1 Department of Informatics and Mathematical Modeling, Technical University of Denmark2 Department of Applied Mathematics and Computer Science, Technical University of Denmark
Computational models of the blood flow in the heart are a useful tool for studying the functioning of the heart. The purpose of this thesis is to achieve a better understanding of hemodynamics of the normal and diseased hearts through the use of a computational model and magnetic resonance (MR) data. We present a 2D computational model of the blood flow in the left side of the heart. The work is based on Peskin and McQueen's 2D model dimensioned to data on the dog heart, which we improve and adjust using physiological knowledge and MR velocity data to achieve a model of the human heart. The improvements require changing the geometry, the timing, the mechanical activation of the heart musculature, and the afterload. Furthermore, we introduce a tethering of the otherwise freely floating heart. We evaluate the model from a computational and modelling point of view and find a set of reasonable parameter values. This is our reference model, which gives representative simulation results. We compare a simulation using our reference model with an MR velocity data set obtained from a healthy human. The comparison is carried out for the intraventricular velocity field and the velocity time curves over the mitral ring and across the aortic outflow tract. The comparison between elocity fields shows a reasonably fair agreement in the general flow pattern: a wide inflow jet, the formation of an anterior vortex during filling, and an outflow jet through the outflow tract. There are some disagreements in the detailed flow pattern, in particular with regard to the vortex patterns. The velocity time curves from the simulation show good agreement with MR data. The timing in the simulation is practically the same as in the MR data, while there are some differences between the shapes and maximum values of the velocity curves. We use our 2D model to perform investigations of certain mechanisms involved in heart diseases affecting the diastolic functioning of the heart. To be able to simulate pathological conditions we improve the model for the mechanical activation of the heart muscle. We find that it is not possible to successfully simulate an ischemic apical region by letting the relaxation be slower in the apical region. However, we are able to successfully model a global ischemic left ventricle through a slower relaxation of the entire ventricle and to model a myocardial infarction affecting the apex by letting the apical region be inactive. In both of these cases the simulation results compare well with clinically observed data on dogs and humans. We present Peskin and McQueen's 3D model of the entire human heart and the nearby great vessels. We perform a simulation with the model, where we adjust the timing to be the same as in our reference 2D model. Unfortunately, the results do not compare very well with MR data. In particular, the flow and velocity over the mitral ring are not in good agreement, and the pressure in the ventricles is far too high. Furthermore, the 3D model is computationally very demanding. This, together with the disagreement with MR data, makes it unfeasible to use the 3D model as a tool for investigating the hemodynamics of the heart. However, the 3D model gives insight into the vortex pattern in the left ventricle. A clear vortex ring is formed below the mitral valve during filling, and in a cut-away view this ring is seen as two distinct vortices, similar to the vortices formed in our 2D model.
diastolic functioning of the heart; left ventricular blood flow; MR data; heart simulation