An effective heterogeneous whole-heart mathematical model of cardiac induction system with heart rate variability

Abstract

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.

An effective mathematical model of cardiac electrical activities for Bundle Branch Blocks

“…A modified model is presented in this section. It depends mainly on the work developed in [5] and utilized in [6,7]. The heart is represented by two main components, the cardiac conduction system, and the atrial and ventricular muscles.…”

“…Each process is represented by an AP model. The motivation of utilizing the AP model instead of the of the Fitz-Hugh-Nagumo (FHN) model used in [5][6][7] is that the action potential produced by the AP model has greater resemblance to the myocardial action potential with no super-repolarized state which could be developed in FHN model. Also, the additional parameter 𝜸 𝟎 termed as refractoriness controls the action potential duration (APD) [2,8] which is very important in modeling BBB.…”

“…Many heart disorders have been represented by modified models to the model of Ryzhii and Ryzhii [5]. For instance, Elkaranshawy et al [6] incorporate three pathological conditions, namely, the tall T wave, ECG with U wave, and the Wolf-Parkinson-White syndrome. Cardarilli et al [7] simulate the bundle branch blocks by using two VDP oscillators to represent the right and the left bundle branches of the His-Purkinje system instead of only one oscillator in the original model.…”

Mathematical model for dynamic interaction between tumor, immune system, and combined radiotherapy and chemotherapy based on experimental data

“…Mathematical models have been developed to describe some biological processes, for example cardiac induction system [18], hepatitis C virus [19,20], muscle activation dynamics [21], neurons models [22] and analysis for tumor-immune interaction [23]. A review of tumor immunological models can be found in [24].…”

GPU accelerated digital twins of the human heart open new routes for cardiovascular research

“…Considerable efforts have been made in the last decade to produce digital twins for clinical applications and cardiac modelling has been among the fastest growing fields. Leaving aside the wealth of literature dealing with individual parts of the heart, recent examples include the computational investigation of electromechanical features [1][2][3] , the influence of cardiac contraction on the electrocardiogram (ECG) 4 and of the heart rate variability 5 ; recent review papers 6,7 give a detailed account of whole-heart electromechanical models.…”