85 clinical computerised tomography (CT) scans were used with informed consent by University College London Hospital (UCLH), consisting of non-AF patients examined for moderate coronary disease. The average participant age was 61.5 years, with 48 of the 85 of male sex. As this dataset is composed of control cases, not associated with thromboembolic risk, this study focuses on anatomical detail. Images are 512 × 512 pixels, with a pixel spacing of 0.488 mm × 0.488 mm, and a slice thickness of 0.625 mm acquired with the GE Discovery STE scanner. The manual segmentation protocol of full left atria was adapted from previous studies (Bosi et al., 2018; Capelli et al., 2012) to include measurements of contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR), following clinically recommended protocols (Marques et al., 2018), to ensure image (and hence later LAA shape) viability (Figure 2A). To summarise this process briefly, following calculation of CNR and SNR, 85 segmentation masks were generated in Mimics 24.0 (Materialise, Belgium) from the dye contrast threshold. These masks were manually processed by a segmentation expert to select only left atrial structures, including the LAA, pulmonary vein trunks and a mitral plane. After segmentation, each of the 85 left atria was evaluated by an expert cardiac anatomist to focus on chicken wing and non-chicken wing labels only. 21 LAAs were categorised as chicken wing and the remaining 64 as non-chicken wing.

Then, the full left atria, as surface models, were meshed using triangular elements of 0.5 mm edge length for subsequent LAA definition. To keep the process as objective as possible and preserve all anatomical details, the following approaches were taken. To ensure an objective definition of LAA ostial planes (conventionally defined through subjective manual assessment (Hołda et al., 2017)), a fully automatic LAA detection algorithm (Martorana et al.) was applied to all 85 segmented anatomies (Figure 2B). Briefly, this LAA detection method is based of distance analysis of computationally skeletonised left atria to automatically identify the LAA ostial plane, thus allowing LAA detection (Martorana et al.). To ensure normalisation across all detected LAAs, each mesh was then scaled to the same arbitrary volume (6,000 mm³, close to the average mesh volume). Global registration of the detected LAAs was performed via the Super4PCS algorithm (Mellado et al., 2014) to a single case, followed by local iterative closest point (ICP) (Rusinkiewicz and Levoy, 2001) and multiview registration (Pulli, 1999) across the full dataset (Figure 2C). Local ICP and multiview registration were repeated until all possible pairs fell within alignment distance. For 2000 sample points describing each anatomy chosen at each ICP iteration, the chosen minimal starting distance was 10 mm, reduced iteratively so that 80% of the samples would lie at a distance lower than 0.5 mm. Up to this point, no LAA structural definition was lost (i.e., shapes are fully inclusive of objectively defined LAA ostia, full surface structure, bending and anatomical lobes and trabeculae), ensuring that LAA shapes match ‘all the geometrical information that remains when location, scale and rotational effects are filtered out from an object, as per Kendall’s definition of shape (Kendall, 1977).

Based on the surface mesh generated for the 85 LAAs, simplified datasets of the registered LAA meshes were generated in MeshLab (Cignoni et al., 2008). Poisson surface reconstruction creates watertight surfaces from point sets with oriented surface normals, with set reconstruction depths corresponding to effective voxel resolutions (Kazhdan and Hoppe, 2013). To simplify the intricate meshes, a reduction factor of 2-times, 4-times, 8-times and 16-times was first applied to the point sets of LAA meshes in the original trabeculated dataset, with preservation of the original surface normals. To sequentially reduce intricate features such as trabeculae for surface reconstruction, the minimum sampling density was set as the reduction factor for each simplified dataset. To ensure less reconstruction bias due to the reduced number of points, the surface reconstruction depth d (which corresponds to solving on a voxel grid whose resolution is no larger than (2 ^d )³ (Kazhdan and Hoppe, 2013)) was specified for each simplification as equal to 8, 7, 6 and 5. The simplified variations of the intricate dataset are shown in Figure 3: LAA surface reconstruction with 4-times reduction results in fully removed trabeculae; further reductions may lead to greater loss in lobar definition.

LAA SSA was applied with the explicit method in ShapeWorks software, the most commonly studied “off-the-shelf” software for LAA shape analysis (Goparaju et al., 2022; Goparaju et al., 2018; Bhalodia et al., 2010; Bieging et al., 2021; Adams et al., 2023; Adams et al., 2022). All analyses were run on an AMD Ryzen 9 7950X3D 16-Core Processor, 4201 Mhz, 16 Core(s), 32 Logical Processor(s). The workflow for the SSA is laid out in Figure 4 and described below. The SSA model was run with 1,024 particles in multiscale from 128 (so that the initialisation and optimisation of particle position is rerun for each particle split), and principal component analysis (PCA) of the final particle correspondences was computed. Parameter selection (featuring a low initial weighting of particle position with a very high iteration number per particle split, and a high final optimised weighting (Cates et al., 2017)) was iteratively adjusted to balance SSA model evaluation metrics of compactness, generalisation and specificity (Davies, 2002) as implemented by ShapeWorks (Shape Model Evaluation). Briefly, compactness score C n m , the degree to which a model has captured the morphological variation within a dataset, is defined as the sum of the eigenvalues λ i up to the selected number of PC modes n m , summarised as: C n m = ∑ i = 1 n m λ i . Generalisation score G ^ n m , a measure of a SSA model’s ability to represent unseen shapes from a given dataset, may be quantified with the approximation error (Euclidean distance, in mm) between any held-out shape instance x j and its corresponding SSA model reconstruction x ∼ j , summarised as G ^ n m = 1 n s ∑ j = 1 n s x j − x ∼ j , where n s is the number of samples. Specificity score S ^ n m , a measure of the plausibility of SSA model-generated shapes, may be computed as the approximation error (Euclidean distance, in mm) between any randomly sampled shape y A and its nearest training sample x i , summarised as S ^ n m ≐ 1 M ∑ A = 1 M min i y A − x i where M is the number of random samples taken. Final parameters were chosen to increase compactness i.e., the morphological variation captured by SSA, as desirable for clustering, despite lowered specificity and generalisation.

For clarity, clustering analyses are only presented between the original trabeculated LAA surface versus the 4-times reduced dataset. 4-times reduction was chosen as it presents a clear reduction of fine anatomical detail loss, i.e., loss of trabeculae, but largely preserves secondary lobe structure. These two datasets are referred to as the “trabeculated dataset” versus the “simplified dataset” in the results section. Agglomerative hierarchical clustering was applied with MATLAB functions. Complete linkage and correlation distance were chosen; the former to ensure more compact clustering (Ezugwu et al., 2022) and the latter so that anti-correlated objects (i.e., chicken wing-like and non-chicken wing-like shapes) are as far apart as possible (van Dongen and Enright, 2012). The number of PCs accounting for 85% of the total variance (Cangelosi and Goriely, 2007) in the trabeculated dataset was retained for subsequent hierarchical clustering analysis, and the optimal number of clusters was calculated with the silhouette metric (Rousseeuw, 1987), to determine the cut-off value on the dendrograms. Clustering performance evaluation was performed with respect to the previously defined clinical labels, using the adjusted mutual information (AMI) score (Vinh et al., 2010) as the assessment metric. AMI is a measure of similarity (mutual information (MI)) between two labels of the same data, adjusted for chance. For two clusterings U and V: A M I U , V = M I U , V − E M I U , V average H U ,   H V − E M I U , V

SSA took between 27.8 and 31.3 min to run for each dataset, regardless of anatomical intricacy. The results are presented in terms of visual geometric correspondence (Figure 5) and model evaluation score differences between the trabeculated and simplified datasets with increasing number of PCs (Figure 6).

Hierarchical clustering results are presented between the original “trabeculated” dataset, and the representative “simplified” dataset of 4-times reduction, with dendrogram results in Figure 7 and visualisation of the data distribution in Figure 8. 10 PCs were found to account for 86.1% of the cumulative variance for the trabeculated dataset, with the optimal number of clusters determined as 2 from a silhouette score of 0.7948. Following the increase in shape model compactness with reduction factor, 10 PCs instead accounted for 92.6% of the cumulative variance for the simplified dataset, with the optimal number of clusters again determined as 2 from a silhouette score of 0.7458. For both datasets, dendrograms with the 2 optimal clusters are presented in Figure 7 and are highlighted on the trabeculated PCA distribution (showing PC1 against PC2) in Figure 8. Figure 8 also records the AMI score of each dataset to the clinical labels.

With selected parameters for SSA and clustering, results suggest that LAA shape categorisation via hierarchical clustering performs better with preservation of full anatomical details (the “trabeculated dataset”) than with trabecular detail loss (called the “simplified dataset”). While greater LAA anatomical simplification directly corresponds with better SSA model evaluation scores for compactness, specificity and generalisation (Figure 6), it was hypothesised that the loss of trabecular detail affects the preservation of morphological variation pertinent for LAA shape categorisation (Figures 3 and 5).

Between the trabeculated and simplified datasets, the improvement to SSA evaluation with reduction at the 10 PCs used for subsequent clustering is as follows: +0.065 compactness, −0.47 mm specificity and −0.86 mm generalisation (Figure 6). This is expected as the shape simplification process has led to a decrease in anatomical trabeculae and lobar definition that would have accounted for greater morphological difference between shapes. This implies that increasing anatomical simplification increases both the SSA model’s ability to plausibly generate LAA shapes within simplified datasets and how well the model may generally represent unseen LAA shapes. However, as greater reduction by 8-times and 16-times visually affects even LAA lobar structure (Figure 3), it is thought that the greater anatomical simplification affects the geometric correspondence between shapes (Figure 5). Therefore, reduction by 4-times was selected as the simplified dataset for subsequent clustering comparisons. For visual comparison between PC1 and PC2 for these two datasets (Figure 5), PC1 captures chicken wing-like and non-chicken wing-like bending angle. PC2 instead describes LAA shapes with smaller or larger secondary lobes.

In contrast, increasing LAA reduction in SSA lowered clustering performance. The simplified model clusters, with a low AMI score of 0.1214, are mainly overlapping in the +PC1 and +PC2 quadrant (Figure 8), with 29 shapes being assigned differently to human assessment. This suggests that while + PC2 is associated with smaller secondary lobes, the inclusion of secondary lobe detail, e.g., trabeculae, better separates chicken wing-like shapes. On the trabeculated model clusters of Figure 8, the higher AMI score of 0.6715 corresponds with good cluster separation on the trabeculated PCA distribution, with only four shapes assigned differently to human assessment. This clustering is also more stable, with the same clusters being achieved for 90% and 95% cumulative variance. Therefore, these results may justify the preservation of intricate anatomical details, particularly LAA trabeculae, for shape categorisation with hierarchical clustering, despite improvements to pure SSA evaluation scores. In terms of computation time, SSA was less affected by the anatomical differences between datasets rather than the parameters chosen, taking between 27.8 and 31.3 min to run on the same AMD Ryzen 9 7950X3D 16-Core Processor, 4201 Mhz, 16 Core(s), 32 Logical Processor(s).

The applicability of the proposed LAA SSA model and clustering is limited by the analysed number of anatomies in the original dataset. This is particularly important for highly diverse anatomies such as the LAA, where it is highly likely for morphologies to demonstrate categorical variance beyond subjective clinical classification, even without considering fine anatomical details. In comparison with other LAA works, the number of LAAs utilised in our study (85 in total) lies between other studies, which can vary from 20 (Ahmad et al., 2024) to 130 (Goparaju et al., 2022). However, no other SSA study to our knowledge has preserved our level of LAA anatomical detail, which is the basis for this study.

Some limitations are related to operator-dependent steps in our workflow. Firstly, the manual left atrial segmentation (prior to fully automatic LAA detection) requires user definition of contrast threshold (aided by the additional mathematical CNR measurement protocol) and human effort and time to ensure segmentation is not affected by unwanted imaging artefacts. The second operator-dependent step is the clinical classification used to obtain the clinical labels to which clustering is compared in AMI scoring; clinical subjectivity was minimised in this study by focusing clinical labels to chicken wing versus non-chicken which is known to present the greatest morphological difference of bending angle (Yaghi et al., 2020). Two of the aforementioned LAA SSA studies have aimed to tackle the segmentation problem via deep learning (Juhl et al., 2024; Ahmad et al., 2024); however, as already stated, these works do not fully capture the same level of anatomical detail, presenting very smooth meshes, i.e., without trabeculae. Furthermore, the fully automatic LAA detection of the ostial plane utilised in our study may be further advantageous over both these studies that either cut the shape where it is narrowest (Juhl et al., 2024) (which describes an anatomical region generally different from the ostium definition) or perform manual clipping of left atrial meshes (Ahmad et al., 2024).

Finally, it should be noted that while a pixel spacing of 0.488 mm from CT is high for conventional clinical scans, even higher resolutions exist for alternative ex-vivo imaging-based studies e.g., microCT, synchrotron-based or photon-counting CT imaging. This study indicates that clustering of anatomies acquired with smaller pixel spacing performs significantly better than lower resolutions, which suggests that even higher resolution scan data could improve the results further. To increase the reliability and statistical significance of this work, it would be beneficial to incorporate more LAA morphologies in the SSA performed; however, it was not possible to include datasets acquired from publicly accessible databases (Atria Segmentation Challenge 2018; Karim et al., 2018) as they either did not match the imaging modality and/or the required resolution.