# Taking mathematics to heart

##### Mar 14, 2011

Did you know that heart attacks can give you mathematics? That statement appears on the web site of James Keener, who works in the mathematics of cardiology. This area has many problems that are ripe for unified attack by mathematicians, clinicians, and biomedical engineers. In an article to appear in the April 2011 issue of the Notices of the American Mathematical Society, John W. Cain, a mathematician at Virginia Commonwealth University, presents a survey of six ongoing Challenge Problems in mathematical cardiology. Cain's article emphasizes cardiac electrophysiology, because some of the most exciting research problems in mathematical cardiology involve electrical wave propagation in heart tissue.

At some point in our lives, many of us will undergo an electrocardiogram (ECG), a recording of electrical activity in the . To understand where these tiny electrical currents originate, we must zoom in to the molecular level. Bodily fluids, such as blood, contain positively charged ions. When these ions traverse cell membranes, they cause electrical currents, which in turn elicit changes in the voltage V across the membrane. If a sufficiently strong stimulus current is applied to a sufficiently well-rested cell, then the cell experiences an "action potential": V suddenly spikes and remains elevated for a prolonged interval. These action potentials govern heartbeat patterns and are therefore critical to understanding and treating disorders like arrhythmia () and in particular tachycardia (faster than normal heart rhythms).

Taking the Nobel Prize-winning work of Hodgkin and Huxley as a starting point, researchers have created mathematical models of the cardiac action potential by viewing the cardiac cell membrane as an . A major challenge that Cain identifies is striking a balance between feasiblity and complexity: Minimize complications in the model, so that it is amenable to mathematical analysis, but add sufficient detail, so that the model reproduces as much clinically relevant data as possible. The equations that govern the model---nonlinear partial differential equations---cannot be solved explicitly, and solutions must be obtained through approximation by numerical methods. Adding further complications are the intricate geometry of the heart, with its four chambers and connections to veins and arteries, and the fact that different types of cardiac tissue have different conduction properties.

Cain goes on to discuss various cardiac phenomena and the mathematics that can be used to describe them. One example is heart rhythm: The regular, coordinated contraction of the heart muscle that pumps blood through the body. Improving the understanding and treatment of irregularities in that rhythm is critical in the fight against heart disease.

A healthy heart does not beat in a perfectly regular pattern; in fact, such a pattern would be a sign of potentially serious pathologies. The body's autonomic nervous system uses neurotransmitters to speed up or slow down the heart, and tiny fluctuations in those substances induce variability in the intervals between consecutive beats. The RR interval is the interval between consecutive heartbeats measured in an ECG. Attempts to quantify heart rate variability (HRV) usually involve analyzing time series of RR intervals.

Unfortunately, some ways of analyzing RR time series give the same results for patients with healthy hearts and for those with fatal cardiac abnormalities. One challenge for mathematicians and statisticians is to devise quantitative methods for distinguishing between the RR time series of people with healthy hearts and the RR time series of those with cardiac pathologies. Cain asks, Can some pathologies be diagnosed solely by analysis of RR time series and, if so, which ones? To spot subtle pathologies, methods are needed for quantifying the "regularity" of a cardiac rhythm. Also, given the existing array of diagnostic tests that clinicians have at their disposal, there could be advantages in the use of "automated" mathematical/statistical methods.

Explore further: Optimising the future with mathematics

More information: Cain's article, "Taking Math to Heart: Mathematical Challenges in Cardiac Electrophysiology", is freely available on the Notices web site - www.ams.org/notices.

Provided by American Mathematical Society

## Related Stories

#### Researchers examine developing hearts in chickens to find solutions for human heart abnormalities (Video)

Jan 21, 2009

When it is head versus heart, the heart comes first. The heart is the first organ to develop and is critical in supplying blood to the rest of the body. Yet, little is known about the complex processes that regulate the heartbeat. ...

#### Keeping the rhythm of life in sync

May 28, 2008

Beyond symbolically holding our feelings of love and compassion, the heart is a very efficient pump with a steady beat that provides the rhythm of life. Abnormal rhythm in the heart is a condition known as cardiac arrhythmia. ...

#### Hospitals should be aware of rare, life-threatening heart rhythm

Feb 08, 2010

(PhysOrg.com) -- Hospital care providers need to be more aware that cardiac arrest from a medication-induced heart rhythm problem is a rare but potentially catastrophic event in patients, according to a joint scientific statement ...

#### Secrets of the Heart's Signals

Jan 10, 2007

Natalia Trayanova's research team works on understanding the heart's natural electrical signaling process. The director of the Computational Cardiac Electrophysiology Lab, she is a faculty member in the biomedical engineering ...

#### DNA sequence variations linked to electrical signal conduction in the heart

Nov 14, 2010

(PhysOrg.com) -- Scientists studying genetic data from nearly 50,000 people have uncovered several DNA sequence variations associated with the electrical impulses that make the heart beat. The findings, reported in Nature Ge ...

#### New mathematical model could aid studies of cardiac muscle

Jul 26, 2010

Researchers have developed a new mathematical model that may provide a simpler and better way of predicting ventricular function during the cardiac cycle. The new model could help researchers improve treatment options for ...

## Recommended for you

#### Optimising the future with mathematics

5 hours ago

How will science address the challenges of the future? In collaboration with Australia's chief scientist Ian Chubb, we're asking how each science discipline will contribute to Australia now and in the fu ...

#### Strong teams attract crowds for international cricket

Mar 06, 2014

The strength of the team—not the promise of a close contest—is the biggest draw to crowds in international cricket, new research has found.

#### Improving radiation therapies for cancer mathematically

Mar 05, 2014

In a paper published in December in the SIAM Journal on Scientific Computing, authors Li-Tien Cheng, Bin Dong, Chunhua Men, Xun Jia, and Steve Jiang propose a method to optimize radiation therapy treatments in cancer patien ...

#### Computational study finds maximum packing density of 55,000 different shapes

Mar 05, 2014

A team of researchers at the University of Michigan has used computational and analytical analysis to find the maximum packing density of 55,000 uniquely shaped particles. In their paper published in the ...

#### Secret to the perfect pancake is discovered

Mar 04, 2014

In a collaboration with Meadowhall Shopping Centre, students from the University's Maths Society (SUMS) developed, trialled and tested a formula which enables pancake-lovers across the world to rustle-up ...

## More news stories

#### Study shows men and women both biased against women's math abilities

(Phys.org) —A study conducted by business and economic researchers Ernesto Reuben, Paola Sapienza, and Luigi Zingales, has found that both men and women hold biases against women's math abilities. In their ...

#### Study finds investors prefer good-looking male backed entrepreneurial ventures

(Phys.org) —A study conducted by a team of researchers from Harvard, Wharton and MIT has revealed that venture capitalists prefer to back entrepreneurial opportunities when pitched by a man and that they ...

When it comes to shopping for gifts, we try to select things we think people both want and need. According to a new study in the Journal of Consumer Research, focusing too much on the gift recipient can lead to giving the gi ...

#### What's the upside of feeling too sad for chocolate?

The instant gratification and the pleasure derived from consuming excessive chocolate and deep-fried foods can lead way to a double-edged sword of negative consequences ranging from weight gain to feelings of low self-esteem. ...

#### Power play: Empowered consumers are more likely to switch brands

As consumers, we form favorite brands and select services providers from a plethora of choices. According to a new study in the Journal of Consumer Research, how powerful we feel in our daily lives may impact our likelihood of swi ...

#### Sharp or flat: Gene clues into musical ability

Music surfaces frequently in the great Nature vs. Nurture debate: Why can someone be a virtuoso pianist yet their neighbour be a musical duffer? Does the answer lie in genes or upbringing?

#### Researchers closer to improving safety, effectiveness of lithium therapy

Lithium, one of the oldest and most widely used drugs to treat neuropsychiatric illnesses, such as bipolar disorder, has a serious drawback – toxicity. In a continued effort to find a safer form of lithium, ...

#### Timid jumping spider uses ant as bodyguard

A timid jumping spider uses the scent of ants as a secret weapon to save itself from becoming the somewhat soggy prey of the predatory spitting spider. The downside to this plan is that jumping spiders are ...

#### Diets high in animal protein may help prevent functional decline in elderly individuals

A diet high in protein, particularly animal protein, may help elderly individuals function at higher levels physically, psychologically, and socially, according to a study published in the Journal of the American Geriatrics So ...

#### Dynamic stressing of a global system of faults results in rare seismic silence

In the global aftershock zone that followed the major April 2012 Indian Ocean earthquake, seismologists noticed an unusual pattern – a dynamic "stress shadow," or period of seismic silence when some faults near failure ...