Patient-Specific Hemodynamic Simulation for Predicting Stroke Laterality in Cardiac Embolism
Article information
Abstract
Background and Purpose
Cardioembolic sources account for 20%–30% of acute ischemic strokes (AIS), often with high morbidity. Conventional imaging confirms etiology retrospectively but lacks insight into the dynamic behavior of embolic transport. We aimed to predict stroke laterality by integrating patient-specific computational fluid dynamics (CFD) simulations with robust Bayesian logistic regression modeling.
Methods
Eight patients (median age 77.5 years; 2 females) with anterior circulation AIS of confirmed cardiac origin underwent high-resolution computed tomography angiography. Vascular geometries were segmented to generate CFD models simulating physiologic pulsatile flow. In each cardiac cycle, 1,000 massless particles were released at the aortic inlet. Two features were derived: x1 (long-term embolic bias over 10 seconds) and x2 (short-term embolic bias during the first cardiac cycle). These were used as predictors in a robust Bayesian logistic regression model.
Results
The right internal carotid artery (ICA) received more embolic particles (mean 34/s) than the left ICA (mean 28/s). Patients with right-sided strokes had higher x1 (median 0.27 vs. -0.44) and lower x2 (median -0.82 vs. 0.56) than those with left-sided strokes. The model yielded posterior mean coefficients of 1.51 (95% credible interval [CrI]: -0.46 to 4.11) for x1 and -1.96 (95% CrI: -4.88 to 0.20) for x2, achieving complete separation of stroke patients by laterality in this pilot cohort.
Conclusion
The combination of CFD-based embolic modeling and Bayesian analysis accurately predicted stroke laterality in cardioembolic AIS, exposing distinct patient-specific embolic transport dynamics.
Introduction
Acute ischemic stroke (AIS) remains one of the leading causes of death and long-term disability worldwide, with an estimated 5.5 million deaths annually. Millions of people suffer from persistent neurological impairments [1]. Approximately 20%–30% of all ischemic strokes are attributed to embolic events originating from the heart, a condition known as cardiac embolism [2]. The risk of embolism is elevated in patients with known cardiac causes, such as atrial fibrillation, valvular heart disease, and heart failure [3,4]. Cardiac emboli can travel through the aorta and its branches into the carotid and vertebral arteries, frequently lodging in intracranial vessels such as the middle cerebral artery or anterior cerebral artery, thereby causing ischemic strokes of varying locations and severities [5]. Previous clinical investigations, including Kim et al. [6], have demonstrated a right-sided dominance in cardioembolic stroke distribution, especially when compared to aortogenic sources.
Current diagnostic methods, such as computed tomography (CT), magnetic resonance imaging (MRI), and echocardiograms, are effective in identifying plausible stroke causes and in retrospectively attributing stroke etiology; however, they provide limited insight into the dynamic nature of embolic trajectories. This is particularly challenging in patients with complex vascular anatomies or multiple potential sources of emboli [7], such as concomitant ipsilateral carotid stenosis.
Advances in computational techniques have introduced the field of computational fluid dynamics (CFD), a numerical approach for simulating fluid flow and related phenomena by solving the governing equations of fluid motion, that is, the Navier-Stokes equations [8].
CFD can model patient-specific hemodynamics by incorporating detailed anatomical reconstruction from imaging data. This enables the simulation of how blood and suspended particles, including emboli, move through the cerebral vasculature under physiologically relevant conditions [9] and helps predict where emboli are likely to travel, how they branch off into different vascular territories, and where they might ultimately lodge [10].
This study aims to bridge the conceptual gap between static imaging data and the dynamic nature of embolic strokes by using CFD simulations combined with Bayesian logistic regression to calculate the likelihood of right versus left-sided stroke in patients with cardiac embolic sources. We hypothesized that CFD-based analysis of embolic trajectories, coupled with robust statistical modeling, can provide novel insights into stroke risk and contribute to a more individualized approach to stroke prediction and prevention.
Methods
Patient selection and data acquisition
This study included eight patients diagnosed with embolic AIS in the anterior circulation attributable to a known cardiac source according to the Trial of ORG 10172 in Acute Stroke Treatment (TOAST) classification of stroke subtypes [11], i.e., the presence of atrial fibrillation or severely decreased left ventricle ejection fraction with severe wall-motion abnormalities, and the absence of any ipsilateral carotid stenosis >50%. Four patients were selected with right-sided stroke and four with left-sided stroke. Stroke laterality was determined based on the hemisphere that bore the full weight of the acute infarct volume on diffusion-weighted imaging (Supplementary Figure 1). Patients with bilateral infarcts were excluded. Inclusion criteria included documented atrial fibrillation or severely decreased left ventricular ejection fraction, complete cerebrovascular and brain MRI data, and absence of ipsilateral carotid atherosclerotic plaques causing >50% stenosis. Patients with non-cardiac causes of stroke or with incomplete data were excluded. The IRB waived the need for ethics approval and patient consent for the collection, analysis, and publication of the retrospectively obtained and anonymized data for this non-interventional study. The patient imaging data were de-identified.
All patients underwent contrast-enhanced computed tomography angiography (CTA) from the aortic arch to the cerebral circulation, using a high-resolution multidetector CT scanner (Supria, Hitachi Inc., Tokyo, Japan). The scanning protocol ensured isotropic voxel reconstruction (slice thickness, 0.5 mm). Arterial- phase imaging facilitates optimal visualization of vascular structures.
CT angiogram segmentation and mesh generation
CTA images were imported into 3D Slicer [12] (Version 5.2) for vascular segmentation. The aorta, brachiocephalic trunk, subclavian arteries, bilateral common carotid arteries, proximal internal carotid artery (ICA), and external carotid artery (ECA), distal to just beyond the common carotid artery bifurcation, were segmented using a combination of threshold-based algorithms and manual refinements. The segmented geometries were exported in the stereolithography (STL) format.
The subsequent mesh cleanup and optimization steps were performed using Autodesk 3ds Max (Autodesk, Inc., San Francisco, CA, USA) and COMSOL Multiphysics (Version 6.2, COMSOL Inc., Stockholm, Sweden). Artifacts and non-manifold edges were removed, and the meshes were refined to ensure homogeneous density. Models were meshed using COMSOL’s predefined “Normal” configuration for laminar flow CFD simulations, which adaptively chooses meshing parameters based on the task at hand.
CFD setup
Blood flow was modeled as an incompressible, Newtonian fluid with a dynamic viscosity of 0.0035 Pa·s and a density of 1,060 kg/m3. A laminar flow assumption was employed, and the vessel walls were treated as rigid under no-slip boundary conditions.
Inlet and outlet boundary conditions
A parabolic velocity profile was imposed on the aortic inlet (Figure 1). The velocity field in the z-direction (with the aortic inlet lying on the xy-plane and its center positioned at x=0, y=0) was defined as:
Simulated velocity streamlines at times (A) 0.15 s, (B) 0.20 s, (C) 0.50 s, and (D) 1.15 s colored by magnitude from a patient with left-sided stroke. Note the parabolic velocity profile at the aortic inlet (A).
Here, R is the inlet radius, and we used N=2 to define a parabolic velocity profile. The mean velocity waveform vmean(t) was derived from literature-based flow-rate data [13], normalized and adjusted by stroke volume (SVtarget=96.6 cm3/s) [14] and heart rate (60 bpm). Thus, the mean flow rate Q− was 96.6 cm3/s. Systolic and diastolic pressures (Psys, Pdia) were set to 120 mm Hg and 80 mm Hg, respectively, and the mean arterial pressure was approximated as 95 mm Hg.
The 2-element Windkessel model [15] was employed to simulate arterial blood pressure dynamics, incorporating the fundamental physiological properties of vascular resistance and compliance. The governing ordinary differential equation (ODE) is expressed as:
where P(t) represents arterial blood pressure at time t, Qin(t) denotes the blood inflow (e.g., cardiac output), R is the vascular resistance, and C is the arterial compliance. This model characterizes the rate of change in arterial pressure by balancing the inflow of blood against pressure dissipation through vascular resistance and the storage capacity of the arterial system. Outlet boundary conditions were prescribed using this model, which was solved using COMSOL’s Global ODEs and differential-algebraic systems of equations (DAEs) module.
Literature-based flow splits [16] were used to guide the outlet flow distributions, as follows:
• Aortic descending outlet QAOO=70 cm3/s
• Subclavian artery QSC=5.55 cm3/s
• Internal carotid artery QICA=4.41 cm3/s
• External carotid artery QECA=3.1 cm3/s
Total compliance (Ctotal) and resistance (Rtotal) were calculated [17] as:
where Δt is the time interval between the maximum flow rate (Qmax) and the minimum flow rate (Qmin) in a single cardiac cycle. Branch-specific compliance (Cbranch) and resistance (Rbranch) were determined by scaling these totals proportionally by the ratio of the branch’s flow rate to the mean flow rate:
The flow rate at each outlet was computed as follows:
where u and n are the velocity and outward-pointing normal vectors, respectively.
CFD simulations
Time-dependent simulations were performed using a segregated solver within COMSOL. The solution was advanced over multiple cardiac cycles (10 s in total) to achieve a periodic flow state.
Particle tracking and data collection
Embolic particles were modeled as massless tracers, advected by the blood velocity field using the COMSOL’s “Particle Tracing for Fluid Flow” module. At the onset of each systole, 1,000 particles were released at the aortic inlet. The particle distribution at release was proportional to the local velocity magnitude, ensuring that the regions of higher flow contributed more particles. The particles followed the flow streamlines with no additional forces considered (Figure 2).
Particle trajectories at times (A) 0.15 s, (B) 0.20 s, (C) 0.50 s, and (D) 1.15 s colored by their velocity magnitudes from a patient with left-sided stroke.
Particle trajectories were recorded over the simulation, and their final distributions among the outlets of interest (e.g., right and left ICAs) were documented. This provides a direct assessment of embolic transport patterns under patient-specific anatomical and hemodynamic conditions.
Calculation of model features
Two features were derived from the simulation results for subsequent statistical analysis. The first feature, x1 or the long-term embolic bias, was defined as the area between the right and left cumulative number of particles passing through the ICAs over the entire simulation:
where Ncside(t) is the cumulative number of particles passing through the ICAs from time 0 until t.
The second feature, x2 or the short-term embolic bias, was similarly defined as the area between the right and left cumulative number of particles passing through the ICAs over the first release of particles (1.15 s):
The features are shown in Figure 3 as shaded areas. The 1.15-second interval was selected to align with the peak systolic flow-rate derived from the inflow waveform employed in simulations (Supplementary Figure 2). The features were then normalized by subtracting the mean and dividing by the standard deviation.
Comparison of the mean number of particles crossing the right internal carotid artery (ICA) and left ICA over time for patients with left-sided (A) and right-sided (B) strokes. The graph shows that patient-specific computational fluid dynamic simulations predict a larger tendency for particles to cross right ICA in patients with right-sided strokes compared with those with left-sided strokes. The red shaded areas in the plots correspond to the difference of the values and contribute to the designing of our features x1 and x2.
Bayesian logistic regression model
A robust Bayesian logistic regression model was constructed to relate the probability of a right-sided stroke outcome to the features x1 and x2. The non-informative prior distributions for the coefficients βx1 and βx2, and the intercept α were specified as independent Student’s t distributions with μ=0, σ=1, and ν=3:
The linear predictor is expressed as follows:
and the probability of a right-sided stroke:
Observed stroke laterality was modeled as a Bernoulli random variable with probability θ:
Inference was performed using Markov Chain Monte Carlo (MCMC) sampling to estimate posterior distributions of the parameters. Posterior predictive checks were used to verify the model’s suitability. Model convergence was assessed using effective sample size (ESS) for bulk and tail estimates, ensuring sufficient sampling efficiency, and the Rˆ diagnostic, with values close to 1.0 indicating well-mixed chains and convergence. We performed Bayesian leave-one-out cross-validation (LOO-CV) to evaluate the model generalizabilty.
Statistical analysis
Descriptive statistics were reported, as appropriate, using mean±standard deviations or median (interquartile ranges). One-sample t-test was employed for comparing the study patients’ mean flow rates with reference values and then the P-values were adjusted using Bonferroni’s correction for multiple tests. All analyses, including the MCMC-based Bayesian inference, were conducted using PyMC, Version 5.2 [18]. P-values less than 0.05 were considered statistically significant.
Results
Patient demographics and imaging characteristics
Eight patients with acute embolic ischemic stroke in the anterior circulation and a documented cardiac source were included in this study, with four presenting right-sided strokes and four presenting left-sided strokes (Table 1). The median age was 77.5 years (range 68–93), and 2/8 patients were female. The common cardiac conditions included atrial fibrillation (n=7) and heart failure (n=3).
Demographic and baseline clinical characteristics of the studied patients
Hemodynamic simulations and simulation validity
The mean flow rates at the key vascular segments were consistent with the literature values. For instance, the average flow rate at the aortic descending outlet across all patients (
Average number of particles per second and flow rate of different arterial branches across all patients derived from the simulated dataset
The pressure distributions within the aortic arch and its major branches fell within the expected physiological range (Supplementary Figure 3). The no-slip boundary condition and prescribed laminar profile at the inlet produced a stable parabolic velocity distribution (Figure 1).
Particle tracking and embolic distributions
Among all 8 studied patients, the right internal carotid artery (RICA) and left internal carotid artery (LICA) received an average of 34 and 28 particles per second, respectively (Table 2). Patients with right-sided stroke exhibited a higher ratio of particles destined for RICA than did patients with left-sided stroke (Figure 3). The simulation animations are available in Supplementary Videos.
Derived features (x1 and x2)
Patients with right-sided stroke displayed higher x1 values (median 0.27) compared to those with left-sided strokes (median -0.44), indicating the full 10-second CFD simulations predicted a relative increase in particle counts directed toward the right hemisphere in patients with right-sided stroke. Focusing on the first cardiac cycle, x2 values, the opposite trend is observed: median x2 values were 0.56 and -0.82 for patients with left and right-sided strokes, respectively, showing that the patients with right-sided stroke receive fewer particles through RICA compared to patients with left-sided stroke in the first release of particles. In other words, higher x1 values correspond to a higher chance of right-sided stroke and higher x2 values correspond to a higher chance of left-sided stroke.
Bayesian logistic regression
The robust Bayesian logistic regression model, incorporating x1 (capturing the accumulated differences of number of particles passing through right vs. left ICA, or the long-term embolic bias) and x2 (capturing the accumulated differences of number of particles through right vs. left ICA in the first cardiac cycle, or the short-term embolic bias), provided posterior estimates for βx1 and βx2 (Supplementary Figure 4). The posterior mean for βx1 was 1.51 (95% credible interval [CrI] -0.46 to 4.11) and for βx2 was -1.96 (95% CrI -4.88 to 0.20). Posterior predictions of the model for the patients’ stroke laterality demonstrated complete separation of patients with high confidence (Figure 4). All ESS for the bulk and tail estimates exceeded 2,000, indicating convergence and sufficient sampling efficiency. All Rˆ values were 1.0, confirming that the Markov chains mixed well and reached convergence across all model parameters. We compared four logistic regression models using Pareto-smoothed importance-sampling leave-one-out cross-validation (PSIS-LOO): the full model with both predictors (x1, x2) and an intercept, two single-predictor models plus intercepts, and a null (intercept-only) model. The full model achieved the highest expected log predictive density (ELPD=-2.88) with low effective complexity (ploo≈0.97), outperforming the x2-only and x1-only models by ΔELPD=1.54 and 2.46, respectively. Model weights strongly favored the full model, and no Pareto-k warnings were observed. These results support the inclusion of both predictors and an intercept as the most predictive and stable specification.
Posterior predictive probabilities (bars) for each patient. The top row depicts the posterior predictive probabilities for patients with left-sided stroke and the bottom row depicts the posterior predictive probabilities of patients with right-sided stroke. The vertical dashed lines highlight the observed stroke laterality. This indicates complete accuracy of the model in predicting the laterality of stroke since all posterior predictions are in line with the observed outcomes. Furthermore, this emphasizes the robustness of the input features as they allow such discrimination.
The decision boundary of the model is shown in Figure 5. We observe that the features engineered for this task (x1, x2) linearly separate all of our patients with a sizeable margin. In other words, the input features selected for this task allow for an easy discrimination of the stroke laterality.
Our model decision boundary at different thresholds (indicated by dashed and solid lines) completely separates the data into their observed outcomes. This emphasizes the robustness of the input features x1 and x2, which facilitate such separation into clearly distinct clusters.
Discussion
CFD provides a powerful framework for modeling blood flow by solving the Navier–Stokes equations and allows for detailed hemodynamic analysis in patient-specific vascular geometries. In cardiovascular applications, CFD enables the simulation of embolic transport under physiologically relevant conditions and offers insights that are not readily obtainable from conventional imaging alone. Even though CFD has been widely applied in studying aneurysm hemodynamics and large-vessel flow dynamics [19], its use in predicting embolic trajectories in AIS remains underexplored. This proof-of-concept study tried to bridge that gap and quantify the relationship between embolic transport patterns and stroke laterality in patients with known cardiac embolic sources.
Our findings indicate that embolic particles tend to enter the RICA both in patients with left and right stroke, probably due to the natural anatomical configuration of the aortic arch. This aligns with prior clinical observations [6] and provides a hemodynamic explanation for the rightward embolic bias seen in cardioembolic infarction. We also observed that in patients with right stroke, the ratio of particles destined for RICA is dramatically higher than in patients with left stroke (x1). The effect is interestingly inverse when considering the burst release of particles (x2), as we observed that in patients with left stroke, more particles reach the RICA than LICA in the first 1.15 seconds, compared to patients with right stroke.
Physiologically, the divergent behavior of x1 (10-second cumulative bias) and x2 (1.15-second early-systolic bias) reflects two distinct flow regimes within the aortic arch. During the rapid acceleration of systole, the interval captured by x2, the inertial jet follows the greater curvature of the aortic arch, channeling a burst of momentum into the brachiocephalic trunk, which tends to favor right-sided embolic trajectories regardless of subtle anatomical differences. Over multiple cycles, however, the residence-time effects captured by x1 amplify patient-specific factors such as carotid take-off angle, distal vascular resistance, and arch torsion. In anatomies that promote recirculation toward the left common carotid artery, these cumulative influences can shift the net embolic flux to the left, resulting in a leftward x1 even when x2 is transiently rightward. Thus, the opposing signs of these two features reflect impulse-dominated versus geometry-filtered hemodynamics, and their combined use captures both the immediate and long-term determinants of embolic destination.
The accuracy of our CFD simulations was validated by comparing blood flow rates and pressure distributions to known physiological values as they demonstrated strong agreement with established data. The use of a 2-element Windkessel model for boundary conditions further ensured a realistic representation of downstream vascular elastic behavior.
These patient-specific hemodynamic findings were linked to stroke outcomes using a robust Bayesian logistic regression model. By employing non-informative priors, our Bayesian approach provided probabilistic assessments of stroke laterality while accounting for the inherent uncertainty in small-sample settings. The engineered features, x1 and x2, effectively captured embolic transport patterns, both averaged over time and in burst release scenarios. Although the posterior credible intervals for regression coefficients were relatively wide, the posterior predictive checks confirmed the model’s suitability in capturing the dependence of stroke laterality on simulation-derived predictors.
Despite the promise of this integrated computational approach, several limitations must be acknowledged. The small sample size (n=8) limits the statistical power of the findings and necessitates larger studies to validate these results. Additionally, the assumption of rigid vessel walls and Newtonian blood flow simplifies the true hemodynamic behavior and could potentially underestimate the role of vessel compliance and non-Newtonian effects. Although these assumptions are standard in many CFD studies, future work incorporating deformable wall models and blood viscosity variations could enhance accuracy. Another key limitation of our approach is the modeling of emboli as massless, neutrally buoyant tracers that strictly follow blood flow streamlines. This simplification omits important physical properties of real emboli, such as mass, size, inertia, and buoyancy. In reality, cardioembolic clots vary widely in size and composition and can deviate from flow paths due to gravitational forces, centrifugal drift, and inertial lag, particularly within the curved geometry and pulsatile flow of the aortic arch. Ignoring these effects may underestimate the true variability in embolic trajectories and potentially overstate the predictive power of our streamline-based features.
From a clinical perspective, patient-specific CFD modeling of embolic trajectories offers several concrete avenues for personalized care. First, by quantifying whether hemodynamics preferentially deliver emboli to the dominant or non-dominant hemisphere, clinicians can identify individuals in whom a future stroke would carry disproportionate functional cost; these patients could be prioritized for prolonged rhythm monitoring, earlier escalation from antiplatelet to anticoagulation therapy, or elective left-atrial-appendage closure. Second, a documented right- or left-hemispheric embolic bias can guide side-specific neuromonitoring and selective shunting during cardiac or aortic surgery—settings in which embolic load is intrinsically high. Third, repeating the CFD analysis after pharmacological optimization or structural intervention provides a non-invasive biomarker of treatment response and enables adaptive secondary-prevention strategies. Finally, in cryptogenic stroke or cases with borderline indications for intensive prevention, demonstrating a consistent hemodynamic bias supplies mechanistic evidence that justifies moving from watchful waiting to active therapy; conversely, a neutral model may support a conservative approach. These potential applications delineate a translational pathway from bench-top simulation to bedside risk stratification that now warrants prospective evaluation in larger cohorts.
Future research should focus on expanding the dataset to improve the generalizability of findings. Additionally, integrating physics-informed neural networks into the CFD workflow could accelerate simulations and reduce computational costs while maintaining reasonable accuracy. Automated segmentation using deep learning could further streamline the workflow and facilitate large-scale clinical implementation. Prospective studies that link CFD-derived embolic risk profiles to real-world stroke incidence will be critical in validating the clinical utility of this approach.
Conclusions
This study demonstrates the feasibility and utility of integrating patient-specific CFD simulations with robust Bayesian logistic regression to predict stroke laterality in patients with cardiac embolism. By leveraging high-resolution vascular imaging and physiologically realistic flow modeling, we were able to simulate embolic trajectories in the cerebral circulation with precision. Two novel hemodynamic features—x1 representing long-term embolic flow bias and x2 representing short-term bias—were engineered to quantify embolic asymmetry. These features, derived directly from flow-based particle tracking, successfully discriminated between right- and left-sided strokes in all patients studied.
Our findings reveal that while the right ICA generally receives a higher proportion of embolic particles due to anatomical flow dynamics, patient-specific differences in embolic behavior are captured effectively through CFD. The x1 feature showed a strong association with the side of stroke over the full simulation window, whereas x2 captured transient dynamics within the first cardiac cycle—stressing the temporal complexity of embolic transport. The Bayesian model, using only these two features, achieved complete predictive accuracy in our cohort, accentuating the discriminative power of CFD-derived embolic metrics.
Beyond stroke laterality prediction, this work establishes a framework for future applications in personalized stroke risk assessment. It may guide targeted interventions, such as optimizing anticoagulation or tailoring monitoring strategies in high-risk patients. Furthermore, the methodology is extendable to other embolic phenomena, including cryptogenic stroke, paradoxical embolism, and perioperative embolic risk.
Overall, this proof-of-concept study tries to bridge the gap between static imaging and dynamic pathophysiology, proposing a novel computational approach with both mechanistic insight and clinical relevance. Future work should aim to validate these findings in larger cohorts and explore integration with machine learning pipelines for real-time, automated stroke risk prediction.
Supplementary materials
Supplementary materials related to this article can be found online at https://doi.org/10.5853/jos.2025.01571.
Diffusion-weighted images from two of our cases. In (A), a right-sided stroke is observed, and in (B), a left-sided stroke is observed. Similar to these two samples, when evaluating the laterality of the stroke, we only included patients whose stroke volume was entirely confined to a single hemisphere.
Inlet flow-rate profile used for all patients. Heart rate was fixed to 60 bpm and the total simulation time was 10 seconds. Note the 1.15 s mark aligns with the peak flow-rate through the aorta and hence the rationale behind our x2 feature.
Simulated pressure distribution across times 0.15, 0.20, 0.50, and 1.15 s in the mesh-segmented vasculature of a patient with left stroke
Prior (blue) and posterior (orange) distributions of the model coefficients. The left subplot depicts the prior and posterior distributions of the x1 coefficient, where we observe a rightward shift in the mean and a narrowing of the posterior. The right subplot depicts the prior and posterior distributions of the x2 coefficient, where we observe a leftward shift of the mean and a narrowing of the posterior distribution. This suggests that higher x1 values correspond to a higher chance of the patient having a right-sided stroke and higher x2 values correspond to a higher chance of a patient having a leftsided stroke.
The animations depict the trajectories of massless particles advected by the velocity field through the vasculature of differentpatients. The particles are released at one second intervals, starting from 0.15 s. Each systole, 1,000 particles are released into the system via the aortic inlet. The particles are colored based on their velocity (cm/s). Videos 1–4 depict patients with left stroke, and Videos 5–8 depict patients with right stroke.
Notes
Funding statement
None
Conflicts of interest
The authors have no financial conflicts of interest.
Author contribution
Conceptualization: PM. Study design: PM. Methodology: MI. Data collection: PM. Investigation: MI, DZ. Statistical analysis: MI. Writing—original draft: MI, DZ. Writing—review & editing: PM, DSL. Approval of final manuscript: all authors.
Acknowledgments
Data supporting the findings of this study are available from the corresponding author upon request.