An experimental method for evaluating constitutive models of myocardium in in vivo hearts

Abstract

A new experimental method for the evaluation of myocardial constitutive models combines magnetic resonance (MR) radiofrequency (RF) tissue-tagging techniques with iterative two-dimensional (2-D) nonlinear finite element (FE) analysis. For demonstration, a nonlinear isotropic constitutive model for passive diastolic expansion in the in vivo canine heart is evaluated. A 2-D early diastolic FE mesh was constructed with loading parameters for the ventricular chambers taken from mean early diastolic-to-late diastolic pressure changes measured during MR imaging. FE solution was performed for regional, intramyocardial ventricular wall strains using small-strain, small-displacement theory. Corresponding regional ventricular wall strains were computed independently using MR images that incorporated RF tissue tagging. Two unknown parameters were determined for an exponential strain energy function that maximized agreement between observed (from MR) and predicted (from FE analysis) regional wall strains. Extension of this methodology will provide a framework in which to evaluate the quality of myocardial constitutive models of arbitrary complexity on a regional basis.

A dynamic elastic model for segmentation and tracking of the heart in MR image sequences

“…Some authors feel that statistical models are too dependent on the training data, and cannot account for all the variability in real patients. For example, Creswell et al (1994) were the first to propose a FEM deformable elastic model to analyze cardiac images. In the field of segmentation of echocardiographic images, Gérard et al (2002) proposed a 3D deformable model based on a simplex mesh.…”

Myocardial material property determination in the in vivo heart using magnetic resonance imaging

“…The models were constructed by selecting contour points around the epicardium, LV and RV. The LV, RV and epicardium were approximated by closed 3rd order B-spline curves [18]. A pversion FE mesh of 16 to 21 2-D ouadrilateral elements 157 was constructed with 1198 to 1578 degrees of freedom (DOF) (see Appendix).…”

“…Elements of the J matrix (first derivatives of residuals with respect to the parameters) are obtained using forward finite difference approximations: (18) The difference approximations are made by solving the forward FE problem an additional time for each parameter at every iteration with each parameter separately incremented by a small amount, 5bi. For a 2-D problem, J is a 2m × q matrix where q is the number of parameters and m is the number of data points.…”

Cardiac Motion and Elasticity Characterization with Iterative Sequential $\mathcal{H}_\infty$ Criteria

“…There have been a number of efforts on the parameter identification of the myocardium, where the basic idea is to minimize some criteria that measure the goodness of fit between the model-predicted and the data-derived mechanical responses [1,9]. More recently, an expectation-maximization (EM) strategy is proposed to estimate the composite tissue mechanical properties by using displacements reconstructed from MR tagging data [4].…”