A Cycle-Consistent Graph Surrogate for Full-Cycle Left Ventricular Myocardial Biomechanics

Image-based patient-specific simulation of left ventricular (LV) mechanics is valuable for understanding cardiac function and supporting clinical intervention planning, but conventional finite-element analysis (FEA) is computationally intensive. Current graph-based surrogates do not have full-cycle prediction capabilities, and physics-informed neural networks often struggle to converge on complex cardiac geometries. We present CardioGraphFENet (CGFENet), a unified graph-based surrogate for rapid full-cycle estimation of LV myocardial biomechanics, supervised by a large FEA simulation dataset. The proposed model integrates (i) a global–local graph encoder to capture mesh features with weak-form-inspired global coupling, (ii) a gated recurrent unit-based temporal encoder conditioned on the target volume-time signal to model cycle-coherent dynamics, and (iii) a cycle-consistent bidirectional formulation for both loading and inverse unloading within a single framework. These strategies enable high fidelity with respect to traditional FEA ground truths and produce physiologically plausible pressure-volume loops that match FEA results when coupled with a lumped-parameter model. In particular, the cycle-consistency strategy enables a significant reduction in FEA supervision with only minimal loss in accuracy.

💡 Research Summary

This paper introduces CardioGraphFENet (CGFENet), a unified graph‑based surrogate model that can predict left‑ventricular (LV) biomechanics over an entire cardiac cycle with high fidelity and dramatically reduced computational cost compared with conventional finite‑element analysis (FEA). The authors identify three major limitations of existing approaches: (1) traditional FEA is too slow for clinical use; (2) current graph‑based surrogates either handle only a single loading phase or require fixed mesh topology; and (3) physics‑informed neural networks (PINNs) struggle to converge on realistic, high‑resolution cardiac geometries. CGFENet addresses these gaps through three key innovations.

First, a global‑local graph encoder processes the unstructured LV mesh. Node features consist of 3‑D coordinates, a tissue label (endocardium, epicardium, interior), and globally broadcast descriptors (LV volume, mean/min/max wall thickness). Stacked GATv2 residual blocks perform local message passing, while a lightweight global token obtained by mean‑pooling is fused back to all nodes via cross‑attention. This design injects a weak‑form‑inspired global coupling into the graph, enabling the network to learn the global pressure‑volume relationship that FEA enforces. The encoder outputs a node‑wise latent for displacement decoding and a pooled global latent for pressure prediction.

Second, a GRU‑based temporal encoder models the dynamics of a prescribed volume‑time (V‑t) signal. For each time step the input vector contains the target volume, the volume offset ΔV, and sinusoidal encodings of normalized cardiac time (sin(2πt/T₀), cos(2πt/T₀)). An MLP first embeds this vector, then a gated recurrent unit propagates it across the cycle, producing a temporal latent sequence that captures history‑dependent dynamics. Ablation experiments show that removing recurrence degrades pressure accuracy (RMSE rises from 1.70 mmHg to 2.43 mmHg) and yields less smooth waveforms, confirming the importance of the recurrent module.

Third, a cycle‑consistent bidirectional formulation ties together forward loading (zero‑pressure mesh → loaded mesh + pressure) and inverse unloading (loaded mesh → zero‑pressure mesh) within a single network. During training the model performs a loading → unloading → re‑loading loop; the loss penalizes discrepancies between the original loaded mesh and the re‑loaded mesh, as well as between the original unloaded mesh and the re‑unloaded mesh. This constraint forces the two branches to act as approximate inverses, providing a strong regularizer that dramatically reduces the amount of paired FEA supervision required. Experiments varying the supervision ratio (fraction of meshes with ground‑truth FEA labels) demonstrate that with cycle consistency the vertex accuracy (<1 mm) remains above 0.88 even when only 10 % of meshes are labeled, whereas without the constraint performance collapses to 0.25.

The dataset comprises 67 distinct LV meshes generated from a statistical shape model trained on 1,991 asymptomatic subjects. Each mesh is tetrahedralized (Gmsh), then subjected to an inverse‑unloading step to obtain a zero‑pressure reference configuration. Forward FEA is run over a wide range of cavity volumes (40–160 mL, 50 samples) and 800 time points per cycle, yielding 1,814,146 supervised (pressure, volume, time, displacement) states. All simulations use a Fung‑type material model with identical adult parameters.

Performance is evaluated against two recent graph surrogates: GraphUNet and MeshGraphNet. CGFENet achieves the lowest displacement RMSE (0.39 mm), highest vertex accuracy (<1 mm: 0.90), and smallest Hausdorff distance (0.99 mm) for the forward loading task. For inverse unloading, CGFENet also outperforms baselines (RMSE 0.30 mm, accuracy 0.93). Pressure prediction reaches R² = 0.98 and RMSE = 1.70 mmHg, surpassing GraphUNet (RMSE ≈ 5.8 mmHg) and matching MeshGraphNet’s R² but with lower error. Ablation studies confirm that each component (GRU, global‑local fusion, cycle consistency) contributes meaningfully; removing cycle consistency most severely harms unloading accuracy and supervision efficiency.

Finally, the authors couple CGFENet with a lumped‑parameter circulatory model to close the pressure‑volume loop. After predicting the zero‑pressure mesh from an end‑diastolic image, the loading branch is queried over a dense grid of (V, t) pairs, producing a patient‑specific P‑V‑t lookup table. The lumped‑parameter model then iteratively queries this table to update circulatory variables, achieving real‑time (milliseconds) whole‑heart simulations without any iterative FEA solves. This demonstrates the practical utility of CGFENet for rapid, patient‑specific digital twins, surgical planning, and therapy optimization.

In summary, CGFENet presents a novel, cycle‑consistent graph neural network surrogate that delivers full‑cycle LV biomechanics with accuracy comparable to high‑resolution FEA while requiring far fewer labeled simulations. Its architecture—global‑local graph encoding, recurrent temporal modeling, and bidirectional cycle regularization—offers a blueprint for extending surrogate modeling to other cardiac chambers, variable material properties, and broader clinical workflows.