**WASHINGTON **— Kevin Lee, 17, has always found the heart interesting. “It maintains a steady rhythm for millions of beats,” he says. Then, suddenly, “it can fail without any explanation.” But three years ago, the heart-obsessed senior at University High School in Irvine, Calif., was no longer content to sit on the sidelines. “I saw all these stories in the news about these athletes suddenly collapsing and dying,” he recalls. “I thought, if I could find the reasons why that could happen, I could find ways to treat those conditions and ways to prevent them.”

He hasn’t succeeded. At least not yet. But Kevin has made some stunning progress, using math to show how the shape of the heart changes as it contracts, or beats. And he can now relate those changes to the electrical signals that tell the heart when it’s time to beat.

Kevin presented his findings this week at the Intel Science Talent Search in Washington, D.C. Each year, Society for Science & the Public brings together 40 high school seniors to share their impressive research achievements with the public.

The heart is made of strong, elastic and tough muscle. A bundle of cells inside the heart called the sinoatrial node sends out electrical signals directing the organ to contract. With each beat, the heart pumps blood in and out. Blood that is coming from the body circulates to the lungs where it takes up oxygen. Then it moves out and around to deliver that oxygen where it’s needed. Throughout each contraction, the heart muscle radically changes its shape.

Current computer simulations of how the heart beats have been based on the pacing of the electrical signals from the sinoatrial node. But they don’t include the changing shape of the heart muscle as it contracts. Kevin says those existing models rely on a string of polynomials. These are mathematical expressions (using only addition, subtraction and multiplication), and they must change at every time interval within a heartbeat. To understand heart motion, Kevin says, “you also have to account for the heart’s elasticity, how it rebounds back…it just becomes a nightmare.”

He decided to take a new approach. Kevin worked with *partial differential equations*. This alternative way allows him to mathematically express heartbeats and is specifically designed to include numbers that are constantly changing over time — like those numbers describing how a heart changes shape when it contracts. Instead of piling one type of mathematical expression atop another, partial differential equations allow the heart muscle and the electrical signals of the heartbeat to move together, Kevin explains.

The teen hopes that his model will help scientists better understand how the heart beats — and what happens when the muscle loses its regular rhythm. Those pacing problems, known as cardiac arrhythmias, can lead to severe health problems, and to the sudden death of the athletes that Kevin heard about on the news. By better understanding how heart signals relate both to the timing of heartbeats and the shape of a contracting heart, Kevin believes medical companies might be able to make drugs and devices that more safely and reliably stabilize unhealthy hearts.

### Power Words

**cardiac** Relating to the heart.

**cardiac arrhythmia** Irregular heartbeat. There are several types of arrhythmias; the heart can beat too fast, too slow, or in a pattern that’s not normal. Some arrhythmias are mild and have little if any effect, while others can be life-threatening.

**equation **In mathematics, the statement that two quantities are equal. In geometry, equations are often used to determine the shape of a curve or surface.

**function** A relationship between two or more variables in which one variable (the dependent one) is exactly determined by the value of the other variables.

**model** A simulation of a real-world event that’s developed to predict an outcome.

**partial differential equation** A mathematical equation that can show how variables change over time. Ordinary differential equations can only deal with one variable at a time.

**polynomial** A mathematical expression that uses only addition, subtraction and multiplication. It is used in math and science to describe situations that have many different variables contributing to them.

**simulate** To deceive in some way by imitating the form or function of something. A simulated dietary fat, for instance, may deceive the mouth that it has tasted a real fat because it has the same feel on the tongue — without having any calories. A simulated sense of touch may fool the brain into thinking a finger has touched something even though a hand may no longer exists and has been replaced by a synthetic limb. (in computing) To try and imitate the conditions, functions or appearance of something. Systems that do this are referred to as **simulations**.

**sinoatrial node** A bundle of cells in the heart that sends electrical signals to the rest of the muscle, telling it when to contract. This node can work on its own. It also receives information from the brain about when to slow or speed up the heartbeat.