[Paper Review] Real-time whole-heart electromechanical simulations using Latent Neural Ordinary Differential Equations

Matteo Salvador, Marina Strocchi+4 more|arXiv (Cornell University)|Jun 8, 2023

Cardiovascular Function and Risk FactorsMedicine3 citations

TL;DR

This paper introduces a Latent Neural Ordinary Differential Equation (LNODE) surrogate model that enables real-time, whole-heart electromechanical simulations—achieving 300× speedup on a standard laptop—by learning from 400 3D-0D closed-loop simulations of a heart failure patient. The model supports global sensitivity analysis and robust parameter estimation with uncertainty quantification in just 3 hours on a single CPU.

ABSTRACT

Cardiac digital twins provide a physics and physiology informed framework to deliver predictive and personalized medicine. However, high-fidelity multi-scale cardiac models remain a barrier to adoption due to their extensive computational costs and the high number of model evaluations needed for patient-specific personalization. Artificial Intelligence-based methods can make the creation of fast and accurate whole-heart digital twins feasible. In this work, we use Latent Neural Ordinary Differential Equations (LNODEs) to learn the temporal pressure-volume dynamics of a heart failure patient. Our surrogate model based on LNODEs is trained from 400 3D-0D whole-heart closed-loop electromechanical simulations while accounting for 43 model parameters, describing single cell through to whole organ and cardiovascular hemodynamics. The trained LNODEs provides a compact and efficient representation of the 3D-0D model in a latent space by means of a feedforward fully-connected Artificial Neural Network that retains 3 hidden layers with 13 neurons per layer and allows for 300x real-time numerical simulations of the cardiac function on a single processor of a standard laptop. This surrogate model is employed to perform global sensitivity analysis and robust parameter estimation with uncertainty quantification in 3 hours of computations, still on a single processor. We match pressure and volume time traces unseen by the LNODEs during the training phase and we calibrate 4 to 11 model parameters while also providing their posterior distribution. This paper introduces the most advanced surrogate model of cardiac function available in the literature and opens new important venues for parameter calibration in cardiac digital twins.

Motivation & Objective

• Address the high computational cost of high-fidelity whole-heart electromechanical simulations, which limits clinical adoption of cardiac digital twins.
• Develop a surrogate model that enables fast, accurate, and personalized simulations of cardiac function on standard hardware.
• Enable global sensitivity analysis and robust parameter estimation with uncertainty quantification using a single processor.
• Calibrate 4–11 model parameters by matching unseen pressure and volume time traces from 5 test simulations.
• Demonstrate the feasibility of real-time, patient-specific cardiac simulations using a compact, physics-informed machine learning framework.

Proposed method

• Train a Latent Neural Ordinary Differential Equation (LNODE) on 405 3D-0D whole-heart closed-loop simulations of a heart failure patient, varying 43 model parameters across electrophysiology, mechanics, and hemodynamics.
• Use a feedforward fully-connected neural network with 3 hidden layers of 13 neurons each to embed the 3D-0D model dynamics into a low-dimensional latent space.
• Design a custom loss function that minimizes relative errors (2–5%) in pressure and volume transients, even with limited training data relative to parameter space dimensionality.
• Apply Bayesian inference via Maximum a Posteriori (MAP) and Hamiltonian Monte Carlo (HMC) for robust parameter estimation with uncertainty quantification.
• Leverage automatic differentiation and matrix-free adjoint methods to efficiently compute gradients during optimization.
• Validate the surrogate model on 5 unseen 3D-0D simulations, matching pressure and volume time traces with high fidelity.

Experimental results

Research questions

• RQ1 Can a Latent Neural ODE surrogate model achieve real-time whole-heart electromechanical simulations while preserving accuracy and physiological fidelity?
• RQ2 To what extent can LNODEs generalize to unseen parameter configurations and accurately predict pressure and volume dynamics in a heart failure patient?
• RQ3 How effective is the LNODE-based framework for global sensitivity analysis in identifying key model parameters influencing cardiac output variability?
• RQ4 Can robust parameter estimation with uncertainty quantification be performed efficiently on a single CPU using this surrogate model?
• RQ5 What is the computational efficiency and scalability of the LNODE framework compared to full 3D-0D simulations?

Key findings

• The LNODE surrogate model achieves 300× real-time simulation speedup on a single CPU, enabling whole-heart simulations in real time.
• The model generalizes well to unseen simulations, achieving relative errors of 2–5% in pressure and volume predictions across 5 test cases.
• Global sensitivity analysis using Sobol indices reveals that parameters related to calcium handling and ion channel conductances (e.g., $g_{ ext{CaL}}^{ ext{CRN}}$, $ca_{50}^{ ext{CRN-Land}}$) significantly influence hemodynamic outputs.
• Robust parameter estimation with uncertainty quantification was completed in 3 hours on a single processor, with posterior distributions of 4–11 parameters well-calibrated to ground truth values.
• The posterior mean estimates of model parameters across 5 test simulations were within ±0.31 of the true values, with standard deviations of ±0.09 to ±0.31 depending on the parameter.
• The framework successfully calibrated hemodynamic parameters such as systemic ($R^{ ext{sys}}$) and pulmonary ($R^{ ext{pulm}}$) resistance, with mean estimates within 0.16–0.38 of ground truth.