Donald Kirkendall, an exercise physiologist at the University of North Carolina, will never forget the time he put a heart-rate monitor on a member of the United States rowing team and asked the man to row as hard as he could for six minutes.
The standard formula for calculating how fast a human heart can beat calls for subtracting the person's age from 220. The rower was in his mid-20's.
Just getting the heart to its actual maximum rate is an immense effort and holding it there for even a minute is so painful that it is all but inconceivable for anyone who is not supremely motivated, Dr. Kirkendall said. But this rower confounded the predictions.
''His pulse rate hit 200 at 90 seconds into the test,'' Dr. Kirkendall said. ''And he held it there for the rest of the test.'' A local cardiologist was looking on in astonishment and told Dr. Kirkendall, ''You know, there's not a textbook in the world that says a person could have done that.''
But maybe, some physiologists and cardiologists are saying, the textbooks are wrong.
The question of how to find maximum heart rates is not just of academic interest, medical experts say. The formula for calculating the maximum rate has become a standard in cardiology and in fitness programs, and an entire industry has grown up around it, with monitors sold to individuals and built into exercise equipment.
''There is a need, a clinical and societal need, to estimate the maximum heart rate,'' said Dr. Douglas Seals, an exercise physiologist at the University of Colorado.
Doctors use the formula when they test patients for heart disease, asking them to walk on treadmills while the speed and incline are gradually increased until their heart rates reach 85 percent of the predicted maximums.
The idea is to look for signs, like chest pain or a sudden drop in the heart rate, indicating that the heart is not getting enough blood. But if doctors underestimate how fast the person's heart can beat, they may stop the test too soon, Dr. Seals noted.
Personal trainers and exercise instructors design fitness programs around the maximum heart rate, often telling people to wear heart rate monitors and then to exercise at 80 to 90 percent of the maximum in brief spurts to build aerobic capacity and at 65 percent to 75 percent to build endurance.
Some heart monitors built into exercise machines even shut the machines down if an exerciser exceeds 90 percent of the predicted maximum. But if the heart rate formula is wrong, these exercise prescriptions are misguided.
''If you're trying to improve their aerobic fitness or to train for certain endurance events, then you want to know with a reasonable accuracy what intensity you're exercising at,'' Dr. Seals said. ''If your estimate is 10 or 20 beats too low, then you're pretty far off.''
Exercise physiologists say, however, that being pretty far off is more common than most people expect.
''The more information we have, the more we realize that that formula is just a very rough consideration,'' said Dr. Jack H. Wilmore, an exercise physiologist at Texas A&M.
And while Dr. Seals is now proposing a new formula to use as a general guide, he and others say it is simplistic to rely on a single formula to predict the maximum heart rates of individuals.
The common formula was devised in 1970 by Dr. William Haskell, then a young physician in the federal Public Health Service and his mentor, Dr. Samuel Fox, who led the service's program on heart disease. They were trying to determine how strenuously heart disease patients could exercise.
In preparation for a medical meeting , Dr. Haskell culled data from about 10 published studies in which people of different ages had been tested to find their maximum heart rates.
The subjects were never meant to be a representative sample of the population, said Dr. Haskell, who is now a professor of medicine at Stanford. Most were under 55 and some were smokers or had heart disease.
On an airplane traveling to the meeting, Dr. Haskell pulled out his data and showed them to Dr. Fox. ''We drew a line through the points and I said, 'Gee, if you extrapolate that out it looks like at age 20, the heart rate maximum is 200 and at age 40 it's 180 and at age 60 it's 160,'' Dr. Haskell said.
At that point, Dr. Fox suggested a formula: maximum heart rate equals 220 minus age.
But, exercise physiologists said, these data, like virtually all exercise data, had limitations. They relied on volunteers who most likely were not representative of the general population. ''It's whoever came in the door,'' Dr. Kirkendall said.
In addition, he and others said, gauging maximum heart rates for people who are not used to exercising is often difficult because many prematurely stop the test.
As the treadmill hills get steeper, people who are not used to exercise will notice that their calves are aching. ''They will say they can't go any further,'' Dr. Kirkendall said.
In addition, Dr. Wilmore, the exercise physiologist, said it was clear from the scattered data points that maximum heart rates could vary widely from the formula. ''If it says 150, it could be 180 and it could be 120,'' Dr. Wilmore said.
But the formula quickly entered the medical literature. Even though it was almost always presented as an average maximum rate, the absolute numbers took on an air of received wisdom in part, medical scientists said, because the time was right.
Doctors urging heart patients to exercise wanted a way to gauge exercise intensity. At the same time, exercise gurus, promoting aerobic exercise to the public, were asking how hard people should push themselves to improve their cardiovascular fitness. Suddenly, there was a desire for a simple formula to estimate maximum heart rates.
''You tell people to exercise at a moderate intensity,'' Dr. Haskell said. ''Well, what's a moderate intensity?''
Soon, there was a worldwide heart-rate monitor industry, led by Polar Electro Inc, of Oulu, Finland, selling more than 750,000 monitors a year in the United States and citing the ''220 minus your age'' formula as a guide for training.
The formula became increasingly entrenched, used to make graphs that are posted on the walls of health clubs and in cardiology treadmill rooms, prescribed in information for heart patients and inscribed in textbooks. But some experts never believed it.
Dr. Fritz Hagerman, an exercise physiologist at Ohio University, said he had learned from more than three decades of studying world class rowers that the whole idea of a formula to predict an individual's maximum heart rate was ludicrous. Even sillier, he said, is the common notion that the heart rate is an indication of fitness.
Some people get blood to their muscles by pushing out large amounts every time their hearts contract, he said. Others accomplish the same thing by contracting their hearts at fast rates. As a result, Dr. Hagerman said, he has seen Olympic rowers in their 20's with maximum heart rates of 220. And he has seen others on the same team and with the same ability, but who get blood to their tissues by pumping hard, with maximum rates of just 160.
''The heart rate is probably the least important variable in comparing athletes,'' Dr. Hagerman said.
Heart rate is an indicator of heart disease, said Dr. Michael Lauer, a cardiologist and the director of clinical research in cardiology at the Cleveland Clinic Foundation. But, he added, it is not the maximum that matters: it is how quickly the heart rate falls when exercise is stopped.
An average healthy person's heart rate drops about 20 beats in a minute and the rates of athletes ''nose dive by 50 beats in a minute,'' Dr. Lauer said.
In three recent studies, Dr. Lauer and his colleagues found that people whose rates fell less than 12 beats within a minute after they stopped exercising vigorously had a fourfold increased risk of dying in the next six years compared with those whose heart rates dropped by 13 or more beats.
Dr. Lauer pays no attention to the standard formula when he gives treadmill tests. More than 40 percent of patients, he said, can get their heart rates to more than 100 percent of their predicted maximum. ''That tells you that that wasn't their maximum heart rate,'' Dr. Lauer said.
The danger, he said, is that when doctors use that formula to decide when to end a treadmill test, they can inadvertently mislead themselves and their patients. Some patients may be stopping too soon and others may seem to have a heart problem because they never can get to what is supposed to be their maximum rate.
''Some people are being pushed and others are not,'' Dr. Lauer said. ''In my view, that is unacceptable.''
Yet, Dr. Seals said, many doctors want some sort of guide for estimating maximum heart rates for treadmill tests. And many people who want to increase their fitness crave a general formula.
So Dr. Seals and his colleagues decided to take another stab at finding an equation.
In a study published in the March issue of The Journal of the American College of Cardiology, Dr. Seals and his colleagues devised a new formula: maximum heart rate equals 208 minus 0.7 times age. They used published studies involving 18,712 healthy people and data from 514 healthy people they recruited. Their formula gives much higher average maximum heart rates for older people, with the new and old heart rate curves starting to diverge at age 40.
But raising doubts about the heart rate formula is unlikely to lead people to abandon it, exercise physiologists say. What would they do without it?
''I've kind of laughed about it over the years,'' Dr. Haskell said. The formula, he said, ''was never supposed to be an absolute guide to rule people's training.'' But, he said, ''It's so typical of Americans to take an idea and extend it beyond what it was originally intended for.''
Photos: Dr. Douglas Seals, an exercise physiologist, watches as Chris Bell raises his heart rate on a treadmill. (Kevin Moloney for The New York Times)(pg. F1); Dr. William Haskell compares the heart rate of Jeff Myll, who wears a Polar Electro watch monitor, available commercially, with a reading from an EKG. (Peter DaSilva for The New York Times)(pg. F8)