Polynomial chaos expansion surrogate modeling of passive cardiac mechanics using the Holzapfel-Ogden constitutive model

Cardiovascular diseases, such as heart failure and hypertrophic cardiomyopathy, may cause changes in the heart, resulting in modifications of its biomechanical response. The medical exam information is very useful but insufficient for an early diagnosis. Then, computational models and patient-specific simulations can provide new information about heart function in normal or pathological conditions. Personalized simulations usually involve parameter estimation and geometry reconstruction from medical data, which are steps subjected to many sources of uncertainties. Therefore, it is important to know how these uncertainties influence clinical quantities computed from the simulations and which inputs are responsible for this output variability. Studies of uncertainty quantification, sensitivity analysis, and parameter estimation using evaluations of the cardiac model based on partial differential equations demand a substantial computational effort, being important to find cheap alternatives for conducting these analyses. The present work proposes using Polynomial Chaos Expansion surrogate modeling to accelerate uncertainty quantification, global sensitivity analysis, and parameter estimation for the Holzapfel-Ogden model of cardiac tissue during the passive filling phase. The results showed which outputs are most impacted by uncertainties in constitutive parameters, while the SA identified which ones are the most influential and which are negligible. Finally, using surrogate models, we showed how parameter estimation could be accelerated and improved using the sensitivity analysis results via the input fixing strategy.

Automated summary

Cardiovascular diseases can affect the heart's biomechanical response, and personalized simulations provide new information about heart function. It is important to study the uncertainties and influential inputs in computational models for cardiac analysis, as well as find cost-effective alternatives for conducting these analyses.