(I've even
seen some topological(!) reasons to think that if it does
go near the heart, a strong shock is safer than a weak one. [...])
I remember
some magazine article dealing with this years ago.
Apparently there's a range of current (through the heart) that below
the range, nothing much happens. Above the range, the heart stops.
Within it, though, you get ventricular fibrillation...
That's pretty close to what I saw.
The sketch of the argument:
Draw a graph with shock intensity on the Y axis and shock timing, as a
proportion of the way through the normal heartbeat period, on the X
axis. Consider a path that includes the X axis, vertical lines just
inside the edges of the graph, and a line joining the last two at some
high level of shock. For each point on the graph, consider the phase
shift between the original heartbeat and the heartbeat after the shock.
At zero intensity, of course, nothing happens. If the shock is
correctly sychronized, the phase is unchanged. And a strong shock will
restart the heartbeat in sync with the shock (this is basically what
defibrillators do).
This means we have a closed path, and a variable which can be expressed
as an angle, such that the variable makes a full circuit of the
possible angles as we walk around the path. Bringing in topology, this
means there exists at least one point inside the path at which the
variable's value is discontinuous or undefined. Physically, the most
reasonable interpretation is that there is a (probably small) area on
the intensity-vs-timing graph inside which the heart goes into
fibrillation rather than resuming a regular beat.
Of course, there are many respects in which the mathematics might not
match reality; perhaps most notably, I'm not convinced the assumptions
involved in modeling the new heartbeat phase as a continuous function
are valid. But I certainly find it a thought-provoking argument.
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