HeartUnloadNet: Direct Cardiac Unloading

• HeartUnloadNet is a weakly-supervised cycle-consistent graph neural framework that predicts the unloaded left ventricular geometry from clinical end-diastolic meshes.
• It integrates multi-head graph attention, cross-attention fusion of physiological parameters, and bidirectional decoding to achieve sub-millimeter accuracy (DSC 0.986) and ≈20 ms inference time.
• Cycle-consistency and data-efficient training allow robust performance with as little as 1-3% supervision, paving the way for real-time, patient-specific cardiac analyses.

HeartUnloadNet is a weakly-supervised cycle-consistent graph neural framework developed for direct prediction of the unloaded (zero-stress, zero-pressure) left ventricular (LV) geometry from clinical end-diastolic (ED) states. The method addresses the fundamental challenge that clinical cardiac images inherently capture the myocardium under load, whereas biomechanical simulations and continuum-mechanics analyses critically require the geometrically unpressurized reference as baseline. Unlike traditional approaches relying on computationally prohibitive and often unstable inverse finite element (FE) solvers, HeartUnloadNet delivers sub-millimeter accurate unloaded predictions from meshed diastolic heart models and physiological parameters, achieving real-time inference in clinical contexts (Mu et al., 24 Jul 2025).

1. Biomechanical Motivation and Clinical Context

Cardiac continuum-mechanics analyses—including patient-specific stress, strain, and material parameter estimation—require the reference configuration of the myocardium in a state devoid of luminal load. This "unloaded" geometry underpins baseline calculations and is the starting point for FE simulations of ventricular mechanics under physiological and interventional loading. However, the unloaded state is never observable in vivo due to constant blood pressure; images (MRI or CT) only depict the loaded states, especially at end-diastole (ED). Inverse FE solvers, the historical gold standard, iteratively deform an initial mesh to one that, when loaded with prescribed pressure and constitutive material parameters, matches the observed clinical geometry. These methods are computationally intensive ($O(10^3\!-\!10^4)$ s per case), sensitive to mesh and model choices, and can converge suboptimally, posing a barrier to widespread clinical personalization.

2. Input Data and Representation

HeartUnloadNet accepts as input:

• A tetrahedral mesh representing the LV at ED, $M_{ED} = (X, E)$, with $n$ nodes, where $X \in \mathbb{R}^{n \times 3}$ undergoes global normalization.
• Four global physiological parameters:
  1. End-diastolic (ED) pressure $p_{ED}$ in the clinical range $[4, 14]$ mmHg;
  2. Myocardial stiffness scale $C \in \{50,100,\ldots,300\}$ Pa;
  3. Endocardial helix angle $\theta_{endo} \in \{60^\circ, 65^\circ, 70^\circ\}$;
  4. Epicardial helix angle $$\theta_{epi} \in \{-60^\circ, -65^\circ, -70^\circ\}$$.

The mesh is represented via normalized coordinates as node features $H^{(0)} \in \mathbb{R}^{n \times 3}$, with edges $M_{ED} = (X, E)$0 defining one-hop graph neighborhoods $M_{ED} = (X, E)$1. The physiological parameters are linearly normalized, concatenated into $M_{ED} = (X, E)$2, and projected by a multilayer perceptron (MLP) into $M_{ED} = (X, E)$3.

3. Graph Attention Architecture

The architecture integrates mesh topology and global physiological context through a shared encoder and dual spatial decoders:

• Graph-Attention Encoder: Three layers of multi-head graph attention (GAT) update per-node features, each layer performing, for every node $M_{ED} = (X, E)$4 and attention head $M_{ED} = (X, E)$5:

$M_{ED} = (X, E)$6

$M_{ED} = (X, E)$7

$M_{ED} = (X, E)$8

with residual connections stabilizing training and supporting arbitrary mesh size and topology.

• Global Pooling and Cross-Attention Fusion: A global mesh embedding $M_{ED} = (X, E)$9 is obtained by mean-pooling node features after GAT layers, fused with $n$0 through a cross-attention block:

$n$1

$n$2

This fusion allows every node to attend selectively to the global physiological context when encoding geometric information.

• Bidirectional Decoding: Two small MLP decoders predict per-node displacements for unloading (ED $n$3 unloaded) and reloading (unloaded $n$4 ED), both leveraging the shared fused features $n$5.

4. Learning Methodology: Cycle-Consistency and Weak Supervision

HeartUnloadNet employs an explicit cycle-consistency strategy, supporting learning with only partial supervision and improving prediction accuracy:

• Forward (Unloading) Mapping: $n$6 $n$7, producing $n$8.

• Backward (Reloading) Mapping: $n$9 $X \in \mathbb{R}^{n \times 3}$0, yielding $X \in \mathbb{R}^{n \times 3}$1.
• Supervised Loss:

$X \in \mathbb{R}^{n \times 3}$2

with $X \in \mathbb{R}^{n \times 3}$3 the ground-truth unloaded mesh from FE.

• Cycle-Consistency Loss:

$X \in \mathbb{R}^{n \times 3}$4

• Total Loss: $X \in \mathbb{R}^{n \times 3}$5, $X \in \mathbb{R}^{n \times 3}$6.

By enforcing that $X \in \mathbb{R}^{n \times 3}$7, the network extracts self-supervisory signals, substantially reducing the necessity for labeled synthetic FE pairs.

5. Simulation Dataset, Train/Test Protocol, and Optimization

The training dataset comprises 20,700 synthetic LV mesh/parameter cases, derived as follows:

• Shape Generation: 60 anatomical LV base shapes sampled from a principal component model (PCA) learned on 1,991 subjects (MESA cohort).
• Parameter Sampling: Combinatoric variation over $X \in \mathbb{R}^{n \times 3}$8, $X \in \mathbb{R}^{n \times 3}$9, $p_{ED}$0, $p_{ED}$1 yields $p_{ED}$2 main cases, augmented to $p_{ED}$3 by additional mesh sampling.
• Mesh Construction: Tetrahedralization via Gmsh, with $p_{ED}$4–$p_{ED}$5 nodes per mesh.
• Splits: Default—42 shapes (13,890 cases) for training, 18 for testing (6,810 cases).
• Leave-One-Value-Out (LOVO): Model generalization assessed by holding out one value of each parameter in turn.
• Weak Supervision: Cycle-loss supports training with as little as 1% supervision (down to ≈200 ground-truth meshes).
• Optimization: AdamW optimizer (lr $p_{ED}$6, wd $p_{ED}$7), batch size 16, up to 1,000 epochs, early stopping (patience=50), dropout 0.1, hidden dimension $p_{ED}$8, $p_{ED}$9 GAT heads.

6. Quantitative Evaluation and Comparative Performance

Performance is reported using three geometric metrics:

• Dice Similarity Coefficient (DSC): Fraction of mesh nodes within 0.1 mm

$[4, 14]$0

• Hausdorff Distance (HD):

$[4, 14]$1

• Mean Distance (MD):

$[4, 14]$2

On the held-out test split (6,810 cases):

Method	DSC ($[4, 14]$3)	HD $[4, 14]$4" title="" rel="nofollow" data-turbo="false" class="assistant-link">cm	MD $[4, 14]$5" title="" rel="nofollow" data-turbo="false" class="assistant-link">cm	Inference Time $[4, 14]$6" title="" rel="nofollow" data-turbo="false" class="assistant-link">s/case
HeartUnloadNet	$[4, 14]$7	$[4, 14]$8	$[4, 14]$9	$C \in \{50,100,\ldots,300\}$0
Inverse FE	$C \in \{50,100,\ldots,300\}$1	$C \in \{50,100,\ldots,300\}$2	—	$C \in \{50,100,\ldots,300\}$3

HeartUnloadNet is over $C \in \{50,100,\ldots,300\}$4 faster and more accurate than traditional inverse FE methods (Mu et al., 24 Jul 2025).

7. Ablation Analyses and Data Efficiency

Ablation experiments demonstrate the contribution of architectural components and cycle-consistency loss:

• Cycle-Consistency Loss: Removing cycle-loss decreases DSC from 0.986 to 0.933.
• Co-Attention Fusion: Its removal increases HD from 0.083 to 0.094.
• Alternative Graph Models: Replacing GAT with GCN drops DSC from 0.986 to 0.778.
• Pooling Variants: Max-pooling instead of mean-pooling reduces DSC to 0.934.
• Decoder Variants: Using GAT decoders in place of MLPs leads to DSC of 0.725.

Regarding data efficiency:

• With only 3% (≈200) of supervision pairs and cycle-loss, DSC remains 0.971 and HD at 0.085 cm. In the absence of cycle-loss, DSC drops precipitously to 0.712.
• At 1% supervision, only the cycle-consistent architecture maintains usable accuracy (DSC≈0.62).

These results confirm that each design element—graph attention, cross-attention fusion, and cycle-consistency—is critical for achieving both high accuracy and data efficiency.

8. Limitations, Future Work, and Clinical Implications

Limitations:

• Entire training set is synthesized from population-normal LV PCA shapes. Generalization to pathological ventricular geometries is unproven.
• Only passive diastolic mechanics are considered; active contraction and full cardiac cycle modeling remain out of scope.

Potential Extensions:

• Incorporating physics-informed losses, such as energy-based regularization, to further reduce supervised data requirements.
• Extending the architecture to multi-phase graph models for active contraction and systolic mechanics.
• Incorporating simulated image registration error or mesh noise to enhance real-world robustness.

Clinical Implications:

• With $C \in \{50,100,\ldots,300\}$5 ms inference per patient, HeartUnloadNet can be embedded in real-time MRI/CT analysis pipelines for rapid unloaded geometry estimation, supporting on-the-fly stress/strain analytics.
• Enables accelerated patient-specific simulation for surgical planning or device assessment.
• Represents the first fully data-driven surrogate for FE-based unloading of the heart, substantially lowering computational barriers to personalized cardiac biomechanics.

In summary, HeartUnloadNet leverages graph-attention mechanisms, global physiological context encoding, and cycle-consistent weak supervision to predict unloaded cardiac geometry with sub-millimeter accuracy and extreme computational efficiency. Its parameter-aware, data-efficient, and mesh-agnostic design constitutes a significant advancement over traditional and prior deep-learning surrogates, indicating substantial potential for real-time clinical and research deployment (Mu et al., 24 Jul 2025).