Flow-based conditional cardiac anatomy generation for virtual cohorts

CAN-FLOW is a two-step Conditional ANatomy generation framework based on normalizing FLOWs that first learns geometry-only latent representations of diffeomorphic cardiac shape momenta and then models their sex-, age-, and body-mass-index-dependent distribution with a conditional normalizing flow. We trained CAN-FLOW on 2,208 healthy UK Biobank subjects and compared it with cVAEs across regularization strengths. CAN-FLOW generated plausible stochastic biventricular anatomies that better reproduced clinical phenotype distributions, metadata-dependent trends, subgroup variability, point-cloud coverage, and high-dimensional shape variability. Together, these results establish CAN-FLOW as a shareable framework for generating realistic, stochastically varying, metadata-conditioned biventricular anatomies for virtual cohort construction and in silico clinical trial workflows.

The paper introduces CAN-FLOW to address a central requirement for synthetic generation of organ anatomies: synthetic cohorts should contain plausible anatomies while preserving the subpopulation-specific, i.e. metadata-conditioned, distributional breadth of true subject-specific anatomy variability. In the present cardiac application, these subpopulations were stratified by sex, age, and body mass index. CAN-FLOW separates geometry-only representation learning from metadata-conditioned density estimation. An autoencoder first learns compact representations of diffeomorphic momenta which capture the essential variations in cardiac shape, and a conditional normalizing flow then models metadata-dependent distribution of these representations. Across clinical phenotype-based, diffeomorphic shape momenta-based, and high-dimensional surface point-cloud evaluations, CAN-FLOW generated virtual cohorts that more faithfully preserved the variability of a real UK Biobank-derived cohort than traditional cVAE baselines.

The most important improvement of CAN-FLOW is not simply the generation of plausible biventricular shapes, but the preservation of distributional spread. The cVAE baselines achieved lower MMD values, indicating close nearest-neighbor similarity to individual real anatomies. However, they consistently showed lower coverage and reduced anatomical variability. In contrast, CAN-FLOW better reproduced the tails of the phenotypic distributions, achieved higher cohort shape phenotype and shape distribution coverage, and more closely matched PCA-based shape and node-wise distance variability patterns. For virtual cohort applications, this trade-off is important: a cohort of highly average anatomies may appear realistic while still underrepresenting the anatomical variability required for representative in silico clinical studies.

Beyond matching aggregate cohort distributions, CAN-FLOW also better preserved conditioning-dependent anatomical distributions. Synthetic cohorts generated by CAN-FLOW more closely reproduced phenotype trends with respect to sex, age, and body mass index. Additionally, they better captured anatomical variability within a targeted subgroup of the overall population. This distinction is important because conditional virtual cohorts should reflect the expected anatomy of the subgroup under study, not only the global population average. Preserving subgroup-specific anatomical heterogeneity is particularly relevant when virtual cohorts are used to test robustness across plausible anatomical configurations.

The improved performance of CAN-FLOW can be interpreted in terms of its two-step formulation. In cVAEs, the encoder and decoder are trained jointly while the latent distribution is regularized toward a shared, typically Gaussian, prior. This formulation supports sampling, but may underrepresent metadata-dependent anatomical variability. CAN-FLOW instead leaves the geometry-only latent space unconstrained during autoencoder training and learns its conditional distribution separately with a normalizing flow. We showed this separation helps to preserve anatomical variability while still enabling controllable generation. Supplementary ablation studies further support this interpretation, showing that CAN-FLOW retained its advantage across different flow hyperparameters and latent-space dimensionalities, as reported in Appendix B.4 and Appendix B.5. These analyses suggest that the observed gains arise primarily from the two-step generative formulation rather than from a highly optimized flow architecture.

A further application of conditional anatomy generation is the construction of normative shape references. Because CAN-FLOW learns a distribution of healthy biventricular anatomies conditioned on subject metadata, it could potentially be used to quantify how far an observed anatomy deviates from the expected healthy shape distribution for a given subject profile. For example, the anatomy of a new subject could be compared against a metadata-matched synthetic healthy cohort to derive a conditional shape-distance score. Such scores may eventually support the detection or stratification of abnormal cardiac remodeling. The present study does not evaluate diagnostic performance, and this application will require validation in independent diseased cohorts with appropriate clinical labels and outcome data.

Several aspects of our study define the scope within which these results should be interpreted. First, CAN-FLOW was trained and evaluated on healthy UK Biobank participants, and therefore learns a normative distribution of end-diastolic biventricular anatomy within this source population rather than a universal reference for healthy cardiac anatomy. As with any population imaging cohort, the learned distribution may reflect the demographic composition, recruitment patterns, imaging protocol, and health profile of the underlying cohort. Second, the present implementation considers static end-diastolic anatomy only. This scope matches the central aim of our study: to learn conditional population-level variability in cardiac shape, rather than cardiac motion. Extending the framework to time-resolved cardiac anatomy would be a distinct generative task, requiring not only plausible anatomy at each phase but also phase-consistent motion, temporal smoothness, and physiologically coherent deformation trajectories. Third, all generated anatomies inherit the assumptions of the upstream cardiac magnetic resonance imaging to mesh and diffeomorphic registration pipeline, including potential segmentation, mesh-fitting, and correspondence errors.

Future work should evaluate CAN-FLOW as part of broader trustworthy synthetic-data pipelines for virtual human organ twin research. This will require validation in external cohorts, diseased populations, and underrepresented subgroups to assess whether conditional synthetic anatomies preserve clinically relevant variability beyond the healthy UK Biobank population studied here. By generating metadata-conditioned anatomies without directly sharing individual image-derived meshes, this approach may provide a pathway toward more accessible and privacy-conscious virtual anatomy cohorts. The same strategy may be extended to other anatomical structures or multi-organ cardiac models, provided that suitable shape representations and preprocessing pipelines are available. More broadly, these results support conditional anatomical shape generation as a step toward trustworthy, population-specific virtual cohorts for cardiac digital twins and in silico trials.

Improvements to AI systems:

1. Two-step generative framework for conditional anatomy synthesis: Replace joint encoder-decoder training with a two-step pipeline—first, train an unconstrained autoencoder to learn geometry-only latent representations (e.g., diffeomorphic shape momenta), then fit a conditional normalizing flow to model the metadata-dependent distribution of those latents. This avoids the variability-suppressing regularization of cVAEs and preserves subgroup-specific distributional breadth.

2. Distribution-aware evaluation metrics for generative models: Integrate evaluation criteria that go beyond nearest-neighbor similarity (e.g., MMD) to include coverage of phenotypic tails, PCA-based shape variance, node-wise distance variability, and subgroup-specific spread. This ensures synthetic cohorts are not just plausible but statistically representative.

3. Metadata-conditioned density estimation with normalizing flows: Use conditional normalizing flows (rather than Gaussian priors) to model latent distributions as explicit functions of covariates like sex, age, and BMI. This enables precise control over subpopulation trends and preserves within-group heterogeneity.

4. Normative shape deviation scoring for anomaly detection: Leverage the learned conditional distribution to compute a metadata-matched shape-distance score—comparing a new subject’s anatomy against a synthetic cohort generated for their specific profile. This can flag abnormal cardiac remodeling without requiring disease labels at training time.

5. Privacy-preserving virtual cohort generation: Generate synthetic anatomies directly from learned distributions without sharing individual image-derived meshes, enabling construction of shareable, metadata-conditioned virtual cohorts for multi-site studies or in silico trials.

What the improved AI system can do:

• Generate stochastic, realistic biventricular anatomies that faithfully reproduce the full distributional variability of a real population (including tails and subgroup-specific spread) conditioned on sex, age, and BMI.

• Outperform cVAEs in preserving high-dimensional shape variability and coverage, while maintaining controllability over metadata-dependent trends.

• Provide a normative reference for healthy cardiac shape at end-diastole, enabling conditional anomaly scoring to detect or stratify abnormal remodeling in new subjects.

• Support construction of privacy-conscious, shareable virtual cohorts for cardiac digital twin research and in silico clinical trials, with potential extension to other organs or time-resolved motion if suitable shape representations exist.

Cardiac digital twin research is moving from subject-specific anatomical replicas toward virtual cohorts that represent clinically relevant population subgroups. Yet access to representative imaging-derived anatomy datasets remains limited by cohort size, subgroup sparsity, and data-sharing constraints. Conditional generative models could help address this gap, but virtual cohorts are useful only if they preserve realistic, metadata-dependent anatomical variability. Existing cardiac anatomy generators largely rely on conditional variational autoencoders (cVAEs), which couple representation learning and metadata conditioning through a shared regularized latent prior. We introduce CAN-FLOW, a two-step Conditional ANatomy generation framework based on normalizing FLOWs that first learns geometry-only latent representations of diffeomorphic cardiac shape momenta and then models their sex-, age-, and body-mass-index-dependent distribution with a conditional normalizing flow. We trained CAN-FLOW on 2,208 healthy UK Biobank subjects and compared it with cVAEs across regularization strengths. CAN-FLOW generated plausible stochastic biventricular anatomies that better reproduced clinical phenotype distributions, metadata-dependent trends, subgroup variability, point-cloud coverage, and high-dimensional shape variability. Together, these results establish CAN-FLOW as a shareable framework for generating realistic, stochastically varying, metadata-conditioned biventricular anatomies for virtual cohort construction and in silico clinical trial workflows.