Basic Principles of Bioengineering

Look at the three cylinders above. Each is constructed from the same amount of material. The bar on the top left
is solid and so is the narrowest bar, whilst the cylinder at the top right is twice the diameter and so is hollow and
thin-walled since the cylinders are the same length and their solid cross-sectional areas are the same. Now,
because their cross-sectional areas are the same they are equally strong in tension or compression, but they
differ in one very important property - can you decide which bar would be the easiest to bend out of the two top
bars?

The answer is that it depends. The wider bar is certainly harder to bend by virtue that it is wider, but the walls
are thin and prone to buckle inwards. It's rather like bending a cardboard toilet roll inner tube - it is quite stiff until
one of the walls caves in and then it bends easily. Now take a look at the bottom cylinder. This cylinder also
contains the same amount of material and has the same length and solid cross-sectional area. I would guess
that this would be the hardest cylinder to bend, not only is it fairly wide, but its walls are quite thick, so although it
is narrower than the second cylinder it is less prone to buckle but is wider than the first cylinder and so harder to
bend. That's my guess, of course we can do mathematical calculations to better ascertain which cylinder will be
the hardest to bend, but I shall not go that deep here.

So, what has this got to do with biology? Lots: firstly, the bones in your legs are hollow cylinders, rather like the
third cylinder above, if you are healthy. This means that your legs have optimised their strength against bending
without compromising their strength in compression or tension. Now, why not simply have a wider bone that is
solid? Well, firstly materials are expensive! If you were designing a building or the hull of a ship or whatever, you
would not design it with limitless resources in mind, instead you would have to minimise costs without
compromising performance. This is why battle tanks have thicker armour at the front, where they are most likely
to be hit, and thinner armour at the back and under-belly. This makes sense, for a given amount of material you
can increased the odds of the tank's survival, even though you have introduced a slight weakness in the rear.
Nature adheres to the same principles, organisms invest a lot of energy acquiring the materials that they need,
and some materials like the calcium in your bones are not in endless supply! Nature has to be economical. Also,
there are weight considerations. You could give your tank the thickest armour in the world, quite easily, but
would it be able to move without an enormous engine that guzzles up all your oil supply? A thick solid cylinder is
stronger than a hollow thick cylinder, as one would expect, but the solid bone requires a lot more material and is
heavier and so is more expensive. However, it just so happens that when you try to bend or twist a cylinder, most
of the force is resisted by the material in the outer layers, so a hollow cylinder is not much weaker.

One of the great things about bones though is that they are 'intelligent materials'. That is they respond to the
environment - they repair themselves if broken, but they also strengthen themselves if needed and can even
reshape themselves. This is called bone remodelling and it occurs throughout life, though as one gets older the
rate of bone loss eventually exceeds the rate of bone deposition which leads to weakening of the bones.
Exercise effects the bones massively. Weight-lifting in particular can double the cross-sectional area of bones,
over several years, especially where the bones bear the greatest strain; otherwise as your muscles double in
strength they would break your own bones! In the adult animal, bones can not grow much wider, but the walls
can thicken considerably. For example, section the bone in the arm of a professional tennis player and you will
see that it has thickened greatly. Look at the skeleton of a mediaeval archer and you will see that the arm bones
are greatly thickened, especially the left arm if he was right-handed (some longbows required 200 pounds (90
kg) of force to draw them, so archers needed big muscles!). Bones are also protective of course, and the skull is
the densest (not necessarily the thickest though!) bone in the body to protect your valuable brain! Again this is
the same principle that our tank builders employ.

Young trees have solid trunks, however, as many large tree species mature their trunks become hollow. As a
tree grows it adds cones of new wood to itself, so imagine a cone and then slipping a slightly larger cone on top
of it, do this once a year and that's pretty much how a tree trunk and its branches grow. Cut across a tree trunk
or branch and you will see a series of growth rings, one for each year that the tree has lived. The wood in the
centre is called the heartwood and is often a slightly different colour. This heartwood is the oldest part of the
trunk or branch and no longer serves to transport materials around the plant, it is more or less dead tissue
technically speaking. Eventually fungi get into this heartwood, especially if a wound exposes it to the outside
world, and attack the dead heartwood. These fungi do not usually attack the healthy living wood around the
outside. Over many years the fungi rot away the heartwood, leaving a large, old hollow tree trunk. This is far
from bad news for the tree, however, as it benefits in two ways. Firstly, although it has lost a little bit of
supporting wood from its centre, this is more than off-set by the fact that the tree is now much lighter and so has
far less weight to hold up, whilst having a wide trunk that is hard for the wind to bend and break - indeed the
wind may just whistles straight through it. Second, the decomposed heartwood has rotted down inside the trunk
to carpet the bottom with excellent compost and many trees exploit this by growing roots down the inside of their
trunks to tap this rich compost for nutrients; so the tree has recycled its old dead parts, with the help of fungi.

Well, tree surgeons are starting to wise up. They used to think that an old hollow tree was unstable and
dangerous and tended to cut them down. Of course extremely old trees may contain dead branches that are a
potential threat to passers by, should they fall, but all too often the surgeons remove much more healthy wood
than is needed. However, safety must come first in busy public places. Old pollards may also become unstable
and prone to collapse - nothing last forever! However, many trees can get centuries of healthy living out of their
old hollow bodies. Statistics have also verified that young, tall and slender trees are much more likely to be
thrown down by high winds than the old, thick hollow trees.

The race for the light

Trees have to compromise. A young tree could concentrate on growing a thick stem before it grows tall, but then
it would lose out to its competitors who take the risk and reach the light first and shade the shorter tree. Trees
are intelligent (in an engineering sense!), however, and they will invest more in tall thin stems when growing
close together as they compete for light. Neighbouring trees will also shelter them from the wind, so tall slender
trees can huddle together safely, indeed most trees are lost in high winds when having grown up tall and slim
they are then exposed by people cutting down their neighbours! Contrary, when a tree is growing alone and
senses the full force of the wind, then it will grow a shorter and thicker trunk. Trees will also grow thicker and
bush out more by producing lots of smaller branches if they are damaged by grazers or wood-cutters. Old
pollards that have been repeatedly pruned over many years are the thickest and stoutest trees of all and also
tend to live longer as they have spent more time growing and less time producing seed but compensate by living
longer to seed more often.

Hardwoods and softwoods

Most wood is quite hard really (!) but softwood is relatively less hard than hardwood. Softwoods include the
conifers, like pine trees, whilst hardwoods include the broad-leaved trees, such as the oak, beech and birch.
Actually, putting technical definitions of hardness aside, softwood is usually less dense, as the following table
illustrates (Balsa is an exception explained elsewhere).

Tree                                                Wood                        Density (kg per cubic metre)

Scots Pine
(
Pinus sylvestris)                           softwood                                         510

N. American Sequoia
(
Sequoia sempervirens)                softwood                                         420

Ebony
(
Diospyros)                                   hardwood                                  1000-1090

Oak
(
Quercus)                                     hardwood                                        720

Ironwood
(
Lignum vitae)                               hardwood                                      1230

Balsa
(
Ochroma lagopus)                       hardwood                                    100-250

This is one of the principle reasons why pine trees are fast growing - they invest in less dense and less strong
wood. However, conifer wood tends to quite elastic and less brittle, which enables the trees to sway in the wind
without snapping easily. The tallest trees are softwoods, like the Sequoia, in which the reduced density means
that the tree has proportionately less weight to support and so can grow taller.

The same engineering principles are used in the bones of mammals. Consider a typical long bone (such as the
human femur or thigh bone) found in the limbs of such animals, like that shown below:
This bone is a hollow tube, for the same reasons that the trunks of old trees are hollow - it increases the
resistance of the bone to bending and twisting. Only the bones of very large animals, like elephants, are solid
throughout. Otherwise, the central cavity contains bone marrow. The solid wall of the bone is made of very
hard compact bone. The actual cross-sectional area of compact bone depends upon the stresses placed upon
the bone, which is mostly due to the contraction of muscles, with the area being approximately proportional to
muscle strength or lean body mass (note lean not total). The thickness of the walls can increase massively with
exercise, especially weight-training. In general, the actual size of the bone seems to be genetically and
nutritionally determined, but the thickness of the walls depends upon the forces placed upon the bones in the
adult animal (and on the availability of calcium). If we take a slice through the bone, as shown above, and look
at one wedge of this bone, then we see a structure like that shown in the model below:
We see that the compact bone is made up of groups of concentric cylinders of bones, called Haversian units
(osteons)
, sandwiched between two larger hollow cylinders of bone. This type of compact bone is also called
Haversian bone. Each Haversian unit has a central canal or hollow that runs straight through the middle of it,
and usually contains one or two small blood vessels or microvessels (shown here in red) and sometimes
nerves and lymphatic vessels. In a large bone there are many more haversian units than shown in this
illustration! The cylinders are embedded in a cement substance. The Haversian cylinders are arranged like
columns in a building - they are aligned with the predominant compressive force that the bone experiences,
so that when they are loaded, the force tries to shorten them. (A compressive force is a squashing force).
Being about twice as strong as reinforced concrete, the bone cylinders are excellent at resisting
compression. The diagram below shows a section through some of the Haversian units, showing the hollow
central canals filled with blood vessels:
Bone consists in large part (70%) of a stony mineral component - actually small crystals of a mineral called
hydroxyapatite (a calcium phosphate - hence the requirement for calcium to build bones). However, stone
columns tend to crumble if they are stretched (placed under tension - a tensile force tries to pull something
apart by stretching it) or if a force tries to bend them. Indeed, if stone columns are not exactly straight, then
they will slowly crumble as one side slowly collapses - so stone is strong in compression, but weaker in tension
and especially weak to bending forces. Bone overcomes these limitations to a large degree in much the same
way as does reinforced concrete. The hydroxyapatite acts like the stony matrix of concrete, by resisting
compression. Dispersed within this matrix of hydroxyapatite are very strong rope-like protein fibres, made of
the protein
collagen, which is as strong as steel. Steel is not very good at resisting compression, as is stone,
as it tends to buckle, but it is good at resisting tension. In this way, reinforced concrete, with steel cables
embedded in a stony matrix, is good at resisting compression and tension. Bone is similar good at resisting
compression and tension, only more so than reinforced concrete, in fact bone is as strong as many of the
very light. The human skeleton
accounts for only about 20% of the body mass. Compact bone is similar to very hard plastic in weight and feel.

Bone also has one other tremendous advantage over steel, other alloys, and reinforced concrete - its
tremendous fatigue resistance. This is due in large part to crack-stopping mechanisms. Once a material
begins to fail and cracks, the cracks spread very easily. One way to stop cracks spreading is to have a
laminate or composite material. Once a crack encounters a new layer of material, it stops, unless the force
driving it is great enough to crack the new layer of material as well, as much of its energy is dissipated. In
short, getting cracks going in the first place takes a lot of energy, but it takes only a small amount of energy to
make existing cracks larger. Each separate layer of material has to be cracked for a composite or laminar
material to fail.
Bone is a composite material, it is made of collagen fibres embedded in a mineral matrix, and it
is laminate
- the various cylinders and sheets of bone constitute separate layers, each of which must be
cracked to break the bone. Bones can continue to function even when they are riddled with lots of tiny cracks
- they have tremendous fatigue resistance. Indeed, even if the body could not repair bone, it is estimated that
bones would last 20 years of normal use, a lot longer than most man-made materials subjected to the same
stresses!

This brings us on to another great advantage of bone - it is a living material which means that it can be
repaired (within reason)! Bone is also an intelligent material - it responds to the demands placed upon it by
strengthening itself as needed. Dispersed within the bone matrix are living cells. These cells are trapped
inside the bone, sitting inside tiny cavities, called
lacunae, but they are connected to one another via narrow
canals, called
canaliculi (the lacunae and canaliculi are not shown in the diagrams above). The cells
communicate with one another by sending electrical signals to one another via long narrow extensions (like
wires) that sit inside the canaliculi. Together they form a stress-sensing network. They detect the patterns of
stress being placed upon the bone and signal to other cells where the bone needs strengthening and
thickening, and where so much bone is not actually needed. In this way, bones can thicken and strengthen
over time, but they can also change shape. They are economical - they will only thicken where needed. All in
all, bone is a smart and highly sophisticated engineering material!
 Biomechanics
Muscle and bone - the musculoskeletal system

Different muscles for different tasks. We may cover muscles in detail in a future article, but here some useful parameters relating
to musculoskeletal mechanics will be given. The force generated by vertebrate and insect muscles is approximately constant at
about 3-10 kg per square cm (about 3 for the frog, 6-10 for humans, 3-7 in insects). The apparent strength of insects, many of
whom can easily carry 2-3 times their body weight (7-10 times for ants) is due mainly to scaling. If we keep proportions fixed, and
then double the length of a limb, so that the muscles are twice as long, then the cross-sectional area of the muscle will quadruple
and its volume and mass increase 8-fold. Since muscle strength is proportional to cross-sectional area (all other things being
equal) the larger limb, although 4-times stronger is 8-times as heavy, so its strength to weight ratio has decreased. Thus smaller
animals tend to have much higher strength to weight ratios. That said, there are also intrinsic differences in muscles themselves.
Some muscles have more
fast-fibres, meaning they can contract faster and also more strongly but fatigue more quickly than
slow-fibres which are built for endurance rather than speed or strength. Sprinters with the 'fast-gene' may have more fast-fibres,
although training can to some extent change fibre type (though perhaps not completely). However, slow-fibres are more useful for
a marathon runner. Fibre type differs also with muscle function. Muscles may be
phasic, contracting periodically to move the
body, others
tonic, maintaining constant tension at fixed length to maintain body posture. (Though most muscles will perform
both tasks to some degree). Fast-fibres are redder (dark meat) and usually thinner and respire mostly aerobically. Fast fibres are
whiter, thicker and respire mostly anaerobically (some sprinters hold their breath during a sprint, building up lactic acid and an
oxygen debt which they recover after the race). Different species, adapted for different tasks, will have different proportions of
fibre types. Cheetahs, for example, being adapted for speed, have a large proportion of fast-fibres.

Reading the scientific literature on biomechanics reveals some points which are often misunderstood or poorly explained. The
following list is a checklist of things to consider in comparative physiology and also a list of information that answers commonly
asked questions about musculoskeletal mechanics. Comparative physiology is difficult, since comparing very different body types
on any given task can be very unfair and misleading. However, science has gone a long way to dispel some of the common myths
that were once so prevalent, like the stories of snakes 'out-running' horses! (A snake may be able to strike faster than a horse
can move, over a metre or two, but no species of snake can 'outrun' a horse!). No doubt many similar myths and inaccuracies still
abound.

• The ratio of bone mass to muscle mass is essentially fixed throughout the animal kingdom, especially when considering
similar groups such as mammals. (See, however, the note about cross-sectional area below). The greatest forces acting on
bones are not due to body weight. The addition of fat appears to have no effect on the total amount of bone - bone mass is
proportional to lean body mass not total body mass. Comparisons of different populations of humans, for example, reveal
very little if any differences in bone mass between individuals of the same lean mass. When corrections for lean mass are
made, the same bone : body mass ratio is usually obtained. That said, bone mass is not a direct measure of an animal's
strength, since the efficiency of the various joint levers depends on the shape of the limb and the site of muscle attachment
- in some limbs a stronger muscle may generate less effective force.

• More specifically it is muscular strength that most strongly determines the amount of bone present. The muscles act as
levers, which means that they often have to work at mechanically awkward angles. When a powerlifter squats or deadlifts a
200 kg weight, the force of compression acting on the vertebrae of the spine may approach 10 000 N, equivalent to a 1000
kg mass squashing the spine! This is because the muscles have to pull with a force several times greater than the weight
they are lifting to compensate for awkward leverage. This means that muscle strength generally exerts a much greater
force on the skeleton than impacts from running or jumping. This is why powerlifting is the best activity for stimulating bone
remodelling and growth in adults. However, running, and sprinting in particular, appears to be the best way to develop the
hip bone, since most weightlifting movements do not place great stresses on the hip joints. Tennis players also have
massive bone development in their forearms, with massive thickening of the walls of the bone, such that it can become
almost solid in cross-section. Whether this is due to the increase in forearm muscle strength or impact, I am not certain.
Clearly, an animal's design often necessitates that muscles work at bad leverage - limbs require mobility and flexibility and
speed of movement. Consider the shoulder joint of humans, it is a ball-and-socket joint operated by relatively small
(deltoid) muscles. Such an arrangement is much weaker than the hinge joint of the elbow, but the shoulder has sacrificed
strength for range of movement, as it can be raised and rotated in almost any direction to any desired degree.

• Increasing muscle strength often necessitates an increase in bone strength. Considering the massive forces placed on
bones by contracting muscles, it is not surprising that when a person trains and increases their muscle strength say 2-3
fold (it could be more with steroid use!) then their bones must similarly increase in strength, otherwise their new muscles
would break the bones upon contracting! Such changes will be specific to those parts of the skeleton where the stresses
act - not all parts of a bone are stressed to the same degree when a muscle contracts.

• Differences in strength between two individuals in which their muscles are the same size does not necessarily imply a
difference in muscle biochemistry. Consider the biceps arm muscle of humans, for example. Simply increasing the distance
between the tendon attachment on the forearm and the pivot at the elbow joint by 50% (typically 2 cm) will increase lifting
strength by 50%, but at the cost of reducing speed. Of course muscle biochemistry is also a factor, if one person has more
fast-twitch muscle fibres, then their muscle will be stronger even if it has the same cross-sectional area. Thus, one
individual may have twice the strength of another, in any given movement, even if their muscles are the same size. When
all factors are considered, it is no wonder that differences in strength between different species of animals of the same size
(for a specific given task) may differ by as much as an order of magnitude, that is ten-fold (indeed such differences are
found even within the same species: a champion human powerlifter deadlifting close to 1000 lb is some 5-times as strong
as an average man (taking the average healthy man to be able to deadlift 200 lb), on this task, and ten-times as strong as
some healthy individuals!).

• Superman appears to be an impossibility. Evolution does not perfect organisms, it simply gives them what they need to
survive and reproduce, and it may be possible to breed super-athletes or make super-robots in future (and what is alien
life on other worlds capable of?), however, there are always fundamental engineering compromises to be made. Take the
example of the biceps muscle just given above - the tendon attachment which gives the lesser strength confers greater
speed of motion. Power, speed and strength are NOT equivalent. If one is, for example, comparing the ability of two
different mammalian species to jump, does one compare speed, strength or power output? The answer is not obvious. One
study compared jumping in humans and chimpanzees and found that the power output of the legs was equal between the
two species, although the chimpanzee with its shorter legs had half the muscle mass. We can not, however, conclude that
the chimpanzee muscles are intrinsically different without considering the effects of the different leverages. Also, it is not
clear that power output is the correct comparison or that it can even be obtained without considering the efficiency of the
levers involved. Different systems are designed to operate in different ways. Generally, however, longer limbs are faster
but weaker, shorter and thicker muscles are stronger but slower, and power output is proportional to muscle volume (so
long as the muscles are operating equivalent lever systems to enable comparable measurements of muscle power output).
Muscle response to training is often quite specific - they will develop greatest strength/power at the speed at which they are
trained. Training for speed, strength, endurance or power require different training regimens. One only has to look at the
diversity in body shapes among athletes to realise that each body type has its advantages and disadvantages. Another
good example is to compare millipedes  with centipedes. Millipedes have short, strong legs for plowing through obstacles,
whilst centipedes have longer, but relatively weaker legs (their leverage makes them weaker for an equivalent muscle
contractile force) for hunting.

• The size of joint surfaces is often used as an indicator of strength. However, one study on sheep found no such
correlation. This is not surprising, it is the shaft of long bones, with its hard compact bone, which bears the stresses of
contracting muscles, whilst the joints, with their low-density spongy bone, act primarily as shock-absorbers and their
development in athletes appears to correlate much more with impact stresses rather than to muscle strength. This also
illustrates that large masses of spongy bone can sometimes be more important to a bone's mechanical function than hard
bone. Think of how light a human vertebra is - that's because it consists largely of spongy bone which has a shock-
absorbing function (it resists periodic compression). Jaw bones also consist largely of a honeycomb structure, again for
shock absorption. The size of muscle attachment areas (tendon cross-sections) possibly does not correlate well to muscle
strength, since different fibre types may have different contractile strengths for a given fibre diameter and, as we have
seen, differences in muscle thickness, which must largely determine tendon thickness, only accounts for about 50% of the
strength variation seen in humans, and probably much less when different species are compared. Indeed, it is not obvious
exactly which mechanical requirements determine tendon cross-sectional area. The best indicator of strength appears to
be total cross-sectional area of bone, which, as we have seen, is  in a fixed ratio to lean body mass or perhaps more-so
muscle strength. However, in different shaped skeletons the stresses may be distributed differently, in which case simply
comparing a single cross-section could be misleading.

• Bipeds have different musculoskeletal mechanics. Humans have relatively light bones when compared to animals of the
same size. This is predominantly due to their bipedal mode of locomotion. The densest bone in the human body is the
skull, with a density of 2 g/cm3 (a relative density of 2 when compared to water) which is about the maximum for bone,
since it performs a vital protective system. The next densest are the femurs (thigh bones) with a density of around 1.75,
which is comparable to the limb bones of other large mammals (and will increase significantly with strength training). The
arm bones, which perform much less work, however, typically have a density of only about 1.35 (more in strength athletes
of course) and the vertebrae are extremely light as they consist almost entirely of spongy bone which facilitates their vital
shock-absorbing function as they hold the body upright and absorb impacts (they are, nevertheless, extremely strong).
The biped Tyrannosaurus rex took this development to a greater extreme, with a massive forearm reduction. Humans are
not particularly fast bipeds (a good human sprinter is about medium-speed as far as mammals go) but they do benefit from
the low energy-cost of bipedal locomotion. For example, humans have half the maximum mitochondrial respiratory capacity
of quadrupeds, since they only need to power about half their muscles at once when locomoting, so they need less oxygen.
Indeed, trained humans excel in being able to travel over long distances and humans are built more for endurance than
speed or strength, which tallies with the mode of hunting employed by some modern tribes-people, in which fast animals
are tracked over great distances, until the animal is too exhausted to resist. Minimising the weight of the upper body would
be advantageous for this mode of hunting, though powerful or fast arms would be needed to operate bows and spears
(remember speed, power and strength are not equivalent). Some groups of prehistoric humans, such as the Neanderthals,
appear instead to have been ambush hunters, a task which favours a stronger build not necessarily good for distance
running. Again, different designs suite different purposes.

• It has been said that the bones of prehistoric animals are often heavier and thicker than their living descendants. This is to
be expected since tougher bone fragments are more likely to survive over long periods of time - there is a sampling bias
which ought to mean that bone fragments from those individuals with heavier bones should be statistically more frequent in
the fossil record. Human remains often consist of leg and skull bones, because these are the densest bones in the human
body.

• The most powerful muscles in the animal kingdom, in terms of Watts of power consumed, are the flight muscles of
hummingbirds and certain insects, which have equivalent values. Older reports that insect flight muscles were as powerful,
weight-for-weight, as aircraft engines were due to a miscalculation!. However, it is worth noting that the (minimum) energy
cost, and hence efficiency, of locomotion in animals exceeds that of most human-made machines (though the latter are
improving and reaching comparable levels). Swimming in fish is the most efficient, followed by flight in birds, bats and
insects, followed by walking/running and jumping. Movement on land is difficult and consequently the least efficient of these
three modes of animal locomotion. Efficient automobiles like the Volkswagen compare favourably with running animals,
whilst the ever-efficient bicycle is almost efficient as is swimming in fish, though as anyone who as ever cycled knows,
cycling uphill is very inefficient (and wheels are of much less use over very rugged terrain)! Snake locomotion appears to
be especially energy-efficient, being comparable to the energy-efficiency of locomotion in flying animals. Similarly, jumping
in kangaroos is also very efficient.

• This brings me to a final FAQ - why don't living organisms have wheels? First of all, some do in fact use the principle of the
wheel. It is used, for example, in the electric motors of bacterial flagella, and some protozoa with spherical bodies move by
rolling themselves along! Wheels may be good on smooth flat roads, but they cope much less well with rugged
environments and are not very good for climbing trees and so would be of limited use in the natural environments in which
most organisms compete. Whether future vehicles for use on rugged planets in space exploration continue to use wheels
(or caterpillar tracks) or use robotic legs instead is food for thought!

The cross-sectional area of bone is a misleading measure of bone strength

If bones were designed to withstand static loading only then they would likely be narrow solid rods; narrow in order to reduce their
self-loading. However, the main forces acting on bones, during normal function, is most likely that due to muscle contraction.
Muscles often act at a leverage disadvantage (compromising strength of the joint for speed or range of movement) which means
they typically exert far greater forces on bones than the loads they are lifting. (Basic lever calculations show this to be the case).
This means that bones are subject to bending forces. This explains why the bones of many animals are hollow: what matters in
dynamic loading is not the cross-sectional area of the bone but rather the modulus of bending, which depends also on how far
the bone material is from the central axis. A hollow bone of lower cross-sectional area can achieve greater strength, in terms of
resistance to bending, than a more solid bone with a higher cross-sectional area but narrow outer diameter. It is harder to bend a
wide hollow pipe than a narrow solid one. However, there has to be a compromise. As the same amount of material is distributed
further from the central axis, by making the hollow cavity wider, the wall naturally becomes thinner. If the wall becomes too thin
then it is prone to buckling, or easily damaged by asymmetrical loading or by side blows.

Bone density can also be a misleading measure of bone strength

Generally speaking, denser materials tend to be stronger; this is our common experience of objects. However, sometimes a
lighter honeycomb structure can do the job better. This is especially true if a bone needs to absorb shocks. Human vertebrae are
extremely light, since they are made almost entirely of spongy bone which acts as an efficient shock absorber. The tiny
honeycomb struts can bend and give slightly, whereas a more solid and denser bone might shatter due to being too brittle. It is
difficult to break a rubber ball by throwing it! Similarly, the bones of the human skull usually consist of two solid dense sheets
separated by a layer of spongy bone. This sandwich structure combines the need for denseness to resist excessive deformation
which might damage the brain, with some sponginess to reduce the brittleness of the bone. This theoretically makes the skull
more resilient to compressive forces and to blows. Similarly, the mandible has a rather spongy structure to take the impacts of
chewing. Interestingly, another apparent myth is that the small human mandible is relatively weak. Measurements refute this and
suggest that the human mandible, which is small since the biting surface is small compared to the size of the cranium, is
nevertheless a very strong joint: according to some published measurements the pressure and total bite force exerted is
comparable to that of other mammals, including apes. The reduction in relative mandible surface reflects several factors: the jaw
is small compared to the large cranium; a large biting surface is needed in animals which chew tough vegetable matter, which
humans seldom do and is reduced in carnivores and omnivores; this might better balance the skull for more efficient bipedal
locomotion (in the absence of a counterbalancing tail); finally, a small reduction which may contribute to problems of overcrowded
teeth is apparently correlated with urbanisation and is due to some environmental factor, possibly pollution clogging the airways
leading to more mouth breathing, or perhaps some other factor of city life.

The size of bony attachments for muscles may also be misleading

Clearly, large animals with powerful locomotory muscles have large bony crests and ridges to support the attachment of these
muscles to the skeleton. However, one study in sheep showed no correlation between the size of bony attachments and physical
strength; perhaps interspecies differences are small and may be due to other factors. This may depend to some extent on how
the skeleton develops. Human bodybuilders have enormous bony ridges for muscle attachment: this supports the sudden
expansion in muscle later in life by increasing both the larger surface area needed for tendon attachment and the bone's
modulus of bending in the most stressed direction, and so may be equivalent to having a larger diameter cylinder with muscle
attached over a larger, but less ridged, surface. Another point to bear in mind is that in life, muscle attachment sites are often
largely cartilaginous (fibrocartilage). Continual use of the muscles may stimulate some of this cartilage to ossify, which may vary
with individual and also on age and the frequency of exercise as much as on muscle strength.

All in all, existing analyses of animal skeletons are, in my opinion, rather crude and lacking computational rigour. Nevertheless,
the adaptability of skeletons and their evolution is a fascinating area of biology. Bone is a remarkable material, combining
unusual strength with lightness and extreme durability and it is a living tissue capable of sensing and responding to the demands
placed upon it.
Article updated: 14/8/2015