A Theoretical and Lightly Look at AV(atriaventricular) Blocks

This writing will be about heart and mathematics, so the formula of love :(

Dividing AV blocks as first degree, second degree and third-degree blocks is a well established description in cardiology textbooks and highly used method in clinical practice. But when we look at their discrimination we can’t be sure whether one block is a second degree(more specifically Mobitz type 2) or third-degree block. A similar but not the same type of dilemma(f.e. sometimes can’t be sure about a test’s results or discrimination’s reliability) is a widely seen and mostly acceptable situation in medicine because while you are trying to gain from specifity side you lose sensitivity and vice versa. And on a reasonable point, you have to draw the line and use that method by considering strong and weak sides. But in our situation things are a bit different, not only we sometimes can’t be sure about whether one block is a second degree or third degree, we never can be sure about that. So why are we using this discrimination while we never can be sure? Because mostly our sureness level is high enough. And that can justify our practice.

For making things more clear let’s talk about AV blocks and Lagrange interpolation. Starting with AV blocks firstly we divide AV blocks to three types(first, second end third degrees) and after we subdivide second degree blocks two subtypes(Type 1 or Mobitz type 1 or Wenkebach and Type 2 or Mobitz type 2). Before more talking about types and subtypes let’s make a general definition of AV blocks. AV blocks are abnormalities that delay conduction of the heart rhythms around the AV nodal region and hence mostly cause different cardiac bradycardias. What is the normal rhythm or conduction of the heart or what are the other causes of bradycardias are outside of the content of this text and I will only explain AV blocks. The place that shows clinicians AV node conduction and conduction abnormalities on EKG is the PR interval. 

Below is a schematic representation that shows the PR interval and other intervals and segments.

Schematic representation of different segments and intervals on EKG

AV blocks on EKG

In first-degree AV block, the impulse conducting from atria to ventricles through the atrioventricular node(AV node) is delayed and travels slower than normal. We see that delaying on EKG as a prolongation of PR interval specifically more than 0.20 seconds(normal range is between 0.12 and 0.20). And also this prolongation does not change between different PR intervals.

When examining second-degree AV blocks I already said we subdivide these blocks as Mobitz Type-1 and Mobitz Type-2.

Mobitz Type-1 blocks refer to blocks that slow the conduction of the AV node progressively. On EKG we saw this as prolongation of PR interval progressively and after some prolongation finally a dropped beat(a P wave not followed by ORS complex).

Mobitz Type-2 blocks reflect the sudden failure of the His-Purkinje cells’ conduction. On EKG we saw this as steady, unchanged PR intervals beat to beat but sometimes dropped beats. As depending on the relation between P waves and ORS complexes sometimes it is named 2:1, 3:1, etc.

Third-degree AV blocks occur when the conduction from the atria can not reach the ventricle hence there is no communication between two, so ventricles generate its own rhythm. On EKG we see this as unrelation between P waves and ORS complexes, meaning P waves and ORS waves are not in 1:1 ratio.

After examining AV blocks now we can talk about the Lagrange interpolation. Lagrange interpolation basically says one can always find a polynomial that takes on certain values on arbitrary points independent of that arbitrary points’ count. In other words, there is always a polynomial that describes a set of points(like (x,y)) with finite numbers. (If you are asking what it says not basically? I don't know but here is a description of Lagrange interpolation with some examples)

General description of the theorem as follows.

Lagrange Interpolation

By taking into consideration these two earlier entities(AV blocks and Lagrange interpolation) finally I am ready to make my point. At the third-degree AV blocks by definition, there must be no relation between P segments and ORS complexes but we can’t be sure about that. For example on a one minute EKG record 80 beat P segment and 30 ORS complex usually taken as unrelated and hence complete AV block. But it is also possible, that scene stems from an 8:5 Mobitz type 2 block. (Every eight P segment, there is 5 skipped beat)

As I said at the beginning of the writing, this treaty is not a clinically reasonable treaty because- if we continue with our earlier example again- when you see an 80 to 30 ratio between P segments and ORS complexes. Due to the 80 is a proper number for P segments that its rhythm stems from SA node(between 60-100 is normal) and 30 is a proper number for ORS complexes that its rhythm stems from ventricles(between 20-40 is normal). So it is very reasonable to assume that these two rhythms are unrelated and one is stems from SA node and the other is from ventricles.

Why I wrote this-from a clinical perspective-complete nonsense writing? Because back in my cardiology internship days this relation caught my attention and I wanted to write something about it and also it was funny. Sometimes making something just for the sake of its own, disregard of its usefulness is an activity I really enjoy and unfortunately benefit from newly.