Laminar structure of the heart: a mathematical model

Abstract

A mathematical description of cardiac anatomy is presented for use with finite element models of the electrical activation and mechanical function of the heart. The geometry of the heart is given in terms of prolate spheroidal coordinates defined at the nodes of a finite element mesh and interpolated within elements by a combination of linear Lagrange and cubic Hermite basis functions. Cardiac microstructure is assumed to have three axes of symmetry: one aligned with the muscle fiber orientation (the fiber axis); a second set orthogonal to the fiber direction and lying in the newly identified myocardial sheet plane (the sheet axis); and a third set orthogonal to the first two, in the sheet-normal direction. The geometry, fiber-axis direction, and sheet-axis direction of a dog heart are fitted with parameters defined at the nodes of the finite element mesh. The fiber and sheet orientation parameters are defined with respect to the ventricular geometry such that 1) they can be applied to any heart of known dimensions, and 2) they can be used for the same heart at various states of deformation, as is needed, for example, in continuum models of ventricular contraction.

Sharing and reusing cardiovascular anatomical models over the Web: a step towards the implementation of the virtual physiological human project

“…The Web page shown in figure 2 will be displayed as a result of this selection. Currently, the list contains the following models: ABI model of the cardiac ventricles (Nielsen et al 1991;LeGrice et al 1997), INRIA model of the cardiac ventricles (Peyrat et al 2007), which includes both coarse-and fine-grain versions (Lamecker et al 2009), INRIA Aorta, Philips Whole-Heart (Lorenz & von Berg 2006), Philips Whole-Heart with Extended Vessels (Peters et al 2008), Philips Hamburg Left Atrium with multiple anatomical variations (Lorenz & von Berg 2006), Sheffield Aorta (Barber et al 2007) and finally the UPF-CISTIB Biventricular Heart Atlas (Ordas et al 2007). The original authors have set the accessibility of the geometric data for each model.…”

“…manual measurement or statistical analysis of magnetic resonance imagings (MRIs)). The first model on the list, the ABI model of the cardiac ventricles (figure 3a), was produced by manual measurements on a whole canine heart in diastole (Nielsen et al 1991;LeGrice et al 1997). Except for this model, all the remaining geometries represent human hearts or part thereof.…”

“…hosting them as static Web resources linked to HTML pages. For example, the Auckland canine heart model (Nielsen et al 1991;LeGrice et al 1997), one of the most reused computer models of the cardiac ventricles, has been available through the website of the Auckland Bioengineering Institute (ABI) for many years. As a consequence, considerable time is required to discover current and past applications of the Auckland model.…”

Unique parameter identification for cardiac diagnosis in critical care using minimal data sets

“…For example multi-scale modelling approaches utilizing finite elements have successfully explained complex behaviour of the heart [9][10][11]. Although this paper does not seek to compare to finite elements in any way, it does represent the extreme case where knowledge of complex geometry of blood vessels (e.g.…”

Efficient implementation of non-linear valve law and ventricular interaction dynamics in the minimal cardiac model

“…Most current approaches to modelling the CVS can be grouped into either Finite Element (FE) or PressureVolume (PV) approaches. FE techniques offer potentially very accurate results but require very detailed patient specific information such as muscle fibre orientations, structures and mechanical properties which is not readily available in intensive care [1][2][3][4]. Furthermore, the computational power required is currently too extreme for clinical use.…”