Augmented lead equations

Question

Extremely confused with augmented lead equations. Apparently -

aVL = (Lead I - Lead III) ÷2

-aVR = (Lead I + Lead II) ÷2

aVF = (Lead II + Lead III) ÷2

I can't figure out why we're subtracting Lead III from Lead I in the first equation if we're supposed to calculate average? The second equation makes the most sense to me. In the 3rd equation, why are we adding leads 2 and 3 and not leads 1 and 3?

Answer 1

I think there must be an error somewhere in the Vector Diagram for Lead III. I believe it should be pointing down-left to 8:00 not up-right to 2:00 as shown up in yellow image below. (yes it is confusing)

Kirchhoff’s second law states that the algebraic sum of all the voltages around any closed path in a circuit equals zero.

This is only true when the proper polarities are followed.

• the augmented vector foot (aVF) is positive (+ve) and perpendicular to (or normal to) Lead I
• the augmented vector right (aVR) is negative (-ve) is normal to Lead II
• the augmented vector left (aVL) is positive (+ve) in relation to aVR and normal to Lead III, but negative (-v) in relation to aVF.

Summary

I + III + (-II) = 0; or I + III = II using Kirchoff's Voltage Law with Einthoven's Triangle

: aVF ┴ Lead I :
: aVR ┴ Lead II :
: aVL ┴ Lead III :
Note Foot means same as Left Leg, LL where electrical voltage E is measured. and right leg RL by convention is driven by negative feedback to null the common mode (CM) antenna effects of the body. But technically, it makes no difference which leg is used if swapped with the RLD feedback, so it is abbreviated to just Foot as in aVF.

This negative feedback potential is more than a thousand times bigger than the sensed voltages and due to the amplifier gigaohm impedances draws no significant current. But this accurately nulls the common mode antenna effects with very high gain > 1e6. However, reversing any vector differential lead polarities may result in an incorrect diagnosis.

above Reference: VOL. 11 NO. 1 2010 REVIEWS IN CARDIOVASCULAR MEDICINE p33

You are not alone in confusion looking at the triangle. The triangle appears to be equilateral vectors that don't add up. The red arrows simply show the direction of the positive differential pairs.

Reference: https://www.sciencedirect.com/topics/materials-science/ecg-leads
https://www.wikiwand.com/en/Einthoven's_triangle

Other info

• "GROUND" in electrical/electronic circuits means a perfect 0V by definition but only at that location.

• Creating this "virtual ground" must not have interference

  • This is created by shielded signals and INstrument Amplifiers (INA) with negative feedback from the neutral points (GT) of the Diff. probes'.
  • This is found on the CM gain resistor then splitting into two 0.1% resistors and 100 pF caps so as not to conduct 50/60 Hz as the tolerance errors on a larger cap values could seriously degrade the Common Mode Rejection Ratio (CMRR) and thus the creation of the virtual ground or Ground Terminal or .and then filtering and sending this signal back to right leg drive (RLD) or somewhere nearby to cancel as much AC grid field noise and AM radio noise that radiates everywhere.

• One study reported approximately 2% lead misplacement in more than 10,000 ECGs analyzed. Another study reported the incidence of lead misplacement in 0.4% of ECGs performed in an outpatient cardiology clinic and in 4% of ECGs performed in the intensive care unit. VOL. 11 NO. 1 2010 REVIEWS IN CARDIOVASCULAR MEDICINE p34 Einthoven’s Triangle Transparency

Your missing citation was essentially the following;

• +aVL = ( I - III ) ÷2

• -aVR = ( I + II ) ÷2

• +aVF = ( II + III) ÷2

"Science direct" shows an Einthoven (et al.) Vector Diagram with the neutral central point called the "Wilson Central Terminal" (WCT) or GT in diagram, which I assume means "Ground Terminal". However Lead III arrow is reversed.