'No honeycomb is built without a bee adding circle to circle, cell to cell, the wax and honey of a mausoleum, this round dome proves its maker is alive.'

Robert Lowell

At times our restless imaginations seek insights unencumbered by what we definitely know. We observe nature then read and wander in imaginary spaces. We then return to nature to see if some of the things we imagined are there and whether there or not, we pose questions. We realize everything we see connects with so many things we do not.

This book is like this.

We know so little about the inner workings of the smallest insects. But insect ideas may serve us best when we design our smallest tools and machines. This book is not a complete study. So please do not approach it as such. It is a farrago, a potpourri of related ideas and some of their ramifications. To experts in the disciplines touched upon, coverage may appear elementary, but because this book tries to pose new questions to entomologists, systems biologists, physiologists, mathematicians, engineers and computer scientists and anybody else having interest, its scope must be general. I hope everyone will read for a big overview of how bees move things around in their bodies and afterwards are sufficiently motivated to have their own thoughts. How much of the imaginary does our real world exclude anyway?


This book arose from a paper, 'Insects Separate Diffusing Particles in Parallel,' presented at the 2001 Fourth International Conference on Modeling and Simulation of Microsystems. Discussions of how the circulations of insects and other invertebrates transfer heat, mass and momentum within microfluids through phase interfaces of complicated geometries at sizes important for developing our own compact energy and chemical systems suggested to me that many groups searching for similar grails did not talk to each other. Systems modelers, computer scientists, mathematicians and engineers were largely unaware of how insects did the things smaller and better that they were trying to do. On the other hand, entomologists and biological "types" were conspicuous by their absence from this meeting. Hence this book.

James Lawry

California Academy of Sciences, San Francisco

Chapter one


Introductory Note

I hope many people from numerous disciplines will leaf through and perhaps even read this book. Because mathematics and especially equations discourage so many readers, I present quantitative ideas verbally, but for more formal coverage, I annotate several seminal papers and general references in the references section. I also omit tables, graphs and many figures, because more up-to-date and deeper examples are online. I hope The Incredible Shrinking Bee stimulates diverse reading, heated discussions, and many new ideas.

Why Study Bees?

This book shows how we may use bees and other insects as models for our smallest machines. Insects and spiders are all smaller than our smallest 'stand alone' devices. Some can pass through a needle's eye. Because insects circulate their blood differently than we do ours, insects can be small. Bees are master miniaturists. Might we ever create machines as small and as competent as bees?

Vector Competency

Apart from suggesting ideas for micro-machines, understanding transport of fluids within insects may have enormous health implications. ARBO or arthropod-borne diseases kill people and animals. All major groups of pathogens have evolved into arthropod vectors, and at least six groups of arthropods evolved blood feeding. We have today arthropod-borne viruses, tick-borne rick-ettsial diseases, and mosquito-borne malaria and yellow fever. How well an insect transmits disease is its vector competency. Vector competency depends upon biochemical, physical, genetic and environmental factors. Interfering with a vector's competence is one way to control the vector as well as spread of the disease.

Role of Circulation in Disease

Insects and ticks counter a host's blood clotting mechanism, and to be successfully transmitted, parasites must overcome biochemical and physical barriers. Usually arthropods ingest pathogens from a vertebrate host during a blood meal. Pathogens then emerge from the blood meal in the gut of the arthropod and then pass through the wall of the gut into the cavity of the circulatory system: the hemocoel. Within the cavity of the hemocoel, hemolymph or insect blood circulates the pathogens throughout the body and to the salivary glands. The pathogens invade the salivary glands, and the arthropod's next blood meal transmits the virus into its victim.

For example, for viral infections such as dengue, RNA viruses persist in nature because blood-eating arthropods keep passing viruses to new hosts. The viruses multiply in the hosts' blood to very high numbers, so when the next arthropod vector ingests them with its meal, the viruses then multiply in the tissues of the arthropod before passing on to a new vertebrate host.

A better-known example is malaria. Soon after a mosquito ingests a blood meal, male and female malarial gametes emerge and join to form zygotes within the blood in the gut of the mosquito. After about two days, the zygotes penetrate the wall of the midgut of the mosquito where in about a week they become oocysts. Inside the oocysts, the parasites multiply into thousands of sporozoites. Then on about day twelve, the sporo-zoites enter the mosquito's hemocoel where the parasites flow with the hemolymph to invade the salivary glands, so that during the next blood meal, the mosquito injects malarial sporozoites into its new host.

Were we to understand hemolymph's circulation more deeply, we might physically block parasites in vectors and reduce vector competency. Malaria kills more than one million people a year. Most are in Africa: pregnant women and children under five. Despite new drugs and better mosquito nets, deaths may be increasing because of breakdowns in public health systems. Moreover, mosquitoes eventually develop resistance to DDT and all other chemical pesticides used on them so far (Ref: Arthropod Vectors).

Insect Circulation Differs From Ours

Insect blood does not carry oxygen. Instead, insects use separate conduits called tracheae to transport oxygen. These little tubes convey atmospheric oxygen directly to cells and muscles through tiny portholes in their skeletons. Keeping oxygen transport separate from insect blood sets a maximum upper limit to how large insects can be; the largest were about thirteen inches. Compartmentalized circulatory and respiratory systems permit insects to be very small.

Millions of Years of Research and Development

Insects arose at least 350 million years ago, and over deep geological time the trial and error processes of evolution created the diverse bodies of present day insects. Evolution adapted insects to their changing world. Bodies of today's insects compared with those of fossils are miniaturized and more efficient. We know little about the lives of the earliest insects, as we know so little about life in the Devonian Period of the Paleozoic Era. The earliest insects were large. They crawled, could not fly, and were adapted to cold. Even though the world warmed, some ancient traits survived. For example, adult midges of one species can still walk on ice with their bodies at minus eighteen degrees centigrade. Evolutionary R and D provide today's scientists and engineers with a plethora of highly varied, self-contained, fuzzy black boxes that are cheap to produce, versatile and robust. If we learn what's inside these boxes and how they work, we may plagiarize insect ideas, modify and adapt the insect plan and build smaller machines.


To build small, we must first see the world and learn about it anew 'through insect eyes.' As mammals, we often think 'mammalianly' and imagine that other animals do things the way we do them, so when we design our devices, we may first try to make them too big. We then may try to shrink our larger machines. But in their small world, insects face different 'issues.' For example gravity poses little problem; insects fall without injury and can land upside down on ceilings, but water is a menace. Surface tension traps unwary drinkers requiring insects to have long legs and special mouth-parts to avoid the dangers of drink. Insects have mastered small.

Masters of Small

Each bee is a compact packaged web of connected and closely interwoven subsystems. Each subsystem fits perfectly together with all her others, as insects do not tolerate extraneous redundancy. Extra weight only increases need for energy, and fuel is expensive. As knowledgeable wilderness survivalists, bees reduce weight wherever possible. Unlike many of our human miniature systems, bees remain unattached by wires or tubes to batteries or fuel reservoirs. Instead, bees carry their fuel close to their motors. Without being tethered, bees fly, crawl and behave socially. Having their skeletons on the outside leaves large unobstructed spaces inside their bodies.

Inside, a bee has a built-in pilot, motors driving powerful wings and legs, and a circulating supply of fuel. Her body specializes in circulating fluids and gases through pumps and tubes. As her respiratory tubes deliver oxygen directly to where it is needed, she may slowly circulate her blood that not only distributes fuel but also dissipates wastes, heat and carbon dioxide.

A bee coordinates her inside activities with her outside world. Eyes, chemical receptors and hairs sensitive to contact and pressure direct her nervous system to create patterns of electrical messages. These messages pass to muscles and glands, signaling them to contract or squirt. Although a few integration centers such as her brain and other neural centers coordinate some of her activities, she mostly employs many local control centers that are not hard-wired to a central processor to tell her body parts what to do when her life changes.

Bee Fluid Dynamics

If we learn how blood moves inside bees, we should be able to produce similar flows within our own fluid-filled systems built around other ideas stolen from insect circulations. Our model bees could then show us how best to create and exploit control and delivery systems in our smallest devices.

How Can Bees Be So Small?

This book introduces the bee's circulation that can be more useful than the vertebrate system as a model for our small mechanical systems. The insect body is versatile. It shrinks easily, but ours is built too big to shrink very far. Insects have evolved a way to circulate blood in their bodies using a system that also functions in larger arthropods, like crabs and lobsters, but also, not only does a bee's circulation work when shrunk, but it works best in the smallest forms. In fact, the smaller an insect is, the better its circulation appears to work. Before we show why bees can be small, let's see why we cannot shrink a woman down as small as a bee.

The Non-incredible Non-shrinking Woman

Like bees we also are pump-tube systems. Unlike bees, however, our pump-tube vertebrate circulations include our lungs. Compared to insects, our vertebrate circulation is a 'closed' system while the bee's circulation is 'open.' A closed circulation has arteries, capillaries and veins. In animals with backbones, a heart-pump squeezes blood through tubes that go first to gills or lungs, and then this blood, now filled with oxygen and still staying within tubes, goes out all over the body before coming back to the heart. A closed tubular system like ours made small enough to supply an insect would not work.

Printer Analogy

Why not? Imagine a printer having plastic tubes and a head of driving pressure to transport ink from a reservoir to where ink is needed. Were this printer shrunk down to the size of a bee, the pump-tube system would stop distributing ink. The bores of the tubes would now be too small, and the resistance the tubes would place on the pump would easily overcome any pressure the pump could generate to force fluid through the narrow bores. Also a shrunken pump would not work. The smaller a pump is, the less force the pump can produce, and the smaller the volume the pump can eject each time it squeezes. So how do insects move fluids around their bodies and still manage to be small?

Organs Float in a Barrel of Blood

Insects and spiders are hollow. Their skeletons are on the outside, and the big space inside them contains their blood. This cavernous space also houses their organs. In some large insects and caterpillars it's like apples in a barrel of blood. The body space is the 'space of blood' or the hemocoel, and the organs, mostly tethered, float in the blood. The hemocoel contains a variable amount of watery fluid together with blood cells and dissolved nutrients. This blood or hemolymph washes over and bathes the insect's organs. How is this possible? Don't insect organs need to breathe? Yes, they do but not through their blood.

Open Pumps Slosh Insect Blood

One or more open pumps circulate blood in the hemocoel. An open circulation lacks capillaries and veins. It's more like a swimming pool hooked to a filter pump that circulates the water. Imagine yourself standing in a pool of water pumping a foot pump one uses to fill air mattresses and plastic balls. You supply the energy for the pump. As your foot rises, the pumping chamber expands drawing water in through the inlet valve. When your foot descends and squeezes the water trapped in the pump, the increasing water pressure closes the inlet valve that prevents back flow from the pump. As the water pressure in the chamber continues to increase, the outlet valve opens. Now water ejects into the pool. If the pool is initially still, but you keep pumping, water begins to circulate slowly. This open pump system lacks tubes for distributing and collecting water, but it circulates the pool.

The Insect Pump: The Dorsal Vessel

The largest pump in the insect hemocoel is the dorsal vessel (Figure 5.2 in Chapter 5). The dorsal vessel is a small-bore tubular pump running along the top of the abdomen, and like the foot pump, the dorsal vessel is open. This heart-pump circulates the watery hemolymph of the hemocoel and operates in concert with one or more, smaller secondary pumps at the bases of wings or legs where these join the body. The accessory pumps direct blood from the hemocoel into the legs and antennae supplying their muscles before it drains back into the hemocoel.

Unidirectional Flow in the Dorsal Vessel

As in the foot-pump, valves in the dorsal vessel encourage flow in one direction, and in bees, this direction is most often from abdomen to head. Blood from the hemocoel enters the dorsal vessel through little holes all along its length. Then moving rings of muscle, that resemble the waves of peristalsis that push food through an intestine, push the blood forward or backward in the dorsal vessel to a new location where blood leaks out again into the hemocoel. Contracting muscles inside the hemocoel that move wings and legs, together with the jiggling of walking and the shakings of pitching and yawing as she walks or flies, enhance our bee's circulation. In this way she circulates her blood but keeps it at a low pressure.

Where Does Her Blood Go?

Blood from the dorsal vessel enters her head and dribbles out over her brain. Blood then flows backwards through the hemocoel of her head and body contacting her muscles, digestive tract and glands. Blood entering the appendages supplies muscles, sense organs and glands of the legs, antennae and wings. Afterwards, blood returns to the dorsal vessel for the next squeeze. Now what does her blood do?

A Marxian Distribution

The blood of insects is not red because it has no hemoglobin and does not carry oxygen. Hemolymph is mostly water and dissolved salts. Cells, digested food products, hormones, wastes, antibodies and even parasites and viruses travel with the hemolymph. As the hemolymph washes over and contacts each organ, each organ of the body takes the things it needs from the blood and also contributes waste substances back into this same blood in a truly Marxian manner: to each organ according to its need; from each organ according to its ability.

Blood Paths Stay Short and Mostly Outside Tubes

Remember there is a huge advantage in having a hemocoel. In the cavity of the hemocoel there is no need for blood going between two places to return to the heart each time in order to be able to go somewhere else. Short distances in the hemocoel and the ability of blood to move to any point in the hemocoel from any other point without going back to the heart or passing through a tube make it possible for substances to distribute and follow shorter paths than the blood in a vertebrate could do.

Low Blood Pressure Promotes Longevity

Most of the time blood in the hemocoel remains outside tubes and at low pressure. Having a low blood pressure when blood volume is so tiny means that small holes in the skeleton do not always cause exsanguinations. In this way a bee can lose a leg, but its blood can still distribute and collect things directly from the organs while she now on five legs limps away.

Hemocoels Adjust to Changes in Volume

During hot periods when water is scarce, insects retain water within their tissues, so there may be less blood inside the hemo-coel. Shrinking the volume of circulating blood in a vertebrate might reduce blood pressure so much that the heart would fail.

Low-volume heart failure does not plague insects. In fact, the opposite happens, and exchange improves. With a reduced volume of blood, the hemocoel becomes more efficient. In a smaller fluid volume, dissolved materials must now confine themselves to move within thin, moist films that line the external surfaces of organs and the walls of the cavity. Here receptors that are on or in the surfaces still can respond to changes in concentrations telling the system which materials and metabolites are to be removed or added to these flows. Because there is less fluid now, distances for travel have shortened, so fewer molecules get lost.

Zoom In

At microscopic dimensions, surface contours and asperities project into the hemocoel. What appears to be just a simple wet flat interior surface, at high magnification includes geometries that change as the volume of fluid in the bee falls during desiccation and rises when she feeds. These microscopic interruptions within an organ's contour can determine how blood flows over organs and surfaces. It is what happens when a swiftly flowing creek dwindles in the summer to a trickle; now a greater portion of what flow remains contacts the stones. What at full hydration is a three-dimensional volume in drier times becomes smaller but also thinner and thinner, behaving more and more as would a moist almost two-dimensional film.

Control Points

To move dissolved substances from the hemocoel into and out of cells, micro-quantities of liquid and solid materials, often together, must traverse complicated phase interfaces having complex geometries of their own. Control points for choices occur at these boundary points. Individual local controllers acting simultaneously over all interfaces together throughout the bee determine what the entire system does as a whole.

A Mobile Service Economy

Because some organs are free to move within the hemocoel, they can drift with the flow to places where they are needed. For example, the bee's kidney or the Malpighian Tubules are long flexible tubes. Resembling a hose attached to a pipe at one end, each tubule floats in and is free to move with the hemolymph. The tethered ends attach to and feed into the alimentary canal. Wastes enter the free ends of the tubules and move along each tubule to exit into the alimentary canal. During drier periods, the free ends of these Malpighian Tubules slide around eventually coming to lie in the fluid filled gutters between organs. Services have moved to where they are needed.

Hemocoels Shrink But Still Coordinate

The properties of the changing thickness of the film of hemolymph help us understand how hemocoels can shrink without destroying the bee's coordination of services. Analogy: imagine a series of machines connected by wires in a room. As the room shrinks the machines squeeze closer together, and the wires begin to take up more and more of the decreasing volume, until at very small volumes when the machines are closest together, the spaces between the machines now hold mostly wires.

However, in the hemocoel the organ 'parts' of the system select what they need independently. Organs 'decide' on their own what each needs and what wastes to eliminate without the need of a large heavy brain and a system of nerve-cables to coordinate their behaviors. Because blood moving in the hemocoel transfers heat, mass and momentum to all parts of the bee without need of a central controller, an engineered model of a hemocoel might excel at sorting and distributing different cells and molecules, let's call them scalars, over space and time. A hemocoel model would be incredibly space and time efficient. Why? Because as our modeled hemocoel shrinks, and its circulating volume of hemolymph gets smaller, the distances blood must travel between pick up and delivery points shorten, so that the distribution-collection system becomes more efficient the more it is shrunk.

Why Model Hemocoels?

We might model hemocoels because hemocoels sort and synthesize, and because their control is diffuse, hemocoels avoid point defects. Now let's see what this means.


The micro-mechanical subsystems of a hemocoel when modeled or copied into future devices, may eventually be able to sort individual molecules from moving mixtures of different molecules, possibly to provide flows of input materials to arrays of systems oriented in space. Arrays may be a single surface or any number of layers. Our arrays then in turn might process their molecules linearly or in parallel in a deterministic manner. Bees linearly as well as parallel process recycled subunits of chitin during molting to make new cuticle. In our own machines, newly synthesized molecules might be collected together to form or accrete into complex floating or stationary patterns of components that then might unite forming new structures.

Diffuse Control

The local active surfaces of the hemocoel prevent obstructions. Theoretically at least, control of the hemocoel may occur along any boundaries where organs contact the hemolymph. 'Choices' are at any points on these boundaries. Taken together, places where absorption and elimination from organs and cells occur become not only the control points for what goes in and comes out of each organ, but together these choice points form the controller of the entire system as well. By controlling individually their receptors and surfaces, each cell and organ can regulate what it takes in and puts out according to immediate localized need without relying on outside information coming from a distant central processor. Because control of the hemocoel is largely a diffused function spread over so much area, the hemocoel remains controlled and robust even if point blockages develop.

Hemocoel as Microprocessor

It is tempting to think of the hemocoel as a kind of microprocessor. After all, because the hemocoel parallel processes, it is great at what computer scientists call pipelining where all the steps of a sequence operate concurrently. If each stage is time limited, the time saved by the hemocoel in pipelining is proportional to the number of stages. Low level 'instructions' given to the 'hardware' would include the dynamics of the hemolymph. The number of stages completed each second as with a processor is the 'clock rate,' so that a personal computer with a 200-megahertz clock then executes 200 million stages each second. Many computers have more stages and higher clock rates. The hemocoel is perfectly situated to incorporate 'suprascalar' tasks in which it performs more than one set of instructions at each stage. Because the controlled entities of biological systems are most often cells, we can imagine a cache or a small amount of memory kept right at the site of the processor itself. The cache retains the parts of a program that the system most frequently uses, thereby avoiding calling on more distant memory repositories.

Safety Factors

Hemocoels have huge loading tolerances or safety factors that are much larger than those for pump-tube systems. Hemocoels work when very full or almost empty. Were we to incorporate such loading tolerances into our models, we could learn what redundancies and fail-safe mechanisms we might need to prevent failure of our smallest devices. For example, small machines are believed to have many locations within them where a point defect can cause the entire machine to fail. As in the human circulation, an embolus in a coronary or cerebral artery can spell disaster. This default assumption, however, does not usually apply to machines built on the macro-scale, as tolerances are larger, and many macro-machines can continue to function despite numerous point defects. Because blockage of the entire flow through a hemocoel does not occur even with a large number of point blockages, we might use macro-machine assumptions in modeling this small system, so that we might tolerate even a high density of point defects in our designs. What should become important for our hemocoel models are the shapes or configurations of the surfaces inside the hemocoel and their fluid interfaces.

New Models and New Control Systems

Understanding insect fluid dynamics so as to be able to model a hemocoel might lend novel insight into creating potentially useful control systems for our smallest devices by reducing the number of centralized controllers and their connecting 'wires.' Remember: too much fluid in a pump-tube system, like our heart and blood vessels, can cause pump failure (congestive heart failure) and lead to overall system failure (death). One human remedy may be to take a diuretic to get rid of the excess fluid or to increase heart or pump function with digitalis, but all the organs of the insect hemocoel during fluid overload continue to function without tampering from without. Many regulators of insect physiology are close to the functions they control because distances inside insects are by definition short. Short distances mean fewer 'wires,' shorter wires, and less weight.

Shrinking Increases Efficiency

So let's imagine that we somehow construct a model hemocoel. Then let's imagine shrinking our model all the way down to the size of a bee, and that we watch what happens. Unlike our own pump-tube system, the smallest hemocoel is most efficient. The hemocoel mechanism eliminates any need for the pumps to maintain a high head of sustained pressure. The system conserves energy as distances are short, and because it requires minimal energy to wash the blood over the organs in a large open system at low pressure. Hemocoels are less prone to interruption by clots. A clot at one location does not stop blood flowing around it to other places. In a pump-tube system a clot in a coronary or cerebral artery is so devastating because once a critical artery blocks, there are almost no alternate routes for blood to follow.

Our Bottom Line: Hemocoels Adapt to Changes That Would Block Closed Pump Tube Systems

Remember, hemocoels can adapt easily to changes of volume that occur when the cavity is too full or almost empty, but unlike pumptube systems, hemocoels are most efficient when fluid volumes are smallest.

Three D Becomes Two D

Think of it this way. Imagine a large hemocoel shrinking smaller and smaller. As the fluid volume grows less and less, at one point this volume eventually becomes just a layer of moisture lining the inside walls of the cavity and the surfaces of the organs. We can see an example with the naked eye if we open the hemocoel of a cicada or locust in the summer. The body cavity is moist inside, but there's not much free fluid. Diffusion of substances within an almost two-dimensional plane film permits maximal control of diffusing substances, as these now can never get lost in the volume of the film. Given infinite time, a randomly moving particle on a plane contacts every point of the plane. In an almost two-dimensional layer of fluid the probability of a molecule moving randomly by Brownian motion from one point to any other in the surface approaches one. However, in a three-dimensional volume of fluid things are very different. There are so many ways for particles to get lost. Not only may a particle diffuse along all four compass directions, but it can go up and down as well. Now the probability is closer to a third for a particle leaving a specific place and arriving at another by diffusion alone. Two-thirds of the particles never arrive. In three dimensions unless a particle leaves a place and arrives at its destination in just a few steps, it never arrives. However, pumping of the dorsal vessel and jiggling from walking and flying may add convection to diffusion, so having a heart makes all our chances better.

Now You Have It

So now you know what The Incredible Shrinking Bee is about. Chapter 1 is the shortest, simplest statement of it. In Chapter 2, we compare bees with our micro-mechanical devices such as they are.

Chapter two

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