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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.
What about tree trunks?
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.
Click here to see how hollow tree trunks benefit others.
So what about tree surgeons?
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.
What about animals?
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:
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.
What about tree trunks?
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.
Click here to see how hollow tree trunks benefit others.
So what about tree surgeons?
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.
What about animals?
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:
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:
(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
toughest metal alloys. Bone also has the additional advantage of being 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!
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
toughest metal alloys. Bone also has the additional advantage of being 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!
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