COR Group, ITACA Institute, Universitat Politècnica de València, Valencia, Spain; Corify Care SL, Madrid, Spain.
COR Group, ITACA Institute, Universitat Politècnica de València, Valencia, Spain.
Comput Biol Med. 2024 Nov;182:109141. doi: 10.1016/j.compbiomed.2024.109141. Epub 2024 Sep 18.
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.
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.
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.
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.
在心电图影像（ECGI）中，选择最佳正则化参数（λ）对于获得准确的逆电图至关重要。信号和几何不确定性对逆问题正则化的影响尚未得到彻底量化，也没有建立确定当 λ 由于这些不确定性而处于次优状态的方法。本研究介绍了一种使用 Tikhonov 正则化和 L 曲线优化选择 λ 的新方法，特别是针对体表电位图（BSPM）信号中的电噪声和心脏网格的几何不准确性的影响。
使用 19 个心房模拟（5 个正常节律和 14 个心房颤动），确保基质复杂性和激活模式的可变性，用于计算加入从 40dB 到-3dB 的白高斯噪声的 ECGI。应用心脏网格位移（1-3cm）模拟心房定位的不确定性，并研究其对 L 曲线形状的影响。量化正则化参数、最大曲率和 L 曲线的最水平角（β）。此外，还使用来自真实患者的 BSPM 信号验证我们的发现。
L 曲线的最大曲率与信噪比和心房定位误差呈反比关系。相反，β角与电噪声直接相关，不受几何误差的影响。我们基于β角调整 λ 的方法提供了比传统基于角的方法更可靠的 ECGI 解决方案。我们的发现已通过模拟和真实患者数据得到验证，具有实际适用性。
根据数据中的噪声量（或β角）调整 λ 可以比仅在 L 曲线的角处找到的 λ 找到更优的 ECGI 解决方案。当正确选择正则化参数时，即使存在不确定性，ECGI 激活图中的相关信息也可以得到保留。提出的正则化参数选择标准有可能提高 ECGI 解决方案的准确性和可靠性。
