA, in Figure 1, we present a set of biomarkers derived from dynamic meshes, which were generated based on CMR
data. Notably, control patients, with the exception of C1, show larger maximum and minimum LA volumes in comparison to
stroke patients. Moreover, stroke patients generally exhibit lower stroke volumes (SV) compared to the control group. However,
in terms of ejection fraction (EF) of the LA chamber, a clear differentiation between the two categories is not readily apparent.
Additionally, we perform a similar analysis on the LAA across various time frames. Similar to the LA, we observe that
control cases tend to have a larger LAA volume, with the exception of C1. Furthermore, similar to the primary chamber, stroke
patients typically exhibit reduced SV, while EF does not distinguish between the two categories. For the LAA, we additionally
compute the ostium area (OA) and the tortuosity (
τ
) at the time corresponding to the minimum LA volume, which coincides
with the closure of the mitral valve (MV). Large tortuosity values usually reflect the complexity of LAA shape
44
. Nonetheless,
both of these features did not reveal specific discernible patterns. It is worth noting that stroke patients generally demonstrated a
narrower range of variation in these measurements when compared to the control group, despite the lack of a distinctive pattern.
Results from hemodynamic simulations
To explore the atrial hemodynamics, we now showcase the outcomes of our personalized CFD simulations. Figure 2presents
the transient data of LA volumes and flowrates calculated at the MV section for both control and stroke cases. Consistent with
our functional data, stroke patients consistently exhibit diminished LA volumes. Similarly, our simulation results indicate
reduced flowrates at the valve section in stroke patients. Additionally, we evaluate the MV flowrate during the E-wave and
A-wave for all patients, as detailed in Table 2. Notably, our findings reveal that the EA ratio does not serve as a discriminating
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(a) control: C1 (b) control: C2 (c) control: C3 (d) control: C4
(e) stroke: S1 (f) stroke: S2 (g) stroke: S3 (h) stroke: S4
|⟨u
u
u⟩| [m/s]
Figure 3. Volume rendering of phase-averaged velocity magnitude with glyphs of velocity at the A-wave peak. Top (a-d):
control cases; bottom (e-h): stroke cases.
factor for assessing stroke risk.
Figure 3is a visual representation of the phase-averaged blood velocity captured at the A-wave peaks. These time points
were determined by examining the transient MV flowrates (Figure 2). A common observation across all cases reveals a dynamic
mixing of blood within the LA, as it courses toward the MV section, giving rise to an intricate blood flow pattern. Our analysis
indicates larger velocities in proximity to the pulmonary veins, while the blood flow in the LAA exhibits a considerably slower
pace. In stark contrast to the control cases, stroke patients consistently display reduced velocity in the pulmonary veins, the LA,
and its appendage. This aligns with the MV flowrate measurements depicted in Figure 2.
To assess comprehensively the impact of stroke on atrial flows, we calculate various hemodynamic features that gauge
endothelial susceptibility and the likelihood of thrombus formation. These include:
• Flow Stasis (FS), representing the fraction of time during a heartbeat in which the velocity falls below 0.1 m/s21,48.
• Time Averaged Wall Shear Stress (TAWSS), serving as an average measure of shear stress at endocardial walls.
•
Oscillatory Shear Index (OSI), quantifying the degree of change in wall shear stress (WSS) throughout the cardiac cycle.
•
Relative Residence Time (RRT), proportional to the residence time of blood particles near the wall, identifying areas
with both low and oscillatory WSS49,50.
•
Endothelial Cell Activation Potential (ECAP), detecting regions characterized by oscillatory and low-stress conditions
51
.
In Figure 4, boxplots illustrate the distribution of hemodynamic features computed for the entire LA at the top and its auricle at
the bottom, discerning between stroke and non-stroke cases. Notably, both groups display substantial variability in results,
marked also by the presence of numerous outliers. Focusing on the median values, our analysis for the LA reveals that
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Figure 4. Boxplots of hemodynamics features computed with patient-specific CFD simulations in the LA. From the left to the
right: FS, TAWSS, OSI, RRT, and ECAP. In blue (
■
), control cases; in red (
■
), stroke cases. The same analysis for the LAA is
provided in Supplementary Figure 1 in Supplementary Material.
all the examined features effectively differentiate between stroke and non-stroke cases, with the exception of S4 (see also
Supplementary Table 1 in Supplementary Material). Specifically, stroke cases exhibit higher FS, reduced TAWSS, and elevated
OSI, RRT and ECAP. This pattern is notably pronounced in the LA. In contrast, the LAA does not exhibit a discernible
distinction between the two subgroups (results for the LAA are provided in Supplementary Figure 1 and Supplementary Table 1
in Supplementary Material). The nuanced variations between the main chamber and its auricle underscore the complexity of
hemodynamic responses in stroke and non-stroke scenarios. This also suggests the need to incorporate additional patient-specific
data into our analysis, such as anatomical and functional measurements from CMR scans.
Merging functional data with hemodynamics features
In our pursuit of a comprehensive understanding of atrial hemodynamics and its implications for predicting stroke risk, we
focus on the median values of each hemodynamic feature. We plot these values against a set of biomarkers directly derived from
CMR data, encompassing functional parameters such as maximum and minimum LA volumes, SV, EF, and BPM. We show
these results in Figure 5, leveraging a logistic regression model with a binomial distribution to distinguish between stroke and
non-stroke subgroups. The black dashed lines in the plot represent the predictions of the logistic model within the parameter
space of interest. The logistic regression line on the plot serves as a predictive boundary. When this line effectively separates
the data points (stroke and control groups), it indicates a correlation between the hemodynamic features and functional data in
terms of stroke prediction. Remarkably, the maximum LA volume emerges as a robust discriminator between the two groups
when plotted against all hemodynamic features, with the exception of TAWSS. Conversely, the minimum volume serves as a
discriminant for the FS only. Furthermore, atrial SV consistently proves to be a reliable metric for segregating the subgroups,
while the EF of the LA falls short in discerning differences across all hemodynamic features. Interestingly, BPM emerges as a
clear distinguishing factor between the two subgroups. Notably, the inclusion of functional measurements, such as SV and
BPM, has a transformative effect, reclassifying case S4 from an outlier to a position within the stroke area of the plot.
In Figure 6, we extend our study to focus on the LAA, considering both functional and anatomical measurements. These
encompass maximum and minimum LAA volumes, LAA SV, LAA EF, BPM, tortuosity, and OA. In contrast to the LA,
identifying a functional feature capable of effectively distinguishing between the stroke and non-stroke subgroups proves to
be a more intricate challenge for the LAA. Remarkably, our investigation reveals that LAA SV emerges as a the only robust
measure that adeptly characterizes the two subgroups across all considered hemodynamic features in this study. It is noteworthy
to mention that, in the absence of any functional measure, the mechanistic insights provided solely by hemodynamic features
fall short in distinguishing the two groups for the LAA.
A look into the transitional-to-turbulence regime
To delve into the impact of stroke on the transitional-to-turbulence regime that may occur in atrial flows
50
, in Figure 7a, we
present the temporal evolution of kinetic energy (
Ek
) and enstrophy (
S
) for both control and stroke patients. Consistently
with elevated flow stasis and diminished velocities, stroke patients exhibit lower kinetic energies. However, the enstrophy,
representing vorticity production and dissipation, i.e. a measure of turbulence
50,52,53
, does not reveal a discernible pattern
between stroke and control patients.
For a more in-depth exploration of the effects of stroke on turbulence, we analyze the vorticity magnitude (
|ω
ω
ω|
) at three
distinct phases of the heartbeat: E-wave peak, A-wave peak, and systolic filling (when the MV is closed) for both the LA and the
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LAA. As with previous features, we plot these results against various functional measurements of the LA. Figure 7b specifically
showcases the outcomes for measurements demonstrating correlation. Similar to previous hemodynamic features, we observe
correlations with LA maximum volume, LA SV (except for
|ω
ω
ω|(A)
, which presents an outlier), BPM, and LAA SV. For a
comprehensive view of the additional results against all functional features see Supplementary Figure 2 and Supplementary
Figure 3 in Supplementary Material.
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Figure 5. Medians of hemodynamics features in the LA against functional data from CMR. In blue (
■
), control cases; in red
(
■
), stroke cases. The black-dashed line is obtained by running logistic regression. From top to the bottom: FS, TAWSS, OSI,
RRT, and ECAP are plotted against maximum LA volume, minimum LA volume, LA SV, LA EF, and BPM (from left to right).
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Figure 6. Medians of hemodynamics features in the LAA against functional data from CMR. In blue (
■
), control cases; in red
(
■
), stroke cases. The black-dashed line is obtained by running logistic regression. From top to the bottom: FS, TAWSS, OSI,
RRT, and ECAP are plotted against maximum LAA volume, minimum LAA volume, LAA SV, LAA EF, BPM, tortuosity, and
OA (from left to right).
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(a)
(b)
Figure 7. A look into turbulence. (a) Kinetic energy Ekand enstrophy Sversus time for the control and stroke cases. (b)
Medians of vorticity magnitude against functional data from CMR. In blue (■), control cases; in red (■), stroke cases. The
black-dashed line is obtained by running logistic regression. From top to the bottom: vorticity magnitude at E-wave, A-wave,
and systolic peak (MV closed) are plotted against LA maximum volume, LA SV, BPM, and LAA SV (from left to right).
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LA LAA
vs no yes no yes
functional?
Vmax
LA Vmin
LA SVLA EFLA
BPM
Vmax
LAA Vmin
LAA SVLAA EFLAA
BPM
τOA
FS
TAWSS
OSI
RRT
ECAP
|ω
ω
ω|(E)
|ω
ω
ω|(A)
|ω
ω
ω|(S)
■: correlated ■: not-correlated
Table 3. Correlation between hemodynamic features (derived from CFD simulations) and functional measurements (from
CMR) for the LA and LAA. ■and ■indicate correlation and non-correlation, respectively, in distinguishing stroke by
non-stroke cases.
Discussion
The objective of this paper was to deliver precise and personalized assessments of stroke risk through patient-specific LA
hemodynamic simulations. The study integrated functional characteristics obtained from CMR with hemodynamic insights
derived from patient-specific CFD simulations, which considered the motion of the LA. Standalone analyses of functional and
hemodynamic features did not distinctly differentiate between stroke and control cases. However, through a synergistic merging
of these variables, a clear distinction between the two groups emerged, offering a personalized and mechanistic assessment of
stroke risk.
Our cohort comprised eight patients, evenly split between control and stroke cases. While a majority of previous works on
assessing left atrial hemodynamics for stroke and thrombosis risk focused on patients with AF, our cohort does not include any
AF patients. This study presents a framework that gives insight into stroke risk metrics for populations who had stroke but
who not necessarily had episodes of AF. Indeed, many of the previous computational and clinical studies are solely focused on
the link between atrial hemodynamics and stroke risk in AF patients only. This enabled us to provide broader observations
regarding the connection between LA hemodynamics, LA functioning and stroke, irrespective of the precurring pathology.
Most of the CFD research works on this topic assume rigid LA wall, whereas the works in which a realistic displacement is
included are always confined to a small number of patients. In this paper, we incorporated CINE CMR in our patient-specific
simulations and, to the best of our knowledge, this is the study with the largest cohort of patients utilizing patient-specific LA
motion. This is a crucial aspect in atrial CFD simulations since, as often evidenced in the literature
22,26,27,41
, incorporating
motion into hemodynamic simulations yields diverse flow fields in the left atrium, potentially influencing the accuracy of
hemodynamic biomarkers used in stroke risk assessment.
By analyzing features directly extracted from CMR, we observed that stroke patients generally exhibited lower volumes,
BPM, and SV. However, a clear threshold between the two subgroups was elusive for these features. Surprisingly, left atrial EF
failed to distinguish between the two subgroups. Similar trends were noted in the LAA, where lower volumes and SV were
observed for stroke cases, yet no distinct threshold emerged for any features, including LAA EF. This suggested the limited
utility of EF as a stroke risk assessment biomarker (for both LA and LAA), possibly influenced by the inherent uncertainty
associated with its definition.
Turning to hemodynamic simulations, our findings demonstrated that stroke patients generally exhibited lower velocities,
increased blood stasis, reduced wall shear stress, and higher values of OSI, RRT, and ECAP. However, this trend applied to all
cases except one: an outlier in standalone CFD analysis. Additionally, stroke patients displayed lower kinetic energies, and
only the vorticity magnitude at the A-wave could effectively differentiate between the two groups for all patients. Despite a
clear pattern observable between stroke and control cases, outliers consistently appeared for almost all features, precluding the
identification of some clear-cut hemodynamics features for distinguishing between the two groups, as we summarize in Table 3.
To address variability in chamber functionalities, geometries, and contractile properties, we standardized our findings with
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CONTROL
STROKE
C1 C2 C3 C4
S1 S2 S3 S4
Figure 8. Tetrahedral meshes of the LA for the CFD simulations: control (top) and stroke (bottom) patients.
functional metrics. This approach, characterizing hemodynamic metrics with respect to maximum volume, SV and BPM,
provided a clearer distinction between stroke and control cases across all hemodynamic features considered in this study.
Similar challenges were noted for both the LA and the LAA in standalone assessments; however, standardizing fluid dynamics
results with LAA SV revealed a clear division between the two groups. We provide a clear picture of this standardization
in Table 3. Thus, our investigation unveiled a crucial clinical insight: the normalization of hemodynamic features based on
ejection fraction failed to differentiate between stroke and control patients. In contrast, normalization with stroke volume
revealed a clear and clinically significant distinction, applicable to both the left atrium and its appendage. These findings have
noteworthy implications for precise stroke risk assessment in clinical settings.
While emphasizing the crucial need to merge these datasets, we underscore the importance of incorporating chamber
motion in simulations and data analysis. This highlights the implicit impact of the common assumption of treating the atrium
endocardium as rigid in CFD models: a simplification that streamlines the computational process but may lead to potentially
inaccurate estimations of stroke risk. Our results align with recent work by Sanatkani et al
37
, which also discusses the potential
overestimation of thrombogenic risk in the common assumption of rigid walls.
This work has a few limitations. While incorporating patient-specific atrium motion enhanced the reliability of our results,
it constrained us to a relatively small number of patients. Nevertheless, to our knowledge, this study boasts the largest cohort
of patients utilizing patient-specific LA motion. As part of future directions, we aim to expand the study to include a larger
number of patients, with a consideration for potential sex differences
54,55
. Additionally, we anticipate that utilizing dynamic CT
images, as opposed to CINE MRI, might yield different results owing to superior image resolution. However, implementing an
Arbitrary Lagrangian Eulerian approach for mesh motion in the CFD model may encounter challenges with intricate geometries
and displacements. Our CFD model has its own set of limitations. To streamline the process, we do not explicitly model the
MV, which can introduce artifacts in velocity profiles, such as abrupt closures in flowrate profiles. Nevertheless, we believe
that this may not significantly impact the computation of hemodynamic features. Moreover, due to a lack of measurements
regarding velocity/flow at the pulmonary veins inlets, we make an assumption of a constant physiological pressure for all
patients in this paper. This assumption could be relaxed with the availability of pulmonary veins velocity data, for example,
from echocardiographic images. Additionally, in terms of data analysis, we posit that further insights could be gleaned from
features extracted from Lagrangian simulations, such as the mean age of blood particles – a metric reflecting blood stagnation
in the LA and its appendage specifically21.
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Wall: no-slip
(cine CMR)
PVs sections: Neumann
(pin = 10 mmHg)
MV section:
switching
MV open
Neumann
MV closed
no-slip
(pout = 5 mmHg)
Figure 9. LA computational domain with boundary portions (top). On the inlet section, we prescribe constant pressure equal
to 10 mmHg; on the wall, a no-slip condition with patient-specific displacement; on the outlet section, switching boundary
condition: no-slip when the MV is closed and pressure equation to 5 mmHg when the MV is open.
Methods
We outline the methodologies employed in our analysis. Initially, we detail our CMR data and the devised preprocessing
pipeline for the images. Subsequently, we introduce the mathematical models, data assimilation techniques, numerical methods,
and simulation software employed for our personalized computational fluid dynamics CFD simulations. Finally, we define key
functional and hemodynamic features utilized in assessing stroke risk.
Patient-specific data and preprocessing
We consider a cohort of 8 patients: 4 control and 4 with history of stroke. These subjects were part of a larger cohort presented
in Morris et al.
56
, where they conducted CMR studies using either a 1.5 Tesla or 3 Tesla MR scanner (manufactured by Siemens
Healthcare in Erlangen, Germany). The CMR procedures encompassed CINE CMR, CE magnetic resonance angiography
(MRA), and 3D late gadolinium enhancement (LGE) CMR. CINE CMR scans were obtained in either the axial or the standard
4-chamber orientation56.
These three types of image sequences are combined to eventually produce dynamic meshes. Specifically, a cardiac imaging
expert carried out manual segmentation of the LA anatomy from the high-resolution MRA and LGE image. The time-dependent
CMR images were then reconstructed from a series of CINE image stacks covering the entire chamber with small or no gap
between slices. Then, individual 3D volumes were extracted and reconstructed for each time point of the cardiac cycle from the
time-dependent 3D images. Manual segmentation of the LA anatomy from the high-resolution MRA and LGE image was
done using the freely-available image processing software itk-SNAP
57,58
. Further details on CMR data and the computational
pipeline to recover dynamic meshes can be found in the work by Morris et al
56
. For each patient, we have either 25, 30, 35, or
40 time frames available, depending on the patient. Given the dynamic meshes, we developed a semi-automatic preprocessing
pipeline aimed at generating a static volumetric mesh for the CFD simulation and a displacement field (defined with respect to
the static mesh configuration) to displace the static mesh over time. In our semi-automatic pipeline, we combine
pvpython59
and
vmtk60,61
preprocessing tools. We generate tetrahedral meshes of the 8 atria with a uniform mesh size approximately
equal to 0.8mm, as we report in Figure 8.
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Modeling and simulation
We model the blood flow in the LA as an incompressible viscous fluid with constant density
ρ=1.06 ·103kg/m3
and
constant dynamic viscosity
µ=3.5·10−3kg/(ms)
. We use the incompressible Navier-Stokes equations expressed in the
Arbitrary Lagrangian Eulerian (ALE) framework
62
. We set our fluid dynamics domain in
Ωt
delimited by
∂Ωt=Γw
t∪
ΓMV
t∪ΓPV
t
. These boundaries are the endocardial wall, MV section, and pulmonary veins (PVs) sections, respectively.
The subscript
t
denotes the current (i.e. deformed) configuration of the domain and the subscript
0
denotes the reference
(corresponding to the initial) configuration. The domain at any time
t
is defined in terms of a displacement field
d
d
d
as
Ωt=x
x
x∈R3:x
x
x=x
x
x0+d
d
d(x
x
x0,t),x
x
x0∈Ω0.
We consider a temporal domain
(0,Tf)
, with
Tf=10THB
, where
THB
is the heartbeat
period, a patient-specific data. We simulate 10 beats in order to allow the flow to reach a periodic steady-state solution and to
neglect the influence of a null velocity initial condition.
The patient-specific displacement is defined for a discrete number of time frames, with a much coarser resolution than the
one required by the CFD problem. Thus, we use smoothing splines
63
to approximate the imaging displacement field in time.
We found that this choice – in contrast to other standard approximating or interpolating functions – allows for the reduction of
the noise unavoidably introduced in the simulation by the patient-specific data. Let
d
d
d∂Ω
be the displacement field on the LA
boundary
∂Ωt
and on the temporal domain
(0,Tf)
. We compute the displacement of the volumetric mesh
d
d
d
(i.e. interior mesh
points) with the following harmonic lifting problem:





−∇
∇
∇·
·
·(ψ∇
∇
∇d
d
d) = 0
0
0 in Ω0×(0,Tf),(1a)
d
d
d=d
d
d∂Ω(x
x
x,t)on Γw
0×(0,Tf),(1b)
(∇
∇
∇d
d
d)n
n
n=0
0
0 on ΓPV
0∪ΓMV
0×(0,Tf),(1c)
where
n
n
n
is the outward pointing normal and
ψ(x
x
x)
is a spatially varying stiffening factor used to avoid mesh element distortion
according to the boundary-based stiffening approach proposed in
64
:
ψ(x
x
x) = max(d(x
x
x),α)−βin Ω0.d
is the distance from the
LA boundary,
α
and
β
are two parameters that we set equal to
α=1.5mm
and
β=2
, as in
65
. Notice that, in Equation (1),
we prescribe natural homogeneous conditions on the PVs and MV sections since the displacement obtained from the images
is defined on the endocardial wall only, i.e. where we prescribe Dirichlet conditions. As a matter of fact,
ΓPV
0
and
ΓMV
0
are
artificial boundaries required to prescribe inlet and outlet boundary conditions in the CFD problem. The ALE velocity
u
u
uALE
is
then computed by deriving d
d
dwith respect to time.
Let
u
u
u
and
p
be the blood velocity and pressure fields. The incompressible Navier-Stokes equations in the ALE framework
endowed with boundary and initial conditions read:





























ρ∂u
u
u
∂t+u
u
u−u
u
uALE·∇
∇
∇u
u
u−∇
∇
∇·
·
·µ(∇
∇
∇u
u
u+∇
∇
∇⊤u
u
u)+∇
∇
∇p=0
0
0 in Ωt×(0,Tf), (2a)
∇
∇
∇·
·
·u
u
u=0 in Ωt×(0,Tf), (2b)
u
u
u=u
u
uALE on Γw
t×(0,Tf), (2c)
µ(∇
∇
∇u
u
u+∇
∇
∇Tu
u
u)n
n
n−pn
n
n=−pinn
n
non ΓPV
t×(0,Tf)(2d)
µ(∇
∇
∇u
u
u+∇
∇
∇Tu
u
u)n
n
n−pn
n
n=−poutn
n
non ΓMV
t, if MV is open, (2e)
u
u
u=u
u
uALE on ΓMV
t, if MV is closed, (2f)
u
u
u=0
0
0 in Ω0× {0}. (2g)
In Figure 9, we provide a graphical sketch of the domain and the boundary conditions we set. We prescribe the ALE velocity
on the lateral wall (no-slip condition). On the inlet sections, since we do not have any data in terms of flowrate or pressure,
we set Neumann boundary conditions with a pressure
pin =10 mmHg
, which represents a physiological value measured in
the pulmonary veins
66
. On the outlet section, to mimic the opening and closing of the MV, we switch boundary conditions
from natural to essential, and vice-versa. Specifically, as done in
50
, we set a no-slip condition if the MV is closed; if the MV is
open, we prescribe a physiological value of ventricular pressure during ventricular diastole
67
:
pout =5 mmHg
. We switch the
boundary condition when the LA volume reaches a minimum or maximum, as displayed in Figure 9. Furthermore, we include
backflow stabilization in all the Neumann boundaries68,69. We start the simulation with a null initial condition.
We discretize the Navier-Stokes equations in space by the Finite Element (FE) method. We use linear FEs for both velocity
and pressure with VMS-LES stabilization
70
, acting also as a turbulence model to account for possible transition-to-turbulence
effects in the LA
50
. We treat the nonlinear convection term semi-implicitly, as detailed in
70
. Time integration is carried out with
an implicit Euler method, with a constant time step size ∆t=5·10−4s.
We solve the CFD problem using
lifex71
, a high-performance
C++
FE library developed within the iHEART project
at Politecnico di Milano.
lifex
is mainly focused on cardiac simulations, and based on the
deal.II
finite element
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l
d
Figure 10. LAA and its centerline for the computation of the tortuosity.
core
72–74
. The source code of the
lifex
module for hemodynamics simulations, referred to as
lifex-cfd
, has been recently
released
75,76
. Simulation analogous to the one presented in this paper can be carried out with the open source version we
released. We run numerical simulations in parallel with 192 cores on the GALILEO100 supercomputer (528 computing nodes
each 2 x CPU Intel CascadeLake 8260, with 24 cores each, 2.4 GHz, 384GB RAM) at the CINECA supercomputing center,
using 288 cores. The simulation of ten beats for a single patient took about 24 hours.
Computation of biomarkers
To assess geometrical features of the LAA, we compute its tortuosity as
44
:
τ=ℓ
d−1
, with
ℓ
representing the LAA centerline
length and dthe Euclidean distance of its endpoints. A graphical representation is provided in Figure 10.
We provide a definition of the hemodynamics features considered in this study. All the features are computed using
the phase-averaged velocity on the LA boundary in the reference (initial) configuration. We first remove the influence
of a null velocity initial condition by discarding the first two heartbeats. Then, we compute the phase-averaged velocity
⟨u
u
u⟩(x
x
x,t)∈Ωt×(0,THB)using the remaining eight beats as:
⟨u
u
u⟩(x
x
x,t) = 1
8
10
∑
n=3
u
u
u(x
x
x,t+ (n−1)THB).
We define the Flow Stasis (FS) as21
FS(x
x
x) = 1
THB ZTHB
0
χ{|⟨u
u
u⟩(x
x
x,t)|≤0.1m/s}(x
x
x,t)dtin Ω0.
Notice that we defined the flow stasis using a threshold value
0.1 m/s
, a value consistent with the sensitivity study carried out
in48. Let τ(⟨u
u
u⟩) = µ∇
∇
∇⟨u
u
u⟩+∇
∇
∇⊤⟨u
u
u⟩be the viscous stress tensor, the Wall Shear Stress (WSS) vector is defined as
WSS(⟨u
u
u⟩) = τ(⟨u
u
u⟩)n
n
n−(τ(⟨u
u
u⟩)n
n
n·n
n
n)n
n
non ∂Ω0×(0,THB),
the Time Averaged Wall Shear Stress (TAWSS) as77
TAWSS(⟨u
u
u⟩) = 1
THB ZTHB
0
|WSS(⟨u
u
u⟩)|dton ∂Ω0,
the Oscillatory Shear Index (OSI) as78
OSI(⟨u
u
u⟩) = 1
2
1−

RTHB
0WSS(⟨u
u
u⟩)dt


RTHB
0|WSS(⟨u
u
u⟩)|dt
on ∂Ω0,
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the Relative Residence Time (RRT) as79
RRT(⟨u
u
u⟩) = (1−2OSI(⟨u
u
u⟩)) 1
THB ZTHB
0
|WSS(⟨u
u
u⟩)|dt−1
on ∂Ω0,
and the Endothelial Cell Activation Potential (ECAP) as51
ECAP(⟨u
u
u⟩) = OSI(⟨u
u
u⟩)
TAWSS(⟨u
u
u⟩)on ∂Ω0.
The kinetic energy and the enstrophy are respectively computed as:
Ek=1
2ZΩ0
|⟨u
u
u⟩|2dx
x
x3,S=1
2ZΩ0
|ω
ω
ω|2dx
x
x3,
where ω
ω
ω=∇× ⟨u
u
u⟩is the phase-averaged vorticity vector.
References
1. Dritsas, E. & Trigka, M. Stroke risk prediction with machine learning techniques. Sensors 22, 4670 (2022).
2. Hankey, G. J. Potential new risk factors for ischemic stroke: what is their potential? Stroke 37, 2181–2188 (2006).
3.
Johansen, M. C., Doria de Vasconcellos, H., Nazarian, S., Lima, J. A. & Gottesman, R. F. The investigation of left atrial
structure and stroke etiology: The I-LASER study. J. Am. Hear. Assoc. 10, e018766 (2021).
4.
Benjamin, E. J., D’Agostino, R. B., Belanger, A. J., Wolf, P. A. & Levy, D. Left atrial size and the risk of stroke and death:
the framingham heart study. Circulation 92, 835–841 (1995).
5.
Lee, J. M. et al. Why is left atrial appendage morphology related to strokes? an analysis of the flow velocity and orifice
size of the left atrial appendage. J. Cardiovasc. Electrophysiol. 26, 922–927 (2015).
6.
Bieging, E. T. et al. Statistical shape analysis of the left atrial appendage predicts stroke in atrial fibrillation. The
international journal cardiovascular imaging 37, 2521–2527 (2021).
7.
Burrell, L. D., Horne, B. D., Anderson, J. L., Muhlestein, J. B. & Whisenant, B. K. Usefulness of left atrial appendage
volume as a predictor of embolic stroke in patients with atrial fibrillation. The Am. journal cardiology 112, 1148–1152
(2013).
8.
Roth, E. J. Heart disease in patients with stroke. part ii: Impact and implications for rehabilitation. Arch. physical medicine
rehabilitation 75, 94–101 (1994).
9. Ergul, A., Hafez, S., Fouda, A. & Fagan, S. C. Impact of comorbidities on acute injury and recovery in preclinical stroke
research: focus on hypertension and diabetes. Transl. stroke research 7, 248–260 (2016).
10.
Cipolla, M. J., Liebeskind, D. S. & Chan, S.-L. The importance of comorbidities in ischemic stroke: Impact of hypertension
on the cerebral circulation. J. Cereb. Blood Flow & Metab. 38, 2129–2149 (2018).
11.
Harb, S. et al. Effect of anticoagulation on mortality by chadsvasc score in patients with atrial fibrillation: comparison to
patients without atrial fibrillation. In European Heart Journal, vol. 39, 1075–1075 (Oxford University Press, 2018).
12.
January, C. T. et al. 2019 AHA/ACC/HRS focused update of the 2014 AHA/ACC/HRS guideline for the management of
patients with atrial fibrillation: a report of the american college of cardiology/american heart association task force on
clinical practice guidelines and the heart rhythm society in collaboration with the society of thoracic surgeons. Circulation
140, e125–e151 (2019).
13.
Steiner, T., Rosand, J. & Diringer, M. Intracerebral hemorrhage associated with oral anticoagulant therapy: current
practices and unresolved questions. Stroke 37, 256–262 (2006).
14.
Chen, L. Y. et al. CHA2DS2-VASc score and stroke prediction in atrial fibrillation in whites, blacks, and hispanics. Stroke
50, 28–33 (2019).
15.
Zhang, J. et al. The interpretation of CHA2DS2-VASc score components in clinical practice: a joint survey by the european
heart rhythm association (EHRA) scientific initiatives committee, the EHRA young electrophysiologists, the association of
cardiovascular nursing and allied professionals, and the european society of cardiology council on stroke. EP Eur. 23,
314–322 (2021).
16/20
.CC-BY-NC-ND 4.0 International licenseavailable under a
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprintthis version posted January 15, 2024. ; https://doi.org/10.1101/2024.01.11.575156doi: bioRxiv preprint

16.
Sun, Y. et al. Finding low CHA2DS2-VASc scores unreliable? why not give morphological and hemodynamic methods a
try? Front. Cardiovasc. Medicine 9, 1032736 (2023).
17.
Lodzi´
nski, P. et al. Trends in antithrombotic management of patients with atrial fibrillation: A report from the polish part
of the eurobservational research programme-atrial fibrillation general long-term registry. Polskie Archiwum Medycyny
Wewnetrznej 130, 196–205 (2020).
18.
Goldstein, L. B. et al. Guidelines for the primary prevention of stroke: a guideline for healthcare professionals from the
american heart association/american stroke association. Stroke 42, 517–584 (2011).
19.
Kirchhof, P. et al. Anticoagulation with edoxaban in patients with atrial high-rate episodes. New Engl. J. Medicine 389,
1167–1179 (2023).
20.
Wang, Y. et al. Numerical prediction of thrombosis risk in left atrium under atrial fibrillation. Math. Biosci. Eng 17,
2348–2360 (2020).
21.
Corti, M., Zingaro, A., Dede’, L. & Quarteroni, A. M. Impact of atrial fibrillation on left atrium haemodynamics: A
computational fluid dynamics study. Comput. Biol. Medicine 150, 106143 (2022).
22.
Dueñas-Pamplona, J., Sierra-Pallares, J., García, J., Castro, F. & Munoz-Paniagua, J. Boundary-condition analysis of an
idealized left atrium model. Annals Biomed. Eng. 49, 1507–1520 (2021).
23.
Mill, J. et al. Patient-specific flow simulation analysis to predict device-related thrombosis in left atrial appendage occluders.
REC: Interv. Cardiol. 2021; 3 (4): 278-85. (2021).
24.
Aguado, A. M. et al. In silico optimization of left atrial appendage occluder implantation using interactive and modeling
tools. Front. physiology 237 (2019).
25.
Mill, J. et al. Sensitivity analysis of in silico fluid simulations to predict thrombus formation after left atrial appendage
occlusion. Mathematics 9, 2304 (2021).
26.
García-Villalba, M. et al. Demonstration of patient-specific simulations to assess left atrial appendage thrombogenesis risk.
Front. physiology 12, 596596 (2021).
27.
Masci, A. et al. A proof of concept for computational fluid dynamic analysis of the left atrium in atrial fibrillation on a
patient-specific basis. J. Biomech. Eng. 142, 011002 (2020).
28.
Zingaro, A. et al. Po-01-210 stroke risk is identified by slow blood flow and stagnant blood particles in the left atrium.
Hear. Rhythm. 20, S161–S162 (2023).
29.
Paliwal, N. et al. Presence of left atrial fibrosis may contribute to aberrant hemodynamics and increased risk of stroke in
atrial fibrillation patients. Front. Physiol. 684 (2021).
30.
Durán, E. et al. Pulmonary vein flow split effects in patient-specific simulations of left atrial flow. Comput. Biol. Medicine
107128 (2023).
31.
Gonzalo, A. et al. Non-newtonian blood rheology impacts left atrial stasis in patient-specific simulations. Int. J. for Numer.
Methods Biomed. Eng. 38, e3597 (2022).
32.
Morales Ferez, X. et al. Deep learning framework for real-time estimation of in-silico thrombotic risk indices in the left
atrial appendage. Front. Physiol. 12, 694945 (2021).
33.
García-Isla, G. et al. Sensitivity analysis of geometrical parameters to study haemodynamics and thrombus formation in
the left atrial appendage. Int. journal for numerical methods biomedical engineering 34, e3100 (2018).
34.
Bosi, G. M. et al. Computational fluid dynamic analysis of the left atrial appendage to predict thrombosis risk. Front.
cardiovascular medicine 5, 34 (2018).
35.
Pons, M. I. et al. Joint analysis of morphological parameters and in silico haemodynamics of the left atrial appendage for
thrombogenic risk assessment. J. Interv. Cardiol. 2022 (2022).
36.
Wang, L., Wang, Z., Fang, R. & Li, Z.-Y. Evaluation of stroke risk in patients with atrial fibrillation using morphological
and hemodynamic characteristics. Front. Cardiovasc. Medicine 9, 842364 (2022).
37.
Sanatkhani, S. et al. Subject-specific factors affecting particle residence time distribution of left atrial appendage in atrial
fibrillation: A computational model-based study. Front. Cardiovasc. Medicine 10, 1070498 (2023).
38.
Valvez, S., Oliveira-Santos, M., Piedade, A. P., Gonçalves, L. & Amaro, A. M. Computational flow dynamic analysis in
left atrial appendage thrombus formation risk: A review. Appl. Sci. 13, 8201 (2023).
17/20
.CC-BY-NC-ND 4.0 International licenseavailable under a
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprintthis version posted January 15, 2024. ; https://doi.org/10.1101/2024.01.11.575156doi: bioRxiv preprint

39.
Qureshi, A. et al. Mechanistic modelling of virchows triad to assess thrombogenicity and stroke risk in atrial fibrillation
patients. Eur. Hear. Journal-Digital Heal. 3, ztac076–2788 (2022).
40.
Dueñas-Pamplona, J. et al. Reduced-order models of endocardial shear stress patterns in the left atrial appendage from a
data-augmented patient-specific database. arXiv preprint arXiv:2310.05443 (2023).
41.
Vella, D., Monteleone, A., Musotto, G., Bosi, G. M. & Burriesci, G. Effect of the alterations in contractility and morphology
produced by atrial fibrillation on the thrombosis potential of the left atrial appendage. Front. Bioeng. Biotechnol. 9, 586041
(2021).
42.
Chen, S.-A. et al. Right atrial focal atrial fibrillation: electrophysiologic characteristics and radiofrequency catheter
ablation. J. cardiovascular electrophysiology 10, 328–335 (1999).
43.
Musotto, G. et al. The role of patient-specific morphological features of the left atrial appendage on the thromboembolic
risk under atrial fibrillation. Front. Cardiovasc. Medicine 9, 894187 (2022).
44.
Masci, A. et al. The impact of left atrium appendage morphology on stroke risk assessment in atrial fibrillation: a
computational fluid dynamics study. Front. physiology 9, 1938 (2019).
45.
Zingaro, A. et al. A geometric multiscale model for the numerical simulation of blood flow in the human left heart. Discret.
Continous Dyn. Syst. - S 15, 2391–2427 (2022).
46.
Otani, T. et al. A computational framework for personalized blood flow analysis in the human left atrium. Annals
biomedical engineering 44, 3284–3294 (2016).
47.
Qureshi, A. et al. Modelling blood flow and biochemical reactions underlying thrombogenesis in atrial fibrillation. In
International Conference on Functional Imaging and Modeling of the Heart, 435–444 (Springer, 2023).
48.
Markl, M. et al. Left atrial 4D flow MRI: stasis and velocity mapping in patients with atrial fibrillation. Investig. radiology
51, 147 (2016).
49.
Domanin, M. et al. Computational fluid-dynamic analysis after carotid endarterectomy: patch graft versus direct suture
closure. Annals vascular surgery 44, 325–335 (2017).
50.
Zingaro, A., Dede’, L., Menghini, F. & Quarteroni, A. Hemodynamics of the heart’s left atrium based on a variational
multiscale-LES numerical method. Eur. J. Mech. 89, 380–400 (2021).
51.
Di Achille, P., Tellides, G., Figueroa, C. & Humphrey, J. A haemodynamic predictor of intraluminal thrombus formation in
abdominal aortic aneurysms. Proc. Royal Soc. A: Math. Phys. Eng. Sci. 470, 20140163 (2014).
52.
Lupo, A., Mokhov, I., Dostoglou, S., Kunz, A. & Burkhardt, J. Assessment of the impact of the planetary scale on the
decay of blocking and the use of phase diagrams and enstrophy as a diagnostic. Izvestiya, Atmospheric Ocean. Phys. 43,
45–51 (2007).
53. Umeki, M. Numerical simulation of plane poiseuille turbulence. Fluid dynamics research 13, 67 (1994).
54.
St Pierre, S. R., Peirlinck, M. & Kuhl, E. Sex matters: a comprehensive comparison of female and male hearts. Front.
Physiol. 13, 831179 (2022).
55.
Gonzalez-Martin, P. et al. Ventricular anatomical complexity and sex differences impact predictions from electrophysiolog-
ical computational models. Plos one 18, e0263639 (2023).
56.
Morris, A., Kholmovski, E., Marrouche, N., Cates, J. & Elhabian, S. An image-based approach for 3D left atrium functional
measurements. In 2020 Computing in Cardiology, 1–4 (IEEE, 2020).
57.
Yushkevich, P. A. et al. User-guided 3D active contour segmentation of anatomical structures: Significantly improved
efficiency and reliability. Neuroimage 31, 1116–1128 (2006).
58. itk snap. http://www.itksnap.org/.
59. LLC, M. Pvpython and pvbatch. https://www.paraview.org/Wiki/PvPython_and_PvBatch.
60.
Antiga, L. et al. An image-based modeling framework for patient-specific computational hemodynamics. Med. & Biol.
Eng. & Comput. 46, 1097–1112 (2008).
61.
Fedele, M. & Quarteroni, A. M. Polygonal surface processing and mesh generation tools for numerical simulations of the
complete cardiac function. Int. J. for Numer. Methods Biomed. Eng. 37, e3435 (2021).
62.
Donea, J., Giuliani, S. & Halleux, J.-P. An arbitrary Lagrangian-Eulerian finite element method for transient dynamic
fluid-structure interactions. Comput. Methods Appl. Mech. Eng. 33, 689–723 (1982).
63. De Boor, C. A practical guide to splines, vol. 27 (Springer-Verlag New York, 1978).
18/20
.CC-BY-NC-ND 4.0 International licenseavailable under a
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprintthis version posted January 15, 2024. ; https://doi.org/10.1101/2024.01.11.575156doi: bioRxiv preprint

64.
Jasak, H. & Tukovic, Z. Automatic mesh motion for the unstructured finite volume method. Transactions FAMENA 30,
1–20 (2006).
65.
Zingaro, A., Bucelli, M., Fumagalli, I., Dede’, L. & Quarteroni, A. Modeling isovolumetric phases in cardiac flows by an
augmented resistive immersed implicit surface method. Int. J. for Numer. Methods Biomed. Eng. e3767 (2022).
66.
Ferng, A. Pulmonary arteries and veins. https://www.kenhub.com/en/library/anatomy/pulmonary-arteries-and-veins
(2023).
67. Fowler, N. O. Cardiac Diagnosis and Treatment (Philadelphia, JB Lippincott, 1976).
68.
Bertoglio, C. & Caiazzo, A. A tangential regularization method for backflow stabilization in hemodynamics. J. Comput.
Phys. 261, 162–171 (2014).
69.
Moghadam, M. E., Bazilevs, Y., Hsia, T.-Y., Vignon-Clementel, I. E. & Marsden, A. L. A comparison of outlet boundary
treatments for prevention of backflow divergence with relevance to blood flow simulations. Comput. Mech. 48, 277–291
(2011).
70.
Forti, D. & Dedè, L. Semi-implicit BDF time discretization of the Navier–Stokes equations with VMS-LES modeling in a
high performance computing framework. Comput. & Fluids 117, 168–182 (2015).
71.
Africa, P. C. lifex: A flexible, high performance library for the numerical solution of complex finite element problems.
SoftwareX 20, 101252 (2022).
72. Arndt, D. et al. The deal.II library, version 9.3. J. Numer. Math. 29 (2021).
73.
Arndt, D. et al. The
deal.II
finite element library: design, features, and insights. Comput. & Math. with Appl. DOI:
10.1016/j.camwa.2020.02.022 (2020).
74. Official deal.ii website. https://www.dealii.org/.
75.
Africa, P. C. et al. lifex-cfd: An open-source computational fluid dynamics solver for cardiovascular applications. Comput.
Phys. Commun. 109039 (2023).
76.
Africa, P. C., Fumagalli, I., Bucelli, M. & Zingaro, A. lifex-cfd: an open-source computational fluid dynamics solver for
cardiovascular applications. https://doi.org/10.5281/zenodo.7852089, DOI: 10.5281/zenodo.7852089.
77.
Koizumi, R. et al. Numerical analysis of hemodynamic changes in the left atrium due to atrial fibrillation. J. Biomech. 48,
472–478 (2015).
78.
Ku, D. N., Giddens, D. P., Zarins, C. K. & Glagov, S. Pulsatile flow and atherosclerosis in the human carotid bifurcation.
positive correlation between plaque location and low oscillating shear stress. Arter. An Off. J. Am. Hear. Assoc. Inc. 5,
293–302 (1985).
79.
Himburg, H. A. et al. Spatial comparison between wall shear stress measures and porcine arterial endothelial permeability.
Am. J. Physiol. Circ. Physiol. 286, H1916–H1922 (2004).
Acronyms
ALE arbitrary lagrangian-eulerian
AF atrial fibrillation
BPM beats per minute
CE contrast enhanced
CFD computational fluid dynamics
CHA2DS2-VASc Congestive Heart Failure, Hypertension, Age ≥75 (x2), Diabetes Melitus, Stroke (x2), Vascular Disease,
Age (65-74), Sex Category (female +1)
CMR cardiac magnetic resonance
CPU central processing unit
CT computed tomography
EA early / after wave (ratio)
ECAP endothelial cell activation potential
EF ejection fraction
FE finite element
FS flow stasis
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LA left atrium
LAA left atrial appendage
LGE late gadolinium enhancement
MRA magnetic resonance angiography
MV mitral valve
OA ostium area
OAC oral anticoagulant
OSI oscillatory shear index
PV pulmonary vein
RRT relative residence time
SV stroke volume
TAWSS time-averaged wall shear stress
VMS-LES variational multiscale large eddy simulation
WSS wall shear stress
Acknowledgements
A.Z., L.D., and A.Q. received funding from the Italian Ministry of University and Research (MIUR) within the PRIN (Research
projects of relevant national interest) 2017 “Modeling the heart across the scales: from cardiac cells to the whole organ” Grant
Registration number 2017AXL54F.
Z.A. was supported by grant n. T32 HL007024 from the National Heart, Lung, and Blood Institute, National Institutes of
Health (NIH) and grant n. T32 GM119998 from the NIH National Institute of General Medicine.
L.D. acknowledges the PRIN 2022 (MIUR Italy) research project “Computational modeling of the human heart: from
efficient numerical solvers to cardiac digital twins"; 10.2023–09.2025, Politecnico di Milano, Grant Registration number
202232A8AN. L.D. is member of the INdAM group GNCS “Gruppo Nazionale per il Calcolo Scientifico” (National Group for
Scientific Computing), Italy.
N.A.T. acknowledges National Institutes of Health (NIH) grants n. R01HL166759 and R01HL142496 and the Leducq
Foundation.
Author contributions statement
A.Z.: Conceptualization, methodology, software implementation, simulation, formal analysis, writing (original draft). Z.A.:
Conceptualization, simulation, formal analysis, writing (original draft). E.K.: Data acquisition and processing, writing (review).
K.S.: Data processing, writing (review). L.D.: Conceptualization, supervision, project administration, writing (review). A.Q.:
Funding acquisition, conceptualization, supervision, project administration, writing (review). N.T.: Funding acquisition,
conceptualization, supervision, project administration, formal analysis, writing (review).
Additional information
Accession codes The datasets used and/or analysed during the current study are available from the corresponding author upon
reasonable request. lifex, the software for carrying out simulations, is freely available at75,76.
Competing interests: The authors declare no competing interests.
Conflict of interests: A.K.M. and E.K. are consultants for Marrek Inc. and have an equity interest at Marrek Inc.
20/20
.CC-BY-NC-ND 4.0 International licenseavailable under a
(which was not certified by peer review) is the author/funder, who has granted bioRxiv a license to display the preprint in perpetuity. It is made
The copyright holder for this preprintthis version posted January 15, 2024. ; https://doi.org/10.1101/2024.01.11.575156doi: bioRxiv preprint