Transcript TISSUE ENGINEERING: FUNDAMENTALS AND TOOLS 125:492

BME MEASUREMENT AND
ANALYSIS LABORATORY
125:315
SOFT TISSUE MECHANICS
DAVID SHREIBER
WHY STUDY SOFT TISSUE MECHANICS?
Tendon
http://www.gwc.maricopa.edu/class/bio201/histo
Blood Vessel
Elastic Cartilage
http://www.lumen.luc.edu/lumen
MANY BIOLOGICAL
TISSUES HAVE
EVOLVED TO
PERFORM SPECIFIC
MECHANICAL
FUNCTIONS.
SOMETIMES, THESE
TISSUES FAIL
(PHYSICALLY
AND/OR
FUNCTIONALLY).
WHY IS IT IMPORTANT TO UNDERSTAND THE
MECHANICAL FUNCTION OF TISSUES?
Obviously, prior to implantation, a replacement must be able to meet the
structural requirements necessary to perform its mechanical
function.
– Make sure bioartificial ligament is strong enough to support loads
In many, if not all, cases you must be careful not to “exceed” the
requirements.
– In typical engineering mechanics, we include “safety factors” that
overestimate the structural integrity of the device, typically by at least a
factor of 2.5-3.
– This may not be appropriate for bioengineering bioartificial tissues.
– What might happen if we implanted a ligament that was 3X as stiff as a
normal ligament?
– Can you think of other examples where the “correct” mechanical
properties (not too weak/compliant, not too strong/stiff) are necessary to
ensure long term function?
IN VIVO FLOW PREDICTIONS
What happens to blood flow if a vessel’s mechanical
properties change, say from intimal hyperplasia?
MECHANOTRANSDUCTION
MECHANOSTRUCUTRAL
PROPERTIES
CELLULAR
PHYSIOLOGY
You must consider the cellular response to abnormal mechanical conditions, not just
what you might think would be the “worst case scenario.”
CRITICAL QUESTIONS
What kinds of loads will the tissue experience in vivo?
What dictates the mechanical response of the tissue?
What happens if the tissue/cells experience abnormal loading
conditions?
CRITICAL SCIENCE
Biological: Kinesiology, cell biology
Engineering: Statics, strength of materials, dynamics
WHAT MAKES BIOLOGICAL MATERIALS
DIFFERENT THAN “TRADITIONAL”
ENGINEERING MATERIALS?
HOW DO WE DESCRIBE THE MECHANICAL
PROPERTIES OF A “TYPICAL” MATERIAL?
HOW DO WE DESCRIBE THE MECHANICAL
PROPERTIES OF A “TYPICAL” MATERIAL?
Generally, for most materials you have encountered as engineers, stress is linearly
proportional to strain.
Furthermore, the time scale of loading doesn’t matter….you can bend aluminum quickly or
slowly and the stiffness will be the same.
TYPICAL BIOLOGICAL RESPONSE
MOST BIOLOGICAL TISSUES DEMONSTRATE A NON-LINEAR STRESS-STRAIN
CURVE.
MOST OF THESE CURVES SHOW “STRAIN-STIFFENING” – IE THE MATERIAL IS
STIFFER AT HIGHER STRAINS THAN AT LOWER STRAINS, ALTHOUGH SOME
SHOW THE OPPOSITE (“STRAIN-SOFTENING”).
WHY IS THIS SO?
NON-LINEAR ELASTICITY
REASON #1:
A tissue is not a continuum, but
rather a composite of many
fibers. If you look at the
structural heirarchy of the
tendon, for instance, it consists
of collagen fibers, bundled into
microfibrils, bundled into
subfibrils, bundled into fibrils,
into fascicles, and finally into a
tendon. These subunits may
have different “spring constants”
and may experience loads
differently because of their
orientation and their crimp.
http://hodad.bioen.utah.edu/~weiss/classes/bioen5201_f00/lecture/092700/sld016.htm
FIBERS ARE STRONG IN TENSION
As a tissue is stretched, the fibers
orient in the direction of stretch,
and they become “straight”.
Think of a fiber as a string. If a
string is wavy (crimped), it is very
easy to pull it. The string has
very little resistance to tension
until it is perfectly straight.
Schematic of stress-strain relationship and fiber orientation in skin.
What if you had a bundle of
strings, and different ones
became “straight” at different
strains? As you increase strain,
more and more strings straighten,
and your effective stiffness
increases!
CRIMP AND ELASTICITY
If each fiber is linearly elastic (ie Stress =
strain x stiffness), then when all of the fibers
are straight, the effective stiffness of the
tissue should remain constant, and the
slope of the stress-strain curve should be
linear.
Roughly linear
MULTIPLE COMPONENTS
REASON #2:
Biological tissues are composites
of different kinds of structuralsupporting fibers.
The most common ones are
collagen and elastin.
They have different mechanical
properties.
Elastin is generally believed to
contribute to the low-strain behavior
of tissues, and collagen to the highstrain behavior.
TIME-DEPENDENT BEHAVIOR
Strain rate 1
Strain rate 2
Strain rate 3
Strain rate 1 > strain rate 2 > strain rate 3
WHY DOES THIS HAPPEN?
Tissues are not only composites
of “elastic” structures (if we
assume that collagen and elastin
are, indeed, elastic), but also of
highly charged molecules called
proteoglycans that attract water
and maintain tissue hydration.
The fluid component of tissues
adds complexity to the
mechanical response.
HOW CAN YOU DESCRIBE THE MECHANICAL
PROPERTIES OF BIOLOGICAL TISSUES?
CONSTITUTIVE RELATIONSHIPS
In mechanics, a “law” that describes the fundamental
response of a class of materials.
Each material in a class may have unique properties,
but they all follow the same law.
Example: Stress = Young’s Modulus x strain
This is a constitutive law that describes homogeneous,
isotropic, linear elastic materials. Different materials
materials of this type have different values for E, but
they all follow the same constitutive law.
So what are good constitutive laws for biological tissues?
ELASTICITY
• A material is elastic if you can recover all of the
energy you put into the material. In other words, if
you stretch an elastic material, it will return to its
underformed length upon removal of the load.
LINEAR ELASTIC VS. HYPERELASTIC
Both of these materials are (potentially) elastic…however, one
is linearly elastic (red line), where stress is proportional to
strain, and the other is non-linearly elastic, and more
specifically hyperelastic (black line).
To quantify a linearly elastic material is easy….calculate the
slope of the line, and this = the Elastic Modulus.
To quantify a non-linearly elastic material is not so easy…
One way is to develop a more complicated constitutive law:
Neo-hookean StressStrain law

  2C  12 

1

1 
Another is to caclulate the slope of the “linear” region, and
approximate the strain at which this region begins.
TIME-DEPENDENT MECHANICAL BEHAVIOR
• As discussed previously, all biological tissues
demonstrate time-dependent mechanical behavior
• This allows the tissue to optimally respond to the
dynamics of mechanical loading
• What if your cartilage was just like an elastic piece of
rubber?
VISCOELASTICITY
• Viscoelasticity describes the mechanical response of
tissues that both store and dissipate energy.
• Think of these materials as part viscous liquid and
part elastic solid.
– The viscous part dissipates energy, while the elastic part
stores it.
ELASTIC MODEL
The behavior of viscoelastic materials in uni-axial stress closely resembles that of models built from
discrete elastic and viscous elements.


“Elastic” Spring
e = extension (strain)
Typically with springs, we relate force, F to extension, d through a “spring constant”, k.
We can also think of the spring representative of a material (like a bar).


Normally, F=kd
But in terms of material constants, =Ee
Where E is stiffness or Young’s modulus.
e = extension (strain)
VISCOUS MODEL
The behavior of viscoelastic materials in uni-axial stress closely resembles that of models built from
discrete elastic and viscous elements.


“Fluid” Element =“Viscous”
Dashpot (or damper)
e = extension (strain)
Viscous elements respond to the rate of loading:
The stronger the force, the faster the piston will move; or
The faster the extension, the more force (or stress) is generated.
Recall fluid shear stress:
  
For theselumped parametermodels, we will write:
  e
LUMPED PARAMETER MODELS
• We now have descriptions of elastic and viscous
elements
• Behavior of simple, linear, viscoelastic materials can
be defined by combining these elements in different
configurations.
STANDARD VISCOELASTIC TESTS
Stress Relaxation:
Stress
Deformation
Creep:
Load
Deformation
Time
MAXWELL FLUID
1
2
A MAXWELL FLUID IS A SPRING AND DASHPOT
IN SERIES
MAXWELL FLUID….WHAT DOES THE
RESPONSE LOOK LIKE?
Think about it intuitively….what happens at t=0 when we “instantaneously” apply a stress, 0?
1
2
STANDARD VISCOELASTIC TESTS
Stress Relaxation:
Stress
Deformation
Creep:
Load
Deformation
Time
MAXWELL FLUID….WHAT DOES THE
RESPONSE LOOK LIKE?
3
2.5
2
strain
1.5
stress
1
0.5
0
0
10
Stress = constant
20
30
40
50
Strain = constant
60
70
KELVIN SOLID
1
2
A KELVIN SOLID IS A SPRING AND DASHPOT IN
SERIES
KELVIN SOLID…..WHAT DOES THE
RESPONSE LOOK LIKE?
1
2
Subject this to same load history as before…
STANDARD VISCOELASTIC TESTS
Stress Relaxation:
Stress
Deformation
Creep:
Load
Deformation
Time
KELVIN SOLID…..WHAT DOES THE
RESPONSE LOOK LIKE?
12
10
8
stress
strain
6
4
2
0
0
2
4
6
8
10
12
STANDARD LINEAR SOLID
2
1
3
WHAT DOES THE RESPONSE LOOK LIKE?
STANDARD VISCOELASTIC TESTS
Stress Relaxation:
Stress
Deformation
Creep:
Load
Deformation
Time
STANDARD LINEAR SOLID …..WHAT
DOES THE RESPONSE LOOK LIKE?
12
10
8
6
stress
strain
4
2
0
0
10
20
30
40
50
60
THIS WEEK’S LAB
• Testing of samples in uniaxial tension
• Compare mechanical properties of 2 kinds of
“material”
– Stretch 2 types of samples (rubber and chicken
skin) at different rates
• Make sure to take careful measurements of
the dimensions of the samples! (Why??)
• Plot Stress vs. Strain for different materials
• Quantify modulus (moduli?) and compare
WHAT REALLY HAPPENS
1.
2.
3.
You use the Instron to apply a displacement to one end of the sample. The
computer records how far the grip (and thus one end of the sample) has
moved.
The other end of the sample is fixed (doesn’t move)and is attached in series to
a force transducer that converts force to voltage that can be measured with an
analog-to-digital converted (somewhere in the instrumentation). The force is
also recorded by the computer.
You know how much the sample has deformed (the displacement). If you
measure the gage length of the sample, then you can calculate the
engineering strain:
L Changein length
e

L0
OriginalLength
4.
You know how much force is produced in the material to resist that
deformation. If you know the cross-sectional area of the sample, you can
calculate the engineering stress:
Force

Area
HOW TO QUANTIFY
• STRESS-STRAIN PLOTS
– If linear elastic, the slope
– If non-linear elastic….depends on your ambition
– Basically you need a consistent method of evaluating
mechanical properties to compare one case to the next.
STRESS-STRAIN PLOTS
• We are running load-deflection experiments, not
instantaneous creep or stress-relaxation tests
(although you can run these if you like and there is
extra time! Could be educational (but who would
want that).
Slow displacement
Fast displacement
SAMPLE DIMENSIONS
Sample viewed from side
Gage Length, L0
Length
Width
Area = length x width
BONUS EXPTS WITH THIS WEEK’S LAB
If time allows….or you are interested….
Additional experiments:
1) Crosslink the chicken skin with a formaldehyde
solution or UV light and examine mechanical
response
2) Compare the effect of orientation on the
stress-strain plot in rubber and chicken
samples:
2
1
Vs.
2
1