The National Institute for Computational Sciences

Matters of the Heart

Researchers at the University of Tennessee use Kraken to study cardiac arrhythmias

By Caitlin Elizabeth Rockett

On September 17, 2010, 17-year-old Reggie Garrett was playing football. The senior quarterback had worked hard to improve his game, and in the late summer Texas heat it was clear his work was paying off. In the second quarter, Garrett threw a pass that led to his second touchdown assist of the night, putting his team up 21-0. Garrett ran to the sidelines after the pass, smiling ear-to-ear—and then he collapsed. The young athlete died later that evening at a local hospital.

Reggie Garrett had suffered what is known as sudden cardiac arrest (SCA)—an unexpected cessation of heartbeats due to an irregular rhythm. SCA claims as many as 400,000 lives each year in the United States. SCA can strike people of any age, gender or race, and even those who seem to be in prime physical condition, like Reggie Garrett.

A comprehensive understanding of SCA requires a system-level investigation of the electrical, chemical and mechanical activities of the heart. As these dynamics are difficult if not impossible to monitor and control in a traditional laboratory, scientists like Xiaopeng Zhao of the University of Tennessee are using supercomputers to mathematically model the interconnected systems of the heart. The Cray XT5 known as Kraken, located at the National Institute for Computational Sciences (NICS), is just the machine for the job. Kraken is the fastest supercomputer managed by academia, capable of nearly 1.2 quadrillion calculations per second (petaflops).

“We are solving millions and millions of equations at the same time, and we need to do this many times over,” said Kwai Wong, a computational scientist at NICS and one of Zhao’s research team members. “Extreme parallel computation is necessary.”

The team aims to advance the diagnosis and treatment of cardiac arrhythmias that can lead to SCA by developing a deeper understanding of the interplay of functions of the heart, beginning with models of a canine heart. As they ensure validity in their canine models, they will begin to focus on human heart models.

Heart at work

The heart is essentially a pump, pushing oxygen-rich blood throughout the body, and taking in oxygen-depleted blood to restore it and send it back through the body’s arteries again. But this description only reflects the heart’s mechanical actions, begging the question, “Why does the heart beat in the first place?”

A specialized group of cells leak charged particles into the sinoatrial cells (the so-called “pacemaker” cells) of the organ, creating electrical impulses that drive contractions. A healthy adult heart beats 72 times per minute on average and pumps roughly 2,000 gallons (over 7,000 liters) of blood through the body each day, making heart health essential to overall health.

“It is important to know that SCA is not a heart attack,” Zhao explained. “A heart attack is caused by a blocked or hardened blood vessel in the heart. During a heart attack, heartbeats usually persist and some blood can flow. During SCA there are no heartbeats and no blood flow.”

SCA is caused when the heart’s electrical system fails, typically resulting from a ventricular arrhythmia (VF), where the lower chambers of the heart quiver rather than contract and cease pumping blood. SCA victims lose consciousness within a few seconds as blood stops flowing, and death can occur within minutes if treatment is not received.

“Currently, one in six Americans will die of ventricular fibrillation,” said Zhao. “Existing options for assessing vulnerability to fibrillation and for their treatment are often unreliable or have undesirable side effects.”

Early diagnosis and improved treatments are life-changing possibilities for those at risk for SCA. Simulations by Zhao’s group may hold the key to changing the way heart research is performed, and as such, the way treatment and diagnosis are implemented.

A mathematical heart

Figure 1: Movie: Contraction and relaxation of a 3D dog ventricle with realistic geometry.  

While the heart is complex, computational models make investigating this intricate organ more practical. Zhao and his team begin by describing the functions of the heart with a series of partial differential equations (PDEs).

PDEs allow computational scientists like Wong to build codes capable of solving problems with numerous variables that describe inherent physical properties of the heart such as electrodynamics, fluid flow and elasticity.
A comprehensive model of the heart requires that tens of millions of equations governed by PDEs be solved repeatedly many times over. And the complications don’t end there; scientists must consider varying time and spatial scales within the heart to appropriately calculate these physics-describing math problems. The spatial scale of the heart varies each time the muscle contracts.

“On one hand, physiological processes occur at a very fine timescale,” explained Zhao. “For example, the upstroke of an action potential happens within 1 or 2 milliseconds, and thus we must use a timestep of a fraction of a millisecond to accurately capture upstrokes.” The action potential of the heart is the electrical change that causes a heartbeat.

“On the other hand, diseases and dynamical phenomena occur at a much larger scale,” Zhao continued. “Sometimes these things happen over tens or hundreds of heartbeats. So we have to integrate these small and large time scales with varying spatial scales for a long time, over and over again, to get accurate answers to our questions.”

To solve the equations that describe the heart, Wong has used over a million mathematical points to describe a computational model of the heart, essentially turning the heart into a grid. But unlike a simple, “regular” Cartesian grid with X- and Y-axes such as those we used in high school algebra, the heart is a bit more complicated.

“The more grid points you place on the geometry, the more accurate the representation of the system becomes,” explained Wong. “We began with about 10,000 points on the surface and we’ve continued to refine the grid by adding more points.” Currently, the team’s model contains 1.6 million grid points.

This large and complex grid is impossible to handle without the help of a supercomputer like Kraken. To make the task more workable, the team decomposes the grid into numerous connected regions. Each region is assigned to a different processor, allowing for simultaneous calculations. Separate regions are subsequently combined to get a picture of what is going on in the entire organ.

Results and the future

To understand how the heart’s mechanisms influence each other, the team has combined two models, an electrical and a mechanical model—an incredibly difficult and novel undertaking. Literature on two- and three-dimensional models of cardiac electromechanical coupling or experimental approaches for studying these interactions in the whole heart is limited.

“It has been shown by others in both experimental and simulated studies that mechanical contractions have effects on electrical activities,” said Zhao. “If you just study the electrical activity you get one conclusion, but if you consider only the mechanical contraction, you get a different conclusion. Clearly, there is a great need for us to consider the problem from a system’s approach.”

While Zhao and his team are just in the preliminary stages of their research, their models are developing and they have run phenomenological tests to make sure that their models are agreeing with real life scenarios.

Future simulations will expand the models to give increasingly realistic representations of the heart. The team is working in collaboration with another group to implement a more realistic heart mesh based on Magnetic Resonance Imaging (MRI) techniques.

The team also aims to study a heart phenomenon called alterans, a periodic beat-to-beat variation in the heart’s electrical current, which increases the risk of SCA.

Though their research has only just begun, the team’s models are a giant first step toward a full understanding of the small muscle that powers our bodies every minute of every day.