A bi-atrial statistical shape model for large-scale in silico studies of human atria: model development and application to ECG simulations
AA bi-atrial statistical shape model for large-scale in silico studiesof human atria: model development and application to ECGsimulations
Claudia Nagel a ∗ , Steffen Schuler a , Olaf D¨ossel a ,Axel Loewe a a Institute of Biomedical Engineering, Karlsruhe Institute of Technology, Kaiserstr. 12, 76131 Karlsruhe, Germany ∗ Corresponding author: Claudia Nagel, [email protected]
Abstract
Large-scale electrophysiological simulations to obtain electrocardiograms (ECG) carry the potentialto produce extensive datasets for training of machine learning classifiers to, e.g., discriminate betweendifferent cardiac pathologies. The adoption of simulations for these purposes is limited due to a lackof ready-to-use models covering atrial anatomical variability.We built a bi-atrial statistical shape model (SSM) of the endocardial wall based on 47 segmentedhuman CT and MRI datasets using Gaussian process morphable models. Generalization, specificity,and compactness metrics were evaluated. The SSM was applied to simulate atrial ECGs in 100random volumetric instances.The first eigenmode of our SSM reflects a change of the total volume of both atria, the secondthe asymmetry between left vs. right atrial volume, the third a change in the prominence of theatrial appendages. The SSM is capable of generalizing well to unseen geometries and 95% of the totalshape variance is covered by its first 23 eigenvectors. The P waves in the 12-lead ECG of 100 randominstances showed a duration of 104 . ± . Keywords:
Statistical Shape Modeling; Bi-atrial Shape Model; Electrophysiological Simulation; 12-lead ECG;P waves
A wide range of machine learning approaches have already been proposed for classifying cardiovascular pathologiesbased on the 12-lead electrocardiogram (ECG) (Hannun et al., 2019; Perez Alday et al., 2020; Strodthoff et al.,2020). Since the ECG is a cost-effective, non-invasive and commonly available tool in clinical practice, it isparticularly desirable to identify and diagnose cardiac pathologies only based on the ECG and without the needof further expensive imaging techniques or invasive procedures. However, the training of such classifiers requiresa large, balanced, and reliably labeled dataset. Oftentimes, not all of these prerequisites are met when usingclinically recorded data. Additionally, expert annotations are commonly relied upon to generate the groundtruth labels describing the underlying pathologies for clinical datasets coming along with inter- and intra-observervariabilities significantly affecting the reliability of the ground truth labels (Hannun et al., 2019).These limitations call for simulated synthetic ECG as a source for large, representative and well controlleddatasets. These datasets can be used to directly deduce diagnostic criteria visually (Andlauer et al., 2018) orto train machine learning classifiers to discriminate between different cardiac diseases and healthy individuals(Andlauer et al., 2018). The advantage of using simulated over clinical data lies not only in the precisely knownground truth of the underlying pathology that was defined for the simulation, but also in the possibility to generatea virtually infinite amount of signals for each pathology class.Nevertheless, atrial, ventricular and thoracic geometrical models are needed for conducting electrophysiologicalsimulations to obtain the 12-lead ECG. In this regard, statistical shape models (SSM) allow to compile a widerange of realistic geometries that represent the variability observed in the cohort used to build the SSM. WhileSSMs of the human ventricles (Bai et al., 2015) and torsos (Pishchulin et al., 2017) exist and are publicly available,an open shape model covering both atria covering all relevant anatomical structures for EP simulations (atrialbody, appendages, PVs) is still lacking to the best of our knowledge. a r X i v : . [ ee ss . SP ] F e b ifferent statistical atlases of the human whole heart anatomy (Ecabert et al., 2008; Hoogendoorn et al.,2013; L¨otj¨onen et al., 2004; Ordas et al., 2007; Unberath et al., 2015; Zhuang et al., 2010) have been constructedfor segmentation of magnetic resonance (MR) or computed tomography (CT) images by means of active shapemodeling approaches. However, those models are usually built based on a small number of sample segmentationsor were not made publicly available. Furthermore, different SSMs of only the left atrium (LA) have been presentedin various studies either for the purpose of simulations (Corrado et al., 2020) or for characterizing changes in shapeof the LA (Bieging et al., 2018; Cates et al., 2014; Depa et al., 2010; Varela et al., 2017) in patients with atrialfibrillation. These LA models are built based on a solid number of instances, but lack the right atrium (RA) andoften also the left atrial appendage (LAA). However, these anatomical structures are not only indispensable forthe use case of ECG simulations. They are also of particular importance when investigating the mechanisms oftypical atrial flutter in the RA or bi-atrial flutter and fibrillation. Additionally, the LAA is highly relevant forstudies examining blood clot formation causing stroke (Masci et al., 2019), LAA occlusion as potential therapy(Aguado et al., 2019) and the role of the LAA in the onset and maintenance of atrial fibrillation (Nishimura et al.,2019). Due to the lack of ready-to-use models of the atria, a bi-atrial SSM would cater the need of generatinggeometrical atrial models representing inter-subject anatomical variability. These could be employed to gain acomprehensive understanding of e.g. the underlying mechanisms of the onset and perpetuation of re-entrantactivity during atrial flutter and fibrillation not only in personalized computer models but also in a large patientcohort. Thus, including the shape of the RA in the model as well as making the bi-atrial SSM available to thecommunity, enables large-scale simulation of atrial signals. Although the focus of this paper is the application ofthe SSM for ECG simulations, its field of application is not limited to this particular use case. The bi-atrial modelcan also be exploited for other in silico approaches like continuum-mechanics and fluid simulations. Furthermore,active shape modeling approaches using the novel bi-atrial SSM could facilitate automated segmentation of theatria from CT or MRI datasets.In this work, we built an SSM of both atria from manual segmentations of 47 MR and CT scans. Furthermore,we propose a workflow to generate a volumetric atrial model based on instances of the SSM. We also provide thebi-atrial SSM under the creative commons license CC-BY 4.0 together with 100 exemplary volumetric modelsderived from it including fiber orientation, inter-atrial bridges and material tags (Nagel et al., 2020). The geometric representation as well as the variation in shape among a set of individual three dimensional objectscan be described by SSMs. Point distribution models (Cootes et al., 1995) are the most common subclass of SSMsand require a vectorized point-based representation s n of any individual geometry Γ n comprising M consistentlysampled surface points [ x n , y n , z n ] T : s n = [ x n, , y n, , z n, , . . . , x n,M , y n,M , z n,M ] T . (1)Assuming that the spatial variations of the surface points follow a multivariate normal distribution, a compactrepresentation of the mean and covariance matrix describing the shape variations can be obtained by applyinga principal component analysis (PCA) to the observations s . In this way, all N individual shapes Γ can berepresented by a linear combination of N − v : s n = s + N − (cid:88) k =1 r n,k · (cid:112) σ k · v k , (2)with s being the mean shape vector as well as σ and v representing the eigenvalues and eigenvectors of thecovariance matrix, respectively. r n,k represent the weighting coefficients for the individual eigenvectors. To obtainthis parametric representation of the shape variations from clinical MRI or CT data, a number of preprocessingsteps have to be performed: i) segmenting the images, preferably in a (semi-)automatic manner, ii) rigidly aligningthe resulting shapes in space, iii) establishing a dense correspondence between the individual shapes to obtainthe shape vectors s C that were then subject to PCA. Three independent multi-center, multi-vendor databases (Karim et al., 2018,1; Tobon-Gomez et al., 2015) wereused to build the SSM. Their properties are summarized in Table 1. The images originate either from healthysubjects or from patients suffering from atrial fibrillation. Some of the available images were excluded due tolow signal to noise ratio or incomplete capture of the inferior right atrial body. Only subjects with 4 pulmonaryveins (PVs) were considered because of the limited ability of SSMs to capture only continuous changes of vertexlocations.
In order to obtain the individual instances of both atria, a semi-automatic segmentation of the blood poolrepresenting the endocardial surface of the left and the right atrium from MR and CT images was performed
Dataset Source Number of subjects Voxel resolution using CemrgApp (Razeghi et al., 2020). 2D region growing in several selected slices as well as 3D interpolationwere applied to each image stack. To reduce the impact of noise or image artefacts on the segmentation outcome,details were manually corrected. Fig. 1 shows examples of incorrect segmentation results due to insufficientregion growing performance (left column) and 3D interpolation (middle column) that made a manual correctionindispensable. Automated segmentation with region growing especially failed in 2D planes where both, the LAand the left ventricle are visible, because the mitral valve shows the same image intensity as the LA and theleft ventricle. Therefore, a cutting plane between atrium and ventricle was inserted manually. The drawbacksof 3D interpolation are particularly affecting the areas around the PVs where the interpolated surface tends toclose small gaps between the PVs and the atrial body. For 20 images in dataset 2, a segmentation of the LA wasprovided. However, the LAA was truncated in close proximity to the left atrial body (Tobon-Gomez et al., 2015)in these segmentations. Since we aimed at incorporating the variability of the LAA shape in our model, the LAsegmentations of dataset 2 were adapted to include the full volume of the LAA as shown in Fig. 1 (right column).The resulting segmentations were exported as triangular meshes.
After segmenting the individual instances Γ n of the atria, the different shapes were rigidly aligned in space toavoid a representation of translation and rotation parameters in the eigenmodes of the SSM. This was performedautomatically by means of the iterative closest point (ICP) algorithm that provides a solution to the orthogonalProcrustes problem (Chen and Medioni, 1992). In each iteration i , candidate correspondences [ˆ x n , ˆ y n , ˆ z n ] TR,i between a target mesh Γ n and the reference mesh Γ R were found by attributing to each node in Γ n the point withthe the smallest Euclidean distance in Γ R . Procrustes analysis was then used to estimate the linear transformation T i – consisting of rotation and translation – which yields the best match of the candidate correspondence points − σ and +3 σ . [ˆ x n , ˆ y n , ˆ z n ] TR,i with the reference points [ x R , y R , z R ] T . After applying the estimated transformation T i to thepoints in mesh Γ n : (cid:101) Γ n,i +1 = T i · (cid:101) Γ n,i , with (cid:101) Γ n, = Γ n , (3)new candidate correspondences [ˆ x n , ˆ y n , ˆ z n ] TR,i +1 are recursively found between the transformed mesh (cid:101) Γ n,i +1 and Γ R at each iteration i and used for solving the Procrustes problem. If after several recursive calls of thefunction, either the maximum number of 150 iterations is exceeded or the convergence criterion is fulfilled, anoptimal transformation matrix for the alignment of both shapes Γ n and Γ R is found resulting in a set of N rigidlyaligned shapes Γ A . Each aligned individual instance n comprises M n surface points [ x An, , y An, , z An, , . . . , x An,M n , y An,M n , z An,M n ] T . Inorder to describe the variations in shape of the aligned instances Γ A by means of a point distribution model,correspondence between the vertex IDs among all individual shapes have to be established. Establishing corre-spondence requires to retrieve concordant points in all shapes Γ A , so that the N aligned shapes are not onlyrepresented by the same amount of surface points M but also that each point [ x An,m , y
An,m , z
An,m ] with a specific ID m represents the same anatomical landmark in any arbitrary shape n . For this purpose, we used Gaussian processmorphable models (GPMM) (Luthi et al., 2018) and ScalismoLab (Bouabene et al., 2020) to subject a referenceshape Γ AR to a generic deformation in such a way that the deformed shape (cid:101) Γ AR,n matches the individual alignedshape Γ An in the best possible way. This process then yields a set Γ C of aligned shapes that are characterized byhomologous, corresponding surface points. For this process, we defined three independent generic deformationsby Gaussian process (GP) models. Gaussian kernels described the similarity between two distinct points x and x (cid:48) : k ( x , x (cid:48) ) = s · exp (cid:18) − ( x − x (cid:48) ) l (cid:19) (4)were approximated by the leading eigenfunctions of their Karhunen-Lo`eve expansion as described in Luthiet al. (2018). They were further employed to fit the orientation of the left and right pulmonary veins (LPV,RPV), the atrial body, as well as the left and the right atrial appendages (LAA, RAA). The separation into threedifferent models (atrial body, appendages, PVs) served two different purposes. On the one hand, we were ableto account for the high anatomical variability of the appendages by allowing smaller inter-dependencies spanningbetween the points located on the appendages. On the other hand, the generic model varying the points locatedon the PVs was designed such that only the orientation of the PV ostia but not their length was affected. Theoptimization problem of fitting the GP model (cid:101) Γ AR,n to the individual aligned shapes Γ An was solved with an L-BFGS optimization minimizing the mean squared error between the vertex coordinates of the deformed model (cid:101) Γ AR,n and the target shape Γ An . To accurately fit the PVs, a kernel representing the orientation of the four PVs inanterior-posterior direction in its first four eigenvectors was constructed (Fig. 2). Only the orientation of the PVsand not their length were fitted since the latter highly depends on the segmentation approach and does thereforenot represent a proper observed anatomical variation considering the heterogeneous input data used in this study.A low rank approximation of a GP model with a variance of s b = 50 , l b = 40 at points representing the general atrial body ( b ) and s a = 20 , l a = 20 at the appendages was used to account for the higher anatomical variabilityin the appendage ( a ) regions. The vertices at the distal parts of the superior and inferior caval veins, the coronary sinus, the PVs, as well asthe mitral valve and the tricuspid valve were discarded from the N aligned shape vectors in correspondence s C tolimit the model creation to atrial components relevant for electrophysiological simulations. Applying a PCA tothese cut shape vectors in correspondence s C yields their mean shape s and N − v along withtheir respective variances σ . In this way, an exact reconstruction of any individual shape instance Γ Cn is feasibleby determining the coefficients r n in Eq. 2 with a standard least squares estimation. Furthermore, additionalarbitrary variation shapes Γ var in the span of the N − v can be derived by varying r . Underthe assumption that the values of r are normally distributed among the observed instances Γ Cn , keeping r in theinterval [ − , +3] N − yields realistic artificially generated shapes within the empirically observed variability. The bi-atrial SSM represents the mean shape of the atrial endocardial surface and the variation of all point coor-dinates in space so that any arbitrary variation mesh Γ var can be derived from it. However, a volumetric modelof the atria, including inter-atrial bridges, anatomical labels and fiber orientations is required to perform elec-trophysiological simulations and to obtain realistic body surface P waves. Since a segmentation of the epicardialsurface from conventional MR images is usually not feasible due to an insufficient spatial resolution and a limitedsignal to noise ratio, the epicardial surface was augmented in a postprocessing step assuming a homogeneous atrialwall thickness. To approximate the epicardial surface, the endocardial surface of the variation mesh Γ var wasdilated by 3 mm at each point along the normal direction calculated as the mean of the adjacent triangle normals.Both surfaces were merged and intersections and holes between epi- and endocardium were corrected and closedautomatically using the iso2mesh toolbox (Tran et al., 2020). The closed surface was afterwards remeshed usingInstant Meshes (Jakob et al., 2015) and transformed into a volumetric tetrahedral mesh with an average edgelength of 1 mm using Gmsh (Geuzaine and Remacle, 2009). The algorithms described by Loewe (2016); Wachteret al. (2015) were used to automatically augment the models with Bachmann’s bundle, a coronary sinus and anupper and middle posterior inter-atrial connection between the LA and RA as well as myocardial fiber orientationand anatomical labels. The augmented anatomical structures are visualized in Fig. 3.
100 random instances were derived from the bi-atrial SSM by drawing the eigenvector coefficients r of Eq. 2 from auniform distribution in the range of the minimum and maximum value found in the dataset used to build the SSM.A fast marching (Loewe et al., 2019; Sethian, 1996) simulation was carried out for solving the Eikonal equation onthese 100 geometries to obtain the spread of electrical activation and derive local electrical activation times (LATs)for each node. This sinus rhythm activation was initiated from a sinus node exit site located at the junction ofthe superior caval vein and the RAA (Loewe et al., 2016). The atrial wall was separated into seven differentanatomical regions: regular right and left atrium, inter-atrial connections, valve rings, pectinate muscles, cristaterminalis and inferior isthmus. The conduction velocities along the fiber directions and the anisotropy ratios inthe different regions were chosen as reported previously (Loewe et al., 2016) and are given in in Table 2. Thetransmembrane voltage distribution on the atrial surfaces was obtained by shifting a pre-computed Courtemanche Atrial Region CV T (mm/s) AR Right atrium 739 2.11Left atrium 946 2.11Inter-atrial connections 1093 3.36Valve rings 445 2.11Pectinate muscles 578 3.78Crista Terminalis 607 3.0Inferior isthmus 722 1Figure 4: Eigenmodes of the bi-atrial shape model. The three leading eigenmodes are displayed indifferent rows. Columns 1-3 represent the variation of the eigenvector coefficients. In the fourth column,the anatomical view used to capture the respective eigenmode is depicted. et al. (1998) action potential in time according to the calculated LATs as proposed by (Kahlmann et al., 2017).The ECG forward problem to derive the body surface potentials from the transmembrane distribution on the heartwas solved by means of the boundary element method (Stenroos et al., 2007). Considering computational cost,the surface bounding the heart was sampled at a resolution of 3 mm. Laplacian blurring with optimal blurringparameters as described in Schuler et al. (2019) was applied to the source distribution. The mean shape of thehuman body SSM developed by Pishchulin et al. (2017) served as a reference shape of the torso. The P wave ofthe 12-lead ECG signal was extracted from the body surface potentials at the standardized electrode positions.
Applying a PCA to the cut shape vectors in correspondence s C as described in section 2.5 yields their mean shape s comprising 95.048 triangular cells and 47.528 vertices with an average edge length of 0.862 mm. Furthermore, theeigenvectors and -values of the bi-atrial model were obtained. Fig. 4 shows the shape changes caused by varyingthe coefficients of the first three eigenvectors. The first eigenmode represents a change in the total volume andsize of both atria simultaneously (Fig. 4, first row). The second mode reflects the asymmetry of the LA vs. theRA volume, i.e., the increase of the LA volume and the concurrent decrease of the RA volume. The prominenceof the right and left appendage are encoded in the third eigenmode (Fig. 4, third row). The orientation of thePVs to one another are represented – among other aspects – in the fifth, sixth, and eighth eigenmodes of theSSM. The quality of the bi-atrial SSM was evaluated by first assessing the mean vertex to vertex distances betweenthe meshes in correspondence and their respective original locations from the dataset. For the 47 meshes used tobuild the SSM, this distance was 1 . ± .
25 mm. Furthermore, three standard evaluation criteria for evaluatingthe SSM quality proposed by Huw Davies (2002) were considered: generalization, specificity, and compactness.The generalization metric addressed in section 3.2.1 refers to the ability of the SSM to recreate an instance whoseshape vector was excluded from the dataset used to create the SSM. The specificity metric (section 3.2.2) assessesthe goodness of the model in terms of generating realistic shapes. Furthermore, the compactness (section 3.2.3)metric of the model increases the more the set of eigenvectors can be reduced while still being able to describethe majority of the total shape variance present in the dataset.
To evaluate the generalization quality of the SSM, we used leave-one-out cross-validation and defined N datasetswith N − . mm among allshapes which compares to the order of magnitude of the MRI cross-plane resolution (0 . mm − . mm ). Instance4 holds the lowest Euclidean distances between the vertices of its original and reconstructed shape, whereasinstance 37 is characterized by considerably high error values. Especially the 95th percentile bounds and theoutlier values comprise large vertex to vertex distances. Fig. 6 depicts the approximated atria with the reducedSSM for instance 37. The vertex color represents the Euclidean distance to the corresponding vertex in the originalshape instance 37. Vertices showing larger deviations were located predominantly on the distal part of the rightinferior pulmonary vein (RIPV). The same phenomenon was observed also for instance 47. The specificity of the bi-atrial model was evaluated by generating 1000 random shapes according to Eq. 2 byuniformly sampling r in the interval [ − , Γ C used to build the SSM was assessed in terms of the root meansquare error (rmse) of all vertex-to-vertex distances between the randomly generated and the original shape.The rmse ranged from 5 .
29 to 11 .
73 mm among all 1000 random instances with a mean ± standard deviation of7 . ± .
04 mm. Fig. 7 shows one randomly generated shape with an rmse of 7 .
58 mm in yellow together with itsmost similar instance from the dataset in blue. This case approximately represents the mean rmse value amongall 1000 random shapes.
Fig. 8 depicts the total variance of the dataset explained by the model when including only a limited number ofleading eigenvectors. 90 and 95% of the total shape variance in the individual segmented shapes can be coveredby the SSM when considering only the first 16 and 23 eigenvectors, respectively.
Calculating the P wave on the mean shape of the proposed SSM as described in section 2.7 yields the signals forthe Einthoven, Goldberger and Wilson leads shown in Fig. 9. The P wave duration was extracted for each of the12-lead ECGs simulated on 100 random instances by considering the time difference between the latest detectionof the P wave offset and the earliest P wave onset across all 12 leads. The values of the P wave durations acrossall 100 instances ranged from 80 ms to 118 ms with a mean and standard deviation of 104 . ± . The bi-atrial SSM is provided under the Creative Commons license CC-BY 4.0 together with 100 exemplaryvolumetric models derived from it including fiber orientation, inter-atrial bridges and anatomical labels (Nagelet al., 2020). The SSM is available as an h5 file encoding information about the mean shape’s spatial vertexlocations and their triangulation. Also the eigenvectors and -values resulting from the applying the PCA areincluded. The 100 geometries were generated by varying the eigenvector coefficients r in the [ − , +3] σ range. These anatomical models are provided in VTK file format including fiber orientation as 3D vectors and materialtags as scalar values in the cell data section.
The main result of this study is a point distribution model incorporating the shape variations of the right and theleft atrium as well as their appendages and the PVs. Moreover, we presented a workflow for building a volumetricatrial model from an endocardial surface derived from the SSM. Together with 100 example volumetric geometriesgenerated by varying the coefficients of the principal components uniformly in the [ − , +3] σ range including fiberorientation, inter-atrial bridges and anatomical labels, the SSM is openly available (Nagel et al., 2020).Electrophysiological simulations covering atrial excitation spread and propagation of electrical potentials tothe body surface were conducted on these 100 example shapes. The resulting P wave durations obtained with theproposed SSM of 104 . ± . > cm in two particular cases. The specificity results of 7 . ± .
04 mm leave room forimprovement. However, the low specificity scores do not result from unanatomical characteristics of the generatedshapes. They occur rather due to the small dataset of 47 instances available for selecting the closest shape duringevaluation. Considering the MR slice thickness of predominantly 2 . mm (Tab. 1), a specificity rmse of 7 . mm is in the range of less than 2 voxel diameters with segmentation uncertainty adding to it (Karim et al., 2018).The specificity evaluation of our model therefore indicates that randomly generated shapes produce valid shapes ith an accuracy in the range of the error susceptibility during segmentation.The atria segmented for this study originate from datasets comprising images of not only healthy subjects butalso patients with a known history of atrial fibrillation. LA enlargement has been linked with an increased risk forthis arrhythmia (Andlauer et al., 2018; Broughton et al., 2016; Hamatani et al., 2016). To ensure that our modelis not based on a biased dataset with predominantly enlarged left atria, the LA volume (excluding LAA and PVostia) of the N segmented geometries (82 . ± . ml ) was compared to reference values. Pritchett et al. (2003)considered all age and BMI groups in healthy individuals. Translating their 2D measurements to 3D volumes assuggested by Al-Mohaissen et al. (2013) yields a [ − , +3] σ range of 10-130 ml with the largest LA volume in ourdataset (122 ml) being within that range.To showcase a potential application, we conducted multi-scale electrophysiological simulations on 100 instancesof the shape model. This proof of concept was deliberately based on a simple model not considering locallyheterogeneous atrial wall thickness (Azzolin et al., 2020; Karim et al., 2018), disease-induced remodeling ofmembrane dynamics (Loewe et al., 2014) or diffusive aspects during cardiac depolarization. Also only one torsoshape and no rotation and translation of the atria within the torso are considered. The pipeline to generatevolumetric models and simulation setups from the SSM is prepared for such extensions, though. Future studiesfocusing on repolarization could replace the simplistic Eikonal coupling employed here with a reaction-Eikonalscheme as suggested by Neic et al. (2017).The main advantage of the novel bi-atrial SSM consists in the automated generation of a large number of atrialgeometries. In this way, the cumbersome and time-consuming process of anatomical model generation involvingMRI segmentation and defining bundles and fiber orientation can be facilitated and expedited.Potse et al. (2018) examined the influence of electrical and structural remodeling on the maintenance ofcomplex reentrant activitiy. With our proposed bi-atrial SSM, also the influence of the general atrial anatomy onthe perpetuation and initialization of atrial fibrillation can be quantified.Saha et al. (2016) investigated the effect of endo-epicardial activation delay on the P wave morphology.However, only one atrial geometry was used to deduce models of different atrial wall thicknesses in this study andthe authors state the lack of using different geometries as a limitation of their work. The same limitation is listedin the study of Pezzuto et al. (2018) aiming at quantifying the beat-to-beat variability of P waves in patients withatrial fibrillation. With our SSM, a larger number of different volumetric atrial models is easily acquirable.By means of our bi-atrial SSM, scale-large cohort studies using computer models for simulating atrial activitybecome feasible. Luongo et al. (2020a,2) found a significant influence of the number of atrial anatomies includedon the classification of different types of atrial flutter with a machine learning approach. With the proposed SSM,a large number of geometries can be deduced and used as a basis for in silico big data approaches such as toproduce extensive datasets for machine learning applications. The provided instances are ready to be used offthe shelf in available computational simulation environments such as openCARP for electrophysiology (S´anchezet al., 2020), openFOAM for fluid dynamics (Jasak, 2009) or FEniCS for continuum-mechanics (Alnæs et al.,2015). To the best of our knowledge, we built the first SSM incorporating both atria, their appendages and the orientationof the PVs. The model itself and 100 random volumetric atrial geometries including rule-based fiber orientationand anatomical labelling were made publicly available to the community. These models are ready to be usedoff-the-shelf for electrophysiological simulations. Established quality criteria indicate that the novel SSM can bereduced to a set of 23 eigenvectors and is capable of generalizing well to unseen geometries. P waves simulatedon 100 random instances derived from the SSM reproduce the P wave distribution observed in clinical ECGs ofhealthy individuals. As such, the SSM is suitable to generate comprehensive model cohorts covering the relevantanatomical variability as a basis for large-scale in silico simulations including, but not limited to, ECG simulationsfor machine learning applications.
Funding Statement
This work was supported by the EMPIR programme co-financed by the participating states and from the EuropeanUnion’s Horizon 2020 research and innovation programme under grant MedalCare 18HLT07.
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