Scale: The Universal Laws of Life and Death in Organisms, Cities and Companies

by Geoffrey West

To put it slightly differently: of the infinite number of possibilities for the architecture and dynamics of circulatory systems that could have evolved, and that are space filling with invariant terminal units, the ones that actually did evolve and are shared by all mammals minimize cardiac output.

Networks have evolved so that the energy needed to sustain an average individual’s life and perform the mundane tasks of living is minimized in order to maximize the amount of energy available for sex, reproduction, and the raising of offspring.

Darwinian fitness, which is the genetic contribution of an average individual to the ne...

Optimization principles lie at the very heart of all of the fundamental laws of nature, whether Newton’s laws, Maxwell’s electromagnetic theory, quantum mechanics, Einstein’s theory of relativity, or the grand unified theories of the elementary particles.

All the laws of physics can be derived from the principle of least action which, roughly speaking, states that,

of all the possible configurations that a system can have or that it can follow as it evolves in time, the one that is physically realized is the one that minimizes its action.

tree that is just twenty times taller than another does not have leaves whose diameter is twenty times larger.

both kinds of networks are constrained by the same three postulates: they are space filling, have invariant terminal units, and minimize the energy needed to pump fluid through the system.

keeps us alive—that’s why we have to be continuously breathing. Inhaled oxygen is transported across the surface membranes of our lungs, which are suffused with capillaries, where it is absorbed by our blood and pumped through the cardiovascular system to be delivered to our cells.

Oxygen molecules bind to the iron-rich hemoglobin in blood cells, which act as the carriers of oxygen. It is this oxidation process that is responsible for our blood being red in much the same way that iron turns red when it oxidizes to rust in the atmosphere.

After the blood has delivered its oxygen to the cells, it ...

and turns bluish, which is why veins, which are the vessels that return blood back to the ...

The rate at which oxygen is delivered to cells and likewise the rate at which blood is pumped through our circulatory system are ther...

Similarly, the rate at which oxygen is inhaled through our mouths and into the respiratory system is also a measure of metabolic rate. These two systems are tightly coupled together so blood flow rates, respiratory rates, and metabolic rates are all pro...

hearts beat approximately four times for each breath that is inhaled, regardless o...

The rate at which you use energy to pump blood through the vasculature of your circulatory system is called your cardiac power output.

This energy expenditure is used to overcome the viscous drag, or friction, on blood as it flows through increasingly narrower and narrower vessels in its journey through the aorta, which is the first artery leaving your heart,

down through multiple levels of the network to the tiny capillar...

so almost all of the energy that your heart expends is used to push blood through the tiniest vessels at the end of the network.

One of the basic postulates of our theory is that the network configuration has evolved to minimize cardiac output, that is, the energy needed to pump blood through the system.

When blood leaves the heart, it travels down through the aorta in a wave motion that is generated by the beating of the heart. The frequency of this wave is synchronous with your heart rate, which is about sixty beats a minute.

Light is an electromagnetic wave, so the image that you see is just the reflection from the surface of the mirror of the light waves that originate from your body.

the blood wave traveling along the aorta is partially reflected back when it meets the branch point, the remainder being transmitted down through the daughter arteries. These reflections have potentially very bad consequences because they mean that your heart is effectively pumping against itself.

avoid this potential problem and minimize the work our hearts have to do, the geometry of our circulatory systems has evolved so that there are no reflections at any branch point throughout the network.

there will be no reflections at any branch point if the sum of the cross-sectional areas of the daughter tubes leaving the branch point is the same as the cross-sectional area of the parent tube coming into it.

of area-preserving branching is that the cross-sectional area of the trunk is the same as the sum of the cross-sectional areas of all the tiny branches at the end of the network (the petioles).

pulsatile networks is essentially identical to how national power grids are designed for the efficient transmission of electricity over long distances. This condition of nonreflectivity is called impedance matching. It has multiple applications not only in the working of your body but across a very broad spectrum of technologies that play an important part in your daily life. For example, telephone network systems use matched impedances to minimize echoes on long-distance lines; most loudspeaker systems and musical instruments contain impedance matching mechanisms;

bones in the middle ear provide impedance matching between the eardrum and the inner ear.

the smooth and efficient functioning of social networks, whether in a society, a company, a group activity, and especially in relationships such as marriages and friendships, requires good communication in which information is faithfully transmitted between groups and individuals.

When information is dissipated or “reflected,” such as when one side is not listening, it cannot be faithfully or efficiently processed, inevitably leading to misinterpretation,

process analogous to the loss of energy when impedance...

As blood flows through smaller and smaller vessels on its way down through the network, viscous drag forces become increasingly important, leading to the dissipation of more and more energy.

The effect of this energy loss is to progressively dampen the wave on its way down through the network hierarchy until it eventually loses its pulsatile character and turns into a steady flow.

the nature of the flow makes a transition from being pulsatile in the larger vessels to being...

blood pressures are also predicted to be the same across all mammals, regardless of their size.

The first person to study the physics of blood flow was the polymath Thomas Young. In 1808 he derived the formula for how its velocity depends on the density and elasticity of the arterial walls.

we age, our arteries harden, leading to significant changes in their density and elasticity, and therefore to predictable changes in the flow and pulse velocity of the blood.

The Last Man Who Knew Everything: Thomas Young, the Anonymous Polymath Who Proved Newton Wrong,

Most biological networks like the circulatory system exhibit the intriguing geometric property of being a fractal.

fractals are objects that look approximately the same at all scales or at any level of magnification.

classic example is a cauliflower or a head of broccol...

Fractals are ubiquitous throughout nature, appearing everywhere from lungs and ecosystems to cities, ...

If broccoli is broken into smaller pieces, each piece looks like a reduced-size version of the original.

on the other hand, the object is a fractal, no new pattern or detail arises when the resolution is increased: the same pattern repeats itself over and over again.

This repetitive phenomenon is called self-similarity and is a generic characteristic of fractals.

Analogous to the repetitive scaling exhibited by broccoli are the infinite reflections in parallel mirrors, or the nesting of Russian dolls (matryoshka) of regularly decreasing sizes inside one another.

Because blood flow changes from pulsatile to nonpulsatile as one progresses down the network, our circulatory system is actually not continuously self-similar nor therefore a precise fractal.

the nonpulsatile domain where the flow is dominated by viscous forces, minimizing the amount of power being dissipated leads to a self-similarity in which the radii of successive vessels decrease by a constant factor of the cube root of two 3√2 (= 1.26 . . .), rather than the square root √2 (= 1.41 . . .) as in the pulsatile region.

The space-filling requirement that the network must service the entire volume of the organism at all scales also requires it to be self-similar in terms of the lengths of the vessels.

fill the three-dimensional space, lengths of successive vessels have to decrease by a constant factor of 3√2 with each successive branching and, in contrast to radii, this remains valid down through the entire network, including both the pulsatile and nonpulsatile domains.