A statistical shape modelling framework to extract 3D shape biomarkers from medical imaging data: assessing arch morphology of repaired coarctation of the aorta

Abstract

Background: Medical image analysis in clinical practice is commonly carried out on 2D image data, without fully exploiting the detailed 3D anatomical information that is provided by modern non-invasive medical imaging techniques. In this paper, a statistical shape analysis method is presented, which enables the extraction of 3D anatomical shape features from cardiovascular magnetic resonance (CMR) image data, with no need for manual landmarking. The method was applied to repaired aortic coarctation arches that present complex shapes, with the aim of capturing shape features as biomarkers of potential functional relevance. The method is presented from the user-perspective and is evaluated by comparing results with traditional morphometric measurements.

Methods: Steps required to set up the statistical shape modelling analyses, from pre-processing of the CMR images to parameter setting and strategies to account for size differences and outliers, are described in detail. The anatomical mean shape of 20 aortic arches post-aortic coarctation repair (CoA) was computed based on surface models reconstructed from CMR data. By analysing transformations that deform the mean shape towards each of the individual patient's anatomy, shape patterns related to differences in body surface area (BSA) and ejection fraction (EF) were extracted. The resulting shape vectors, describing shape features in 3D, were compared with traditionally measured 2D and 3D morphometric parameters.

Results: The computed 3D mean shape was close to population mean values of geometric shape descriptors and visually integrated characteristic shape features associated with our population of CoA shapes. After removing size effects due to differences in body surface area (BSA) between patients, distinct 3D shape features of the aortic arch correlated significantly with EF (r = 0.521, p = .022) and were well in agreement with trends as shown by traditional shape descriptors.

Conclusions: The suggested method has the potential to discover previously unknown 3D shape biomarkers from medical imaging data. Thus, it could contribute to improving diagnosis and risk stratification in complex cardiac disease.

Keywords: 3D Shape analysis; Coarctation of the aorta; Computational modelling; Congenital heart disease; Statistical shape model (SSM).

Fig. 1

Point-to-point correspondence problem in complex cardiac morphologies. Widely used parametric methods to build statistical shape models are based on the so called Point Distribution Model (PDM) [5], in which shapes are parameterised by landmarks. Bookstein et al. [40] define landmarks as points on the structure’s surface for which “objectively meaningful and reproducible […] counterparts […]” exist in all other structures present in the dataset. In complex cardiac structures however, those point correspondences are difficult to establish, as illustrated here for two aortic arch models from the CoA cohort

Fig. 2

Forward approach: Transformations of the template characterise individual subject shapes. The statistical shape analysis method is based on analysing subject-specific transformations that deform a computed template shape towards each patient shape rather than considering the actual 3D shapes. The transformations are unique for each subject and comprise all relevant shape features that characterise the subject shape

Fig. 3

Transferring surface shapes into the space of currents: Analogy to 3D laser scanning of objects. Landmarking of the input shapes is avoided by using mathematical currents as non-parametric shape descriptors that model a specific patient shape as a distribution of shape features. Obtaining a currents representation as a surrogate for the actual 3D shape can be compared to probing a surface with a laser beam from different angles and positions

Fig. 4

Influence of the resolution parameter λ_W. One parameter to be set by the user is the currents resolution λ_W, which controls to which degree shape features of the input 3D shape given as a computational mesh (a) are included in the shape’s currents representation. High λ_W values neglect small shape features (b)

Fig. 5

Influence of the stiffness parameter λ_V. The second parameter to be set by the user, λ_V, controls the stiffness or elasticity of the deformation of the template towards each subject shape. Low deformation stiffness values result in too local, unrealistic deformations

Fig. 6

Analysing the output using dimensionality reduction techniques and correlation analyses. PLS regression is used to extract shape patterns most related to a selected response variable as shape modes. Subject-specific deformation vectors, derived from the template computation, constitute the input. Resulting shape modes can be visualised as 3D shape deformations (a). By projecting shape modes onto each subject shape, subject-specific shape vectors X_S can be derived that constitute a numerical representation of the 3D shape features captured by the shape mode (b). X_S is correlated with the selected response parameter as measured on the subjects in order to determine how strongly shape and response are associated (c). Analysis techniques are marked with dashed lines

Fig. 7

Overview of pre-processing steps prior to shape analysis. Cardiac structures of interest are segmented manually or automatically from 3D imaging data (a). Segmented models then are cut, appropriately meshed and smoothed in order to remove irrelevant shape variability (b). Before running the shape analysis, the resulting surface models are aligned i.e. rigidly registered in order to reduce bias due to differences in scaling, transformation and rotation (c). User interaction is marked with dashed lines

Fig. 8

Geometric parameters measured in 2D (a) and 3D (b). Geometric parameters such as diameters D and aortic arch height A and width T were measured manually on 2D CMR image slices according to [17] and [24] (a). 3D parameters were computed semi-automatically using VMTK for all input shapes (b)

Fig. 9

Input surface models of the studied patients post-aortic coarctation repair (a) and computed template (b). Computational surface meshes of 20 aortic arches constituted the input for the shape analysis (a). Coronary arteries and head and neck vessels were removed prior to analysis (3D rotatable models of the arches can be found under www.ucl.ac.uk/cardiac-engineering/research/library-of-3d-anatomies/congenital_defects/coarctations ). The final template (mean shape, blue) computed on the entire population (N = 20 subjects) shows characteristic shape features associated with CoA such as a narrowing in the transverse and isthmus arch section as well as a slightly dilated aortic root and an overall slightly gothic and tortuous arch shape (b)

Fig. 10

Visualisation of the BSA shape mode (a) and correlation with BSA shape vector (b). Shape features associated with deforming the template along the BSA Shape Mode from low (a, top) to high BSA values (a, bottom) from different views as indicated. Low BSA values were associated with a slim, straight and rounded arch shape, whereas moving towards higher BSA values resulted in an overall size increase along with shape deformation towards a more tortuous gothic arch with a slightly dilated root. The measured BSA of the subjects and the shape features as described by the BSA Shape Mode correlated strongly (b)

Fig. 11

Visualisation of the EF Shape Mode. Shape features associated with deforming the template along the EF Shape Mode from low (top) to high EF from different views as indicated. Lower EF was associated with a slim, rather gothic arch shape with a long dilated descending aorta, whereas higher EF was associated with a more rounded arch along with a dilated root and tapering towards a slim descending aorta

Fig. 12

Correlation between EF and EF Shape Vector and visual assessment of results. Measured EF and shape features as described by the EF Shape Mode correlated well. Shape change of the template from a larger arch shape with a slim ascending and a slightly dilated descending aorta was associated with low, negative shape vector values. A smaller arch shape with dilated root and slim descending aorta was associated with high, positive shape vector values (bottom). Compared with the shape of two subjects (CoA1 and CoA12) with low EF at the left, lower spectrum of shape vector values, key shape features supposedly associated with low EF values such as a long, slightly dilated descending and a slim ascending aorta, are depicted correctly by the EF shape mode. On the other side of the shape spectrum, subjects CoA6 and CoA17 presented with a high EF and showed shape features in agreement with the shape mode derived for high EF values. Both shapes were compact, with a shorter, slim descending aorta compared to the ascending aorta, along with a dilated aortic root. Two subjects, who most likely contributed to the relatively weak correlation between EF and the EF shape vector, were subjects CoA5 and CoA15 as marked in red (dashed). Although they presented with similar shapes as CoA6 and CoA17 and thus do show shape features that should be associated with high EF values, their EF values were in the mid-spectrum for CoA5 and even lower than CoA12 for CoA15

Fig. 13

Overview of the template computation using currents. All surface shape models are transferred into their currents representation (a). The user has to set the resolution parameter λ_W to determine which shape features are to be captured. The template is then computed as the mean shape using an alternate algorithm, minimising the distances between template and each subject (b). Thereby, the template shape is initialised as the mean of the currents and then matched with each subject shape. Crucial is the deformation function φⁱ, which is defined by the moment vectors ß that drive the subject-specific deformation of the template. The user has to set the stiffness of those deformations, λ_V. User input is marked with dashed lines