Fractional calculus integration for improved ECG modeling: A McSharry model expansion

IF 1.7 4区医学 Q3 ENGINEERING, BIOMEDICAL

Medical Engineering & Physics Pub Date : 2024-10-01 DOI:10.1016/j.medengphy.2024.104237

Abdelghani Takha , Mohamed Lamine Talbi , Philippe Ravier

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引用次数: 0

Abstract

This study introduces a new method for modeling electrocardiogram (ECG)¹ waveforms using Fractional Differential Equations (FDEs). By incorporating fractional calculus into the well-established McSharry model, the proposed approach achieves improved representation and high precision for a wide range of ECG waveforms. The research focuses on the impact of integrating fractional derivatives into Integer Differential Equation (IDE) models, enhancing the fidelity of ECG signal modeling.

To optimize the model's unknown parameters, a combination of the Predictor-Corrector method for solving FDEs and genetic algorithms for optimization is utilized. The effectiveness of the fractional-order model is assessed through distortion metrics, providing a comprehensive evaluation of the modeling quality.

Comparisons show that the fractional-order model outperforms the traditional McSharry IDE model in modeling quality and compression efficiency. It improves modeling quality by 48.40 % in MSE and compression efficiency by 23.18 % when applied on five beat types of MIT/BIH arrhythmia database. The fractional-order model demonstrates enhanced flexibility while preserving essential McSharry model characteristics, with fractional orders (α) ranging from 0.96 to 0.99 across five beat types.

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改进心电图建模的分数微积分整合：麦克沙利模型扩展

本研究介绍了一种利用分数微分方程（FDE）对心电图（ECG）1 波形进行建模的新方法。通过将分数微积分纳入成熟的 McSharry 模型，所提出的方法改进了对各种心电图波形的表示并提高了精度。为了优化模型的未知参数，研究人员结合使用了用于求解 FDE 的预测器-校正器方法和用于优化的遗传算法。比较表明，分数阶模型在建模质量和压缩效率方面优于传统的 McSharry IDE 模型。在应用于 MIT/BIH 心律失常数据库的五种搏动类型时，该模型的 MSE 提高了 48.40%，压缩效率提高了 23.18%。分数阶模型在保留 McSharry 模型基本特征的同时提高了灵活性，五种搏动类型的分数阶 (α)范围从 0.96 到 0.99 不等。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Medical Engineering & Physics 工程技术-工程：生物医学

CiteScore

4.30

自引率

4.50%

发文量

172

审稿时长

3.0 months

期刊介绍： Medical Engineering & Physics provides a forum for the publication of the latest developments in biomedical engineering, and reflects the essential multidisciplinary nature of the subject. The journal publishes in-depth critical reviews, scientific papers and technical notes. Our focus encompasses the application of the basic principles of physics and engineering to the development of medical devices and technology, with the ultimate aim of producing improvements in the quality of health care.Topics covered include biomechanics, biomaterials, mechanobiology, rehabilitation engineering, biomedical signal processing and medical device development. Medical Engineering & Physics aims to keep both engineers and clinicians abreast of the latest applications of technology to health care.