Comparative Anatomy is Largely the Story of the Struggle to Increase Surface in Proportion to Volume

J. B. S. Haldane’s essay “ On Being the Right Size” is a classic. In the first chapter of Intermediate Physics for Medicine and Biology, Russ Hobbie and I quote it.

You can drop a mouse down a thousand-yard mine shaft; and arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, a horse splashes.

Another line from the essay is nearly as famous.

Comparative anatomy is largely the story of the struggle to increase surface in proportion to volume.

We describe the interplay between surface and volume in Chapter 2 of

Consider the relation of daily food consumption to body mass. This will introduce us to simple scaling arguments. As a first model, we might suppose that each kilogram of tissue has the same metabolic requirement, so that food consumption should be proportional to body mass [or volume]. However, there is a problem with this argument. Most of the food that we consume is converted to heat. The various mechanisms to lose heat-radiation, convection, and perspiration-are all roughly proportional to the surface area of the body rather than its mass.

If ridding our bodies of excess heat is an important issue, then we need to increase surface area without increasing volume. A similar issue arises when getting oxygen to our cells. Our circulatory and respiratory systems are elaborate strategies to increase the area over which oxygen diffuses. This is a key concept where physics and physiology overlap.

You can read Haldane’s essay in its entirety here. Below I quote part of it. Enjoy!

Animals of all kinds find difficulties in size for the following reason. A typical small animal, say a microscopic worm or rotifer, has a smooth skin through which all the oxygen it requires can soak in, a straight gut with sufficient surface to absorb its food, and a single kidney. Increase its dimensions tenfold in every direction, and its weight is increased a thousand times, so that if it is to use its muscles as efficiently as its miniature counterpart, it will need a thousand times as much food and oxygen per day and will excrete a thousand times as much of waste products.

Now if its shape is unaltered its surface will be increased only a hundredfold, and ten times as much oxygen must enter per minute through each square millimetre of skin, ten times as much food through each square millimetre of intestine. When a limit is reached to their absorptive powers their surface has to be increased by some special device. For example, a part of the skin may be drawn out into tufts to make gills or pushed in to make lungs, thus increasing the oxygen-absorbing surface in proportion to the animal’s bulk. A man, for example, has a hundred square yards of lung. Similarly, the gut, instead of being smooth and straight, becomes coiled and develops a velvety surface, and other organs increase in complication. The higher animals are not larger than the lower because they are more complicated. They are more complicated because they are larger. Just the same is true of plants. The simplest plants, such as the green algae growing in stagnant water or on the bark of trees, are mere round cells. The higher plants increase their surface by putting out leaves and roots. Comparative anatomy is largely the story of the struggle to increase surface in proportion to volume. Some of the methods of increasing the surface are useful up to a point, but not capable of a very wide adaptation. For example, while vertebrates carry the oxygen from the gills or lungs all over the body in the blood, insects take air directly to every part of their body by tiny blind tubes called tracheae which open to the surface at many different points. Now, although by their breathing movements they can renew the air in the outer part of the tracheal system, the oxygen has to penetrate the finer branches by means of diffusion. Gases can diffuse easily through very small distances, not many times larger than the average length traveled by a gas molecule between collisions with other molecules. But when such vast journeys-from the point of view of a molecule-as a quarter of an inch have to be made, the process becomes slow. So the portions of an insect’s body more than a quarter of an inch from the air would always be short of oxygen. In consequence hardly any insects are much more than half an inch thick. Land crabs are built on the same general plan as insects, but are much clumsier. Yet like ourselves they carry oxygen around in their blood, and are therefore able to grow far larger than any insects. If the insects had hit on a plan for driving air through their tissues instead of letting it soak in, they might well have become as large as lobsters, though other considerations would have prevented them from becoming as large as man.

Originally published at http://hobbieroth.blogspot.com.

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Brad Roth

Brad Roth

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Professor of Physics at Oakland University and coauthor of the textbook Intermediate Physics for Medicine and Biology.