Robust prediction of parameterized cardiovascular hemodynamics using deep operator networks with time normalization.

Area of Science:

• Cardiovascular physiology
• Computational modeling
• Artificial intelligence in medicine

Background:

• One-dimensional (1D) numerical solvers for cardiovascular hemodynamics are computationally expensive for many-query scenarios.
• Global sensitivity analysis and Bayesian parameter estimation require thousands of iterative evaluations, hindering disease mechanism understanding.

Purpose of the Study:

• To develop a rapid and robust surrogate modeling framework for cardiovascular hemodynamics.
• To overcome the computational limitations of traditional numerical solvers in complex analysis scenarios.

Main Methods:

• A parameterized Deep Operator Network (DeepONet) integrated with a two-step time normalization strategy (cycle and period normalization).
• Explicit encoding of physiological parameters (heart rate, arterial stiffness, arterial length) in the network's trunk.
• Evaluation on simulated 1D cardiovascular cases, including out-of-distribution scenarios.

Main Results:

• High accuracy (RMSE < 0.5 mmHg) within the training distribution.
• Robust performance in out-of-distribution regimes (mean RMSE < 7 mmHg), outperforming standard models.
• Computational acceleration of ~150,000x compared to numerical solvers (0.00038 s/waveform).
• Demonstrated generalizability on a structural dynamics problem.

Conclusions:

• Integrating time normalization with parameterized operator learning enables robust modeling of periodic physiological signals.
• The framework provides a computational foundation for computationally intensive inverse problems and large-scale sensitivity analyses.
• This approach makes previously infeasible analyses practically achievable.