体表势时空分析与测量方法研究
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摘要
心脏电兴奋的传播是时间和空间的函数,无创地获得心电活动的时间和空间信息在心脏电生理研究中是极为重要的。体表标测作为一种用来反映心脏电活动时间和空间信息的心电记录技术,是无创诊断心脏疾病的重要依据。由体表电位推测心脏电活动的实质即求解逆问题,其中等效源模型的选择及其定解方法是关键。近年发展起来的表面Laplacian图技术,与体表电位图比较,更能反映心脏电兴奋的细节,因此,表面Laplacian的近似计算和直接测量的研究备受关注。
本文鉴于目前心电研究领域的上述热点问题,作了以下几个方面的研究:
基于心电发生的拓扑学模型用于逆问题定解的研究,提出将小波变换的奇异点检出特性用于心室除极临界时刻检出。通过对表征边沿特性的李氏指数的研究,确认了检出的微分心电信号奇异点与临界时刻之间存在对应关系,初步证明了该检测方法的有效性。提出了基于最大相关的临界点定位方法,对仿真体表势及其在各种噪声干扰情况下的临界点定位进行了研究,获得较高的定位准确度。
通过对体表标测信号的各时间主成分与各导联信号之间的相关性及奇异值谱的累积能量百分数的分析,获得了合理保留主成分数量的依据,同时对空间主成分的研究印证上述结果;借鉴前人对体表标测导联冗余性的研究,提出了基于误差最小准则的多变量回归的优化导联选择方法。采用顺序前进法和顺序后退法相结合的增l减r法进行优化导联的搜索及结果的比对,总结了优化导联的分布规律,对优化导联选择具有指导意义。
研究了不同观测电极数量及空间位置设置情况下,表面势的样条插值结果与解析计算结果之间的相对误差,并由此计算得到了表面Laplacian;还研究了观测值的不同噪声水平对样条插值结果的影响,得出了具有一定指导意义的结论。
基于九点差分的表面Laplacian计算方法,设计了三极同心圆电极表面Laplacian传感器。理论分析表明:三极同心圆电极传感器的性能优于双极同心圆电极传感器。通过原理性实验与理论计算结果的比对验证了该方法的可行性。将所设计的有源传感电极用于人体实际测量,获得了实际的表面Laplacian心电信号;尝试用一种非线性自适应滤波器自适应地消除工频干扰,结合小波消噪技术将其他噪声进一步消除,获得了较高质量的表面Laplacian心电信号,为该技术的临床应用奠定了基础。
The cardiac activation spread is a spatial and temporal function. Non invasively obtained temporal and spatial information may be important in cardiac electrophysiology exploration. The body surface potential mapping (BSPM), as one of the advanced recording technique, played a significant role in the heart disease diagnosis. Solving the inverse problem is made that the body surface potentials are used to described the cardiac electrical activity. The inverse problem does not posses a unique solution. This difficulty is mitigated by properly selecting the equivalent sources and regularization. The recently developed body surface Laplacian mapping (BSLM) technique was found to provide better spatial resolution for localizing and imaging cardiac activity than BSPM. So it’s great attention that surface Laplacian be approximately calculated from surface potential or directly measured on the body.
This paper mainly discussed the problems about non-invasively mapping cardiac electrical activity as follows.
Based on the topological foundations of electrocardiology, the singularities of the first time derivative of body surface potential was detected by using wavelet transform. The singularity detect results are corresponding to the critical times of ventricular depolarization by estimating local Lipschitz exponents. The method that localized critical points with Maximal Correlation was presented. By simulating the propagating of ventricular depolarization, body surface potentials were calculated. Critical points were localized for simulating potentials and noisy potentials.
The relativities of the temporal principal component of multichannel surface potentials and the cumulated energy percentage were analyzed by singular value decomposition (SVD). Spatial principal component analysis confirmed that result. By using the former researchers’study of the redundancy of the body surface mapping electrodes for reference, an optimal electrode selection method that based on multiple variable linear regression was presented. The performance of the algorithm was evaluated using spatial Root Mean Square (RMS). By combined serial forward search (SFS) and serial backward search (SBS), called Zl-Zr search, the optimal electrode sites were selected and the site distributing role was summarized.
The analytical expression of the potential generated by arbitrarily located in the two layer concentric sphere was rededuced, and the body surface Laplacian were approximately calculated from potential by spline interpolation. The relative error of spline interpolation to analytical potential is calculated for different electrode numbers and locations. A tripolar concentric ring electrode sensor based on the nine-point difference was designed for surface Laplacian sensing. We found that the sensor has a much-improved accuracy with bipolar sensor in estimating the Laplacian operator. The experimental results are in agreement with the theoretical calculations suggesting the feasibility of measuring the surface Laplacian. We picked up the Laplacian ECG from healthy human body surface by the active tripolar sensor. A non-linear adaptive filter and walvelet denoising technique were used to eliminate power line and other interferences, and got the high quality Laplacian ECG signal. It lays the foundation for using such Laplacian ECG to assist in heart disease diagnosis.
本文鉴于目前心电研究领域的上述热点问题,作了以下几个方面的研究:
基于心电发生的拓扑学模型用于逆问题定解的研究,提出将小波变换的奇异点检出特性用于心室除极临界时刻检出。通过对表征边沿特性的李氏指数的研究,确认了检出的微分心电信号奇异点与临界时刻之间存在对应关系,初步证明了该检测方法的有效性。提出了基于最大相关的临界点定位方法,对仿真体表势及其在各种噪声干扰情况下的临界点定位进行了研究,获得较高的定位准确度。
通过对体表标测信号的各时间主成分与各导联信号之间的相关性及奇异值谱的累积能量百分数的分析,获得了合理保留主成分数量的依据,同时对空间主成分的研究印证上述结果;借鉴前人对体表标测导联冗余性的研究,提出了基于误差最小准则的多变量回归的优化导联选择方法。采用顺序前进法和顺序后退法相结合的增l减r法进行优化导联的搜索及结果的比对,总结了优化导联的分布规律,对优化导联选择具有指导意义。
研究了不同观测电极数量及空间位置设置情况下,表面势的样条插值结果与解析计算结果之间的相对误差,并由此计算得到了表面Laplacian;还研究了观测值的不同噪声水平对样条插值结果的影响,得出了具有一定指导意义的结论。
基于九点差分的表面Laplacian计算方法,设计了三极同心圆电极表面Laplacian传感器。理论分析表明:三极同心圆电极传感器的性能优于双极同心圆电极传感器。通过原理性实验与理论计算结果的比对验证了该方法的可行性。将所设计的有源传感电极用于人体实际测量,获得了实际的表面Laplacian心电信号;尝试用一种非线性自适应滤波器自适应地消除工频干扰,结合小波消噪技术将其他噪声进一步消除,获得了较高质量的表面Laplacian心电信号,为该技术的临床应用奠定了基础。
The cardiac activation spread is a spatial and temporal function. Non invasively obtained temporal and spatial information may be important in cardiac electrophysiology exploration. The body surface potential mapping (BSPM), as one of the advanced recording technique, played a significant role in the heart disease diagnosis. Solving the inverse problem is made that the body surface potentials are used to described the cardiac electrical activity. The inverse problem does not posses a unique solution. This difficulty is mitigated by properly selecting the equivalent sources and regularization. The recently developed body surface Laplacian mapping (BSLM) technique was found to provide better spatial resolution for localizing and imaging cardiac activity than BSPM. So it’s great attention that surface Laplacian be approximately calculated from surface potential or directly measured on the body.
This paper mainly discussed the problems about non-invasively mapping cardiac electrical activity as follows.
Based on the topological foundations of electrocardiology, the singularities of the first time derivative of body surface potential was detected by using wavelet transform. The singularity detect results are corresponding to the critical times of ventricular depolarization by estimating local Lipschitz exponents. The method that localized critical points with Maximal Correlation was presented. By simulating the propagating of ventricular depolarization, body surface potentials were calculated. Critical points were localized for simulating potentials and noisy potentials.
The relativities of the temporal principal component of multichannel surface potentials and the cumulated energy percentage were analyzed by singular value decomposition (SVD). Spatial principal component analysis confirmed that result. By using the former researchers’study of the redundancy of the body surface mapping electrodes for reference, an optimal electrode selection method that based on multiple variable linear regression was presented. The performance of the algorithm was evaluated using spatial Root Mean Square (RMS). By combined serial forward search (SFS) and serial backward search (SBS), called Zl-Zr search, the optimal electrode sites were selected and the site distributing role was summarized.
The analytical expression of the potential generated by arbitrarily located in the two layer concentric sphere was rededuced, and the body surface Laplacian were approximately calculated from potential by spline interpolation. The relative error of spline interpolation to analytical potential is calculated for different electrode numbers and locations. A tripolar concentric ring electrode sensor based on the nine-point difference was designed for surface Laplacian sensing. We found that the sensor has a much-improved accuracy with bipolar sensor in estimating the Laplacian operator. The experimental results are in agreement with the theoretical calculations suggesting the feasibility of measuring the surface Laplacian. We picked up the Laplacian ECG from healthy human body surface by the active tripolar sensor. A non-linear adaptive filter and walvelet denoising technique were used to eliminate power line and other interferences, and got the high quality Laplacian ECG signal. It lays the foundation for using such Laplacian ECG to assist in heart disease diagnosis.
引文
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