Publications by authors named "Ismail M Abdelrazik"

2 Publications

  • Page 1 of 1

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

Proc Inst Mech Eng H 2021 Mar 19;235(3):323-335. Epub 2020 Dec 19.

Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria, Egypt.

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.
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http://dx.doi.org/10.1177/0954411920978052DOI Listing
March 2021

Extended Parker-Sochacki method for Michaelis-Menten enzymatic reaction model.

Anal Biochem 2016 Mar 18;496:50-4. Epub 2015 Dec 18.

Department of Engineering Mathematics and Physics, Faculty of Engineering, Alexandria University, Alexandria 21544, Egypt.

In this article, a new approach--namely, the extended Parker-Sochacki method (EPSM)--is presented for solving the Michaelis-Menten nonlinear enzymatic reaction model. The Parker-Sochacki method (PSM) is combined with a new resummation method called the Sumudu-Padé resummation method to obtain approximate analytical solutions for the model. The obtained solutions by the proposed approach are compared with the solutions of PSM and the Runge-Kutta numerical method (RKM). The comparison proves the practicality, efficiency, and correctness of the presented approach. It serves as a basis for solving other nonlinear biochemical reaction models in the future.
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http://dx.doi.org/10.1016/j.ab.2015.11.017DOI Listing
March 2016
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