{"title":"改进心电图成像解决方案:心房 L 曲线优化中正则化参数选择的综合研究","authors":"","doi":"10.1016/j.compbiomed.2024.109141","DOIUrl":null,"url":null,"abstract":"<div><h3>Background</h3><p>In electrocardiographic imaging (ECGI), selecting an optimal regularization parameter (λ) is crucial for obtaining accurate inverse electrograms. The effects of signal and geometry uncertainties on the inverse problem regularization have not been thoroughly quantified, and there is no established methodology to identify when λ is sub-optimal due to these uncertainties. This study introduces a novel approach to λ selection using Tikhonov regularization and L-curve optimization, specifically addressing the impact of electrical noise in body surface potential map (BSPM) signals and geometrical inaccuracies in the cardiac mesh.</p></div><div><h3>Methods</h3><p>Nineteen atrial simulations (5 of regular rhythms and 14 of atrial fibrillation) ensuring variability in substrate complexity and activation patterns were used for computing the ECGI with added white Gaussian noise from 40 dB to -3dB. Cardiac mesh displacements (1–3 cm) were applied to simulate the uncertainty of atrial positioning and study its impact on the L-curve shape. The regularization parameter, the maximum curvature, and the most horizontal angle of the L-curve (β) were quantified. In addition, BSPM signals from real patients were used to validate our findings.</p></div><div><h3>Results</h3><p>The maximum curvature of the L-curve was found to be inversely related to signal-to-noise ratio and atrial positioning errors. In contrast, the β angle is directly related to electrical noise and remains unaffected by geometrical errors. Our proposed adjustment of λ, based on the β angle, provides a more reliable ECGI solution than traditional corner-based methods. Our findings have been validated with simulations and real patient data, demonstrating practical applicability.</p></div><div><h3>Conclusion</h3><p>Adjusting λ based on the amount of noise in the data (or on the β angle) allows finding optimal ECGI solutions than a λ purely found at the corner of the L-curve. It was observed that the relevant information in ECGI activation maps is preserved even under the presence of uncertainties when the regularization parameter is correctly selected. The proposed criteria for regularization parameter selection have the potential to enhance the accuracy and reliability of ECGI solutions.</p></div>","PeriodicalId":10578,"journal":{"name":"Computers in biology and medicine","volume":null,"pages":null},"PeriodicalIF":7.0000,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0010482524012265/pdfft?md5=00ba75c411a8220b072c6a47be025ff1&pid=1-s2.0-S0010482524012265-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Improving electrocardiographic imaging solutions: A comprehensive study on regularization parameter selection in L-curve optimization in the Atria\",\"authors\":\"\",\"doi\":\"10.1016/j.compbiomed.2024.109141\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><h3>Background</h3><p>In electrocardiographic imaging (ECGI), selecting an optimal regularization parameter (λ) is crucial for obtaining accurate inverse electrograms. The effects of signal and geometry uncertainties on the inverse problem regularization have not been thoroughly quantified, and there is no established methodology to identify when λ is sub-optimal due to these uncertainties. This study introduces a novel approach to λ selection using Tikhonov regularization and L-curve optimization, specifically addressing the impact of electrical noise in body surface potential map (BSPM) signals and geometrical inaccuracies in the cardiac mesh.</p></div><div><h3>Methods</h3><p>Nineteen atrial simulations (5 of regular rhythms and 14 of atrial fibrillation) ensuring variability in substrate complexity and activation patterns were used for computing the ECGI with added white Gaussian noise from 40 dB to -3dB. Cardiac mesh displacements (1–3 cm) were applied to simulate the uncertainty of atrial positioning and study its impact on the L-curve shape. The regularization parameter, the maximum curvature, and the most horizontal angle of the L-curve (β) were quantified. In addition, BSPM signals from real patients were used to validate our findings.</p></div><div><h3>Results</h3><p>The maximum curvature of the L-curve was found to be inversely related to signal-to-noise ratio and atrial positioning errors. In contrast, the β angle is directly related to electrical noise and remains unaffected by geometrical errors. Our proposed adjustment of λ, based on the β angle, provides a more reliable ECGI solution than traditional corner-based methods. Our findings have been validated with simulations and real patient data, demonstrating practical applicability.</p></div><div><h3>Conclusion</h3><p>Adjusting λ based on the amount of noise in the data (or on the β angle) allows finding optimal ECGI solutions than a λ purely found at the corner of the L-curve. It was observed that the relevant information in ECGI activation maps is preserved even under the presence of uncertainties when the regularization parameter is correctly selected. The proposed criteria for regularization parameter selection have the potential to enhance the accuracy and reliability of ECGI solutions.</p></div>\",\"PeriodicalId\":10578,\"journal\":{\"name\":\"Computers in biology and medicine\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":7.0000,\"publicationDate\":\"2024-09-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0010482524012265/pdfft?md5=00ba75c411a8220b072c6a47be025ff1&pid=1-s2.0-S0010482524012265-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computers in biology and medicine\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0010482524012265\",\"RegionNum\":2,\"RegionCategory\":\"医学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"BIOLOGY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computers in biology and medicine","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0010482524012265","RegionNum":2,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"BIOLOGY","Score":null,"Total":0}
引用次数: 0
摘要
背景在心电图成像(ECGI)中,选择最佳正则化参数(λ)对于获得精确的反向电图至关重要。信号和几何不确定性对逆问题正则化的影响尚未被彻底量化,也没有既定的方法来确定λ何时因这些不确定性而成为次优参数。本研究介绍了一种使用 Tikhonov 正则化和 L 曲线优化来选择 λ 的新方法,特别解决了体表电位图 (BSPM) 信号中的电噪声和心脏网格中的几何不准确性的影响。方法 19 个心房模拟(5 个常规节律和 14 个心房颤动)确保了基质复杂性和激活模式的可变性,用于计算 ECGI,并添加了 40 dB 到 -3dB 的白高斯噪声。应用心脏网格位移(1-3 厘米)来模拟心房定位的不确定性,并研究其对 L 曲线形状的影响。量化了正则化参数、最大曲率和 L 曲线的最大水平角度 (β)。结果发现 L 型曲线的最大曲率与信噪比和心房定位误差成反比。相反,β 角与电噪声直接相关,不受几何误差的影响。与传统的基于转角的方法相比,我们提出的基于 β 角的 λ 调节方法能提供更可靠的心电图成像解决方案。结论根据数据中的噪声量(或 β 角)调整 λ 可找到最佳的心电图成像解决方案,而不是纯粹在 L 曲线的拐角处找到 λ。据观察,如果正则化参数选择正确,即使存在不确定性,ECGI 激活图中的相关信息也能得到保留。所提出的正则化参数选择标准有望提高心电图成像解决方案的准确性和可靠性。
Improving electrocardiographic imaging solutions: A comprehensive study on regularization parameter selection in L-curve optimization in the Atria
Background
In electrocardiographic imaging (ECGI), selecting an optimal regularization parameter (λ) is crucial for obtaining accurate inverse electrograms. The effects of signal and geometry uncertainties on the inverse problem regularization have not been thoroughly quantified, and there is no established methodology to identify when λ is sub-optimal due to these uncertainties. This study introduces a novel approach to λ selection using Tikhonov regularization and L-curve optimization, specifically addressing the impact of electrical noise in body surface potential map (BSPM) signals and geometrical inaccuracies in the cardiac mesh.
Methods
Nineteen atrial simulations (5 of regular rhythms and 14 of atrial fibrillation) ensuring variability in substrate complexity and activation patterns were used for computing the ECGI with added white Gaussian noise from 40 dB to -3dB. Cardiac mesh displacements (1–3 cm) were applied to simulate the uncertainty of atrial positioning and study its impact on the L-curve shape. The regularization parameter, the maximum curvature, and the most horizontal angle of the L-curve (β) were quantified. In addition, BSPM signals from real patients were used to validate our findings.
Results
The maximum curvature of the L-curve was found to be inversely related to signal-to-noise ratio and atrial positioning errors. In contrast, the β angle is directly related to electrical noise and remains unaffected by geometrical errors. Our proposed adjustment of λ, based on the β angle, provides a more reliable ECGI solution than traditional corner-based methods. Our findings have been validated with simulations and real patient data, demonstrating practical applicability.
Conclusion
Adjusting λ based on the amount of noise in the data (or on the β angle) allows finding optimal ECGI solutions than a λ purely found at the corner of the L-curve. It was observed that the relevant information in ECGI activation maps is preserved even under the presence of uncertainties when the regularization parameter is correctly selected. The proposed criteria for regularization parameter selection have the potential to enhance the accuracy and reliability of ECGI solutions.
期刊介绍:
Computers in Biology and Medicine is an international forum for sharing groundbreaking advancements in the use of computers in bioscience and medicine. This journal serves as a medium for communicating essential research, instruction, ideas, and information regarding the rapidly evolving field of computer applications in these domains. By encouraging the exchange of knowledge, we aim to facilitate progress and innovation in the utilization of computers in biology and medicine.