In-silico trials have already proven their utility across a remarkable range of cardiovascular applications, from planning Fontan surgeries for congenital heart defects to optimizing drug delivery, stent placement, and transcatheter aortic valve implantation, widely known as TAVI. Yet the field suffers from persistent methodological weaknesses. Clinical datasets used to seed these simulations are often small, demographics are inconsistently represented, uncertainty is poorly quantified, and data transparency remains limited. A virtual trial is only as trustworthy as the population it simulates, and building a convincing virtual population requires access to hundreds or thousands of detailed anatomical models that real hospitals simply cannot provide at scale. Synthetic data generation has emerged as the most practical remedy, and machine learning methods have proven the most effective among the available techniques.

Until now, the dominant tool for statistical shape analysis in this domain has been the statistical shape model, or SSM, typically built on principal component analysis. These classical models rest on two restrictive assumptions: that shape variation is essentially linear, and that every shape can be described through point-to-point correspondence with every other shape in the dataset. Both assumptions break down when confronted with the complex, nonlinear deformations of real cardiovascular anatomy, and establishing point correspondence across patient meshes is labor-intensive and error-prone. Nonlinear extensions using kernel methods and manifold learning have partially relaxed these constraints, but they introduce heavy computational overhead and generalize poorly.

The Romanian team’s framework sidesteps these limitations entirely by adopting implicit neural representations, a family of techniques that encode three-dimensional shapes as continuous mathematical functions rather than discrete collections of points or voxels. At the heart of the approach lies a signed distance field, or SDF, a function that assigns to every point in space its distance to the object’s surface, with the sign indicating whether the point lies inside or outside. The surface itself is implicitly defined as the zero-level set of this field. Because a neural SDF is continuous and resolution-independent, it avoids the discretization biases of voxel grids, the memory overhead of volumetric representations, and the topological information loss that plagues point-cloud decoders. Unlike classical mesh-based models, it is also topology-agnostic, meaning the same architecture can represent wildly different anatomical structures.

A key technical innovation concerns how the network is trained. The seminal DeepSDF method of Park and colleagues required ground truth signed distance values, which are only well-defined for watertight surfaces with unambiguous interiors. Real aortic geometries, being open tubular structures reconstructed from cardiac CT scans, are anything but watertight. The researchers instead employed implicit geometric regularization, an approach introduced by Gropp and colleagues that exploits the fact that a true signed distance function satisfies the Eikonal partial differential equation, meaning the gradient of the field has unit magnitude everywhere. By penalizing deviations from this condition at randomly sampled points in space, and by combining it with zero-level constraints on surface points and alignment with surface normal vectors, the network learns a faithful distance field from surface samples alone, with no ground truth distance values required.

Handling non-watertight geometry demanded one further component. When the network’s zero-level set is extracted from an open surface, it produces a closed shape that includes extraneous regions beyond the anatomy of interest. To solve this, the team trained an auxiliary boundary classifier that labels each point as belonging to the inlet, the outlet, or the remaining surface. Fitted planes through the classified inlet and outlet points allow the reconstructed mesh to be precisely truncated, isolating the aortic root. The complete pipeline operates as an autodecoder: each training shape receives a trainable latent vector of 128 dimensions, and a network of roughly 1.7 million parameters, organized in eight fully connected layers with softplus activations and a skip connection, maps these latent codes and spatial coordinates to distance values. At inference, new shapes are decoded through the Marching Cubes algorithm on a 256-cubed grid, then truncated and rescaled to physical dimensions.

The framework was trained on 73 peak-systole aortic surface meshes reconstructed from cardiac CT images of patients scheduled for TAVI procedures, each clinically validated by expert cardiologists. Calcifications were represented as separate meshes, and a second, conditioned implicit network was trained to generate calcium deposits attached to a given aortic shape by receiving the aortic latent vector as an additional input. Reconstruction fidelity was measured with symmetric Chamfer distance, achieving a mean of just 0.135 square millimeters for aortic roots, evidence of high-fidelity geometric representation. New synthetic patients were produced by linearly interpolating between pairs of learned latent vectors, and from this process the team generated a validation cohort of 2,500 synthetic patients stratified by gender.

The critical question is whether these synthetic hearts pass clinical muster, and the answer appears to be yes. The researchers extracted diagnostically relevant features from both real and synthetic cohorts by slicing each mesh at half-millimeter intervals along the blood flow direction, identifying four anatomically significant cross-sections: the aortic annulus, the left ventricular outflow tract, the sino-tubular junction, and the aortic sinus. They also computed aortic valve area using a custom iterative ray-casting algorithm that converged in roughly five iterations and matched ground truth CT measurements with a mean absolute error of 0.092 square centimeters. Synthetic annulus diameters averaged 24.31 plus or minus 1.65 millimeters, closely matching the 24.6 plus or minus 2.4 millimeters reported in clinical literature for aortic stenosis populations. Statistical tests, including the Mann-Whitney U test and Welch’s t-test, found no significant differences in distribution or mean for any feature, and the distribution of aortic stenosis severity, classified as mild, moderate, or severe according to valve area thresholds, aligned well between real and synthetic cohorts.

The calcification results are perhaps the most striking. Generated calcium deposits localized to regions of mechanical stress and geometric irregularity within the conditioned aortic shape, exactly where aortic stenosis pathology develops in real patients. The deposits exhibited realistic size, morphology, and density variations that correlated with stenosis severity, and histogram analysis of 500 synthetic calcifications per shape showed spatial distributions closely matching real ground truth patterns. One acknowledged trade-off is a modest reduction in variance across most anatomical measurements, an expected consequence of latent vector interpolation when generating far more shapes than the original dataset contained. The aortic valve area, notably, preserved its variability, suggesting the primary clinical indicator remains statistically intact. The authors anticipate that clinicians will eventually generate shapes from curated samples representing specific pathological conditions rather than through random interpolation, which should further attenuate the smoothing effect.

The implications extend well beyond the aortic root. The modular architecture generalizes to other cardiovascular structures, including watertight geometries such as heart chambers, where boundary classification becomes unnecessary. The learned latent vectors can serve as compact low-dimensional representations of patient anatomy, conditioning physics-informed surrogate models that predict hemodynamic quantities like transvalvular pressure gradients, paravalvular leakage flow, and wall shear stress across entire synthetic cohorts without running full-scale fluid simulations for each geometry. This could accelerate TAVI in-silico trials, where device performance is acutely sensitive to annulus diameter, sino-tubular junction dimensions, and calcification distribution. Funded by the European Union’s Horizon 2020 program under the SIMCor project, the work points toward a future where virtual patient populations, assembled on demand and tailored to specific study designs, become a standard pillar of cardiovascular device development, reducing the cost, duration, and ethical burden of bringing life-saving technologies to patients.

Subject of Research: Generative deep learning modeling of cardiovascular geometries for in-silico clinical trials

Article Title: Generative modelling of cardiovascular geometries for in-silico trials

Article References: Gasparovici, A., & Serban, A. (2026). Generative modelling of cardiovascular geometries for in-silico trials. Neural Computing and Applications, 38(18), Article 745. https://doi.org/10.1007/s00521-026-12463-8

Image Credits: AI Generated

DOI: 10.1007/s00521-026-12463-8

Keywords: implicit neural representations, signed distance field, in-silico trials, cardiovascular modeling, aortic root, synthetic data generation, TAVI, aortic stenosis, statistical shape models, calcifications, deep learning, virtual patients