Fractal Blood Vessels

There are many more examples of fractal branching patterns in our bodies, and blood vessels are one of the most impressive examples. Every cell in the body must be close to a blood vessel (within about 100 microns) in order to receive oxygen and nutrients. The only way this is possible is through a fractal branching network where blood vessels branch and branch ever smaller, down to the width of a capillary, which is about 8 microns in diameter.

Depending on how they're measured, humans have about 150,000 kilometers of blood vessels - enough to go around the world several times! (Remember, most of these are microscopically tiny capillaries.)

Are you skeptical about this enormous length? Well, let's try to verify it.

According to one study, there are about 250 capillaries/mm³ of body tissue.^REF And according to another study, the average length of a capillary is about ~600 microns, just over half a millimeter.^REF

Using these numbers, we can compute an estimate of the total length of capillaries in a human.

Questions:
How many capillaries are there in a cubic millimeter? [ ]

How long is each capillary, in millimeters? [ ]

What is the total length, in millimeters, of capillaries in a cubic millimeter of body tissue? [ ]

Next we need to figure out how many cubic millimeters there are in the human body.

How many cubic millimeters are there in a cubic centimeter? [ ]

How many cubic centimeters are there in a liter? [ ]

One liter (of water) weighs 1kg, and assuming the body weighs 100 kg, how many liters are then in the body? [ ]

So how many cubic millimeters are in the body? [ ]

Then how many millimeters of capillaries are then in a 100 kg body? [ ]

How long (in millimeters) are the capillaries in one liter of human tissue? [ ]

How long is this distance in meters? [ ]

How long is this distance in kilometers? [ ]

The answer you should get is not quite as long as the number cited above, but that is probably because we're only counting the smallest of the blood vessels, the capillaries.

Note: From this exercise, you can see why scientists generally like to use metric units - imagine how much more cumbersome this calculation would be if we used inches and pounds for our units!)

Insects have a very different respiratory and circulatory system than mammals. Because of their much smaller size, they have a much larger surface area to volume ratio than bigger animals. This allows them to take in oxygen passively through small holes in their bodies called spiracles which branch out into their body tissues, and eliminates the need for lungs to drive the respiration process. Their passive respiratory system helps put an upper limit on the size of insects^REF, and explains why (except in horror movies^REF) we don't see giant insects the size of cats or dogs!

The respiratory system of an insect consists of a network of branches emanating from holes called spiracles.
Photo courtesy of Don Mackean, Biology Resources.com.