An automatic image-processing pipeline able to exploit and combine both 3D WH and temporal information provided by cine CMR images was developed and applied to each subject set of images. First, initial 3D images of the heart (CINE_jt) were obtained from the cine SAX stack via combination of all the images acquired in the same phase of the cardiac cycle, t, based on the trigger time. DICOM tags referring to slice spacing and orientation were used to guarantee correct slice alignment. Despite their low resolution in the long axis plane, CINE_jt images retain the temporal information of the LV motion throughout the full cardiac cycle. To integrate the motion information with the detailed 3D spatial resolution provided by the WH dataset WH_j, synthetic WH images (WH_Syn,jt) were obtained for each of the 20 acquisition frames via non-rigid image registration (17), i.e., a transformation in which WH_j is deformed and morphed to replicate the LV configuration represented in each CINE_jt. More specifically (18), all the CINE_jt were scored depending on the resemblance with WH_j, the latter quantified by the sum of squared difference between voxel intensities similarity measure (SSD). A threshold was set as SSD_Th = 0.5 * SSD_Max, where SSD_Max was the maximum value found for each subject, and CINE_jt with SSD_jt < SSD_Th were classified as “highly similar,” while the others as “poorly similar.” In case of highly similar CINE_jt (usually in the diastolic phase), WH_Syn,jt was generated by directly registering WH_j to CINE_jt. In case of poorly similar CINE_jt (usually in the systolic phase) WH_Syn,jt was generated by registering the previously obtained WH_Syn,j(t−1) to CINE_jt. Image registration and transformation were performed exploiting the open-source library niftyreg (19). Each WH_Syn,jt was segmented using an in-house atlas-based segmentation method previously validated (20, 21), able to automatically label the main cardiac structures of interest.

For each subject, LV myocardium masks obtained from segmentation were converted in surface meshes (LV_jt) and used to build the subject anatomical model using the code Deformetrica (22).

Briefly, a generic anatomical model is the ensemble of a Template mesh, which represents the 3D average of the input shapes, and a set of deformations ϕ_i of the 3D space warping the template to each one of the input shapes (Figure 3). Specifically, deformations are represented by a set of vectors—namely, momenta β_ik—attached in the 3D space to a control point grid. For the latter, the amount of control points k is chosen by the user, while their position is automatically optimized to densely sample the most variable regions of the template shape (22). Parameters to be set by the user are the resolution λ_w of the shape representation (i.e., how fine are the details we want to capture) and the stiffness of the deformation λ_v, both in millimeters (9).

In this case, the template mesh (LV_j,Template) represented the time-averaged subject-specific ventricle shape, and the momenta warped the template to each temporal occurrence within the subject-specific cardiac cycle. As suggested by Bruse et al. (7), the parameters (i.e., resolution λ_w and transformation stiffness λ_v) required to run the computation of each subjects anatomical model were iteratively tuned to maximize the matching of the template with the original shapes. This was quantified by computing the average euclidean surface distance between computed (i.e., template-matched) and original shapes. These values were further averaged between the 20 frames to give a unique value for each subject. Surface distances were computed as the pointwise minimum distance of the input surface from a reference surface by exploiting The Vascular Modeling Toolkit (25) (VMTK, Orobix, Bergamo, Italy; www.vmtk.org) function vmtksurfacedistance. In order to minimize the effect of size and orientation on the next steps of the analysis, all anatomical models were first scaled with respect to each LV_j,Template endocardial volume, and then rigidly aligned (26) throughout a generalized procrustes analysis (27) iterative process on the LV_j,Template endocardial surfaces, implemented with the functions available in the open-source library niftyreg (19).

In order to quantitatively describe anatomical shape and motion variations within a population, we herein extensively adopted an SSA approach (7, 11). As the variation of the data within an anatomical model is described by a large number of momenta vectors, output data are not trivial to analyze and interpret. Therefore, the second step required to analyze variability is to apply dimensionality reduction [i.e., PCA (28)] to the momenta vectors, a common mathematical technique that discards any redundant information while keeping principal contributors to variability. Specifically, momenta vectors are projected onto the space that maximizes their covariance, and only the components—also called modes—that contain most of the information are retained as descriptors. By deforming the template shape along the derived modes toward negative and positive extremes of each mode (±2σ), it is possible to visualize and thus qualitatively assess the dominant global and local shape variations characterizing the examined population. The amount of information carried for each subject by each mode is summarized in the shape vector, i.e., a vector where each entry represents how much the template has to be deformed along the corresponding mode in order to match each specific input shape (7, 10). Analysis of the shape vectors allows quantification of the differences in shape within the population.

Shape analysis was applied separately to the end-diastolic (ED) meshes (LV_ED) and the end-systolic (ES) meshes (LV_ES) (Figure 4). The two groups (i.e., 8 shapes each) were separately processed using the abovementioned SSA framework, i.e., two anatomical models were obtained from only ED and ES shapes, respectively, generating LV_ED,Template, LV_ES,Template, and associated deformations (ϕ_ED,j, ϕ_ES,j). Both the anatomical models modes and shape vector were then computed and analyzed.

The shape variability expressed by each mode (LV_ED,Template ± 2σ_modeED,x, LV_ES,Template ± 2σ_modeES,x) was first qualitatively observed. This visual description, in conjunction with the respective shape vector coefficients, was then used to numerically characterize each subject LV 3D shape at ED or ES, eventually highlighting shape similarities and differences within the joint population of patients and control group.

To extend the SSA framework to the analysis of subject-specific cardiac contraction, motion was interpreted as an ensemble of relatively small, periodical variations of the same shape during the cardiac cycle. In order to describe motion per se without geometrical confounding factors, the effect of the subject-specific shape had to be removed from each anatomical model, hence retaining only the subject-specific motion information. Therefore, we exploited the momenta vectors and control point grids computed within each subject anatomical model (see 2.3.2), and we used them to deform a generic template ventricle (namely, LV_{SuperTemplate}), obtained as the average shape of all the 8 subjects LV_j,Template (Figure 5, 1). As a result, LV_{SuperTemplate} deformed throughout the cardiac cycle following each subject-specific contraction pattern. The same SSA framework described above (see 2.3.3) was then applied to this set of 160 shapes (20 frames for each of the 8 subjects, Figure 5).

The motion patterns characterized by each mode were first qualitatively assessed by visual observation. By exploiting the quantitative information given by the motion vector, each subject’s LV contraction pathway was then numerically described in terms of the identified motion modes. This allowed us to consistently characterize each subject LV dynamics independent from its shape within the same mathematical framework, ideally providing insight into ventricular function and dysfunction.

After PCA, the first four modes were considered the most relevant for ED shape analysis, accounting for 76% (28%Mode₁, 19%Mode₂, 16%Mode₃, 13%Mode₄) of the total shape information present in the population. Figure 9 illustrates the extreme features (±2σ) represented by each mode, in the standard cardiac views. Each depicted shape was obtained by morphing the template shape with the extreme deformation represented by each mode, and the colormap identifies the regions where the highest deformation (in red) occurs. Upon visual inspection, all modes showed a general rounding and circumferential expansion of the basal-mid walls, while the apical region was thinning in Mode_1−2σ and Mode_4−2σ, and rounding in all the other modes, causing a shortening of the ventricle. Mode₁, which reflects the most dominant shape variation in the cohort of patients/controls, was locally characterized by a bulging of the basal inferior and inferolateral walls and the dilation of the mitral valve annulus in Mode_{1 − 2σ}, and by a local outward expansion of the mid anteroseptum and anterior wall in Mode_1 + 2σ. Mode_{2 − 2σ} had an outward dilation and bulging of the mid anteroseptum, the basal inferior and inferolateral walls, while Mode_2 + 2σ did not show substantial local deformations. In Mode_{3 − 2σ}, there was a bulging of the basal inferior wall, while in Mode_3 + 2σ, we observed a mild expansion of the mid anterior wall. Finally, the region of the anteroseptum was predominantly bulging in Mode_{4 − 2σ}, while the mid anterior wall was expanding outward in Mode_4 + 2σ.

Figure 10 shows a boxplot representing the variability of the shape vector entries (Table 2) for control group and AS patients, allowing to describe each subject LV shape numerically according to the modes previously illustrated. In this example population, overall the control group had an ED shape characterized by the negative extreme of Mode₁, the positive extreme of Mode₂ and Mode₃, and a predominantly negative extreme of Mode₄. As expected, the AS patients showed more variability within each mode, with some subjects sitting within the control range of variability, but single subjects being clearly outside the control range. Given the small sample size (n = 4 for each population), no significant difference (p > 0.05 from Mann–Whitney U test) could be found between the two groups medians, for each of the mode. Following the visual results, ED shape of the AS patients was therefore characterized by a local outward expansion of the mid anteroseptum and anterior wall (Mode_1 + 2σ), outward dilation and bulging of the mid anteroseptum, the basal inferior and inferolateral walls (Mode_{2 − 2σ} and Mode_{3 − 2σ}) and mid anterior wall (Mode_4 + 2σ), according to the descriptions above.

As for the ED shape analysis, the first four modes were considered the most relevant for ES shape analysis, capturing 75% (28%Mode₁, 17%Mode₂, 16%Mode₃, 14%Mode₄) of the shape variability in our population. The deformations represented by each mode are shown in Figure 11, as for the ED case. In ES, shape of Mode_{1 − 2σ} was characterized by an overall smaller size, especially locally at the basal inferior and inferolateral walls. In Mode_1 + 2σ, the base was shortening and the mid walls bulging outward, while the mitral valve annulus was circumferentially smaller, and the basal infero- and anteroseptum and mid inferolateral walls were reduced. In Mode_{2 − 2σ}, the apex and the apical walls were bent more anteriorly and toward the right, the basal lateral wall was positioned more posteriorly, and the mitral valve annulus was more dilated, while in Mode_2 + 2σ, the septum was positioned more posteriorly. Shape in Mode_{3 − 2σ} was generally shorter, the apex rounder and slightly bent anteriorly and toward the right, while in Mode_3 + 2σ, the mid walls were circumferentially shrunk, especially in the apical lateral wall. Finally, in Mode_{4 − 2σ}, the septal wall was slightly reduced, especially in the mid inferoseptum, and in Mode_4+2σ, the apex was rounder and bent more posteriorly.

The ES shape vector entries variability for control group and AS patients are represented in the boxplot in Figure 12 and Table 3. As for the ED case, variance of the control group coefficients was overall less than that for the AS patients. In particular, coefficients of the control group were all in the negative extreme for Mode₁, predominantly positive in Mode₂ and predominantly negative in Mode₃ and Mode₄. Even though shape vector entries for single AS patients showed differences from the control group, not all the shape modes could clearly distinguish the two groups, similar to the ED shape analysis. Also in this case, the small sample size (n = 4 for each population) did not allow to show significant difference (p > 0.05 from Mann–Whitney U test) between the two groups medians, for each of the mode.