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InVAErt networks for amortized inference and identifiability analysis of lumped parameter hemodynamic models

Guoxiang Grayson Tong, Carlos A. Sing Long, Daniele E. Schiavazzi

TL;DR

This work tackles parameter identifiability in stiff lumped-parameter cardiovascular models by introducing inVAErt networks, a data-driven digital-twin framework that performs amortized inversion and identifiability analysis. The approach combines an emulator $NN_e$, a flow-based density estimator $NN_f$ using Real-NVP, an input encoder $NN_v$, and a decoder $NN_d$ to recover input parameters from outputs while capturing entire manifolds of solutions via a latent space $\boldsymbol{w}$. Demonstrated on the CVSim-6 six-compartment model with synthetic data and real EHR measurements (including missing data), the method reveals non-identifiable manifolds, handles practical identifiability issues through noise augmentation, and enables missing-data imputation and rapid inversion. The results highlight the potential of inVAErt networks as a scalable, physics-informed digital twin tool for cardiovascular inverse problems with significant implications for data-driven clinical decision support.

Abstract

Estimation of cardiovascular model parameters from electronic health records (EHR) poses a significant challenge primarily due to lack of identifiability. Structural non-identifiability arises when a manifold in the space of parameters is mapped to a common output, while practical non-identifiability can result due to limited data, model misspecification, or noise corruption. To address the resulting ill-posed inverse problem, optimization-based or Bayesian inference approaches typically use regularization, thereby limiting the possibility of discovering multiple solutions. In this study, we use inVAErt networks, a neural network-based, data-driven framework for enhanced digital twin analysis of stiff dynamical systems. We demonstrate the flexibility and effectiveness of inVAErt networks in the context of physiological inversion of a six-compartment lumped parameter hemodynamic model from synthetic data to real data with missing components.

InVAErt networks for amortized inference and identifiability analysis of lumped parameter hemodynamic models

TL;DR

This work tackles parameter identifiability in stiff lumped-parameter cardiovascular models by introducing inVAErt networks, a data-driven digital-twin framework that performs amortized inversion and identifiability analysis. The approach combines an emulator , a flow-based density estimator using Real-NVP, an input encoder , and a decoder to recover input parameters from outputs while capturing entire manifolds of solutions via a latent space . Demonstrated on the CVSim-6 six-compartment model with synthetic data and real EHR measurements (including missing data), the method reveals non-identifiable manifolds, handles practical identifiability issues through noise augmentation, and enables missing-data imputation and rapid inversion. The results highlight the potential of inVAErt networks as a scalable, physics-informed digital twin tool for cardiovascular inverse problems with significant implications for data-driven clinical decision support.

Abstract

Estimation of cardiovascular model parameters from electronic health records (EHR) poses a significant challenge primarily due to lack of identifiability. Structural non-identifiability arises when a manifold in the space of parameters is mapped to a common output, while practical non-identifiability can result due to limited data, model misspecification, or noise corruption. To address the resulting ill-posed inverse problem, optimization-based or Bayesian inference approaches typically use regularization, thereby limiting the possibility of discovering multiple solutions. In this study, we use inVAErt networks, a neural network-based, data-driven framework for enhanced digital twin analysis of stiff dynamical systems. We demonstrate the flexibility and effectiveness of inVAErt networks in the context of physiological inversion of a six-compartment lumped parameter hemodynamic model from synthetic data to real data with missing components.
Paper Structure (22 sections, 17 equations, 14 figures, 10 tables)

This paper contains 22 sections, 17 equations, 14 figures, 10 tables.

Table of Contents

  1. Introduction
  2. Background and notation
  3. Methods
  4. The CVSim-6 hemodynamic model
  5. InVAErt networks
  6. Noise injection as training data augmentation
  7. Numerical experiments
  8. Stiffness analysis
  9. Output selection
  10. Structural non-identifiability analysis with synthetic data
  11. Going beyond point estimates
  12. Analysis of non-identifiable manifolds
  13. Missing data analysis
  14. Inverse problem with real clinical measurements
  15. Inversion results
  16. ...and 7 more sections

Figures (14)

  • Figure 1: Schematic of compartments in the CVSim-6 model.
  • Figure 2: Schematic of all components of an inVAErt network and their interactions.
  • Figure 3: Time history of the eigenvalues of $\mathbf{A}(t)$ plotted over two heart cycles.
  • Figure 4: Radar plots of absolute eigenvector components for maximum SR$(t)$ at $t\sim 9.444$ (s). Associated eigenvalues: $\lambda_1 = -520.95$, $\lambda_2 = -355.93$, $\lambda_3=-3.75$, $\lambda_4= -0.51$, $\lambda_5=6.25\cdot 10^{-4}$, $\lambda_6=2.91\cdot 10^{-5}$.
  • Figure 5: Radar plots of absolute eigenvector components for minimum SR$(t)$ at $t\sim 8.618$ (s). Associated eigenvalues: $\lambda_1 = -4.40$, $\lambda_2 = -1.81$, $\lambda_3=-1.77$, $\lambda_4= -0.64$, $\lambda_5=2.22\cdot 10^{-16}$, $\lambda_6=3.47\cdot 10^{-18}$.
  • ...and 9 more figures

Theorems & Definitions (2)

  • Remark 1
  • Remark 2