Abstract:
We have developed a mathematical representation of ventricular geometry and myocardial architecture using a three-dimensional finite element model which incorporates new information on the layered organization of cardiac muscle cells in ventricular myocardium.
This model has been used to make a detailed and quantitative comparison of cardiac geometry and fibre organization. Extensive geometric measurements were made in dog hearts arrested in diastole and fixed at zero transmural pressure. These measurements included: ventricular epicardial and endocardial surface geometry (25 hearts), muscle fibre orientations (6 hearts), epicardial coronary vessels (24 hearts), and the specialized conduction system (3 hearts). A finite element mesh was fitted to geometric data for each heart and was shown to provide a faithful representation of the ventricular surfaces. RMS fitting errors were: epicardium 0.75 ± 0.18 mm, RV endocardium 1.75 ± 0.36 mm, and LV endocardium 1.24 ± 0.30 mm (with an appropriately refined mesh). Comparison of coronal cross-sections generated from the meshes demonstrated that ventricular shape is very consistent for hearts of similar size. Myocardial fibre fields were fitted to fibre orientation data and compared at matched sites. The fibre fits were shown to be within the range of measurement error. At equivalent sites fibre fields showed consistent regional differences in transmural fibre angle variation. Comparison of the geometric data revealed very similar patterns of both coronary vessel topology and Purkinje fibre distribution.
Two further dog hearts were arrested and fixed as outlined above, and ventricular geometry was measured. The ventricular walls were subdivided into radial base-apex segments from which thick (100 µm) sections were cut. Simple digital imaging procedures were used to characterize the macroscopic organization revealed in a) transmural and b) serial tangential thick sections. These studies confirm that ventricular myocardium is a discrete laminar structure rather than a uniformly branching continuum as has previously been believed. In the transmural plane, myocardial sheets run from endocardium to epicardium in a characteristic pattern which varies at different ventricular sites. It has also been shown that the extent of coupling between adjacent myocardial layers varies transmurally with more extensive interconnections between layers in the subepicardial and subendocardial regions than in the midwall. Our finite element model of cardiac anatomy has been extended to incorporate a representation of the laminar organization of ventricular myocardium. The refined model provides a very good representation of our experimental myocardial sheet data (RMS fitting error = 27°).
Finally we review the approaches to modelling electrical activity in the heart and demonstrate the use of our model in studies of ventricular activation.