Optimal Branching of Vascular Vessels Minimizes Work

xray of a chest showing lungs and bronchioles and bones

Biological Strategy

Mammals

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Liquids include water, as well as body fluids such as blood, gastric juices, nutrient-laden liquids, and more. To survive, many living systems must move such liquids within themselves or between locations. Because of their properties, liquids tend to disperse unless they are confined in some way. To address this, living systems have strategies to confine fluids for transport, and to overcome barriers such as gravity, friction, and other forces. Some of these same barriers also provide opportunities. Trees and giraffes face the same challenge: how to move fluids (water and blood, respectively) upward against gravity. But their strategies are quite different. The tree moves water using capillary action and evaporation, possibly due to water’s properties of polarity and adhesion. The giraffe’s tight skin provides pressure to assist in blood circulation. and keep blood from pooling in the legs.

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Gases of particular importance to living systems are oxygen, carbon dioxide, and nitrogen. Oxygen and carbon dioxide are involved in respiration, so distributing these gases efficiently and effectively is important for a living system’s survival. However, gases are difficult to contain because they disperse easily. To accommodate this, living systems have strategies for confining gases and using gases’ properties to their advantage. For example, prairie dogs and mound-building termites build systems of tunnels and mounds that take advantage of wind to ventilate their underground homes.

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Mammals

Class Mammalia (“breast”): Bats, cats, whales, horses, humans

Mammals make up less than 1% of all animals on earth, but they include some of the most well-known species. We know first-hand some of the characteristics that make mammals unique, like having hair, being able to sweat, and producing milk through mammary glands. Another critical shared feature is a set of highly-specialized teeth. Unlike sharks or alligators, for example, whose teeth are generally all the same size and shape, mammals have differently shaped teeth in different areas of the jaws to target specific foods or foraging strategies.

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Vascular and respiratory vessels in mammals minimize the amount of biological work required to operate by being arranged hierarchically.

Image: Anita (annyta_k) /

Image: Patrick J. Lynch /

“The vessels found in mammalian cardiovascular and respiratory systems are usually arranged in hierarchical structures and a distinctive feature of this arrangement is their multi-stage division or bifurcation. At each generation, the characteristic dimension of the vascular segments will generally become smaller, both in length and diameter.” (Barber and Emerson 2008: 179)

“The branching structures found in mammalian cardiovascular and respiratory systems have evolved, through natural selection, to an optimum arrangement that minimizes the amount of biological work required to operate and maintain the system. The relationship between the diameter of the parent vessel and the optimum diameters of the daughter vessels was first derived by Murray (1926) using the principle of minimum work. This relationship is now known as Murray’s law and states that the cube of the diameter of a parent vessel equals the sum of the cubes of the diameters of the daughter vessels.” (Barber and Emerson 2008: 180)

[This mathematical structure is also found in trees and other organisms that exhibit branching]

Last Updated August 18, 2016

References

Journal article

Optimal design of microfluidic networks using biologically inspired principles

Microfluidics and Nanofluidics | 29/03/2007 | Robert W. Barber, David R. Emerson

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Reference

Journal article

The Physiological Principle of Minimum Work: I. The Vascular System and the Cost of Blood Volume

Proceedings of the National Academy of Sciences | 31/05/2006 | C. D. Murray

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