CFD heart throb
	At first sight this might not seem very interesting from an engineering point of view, since it might appear that we cannot really change anything related to the flow properties of the human heart. But is this true? What about the surgical treatment of deformed hearts, or the artificial valves or heart support pumps that interfere with the natural function of this intriguing masterpiece? With the given progress in these fields, a sound understanding of the detailed function of the heart is mandatory. Since the heart’s function is like that of a pump, a fluid mechanical approach is suggestive. Fig. 1: Grid generation from MRI data     While the overall properties of the heart stay the same, not one heart is exactly like the other. This is especially true when we consider diseased hearts, where there is the imminent need for surgical treatment. A method for the patient specific simulation of the heart's fluid mechanical status would come in handy as a diagnostic tool. The presented work as part of the ‘Karlsruhe Heart Model’ KAHMO aims at providing such a tool. With its powerful scripting language and the possibility to include user coding to implement physical details that are not already taken care of, STAR-CD was our chosen CFD code for tackling this complex problem. In order to get a patient specific numerical model of the heart (or currently the left ventricle) a standard diagnostic technique is used: MRI, magnetic resonance imaging. This measurement technique provides a sliced 4D dataset of the region of interest from which the geometry of the left ventricle can be derived at approximately 18 points of time through the cardiac cycle using geometry recognition techniques. The separate geometries are then automatically meshed with a block structured hexahedral grid using a mesh generation script designed specifically for this purpose. For each given geometry, the resulting grid is topologically identical to all the others. The grid size is 0.3 mio cells. The grid generation steps are shown in figure 1. Movement is realized by moving each vertex along a translatory path interpolated from the known position in the fixed grids by a second order interpolation algorithm. This movement is performed at runtime by a user subroutin Such wall movement and prescribed pressures at the inlet and outlet form the boundary conditions. In combination with varying baffle resistances for the valves and the circulatory resistance, we formulate the problem in a way that can be treated by CFD. Blood is a non-Newtonian fluid modeled after a modified Cross model, which is also implemented as a user subroutine. The calculation is performed for a number of cycles until the solution is cyclically repeated. The results of the simulation show very good quantitative agreement with the typical diagnostic measurements performed in the cardiological practice. Excellent quantitative agreement can be seen in comparison with MRI and Ultrasound flux readings taken on the same occasion as the geometry measurements. Figure 2 shows the flow patterns at two points of time halfway through the filling and ejection cycle respectively. The overall flow pattern is governed by an asymmetrically growing ring vortex system, which develops at the mitral valve and forms sort of a twisted band in four dimensions. The timing of the intraventricular flow is such that the fluid is neither accelerated nor decelerated to a high extend, but moves in a fluid motion during the heart cycle until it reaches the aortic valve just in time to be ejected. Fig. 2: Streamlines at filling and ejection cycle   Fig. 3: Old blood in dyskinetic area The accurate timing of the heart’s pumping movement to the velocities of the blood flowing through it has evolved in the course of evolution. Any interference with this intricate process can yield fatal consequences. The simulation of a common left ventricular disease, which changes this timing shows possible points of interest for the treatment. In the diseased heart in Figure 3, a small area at the tip of the heart is not taking part in the muscular movement (dyskinesia). This creates a cavity at the side where old blood can agglomerate. This problem can be visualized in the simulation by the means of a passive scalar, which represents the old blood. It is easily visible where the problem is located and where a possible surgical treatment has to be applied. Conclusion We have successfully used state-of-the-art commercial CFD software on the complex problem of intraventricular flow. The results that could be obtained for the sound heart contribute to a better understanding of the heart’s function and the application to diseased hearts can bring valuable information to the surgeon. For further information please contact: schenkel@isl.mach.unikarlsruhe.de