Hi Folks,

I'm encountering conceptual problems in trying to think
about Body Mass Index (BMI). Surely these questions
have been discussed in the medical/physiological world,
but I haven't come across any discussion of the issues
raised below and would welcome pointers or comments
from the informed!

BMI is defined as body weight (in kgm) divided by the
square of the height (in metres), and it is trotted out
blandly as an important index of whether one's weight
is excessive.

But: why not the cube of the height? This is my theoretical
question!

Consider two women, say, of identical geometrical shapes,
and with exactly the same mass-proportions of different
tissue types, etc (which themselves are geometrically
exactly similar and distributed in exactly the same ways).
Then in particular their bodies will have identical
densities, and their weights will be in the ratio of the
cubes of their heights.

But say one is 5ft (1.52m) tall, and the other is 6ft (1.83m)
tall. Therefore the BMI of the taller one will be 20%
greater (6/5) than the BMI of the shorter one:

(BMI tall)/(BMI short) = (D*hT^3/hT^2)/(D*hS^3/hS^2)
                       = hT/hS = 6/5 = 1.2

where hT and hS are the heights of the Taller and Shorter,
and D is proportional to their density.

Given the hypothesis in this case that their proportions
of different tissues are identical, and likewise for the
distributions of these tissues, one would expect their
two bodies to be functionally very similar, and therefore
that the 20% difference in BMI is not particularly
meaningful as a comparison of the "healthiness" of their
respective weights. At first blush, one would expect
these two women -- identical in all respects save their
overall size scale -- to be equally healthy.

One can discuss this latter point more critically.

1. The force which a muscle can exert could be expected
to be more closely related to its cross-section than to
its volume, so to move around a greater weight (h^3) a
thicker muscle (h^(3/2)) would be useful, for the same
degree of body functionality. Therefore, on this particular
ground, the taller woman should have thicker muscles and
therefore have a greater BMI for equivalent bodily
functionality.

2. Similarly for the leg-bones (to bear the weight with
equivalent mechanical stress).

3. The flow capacity, for given pressures, of blood in
the major blood vessels, and of air in the airways, will
increase with cross-sectional area (h^2).
On the other hand, the needs of the tissues for blood and
air will be proportional to their volumes (h^3), and so the
larger woman might need proportionately greater cross-sections
(even ignoring the fact that the blood has further to travel),
perhaps again suggesting the need for greater BMI on these
grounds (though this one is more complicated).

So these look like reasons why a taller (heavier) person
might need a relatively thicker body than an equally
healthy thin one.


So: I'm wondering why there is such a fuss being made
about BMI defined as weight/(height^2).

My concern derives from the blatantly prominent role
that BMI thus defined currently plays in discussions of
"healthy weight", obesity, cardiovascular risk, diet, etc.,
to the point where draconian decisions (both for individual
patients and in published statistics about the "health" of
populations) are made on the basis of its value. If it
is questionable on the grounds outlined above, are these
decisions not equally questionable?

My writing about it is prompted by two recent events.

A. Someone recently told me about their check-over by a
nurse. From the account, it seemed that this nurse was on
auto-pilot, apparently reading from some kind of mental
auto-cue. Although only one issue, BMI was assessed in this
draconian way (not adversely as it turned out: "You're fine,
you're in the middle of the healthy range"). But so were all
the other issues.

B. In my local press ("Ely Standard", Feb 3 2005) I read:

  "How an MP got his weight taped and plans to lose 7lbs"

  "MP Malcolm Moss took a break from heavyweight politics
   and had his body mass index measured at a parliamentary
   exhibition -- and vowed to return to the gym as a result.

  "It was part of an education campaign run by Cancer Research
   and the British Heart Foundation last week to raise
   awareness about the impact obesity has on cancer and
   heart disease. MPs and staff were also given advice on
   how to stay active and maintain a healthy weight.

  "Mr Moss's test showed he was just under the threshold for
   the 'overweight' category and he also passed the waistline
   test which is a key indicator for obesity in men -- the
   so-called 'beer-belly' syndrome.

  "Mr Moss, MP for North East Cambridgeshire, said: 'It is
   really important that people know there are simple things
   we can all do to live healthier lives and reduce our
   risk of heart disease and cancer.'

  "'I could do with losing about seven pounds so it is back
   to the gym for me.'

  "The body mass index (BMI) is a simple method to measure
   whether you are within a healthy weight range for your
   height. You can calculate your BMI by dividiing your
   weight in kilograms by your height in metres squared.

  "A BMI of between 18.5 and 25 is OK, 25-30 is overweight,
   and 30-plus puts you in the obese category."

(There was also a photo, which I will spare you.)

From the description of the context, and the quotations of
what he said, I suspect that Mr Moss himself was reading
from an auto-cue -- created by the political message-writers
who set this event up in the first place. The definitive
categorisation of BMI ranges exemplifies the draconian
assessments I refer to above. [These ranges are confirmed
by consulting the British Heart Foundation website:

http://www.bhf.org.uk/questions/
index.asp?secondlevel=1164&thirdlevel=1337

where no attempt is made to introduce gradations based on
age, gender, muscular development derived from work, athletic
training, etc.]

For 5-foot woman with mid-"OK" BMI=22, the geometrically
equivalent 6-foot woman would have BMI=26.4 and be well
into the "overweight" range.

I have nothing against using appropriate measures to assess
whether someone's weight is unhealthily excessive.

My concern is whether BMI is an appropriate measure, given
what I have set out above.

Or have I missed important subtleties in the interpretation
of BMI which, if taken into account, would lead me to conclude
that a 5-foot woman should ideally (BMI=22) weigh 112.6 pounds
(8 stones) while a 6-foot woman with the same BMI should weigh
162.2 pounds (11 stones 8 lbs) [ 112.6*(6/5)^2 = 162.2 ] rather
than the 194.7 pounds (13 stones 13 pounds) which is implied by
scaling up by volume?

However, a female 14-stone 6-footer is perhaps exceptionally
hefty, to be treated with considerable respect; maybe one might
start with a 11.5-stone six-footer and scale back to the little
5-footer who, on a volume basis, would then weigh 6.7 stone
(93 lbs), with a BMI of 18.2 (just below "healthy").

So perhaps there are reasons why body shape is not independent
of height -- maybe a short person needs a relatively thicker
body than a taller one. If so, I'd be interested in what these
reasons are. They would have to contraindicate the reasons I
give above for expecting a taller person to need a relatively
thicker body than a shorter one!

With thanks for any comments,
and best wishes to all,
Ted.


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E-Mail: (Ted Harding) <[log in to unmask]>
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Date: 06-Feb-05                                       Time: 11:53:36
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