An optimal electrode position, atrio-ventricular (AV) and interventricular (VV) delay in cardiac resynchronization therapy (CRT) improves its success. An optimization strategy does not yet exist. A computer model of the Visible Man and a patient heart was used to simulate an atrio-ventricular and a left bundle branch block with 0%, 20% and 40% reduction in interventricular conduction velocity, respectively. The minimum error between physiological excitation and pathology/therapy was automatically computed for 12 different electrode positions. AV and VV delay timing was adjusted accordingly. The results show the importance of individually adjusting the electrode position as well as the timing delays to the patient's anatomy and pathology, which is in accordance with current clinical studies. The presented methods and strategy offer the opportunity to carry out non-invasive, automatic optimization of CRT preoperatively. The model is subject to validation in future clinical studies.
Electrophysiological modeling of the heart enable quantitative description of electrical processes during normal and abnormal excitation. Cell models describe e.g. the properties of the cell membrane and the gating process of ionic channels. New measurement data is available for these channels for physiological and some pathological states. These data should be included in the models to enhance their features. In this work we describe a framework adapting ion channel models to measurement data by using a particle swarm optimization (PSO). Models of ion channels can be described by Hogdkin-Huxley equations or by Markovian models. They consider rate constants that are complex functions depending on the transmembrane voltage. Each transition has two rate constants described by several parameters. These parameters need to be varied in order to minimize the difference between measured and simulated ion channel kinetics. Since this minimization procedure is multidimensional and the function can have several local minima, conventional optimization strategies like Powells algorithm and conjugate gradient do not ensure to find the global minimum. To overcome this, a PSO was implemented that inserts several dependent particles randomly into the search space. It is based on the social behavior of swarms. As the particles are independent during each iteration the procedure can be calculated in parallel. The measurement data used for this work were current traces of a voltage-clamp protocol of reggae mutant hERG channels. The same protocol as for the measurement was assigned to the model of Lu et al. describing hERG function with a Markovian model. The value to be minimized was the sum of mean square errors between measured and simulated currents at certain time instances. Both Powell and PSO were started several times with random starting values. In 94% of the cases PSO found the minimum compared to 16% for Powell. On the other hand PSO needed approximately 100 times more function evaluations. The parallelization decreased the overall time needed by the PSO to about the same amount Powell needed. Therefore, the parallel PSO is a fast and reliable approach for adapting ion channel models to measured data.
Simulation of cardiac excitation is often a trade-off between accuracy and speed. A promising minimal, time-efficient cell model with four state variables has recently been presented together with parametrizations for ventricular cell behaviour. In this work, we adapt the model parameters to reproduce atrial excitation properties as given by the Courtemanche model. The action potential shape is considered as well as the restitution of action potential duration and conduction velocity. Simulation times in a single cell and a tissue patch are compared between the two models. We further present the simulation of a sinus beat on the atria in a realistic 3D geometry using the fitted minimal model in a monodomain simulation.
Student Theses (2)
S. Lurz. Multidimensional adaption of electrophysiological cell models to experimentally characterized pathologies. Institute of Biomedical Engineering, Universität Karlsruhe (TH). Diplomarbeit. 2008
In the course of this diploma thesis the Particle Swarm Algorithm was successfully implemented into the previously existing Script Optimizer environment. Multiple parameters that control its behavior have been thoroughly tested and optimized to guarantee a high rate of successful opti- mizations while keeping the average number of iteration loops at a minimum. Benchmark functions provided a relatively fast way to obtain statistically significant information concerning the effec- tiveness of various parameter setups and the comparison to the existing Powell algorithm. The influence of the swarm size and the allowed maximum number of iteration loops on the optimiza- tions performance were further subjects of investigations.The enhanced Particle Swarm Optimization setup proved to be very robust in terms of a high rate of successful minimizations even for multi-dimensional functions that contain numerous local minima. In direct comparison with an existing optimization algorithm, however, the PSO needed by far more iteration loops for a successful optimization. The results of these experiments showed that it is important to accurately adjust the algorithm to the specific problem at hand.While using the PSO, an individual fitness value needs to be calculated for each particle during one iteration. Those repeated calculations account for the high robustness especially in multiple di- mensions but unfortunately also imply an immense computational work. To reduce the calculation time to an acceptable duration advantage was taken of the independence of the single processes. A technology that is integrated in the Apples Mac OS X operating system called Xgrid offers the possibility to distribute the workload on a cluster of network computers. Thus the optimization framework was altered so that it allowed simultaneous calculations of independent particles. Additionally, the performance of Xgrid was experimentally investigated leading to the conclusion that the jobs that are submitted to the grid need to meet certain requirements to be efficiently split into parallel executable tasks.Based on the experimental findings both the PSO algorithm and the Xgrid architecture were ad- justed to attain optimal performance. The optimization framework was then used to address a practical parameter fitting scenario. The in-vivo measured characteristics of a mutated ion channel should be reproduced by a well-established mathematical cell model. Therefore multiple param- eters that determine the cell models electrophysiological behavior had to be varied according to the used optimization strategy.It could be shown that it is possible to fit an individual ion current in the mathematical cell model of ten Tusscher et al. to the measured data of reggae mutated zERG channels of zebrafish. The parameter fit using the Zhang et al. model of rabbit sinoatrial node cells failed due to the inability of the cell model to adapt its ion current IKr to the measured values.Finally, changes to the optimization framework allowed to approximate the behavior of a relatively new and simplified cell model that allows large scale calculations at relatively low computational costs to the characteristics shown by the well-established and -accepted complex mathematical cell models. An optimization of this simplified Fenton 4 State model to fit the ten Tusscher et al. cell models action potential showed even better results than the adaption published by the inventors of the Fenton 4 State model. The possibilities of the presented optimization framework was concludingly demonstrated by fitting the Fenton 4 State model to the Courtemanche et al. model for human atrial myocytes. A close match of the AP morphology could be achieved allowing the time-saving simulation of atrial arrhythmias in future research projects.
S. Lurz. Entwicklung schneller Optimierungsstrategien für die kardiale Resynchronisationstherapie im Computermodell. Universität Karlsruhe (TH), Institut für Biomedizinische Technik. Bachelorarbeit. 2007