Sex-specific shape models to disentangle sex effects and age-associated anatomical variation in biventricular cardiac anatomy

Abstract

Aims

Age- and sex-related differences in cardiac anatomy are well established using conventional cardiovascular magnetic resonance biomarkers, but their representation in 3D ventricular shape remains unclear. In pooled statistical shape models, leading modes may be dominated by between-sex anatomical variation, potentially obscuring within-sex age-associated variation. This study evaluated whether sex-specific statistical shape models provide a more interpretable representation of age-associated ventricular variation than a sex-agnostic model.

Methods

Biventricular meshes were reconstructed from cine cardiovascular magnetic resonance (CMR) images in a cross-sectional screened asymptomatic Swiss adult cohort aged 18-85 years. End-diastolic anatomies from 185 male and 187 female participants were used to construct statistical shape models for the pooled cohort and separately by sex. Shape modes were interpreted using anatomical visualization, variance decomposition, associations with conventional demographic, anthropometric, and CMR biomarkers.

Results

The first pooled model mode explained 31% of total shape variance, compared with 22% and 19% for the first male- and female-specific modes. In the pooled model, 57% of first-mode variance was attributable to between-sex differences. Age-associated variation in the pooled model was distributed across the first two modes, whereas sex-specific models organized age-associated variation within each sex. In males, the strongest adjusted age association occurred in the second sex-specific mode, which correlated with ventricular volume and mass. In females, age-associated variation was concentrated in the first mode and was inversely associated with ventricular volumes and myocardial mass.

Conclusion

These findings support sex-specific anatomical reference models for capturing within-sex cardiac ageing structure.

Graphical Abstract

Graphical Abstract.

Introduction

In cardiovascular magnetic resonance (CMR), cardiac function is commonly quantified using global indices such as ventricular volumes, ejection fraction (EF), myocardial strain, and valve annular motion.^1-3 These biomarkers show consistent associations with age and sex^4-6 but provide only a limited description of cardiac structure. Measures of ventricular geometry can offer complementary information by reflecting interactions between chamber form, wall stress, and afterload,^7-9 and have been associated with adverse cardiovascular outcomes.^10-12

Statistical shape modelling extends conventional CMR phenotyping by representing cardiac anatomy as a compact set of quantitative descriptors.¹³ Instead of reducing anatomy to a small number of predefined measurements, this approach captures coordinated patterns of three-dimensional variation across the ventricular surfaces. Shape-derived descriptors have been used to characterize physiological and pathological cardiac phenotypes and may capture anatomical information not fully represented by standard volumetric or functional biomarkers.¹⁴ With the increasing availability of large imaging cohorts such as the UK Biobank¹⁵ and Multi-Ethnic Study of Atherosclerosis (MESA),¹⁶ population-level studies have shown that shape-derived descriptors may capture aspects of cardiovascular risk that are not fully reflected by standard biomarkers.^14,17-20

Despite well-established sex differences in cardiac size, function, and remodelling patterns, many shape-based analyses construct a single pooled anatomical model across males and females.^17,21 In such sex-agnostic models, leading modes of variation may reflect global cardiac scale or between-sex differences in mean anatomy. This is not necessarily problematic when the objective is to describe total population variability, but it can complicate interpretation when the objective is to characterize anatomical variation within sex. In particular, if dominant pooled modes are driven by scale or sex-related anatomy, more specific within-sex age-associated patterns may be distributed across multiple components or assigned to lower-ranking modes.^21,22

In parallel, although age-associated trends in conventional CMR biomarkers are well characterized^23-25, the relationship between age and detailed three-dimensional ventricular form remains less clearly defined.^26,27 Findings from MESA²⁸ indicate that cross-sectional cohort-level trends and longitudinal biomarker trajectories may differ, partly because of variation in cardiovascular risk factor profiles. This highlights the need to establish reference patterns in the low-cardiovascular-risk population, both for conventional biomarkers and for shape-derived descriptors, to support more accurate interpretation of age-associated anatomical variations.

It also remains unclear how age-associated biventricular anatomy is represented when shape variability is modelled within sex rather than in a pooled population. A pooled model may provide an efficient description of total anatomical variance, but may conflate age-associated anatomy with global scale and between-sex differences. Conversely, sex-specific models may reorganize the same anatomical information into modes that better reflect within-sex variation and are therefore more directly interpretable in relation to age and conventional CMR biomarkers.

This study evaluated sex-agnostic and sex-specific statistical shape models of end-diastolic biventricular anatomy in a cross-sectional Swiss CMR cohort without manifest cardiovascular disease. We tested whether the leading modes of a pooled model were dominated by global scale and between-sex anatomical variation, and whether sex-specific models provided a more compact and interpretable representation of within-sex age-associated ventricular anatomy. Model interpretability was assessed using anatomical visualization, variance decomposition, associations with conventional CMR biomarkers, and multivariable age associations adjusted for body size and haemodynamic covariates.

Methods

Figure 1 summarizes the analysis workflow. Cine cardiovascular magnetic resonance images from the SwissHeart cohort were segmented automatically and used to fit subject-specific biventricular meshes across the cardiac cycle. End-diastolic biventricular meshes were then used to construct statistical shape models for the pooled cohort and separately for males and females. The resulting anatomical scores were analysed in relation to age, conventional CMR biomarkers, and anthropometric and haemodynamic covariates.

Figure 1.

Overview of the analysis framework. Input data comprised CMR images from 382 volunteers from the SwissHeart study. Long- and short-axis cine images were segmented using nnU-Net models.²⁹ Three-dimensional thorax scans were resampled to cine planes, segmented with the same networks, and used to correct for breath-hold-induced offsets. Segmentation contours were then employed to fit a biventricular mesh at each cardiac frame. The resulting mesh population was used to derive conventional cardiac biomarkers, as well as anatomical sex-agnostic and sex-specific statistical shape models.

Dataset

This study used data from the SwissHeart cohort, a cross-sectional CMR study of asymptomatic adult volunteers aged 18–85 years. All participants provided written informed consent, and the study was approved by the Ethics Committee of the Canton of Zurich, Switzerland.

Imaging was performed on a 1.5 T MR scanner (Philips Healthcare, Best, The Netherlands). Balanced steady-state free precession (bSSFP) cine images were acquired using a short-axis stack covering the entire heart and three long-axis planes (two-, three-, and four-chamber) at a spatial resolution of 1.6 × 1.6 mm² (reconstructed to 1.0 × 1.0 mm²) with 8 mm slice thickness, flip angle 60°, TR/TE 2.6/1.3 ms, temporal resolution 44 ms. Additionally, a respiratory-gated three-dimensional whole-thorax bSSFP scan was acquired in late diastole (acquired/reconstructed spatial resolution: 1.8 × 1.8 × 1.8 mm³/0.8 × 0.8 × 0.8 mm³) to provide anatomical context for registration. Brachial peak systolic and diastolic blood pressures and resting heart rate were measured prior to the CMR examination.

The present analysis included participants of Caucasian/White ethnicity without manifest cardiovascular disease. Manifest cardiovascular disease was defined as a history of myocardial infarction, coronary artery disease, arrhythmia, myocardial hypertrophy, aortic dissection, aortic valve stenosis, cardiomyopathy, atrial fibrillation, valve regurgitation, or hypertension. A total of 193 males and 189 females met these criteria. After exclusion of 10 participants because of automated segmentation or mesh-fitting failure, the final analysis cohort comprised 372 participants, including 185 males and 187 females. Table 1 describes the demographic, anthropometric, and haemodynamic characteristics of the SwissHeart volunteers included in the final analysis cohort (the full cohort characteristics are reported in the Supplementary data online, Table A1).

Table 1.

Demographic, anthropometric, haemodynamic and clinical characteristics of the SwissHeart volunteers included in the final analysis cohort

Characteristics	Males (n = 185)	Females (n = 187)
Demographics
Age, years, mean (SD)	46 (15)	46 (15)
Anthropometrics
Weight, kg, mean (SD)	81 (12)	63 (9)
Height, cm, mean (SD)	180 (7)	166 (7)
BSA, m2, mean (SD)	2.01 (0.16)	1.70 (0.12)
Haemodynamic
SBP, mmHg, mean (SD)	132 (15)	120 (16)
DBP, mmHg, mean (SD)	80 (10)	79 (11)
Clinical characteristics
Diabetes, n (%)	6 (3.2)	0 (0.0)
Dyslipidaemia, n (%)	150 (81.1)	110 (58.8)
Smokers, n (%)	11 (5.9)	20 (10.7)

Values are presented as mean (standard deviation) for continuous variables and as number (%) for categorical variables.

BSA, body surface area; SBP, systolic blood pressure; DBP, diastolic blood pressure.

Image segmentation

All cine CMR sequences were segmented using a five-model ensemble of publicly available nnU-Net models for short- and long-axis cardiac CMR segmentation.^29,30 The segmentation labels were used to extract anatomical contours for subsequent mesh fitting. Segmentation performance was evaluated at end-diastole in a subset of participants by comparing automated contours with expert manual delineations performed in Segment, version 4.1.0.1, Medviso, Lund, Sweden. Segmentation accuracy was quantified using Dice similarity coefficients for the left ventricular (LV) blood pool, right ventricular (RV) blood pool, and LV myocardium in short-axis views. Detailed validation results are reported in the Supplementary data.

Biventricular mesh fitting

Cine acquisitions were corrected for breath-hold-related slice offsets before mesh reconstruction. The respiratory-gated three-dimensional thorax acquisition was used as a spatial reference and was resampled into the cine imaging planes. In-plane offsets in short-axis cine slices were estimated from the displacement between LV blood-pool centroids in the cine-derived and thorax-derived segmentations. For long-axis views, an additional through-plane correction was estimated by identifying the resampled thorax slice with the highest overlap with the corresponding cine segmentation. The thorax acquisition was used only for spatial alignment and not for mesh reconstruction. Full details of the correction procedure are provided in the Supplementary data.

A template biventricular mesh was aligned to each subject using an initial similarity transformation based on anatomical landmarks. Global scaling, rigid rotation, and translation were estimated using a Kabsch-based alignment procedure.^29,31

After initial alignment, non-rigid mesh fitting was performed using a hierarchical free-form deformation framework.³² Coarse and fine deformation grids were optimized to minimize distances between image-derived contours and the corresponding mesh surfaces while enforcing smoothness and regularity of the deformation field. The fitted structures included the LV endocardium, LV epicardium, RV endocardium, septum, valve planes, and great-vessel regions. Because right ventricular myocardial labels were not available from the segmentation network, the RV endocardial surface was fitted directly, whereas the RV epicardial surface was constrained by deformation regularization to preserve biventricular topology. Consequently, right ventricular interpretations were restricted to chamber geometry and global biventricular form.

Mesh fitting was implemented in PyTorch and performed on GPU hardware, NVIDIA TITAN XP, 12 GB VRAM, using the Adam optimizer for 200 iterations per cardiac frame. The mesh fitting pipeline is publicly available at https://gitlab.ethz.ch/ibt-cmr-public/cmrpro.

Method verification included comparison of automated segmentations with expert manual contours and comparison of mesh-derived ventricular volumes with segmentation-derived volumes across the cohort. Detailed verification results are reported in the Supplementary data.

Classical biomarker calculations

LV myocardial mass (LVM) was calculated from the fitted mesh assuming a myocardial density of 1.055 g/mL. LV wall thickness (LVWT) was computed as the mean distance between corresponding LV endocardial and epicardial points. LV and RV blood pool volumes were obtained by closing the endocardial surfaces and computing the enclosed volume. For both ventricles, end-diastolic volume (EDV) and end-systolic volume (ESV) were defined as the maximum and minimum chamber volumes over the cardiac cycle, respectively. EF was computed as $\mathrm{EF}=\frac{\mathrm{EDV}-\mathrm{ESV}}{\mathrm{EDV}}\times 100$. LV sphericity at end-diastole (ED) ${\psi }_{\mathrm{ED}}$ was computed as ${\psi }_{\mathrm{ED}}=\frac{V}{\frac{4}{3}\pi {\left(\frac{L}{2}\right)}^3}$ where V is the blood pool volume and $L$is mitral valve (MV)-apex distance at ED.³³ Classical biomarkers were compared with published reference ranges.^4-6

Statistical biventricular shape models

End-diastolic biventricular meshes were used for statistical shape modelling. Meshes were centred and rigidly aligned to establish a common coordinate frame while preserving global anatomical scale. Scale was retained so that the resulting shape models represented anatomical form, including both size- and shape-related variation. Alignment was performed by orienting the apex-to-mitral-valve axis with the z-axis and the left-ventricular-to-right-ventricular direction with the negative x-axis.

For each participant, the coordinates of all mesh vertices were concatenated into a single shape vector. Principal component analysis was then applied to derive orthonormal modes of biventricular anatomical variation. Modes explaining 95% of cumulative variance were retained. Principal component analysis (PCA) was used because it provides a linear, compact, and directly visualizable representation of population-level shape variation.^15,16 Three PCA models were constructed: one pooled sex-agnostic model using the full cohort, one male-specific model, and one female-specific model. Pooled model modes are denoted PC_G, male-specific modes PC_M, and female-specific modes PC_F. Scores associated with the i-th PCA mode are denoted by zⁱ, with subscript G, M, F indicating the sex-agnostic, male-specific and female-specific models, respectively.

Mode correspondence between PCA spaces was assessed using the absolute scalar product between normalized PCA mode vectors represented in the common vertex-coordinate space. Values close to 0 indicate near-orthogonal anatomical directions, whereas values close to 1 indicate near-identical directions of anatomical variation. The absolute value was used because the sign of PCA modes is arbitrary.

For each mode of the pooled sex-agnostic model, score variance was decomposed into male within-sex variance, female within-sex variance, and between-sex variance. Within-sex components were computed from deviations of individual scores from the corresponding sex-specific mean score. The between-sex component was computed from the weighted squared deviation of each sex-specific mean score from the overall cohort mean score. Each component was expressed as a percentage of total score variance for that mode. This analysis was used to determine whether pooled PCA modes primarily reflected within-sex anatomical variation or differences in mean anatomy between sexes.

Statistical analysis

Continuous variables are reported as mean and standard deviation, and categorical variables as counts and percentages. Age-stratified summaries were used for descriptive visualization only. Primary analyses treated age as a continuous variable.

Associations between anatomical PCA scores and conventional CMR biomarkers were assessed using Pearson correlation coefficients. These correlations were used to aid anatomical interpretation of PCA modes and were not treated as primary inferential tests. Multicollinearity among regression covariates was assessed using Pearson correlation coefficients and variance inflation factors.

The primary analysis tested associations between anatomical PCA scores and age. For each retained PCA mode, the PCA score was modelled as the dependent variable and age as the predictor of interest. Models were adjusted for body surface area, heart rate, systolic blood pressure, and diastolic blood pressure. Sex-specific PCA spaces were analysed separately in males and females. The pooled sex-agnostic PCA space was analysed using a combined model including sex, age, and an age-by-sex interaction, with females coded as 0 and males coded as 1.

Models were fitted using ordinary least squares regression with HC3 heteroskedasticity-robust standard errors. Regression coefficients are reported with robust 95% confidence intervals. Multiple comparisons were controlled using the Benjamini–Hochberg false discovery rate across all retained PCA modes within each model group. For the pooled sex-agnostic model, correction was applied separately to the age effect and the age-by-sex interaction. Unless otherwise specified, reported P-values are -corrected for false discovery rate (FDR), whereas confidence intervals are unadjusted robust confidence intervals.

The incremental contribution of age was quantified by comparing each full model with a covariate-only reduced model. The increase in explained variance is reported as $\mathrm{\Delta }{\mathrm{R}}^2$, and Cohen’s f² was computed from the change in explained variance.

To assess whether sex-specific shape spaces provided a more compact representation of clinically relevant anatomical variation, exploratory downstream prediction analyses were performed. Age prediction was evaluated using regression models including clinical covariates alone, or clinical covariates plus increasing numbers of leading PCA scores. Clinical covariates comprised body surface area, heart rate, systolic blood pressure, and diastolic blood pressure. Additional analyses assessed whether PCA scores improved prediction of conventional CMR biomarkers beyond age and clinical covariates. The biomarker endpoints were left ventricular end-diastolic volume (LVEDV), LVM, right ventricular end-diastolic volume (RVEDV), and LV end-diastolic sphericity.

Sex-specific and sex-agnostic shape representations were compared using the same number of leading PCA scores.

Downstream prediction models were evaluated using cross-validation within the screened cohort. For groups with at least 12 participants, five-fold cross-validation with shuffling was used. For smaller groups, leave-one-out cross-validation was used. Ridge regression models used internal selection of the regularization parameter from 25 logarithmically spaced alpha values. Model performance was summarized using root mean square error and R².

The PCA shape representations were computed once before downstream prediction and were not recomputed within each cross-validation fold. These analyses should therefore be interpreted as exploratory comparisons of the clinical information contained in fixed sex-specific and sex-agnostic shape representations, rather than as fully nested end-to-end out-of-sample validation of the complete shape-modelling pipeline.

Results

Cohort and conventional biomarker analysis

Of the 382 screened participants eligible for this analysis, 10 were excluded because of automated segmentation or mesh-fitting failure, corresponding to a pipeline success rate of 97.4%. The final analysis cohort comprised 372 participants, including 185 males and 187 females.

Automated short-axis segmentations showed Dice similarity coefficients of 0.95 ± 0.03 for the LV blood pool, 0.90 ± 0.04 for the right ventricular blood pool, and 0.82 ± 0.05 for the LV myocardium. Mesh-derived ventricular volumes showed close agreement with segmentation-derived volumes. Additional verification results are reported in the Supplementary data.

Sex- and age-stratified conventional CMR biomarkers are summarized in Tables 2 and 3 (for the full SwissHeart cohort, see Tables A2 and A3 in the Supplementary data). Females had smaller ventricular volumes and higher EF than males. Ventricular volumes were lower in older age groups in both sexes, particularly in females. Figure 2 shows age-stratified mean end-diastolic anatomical differences relative to the 18–29-year reference group. The oldest age group should be interpreted cautiously because of the small number of participants.

Table 2.

Age-stratified cardiac metrics for the male cohort included in this analysis

Biomarker		Age groups
		18–29	30–39	40–49	50–59	60–69	70–85
n	—	45	47	35	33	19	6
Weight	kg	78 (11)	81 (13)	81 (11)	85 (14)	80 (11)	84 (12)
Height	cm	180 (7)	182 (8)	182 (7)	181 (7)	180 (5)	178 (9)
BSA	m2	1.96 (0.16)	2.02 (0.19)	2.02 (0.15)	2.06 (0.19)	2.00 (0.15)	2.04 (0.20)
SBP	mmHg	127 (11)	127 (12)	128 (13)	135 (14)	135 (17)	148 (6)
DBP	mmHg	74 (8)	76 (8)	78 (11)	84 (8)	82 (10)	81 (8)
LVEDV	mL	150 (20)	153 (24)	142 (23)	140 (23)	133 (24)	141 (31)
LVESV	mL	61 (12)	61 (12)	55 (11)	56 (14)	53 (13)	53 (11)
LVEF	%	59 (5)	60 (4)	61 (4)	60 (5)	60 (5)	62 (4)
LVM	g	124 (18)	127 (21)	126 (21)	125 (23)	118 (24)	129 (18)
LVWT	mm	6.6 (0.5)	6.7 (0.5)	6.8 (0.5)	6.7 (0.6)	6.6 (0.5)	6.8 (0.3)
RVEDV	mL	150 (24)	152 (25)	141 (25)	142 (26)	130 (25)	139 (31)
RVESV	mL	62 (15)	62 (15)	56 (16)	57 (15)	55 (13)	53 (11)
RVEF	%	59 (6)	60 (5)	61 (6)	60 (6)	58 (6)	61 (3)
${\mathbf{\Psi }}_{\mathit{E}\mathit{D}}$	—	0.25 (0.04)	0.25 (0.04)	0.23 (0.04)	0.25 (0.04)	0.25 (0.05)	0.27 (0.05)

Values are presented as mean (standard deviation) for weight, height, BSA, systolic and diastolic blood pressures (SBP, DBP), left and right ventricular end-diastolic and end-systolic volumes (LVEDV, LVESV, RVEDV, RVESV), ejection fraction (LVEF, RVEF), LV myocardium mass (LVM), LV wall thickness (LVWT), sphericity at end-diastole (Ψ_ED).

BSA, body surface area; SBP, systolic blood pressure; DBP, diastolic blood pressure; LVEDV, left ventricular end-diastolic volume; LVESV, left ventricular end-systolic volume; RVEDV, right ventricular end-diastolic volume; RVESV, right ventricular end-systolic volume; LVEF, left ventricular ejection fraction; RVEF, right ventricular ejection fraction; LVM, left ventricular myocardial mass; LVWT, left ventricular wall thickness.

Table 3.

Age-stratified cardiac metrics for the female cohort included in this analysis

Biomarker		Age groups
		18–29	30–39	40–49	50–59	60–69	70–85
n	—	40	40	41	37	23	6
Weight	kg	64 (8)	63 (7)	64 (8)	65 (8)	64 (10)	60 (8)
Height	cm	169 (6)	168 (7)	167 (5)	166 (5)	165 (6)	162 (9)
BSA	m2	1.72 (0.13)	1.71 (0.12)	1.72 (0.12)	1.73 (0.11)	1.71 (0.13)	1.64 (0.15)
SBP	mmHg	116 (10)	115 (11)	114 (12)	119 (11)	129 (16)	137 (20)
DBP	mmHg	76 (7)	76 (10)	76 (8)	79 (7)	82 (11)	78 (13)
LVEDV	mL	115 (17)	111 (17)	103 (15)	98 (10)	93 (13)	90 (19)
LVESV	mL	44 (7)	41 (7)	37 (8)	35 (5)	33 (6)	29 (8)
LVEF	%	62 (3)	63 (4)	64 (4)	65 (4)	64 (5)	68 (3)
LVM	g	91 (14)	86 (15)	80 (16)	79 (9)	81 (10)	74 (11)
LVWT	mm	5.9 (0.4)	5.8 (0.4)	5.7 (0.5)	5.7 (0.4)	5.8 (0.5)	5.8 (0.3)
RVEDV	mL	112 (18)	106 (18)	95 (16)	94 (12)	88 (17)	80 (18)
RVESV	mL	44 (11)	38 (10)	33 (9)	32 (6)	31 (8)	27 (10)
RVEF	%	61 (5)	64 (5)	66 (5)	66 (4)	65 (6)	67 (6)
${\mathbf{\Psi }}_{\mathit{E}\mathit{D}}$	—	0.23 (0.05)	0.25 (0.04)	0.24 (0.04)	0.25 (0.05)	0.25 (0.06)	0.26 (0.05)

Values are presented as mean (standard deviation) for weight, height, body surface area (BSA), systolic and diastolic blood pressures (SBP, DBP), left and right ventricular end-diastolic and end-systolic volumes (LVEDV, LVESV, RVEDV, RVESV), ejection fraction (LVEF, RVEF), LV myocardial mass (LVM), LV wall thickness (LVWT), sphericity at end-diastole (Ψ_ED).

Figure 2.

Age-associated differences in end-diastolic ventricular anatomy in males (top row) and females (bottom row), shown as decade-wise group averages relative to the youngest cohort (18–29 years). The colour field represents the signed radial difference between each age-group mean anatomy and the reference anatomy. Positive values indicate an outward spatial offset relative to the reference surface, along the local endocardium-to-epicardium direction, whereas negative values indicate the opposite direction. These values describe between-group anatomical differences and do not represent myocardial motion.

Variance structure and between-sex contribution of PCA models

The sex-agnostic PCA model retained 17 modes to explain 95% of cumulative shape variance. The male-specific model retained 17 modes, and the female-specific model retained 18 modes.

The first mode of the sex-agnostic model explained 31% of total shape variance, compared with 22% and 19% for the first male- and female-specific modes, respectively (Figure 3). From the second mode onwards, the proportion of variance explained by individual modes was more similar across models.

Figure 3.

Explained variance and sex-wise partitioning of sex-agnostic PCA modes. Bars show the percentage of variance explained by each PCA mode for the sex-agnostic, male-specific, and female-specific shape models. Lines show the corresponding cumulative explained variance. Stacked bars indicate the decomposition of sex-agnostic score variance into male within-sex, female within-sex, and between-sex components for each mode.

Variance decomposition showed that the first sex-agnostic mode contained a substantial between-sex component. Between-sex anatomical differences accounted for 57% of its variance, whereas within-male and within-female variance accounted for 26% and 17%, respectively (Figure 3). Subsequent sex-agnostic modes showed minimal between-sex contribution, below 1%, with most variance attributable to within-sex variation.

Cosine similarity analysis showed that correspondence between sex-agnostic and sex-specific PCA modes was not strictly index-preserving (see Figure A1). Leading modes showed partial alignment across model spaces, whereas higher-order modes showed more dispersed correspondence patterns.

Anatomical interpretation of leading modes

Figure 4 shows anatomical variation induced by ±4 SD perturbations along the first five modes of each model. Quantitative changes in conventional anatomical biomarkers are reported in Figure A2.

Figure 4.

Top five leading anatomical modes for the shape models. Top row: sex-agnostic (PC_G); middle row: male sex-specific (PC_M); bottom row: female-specific model (PC_F). Shape variations are shown for ±4 SDs of each anatomical score, with negative scores in light orange and positive scores in light blue.

In the sex-agnostic model, the first mode represented global cardiac size variation, with coordinated changes in left and right ventricular chamber volumes and LVM. The second global mode was associated with variation in LV sphericity and wall-thickness measures, with smaller changes in ventricular volumes. The third mode encoded sphericity-related changes in the anatomy, accompanied by tilting of mitral and tricuspid valves (MV and TV, respectively) planes and a variation of the LV/RV volume ratio. The fourth global mode represented minor changes in variation of sphericity, and a variation in the distance between the LV–RV junctions. The fifth global mode mainly reflected sphericity-related variation affecting both ventricles.

In males, the first sex-specific mode included changes in ventricular size and myocardial mass, with large sphericity-related changes. The second mode showed larger changes in ventricular volumes and wall-thickness-related measures, with limited change in sphericity, leading to mostly global scaling. The third and fifth modes determined large changes in biventricular sphericity as well, while mode four impacted predominantly LV sphericity and a variation in the volume ratio between LV and RV.

In females, the first mode combined changes in sphericity with reductions in blood-pool volume, myocardial mass, and wall-thickness-related measures. The second female-specific mode showed a non-symmetric impact on LV and RV, with increased RV sphericity and, with respect to LV, a variation in the volume ratio between the ventricles. The third mode combined volume- and sphericity-related variation, equally distributed on both ventricles, with a reorientation of valve planes. The fourth female-specific mode determined minor changes in the anatomy of the apical and basal regions, while the fifth mode determined almost uniquely large variations in biventricular sphericity.

Association between anatomical scores and clinical biomarkers

Figure 5 summarizes Pearson correlations between anatomical PCA scores and conventional CMR biomarkers.

Figure 5.

Correlations between anatomical scores and clinical biomarkers in sex-specific and sex-agnostic models. Bubble plots show Pearson correlations between anatomical PCA scores and clinical biomarkers for males, left and females, right. Within each panel, scores from the sex-specific model are shown on the left of the dashed vertical line, and scores from the sex-agnostic model are shown on the right. Bubble size indicates correlation magnitude, and colour indicates correlation direction and strength. Positive correlations are shown in blue and negative correlations in red. Only correlation coefficients with absolute magnitude above 0.2 are labelled.

In males, the strongest volume-related correlations in the sex-specific model were observed for PC_M2, which correlated with left and right ventricular volume and mass biomarkers, with correlation coefficients ranging from 0.62 to 0.85. PC_M1 also correlated positively with body surface area, ventricular volumes, and LVM, but with lower coefficients.

In females, PC_F1 showed a positive association with age and negative correlations with ventricular volumes and LVM, with correlation coefficients ranging from −0.48 to −0.68 for volume and mass biomarkers. PC_F2 and PC_F3 showed positive correlations with body surface area, ventricular volumes, and LVM.

In the sex-agnostic model, PC_G1 showed strong positive correlations with body surface area, ventricular volumes, and LVM in both sexes. PC_G2 showed stronger associations with age-associated variation and was inversely associated with age in both males and females. Sphericity-related variation was represented by higher-order global modes.

Covariate-adjusted age associations in sex-specific and sex-agnostic models

Variance inflation factors were below 3 for all regression covariates, indicating no substantial multicollinearity among age, body surface area, heart rate, systolic blood pressure, and diastolic blood pressure. Scatter plots of age against the leading PCA scores are shown in Figure A3.

In the male-specific PCA space, age was significantly associated with PC_M1, PC_M2, and PC_M6 after false-discovery-rate correction (Table 4). The strongest association was observed for PC_M2, with β = 14.8 × 10⁻³ PCA score units per year, 95% CI 11.9 to 17.7, P < 0.001, ΔR² = 0.251, and Cohen’s f² = 0.451. PC_M1 showed a smaller but significant association with age, β = 9.4 × 10⁻³ PCA score units per year, 95% CI 5.7 to 13.1, P < 0.001, ΔR² = 0.076, and f² = 0.133. PC_M6 showed a weaker association, β = −2.5 × 10⁻³ PCA score units per year, 95% CI −4.4 to −0.6, P = 0.038, ΔR² = 0.028, and f² = 0.030.

Table 4.

Multivariable associations between age and sex-specific anatomical PCA scores

Males					Females
Mode	$\beta \times {10}^{-3}$	P	ΔR2	f 2	Mode	$\beta \times {10}^{-3}$	P	ΔR2	f 2
PCM1	9.4 (5.7, 13.1)	<0.001	0.076	0.133	PCF1	15.6 (12.8, 18.4)	<0.001	0.335	0.619
PCM2	14.8 (11.9, 17.7)	<0.001	0.251	0.451	PCF2	2.4 (−1.5, 6.4)	0.318	0.009	0.011
PCM3	−3.4 (−6.7, −0.0)	0.138	0.021	0.023	PCF3	2.5 (−0.4, 5.5)	0.173	0.015	0.019
PCM4	1.7 (−1.2, 4.6)	0.330	0.006	0.006	PCF4	−1.4 (−4.2, 1.4)	0.381	0.006	0.006
PCM5	0.6 (−2.2, 3.4)	0.735	0.001	0.001	PCF5	2.0 (−0.4, 4.3)	0.188	0.013	0.015
PCM6	−2.5 (−4.4, −0.6)	0.038	0.028	0.030	PCF6	−1.6 (−3.8, 0.5)	0.198	0.014	0.015
PCM7	0.0 (−2.2, 2.2)	0.994	0.000	0.000	PCF7	1.8 (−0.2, 3.9)	0.173	0.020	0.021

Age effects are reported as regression coefficients, β, in PCA score units per year, with HC3 robust 95% confidence intervals. P-values are FDR-corrected across all retained modes within each sex-specific PCA model. ΔR² denotes the incremental variance explained by adding age to the covariate-only model, and f² denotes Cohen’s effect size. β values are scaled by 10⁻³ PCA score units per year. Only the first seven modes are shown.

In the female-specific PCA space, age-associated variation was concentrated in PC_F1. Age was significantly associated with PC_F1 after false-discovery-rate correction, with β = 15.6 × 10⁻³ PCA score units per year, 95% CI 12.8 to 18.4, P < 0.001, ΔR² = 0.335, and f² = 0.619. No other female-specific mode remained significantly associated with age after correction.

In the sex-agnostic PCA space, PC_G2 showed the largest incremental contribution of age and the age-by-sex interaction terms, with ΔR² = 0.220 and f² = 0.324 (Table 5). Age was significantly associated with PC_G2 in both females and males, with negative slopes in both sexes. The age-by-sex interaction for PC_G2 did not remain significant after correction, P = 0.086.

Table 5.

Multivariable associations between age, sex, and sex-agnostic anatomical PCA scores

Mode	${\beta }_F\times {10}^{-3}$	P Female	${\beta }_M\times {10}^{-3}$	P Male	${\beta }_M-{{\beta }^{\circ }}_F\times {10}^{-3}$	P	ΔR2	f 2
PCG1	10.6 (8.3, 12.9)	<0.001	5.4 (2.4, 8.4)	0.002	−5.2 (−8.9, −1.5)	0.044	0.045	0.209
PCG2	−10.7 (−13.8, −7.5)	<0.001	−15.7 (−19.1, −12.3)	<0.001	−5.0 (−9.4, −0.6)	0.086	0.220	0.324
PCG3	4.5 (1.1, 7.9)	0.023	2.9 (−0.2, 6.0)	0.094	−1.6 (−6.3, 3.0)	0.579	0.030	0.032
PCG4	0.2 (−2.7, 3.0)	0.909	0.0 (−2.7, 2.7)	0.980	−0.1 (−4.0, 3.7)	0.948	0.000	0.000
PCG5	−2.3 (−4.6, −0.0)	0.083	0.7 (−1.9, 3.2)	0.612	3.0 (−0.4, 6.3)	0.186	0.011	0.011
PCG6	−1.3 (−3.3, 0.8)	0.323	−3.0 (−5.4, −0.6)	0.036	−1.7 (−4.7, 1.2)	0.367	0.027	0.028
PCG7	−0.6 (−2.3, 1.1)	0.593	−2.0 (−4.0, −0.1)	0.068	−1.4 (−4.0, 1.1)	0.257	0.012	0.013

Age effects are reported as regression coefficients, β, in ${10}^{-3}$ score units per year, with HC3 robust 95% confidence intervals. ${\beta }_{\mathrm{F}}$ denotes the female age slope, ${\beta }_{\mathrm{M}}$ denotes the male age slope. P Female, P Male, and P represent the FDR-corrected values for females, males, and the age-by-sex interaction. $\mathrm{\Delta }{R}^2$ denotes the incremental variance explained by adding age and the age-by-sex interaction to the covariate-only model, and $f^2$ denotes Cohen’s effect size. Only the first seven modes are presented.

PC_G1 also showed significant age associations in both females and males, with positive age slopes in both sexes. The age-by-sex interaction for PC_G1 remained significant after correction, P = 0.044. Smaller age associations were observed for PC_G3 in females and PC_G6 in males. No other age-by-sex interaction remained significant after correction.

Exploratory downstream prediction analyses

Exploratory downstream prediction analyses compared sex-specific and sex-agnostic shape representations using increasing numbers of leading PCA scores (Figure 6). With only the leading PCA mode retained, sex-specific models showed lower age-prediction error than the sex-agnostic model in both sexes, with root mean squared error (RMSE) values of 12.6 vs. 13.5 years in males and 11.3 vs. 12.1 years in females.

Figure 6.

Comparison of sex-specific and sex-agnostic anatomical statistical shape models across an increasing number of retained PCA modes. Left: cross-validated age prediction error for sex-specific and sex-agnostic models expressed as RMSE. Right: biomarker prediction error for sex-specific and sex-agnostic models expressed as RMSE for LVEDV, LVM, RVEDV, and end-diastolic sphericity Ψ.

A similar single-mode pattern was observed for ventricular volume and mass biomarkers. Sex-specific models showed lower RMSE for LVEDV, RVEDV, and LVM in both sexes, whereas differences for end-diastolic sphericity were small. With additional retained modes, performance differences between sex-specific and sex-agnostic representations became smaller and less consistent across endpoints.

Discussion

In this cross-sectional CMR study, sex-agnostic and sex-specific statistical shape models provided complementary but non-equivalent representations of end-diastolic biventricular anatomy. The main finding was that the pooled model was dominated by between-sex anatomical variation, whereas sex-specific models organized within-sex age-associated anatomical variation into more prominent modes. This was supported by the variance decomposition in Figure 3, anatomical mode visualizations in Figure 4, biomarker correlations in Figure 5, and adjusted age-association analyses in Tables 4 and 5.

The first pooled mode explained 31% of total shape variance and contained a large between-sex component, 57% of mode variance, compared with 26% within males and 17% within females (Figure 3). This mode was also strongly associated with body surface area, ventricular volumes, and myocardial mass (Figure 5). It therefore described total population variability well, but was less specific for within-sex age-associated anatomy.

Sex-specific models provided a more direct representation of age-associated variation within each sex. In males, the strongest adjusted age association was observed for PC_M2, which also correlated strongly with ventricular volume and mass biomarkers (Figure 5 and Table 4). In females, age-associated variation was concentrated in PC_F1, which was inversely associated with ventricular volumes and myocardial mass (Figure 5 and Table 4). These findings are consistent with the descriptive biomarker summaries in Tables 2 and 3 and with the anatomical perturbations shown in Figure 4 and Figure A2.

The pooled model also captured age-associated variation, but this information was distributed across multiple modes. PC_G2 showed the largest incremental contribution of age and age-by-sex interaction terms, while PC_G1 also showed significant age associations in both sexes (Table 5). Because PC_G1 was strongly influenced by between-sex anatomy, age-associated information in the pooled model was partly mixed with broader cohort structure. The cosine similarity analysis in Figure A1 further showed that anatomical correspondence between pooled and sex-specific modes was not strictly index-preserving.

The exploratory prediction analyses in Figure 6 supported this interpretation. With only one retained mode, sex-specific models showed lower age-prediction error and generally lower biomarker-prediction error than the sex-agnostic model. With additional modes, performance differences became smaller and less consistent. Thus, the main value of sex-specific modelling was not improved overall prediction, but a more compact and anatomically interpretable organization of within-sex variation.

Together, these findings support the use of sex-specific statistical shape models as complementary reference spaces for population CMR phenotyping. Pooled models remain useful for describing total anatomical variability, whereas sex-specific models may be preferable when the objective is to characterize interpretable within-sex patterns of age-associated ventricular anatomy.

From a clinical translation perspective, the automated segmentation and mesh-fitting pipeline succeeded in 97.4% of eligible cases, supporting technical feasibility for cohort-scale research, and it requires standard CMR acquisitions. The present implementation requires quality control of segmentations and meshes, but future streamlined quality-control procedures could improve deployability in a clinical setting. Once a validated reference space is established, sex-specific scores could provide standardized and anatomically interpretable early measures of an individual's deviation from the reference population. Potential clinical applications would be the assessment of patients with suspected pathological progression whose ventricular volumes, myocardial mass, and EF remain within conventional reference ranges. A pooled model may be less sensitive to this deviation because its leading modes also encode normal differences between male and female anatomy. Such low-dimensional anatomical scores could also provide interpretable input features for machine-learning models, potentially retaining coordinated three-dimensional anatomical information that is not represented by conventional scalar biomarkers.

Before clinical implementation, processing time, test-retest reproducibility, robustness across scanners and acquisition protocols, prognostic value, and incremental clinical utility beyond conventional CMR biomarkers will require prospective evaluation.

Limitations

This study has several limitations. First, the cross-sectional design does not allow direct inference of longitudinal ventricular remodelling. The reported age effects represent population-level age associations rather than within-subject anatomical trajectories, and may reflect cohort effects, residual cardiovascular risk, lifestyle factors, or unmeasured confounders, as previously shown in MESA.²⁸

Secondly, the cohort was restricted to screened Caucasian/White Swiss adults without manifest cardiovascular disease, which limits generalizability to other ethnic groups and populations with different cardiovascular risk profiles. Nevertheless, Moscoloni et al. reported broadly consistent sex-associated patterns in a healthy UK Biobank cohort, including major contributions from chamber size and relative ventricular positioning and persistent sex-related morphological differences after adjustment for age, blood pressure, and body size.²¹ This agreement across two European cohorts supports the robustness of the principal finding that sex is an important determinant of biventricular anatomy, but it does not establish the transportability of the present PCA basis, score distributions, or age-associated patterns. External validation in ethnically and geographically diverse cohorts, using harmonized imaging and modelling procedures, is required before these models can serve as clinical reference standards. Although overt cardiovascular disease and hypertension were excluded, residual risk factors such as dyslipidaemia, smoking, diabetes, or elevated measured blood pressure may still have influenced anatomical variation.

Thirdly, the analysis relied on automated segmentation and mesh fitting. Although method verification showed good segmentation accuracy and close agreement between mesh-derived and segmentation-derived volumes, residual errors may affect localized anatomical features. Because right ventricular myocardial labels were not available, right ventricular interpretations should be limited to chamber geometry and global biventricular form.

Finally, PCA provides a linear and sample-dependent representation of anatomical variability.

Conclusions

Sex-specific statistical shape models provided a complementary representation of end-diastolic biventricular anatomy compared with a pooled sex-agnostic model. In this cross-sectional CMR cohort, the pooled model encoded sex as the dominant covariate direction, whereas sex-specific models concentrated within-sex age-associated anatomical variation into leading modes. These findings support the use of sex-specific anatomical reference spaces when the objective is to characterize interpretable patterns of ventricular shape variation within sex.

Supplementary data

Supplementary data are available at European Heart Journal - Imaging Methods and Practice online.

Author contributions

Stefano Buoso (Conceptualization, Data curation, Formal analysis, Investigation, Methodology, Software, Validation, Visualization, Writing—original draft [lead]), Valery L. Visser (Data curation, Writing—review & editing [supporting]), Pia Leuders (Data curation, Writing—review & editing [supporting]), Tobias Kudelka (Data curation, Writing—review & editing [supporting]), Maximilian Fuetterer (Data curation, Writing—review & editing [supporting]), Christina Spengler (Resources [supporting]), Robert Manka (Funding acquisition, Resources, Writing—review & editing [supporting]), and Sebastian Kozerke (Funding acquisition, Resources [lead], Writing—review & editing [supporting])

Funding

This project was supported by grant #2024-151 of the Strategic Focus Area ‘Personalized Health and Related Technologies (PHRT)’ of the ETH Domain (Swiss Federal Institutes of Technology).

Data availability

The source code for mesh fitting is publicly available at https://gitlab.ethz.ch/ibt-cmr-public/cmrpro.

Access to the data may be considered on reasonable request, subject to the applicable ethics and data-sharing agreement.

Ethics approval and consent

The SwissHeart study was approved by the Ethics Committee of the Canton Zurich BASEC-Nr.2024-01966.

Consent for publication

No identifiable individual information was included in this study.

Declaration of generative AI and AI-assisted technologies in the manuscript preparation process

During the preparation of this work, the authors used ChatGPT by OpenAI to assist with language editing, grammar correction, and rephrasing. After using this tool, the authors reviewed and edited the content as needed and take full responsibility for the content of the published article.

Lead author biography

Stefano Buoso is a senior scientist in biomedical engineering with expertise in cardiovascular magnetic resonance imaging, computational cardiac modelling, and data-driven analysis of heart anatomy and function. His work focuses on using advanced imaging, statistical shape modelling, and machine learning to better understand cardiovascular structure, ageing, and disease. His research bridges engineering, medical imaging, and clinical science, with the aim of developing robust, interpretable tools for biomedical research and translational cardiovascular medicine.