The role of elastin in arterial mechanics Structure function relationships in soft tissues

1
The role of elastin in arterial
mechanicsStructure function relationships in
soft tissues

• Namrata Gundiah
• University of California, San Francisco

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Introduction
3
Arterial microstructure
4
Arterial microstructure
Intima Endothelial cells
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Arterial microstructure
Media Smooth muscle cells, collagen elastin
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Arterial microstructure
Adventitia Collagen fibers
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Complex tissue architecture
Massons trichrome Collagen blue
Verhoeffs Elastic Elastin black
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Diseases affecting arterial mechanics

• Atherosclerosis
• Abdominal Aortic Aneurysms
• Aortic Dissections
• Supravalvular aortic stenosis
• Williams syndrome
• Marfans syndrome
• Cutis laxa
• etc.

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Mechanical properties of arteries
Roach, M.R. et al, Can. J. Biochem. Physiol.,
35 181-190 (1957).
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How do you study the mechanics of materials?
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Arterial Behavior

• Arteries are composite structures
• Rubbery protein elastin and high strength
  collagen
• Nonlinear elastic structures undergoing large
  deformations
• Anisotropic

• Viscoelastic

• Pseudoelastic

• How is stress related to strain Constitutive
  equations

Fung, Y.C. (1979)
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Continuum mechanical framework
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Biaxial test Preliminaries

• Material is sufficiently thin such that plane
  stress exists in samples and top and bottom of
  sample is traction free
• Kinematics Deformations are homogeneous
• Assuming incompressibility
• Equilibrium
• Constitutive law 1. Using tissue compressibility
  and symmetry
• 2. Phenomenological model

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Measurement of tissue mechanicsBiaxial stretcher
design
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Data from biaxial experiment
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1. Phenomenological model

• Fung strain energy function

1 circ 2 long Eij Green strain cij material
parameters
Cauchy stresses
Best fit parameters obtained using
Levenberg-Marquardt algorithm
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2. Function using material symmetry

• Define strain invariants
• For isotropic and incompressible material
• Need to know symmetry in the underlying
  microstructure.
• Transverse isotropy 5 parameters
• Orthotropy 9 parameters

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Elastin Isolation

• Goal to completely remove collagen,
  proteoglycans and other contaminants
• Hot alkali treatment
• Repeated autoclaving followed by extraction with
  6 mol/L guanidine hydrochloride

1 Lansing. (1952) 2 Gosline. JM (1996).
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Elastin architecture

• Axially oriented fibers towards intima and
  adventitia
• Circumferential elastin fibers in media.

N. Gundiah et al, J. Biomech (2007)
20
Histology Results

• Circumferential sections
• Elastin fibers in concentric circles in the media
• Transverse sections
• Elastin in adventitia and intima is
  axially-oriented.
• Elastin in media is circumferentially-oriented.
• Elastin microstructure in porcine arteries can be
  described using orthotropic symmetry

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Orthotropic material

• Assume orthotropic

,
f90 for orthogonal fiber families
CFTF is the right Cauchy Green tensor
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Theoretical considerations

• Deformation homogeneous
• li are the stretches in the three directions
• Unit vectors
• Strain energy function for arterial elastin
  networks
• Define subclass

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Rivlin Saunders protocol

• Perform planar biaxial experiments keeping I1
  constant and get dependence of W1, W4 on I4
• Repeat experiments keeping I4 constant

• Constant I1 experiments violates pseudoelasticity
  requirement

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Experimental design
Left Cauchy Green tensor
For biaxial experiments
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Results from biaxial experiments
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Constant I4 experiments W1 and W4 dependence
Gundiah et al, unpublished
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W4 dependence on I4
SEF has second order dependence on I4, hence on
I6 We propose semi-empirical form, similar to
standard reinforcing model Coefficients c0, c1
and c2 determined by fitting equibiaxial data to
new SEF using the Levenberg-Marquardt optimization
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Fits to new Strain Energy Function
c0 73.96 22.51 kPa, c1 1.18 1.79 kPa c2
0.8 1.26 kPa
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Mechanical properties of arteries
Roach, M.R. et al, Can. J. Biochem. Physiol.,
35 181-190 (1957).
30
Mechanical Test Results

• Strain energy function for arteries
• Isotropic contribution mainly due to elastin
• Anisotropic contribution due to collagen fiber
  layout

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How do elastin collagen influence arterial
behavior?
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Acknowledgements

• Prof Lisa Pruitt, UC Berkeley/ UC San Francisco
• Dr Mark Ratcliffe UCSF/ VAMC for use of biaxial
  stretcher
• Jesse Woo Debby Chang for help with histology
• NSF grant CMS0106010 to UC Berkeley

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Uniaxial Test Results
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Is it a Mooney-Rivlin material?

• Use uniaxial stress-strain data
• Mooney-Rivlin Strain energy function
• Uniaxial tension experiments
• Plot of Vs

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Is Elastin a Mooney-Rivlin material?
Equation
N. Gundiah et al, J. Biomech (2007)
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Mooney-Rivlin material?
Not a Mooney-Rivlin material
c01 kPa c10 kPa
Autoclaving 162.57 115.44 -234.62 166.23
Hot Alkali 76.94 27.76 -24.89 35.11

• Baker-Ericksen inequalities
• c01, c10 0
• Greater principal stress occurs always in the
  direction of the greater principal stretch

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Constant I1 W1 and W4 dependence
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Conclusions

• neo-Hookean term dominant.
• elastin modulus is 522.71 kPa
• From Holzapfel1 and Zulliger2 models (obtained by
  fitting experimental data on arteries), we get
  elastin modulus of 308.2 kPa and 337.32 kPa
  respectively which is lower than those
  experimentally determined.

Gundiah, N. et al, J. Biomech. v40 (2007)
586-594 1 Holzapfel, GA et al, 1996, Comm. Num.
Meth. Engg, v12 n8 (1996) 507-517. 2 Zulliger, MA
et al, J Biomech, v37 (2004) 989-1000