Abstract:

This study deals with a mathematical model of the cellular action potential with its underlying ionic currents in human myocardium based on the Luo-Rudy phase II cell model. The activation process is calculated in a three dimensional patch taking into account the behaviour of each single cell membrane and an anisotropic pattern as it is known for the right ventricel. The propagation is simulated using the Finite Difference Method in Time.

Abstract:

Wir präsentieren einen Algorithmus zur Erstellung von Finite Elemente Modellen des menschlichen Körpers. Ein von uns entwickelter Netzgenerator zerlegt ein durch Voxeldaten vorgegebenes Volumen in ein unstrukturiertes Tetraedergitter, welches das Delaunay Kriterium erfüllt. Sind die Ausgangsdaten gewebeklassifiziert, so erfolgt die Modellerzeugung basierend auf einem Teile und Herrsche Algorithmus automatisch, bei unklassifizierten Voxeldaten können unterstützend Grenzflächen mit Aktiven Konturen oder Marching Cubes erzeugt werden.

Abstract:

The coronary arteries supply the heart muscle with oxygenated blood to ensure a proper heart function. When this process is disturbed, it can have detrimental impacts on the physical conditions of the human body and can be lethal in many cases. One main reason for the malfunction of the blood sustenance of the heart can be a coronary myocardial infaction which typically occurs in connection with plaque depositions within the coronary arteries. The label plaque is a hypernym for material depositions e.g. calcium and fat in the arteries for patients who suffer from coronary artery disease and can be divided in two categories: Critically stenotic plaque and vulnerable or high risk plaque. For that reason, it is of high clinical relevance to further examine the phenomena related to heart attacks which can be executed from a fluid mechanical standpoint through fluid flow simulations. In this thesis, the simulation software COMSOL Multiphysics which utilizes the finite element method (FEM) to obtain numerical solutions was used to create models to represent the artery geometry and the blood flow inside the lumen area. First of all, a model with an idealized, rigid, cylindrical geometry was built and the solutions were compared to the analytically calculated quantities for the occuring axial flow velocity and wall shear stress assuming laminar flow. With this, it could be determined that the FEM delivers acceptably accurate results and therefore the basic validation for the model was ensured. Second, an idealized rotational symmetrical, cylindical model for the plaque and artery geometries was set up wich allows to switch parametrically between different levels of stenosis and other geometric entities. Material properties were assigned to asses the fluid structure interaction between the laminar flow and the solid mechanical components with the multiphysics package in the software. To evaluate patient specific clinical data, a general imaging pipeline that descibes the different steps necessary in the workflow of building a model to analyze fluid mechanic effects on the base of computed tomography images was formulated. Finally, a seperate model based on computed tomography images that were provided by the cardiology clinic Theresienkrankenhaus Mannheim was implemented. For all simulations, a pulsatile pressure condition was used as a boundary condition to represent the pumping mechanism of the myocard. In the next step, the velocity profiles, the pressure distributions and developments over the artery length and the occuring shear stresses were calculated and visualized for the models, respectively. The results of the simulations indicate that the localization of critical stenosis based on the quantitative data for the shear rate, the pressure change and the blood velocity can be assisted. With the color coded visualization of the dimensions and the generation of relevant two dimensional plots, the mechanical phenomena can be illustrated. Lastly, the three dimensional wall shear stress animations over several cardiac cycles can support identifying especially critical regions of the arterial wall.