Why do we need another book about atrial fibrillation?

Despite the numerous good books available on the topic, there are several reasons I think it is worthwhile writing yet another book about atrial fibrillation (AF). Fibrillation involves elegant physiology that is not widely taught or understood, and as a result there are widespread misconceptions or ill‐conceived beliefs about AF. Electrophysiology (EP) in general is an aesthetically attractive intellectual endeavor: it makes sense and lends itself well to deductive reasoning. If you think about the fundamental principles of EP, you can figure out most things, with no need for rote memorization. AF takes this deductive process to extremes: “if this is true, then that must be true,” ad nauseam. We start by thinking about propagation in waves that traverse the tissue. Next, we think about more than one wave propagating at the same time, and consider how they interact. The outcome of such interactions is widely varied and depends in large part upon the timing and location of wave collisions. In AF there are numerous waves, traveling in random directions at random intervals, and hence the “space of possible interactions” is perpetually scanned; everything that can happen does happen. This roiling, random, and chaotic activation seems inscrutable and unpredictable. However, as we will see in this book, the immense complexity of activation during AF becomes tractable via consideration of the principles of waves and their interactions.

There is a second important reason to delve deeply into AF: we don't currently have adequate treatments. The inadequacy is in part due to our inability to identify what drives AF in individual patients. There is still wide disagreement among the “experts” as to what the mechanism of AF in humans is.

What type of problem is fibrillation?

For a long time now, academic institutions have been organized around specific disciplines: biology departments, mathematics departments, etc. This binning has been quite useful, helping to focus intellectual pursuits into discrete groups. There are many types of problems. Some – like “At what angle should I tilt my canon to maximize the distance that my cannonballs fly?” – are mono‐disciplinic. Answering this question really only requires Newtonian mechanics. It can be solved entirely within the physics department, without need for outside consultation. There are, however, other types of problems that are more complex and do not lend themselves to analytic solutions (i.e. a formula which takes inputs and produces inevitable outputs). For instance, “How does the spread of electrical activity in the heart become disorganized, producing the abnormal heart rhythm, atrial fibrillation?” This is a problem that, as we shall see, simply cannot be solved by plugging numbers into an equation. It isn't that there is an equation out there waiting to be derived but currently too complicated for our not‐yet‐up‐to‐the‐task brains. Rather, it is that this is an entirely different type of problem, which simply cannot be solved with a formula. That may seem strange. Surely we live in a universe where the laws of physics determine what can and can't happen? This is true; there are rules. Not just anything can happen. It turns out that just because there is no formula directly describing how a system evolves does not mean that there are no rules governing the system's behavior. It also does not mean that we can't understand how the system works, or that we can't use this understanding to manipulate the system in a predictable way.

There are problems that involve “complex, non‐linear, dynamic systems.” These types of problems are significantly more slippery when subjected to inquisition. Let's talk about a classic example, the weather. There are laws of physics that constrain what can happen. But alas, the cuffs are not on too tightly: there is an awful lot that can happen. In fact, even if you make a gazillion measurements about the weather now (like temperature, wind speed, butterfly wing flappings), you would still be very hard pressed to figure out what the weather will be like in a week. And certainly, you'd know almost nothing at all about the weather in a month.

Why is that? Surely weather is simply the result of a bunch of air molecules¹ and water droplets banging into each other? And if that's true, and we know that, say, force equals mass times acceleration, we can simply calculate what happens next, and then next, and then… until we arrive at tomorrow, right? Well, yes and no. We can figure out the result of each individual interaction (air molecule vs. air molecule), but there are a bunch of them. So, it is theoretically possible yet completely impractical.

There's a subtle wrinkle in the story. You can't plug a bunch of numbers into a formula and simply use 24 hours instead of one millisecond² and derive what the status of things will be at some arbitrary point in the future. You have to put one millisecond into your formula, derive the answer (what the state of things will be next), and then you plug that answer back into your formula and ask about the next moment. This is an important distinction. There's no jumping ahead, you have to figure things out iteratively. And it gets worse. This process of iterative, stepwise calculation is linear, meaning you do one thing and then another and then another sequentially. These sorts of things are far less complex than systems in which things happen in parallel. We can't simply follow a single air molecule from one moment to the next until some future time, because we need to know what other air molecules it will hit, where they will be coming from, and with how much force. And to know that, we need to know what air molecules those air molecules were hit by, etc., etc., etc. This is a non‐linear system: what happens to any component of the system depends upon what happens to all the other components of the system.³

When you think about what our predecessors figured out and handed down in the halls of science, a lot more linear problems have been solved than non‐linear ones. Why? Because they're easier to solve. But there are ways to address non‐linear problems. An interesting aspect of non‐linear problems is that, often, small changes in the state of their elements can very quickly result in dramatic changes in outcome. With many elements that are highly sensitive to initial conditions, it can seem that a system is entirely random and therefore not rule‐bound. This is captured in the popular expression the “butterfly effect.” But “randomness” and “rule‐based” are not mutually exclusive notions.

It's pretty hard to figure out what will happen when you flip a coin once, but it's much easier to figure out what will happen if you flip it many, many times. Statistics may be boring, but it is extremely useful (and clever). Statistics allows one to wring the most out of what appears to be no information. When it comes to poor data, more is actually better!

Structure of the book

Explaining atrial fibrillation is challenging. It’s hard to know where to start, because understanding each part of the story seems to depend upon understanding some other part of the story. The issue is that AF is a complex, non‐linear process; everything is interdependent. The way I’ve chosen to structure the story is to talk about individual parts: the basic physiology of propagation and reentry (“rules of the game”), followed by the various mechanisms that can drive AF. Next I’ll discuss the higher‐order dynamics of fibrillation, how the parts interact.

All this information would be for naught if we could not make use of it to treat our patients. To do that, we need to determine what’s driving fibrillation in individual patients. So, I’ll cover how we can map AF; fibrillation poses some specific challenges for electrode mapping. Finally, it’s necessary but not sufficient simply to have a “picture” of fibrillation in our patient. I’ll finish with how to leverage our understanding of AF dynamics to intervene and alter atrial physiology to prevent fibrillation.

There are several people who have contributed to the work that is described throughout this text. They are the people I refer to when I say that work was done at “our” institution or that “we” did a study. These are we:

Jason Bates and Oliver Bates contributed mightily to the development of the computational model that we use in our lab. Both contributed to the studies we performed with the model as well. All of the following were instrumental in the various studies we've performed, which inform the pages of this book: Bryce Benson, Richard Carrick, Nicole Habel, Nathaniel Thompson, Daniel Correa de Sa, Justin Stinnett‐Donnelly, Philip Bileau, Ethan Tischler, Keryn Palmer, Pierre Znojkiewicz, Joachim Müller, Jeffrey Buzas, Arshia Noori, Nicholas Hardin, Steve Bell, James Calame, Vadim Petrov‐Kondratov, Bryan Mason, Shruti Sharma, Gagan Mirchandani, Daniel Lustgarten, Deborah Janks, Andreas Karnbach, Susan Calame, Laura Unger, and Srinath Yeshwant. I'd also like to thank Ashley LaScala for her help preparing the manuscript.

My mentor, Burton Sobel, requires special mention for the tremendous role he played in the evolution of both the ideas and the lab group.