Introduction: In classical homogeneous conducting sphere with a centric dipole model the voltage in the frontal plane leads are dot products between the heart vector and the lead axes which define the hexaxial reference system.
In present use for some applications, e.g. electrocardiogram-derived respiration, lead pairs I and III or I and aVF are used in axis calculation without further consideration of scaling and angle between the leads. This may cause an error up to 30°. Geometric derived formula exist, but is inconvenient in usage.
Aims: Correct systematic equations for determining the heart vector and mean electrical axis (MEA) from any pair of leads in the hexaxial reference system are derived.
Methods: Different definition of net potential such as the common max + min value of QRS (Vrs), area under the curve (Varea), and sum of QRS (Vsum) are used in the calculation of the MEA.
The MEA is then used to test the fidelity of signal averaging on a dataset from the North Sea Race Endurance study. Since the MEA can be calculated from any pair of leads in the frontal plane, it is reasonable to believe that signal averaging does not destroy this invariant property. Variation between MEA derived from different lead pairs is used as an assessment criteria.
Results: With Vrs, 95.0% of the ECGs had a standard deviation with less than 15° between the lead pairs, 98.9% with Varea, and 98.8% with Vsum. 63 ECGs have (left axis deviation) LAD, 46 (right axis deviation) RAD, 2902 normal, and 1 undefine for Vrs. 106 LAD, 76 RAD, 2824 normal, and 6 undefine for Varea. 108 LAD, 78 RAD, 2821 normal, and 7 undefine for Vsum.
Conclusion: Varea and Vsum give less variability between the lead pairs and clinical fidelity should be based on them.