The main objective of this research work is to develop an effective mathematical model of cardiac conduction system using a heterogeneous whole-heart model. The model is in the form of a system of modified Van der Pol and FitzHugh-Nagumo differential equations capable of describing the heart dynamics. The proposed model extends the range of normal and pathological electrocardiogram (ECG) waveforms that can be generated by the model. The effects of the respiratory sinus arrhythmia (RSA) and the Mayer waves (MW) are both incorporated to modulate the intrinsic frequency of the main oscillator that represents the sinoatrial node. Also, three pathological conditions are incorporated into the model. The heart rate variability (HRV) phenomenon is incorporated into the synthetic ECGs produced which yields valuable information about the cardiovascular health and the performance of the autonomic nervous system. The spectral analysis of the generated RR tachogram delivers power spectrums that resemble those obtained from real recordings. Also, the proposed model generates synthetic ECGs that characteristic the three considered pathological conditions, namely, the tall T wave, the ECG with U wave, and the Wolff-Parkinson-White syndrome. In general, the significance of this research work is in developing a mathematical model that represents the interactions between different pacemakers and allows analysis of cardiac rhythms. To show the effectiveness and the accuracy of the presented model, the results are compared to published results. The proposed model can be a useful tool to study the influences of different physiological conditions on the profile of the ECG. The synthetic ECG signals produced can be used as signal sources for the assessment of diagnostic ECG signal processing devices.

这项研究工作的主要目标是使用异质全心模型开发心脏传导系统的有效数学模型。该模型采用能够描述心脏动力学的修正 Van der Pol 和 FitzHugh-Nagumo 微分方程系统的形式。所提出的模型扩展了模型可以生成的正常和病理心电图 (ECG) 波形的范围。呼吸性窦性心律失常 (RSA) 和 Mayer 波 (MW) 的影响都被结合起来，以调节代表窦房结的主振荡器的固有频率。此外，三个病理条件被纳入模型。心率变异性 (HRV) 现象被纳入合成心电图，产生关于心血管健康和自主神经系统性能的宝贵信息。生成的 RR 转速图的频谱分析提供的功率谱类似于从真实记录中获得的功率谱。此外，所提出的模型生成具有三种考虑的病理状况的合成心电图，即高 T 波、带有 U 波的心电图和沃尔夫-帕金森-怀特综合征。总的来说，这项研究工作的意义在于开发一个数学模型，该模型代表不同起搏器之间的相互作用并允许分析心律。为了显示所提出模型的有效性和准确性，将结果与已发布的结果进行比较。所提出的模型可以成为研究不同生理条件对 ECG 剖面影响的有用工具。产生的合成 ECG 信号可用作评估诊断 ECG 信号处理设备的信号源。