Completing the Cabrera Circle: deriving adaptable leads from ECG limb leads by combining constraints with a...

Objective.We present a concept for processing 6-lead electrocardiography (ECG) signals which can be applied to various use cases in quantitative electrocardiography.Approach.Our work builds upon the mathematics of the well-known Cabrera sequence which is a re-sorting of the six limb leads (I,II,III,aVR,aVL,aVF) into a clockwise and physiologically-interpretable order. By deriving correction factors for harmonizing lead strengths and choosing an appropriate basis for the leads, we extend this concept towards what we call the 'Cabrera Circle' based on a mathematically sound foundation.Main results.To demonstrate the practical effectiveness and relevance of this concept, we analyze its suitability for deriving interpolated leads between the six limb leads and a 'radial' lead which both can be useful for specific use cases. We focus on the use cases of i) determination of the electrical heart axis by proposing a novel interactive tool for reconstructing the heart's vector loop and ii) improving accuracy in time of automatic R-wave detection and T-wave delineation in 6-lead ECG. For the first use case, we derive an equation which allows projections of the 2-dimensional vector loops to arbitrary angles of the Cabrera Circle. For the second use case, we apply several state-of-the-art algorithms to a freely-available 12-lead dataset (Lobachevsky University Database). Out-of-the-box results show that the derived radial lead outperforms the other limb leads (I,II,III,aVR,aVL,aVF) by improving F1 scores of R-peak and T-peak detection by 0.61 and 2.12, respectively. Results of on- and offset computations are also improved but on a smaller scale.Significance.In summary, the Cabrera Circle offers a methodology that might be useful for quantitative electrocardiography of the 6-lead subsystem-especially in the digital age.