@inbook {42581,
	title = {A Bayesian Approach to Parameter Estimation in Cardiac Mechanics},
	booktitle = {Solid (Bio) mechanics: Challenges of the Next Decade},
	year = {2022},
	month = {06/2022},
	pages = {245{\textendash}256},
	publisher = {Springer},
	organization = {Springer},
	address = {Cham},
	abstract = {Computational models of cardiac mechanics have been shown to capture the general mechanical function of the heart, and have been parameterized based on in vivo patient data to accurately reproduce the heart function of individual patients. Pre- vious attempts for creating such patient-specific problem have typically been based on solving a deterministic inverse problem, which minimizes the misfit between cer- tain model outputs and measured values. While this approach is robust and efficient, and has shown good agreement between model results and patient data, it does not provide any information about the uncertainty in the resulting model parameters. We here present a parameter estimation framework based on a Bayesian approach, which estimates probability density functions (PDFs) of material parameters based on uncertain input values. The method is based on sampling the parameter space and solving the associated forward model for each sample, which may lead to a substantial computational problem if multiple parameters are considered.\&nbsp;However,\&nbsp;the model also offers additional information in the form of univariate or multivariate PDFs for the estimated parameters. We investigate the potential of the methodology by solving a simple parameter estimation problem in passive left ventricular mechan- ics, and show that the results are in agreement with previous results obtained with a deterministic parameter estimation method.},
	issn = {ISBN 978-3-030-92338-9},
	doi = {10.1007/978-3-030-92339-6_10},
	url = {https://doi.org/10.1007/978-3-030-92339-6_10},
	author = {Sundnes, Joakim and Rodr{\'\i}guez-Cantano, Roc{\'\i}o},
	editor = {Sommer, Gerhard and Li, Kewei and Daniel Ch. {Haspinger} and Raymond W. {Ogden}}
}
@article {Simula.SC.662,
	title = {On Modelling and Analysis of Healthy and Pathological Human Mitral Valves: Two Case Studies},
	journal = {Journal of the Mechanical Behavior of Biomedical Materials},
	volume = {3},
	number = {2},
	year = {2010},
	month = {February},
	pages = {167-177},
	abstract = {Biomechanical data and related constitutive modelling of the mitral apparatus served as a basis for finite element analyses to better understand the physiology of mitral valves in health and disease. Human anterior and posterior leaflets and chordae tendinae from an elderly heart showing no disease and a hypertrophic obstructive cardiomyopathic heart (HOCM) were mechanically tested by means of uniaxial cyclic extension tests under quasi-static conditions. Experimental data for the leaflets and the chordae tendinae showed highly nonlinear mechanical behaviours and the leaflets were anisotropic. The mitral valve from the HOCM heart exhibited a significantly softer behaviour than the valve from the healthy one. A comparison with porcine data was included because many previous mitral modelling studies have been based on porcine data. Some differences in mechanical response were observed. Material parameters for hyperelastic, transversely isotropic constitutive laws were determined. The experimental data and the related model parameters were used in two finite element studies to investigate the effects of the material properties on the mitral valve response during systole. The analyses showed that during systole the mitral valve from the HOCM heart bulged into the left atrium by taking on the shape of a balloon, whereas the anterior leaflet of the healthy valve remained in the left ventricle.},
	doi = {10.1016/j.jmbbm.2009.05.004},
	author = {Victorien Emile {Prot} and Bj{\o}rn H. {Skallerud} and Sommer, Gerhard and Gerhard A. {Holzapfel}}
}
