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


Introduction

Introduction


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

Arterial microstructure


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

Arterial microstructure

Intima Endothelial cells


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

Arterial microstructure

Media Smooth muscle cells, collagen & elastin


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

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).


How do you study the mechanics of materials

How do you study the mechanics of materials?


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)


Continuum mechanical framework

Continuum mechanical framework


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


Data from biaxial experiment

Data from biaxial experiment


1 phenomenological model

1. Phenomenological model

  • Fung strain energy function

1: circ2: 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


Results from biaxial experiments

Results from 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


How do elastin collagen influence arterial behavior

How do elastin & collagen influence arterial behavior?


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


Uniaxial test results

Uniaxial Test Results


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 ofVs


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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