A comparative analysis of metamodels for 0D cardiovascular models, and pipeline for sensitivity analysis, parameter estimation, and uncertainty quantification

TL;DR

The paper tackles the computational burden of sensitivity analysis, parameter estimation, and uncertainty quantification in zero-dimensional cardiovascular models. It proposes a pipeline that builds surrogates using neural networks, Polynomial Chaos Expansion, and Gaussian Processes across three 0D problems, with synthetic data generated for training. Neural networks consistently deliver the best accuracy and efficiency, while PCE affords analytic Sobol indices on larger datasets and GP provides probabilistic uncertainty estimates. The work demonstrates a full NN-based pipeline and provides open-source code, supporting rapid, patient-specific analyses and digital-twin development in cardiovascular applications.

Abstract

Zero-dimensional (0D) cardiovascular models are reduced-order models used to study global circulation dynamics and transport. They provide estimates of biomarkers (such as pressure, flow rates, and concentrations) for surgery planning and boundary conditions for high-fidelity 3D models. Although their computational cost is low, tasks like parameter estimation and uncertainty quantification require many model evaluations, making them computationally expensive. This motivates building metamodels. In this work, we propose a pipeline from 0D models to metamodel building for tasks such as sensitivity analysis, parameter estimation, and uncertainty quantification. Three strategies are explored: Neural Networks, Polynomial Chaos Expansion, and Gaussian Processes, applied to three different 0D models. The first model predicts portal vein pressure after surgery, considering liver hemodynamics and global circulation. The second simulates whole-body circulation under pulmonary arterial hypertension before and after shunt insertion. The third assesses organ blood perfusion after revascularization surgery, focusing on contrast agent transport, requiring specific metamodel treatment. Metamodels are trained and tested on synthetic data. Neural networks proved the most efficient in terms of result quality, computational time, and ease for parameter estimation, sensitivity analysis, and uncertainty quantification. Finally, we demonstrate the full pipeline with a neural network as the emulator.

Figures (13)

• Figure 1: Schematic representation of the suggested pipeline for 0D model meta-analysis. An application of this pipeline is presented in section \ref{['section:application']}
• Figure 2: Schematic for Model 1, for prediction of hemodynamic change after liver resection audebert2017partialgolse2021predicting It is composed of the left and right parts of the heart, pulmonary circulation, digestive organs, two hemi-livers and remaining circulation.
• Figure 3: Schematic diagram of the PAH model with integrated conduit shunt. $Q$ represents the volumetric flow-rate. The non-linear resistances are extracted after tuning with the 3D model of the shunt region. The heart and circulatory system are studied in more details compared to the first model.
• Figure 4: Schematic diagram of the hemodynamic and transport model for assessing perfusion in the organ of interest. The top red dashed box is the key for the hemodynamics model and the bottom green box is the key to the transport model. Here the heart is modelled by a simple flow generator (see above for more precise heart models). Hemodynamics is solved before transport. The $h(t)$ function represents the transformation undergone by the compartment input signal through the convolution relation $c_\mathrm{out} = h * c_\mathrm{in}$. Parameters $\tau$ depend on the organs and the hemodynamics properties.
• Figure 5: $Q^2$ metric using the testing dataset for the first model.