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We have studied the three-dimensional arrangement of ventricular muscle cells and the associated extracellular connective tissue matrix in dog hearts. Four hearts were potassium-arrested, excised, and perfusion-fixed at zero transmural pressure. Full-thickness segments were cut from the right and left ventricular walls at a series of precisely located sites. Morphology was visualized macroscopically and with scanning electron microscopy in 1) transmural planes of section and 2) planes tangential to the epicardial surface. The appearance of all specimens was consistent with an ordered laminar arrangement of myocytes with extensive cleavage planes between muscle layers. These planes ran radially from endocardium toward epicardium in transmural section and coincided with the local muscle fiber orientation in tangential section. Stereological techniques were used to quantify aspects of this organization. There was no consistent variation in the cellular organization of muscle layers (48.4 +/- 20.4 microns thick and 4 +/- 2 myocytes across) transmurally or in different ventricular regions (23 sites in 6 segments), but there was significant transmural variation in the coupling between adjacent layers. The number of branches between layers decreased twofold from subepicardium to midwall, whereas the length distribution of perimysial collagen fibers connecting muscle layers was greatest in the midwall. We conclude that ventricular myocardium is not a uniformly branching continuum but a laminar hierarchy in which it is possible to identify three axes of material symmetry at any point.

We developed a mathematical representation of ventricular geometry and muscle fiber organization using three-dimensional finite elements referred to a prolate spheroid coordinate system. Within elements, fields are approximated using basis functions with associated parameters defined at the element nodes. Four parameters per node are used to describe ventricular geometry. The radial coordinate is interpolated using cubic Hermite basis functions that preserve slope continuity, while the angular coordinates are interpolated linearly. Two further nodal parameters describe the orientation of myocardial fibers. The orientation of fibers within coordinate planes bounded by epicardial and endocardial surfaces is interpolated linearly, with transmural variation given by cubic Hermite basis functions. Left and right ventricular geometry and myocardial fiber orientations were characterized for a canine heart arrested in diastole and fixed at zero transmural pressure. The geometry was represented by a 24-element ensemble with 41 nodes. Nodal parameters fitted using least squares provided a realistic description of ventricular epicardial [root mean square (RMS) error less than 0.9 mm] and endocardial (RMS error less than 2.6 mm) surfaces. Measured fiber fields were also fitted (RMS error less than 17 degrees) with a 60-element, 99-node mesh obtained by subdividing the 24-element mesh. These methods provide a compact and accurate anatomic description of the ventricles suitable for use in finite element stress analysis, simulation of cardiac electrical activation, and other cardiac field modeling problems.

The interpretation of experimental results from functional medical imaging is complicated by intersubject and interspecies differences in airway geometry. The application of computational models in understanding the significance of these differences requires methods for generation of subject-specific geometric models of the bronchial airway tree. In the current study, curvilinear airway centerline and diameter models have been fitted to human and ovine bronchial trees using detailed data segmented from multidetector row X-ray-computed tomography scans. The trees have been extended to model the entire conducting airway system by using a volume-filling algorithm to generate airway centerline locations within detailed volume descriptions of the lungs or lobes. Analysis of the geometry of the scan-based and model-based airways has verified their consistency with measures from previous anatomic studies and has provided new anatomic data for the ovine bronchial tree. With the use of an identical parameter set, the volume-filling algorithm has produced airway trees with branching asymmetry appropriate for the human and ovine lung, demonstrating the dependence of the method on the shape of the lung or lobe volume. The modeling approach that has been developed can be applied to any level of detail of the airway tree and into any volume shape for the lung; hence it can be used directly for different individuals or animals and for any number of scan-based airways. The resulting models are subject-specific computational meshes with anatomically consistent geometry, suitable for application in simulation studies.

An efficient finite difference model of blood flow through the coronary vessels is developed and applied to a geometric model of the largest six generations of the coronary arterial network. By constraining the form of the velocity profile across the vessel radius, the three-dimensional Navier-Stokes equations are reduced to one-dimensional equations governing conservation of mass and momentum. These equations are coupled to a pressure-radius relationship characterizing the elasticity of the vessel wall to describe the transient blood flow through a vessel segment. The two step Lax-Wendroff finite difference method is used to numerically solve these equations. The flow through bifurcations, where three vessel segments join, is governed by the equations of conservation of mass and momentum. The solution to these simultaneous equations is calculated using the multidimensional Newton-Raphson method. Simulations of blood flow through a geometric model of the coronary network are presented demonstrating physiologically realistic flow rates, washout curves, and pressure distributions.