Integrating anatomy and electrophysiology in the healthy human heart: Insights from biventricular statistical shape analysis using universal coordinates

The heart is a complex and highly variable organ, both in shape and function, constituting an essential part of the human body [1, 2]. Computational modeling of the heart is a challenging task, usually addressed by complex mathematical models and numerical methods, combining clinical measurements and partial differential equations (PDEs) [3, 4].

Cardiac models can be adapted to represent the actual anatomy and function of individual patients, leading to the concept of a cardiac digital twin (CDT). CDTs are virtual, subject-specific heart models that closely mirror the structure and function of their physical counterparts [5]. Beyond enhancing fundamental understanding of cardiovascular physiology and pathophysiology [6], direct clinical applications of CDTs include surgical planning [7], prediction of clinical outcomes [8], and risk assessment [9, 10]. As such, these models have the potential to improve patient outcomes via personalized and preventative medicine. CDTs focus on modeling a single aspect of the cardiovascular system, such as electrophysiology (EP), mechanical function, or hemodynamics, or a combination thereof.

Regardless of the specific aspect(s) of the cardiovascular system that a model targets, the anatomy of the individual needs to be taken into account. As such, defining a computational mesh representing this anatomy is a common step in the construction of all types of CDTs. This discrete, multi-label mesh is typically derived from cardiac computed tomography (CT) or magnetic resonance (MR) imaging of the subject. It delineates the computational domains for discretizing and numerically solving the PDEs governing the system. The process of creating a mesh that matches subject-specific anatomy is known as anatomical twinning [11].

On a broader scale, digital twins can be extended from individuals to populations, leading to the concept of virtual cohorts. These virtual cohorts enable in silico clinical trials that offer several advantages over traditional approaches, such as reducing the need for real patients to undergo experimental treatments, minimizing the risk of failed trials and associated financial costs, and optimizing trial design [12, 13]. Constructing an accurate anatomical representation of the target population is a crucial first step in the pipeline for developing functional, population-level CDTs.

Statistical shape modeling offers a powerful means to study and represent individual variation within a broader population framework [14, 15, 16, 17, 18, 19, 20]. Cardiac statistical shape models (SSMs), which capture population-level anatomical variations, closely relate to patient-level CDTs in the applied methodology, since both rely on anatomical twinning. Moreover, these models allow the creation of representative synthetic populations, enhancing virtual cohort studies and providing an anatomical building block for population-level CDTs.

Statistical shape modeling enables a mathematically rigorous assessment of shape variability within a population through principal component analysis (PCA) [15, 21]. In the field of computational cardiology, there are numerous applications for such statistical shape models (SSMs), many of which are directly or indirectly related to the concept of CDTs.

(1) Synthetic data generation: An SSM can be leveraged to generate synthetic heart geometries that cover the shape variability present in the training population. These synthetic geometries blend the characteristics of existing hearts and can be limited to remain within the same statistical distribution as the original data. The use of synthetic data offers two main advantages. First, since the synthetic geometries do not correspond to real individuals, they do not contain direct sensitive health information. As such, they can be made publicly available without privacy concerns. Second, SSMs allow for repeated sampling from the statistical shape distribution approximated by the training data, enabling the generation of a virtually unlimited number of synthetic, yet realistic heart geometries. These two elements directly address data availability challenges in CDT development, where high-quality tomographic imaging is often required for anatomical twinning, but scarce [22, 11]. By offering a scalable alternative, synthetic data generated from SSMs could help alleviate this limitation. Representative, synthetic geometries obtained from SSMs are also of great use in virtual clinical trials [13] and large-scale simulation studies [23].

(2) Dimensionality reduction and machine learning (ML): The incorporation of ML and deep learning (DL) into CDT construction pipelines holds great promise for the personalization of CDTs using functional data [11, 24, 25]. However, these algorithms typically require large volumes of training data, preferably in a suitable input format. Highly complex tomography imaging or computational mesh formats might not be optimal for certain ML and DL frameworks. Statistical shape analysis, with its dimensionality reduction capabilities, can represent complex heart geometries in a more efficient and possibly more compatible format. As such, SSMs enable and facilitate the integration of DL and ML into CDT technology. Moreover, the ability to generate large amounts of synthetic data through SSMs addresses the data-intensive requirements of ML and DL, further supporting their integration into CDT pipelines. Additionally, cardiac SSMs support applications in automated segmentation algorithms [26, 27].

(3) Statistical analysis: A cardiac SSM offers valuable, quantitative insights into heart shape variability, which can in turn be linked to other health-related data, such as electrophysiological measurements and demographic information, through statistical analyses [18, 19, 20]. As such, cardiac SSM are valuable tools for advancing our fundamental understanding of cardiac anatomy, notably in relation to other clinically relevant features, such as electrocardiograms (ECGs).

(4) Baseline anatomical framework: SSMs of healthy cardiac anatomy may offer a robust foundation for developing SSMs related to cardiovascular diseases and spatiotemporal variation in heart anatomy, by modeling static, healthy cardiac anatomy as a reference point.

Previous work in cardiac SSM development provides meaningful insights into cardiac anatomy of various scopes (biventricular anatomy in [16, 17, 20], four-chamber cardiac anatomy in [18], and bi-atrial anatomy in [19]). However, some limitations can be identified. The spatial resolution of the input data is often limited compared to the clinical state-of-the-art [28, 16, 17, 19, 20]. Furthermore, some studies include only a limited and possibly insufficient number of subjects in their shape analysis, such as 19 shapes in [18] and 47 shapes in [19]. Such limitations are often related to the lack of automatic workflows for the generation of training geometries, resulting in time-consuming manual processes, especially in the segmentation step [17, 18, 19]. Moreover, some studies include subjects suffering from cardiovascular disease, meaning that the resulting SSM is likely not representative of a healthy population [17, 19, 20]. In terms of methodology, none of the studies leverage the recent advancements in the field of cardiac modeling, specifically designed for registration purposes, i.e. the implementation of universal cardiac coordinate systems [29, 30, 11, 31]. Additionally, although cardiac SSM studies usually include the release of synthetic cohorts, many of these cohorts only feature surface meshes [16, 17], and as such are not suitable for direct use in downstream applications, such as finite element simulations. Notable exceptions are [18] and [19], which include the publication of volumetric four-chamber meshes and volumetric bi-atrial meshes, respectively. Lastly, while [18] and [19] have studied the relationship between anatomical features, defined by their cardiac SSM, and in silico functional measurements of the heart, the impact of anatomical differences on functional measurements in real-world patients, which have the power to either validate these simulation findings or indicate modeling flaws, remains understudied.

In this work, we develop a biventricular SSM from high-resolution cardiac CT scans from 271 healthy individuals. Our work advances the state-of-the-art in cardiac statistical shape modeling and CDT technology by:

1. 1.

   Dataset construction: We use a large dataset comprising 271 high-resolution (submillimeter) CT images from a healthy, mixed-sex population, enhancing accuracy and anatomical detail of the SSM. Moreover, fully automated segmentation and anatomical model generation workflows are implemented to build the SSM training dataset. This automated anatomical twinning approach directly enables building patient-level, anatomical, biventricular CDTs.

2. 2.

   Statistical shape modeling: We establish lightweight correspondence between point clouds of distinct geometries, leveraging universal ventricular coordinates (UVCs) [29], effectively eliminating the computationally expensive nonlinear registration step typically required for SSM construction.

3. 3.

   Providing high-quality meshes for downstream applications: We provide a detailed biventricular SSM, together with a synthetic cohort of 100 ready-to-use biventricular meshes, including anatomical labels and fibers, representative of healthy biventricular anatomy. The virtual anatomical cohort represents a building block towards a population-level CDT.

4. 4.

   Quantifying relationships with biventricular anatomy: We study and quantify the relation between biventricular anatomy and clinically measured ECGs and demographic variables, leveraging statistical shape analysis and automated ECG delineation.

The SSM, trained on the complete dataset of 271 biventricular geometries, achieves substantial dimensionality reduction. Specifically, the first 3 PCs account for 40.34%, 11.19%, and 9.59% of the shape variability in the population, respectively. The first 16, 29, and 94 PCs collectively explain 90%, 95%, and 99% of the biventricular shape variability, respectively. The primary modes of variation encoded by the first few PCs are as follows: the first PC represents overall ventricular size, the second PC captures the shape and elongation of the ventricles, with the RV showing the most notable changes, and the third PC describes the relative positioning between the LV and RV, along the apical-basal axis (see Figure 7 for detailed views). Additional PCs are mostly connected to RV shape.

Employing the LOOCV method, the reconstruction error was calculated for each leave-out geometry. The average reconstruction error obtained in this experiment was equal to 0.61 $\text{\,}\mathrm{mm}$, only slightly higher than the spatial resolution of the CT scans used for building the training set of the SSM. Figure 8 shows the pointwise reconstruction errors mapped onto the mesh for a random subject, showing that the largest errors (8.83 $\text{\,}\mathrm{mm}$) are located at the RV apex, followed by the ventricular base, particularly at the junction between the LV and RV. To determine if this trend is consistent across geometries, we mapped the average pointwise reconstruction error, which ranges from 0.36 to 3.29 $\text{\,}\mathrm{mm}$ across the different points, from the entire LOOCV experiment onto the mean biventricular geometry, as shown in Figure 8. This similarly highlights the basal region of both ventricles as the area with the highest error, along with a smaller area at the apex, near the junction between the LV and RV, but also shows a relatively uniform error distribution without excessively error-prone regions.

Figure 9 illustrates the distribution of the reconstruction errors for the full SSM across the demographic groups included in this study. The mean reconstruction error for the female group was 0.54 $\text{\,}\mathrm{mm}$, while those for the male control group, male early-onset athletes, and male late-onset athletes were 0.63 $\text{\,}\mathrm{mm}$, 0.66 $\text{\,}\mathrm{mm}$ and 0.62 $\text{\,}\mathrm{mm}$, respectively. The results show that the female group can be approximated with a slightly smaller reconstruction error. No substantial differences in reconstruction accuracy were obtained for the other groups, indicating that the full SSM is equally effective in representing biventricular geometries across the three demographic groups of the male population. An additional analysis in B shows that this effect is not caused by the slight demographic imbalance in the dataset, and C shows that the smaller reconstruction errors associated with female harts can largely, but not entirely be explained by heart size factors.

Figure 10 illustrates the results of LOOCV experiments conducted on data subsets of different sizes. The trend demonstrates that increasing the dataset size improves the SSM accuracy in representing healthy biventricular anatomies. Specifically, as the dataset size grows, the mean reconstruction error decreases significantly, from 1.37 $\text{\,}\mathrm{mm}$ with 56 subjects to 0.61 $\text{\,}\mathrm{mm}$ with all 271 subjects, indicating that further dataset expansion could potentially enhance the model performance even more.

A qualitative comparison of the first three SSM modes between the biased and unbiased SSMs revealed that the interpretation of these PCs was consistent, indicating a similar anatomical variation was captured with male-only, female-only and mixed-sex datasets.

Next, a quantitative analysis of the impact of sex-related anatomical differences on the SSM was conducted. The results of reconstructing male and female geometries on two sex-biased SSMs, and one unbiased SSM, are shown in Figure 11. For the reconstruction of male geometries, the reconstruction error was highest, namely 1.48 $\text{\,}\mathrm{mm}$, when using an opposite-sex SSM. The reconstruction error when using a same- or mixed-sex SSM was lower, respectively 1.36 and 1.37 $\text{\,}\mathrm{mm}$. The same holds for female geometries, where an opposite-, same- and mixed-sex SSM leads to reconstruction errors equal to 1.22, 1.13, and 1.16 $\text{\,}\mathrm{mm}$, respectively. For an additional analysis of the influence of sex-related anatomical differences on SSM representativeness, independent of heart size, we refer to C.

Regarding the distribution of PC scores across different demographic groups, we observed a statistically significant difference between the female group and the male control population in this dataset on the first PC (see Section 3.6 and Figure 12).

Figure 13 displays three example geometries of the synthetic cohort, generated by sampling from 94 PCs. The synthetic geometries were resampled to a mesh resolution of 0.9 $\text{\,}\mathrm{mm}$, and augmented with anatomical labels and fiber architectures.

The correlation analysis between PC scores and ECG-derived features revealed eight statistically significant correlations between biventricular anatomy and EP in our study population, of which the strongest and most significant one was the correlation between PC1 and RRint, with a correlation coefficient equal to -0.50. Furthermore, six statistically significant correlations were found between anatomical components and numerical demographic features, the strongest ones being the correlation between PC1 and height, followed by PC1 and BSA, with correlation coefficients equal to -0.62 and -0.55, respectively. The complete list of correlation coefficients is available in Table 3. The difference between the scores of PC1 was significant between all demographic groups that were compared in statistical tests, except between the male early-onset athletes and the male late-onset athletes. For PC2 and PC3, no such statistically significant differences between demographic groups was identified. The relevant distributions are shown in D.

The biventricular SSM, including PCs, derived from the full population, is made publicly available on Zenodo doi:10.5281/zenodo.14261122, along with a synthetic cohort of 100 biventricular, volumetric meshes, including fiber orientation and anatomical tags for LV and RV endo- and epicardium, and LV septum. The volumetric meshes of the synthetic cohort are provided in VTK format. Code to generate surface meshes from the published SSMs, by sampling PC scores, is made available in the Github repository https://github.com/LoreVanSantvliet/BiventricularSSM.

We establish the use of UVCs as a viable, lightweight alternative to traditional, nonlinear registration approaches typically used for shape registration, e.g. in [16, 17, 19]. This novel approach offers fine-grained control over the number and placement of points within the geometries. By employing UVCs, we streamline the SSM construction process and enable straightforward surface reconstruction from point cloud data. This flexibility and efficiency make UVC-based correspondence an attractive option for applications requiring fine-grained anatomical alignment, such as SSM construction.

The first PC of the SSM primarily represents biventricular size, consistent with prior findings that chamber size is a dominant source of anatomical variability in cardiac SSMs [16, 17, 18, 19]. The second and third main PCs also echo patterns observed in previous studies: sphericity or elongation of chambers aligns with observations in [16, 17, 18], while relative position and orientation of heart chambers are consistent with findings from [18]. These similarities underscore the robustness of our SSM main components in capturing universal patterns of cardiac variability. The absence of unexpected components additionally provides an indirect validation of the suitability of UVC-based sampling in the SSM construction pipeline.

Our SSM captures 90% of the anatomical variance in the population in 16 PCs, 95% in 29 PCs, and 99% in 94 PCs. These results closely align with previous studies on cardiac SSMs. For instance, Mauger et al. [17] reported that the first 50 PCs encoded 92.1% of shape variance in a larger biventricular dataset of 4 329 subjects. Bai et al. [16] showed that the first 8 PCs of their SSM, extracted from 1 093 subjects, explained over 90% of the shape variance for the LV. Rodero et al. [18] found that only 9 PCs were sufficient to capture 90% of the variance of four-chamber shape variability, in a study incorporating 19 subjects. Nagel et al. [19] found that 18 and 24 PCs accounted for 90% and 95% of the total shape variance, respectively, in a dataset of 47 geometries. These differences between studies likely stem from various methodological factors, such as the spatial resolution of the tomographic images, the size and diversity of the dataset, the segmentation, alignment, and registration approaches, and the anatomical scope of the SSM.

The average reconstruction error of 0.61 $\text{\,}\mathrm{mm}$ in our LOOCV experiment is in line with values reported in the literature. A median reconstruction error of 1.56 $\text{\,}\mathrm{mm}$ is reported for the atria in [19], while a mean reconstruction error around 0.15 $\text{\,}\mathrm{mm}$ is reported for the ventricles in [16]. However, this last, notably small reconstruction error was calculated on the set of geometries used for the SSM training, limiting the comparability to our metric. In [17], the authors reported fitting errors ranging from 1.2 to 1.5 $\text{\,}\mathrm{mm}$ for ventricular models, computed by point-to-surface distances for the registration step specifically, thus not aligning with our approach. Due to the absence of a standardized way of measuring SSM performance, comparing SSM quality across works in the literature remains a challenging task. However, by comparing our LOOCV metric with the identically computed one reported in [19], we conclude that our SSM offers competitive representativeness for biventricular geometries in a healthy population.

Our study population includes both male and female subjects, enabling the investigation of sex-related differences in our cardiac SSM. Previously, [58, 59, 60] reported that female ventricles are significantly smaller than male ones, based on various measurements of both the LV and RV, such as ventricular mass, volume, diameters, and lengths. Our study replicates such findings by showing that on average, female ventricles are smaller in size (as captured by PC1) than those of male individuals in the control population, as shown in Figure 12. This finding is statistically significant, as explained in Section 3.6.

However, St. Pierre et al. point out that the female heart is not just a small version of the male heart, i.e. the differences are more complex than those obtained from simple geometric scaling [49]. More specifically, in [49], the authors indicated a non-isometric scaling of myocardial wall thickness with ventricular mass, for both the LV and RV. While the first PC of our SSM appears to capture size differences, it remains unclear whether this represents simple geometric scaling or incorporates other structural variations. Further investigation is needed to explore these aspects in more detail. While patient-specific LV myocardial thickness is preserved in our anatomical generation pipeline, variations in the RV myocardial thickness are not captured, but fixed, as explained in Section 2.1.3.

Statistically significant differences were also observed in PC1 between the healthy control group, and both early- and late-onset athletes, indicating that both groups of male athletes have significantly larger ventricles compared to male subjects in the healthy control group. This finding is consistent with existing literature on athletic hearts. Morganroth et al. reported an increased LV end-diastolic volume and mass for athletes engaging in isotonic exercise, compared to healthy controls [61]. Similarly, Oxborough et al. found that RV chamber dimensions in athletes often exceed normal ranges, particularly towards the large end of the spectrum [62].

There is a growing interest in sex-related differences in cardiac anatomy and function, as these differences are crucial for enhancing cardiovascular care and ensuring equitable treatment across sexes [63, 64, 49, 65]. We performed a variety of experiments to assess the impact of sex on the performance and representativeness of the SSM. As described in Section 4.3, one key finding was the significant difference in biventricular size that we observed between female subjects of our study population, and male subjects belonging to the healthy control group. This sex-related difference is consistent with findings by Burns et al. [20].

Our results highlight the importance of using unbiased datasets in terms of sex, in order to be representative of both male and female anatomy. For both sexes, an unbiased SSM performed a better reconstruction than a biased SSM built from geometries of the opposite sex. The difference in reconstruction error when using a biased SSM built from geometries from the same sex or using an unbiased SSM, was minor in both cases. Notably, we found the average reconstruction error for female subjects to be consistently smaller than for male subjects, regardless of whether the SSM used for reconstruction is biased or not, probably due to the overall smaller heart size.

We investigated the reconstruction error in a series of LOOCV experiments varying the SSM training set size. The decreasing trend in reconstruction error when increasing the training set size is in line with the findings of Bai et al. [16], who showed a substantial reduction in reconstruction error for ventricular geometries with dataset sizes up to 400-600 subjects, when only the first 100 PCs were considered for reconstruction. Our findings, combined with those of Bai et al., suggest that a straightforward improvement to our model would be to include an even larger number of healthy subjects. This could not only further reduce reconstruction error, but also increase the statistical power when correlating PC scores to other health-related variables, possibly enabling the identification of additional, significant sex-related differences between PCs.

Leveraging the diversity captured by our biventricular SSM, we created a synthetic cohort of anatomically detailed biventricular meshes. The geometries in this cohort were each annotated with anatomical labels and fiber orientations. This cohort, and possibly even more synthetic geometries derived from our SSM, can be used for large-scale simulation studies. In addition to the fundamental insights that large-scale simulation studies can provide on simulation technology, for example by clarifying their parameter sensitivities and uncertainties [66], they can also be used to create simulation databases [23]. Simulation databases, in turn, are a useful resource for training data-driven calibration models to perform automated functional personalization (calibration) of patient-level CDTs. A simulation database suitable for training advanced, anatomy-aware, data-driven calibration models, such as DL models, needs to be large and diverse. Both of these requirements are made more accessible by the release of our SSM, which offers anatomical diversity without requiring researchers to access or process sensitive health data, and which offers the ability to generate a virtually unlimited amount of synthetic, yet realistic heart shapes.

Additionally, the synthetic cohort itself serves as an important building block toward population-level CDTs. Such CDTs, also called virtual cohorts, have application potential in virtual clinical trials [12, 13]. We envision the use of our anatomical cohort of ready-to-use biventricular meshes, representative of a healthy population, to create a healthy virtual control population for such trials.

In an exploratory analysis, we identify several statistically significant correlations between PC scores and other health-related variables in our study population. For reasons related to statistical power, we limit the number of statistical tests in two ways. First, we only consider the first three PCs. Secondly, for amplitude-related features, which could in principle be derived from any lead, we select only two leads: lead II for its general clinical relevance [67] and lead V6 for its connection to hypertrophy [68].

Among all amplitude-related ECG features, only R and S wave amplitude were found to be significantly correlated with anatomical features. More specifically, we observe a negative correlation between PC1 and Ramp of both lead II and lead V6, indicating that larger ventricles are associated with larger R wave amplitudes. Additionally, a positive correlation between PC1 and S wave amplitude of lead II, combined with the fact that S wave amplitudes are negative, suggests that larger hearts have larger S waves. Furthermore, a negative correlation between PC2 and Ramp of lead II is detected, suggesting that more elongated ventricles are associated with larger R waves.

The positive correlation between heart size and R wave amplitude is consistent with simulation-based findings: Zappon et al. [66] observed an increase in simulated R wave amplitude in lead II and lead V6 when increasing heart size by geometric scaling, although their analysis was based on a single geometry. Moreover, the increase of R wave amplitude in lead V6 is consistent with diagnostic criteria for ventricular hypertrophy [68].

For interval-related features, a significant positive correlation was found between PC1 and RRint, QTint, and Tdur. This indicates that larger hearts tend to have longer RR and QT intervals, as well as longer T waves. Notably, no significant correlation was found between PC1 and QTcint, where QT interval length is corrected for the influence of the overall RR interval duration.

The positive correlation between heart size and RR interval is consistent with prior research: LV mass index has been related to the RR interval through correlation with the heart rate [69]. Additionally, Burns et al. also detected a significant negative correlation between heart size and heart rate [20]. In electromechanical simulations, Rodero et al. [18] observed a positive correlation between the second mode of variation in their SSM, encoding heart size, and the duration of systole, closely related to the QT interval. This supports our findings that larger hearts tend to have longer QT intervals. We did not, however, find studies validating the correlation between PC1 and T wave duration.

Finally, we found a negative correlation between PC1 and the electrical axis, either indicating a relation between heart size and orientation, or revealing a bias introduced by heart size when calculating the electrical axis based on ECG signals.

Regarding demographic features, the first PC, which encodes ventricular size, is negatively correlated with height, weight, and BSA. This suggests that larger values for each of these demographic variables are associated with larger ventricles. Additionally, a negative correlation is present between PC2 and height, indicating that taller subjects tend to have more elongated ventricles. The positive correlation between PC2 and BMI indicates that individuals with a higher BMI tend to have more round ventricles. Finally, there is a positive correlation between age and PC1, implying that older subjects typically have smaller hearts in our study population.

The significant correlation between a principal component encoding ventricular size and height is confirmed in [20]. Both the correlation between ventricle elongation and BMI, and between heart size and age are consistent with findings of Burns et al. [20] as well. Moreover, the correlations of height, weight and BSA with PC1 aligns with the work of Hense et al. [70], who identified significant positive correlations between LV mass on the one hand, and weight, height, and BMI on the other hand. However, LV mass and BSA correlation were not investigated in this study. Finally, in a series of multivariate linear regression analyses, Pfaffenberger et al. [60] examined the influence of demographic factors on a range of variables related to ventricular size (LV end-diastolic and end-systolic diameter, LV end-diastolic and end-systolic volume, RV end-diastolic diameter, RV end-diastolic area). They found significant effects of height, weight, and BSA on most of these variables, consistent with our results.

Our automated workflow for anatomical twinning is directly applicable for generating patient-level CDTs. Beyond this methodological applicability, the insights that are drawn from our statistical analysis of the relationship between ventricular anatomy and electrophysiology, are more broadly useful for CDT research. As an example, we propose their use for establishing which anatomical factors are most important to capture in a CDT. For example, statistical correlations revealed in this work, presented in Table 3, confirm that especially heart size is very important to model accurately in CDTs, as it has a significant effect on many different aspects of clinical ECGs.

A second possible application of the statistical insights is in validation of CDT simulation technology. Validation of CDT technology is highly challenging [5]. How can we confirm that a set of PDEs adequately reflects the physiological behavior of the cardiovascular (sub)system under investigation for a given application? Validation approaches for cardiac digital twins in healthcare rely on different types of evidence [71]. The first category consists of evidence related to the mathematical equations employed, including modeling assumptions and parameters. The second category, calibration evidence, involves demonstrating alignment between the model’s simulated or predicted results and the clinical data used for calibration. Finally, validation evidence pertains to the model’s ability to accurately replicate real-world data that was not used at any stage of model construction.

Linking anatomical analysis results to clinical, ECG-derived features and demographic information, provides a foundation for validating the simulation technology underlying CDTs of cardiac EP. Statistically significant correlations between anatomical factors and clinical ECG-derived features should also appear between these same geometrical factors and simulation-based ECG features. Such findings can thus be used to verify whether existing modeling equations display the behavior observed in clinical reality. These correlations can serve as calibration or validation evidence, depending on whether the validation would be conducted on subjects used for building the SSM or on independent ones. As such, we propose the use of the SSM in the context of CDT validation as a possible future extension of our work.

For male subjects, data was derived from the Master@Heart study, a prospective cohort trial including athletes and healthy control subjects [32]. For female subjects, on the other hand, data was obtained from a clinical referral of the subjects to a cardiac CT. These subjects can still be considered healthy, since they are not diagnosed with any cardiovascular disease, and subjects that presented with more than three cardiovascular risk factors were excluded. However, their healthy status might still not match that of subjects in the Master@Heart study, with more selective exclusion criteria.

Our SSM covers biventricular cardiac anatomy below the cardiac valves, excluding the non-conductive cardiac skeleton. Given the electrophysiological focus of our work, this non-conductive tissue is less important to incorporate into our SSM. However, for enabling the use of the provided meshes for mechanical or hemodynamical modeling, valvular anatomy should be included. In this case, an adapted UVC system that includes cardiac valves, such as the one provided in [72], could be valuable for extending our UVC-based approach to establish correspondence between geometries to valvular structures. If the extended UVCs are ordered in a sufficiently regular fashion in Cartesian space to enable subsequent triangulation, as covered in section 2.2.1, an extension of the SSM towards additional anatomical structures would then be straightforward. However, incorporating additional structures, and hence possibly introducing additional anatomical variability is expected to further increase data requirements for obtaining a representative SSM.

Additionally to the ventricles, our SSM could be extended towards the atrial structures as well, leading to a four-chamber SSM. Given the importance of the atria in establishing P wave morphology, this would be an interesting extension, allowing further investigation of relationships between cardiac anatomy and electrophysiology. Given that atria are structurally highly complex [19], arguably even more so that ventricles, it is expected that a larger dataset would be more suitable for this extension. To include the atria, the correspondence establishment could be extended by making use of universal atrial coordinates [30, 31] in addition to UVCs. Similarly to before, the ordering of these coordinates needs to be sufficiently regular as to allow subsequent triangulation, possibly with the aid of Laplacian smoothing. A suitable sampling scheme over the different atrial coordinates needs to be devised, leading to an additional number of points per mesh, thus an additional number of input features for the PCA.

The results described in Section 3.3 reveal that increasing the dataset would likely lead to further improvements of the SSM. The UK Biobank, used in [17, 20], is a suitable resource for increasing the dataset size, although the imaging resolution of these cardiac MR images is lower than the resolution of CT scans used in this study.