Statistical Evaluation of Transformation Methods Accuracy on Derived Pathological Vectorcardiographic Leads

Abstract

Objective: Vectorcardiography (VCG) as an alternative form of ECG provides important spatial information about the electrical activity of the heart. It achieves higher sensitivity in the detection of some pathologies such as myocardial infarction, ischemia and hypertrophy. However, vectorcardiography is not commonly measured in clinical practice, and for this reason mathematical transformations have been developed to obtain derived VCG leads, which in application in current systems and subsequent analysis can contribute to early diagnosis and obtaining other useful information about the electrical activity of the heart. Methods and procedures: The most frequently used transformation methods are compared, namely the Kors regression method, the Inverse Dower transformation, QLSV and the Quasi-orthogonal transformation. These transformation methods were used on 30 randomly selected records with a diagnosis of myocardial infarction from the Physikalisch-Technische Bundesanstalt (PTB) database and their accuracy was evaluated based on the calculation of the mean square error (MSE). MSE was subjected to statistical evaluation at a significance level of 0.05. Results: Based on statistical testing using the nonparametric multiselective Kruskall-Wallis test and subsequent post-hoc analysis using the Dunn method, the Kors regression as a whole method achieved the most accurate transformation. Conclusion: The results of statistical analysis provide an evaluation of the accuracy of several transformation methods for deriving orthogonal leads, for possible application in measuring and evaluation systems, which may contribute to the correct choice of method for subsequent analysis of electrical activity of the heart at orthogonal leads to predict various diseases.

Forward problem of electrocardiography based on cardiac source vector orientations

“…The VCG can be extracted from the standard 12-lead ECG system in clinical applications, employing the VCG transformation matrices [22][23][24]. Kors regression transformation method (KRT), Inverse Dower transformation (IDT), Q Least Square Value Transformation (QLSV), P Least Square Value Transformation (PLSV), and Kors quasi-orthogonal transformation are some of the methods used to extract VCG from the measured ECG signals based on transformation matrices [22,23,25,26]. These transformation matrices can be obtained based on a mathematical model of the torso (e.g., inverse Dower) or by regression approach for directly measured ECG and VCG (e.g., the Kors transformation) [27].…”

“…These transformation matrices can be obtained based on a mathematical model of the torso (e.g., inverse Dower) or by regression approach for directly measured ECG and VCG (e.g., the Kors transformation) [27]. VCG signals with the 3-orthogonal leads than the 12 lead ECG have proven to be useful methods for diagnosing various cardiac disorders, such as myocardial infarction, ischemia, ventricular hypertrophy, myocardial scars, long QT syndrome [22,23,[25][26][27][28].…”

“…The current work focuses on employing the unit vectors of VCG extracted using Kors Regression Transformation (KRT), Inverse Dower Transformation (IDT), and Linear Regression Based Transformation (LRBTQLSV) [26,27] methods with an emphasis on QRS complex. Here, an abnormal condition of unusual R-wave amplitudes in acute ischemia is indicated to highlight the significance of the unit vector VCG-based lead field in the non-invasive detection of the mentioned cardiac disorder.…”

“…Kors Regression transformation (KRT): Kors Regression transformation (regression-based approach) is one of the most widely used VCG extraction approaches to obtain the leads X and Y more accurately than other methods [26]. This approach relies on mathematical regression to calculate the coefficients of the matrix.…”

“…This approach relies on mathematical regression to calculate the coefficients of the matrix. The reconstruction coefficients in [26] were obtained by minimizing the Mean Squared Error (MSE) between the measured and derived VCG [27]. The studies [23] and [26] described the Kors regression-based transformation as suitable for representing the QRS-T angle, as the values obtained from using this method did not differ much from the values of Frank's lead system.…”