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

TL;DR

The paper addresses the computational burden of image-based LV finite-element analysis by introducing CGFENet, a cycle-consistent graph surrogate capable of full-cycle LV mechanics on arbitrary meshes. The model combines a Graph Fusion Encoder and a GRU-based temporal encoder to map volume-time inputs to pressure and displacement while recovering the unloaded configuration, all within a cycle-consistent framework that enforces near-inverses between loading and unloading. Key contributions include a cycle-consistent, mesh-agnostic surrogate, explicit global coupling for P–V consistency, and effective supervision strategies that reduce FE labeling needs while maintaining accuracy. When integrated with a lumped-parameter model, CGFENet yields physiologically plausible P-V loops with substantial speed-ups, enabling time-critical, image-driven cardiac simulations for planning and decision support.

Abstract

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.

Figures (3)

• Figure 1: Overall architecture of CGFENet. A dual-stream design encodes LV geometry (graph encoder) and the V--t signal (temporal encoder) into a shared latent space. The fused latent drives two task heads for forward loading (pressure and displacement) and inverse unloading (zero-pressure recovery), while a cycle-consistent constraint regularises the two mappings across the cardiac cycle. A pre-trained mesh-parameter estimator (frozen) provides the shared global features used in Fig. \ref{['FIG:Encoder']}.
• Figure 2: Graph Fusion Encoder. LV mesh is represented as $(\mathbf{X},\mathrm{edge})$ with node-wise features (coordinates and labels) and shared global descriptors $(V_{LV},W_{\mathrm{mean}},W_{\min},W_{\max})$, applies $N$ stacked residual GATv2 blocks, and injects FEA-inspired global coupling via a mean-pooled chamber token fused back to nodes through cross-attention, producing local and global graph latents.
• Figure 3: Qualitative full-cycle and geometry evaluation on representative cases. (a) lumped-parameter-coupled P--V loops for four cases, comparing CGFENet predictions with FE references. (b) Surface visualisations at ED and end-systole (ES) for one case: CGFENet and FE show displacement magnitude relative to the zero-pressure configuration, while Difference reports the vertex-wise discrepancy (CGFENet minus FE).