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When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias
The description for this book, When Time Breaks The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias, will be forthcoming.
Hardcover
First published January 1, 1987
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April 28, 2024
Winfree starts by examining the problem of cardiac arrhythmias and their critical periods, during which a stimulus can knock the beat off its track, a catastrophe for its host. Recently, this rare yet often fatal phenomenon popped up with Demar Hamlin during a routine tackle in an NFL game (thankfully, CPR on the field let doctors revive him and he was playing again the next season). But it demonstrates an extremely interesting phenomenon to the scientist: how could the rhythm of the heartbeat, which otherwise can suffer any shock, fail at this one exact moment?
This is where the three-dimensional dynamics of electrochemical waves come in. Now, you can't actually see what's going on inside the heart muscle, so we have to find a model that explains what we can see - including the critical period that can induce arrhythmia. If you just look at the surface, though, you can see something analogous to the Belousov-Zhabotinsky reaction, to which Winfree's attention turns as a model species of these kinds of systems. In both of these he demonstrates the topological techniques to capture the existence of singularities, either of the critical point in the phase space of the heart beat, or the generating point (or pair of points) at the center of a spiral in a BZ reaction. What's behind that 2-dimensional spiral, he shows, is a 3-dimensional scroll wave, similar to those you might see in turbulence. With his student Steven Strogatz, Winfree explored how the topological properties of the scroll wave determined their dynamics, whether in the purely chemical BZ reaction, heart tissue, or even the brain.
Why read this book? Hasn't the science advanced greatly since 1987? Well, I don't really care that much about the narrow problem of cardiac arrhythmias, but the broader issue of nonlinear wave computing (not that Winfree ever calls it that) is underlying a lot of mysteries in 2024, both in human and perhaps machine intelligence. Winfree writes with clear language, and I came away from the book with a much better understanding of topology, though it did take me a while to read. Don't skip the appendices, as I almost did.
This is where the three-dimensional dynamics of electrochemical waves come in. Now, you can't actually see what's going on inside the heart muscle, so we have to find a model that explains what we can see - including the critical period that can induce arrhythmia. If you just look at the surface, though, you can see something analogous to the Belousov-Zhabotinsky reaction, to which Winfree's attention turns as a model species of these kinds of systems. In both of these he demonstrates the topological techniques to capture the existence of singularities, either of the critical point in the phase space of the heart beat, or the generating point (or pair of points) at the center of a spiral in a BZ reaction. What's behind that 2-dimensional spiral, he shows, is a 3-dimensional scroll wave, similar to those you might see in turbulence. With his student Steven Strogatz, Winfree explored how the topological properties of the scroll wave determined their dynamics, whether in the purely chemical BZ reaction, heart tissue, or even the brain.
Why read this book? Hasn't the science advanced greatly since 1987? Well, I don't really care that much about the narrow problem of cardiac arrhythmias, but the broader issue of nonlinear wave computing (not that Winfree ever calls it that) is underlying a lot of mysteries in 2024, both in human and perhaps machine intelligence. Winfree writes with clear language, and I came away from the book with a much better understanding of topology, though it did take me a while to read. Don't skip the appendices, as I almost did.
Displaying 1 of 1 review