Here’s my first post on an unexplained result.
Normally at a ‘steady pacing’ rate cardiac tissue will recover enough to let the next wave through. But there’s a maximum rate you can achieve: if you try to pace faster than this, then you’ll generally just stimulate the area around the pacing site, and the wave will not propagate at all. (This maximum rate is generally considered to be decided by the time it takes for fast sodium channel recovery from inactivation, i.e. cells’ sodium channels aren’t ready to open if you pace too fast).
I was doing a standard bidomain simulation, on a 2D slab of 1cm x 0.25 cm , with the Li mouse model (2010). I whacked in an almighty pacing rate of 22Hz (cycle length 45ms), as I just wanted to see what I could get away with. This isn’t as crazy as it sounds because a mouse that is just sitting around has a resting heart rate of about 11Hz.
Here’s a video of what happened:
This is roughly what you can see:
- One pace going across as normal, everything fine.
- Second pace propagates more slowly and with a lower amplitude (peak voltage of ~0mV instead of ~20mV). It’s normal for the wave to ‘settle’ on subsequent paces as the cell models get to an appropriate steady state (really a limit cycle).
- It’s the recovery from the second pace that is really interesting. The left-hand half of the tissue appears to want to do an early after-depolarization (EAD) and goes to a pseudo-steady plateau voltage, whilst the right hand side recovers to pretty much resting membrane potential. This sets up what I’d call a ‘standing wave’ in space through time.
- This standing wave hangs about for quite a while (about 100-220 ms: a long time for a mouse).
- Eventually the tissue on the right recovers enough to let another wave through at 220ms ish. Then back to the standing situation (but a bit further right) for another 120ms until it lets another wave through at about 360ms.
It’s pretty surprising to me that the models on the right would be repolarizing themselves at the same rate as the ones on the left are depolarizing themselves to allow a pseudo-steady standing solution. Even though the pacing rate is pretty fast, injecting depolarizing current on the left, I’d probably also have expected to see the cells on the left repolarize at some point.
Please let me know of any simulation or experimental work that has reported anything like this before. If anyone would like to investigate, please do! The Chaste code for simulating this can be downloaded from this link, which will work with the current revision (and probably the upcoming release 3.2) of Chaste. The Li model includes the Bondarenko Markov model for the fast sodium channel, which might be a place to start looking for some answers…
 Well initially it was on a 0.5 x 0.5cm mesh (since mouse hearts don’t get to 1cm long!), but it makes a nicer movie and is easier to see on a 1cm domain. Note that this simulation is all symmetric in ‘y’, so you’d get the same result in a 1cm 1D domain.