Heart

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The sole purpose of the heart is to pump blood, about 5 to 6 liters of blood every minute when a person is resting. It pumps about seventy times per minute. If the blood flow to your brain would stop for only 5 seconds, you lose consciousness. Four minutes later, permanent brain damage starts.

Our heart has four chambers: two atria and two ventricles

Each heart cell is a mini chemical battery, that pumps ions in or out. In the idle state, the inside of each heart cell is \(-80\,\rm{mV}\) relative to its outside. When the cells are at \(+20\,\rm{mV}\), they contract.

Cardiac cycle phases

Phases of a heart beat:

1. A heart beat starts with pacemaker cells, near the right atrium, changing their potential from \(-80\,\rm{mV}\) to \(+20\,\rm{mV}\).
2. Atria
   1. The neighboring cells of the atria follow, and the depolarization wave propagates, changing their potential from \(-80\,\rm{mV}\) to \(+20\,\rm{mV}\). This causes the atria to contract. (P wave)
   2. When the wave reaches the AV node it pauses to allows the atria to contract fully, emptying their blood into the ventricles. (PR interval)
   3. The wave continues through to the ventricles (step 3.1), and the atria cells return to \(-80\,\rm{mV}\) starting a repolarization wave in the atria. (overlaps with QRS complex)
3. Ventricles
   1. The depolarization wave continues to the ventricles, changing their potential from \(-80\,\rm{mV}\) to \(+20\,\rm{mV}\). This causes these ventricles to contract, and send the blood to the organs and lungs. (QRS complex)
   2. After about \(0.2\,\rm{s}\), the cells return to \(-80\,\rm{mV}\) starting a repolarization wave in the ventricles. This wave goes from below to above. (T wave)
4. The heart waits for another message from the pacemaker cells.

At the cellular level

A closer look at the individual heart cells

1. At idle, the inside of a heart cell is at \(-80\,\rm{mV}\) compared to its outside. That means it has repelled positive ions. so the inside is negative. There is no \(\vec E\)-field outside, because if you put a Gaussian surface around it, there is no net charge inside. But there is an electric field across the cell walls.

   

2. During depolarization, the potential difference changes from \(-80\,\rm{mV}\) to \(+20\,\rm{mV}\). For simplicity, we will assume it changes to \(0\,\rm{mV}\). The depolarization waves goes from top to bottom. When the depolarization wave is halfway down the cell, the top potential is zero. The cell has pulled the positive ions back inside. You now have a minus layer on top of a positive layer. That creates an electric field, that has roughly the shape of an electric dipole. So, as the wave goes through the cells, only then do they create a dipole.

   

3. When the wave has passed, the each heart cell is at \(+20\,\rm{mV}\). (the zero was just to make it easier to explain.) Now the inside has positive ions, and the outside has negative ions. The cell is contracted. The external \(\vec E\)-field is zero.

   

4. Now, the repolarization waves comes from below to bring the potential difference back to \(-80\,\rm{mV}\). Again, we will assume the wave is halfway, and it is not \(-80\,\rm{mV}\), but \(0\,\rm{mV}\). Once more, we have a minus layer on top of a positive layer. This creates an electric field, with roughly the shape of an electric dipole.

   

5. After the repolarization wave has passed the heart cells returned to their idle potential difference of \(-80\,\rm{mV}\).

Electric fields

The depolarization wave will run down, and leave behind cells at \(+20\,\rm{mV}\). These cells are contracted. Only the cells where the depolarization occurs, only the ones on the ring, contribute to that electric dipole field.



When the repolarization goes in the other direction, when the heart relaxes, because the cells go back to \(-80\,\rm{mV}\), then again is there an electric dipole field, but only from the cells through which the repolarization wave propagates.



All the dipoles of the depolarization/repolarization band are in the same direction. As the wave is going, the electric field is spreads around the band.



If there is an electric field, there’s going to be a potential difference between different parts of your body. The integral \(\int \vec E\cdot d\vec l\) gives you a potential difference. That is the idea behind an electrocardiogram. Typically there are twelve electrodes attached to arms, legs, head and chest to get as much information about the heart as we can. The maximum potential difference between two electrodes is not more than about two to three millivolts.