This past week was the first meeting of the Top Flight Journal club, sponsored by the NSU chapter of the Society of Physics Students. The venue was the University center Flight Deck:
The paper under discussion, Simple Model for Identifying Critical Regions in Atrial Fibrillation, discusses a new method for simulating the electrical connections between heart cells. In the medical condition called Atrial Fibrillation, the heart’s normal coordinated pumping motion is replaced by a disordered quivering that can lead to blood clots.
It is known that people are much more likely to get atrial fibrillation as they age, but the exact reason remains unclear. In this work, the researchers used a very simple model of the heart in which cardiac cells are connected to each other in horizontal “cables”. With probability v, an additional vertical connection exists between cables.
When v is high – as it is in children, whose hearts have many interconnections between cables – there is no chance for AF. The electrical signal always propagates in a healthy, orderly plane wave across the heart. The signal can’t go backward because of the refractory period each cell needs after being excited. However, the authors show how there can exist a critical value of v below which local ripples called “rotors” can start to form, corresponding to the onset of AF. That is, if v becomes low enough as in older people, there becomes a finite chance of a short circuit forming in which a re-entrant signal can work its way backwards past the region of refractory cells. The result is the formation of localized disturbances that can interrupt the coordination of the heart signal.
This switching between discrete regimes (healthy plane waves to rotors) by changing a continuously varying parameter (v) past a threshold value is the hallmark of “catastrophe theory“. This is like a phase transition in physics, in which the phase (solid, liquid, gas) can be altered by passing through a critical value of the temperature. Here, a continuous variable (the chance of cables being connected, which gradually decreases with age), can suddenly create the risk for AF that did not exist before.
A catastrophe might also occur in the case of communicable diseases. When the fraction of immunized people in the population is above the threshold for herd immunity, potential outbreaks remain contained. The connections between people can be modeled with a Bethe lattice. The chance of a percolating cluster that connects to infinity is a discontinuous function that is zero when the chance of each edge being connect is below the percolation threshold and non-zero above it.