Research Topics
myocardial ischemia
"Myocardial ischemia" is the name of the complex changes that the heart muscle undergoes when it receives too little oxygen. This can be due to obstruction of a coronary artery. However, in many patients ischemic changes occur without a clear obstruction. These patients often have a particular ECG pattern, characterized by a negative shift of the "ST segment" of the ECG. In contrast, patients with a clear obstruction usually have a positive shift in their ST segments.
In the past, this negative ST-segment shift ("ST depression") has been attributed to ischemia limited to the inner part of the heart muscle. Recent computer model studies have indicated that such "subendocardial ischemia" does not lead to ST depression. Our study with a whole-heart model has confirmed this result [1]. We have also provided two alternative explanations: changes in the distribution of gap junctions, or an ischemic area that covers a very large part of the heart. For example, we have shown that ischemia covering the entire ventricular subendocardium can cause the typical ST depression pattern [2,3].
Another aspect of ischemia that we have studied is the distribution of potassium ions in the border of an ischemic area. Potassium plays an important role in the generation of ischemia-related ECG changes. We have shown that more realistic results can be obtained if the model accounts for the dynamics of potassium [4,5]. We are working on a reaction-diffusion model that completely integrates potassium handling. With this model we hope to improve understanding of cardiac arrhythmias that are caused by ischemia.
heterogeneity and the normal ECG
The shape of the ECG has been studied for more than a century, and explanations for most of its features have been given. However, when you actually try to reproduce an ECG with a mathematical model, it becomes clear how little we know about the actual mechanisms. This is a major problem for model developers, and at the same time a major reason for them to do their work: only when we point out the gaps in our knowledge we can pose the right questions and hope to improve our picture of the heart.
Especially the T-wave in the ECG is poorly understood. It depends crucially on heterogeneity of action potential duration in the heart. Several different cell types have been identified, but many of their characteristics are still debated. Moreover, when we put them together in the heart, we find that the information from measurements on single cells does not explain the shape of the T-wave; some unsupported assumptions have to be made to obtain a realistic T-wave. In addition, it turns out that we know too little about the placement of the different cell types in the heart.
| [1] | Trudel et al. IEEE Trans Biomed Eng 2004 |
| [2] | Potse et al, 34th Int Con Electrocardiol, June 2007 |
| [3] | Potse et al., Canadian Cardiovascular Congress. October 2007 |
reaction-diffusion model development
Our first reaction-diffusion model of the human heart worked with 12 million points at a resolution of 0.25 mm [1]. It required 12 GB memory to work, necessitating the use of a supercomputer, then an SGI Origin 2000 (Trudel et al, 2004). Later work (actually published earlier, in 2003) reduced memory consumption to less than 5 GB, making it possible to run the model on a high-end PC [2]. Still, this would require several days computation time. Running on a supercomputer with 16 processors, the model can simulate a full heart beat in 5 hours.
With more realistic membrane models, memory usage quickly goes up, and the perspective of running on a desktop PC becomes more remote [3].
| [1] | Trudel et al. IEEE Trans Biomed Eng 2004 |
| [2] | Potse, Dubé and Gulrajani, Conf IEEE-EMBS 2003 |
| [3] | Potse et al, 34th Int Con Electrocardiol, June 2007 |
bidomain model development
Bidomain models are much harder to solve than monodomain models because they require the solution of a system of linear equations, one equation for each model point, at each time step. Such systems are more difficult to solve when they grow larger. For a human heart, tens of millions of points are necessary. In December 2006 we published the first such model. With this model we have shown that, for ECG simulation, a monodomain model is accurate enough. This is good news for researchers who don't have access to supercomputers: a monodomain model of the human heart can in principle run on a (high-end) PC. Bidomain models remain necessary for the simulation of, for example, defibrillation shocks, and for the simulation of extracellular potentials in the heart. For the latter, however, a shortcut can be taken: propagation of action potentials can be simulated with a monodomain model, and from the results extracellular potentials can be computed at relatively large intervals. This still requires a bidomain model and a supercomputer, but it is about 3 times faster than solving the propagation problem with a bidomain reaction-diffusion model.
| [1] | Potse et al., IEEE Trans Biomed Eng 2006 |
understanding electrograms
Our bidomain model of the human heart is the first model ever that can reliably simulate endocardial catheter signals. A first demonstration of this capability is our study of methods to measure repolarization times in cardiac electrograms [1,2].
We have used the model also to prove the validity of an extremely simple model of cardiac electrograms [3]. This simple model can help to gain insight in these signals.
