Forrester’s Concept in Modeling Heart Dynamics
The paper deals with the Forrester’s approach to analysis of heart electrical dynamics based on the hypothesis that heart belongs to the class of Complex Systems and its dynamics can be described by coupled Van der Pol differential equations with a time lag. The chain of such equations suggested by Ginzburg and Landau was used to describe such states of heart dynamics as normal beatings, fibrillation and ischemia through the kinds of the chain dynamics as regular oscillations, chaotic dynamics and intermittency dynamics of order – disorder type correspondingly. The mathematical model supporting the hypothesis demonstrated all mentioned model modes of heart functioning. During the computer, study of the model another hypothesis has been put forward concerning the existence in the heart dynamics a special oscillatory region, which interacts with ischemia oscillatory region lowering its energy. According to the prediction, both regions had to have different resonant parameters. Taking into account the results of the model study there has been made another prediction about possible synchronization of the heartbeats by applying external periodical perturbation at frequency of about 1 Hz. The pilot data supporting the proposed hypothesis have demonstrated the reality of the suggested hypothesis. In particular, the real ECG and their Fourier spectra of healthy patients corresponded to the model regular ECG and their Fourier spectra. The ECG Fourier spectrum of the patient with a cardio stimulator corresponded to the model synchronization of the ECG and its Fourier spectrum generated by the developed mathematical model. As far as the ECGs and Fourier spectra in patients with differently developed ischemia are concerned, they confirmed the hypothesis about the existing of two interacting oscillatory regions in myocardium: the ischemic and the defending ones. The defending region decreases the volume of the ischemic process through lowering its energy. Summing it up one can conclude that the experimental results confirmed the suggested hypothesis and the prediction following from it.