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In CPR one idea behind chest compressions is that continued compressions lead to a cumulative increase of blood pressure which at some threshold will initiate effective blood circulation throughout the body. One important element though is that any interruptions to chest compressions, even for a few seconds, will rapidly cause the pressure to drop and all cumulative progress up to that point will be lost. (Disclaimer I'm an EMT not a doctor so I may be getting this somewhat wrong.)

I don't know the science or specific numbers super well but it's something along the lines of, "after doing chest compressions for X (e.g. 1) number of minutes, enough blood will build up to initiate some circulation in the body, and all subsequent chest compressions will maintain the pressure and circulation. However an interruption even for Y (e.g. 5-10) seconds will cause the pressure to drop back to essentially zero and another X number of minutes of chest compressions will need to be done in order for circulation to resume.

I'm looking for a formula or way to model this pattern mathematically, so that I can say calculate the blood pressure based on the last few minutes of activity. The first thing that comes to mind is a rolling average, e.g if the average rate of chest compressions in the past 2 minutes is above some threshold then circulation will occur. The problem is this doesn't really properly capture the sudden drop and loss of cumulative progress that will occur from a slight disruption. Having some recency-weighted rolling average doesn't really work either because then it won't capture the lag time between when chest compressions begin and when circulation begins. I know I could do this programmatically with some kind of while-loop but ideally I'd like to express this as a single formula.

If helpful, a somewhat analogous but simpler situation is the idea of a combos in fighting video games. As each move in the combo is executed it increases the damage outputted however a single missed move causes the damage output to reset to the original level. This is an easier situation to model because you could just calculate the damage of a given move as a function of its number in the sequence but to make it more similar to the CPR example, imagine if the game allowed for 1 missed move without damage output decreasing.

Does anyone have an idea of how to model a pattern such as this?

Alex Long
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    To be honest, I think the only ethical way to come up with such a formula is to base it on actual blood pressure data or biological theory, rather than ask mathematicians to come up with a graph with the right shape. If someone proposes a formula that's plausible but incorrect in practice, and that formula gets propagated, people's lives could literally be at stake. Perhaps you could ask on https://biology.stackexchange.com? – Greg Martin Jun 29 '23 at 03:58
  • @GregMartin Thanks for the response. I take your point. Another thing I'm considering though is that if such a formula hasn't been come up with and propagated then the inverse argument is this could SAVE lives. I'm not sure which side I stand on though. In general I was hoping for a more broad take on this pattern though, just for some personal work. E.g. I didn't know if this was already a well documented pattern I just wasn't aware of. Thanks for your response either way. – Alex Long Jun 30 '23 at 00:05
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    "the inverse argument is this could SAVE lives": if you dive into precisely what you mean by "this", you'll come right back to the point I made. – Greg Martin Jun 30 '23 at 02:48

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