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"In regards to the electrocardiogram, there is often a Statement made that,

'The a' in aVF means 'augmented' by a factor of 1.5 for sensitivity adjustment.

If the above statement is true, following equation should be true.

$VF = aVF/1.5$
enter image description here

Here, $VF$ represents the original voltage in the VF direction, VI represents lead I.

If the above Statement is correct, the argument of Heart vector, $\theta$ should be

$\theta = \arctan \left(\frac{VF}{V_I}\right) = arctan\left(\frac{2 VF}{ 3 V_I}\right)$
enter image description here

However, the correct formula by Novosel is as follows, as described below in the British Physiological Society's resource intended to "Beginner" level Medical School students . https://www.physoc.org/magazine-articles/trigonometry-of-the-ecg/

$\theta = arctan \left(\frac{2 VF}{\sqrt{3} VI}\right)$
enter image description here

and my own calculations also lead to the same conclusion.

Therefore, in order to align with this formula:

$\frac{2}{\sqrt3}\frac{aVF}{VI} = \frac{VF}{VI}$
enter image description here

It follows that:

$aVF = \frac{aVF}{2 VF} \approx 0.85 VF$
enter image description here

Hence, aVF seems to be smaller than VF.

My question;

So the Statement that aVF is 1.5 times the true voltage of VF seems to contradict Novosel's formula. What do you think?

After several hours of study after post this question, I actually understood the answer. As a result, I realized that this question can be chunked down to the following question, which can probably be answered by anyone who understands the beginner's course in EKG.

  • What is aVF and where is the potential difference?
  • What is aVF 1.5x?
  • How does the Vectorcardiogram relate to aVF?

References;

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  • The Tex command for describing mathematical expressions is not properly converted into mathematical expressions. Can someone help me? Commented Sep 2, 2023 at 13:41
  • MathJax isn't enabled on this site. Anyway why did you put quotes around your question? Is this copy paste from a different place? Commented Sep 2, 2023 at 16:35
  • Thanks for the info. The quote is a typo. Sorry. Commented Sep 2, 2023 at 16:42
  • Also, looks like you're in the wrong site. This site is for medical questions, not for math questions. I see you also have account on the Math site so easy to get confused. Commented Sep 2, 2023 at 16:49
  • I have never learned about EKG in my math classes. Is the measurement of ECG taught in math class in your country? Commented Sep 2, 2023 at 16:54

1 Answer 1

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To myself 10 hours ago, stumbling through the most rudimentary cardiology course in medical school.

You are confusing two issues.

  • The first is the definition of aVF and VF and its relationship to I~III induction.
  • The second is the relationship between Heart vector and aVF

These are independent concepts. Your question is about how the medical community defined aVF, VF, and Heart vector, and many mathematicians may not even know that such a vector exists, since there is no such vector in mathematics. So the best person to ask your question would be someone who has completed at least a beginner's course in EKG, but unfortunately I have just started working on one of the earlier courses.

First of all, there are two elementary circuit configurations for ECG measurement systems: the Wilson and Goldberger formulas. The Wilson equation measures VL VR and VF, while the Goldberger equation measures aVR, aVF, and aVL. This fact is carefully explained in an excellent learning resource for medical school beginners; https://www.bem.fi/book/15/15.htm

To summarize the important points, enter image description here
and enter image description here

The source of the "1.5x" in your question is this.

On the other hand, the second issue, the relation between aVF and Heart vector, is as described in the excellent resource you cited that the British Physiological Society (not the British Mathematical Society) has provided for medical school beginners; https://www.physoc.org/magazine-articles/trigonometry-of-the-ecg/

However, this resource does not clearly define aVF or I induction. That may have been a bit unkind to someone like you 10 hours ago, who doesn't associate 1.5x and aVF with the above, and who doesn't understand the basics of ECGs at all. But you already know, don't you, that the definitions of aVF and I induction are the same as what was written in the literature earlier?

Ok, First, in the vectorcardiogram, we consider that Heart Vector \mathbf{H}(\mathbf{t}) changes from time to time and its projection to each induction direction is induction I, II, and III. In other words, we have first

enter image description here

To answer your question, we don't need to talk about something as advanced as the variation of the heart vector over time. So let's fix time t. Then, If we think of it in the same way as the common 6-axis coordinate system diagram, we will see that;

enter image description here

Then, eliminating the term cos from equations (1-2-II) and (1-2-III), we obtain

enter image description here

and further by considering Eindt-Haen's equation in (1-6), we obtain enter image description here

Here, Ⅱ+Ⅲ=2aVF  Then,

enter image description here

This is the Novocel's formula you mentioned and described in following article you sited. https://www.physoc.org/magazine-articles/trigonometry-of-the-ecg/

Summing up all the discussion so far, we get the following equation. enter image description here

So, to emphasize again,

Hy is not equal to either VF or aVF.

Therefore, although the current ECG equipment outputs aVF and I induction,

when you want to find the heart vector, it is perfectly OK to plot I induction in the x direction, but you should not write aVF or VF in the aVF direction.

  • **If you really want to use aVF to obtain ECG vector, you must multiply the value of aVF by 1.16, and **
  • **If you really want to use VF to obtain ECG vector, you musts multiply the value of VF by 1.73, and **

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