Parameter estimation in a Holzapfel–Ogden law for healthy myocardium

• Published in: Journal of engineering mathematics 2015-12, Vol.95 (1), p.231-248
• Main Authors: Gao, H., Li, W. G., Cai, L., Berry, C., Luo, X. Y.
• Format: Article
• Language: English
• Subjects: Applications of Mathematics; Computational Mathematics and Numerical Analysis; Diastole; Estimates; In vivo methods and tests; Mathematical and Computational Engineering; Mathematical Modeling and Industrial Mathematics; Mathematical models; Mathematics; Mathematics and Statistics; Myocardium; Nonlinearity; Optimization; Strain; Theoretical and Applied Mechanics
• ISSN: 0022-0833; 1573-2703
• DOI: 10.1007/s10665-014-9740-3

A central problem in biomechanical studies of personalized human left ventricular (LV) modelling is to estimate material properties from in vivo clinical measurements. In this work we evaluate the passive myocardial mechanical properties inversely from the in vivo LV chamber pressure–volume and strain data. The LV myocardium is described using a structure-based orthotropic Holzapfel–Ogden constitutive law with eight parameters. In the first part of the paper we demonstrate how to use a multi-step non-linear least-squares optimization procedure to inversely estimate the parameters from the pressure–volume and strain data obtained from a synthetic LV model in diastole. In the second part, we show that to apply this procedure to clinical situations with limited in vivo data, additional constraints are required in the optimization procedure. Our study, based on three different healthy volunteers, demonstrates that the parameters of the Holzapfel–Ogden law could be extracted from pressure–volume and strain data with a suitable multi-step optimization procedure. Although the uniqueness of the solution cannot be addressed using our approaches, the material response is shown to be robustly determined.