Author: Anil Potharaju

Learn how vectors apply to EKG interpretation, calculate the mean electrical axis using leads I, aVF, and II, and understand the clinical significance of axis deviations. This math isn’t needed for day to day reading of EKGs but if you love math like we do, here goes!

One crucial aspect of EKG interpretation is understanding vectors and how they represent the direction and magnitude of electrical impulses in the heart. This guide starts from the basics of vectors and builds up to calculating the heart’s mean electrical axis, ensuring you gain a solid understanding of this essential concept.

What Is a Vector?

A scalar is a quantity that only has magnitude, or size. Examples of scalars include volume, density, speed, energy, mass, and time.

e.g., the EKG strip is running at 25mm/ second or John is running at 5mph.

A vector on the other hand is quantity that has both magnitude and direction. Examples of vectors include velocity, momentum, force, electromagnetic fields, and weight.

e.g., The speed of the EKG paper is 25 mm per second (defining the magnitude) progressing from left to right on the paper (defining the direction). John is running 5mph North bound is another example.

A vector is typically represented by an arrow:

• Length of the Arrow: Indicates the magnitude.
• Direction of the Arrow: Indicates the direction of the quantity.

Vectors in the Context of an EKG

In an EKG, vectors represent the electrical activity of the heart as it depolarizes and repolarizes:

• Depolarization Vector: Shows the direction and magnitude of electrical impulses as heart muscle cells become electrically active. By convention, a wave of depolarization is considered to be in the direction of the positive electrode.
• Repolarization Vector: Represents the return of heart muscle cells to their resting electrical state. By convention, a wave of repolarization is considered to be in the opposite direction of the positive electrode.

The heart’s electrical activity can be visualized as a series of vectors (since the activity simultaneously spreads in multiple directions) that combine to form the mean electrical axis, reflecting the average direction of electrical depolarization during ventricular contraction. To simplify this, let us consider the following example: One wave of depolarization is left bound by 7mV (so -7mV in lead I) and another is right bound by 12mV (so +12mV in lead I). A electrode in the middle of these two forces would simply record 12 + (-7)= 5mV at an axis of 0 degrees (which is along lead I).

Let us complicate this a lot!

In the image, notice how lead I has a 7 mm positive deflection and 1 mm negative deflection. So the net amplitude is 6 mm positive deflection.

Lead II on the other hand is at 60 degrees to lead I and has a 4 mm positive deflection and a 3 mm negative deflection. So the net amplitude is 1 mm positive deflection.

So we now have two forces: 6 mm at 0 degrees and 1 mm at 60 degrees. So, how do we estimate the direction of depolarization and its amplitude?

Step 1: Understand the Problem

• Net QRS amplitude in Lead I (0°): +6 mm (positive amplitude indicates the depolarization wave is directed toward the positive electrode of Lead I).
• Net QRS amplitude in Lead II (60°): +1 mm (positive amplitude indicates the depolarization wave is directed toward the positive electrode of Lead II).

The goal is to calculate:

1. Magnitude of the resultant depolarization vector (total QRS vector amplitude).
2. Direction (angle) of the resultant depolarization vector relative to Lead I (0°).

Step 2: Represent the Leads as Vectors

Each lead measures the projection of the heart’s electrical depolarization vector onto its axis. To find the resultant vector, we must resolve these projections into their x (horizontal) and y (vertical) components and then combine them.

Lead I (0 degrees)

• Lead I aligns with the x-axis (horizontal).
• The x-component of the depolarization vector is entirely determined by the amplitude in Lead I: XLead I=+6 mm.
• The y-component of the vector in Lead I is zero: YLead I=0 mm.

Lead II (60 degrees)

• The amplitude in Lead II is a combination of both x- and y-components of the depolarization vector. Using trigonometry:
• The x-component is: XLead II=AmplitudeLead II × cos⁡(60∘)=1 mm×0.5= 0.5 mm. How you ask?
  • Note that we know the hypotenuse and need to find out the adjacent side. The angle between the two is 60 degrees.
  • Recollect from math days that cos (short for cosine)= adjacent side/ hypotenuse. Cos 60 is 0.5
  • In this case, cos 60 (since the lead is at a 60 degree angle)= adjacent side (the x component)/ 1mm (the total amplitude on lead 2).
  • The value of Cos 60 is 0.5. So XLeadII/1= 0.5 or XLeadII is 0.5mm
• The y-component is: YLead II=AmplitudeLead II × cos⁡(30)=1 mm×0.866=0.866 mm. How you ask?
  • Note that we know the hypotenuse and need to find out the adjacent side. The angle between the two is 30 degrees.
  • Cos 30 = 0.866
  • In this case, cos 30 (since the lead is at a 30 degree angle to Y-axis)= adjacent side (the Y component)/ 1mm (the total amplitude on lead 2).
  • The value of Cos 30 is 0.866. So YLeadII/1= 0.866 or YLeadII is 0.866 mm

Step 3: Combine the Components

The total x-component of the resultant depolarization vector is the sum of the x-components from Lead I and Lead II:

Xtotalv=vXLead I + XLead II = 6+0.5 =6.5 mm.

The total y-component of the resultant depolarization vector is the y-component from Lead II (since Lead I contributes no y-component):

Ytotal=YLead II=0.866 mm.

Step 4: Calculate the Resultant Vector’s Magnitude

Since we have the X and Y axes, we can use the Pythagorean theorem:

(Hypotenuse)^2= (Side 1^2)+ (Side 2^2)

Hypotenuse= ((side 1^2)+(side 2^2))^(1/2)= ((6.5^2)+(0.866^2))^(1/2)= 6.56 mm

Step 5: Calculate the Direction (Angle)

Finally, we need to estimate the direction of the QRS vector: We can estimate this relatively easily since we already know the opposite side and the adjacent side of the vector.

If you recollect, cot(θ) = adjacent side/ opposite side. In this case, θ is the angle to the QRS vector to lead I. So the opposite side is amplitude along the Y-axis and the adjacent side is the amplitude along the X axis.

So, cot(θ)= 6.5/0.866=7.506

So θ= about 7.6 degrees.

Combining steps 4 and 5, we now know that the axis of the EKG is about 7.6 degrees and the amplitude is about 6.56 mm. Since 1mm is 0.1 mV, the voltage is 0.656 mV.

If you are wondering where you get the numbers for cos, cot, etc. just google them!

Finally, if we were to use an augmented limb lead in the calculation, the voltage will need to be adjusted since the augmented output is typically boosted by 50%. So, if we notice a 3mm net amplitude on aVF, then the actual amplitude is 3/(1+50%)= 2 mm along the Y axis and 0 along the X-axis.

The good news is that if you’ve stuck around thus far, you now understand exactly what the axis means. The great news is that you rarely if ever need measurements this precise! As we go on, we will review how to intuitively get a good enough estimate for the axes!

Precordial leads provide a window into the heart’s electrical activity from the Anterior-Posterior perspective. This post delves into how these leads are placed and what regions of the heart they examine.

What Are Precordial Leads?

Precordial leads are six chest leads (V1 to V6) placed on the anterior thoracic region. They capture the anteroposterior (front-to-back) flow of electrical impulses, offering a detailed view of the heart’s AP plane.

Precordial leads on a standard EKG

On a standard EKG, there are 6 precordial leads. Proper electrode placement is crucial:

• V1: 4th intercostal space, right of the sternum.
• V2: 4th intercostal space, left of the sternum.
• V3: Midway between V2 and V4.
• V4: 5th intercostal space at the midclavicular line.
• V5: Horizontally aligned with V4 at the anterior axillary line.
• V6: Horizontally aligned with V4 and V5 at the midaxillary line.

Regions Viewed by Precordial Leads

• V1 and V2: Septal leads, focusing on the heart’s septum.
• V3 and V4: Anterior leads, viewing the front wall of the heart.
• V5 and V6: Lateral leads, examining the side wall of the heart.

Notice how none of these leads look at the right side of the heart (Right ventricle and its free wall): So, what do we do if we are concerned about a right sided pathology?

Right Sided Leads

We could simply place the leads in a “mirror image pattern”:

• V1R: 4th intercostal space, left of the sternum.
• V2R: 4th intercostal space, right of the sternum.
• V3R: Midway between V2R and V4R.
• V4R: 5th intercostal space at the midclavicular line on the right
• V5R: Horizontally aligned with V4R at the anterior axillary line on the right.
• V6R: Horizontally aligned with V4R and V5R at the midaxillary line on the right.

Generally, on a EKG, we replace V3, V4, and V5 with V4R, V5R, and V6R when we need to evaluate the RV- This provides the information we need in most cases.

How about if we are concerned about the posterior part of the heart?

Posterior Leads

On a standard EKG, there are no posterior leads. So, we use the anterior leads to evaluate the posterior wall of the heart! For instance, Q waves in the posterior wall imply that the net depolarization wave is moving away from the posterior wall. That means it is moving toward the anterior wall and so, R waves in V1 or V2 may signify the presence of Q waves posteriorly.

We could also place leads on the back to better understand the flow of depolarization.

• Lead V7: Left posterior axillary line, in the same horizontal plane as V6.

• Lead V8: Left mid-scapular line (beneath the tip of the left scapula), same horizontal level as V6.

• Lead V9: Left paraspinal region, same horizontal level as V6.

Finally note that the leads do not capture individual waves of depolarization: Instead they capture the net wave of depolarization. This leads us to the next interesting concept- vectors.

The six limb leads help us understand the electrical flow of impulses on the frontal plane. They detect vertical but not anteroposterior ones. These leads are generated by the six chest electrodes, with the EKG machine automatically assigning positive or negative charges to each electrode to form the leads.

Standard Bipolar Limb Leads

Among the six limb leads, three are standard- These are bipolar leads- they measure the voltage difference between two electrodes, one of which is positive and the other negative. A wave of depolarization toward a positive electrode would record a positive deflection. Repolarization would have the opposite effect.

• Lead I is formed by making the left arm positive and the right arm negative (0° orientation).
• Lead II is formed by making the legs positive and the right arm negative (60° orientation).
• Lead III is formed by making the legs positive and the left arm negative (120° orientation).

Augmented Unipolar Limb Leads

The remaining three limb leads are augmented. Unlike the standard limb leads, these leads are unipolar- they measure the electrical potential at one electrode relative to a calculated central reference point, the central terminal.

Central Terminal

The central terminal is an average of the electrical potentials from the three limb electrodes: V central terminal=(RA+LA+LL)/3. This central terminal acts as a neutral reference point, approximating the heart’s electrical center.

• Lead aVL is created by making the left arm positive and other limbs negative (-30° orientation).
• Lead aVR is created by making the right arm positive and other limbs negative (-150° orientation).
• Lead aVF is created by making the legs positive and other limbs negative (90° orientation).

When using the central terminal as the reference, the voltages recorded by the unipolar limb leads are naturally smaller than those in the bipolar leads.To make these signals clinically useful, they are mathematically augmented (amplified) by approximately 50% in the EKG machine. This enhancement is why they are called augmented leads. If the amplitude of the recorded wave in aVF is 3mm, the actual voltage is only 2mm but to make it easier to see, the output is augmented.

Limb Leads and the view they provide

Based on their orientation, each lead provides a different view of the heart on the frontal plane:

• Leads II, III, and aVF are known as inferior leads: As the direction of the vector of each lead suggests, they “look” at the inferior surface of the heart, composed primarily of the inferior aspect of the left ventricle. The Right Coronary Artery usually supplies this part of the heart.
• Leads I and aVL are high lateral leads: They look at the high, left lateral side of the heart, primarily composed of the left ventricle.
• Lead aVR is often overlooked but holds significant clinical importance. It views the heart from the right shoulder, essentially looking at the upper right side of the heart. Typically shows negative deflections because the heart’s overall electrical activity moves away from the right shoulder.

A special focus on aVR, the most overlooked lead?

Abnormalities in aVR are frequently overlooked. However, a few critical conditions may be diagnosed by looking at the lead that is frequently not looked at.

• An ST-segment elevation in aVR with ST-depressions and T-wave inversions in other leads may signify global subendocardial ischemia or significant left main lesion or significant left anterior descending lesion.
• Upright P-waves suggest severe right atrial abnormality.
• In pericarditis, we note widespread ST elevation with PR depression, but ST elevation in aVR is typically absent
• Differentiating Ventricular arrhythmia from Supra ventricular tachycardia with aberrant conduction: The Vereckei algorithm is a stepwise approach using lead aVR to differentiate VT from SVT with aberrancy. The following suggest VT as against SVT with aberrant conduction:
  1. Initial dominant R-Wave in aVR
  2. Initial q- or r-wave in aVR ≥40 ms
  3. Notching on the initial Downstroke
  4. Vt≥Vi in aVR is suggestive of VT: In SVT with aberrant conduction, the initial conduction happens via the Bundle of His: So, the vertical distance travelled by the QRS complex during the initial 40 msec (Vi) is greater than the terminal vertical distance travelled by the QRS complex during the last 40 msec (Vt) (i.e. Vi > Vt). However in VT, typically, the Bundle of His is the last to be depolarized- So the terminal vertical distance travelled by the QRS in the last 40 msec will be ≥ the total vertical distance travelled by QRS complex in the initial 40 msec.