Simulation of Atrial Electrical Activity
Mathematical modeling of biological systems that are of interest in the pharmaceutical industry is a rapidly growing area. The use of mathematical models brings the promise of reducing the high costs and long times associated with the development of new drugs and models are gradually finding their way into the drug development routine.
AstraZeneca, a world leader in cardiovascular medicines, has worked together with FCC in a series of collaboration projects aiming at a better understanding of atrial arrhythmias and of the properties of drugs that successfully can treat them. Atrial fibrillation is the most common form of heart arrhythmia and is associated with a significantly increased risk of stroke.
High age being a risk factor for atrial fibrillation, the growing proportion of older people in the populations of developed countries is expected to increase the incidence of this arrhythmia. Also considering the modest efficacy or potentially serious side effects of existing drugs, the future market of anti-fibrillatory medicines is forecast to show substantial growth.
AstraZeneca believed that a mathematical approach would give insight in the interplay by which different ionic currents shape the action potential, knowledge that could assist in the screening of novel anti-arrhythmic drugs. Starting with implementation and computational analysis of mathematical models describing single canine heart muscle cells, the scope has successively widened to also include simulations of the electrical activity in realistic atrial geometries and models of interactions between drugs and specific ion-channels. These projects have increased the understanding of atrial arrhythmias and have enabled quantitative evaluation of treatment strategies in silico.
Computer models make it possible to relate the dynamics of the action potential propagation in realistic atrial geometries to drug effects at the single cell level. This in turn permits in silico reconstruction and investigation of phenomena like atrial flutter and fibrillation.
FCC has developed a framework for modeling and simulation of electro-chemical activity in large scale cell networks. A geometric model of the canine atria has been constructed utilizing ultra sound imaging data and a realistic fiber structure and cell type distribution has also been incorporated, see figure 1.
Recently, the atrial geometry model has been improved by refining the spatial discretization. In its present state it consists of a network of 70 000 nodes representing the quantitative behavior of a cluster of real cells, each node being an instance of a single cell model. An illustration of a single cell model is shown in figure 2.
The cell models used implement ion-channel mechanisms using the Hodgkin-Huxley paradigm. To gain insight of the quantitative effects of a drug inhibiting a particular ion-channel so called Markov models are believed to provide the necessary level of detail. We have implemented more detailed models of a potassium ion-channel of particular interest using this formalism, see figure 3.
Results and Achievements
The complete atrial tissue model consists of about 2.000.000 coupled nonlinear ordinary differential equations. To meet the computational demands of this model the developed modeling and simulation framework has been translated into a high performance computing setting first tested and executed on FCC’s internal computational servers and recently deployed onto Chalmers Centre for Computational Science and Engineering (C3SE) facilities.
The simulation framework has been used to induce fibrillation and flutter like electro-dynamic activity in cell networks from simple sheets up to realistic atrial geometries as shown in figure 4. In addition, the effect of ion-channel modulation on this behavior has been investigated. The simulations are in good accordance with in vivo observations, have great potential to provide insights into the underlying mechanisms of atrial fibrillation and flutter, and can serve as a tool for prediction of drug effects.
Finding suitable targets and drugs that modulate their activity appropriately is difficult. Some new anti-arrhythmic drugs are targeting multiple ion-channels simultaneously. As the possible combinations of targets, modulation type, and relative strength of the effect on the different targets are overwhelmingly complex, such treatment strategies present an even more difficult problem. Predictive mathematical models may be particularly suited to identify useful multi-target drug profiles. The importance of foresight in choosing drug candidates is pivotal as very few compounds will eventually reach the market. Hence, an interesting area for future development of our atrial modeling efforts would be in silico investigations of different multi-target strategies.
© 2013 Fraunhofer - Chalmers Centre