Expert answer:biomedical (biomechanics)
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BME 201: Foundations of BME
force exerted by their entire body on the
Biomechanics
ground (~900 N)
Text: Saltzman Ch. 10
•
Some definitions
o Statics – study of bodies at __________
Introduction
•
or when forces are in equilibrium.
o Dynamics – study of bodies under action
The combination of __________________
of _________________ forces.
and muscles (connected by ligaments,
tendons, and ______________________)
•
•
The forces generated statically or
provide mechanical support for the human
dynamically can lead to ________________
body (so you can stand up). They also
(change of shape) of biologic materials,
generate the ________________ necessary
depending on the mechanical
to put the body into motion.
__________________ of those materials.
As an introduction to the field of
•
We can quantify how much deformation
biomechanics (the study of the human body
occurs for a material when loaded by using
under static or _____________________
Young’s ________________ (also called
conditions), we will introduce some basic
elastic modulus).
concepts regarding mechanical properties
of materials.
Mechanical properties of materials
•
where
σ = applied stress (F/A)
Biologics (bones, muscles, and the _______
E = Young’s modulus
they consist of) are mechanical objects.
ε = strain (length change for
Thus they can be analyzed with similar
methods as ______-biologics (e.g., cement).
•
σ = Eε
Biological materials are constantly exposed
to ______________. For example, the
standing position produces forces (patient
mass x acceleration due to _____________)
on the bones of the leg. For a 200 lb male,
the force on the head of the ____________
is ~2,000 N. This is around _____ times the
σ
σf
σy
the material,
∆
)
x
P
E
εy
ε
o Since σ is N/m2 (Pa), and ε is unitless,
the units of E are ________.
(aka elastic limit, εy). The stress value at
o Here are some typical values for Young’s
modulus for a variety of materials,
which this occurs is called the ___________
including ____________________ and
_____________ (σy). Above these values,
non-biologics:
the material is said to become plastically
_____________________, and it cannot
Material
E (MPa)
Steel
200,000
Titanium
107,000
Aluminum
70,000
experience without ________________
Concrete
25,000
(breaking) is called the ____________ stress
Bone (long)
15,000-30,000
Wood
11,000
(aka maximum stress, σf).
Poly(methyl methacrylate)
2,000-3,000
Tendon
1,000-2,000
Poly(tetrafluoroethylene)
400-600
Bone (vertebrae)
100-300
Articular cartilage
1-10
Rubber
2.8
Artery
0.1-4
Skin
0.1-2
Brain tissue (grey matter)
0.005
•
Note that the values of E are only valid for a
limited ____________. In other words,
return to its original state when the load is
removed.
•
•
The largest stress that a material can
To summarize, if you load a material below
its εy (e.g., point ______ on the diagram
below), it should return to its original shape
after the load is removed. And the
relaxation will follow the ____________ line
on the stress-strain curve.
•
If you load beyond εy (e.g., point _______),
the relaxation will generally occur along a
line _________________ to the initial
deformation (same slope = E)
going from 0 to A and back to 0
σ
there is a ____________ (called the
B
proportionality limit, P) for each material
A
above which the relationship between
x
stress and strain is no longer ___________.
•
Most materials _______________, or
become altered in an irreversible way, if
they are deformed too much. This value is
called the __________________________
0
ε
going from 0 to B and back to 0
•
σ
Note that elongation and relaxation of an
_________________ material has no net
B
A
energy cost…all of the energy stored during
x
the deformation is ____________________.
You lose energy when deformation goes
beyond the elastic ______________.
ε
0
•
Consider the importance of energy storage
for elastic ______________ structures such
When a material is stressed, ____________
as the aorta. During systole, the aorta
energy (a.k.a. strain energy) is added to the
____________ energy as it stretches out
material
due to increased pressure. During diastole,
1
=
2
that energy is recovered as the aorta
______________ to its original size.
where Uo is the potential energy stored per
unit _________________ in the deformed
material. Note the units here: σ is Pa (which
•
Our discussion thus far has treated
materials as being fairly ____________. For
example, when an ideal elastic material is
exposed to an applied load it will
is 3 ) and ε is unitless (_____).
____________ immediately to a fixed strain
The amount of _______________ energy
and stay that way indefinitely. Many
can thus be determined by finding the
materials exhibit _____________________,
_______ under the stress-strain curve.
which means over time they will continue
σ
to ___________ in response to the load
(the arrows in the graphs below indicate
brittle
when the load is applied).
stiff
S
0
•
•
compliant
Ideal elastic material
ε
So for a given stress, ______, we see that
the _________________ material stores
more energy than the __________ or brittle
materials.
Length
•
t
o Bone has _________________ structure
that spans several length scales
Viscoelastic material
1 nm-1 μm: collagen molecules
Length
assemble into ____________ and
then fibers, forms extracellular
matrix (_________) of bone
t
10 μm-100 μm: ________________
and phosphate ions form
hydroxyapatite ________________,
Ca3(PO4)2, which is the mineral
Mechanical properties of tissues and organs
•
Bone
phase of bone. _________________
o Composed of ________________ phase
(primary bone cells) sit within
(60%), organic collagen-rich __________
pockets called _________________,
(30%), and water (10%). This mixture of
and small passageways through the
soft and hard phases provides some
matrix (__________________)
elasticity and some ________________.
connect the lacunae to blood vessels
for nutrient supply and waste
o Two primary architectures exist. Note
removal.
that most bones have a _____________
of the two.
Compact/cortical
•
•
____________________ layers
around a central (or Haversian)
of bones, denser and more rigid
canal, creating a structure called an
Prominent in __________ bones
______________. The central canal
such as femur and humerus
houses the primary blood supply to
Typically found in interior of
bones, less _____________,
mechanically strong but
lightweight
•
200 μm: osteocytes are arranged in
Typically found near __________
___________/cancellous/trabecular
•
Prominent in rib cage and
__________
the bone.
o Due to the microscopic
__________________ arrangement of
•
Soft connective tissues
o Main functions in support of organs:
bone, its mechanical properties are
Structural _________________
_____________________. In other
Protection from damage
words, when you apply loads in
o Examples
different ______________________ you
Articular ___________________
get different results. This property is
Tendons
called _______________________,
Ligaments
whereas most engineered materials
______________
display _____________________
Blood vessels
(mechanical properties are not
directional).
o Mechanical properties
o Note that bones display high strength to
(note the low Young’s modulus in
weight ratio (similar to ______________
patterns)
our table above)
o Osteoporosis
Often display __________________
properties since material contains
The bones of the skeletal system
fibers (often collagen and elastin)
become ________________ (and
embedded in ______________
weaker) as part of the normal aging
process.
Flexible and __________________
The reduction begins around age 35,
E.g., tensile deformation
σ
with females losing ~____% of
skeletal mass per decade and males
losing ~____%.
When the reduction in bone mass is
I
sufficient to affect normal function,
the condition is called
•
II
III
ε
Phase I – tissue behaves
________________________.
elastically, little resistance to
Results include fracture of bones
stretching since fibers are not
(e.g., hip) when exposed to
_____________________.
___________________ that would
have been ok at a younger age.
•
Phase II – fibers become
generally straightened in
direction of strain, increasing
•
___________________
chest, it would ________________ due
Phase III – fibers are aligned in
to its elastic recoil, just like a balloon.
direction of strain, providing
But when it is in the chest, the chest
________________ to stretching
wall provides an elastic recoil that is
o Arthroscopic surgery
o If the lung were removed from the
equal and _________________ to the
Cartilages are important
lung’s recoil. In other words, the chest
components of articulations
wall recoil ______________ outward,
(__________) by allowing bones to
increasing the volume of the thorax.
glide past each other with minimal
___________________.
However, they are ______________,
thus they heal poorly when
damaged. Often when damage
occurs, ______________ is required
to repair the injury.
Arthroscopic surgery (arthro = joint,
scopic = view) is a minimally invasive
surgery using small ______________
and a camera about the size of a
pencil. The surgeon can repair or
______________ the damaged
tissue (e.g., removal or repair of torn
pieces of articular cartilage in knee)
•
o The lung and chest wall are separated
by thin layer of fluid called the
_____________________ fluid. This
fluid (~1-2 mL) is much smaller than the
volume of the lungs (~4 L), and its role is
to provide _______________________.
Due to the opposing elastic recoils of
the lung and chest wall, the pressure in
Lungs and respiratory function
the intrapleural space is _____________
o Each lung behaves something like a
(-3 mmHg at rest).
__________________. The elasticity of
o If there is a puncture wound in the chest
a balloon’s wall will force air out
wall, the intrapleural space is
through any opening. To remain
_________________ to atmospheric
inflated, the balloon must be _________
pressure. Thus the elastic recoil of the
(no opening for air to exit) or subjected
lung is no longer opposed by the chest
to a __________ that opposes deflation.
wall, causing lung _________________.
This condition is called pneumothorax,
Cell type
Size (μm)
Shape
and can be caused by _______________
RBC
7.5 x 3
Platelet
2 x 0.2
Neutrophil
Lymphocyte
Monocyte
8
7.5
9.1
Biconcave
disc
Biconcave
dis
Sphere
Sphere
Sphere
such as knife stabbings or gunshot
wounds. If only a small portion of lung is
collapsed, it may heal on its own, but
larger injuries can require a chest
_____________ (to remove excess air)
~0.007
<0.002
<0.001
<0.0005
o The __________________ properties of
or surgery.
cells have been measured by a variety of
techniques, including micropipette
Cellular Mechanics
•
Fraction in
blood
~0.997
____________________ and atomic
Cells
force microscopy. Here are some
o Cells are complex objects whose
typical values for Young’s Modulus.
___________________ structure
Note how ____________ these values
determines their ability to deform.
are in comparison to our earlier table of
o Red blood cells (_________) are slightly
Young’s Moduli.
larger than capillaries, thus they must
_________________ in order to pass
Cell type
Fibroblast
Endothelial cell
(spread on surface)
Endothelial cell (in
suspension)
through during circulation.
o White blood cells (WBCs) are much
larger and __________ deformable.
Their mechanical properties are
E (MPa)
1.6x10-3
1.6x10-4
7.5x10-5
important for determining their
________________. For example,
reduced deformability of WBCs is
•
Cytoskeleton
o The cytoskeleton is the internal cell
associated with diseases such as
structure that provides ____________
____________________ and diabetes.
and coordinates cell division and
There are many examples of WBCs
movement.
including neutrophils, lymphocytes, and
________________________.
o 3 important proteins make up the
cytoskeleton
_____________ microfilaments
•
Flexible (E = ___________ MPa),
but unable to withstand tensile
forces
•
o Cartilage is also known to respond to
Microtubules
Stiffer (E = ____________ MPa),
mechanical forces. Chondrocytes
but still have poor tensile
(_________ within cartilage) reduce
strength
their production of ECM proteins when
exposed to ___________ compressive
Intermediate filaments
•
More flexible than actin (E =
forces. When exposed to dynamic
___________ MPa), stronger
forces, the opposite occurs (the ECM
under tension
protein production is ______________).
o The local mechanical properties of the
cell can be controlled by ____________
Outlook
(and disassembly) of cytoskeleton
•
of biomechanics. When you take
proteins into _________________
•
This was an introductory look into the world
Effects of mechanical forces on cells
Biomechanics I (BME 351) and
o Large scale ______________ in the body
Biomechanics II (BME 451), you’ll obviously
can be produced at the microscopic,
go much more in __________ into these
cellular level. For example, muscle
and other topics.
contraction involves forces generated
•
BME 351 – musculoskeletal anatomy, force
by _____________________ machinery
and moment vectors, statics of joints, stress
within skeletal muscles.
and strain, ____________ and compression,
torsion, bending, combined loading, and
o When external mechanical forces are
applied to cells, physiological
material properties of biological tissues
___________________ can change. For
such as ___________, tendons, ligaments,
example, endothelial cells lining the
and cartilage.
lumen of blood vessels will __________
•
BME 451 – musculoskeletal dynamics,
in the direction of external fluid flow (in
kinematics, and kinetics of rigid bodies, and
response to ____________ forces from
_______________________.
fluid). Their intracellular activity (e.g.,
enzyme activity) can also be
_______________ by mechanical forces,
allowing blood vessels to constrict,
______________, or remodel as
needed.
BME 201
Found. of BME
Fall 2017
HW #2
Due Friday, October 20
Name:
1. You may work together but each person should turn in his/her own work in his/her own
handwriting.
Problems
#1
(25 pts) _____________
#2
(20 pts) _____________
/45
Total: _______________
1. Comparing materials using measured data
[25 pts]
The table below shows data collected for two materials: poly(ethylene) and poly
(tetrafluoroethylene).
Strain
Stress (MPa)
Poly(ethylene)
Poly(tetrafluoroethylene)
20
0.022
0.033
50
0.056
0.083
100
0.111
0.167
250
0.278
0.417
400
0.444
0.667
550
0.611
0.917
800
0.941
1.510
950
1.167
1.950
1100
1.667
2.433
1150
2.111
3.011
1170
2.412
3.502
1185
2.712
4.000
A. Plot the stress-strain curves for both materials. Then calculate the Young’s Modulus for each
material. (10 pts)
Hints: Make sure strain is the x-axis and stress is y-axis for your plot. Show both
materials on the same plot to allow for easy comparison. Calculate E for each material
by using the linear region of each plot.
B. Using the graph from part A, for each material determine the approximate strain energy before
plastic deformation begins. (10 pts)
Hint: Display Uo calculations with units MJ/m3.
C. Compare the Young’s Moduli and strain energies for both materials. What do these calculations
tells us about the properties of these materials? (5 pts)
Hint: Confirm with your notes that the values in A and B make sense relatively speaking.
2. Strain Energy
[20 pts]
A. Some articular cartilage (E = 10 MPa) is deformed to a strain of 0.1%. What strain energy is
required to achieve this? Display answer in J/m3. (10 pts)
B. If a long bone (E = 30,000 MPa) is exposed to a stress of 15 MPa, how much strain energy is
stored in the bone? Display answer in kJ/m3. (10 pts)
...
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