Dear 100 Hour Board,
This question is about Limb leads, EKGs, and math vectors:
1.So, in linear algebra I remember a concept about linear independence, or the minimal number of vectors needed to describe some data. From what I remember, it's a vector or set of vectors that cannot be made from combining linear combinations of other vectors. Typically in the 3D world we live in, these vectors cannot be co-planar and be linearly independent, so we just use one in each plane (x,y,z).
2. Now for EKGs: To measure electric pulse magnitude and direction in a heart, three sensors (or leads) are placed on the body: left and right wrists and the left leg. Additionally, we have the augmented leads (AVL, AVR, AVF) and then V1, V2, and so on until V6.
So, why what is the purpose of the extra leads if we are able to mathematically express any three dimensional vector, including amplitude and direction, which is what we want from an EKG? Why do we have the extra leads? Could we theoretically just use three or six leads to get +,- direction (leads only measure differences) and maintain about the same amount of information?
-confused physiology student
My old physiology professor from a million years ago, Ward Rhees, wrote in his textbook that "the twelve limb and chest leads all measure the same electrical activity of the heart, but each one shows the heart from a different viewpoint - much as twelve cameras surrounding an object would all show different angles of the same object." The Wikipedia article about ECG agrees: "Each of the 12 ECG leads records the electrical activity of the heart from a different angle, and therefore align with different anatomical areas of the heart."
I hope this helps.
I don't know anything about EKGs, but I do know about math! What you're thinking of is called a basis, or linearly independent and spanning set of vectors. You're also right that if you want to span all possible vectors with a specific number elements, then the basis is composed of as many vectors as there are elements per vector. However, just because things exist in 3-dimensional space doesn't mean there aren't more things to measure than their shape, introducing the need for more elements per vector, and thus a bigger basis.