The role of elastin in arterial mechanics structure function relationships in soft tissues
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The role of elastin in arterial mechanics Structure function relationships in soft tissues. Namrata Gundiah University of California, San Francisco. Introduction. Arterial microstructure. Arterial microstructure. Intima Endothelial cells. Arterial microstructure.

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

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

Namrata Gundiah

University of California, San Francisco




Arterial microstructure

Intima Endothelial cells


Arterial microstructure

Media Smooth muscle cells, collagen & elastin


Arterial microstructure

Adventitia Collagen fibers


Complex tissue architecture
Complex tissue architecture

Masson’s trichrome

Collagen: blue

Verhoeff’s Elastic

Elastin: black


Diseases affecting arterial mechanics
Diseases affecting arterial mechanics

Atherosclerosis

Abdominal Aortic Aneurysms

Aortic Dissections

Supravalvular aortic stenosis

William’s syndrome

Marfan’s syndrome

Cutis laxa

etc.


Mechanical properties of arteries
Mechanical properties of arteries

Roach, M.R. et al, Can. J. Biochem. & Physiol., 35: 181-190 (1957).



Arterial behavior
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)



Biaxial test preliminaries
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


Measurement of tissue mechanics biaxial stretcher design

Measurement of tissue mechanicsBiaxial stretcher design



1 phenomenological model
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


2 function using material symmetry
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


Elastin isolation
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).


Elastin architecture
Elastin architecture

  • Axially oriented fibers towards intima and adventitia

  • Circumferential elastin fibers in media.

N. Gundiah et al, J. Biomech (2007)


Histology results
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


Orthotropic material
Orthotropic material

  • Assume orthotropic

,

f=90 for orthogonal fiber families

C=FTF is the right Cauchy Green tensor


Theoretical considerations
Theoretical considerations

  • Deformation: homogeneous

    li are the stretches in the three directions

  • Unit vectors

  • Strain energy function for arterial elastin networks:

  • Define subclass


Rivlin saunders protocol
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


Experimental design
Experimental design

Left Cauchy Green tensor

For biaxial experiments



Constant i4 experiments w 1 and w 4 dependence
Constant I4 experiments: W1 and W4 dependence

Gundiah et al, unpublished


W 4 dependence on i 4
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


Fits to new strain energy function
Fits to new Strain Energy Function

c0 = 73.96 ± 22.51 kPa,

c1 = 1.18 ±1.79 kPa

c2 = 0.8 ±1.26 kPa


Mechanical properties of arteries1
Mechanical properties of arteries

Roach, M.R. et al, Can. J. Biochem. & Physiol., 35: 181-190 (1957).


Mechanical test results
Mechanical Test Results

  • Strain energy function for arteries

  • Isotropic contribution mainly due to elastin

  • Anisotropic contribution due to collagen fiber layout



Acknowledgements
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



Is it a mooney rivlin material
Is it a Mooney-Rivlin material?

  • Use uniaxial stress-strain data

  • Mooney-Rivlin Strain energy function:

  • Uniaxial tension experiments

  • Plot of Vs


Is elastin a mooney rivlin material
Is Elastin a Mooney-Rivlin material?

Equation:

N. Gundiah et al, J. Biomech (2007)


Mooney rivlin material
Mooney-Rivlin material?

Not a Mooney-Rivlin material

  • Baker-Ericksen inequalities

    c01, c10 ≥0

    Greater principal stress occurs always in the direction of the greater principal stretch


Constant i 1 w 1 and w 4 dependence
Constant I1: W1 and W4 dependence


Conclusions
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


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