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Using Computers to Model the Heart... Why Bother?

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It's often said that these are exciting times to be a computational biologist, and indeed they are. But beyond the flashy, gee-whiz aspects of computational biology, I find myself excited for another reason: the tools of in silico biology offer us views of biological systems that we wouldn’t otherwise have.


Biological systems are complex and contain an extraordinary amount of information – the human genome contains over three billion letters, for example.  Furthermore, biological systems are comprised of a large number of processes that occur simultaneously over a wide range of scales of both time and space.  Chemical processes within cells can operate on the nanosecond time scale (or even shorter), while at the other extreme lifetimes of organisms are often measured in days or years.  The spatial range scales are similarly wide – individual machines that operate within cells are nanometers in size, while the sizes of individual organs are measured in centimeters, and larger organisms are meters in size.  Depending on the particular problem that you’re interested in, it’s possible that you’ll be trying to wrap your head around processes that differ in time and size by over a millionfold.


What I’ve described above is the multiscale nature of biological systems.  Multiscale is a buzzword that increasingly pops up in discussions of modeling and understanding biological systems, and for good reason.  In medicine, the effects of a disease are often observed at larger scales of time and space – from the enlargement of hearts in some types of cardiomyopathy to the inappropriate proliferation of cells in cancer to the loss of entire limbs due to the consequences of advanced diabetes.  The aforementioned examples are all the result of cascading failures that progress over years in many cases.  However, the causes of disease, and our treatments for them, usually occupy the smaller end of the time-space spectrum – proteins that are defective because of mutated DNA (or environmental damage) and the drugs that target those proteins. 


But why is computational biology becoming increasingly popular?  And what does it get you?  To begin with, computational biology is becoming more popular because it is becoming more accessible.  Processing power has greatly increased over the past couple of decades, while at the same time becoming much cheaper.  This has enabled researchers to extend the bounds of the scales to be explored in both directions – allowing increasingly detailed (and computationally intensive) descriptions of individual cell components, or perhaps simulating very large numbers of cells at the same time.  Also, increased computing power has allowed a wide range of scales to be integrated into the same simulation.  In other words, not only can we model the very small and the very large, but we can do both at the same time.


As for what computational biology gets you, there are at two significant benefits that I’ll touch on here.  The first relates to the fact that biological systems are messy.  Cells, organs, and whole organisms are all made up of a very large number of interconnected parts that interact in complex and often non-intuitive ways.  It's practically impossible to perform an experiment that has only the exact effect that you intended.  If you administer a drug or mutate a gene, you'll likely affect targets along with the one that you're interested in studying, and there's a good chance that you won't even know what those off-target effects are. 

When studying a mathematical proxy of a living system, the perturbations that you make will only directly have an impact on the components that you want.  The results may still be unexpected, but you can be sure that there were no off-target effects.  As an example, if I want to study the consequences of inhibiting a particular sodium channel in a cell, I can do it by applying a drug that is known to inhibit that particular channel.  The problem is, many drugs are promiscuous, interacting with multiple different channels.  So the problem becomes: how much of whatever effect I observe is due to blockade of my sodium channel of interest, and how much of that effect is due to the drug inhibiting some other channel that I'm not interested in? 

With a mathematical model, I can tell the computer to reduce the activity of my sodium channel by some amount, and know that my in silico inhibition is working only on the target that I'm interested in.  What's more, I can specify exactly how much inhibition I want to induce in the model.  Using computer models allows you to make surgically precise changes to your system, reducing confounding effects.


The second significant point pertains to the amount of information that can be gleaned from an experiment.  When doing studies on living tissue, you're often limited in both resolution and the number of different types of measurements you can make at the same time.  Because of technical limitations, you might be able to take measurements once every hour, when really you'd like to see what's going on every minute. 

Worse, you might only be able to take one measurement on a given specimen, because the measuring technique requires something that kills the cell or invalidates all subsequent observations.  Or, maybe you're interested in being able to record five different ion concentrations as they change during an experiment, but current technology only allows you to measure two at the same time.  When performing an experiment in silico, you can measure as many different parameters as you want, as often as you want (as long you have enough memory to store all that data)!


Now, I'd like to provide an example of recent computational biology research – more specifically, computational cardiology research – which will hopefully illustrate the promise of this type of science and how it can be applied to real problems in medicine.


Atrial Fibrillation: A Multiscale Phenomenon


One of the most common cardiac arrhythmias, atrial fibrillation (AF), is estimated to affect millions of patients.  Fibrillation is a condition in which the affected chambers of the heart are not beating in an organized manner, but rather quivering as separate regions beat chaotically.  If fibrillation occurs in the two bottom chambers of the heart (the ventricles), death will ensue within minutes unless the patient is defibrillated.  In AF, the two top chambers (the atria) quiver while the ventricles continue to beat well enough to pump blood to the rest of the body.  The electrocardiogram (ECG) shown below in Figure 1 provides an example of AF.

Left: Figure 1: Normal and atrial fibrillation ECGs. Image Credit: Wikimedia Commons

The bottom tracing in Figure 1 shows a normal ECG.  Each normal heart beat begins with the two atria depolarizing – causing them to contract and force blood down into the ventricles – which shows up as what’s called a P wave (purple arrow) on the ECG.  Shortly afterward, the ventricles depolarize and contract, pumping blood out to the rest of the body.  This shows up as a larger deflection, called the QRS complex, right after the P wave.


In the top tracing, you can see that there are still QRS complexes (although they no longer appear at regular intervals), but there is a conspicuous absence of P waves.  The red arrow points to where one location where a P wave should be In its place we find a squiggly baseline.  The fact that a nice flat baseline interrupted with regular P waves has been replaced with a noisy, squiggly baseline signifies that the atria are not beating in a unified, organized fashion, but rather are dominated by many different regions, each depolarizing chaotically.  Occasionally, an electrical wave manages to propagate down from the atria to the ventricles, producing a QRS complex. 


Fibrillation belongs to a class of arrhythmias called reentrant arrhythmias.  Normally a heart beat is the result of an electrical wave that begins in one location and spreads throughout the rest of the heart in a specific way.  However, under the right conditions, a “short circuit” can develop which allows an electrical wave to rapidly reenter the same region repeatedly.  If you use fluorescent dyes to image a heart while it’s fibrillating, you’ll often see patterns that are in fact rapidly spinning spiral waves.


AF is not life threatening on its own, but it can still be a very serious condition.  AF can cause palpitations, lightheadedness, and shortness of breath.  It can also lead to the development of blood clots which can produce a stroke, and it can lead to a gradual weakening of the heart to the point that fluid begins to back up and congest the lungs.


Previously I mentioned that AF is a reentrant arrhythmia, and that reentry can occur under the right conditions.  One way to help set the stage for reentry is to change the electrical properties of individual cells.  Each cardiac cell contains a large number of ion channels of different types, and the proper function of a cardiac cell depends on a choreography involving all of these ion channels.  Not only must there be the proper number of each type of ion channel, but the individual channels must open and close at the proper times.  A process called ionic remodeling changes the number of ion channels of a given type, potentially creating the conditions necessary for reentry. 


Zooming out a bit in scale, the second way to help set the stage for reentry is to alter the ability for electrical waves to spread from cell to cell.  Even when cells have the correct densities of ion channels, if they are not properly coupled to each other, electrical propagation can become too slow or even eventually fail.  Structural remodeling refers to a constellation of processes that interfere with the normal coupling between cardiac cells.


AF is a difficult problem to study because it involves both ionic and structural modeling, often at the same time.  Both types of remodeling can lead to a heart that’s afflicted with AF, and AF can in turn cause more remodeling.  The feedback loop just goes on and on.  These factors make AF a great candidate for computational cardiology.


Trine Krogh-Madsen at Cornell University’s Weill Medical College is using an anatomically detailed computer model of the atria to study how both types of remodeling can affect the frequency and persistence of AF episodes.  The model consists of about 2 million virtual cells, each with a full complement of ion channels.  It also represents the atria in 3D, including such anatomical features as the pulmonary veins, venae cavae, and tricuspid and bicuspid valve annuli.  The pulmonary veins are annuli are commonly implicated as starting points or anchors for spiral waves during episodes of AF. 


The nice thing about this atrial model is that ionic and structural remodeling can be controlled independently.  The activity of any ion channel can be controlled precisely – mimicking ionic remodeling – and structural remodeling can be simulated by precisely varying the amount of coupling between cells in different regions of the virtual atria.  In some of her simulations, Trine examines different amounts of remodeling in three different ion channels (that have previously been implicated in AF), in others she simulates different degrees of structural remodeling (but no ionic remodeling), and in others she includes both.  Figure 2 below shows a snapshot from a simulation, providing four different views of the virtual atria.  The colors correspond to the membrane voltage (the hotter the color, the more “excited” the tissue is), and the formation of a spiral wave can be clearly seen in the top two views.

Right: Figure 2: 3-D simulation of the atria with an anatomically detailed computer model. Image Credit: Trine Krogh-Madsen (Cornell University Weill Medical College)

What these simulations have revealed is interesting: when the atria experience only ionic remodeling, AF episodes originate mostly around the pulmonary veins, but when the atria have only undergone structural remodeling, the majority of AF is located around the tricuspid annulus.  However, when both types of remodeling are introduced, there is no preference for where AF episodes originate. 


These types of experiments would be extremely difficult (if not impossible) to perform in real tissue, but they yield information that can be used to guide further experiments in living systems.

About the Author: Byron Roberts is currently a graduate student in the Tri-Institutional Training Program in Computational Biology and Medicine. For the past several years, at Weill Cornell Medical College, he has been developing a mathematical model and using it to further explore how cardiac ischemia-reperfusion injury can lead to arrhythmias. Prior to moving to New York, Byron completed his bachelor’s degree in genetics at the University of California, Davis, followed by two years of postgraduate research in brain tumor biology. His research interests are largely motivated by experiences during a past career as an EMT and paramedic. Byron is the author of the Emergent Phenomena blog and can be found on Twitter (@bnroberts).

The views expressed are those of the author and are not necessarily those of Scientific American.

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The views expressed are those of the author and are not necessarily those of Scientific American.

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