It's the start of another year and the body mass index (BMI) is being criticised again . This time a Lancet-commissioned group of experts is denouncing it as a diagnostic tool for obesity. They say that doctors should look at the overall health of a patient when diagnosing obesity, not just rely on this one flawed metric.
Author
- Christian Yates
Senior Lecturer in Mathematical Biology, University of Bath
BMI is calculated by measuring a person's mass in kilograms and then dividing that by the square of their height in metres. For recording and diagnostic purposes, anyone with a BMI below 18.5 is classified as "underweight". The "normal weight" range extends from 18.5 to 24.5 and the "overweight" classification spans 24.5 to 30. "Obesity" is defined as having a BMI above 30.
Given the health implications related to a diagnosis of obesity, or even of being overweight, you might have assumed that the metric used to diagnose these conditions, the BMI, would have a strong theoretical and experimental basis. Sadly this is far from the truth .
While it's true that fatter people typically have a higher BMI, it does not work well as a diagnostic criterion. One of the main problems with BMI is that it can't distinguish between muscle and fat. This is important because excess body fat is a good predictor of heart disease risk. BMI is not.
A recent study suggested if the definition of obesity were instead based on high-percentage body fat, between 15 and 35% of men with non-obese BMIs would be reclassified as obese.
However, it turns out that BMI both under- and over-diagnoses obesity. The same study found that up to half of the people that BMI classified as overweight and over a quarter of BMI-obese individuals were metabolically healthy.
BMI is clearly not an accurate indicator of health. Instead, it would be useful to access a direct measure of the percentage of body fat that is so closely linked to cardiovascular disease. To do that we need to borrow a 2,000-year-old idea from the ancient city-state of Syracuse on the island of Sicily.
This one weird old trick
Around 250BC, Archimedes, the pre-eminent mathematician of antiquity, was asked by Heiro II, king of Syracuse, to help resolve a contentious issue. The king had commissioned a crown of pure gold. After receiving the finished crown and hearing rumours of the metalsmith's less-than-honest reputation, the king worried that he had been cheated and that the metalsmith had used an alloy of gold and some other cheaper, lighter metal. Archimedes was charged with figuring out if the crown was a dud without taking a sample from it or otherwise disfiguring it.
The illustrious mathematician realised that he would need to calculate the crown's density. If the crown were less dense than pure gold, he would know the metalsmith had cheated. The density of pure gold was easily calculated by taking a regularly shaped gold block, working out the volume and then weighing it to find its mass. Dividing the mass by the volume gave the density. So far, so good.
Weighing the crown was easy enough, but the problem came when trying to work out its volume, because of its irregular shape. This problem stumped Archimedes for some time, until one day he decided to take a bath.
As he got into his extremely full tub, he noticed that some of the water overflowed. As he wallowed, he realised that the volume of water that overflowed from a completely full bath would be equal to the submersed volume of his irregularly shaped body. Immediately he had a method for determining the volume, and hence the density, of the crown.
Vitruvius tells us that Archimedes was so happy with his discovery that he jumped straight out of the bath and ran naked and dripping down the street shouting "Eureka!" ("I have found it!") - the original eureka moment.
Sadly, it is unlikely that this is actually how Archimedes solved the problem. Instead, it is more likely that Archimedes used a related idea from hydrostatics (the mechanical properties and behaviour of fluids that are not in motion), which would later become known as Archimedes' principle.
The principle states that an object placed in a fluid (a liquid or a gas) experiences a buoyant force equal to the weight of fluid it displaces. That is, the larger the submerged object, the more fluid it displaces and, consequently, the larger the upward force it experiences. This explains why huge cargo ships float, providing the weight of the ship and its cargo is less than the weight of water they displace.
Using this idea, all Archimedes needed to do was to take a pan balance with the crown on one side and an equal mass of pure gold on the other. In air, the pans would balance. However, when the scales were placed underwater, a fake crown (which would be larger in volume than the same mass of denser gold) would experience a larger buoyant force as it displaced more water, and its pan would consequently rise.
It is precisely this principle from Archimedes that is used when accurately calculating body-fat percentage .
A subject is first weighed in normal conditions and then reweighed while sitting completely submerged on an underwater chair attached to a set of scales. The differences in the dry and underwater weight measurements can then be used to calculate the buoyant force acting on the person while under water, which in turn can be used to determine their volume, given the known density of water.
Their volume can then be used, in conjunction with figures for the density of fat and lean components of the human body , to estimate the percentage of body fat.
While it clearly isn't as easy to use as the basic BMI measurements, and there may be better ways to assess body fat , this 2,000-year-old trick can certainly provide a more useful assessment of health risks.
Christian Yates does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.
