Parameter estimation in a Holzapfel–Ogden law for healthy myocardium

Abstract

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.

Computational Modeling of Healthy Myocardium in Diastole

“…Most recently, Gao et al 5 investigated the feasibility of identifying parameters of the H-O model from non-invasive clinical measurements for healthy myocardium. They introduced an optimization scheme to first identify known parameters of a LV model by generating a set of synthetic strain data and then extended their optimization method to in-vivo models with clinical data.…”

“…In this study we make use of finite element models, which employ the H-O material law, and the optimization scheme proposed by Gao et al 5 to estimate the eight material parameters of the H-O model using in-vivo MRI and pressure data from four healthy porcine LVs. Additionally, the resulting End-Diastolic Pressure-Volume Relationship (EDPVR) of each LV is examined to further explore the influence of the H-O model.…”

Non-invasive Model-Based Assessment of Passive Left-Ventricular Myocardial Stiffness in Healthy Subjects and in Patients with Non-ischemic Dilated Cardiomyopathy

“…In particular, data-derived information such as cavity volumes7 and pressures3,13 has been used to quantify model passive stiffness. The transition from bulk measures to more comprehensive data, such as tissue displacements and strains, has enabled more elaborate approaches for estimating a larger number of parameters12,35 and heterogeneous parameter distributions 25,38. As recent advances in medical imaging offer increasingly more detail on the heart anatomy and regional kinematics, rich datasets for model personalisation and characterisation of passive parameters are becoming more accessible 2,14,39…”

Passive diastolic modelling of human ventricles: Effects of base movement and geometrical heterogeneity

“…Palit plane motion cannot be easily estimated (Gao et al, 2015). In addition, due to lack of 268 patterns/features in cine images, higher uncertainties presents while estimating pixel-wise 269 strain.…”

“…Gao et al (2014) showed that the regional circumferential strains could be estimated 270 correctly from cine images. However, greater discrepancies exists during the estimation of 271 regional radial strains, and therefore, could not be used in FE modelling (Gao et al, 2015). …”