Biomechanics Design Lab: Viscoelasticity of Chicken Femoral

Cartilage

Group 7Priyanka Parajuli, Hemali Patel, Catherine Porter, Shri Rajan, Linh Phan

INTRODUCTION: VISCOELASTICITY ViscosityFluid PropertiesGradual Deformation:Time-dependentEquation: σ = σ(ε)

ElasticitySolid Properties Instantaneous Deformation:Time-independentEquation: σ=σ(ε, Ё)

http://wweb.uta.edu/faculty/ricard/Classes/KINE-3301/Notes/Lesson-14.html

INTRODUCTION: ARTICULAR CARTILAGE

Function:Reduces friction between bones at jointCovers the diarthrodial jointsAlleviates compressive loads at joint

Composition:60-85% water by weight15-22% type II collagen by weightVarious electrolytes (Na+, Cl-, Ca++)Proteoglycans and chondrocytes

http://www.ideasforsurgery.com/glossary/Conclusion: Articular cartilage is a viscoelastic material

INTRODUCTION: ARTICULAR CARTILAGE PROPERTIES Inhomogeneous Multiphasic Material Anisotropic Resistant to Compression

http://www.mdpi.com/2079-4983/3/4/799http://www.spandidos-publications.com/etm/8/5/1357

INTRODUCTION: MAXWELL MODEL

• Spring and dashpot connected in series• Fluid viscoelastic model• Equation:

http://polymodmw.csi.muohio.edu/wp-content/uploads/2013/04/Figure3.jpg

INTRODUCTION: KELVIN-VOIGT MODEL

• Spring and dashpot connected in parallel• Solid viscoelastic model• Equation:

http://polymodmw.csi.muohio.edu/wp-content/uploads/2013/04/Kelvin-Voigt.jpg

INTRODUCTION: STANDARD SOLID MODEL

• Combine Kelvin-Voigt solid model and Maxwell fluid model to derive complex viscoelastic model• Equation:

http://polymodmw.csi.muohio.edu/wp-content/uploads/2013/04/StandardSolid.jpg

INTRODUCTION: INDENTATION TESTS

• Characterize mechanical properties of cartilage outside the body• Stress-Relaxation Test Indent material and maintain constant strain Observe stress response of material Viscoelastic material responds with initial high stress and then decreases over time

• Load-to-Failure Test Constantly increasing stress Last point on σ—ε curve is rupture, failure strength Viscoelastic materials typically have same ultimate and failure strength

https://www.bsbedge.com/astm/astmd6264d6264m-standardOzkaya et al., Fundamentals of biomechanics: Equilibrium, motion, and deformation (3rd ed.)

MOTIVATION: Osteoarthritis, sports injuries, etc. Current replacement grafts and surgical reconstructions often result in complications and instability that worsen current conditions.

Dynamic environment of the human body requires physical characterization of articular cartilage in addition to biological characterization.

Mathematical modeling provides unique insight for further treatment of cartilaginous injuries.

OBJECTIVE:To assess the mechanical and viscoelastic properties of chicken femoral cartilage and model its viscoelastic behavior as a mathematical equation.

MATERIALSStep 1: Preparation of the Sample

• 1 chicken femur (from Publix)

• Large-grit sandpaper• Forceps• Iris scissors • Gloves• Paper towels• Cement mixing bowl• Aluminum cylinder• Bone cement

(Surgical Simplex, Stryker)

• COE Tray Plastic Self-Curing Liquid (Patterson Dental)

• Plumber’s putty• Saline solution• Gauze pads

Step 2: Stress-Relaxation Test

• Prepared Sample• 2.15mm indenter tip• Needle to record

cartilage depth• MTS 858 MiniBionix

(15,000 N load cell)

Step 3: Load-to-Failure Test

• Prepared Sample• 2.15mm indenter tip• Needle to record

cartilage depth• MTS 858 MiniBionix

(15,000 N load cell)

METHODS: PREPARATION OF THE SAMPLE

Clean Chicken Femur Cartilage• Remove

periosteal tissue with sandpaper

• Use iris scissors

Fill Plumber Putty in Aluminum Cylinder• Use putty to

prevent leaking of bone cement

Prepare Bone Cement• Mix 1:1 ratio

of bone cement and self-curing liquid

• Desired thickness: toothpaste-like

Pot the Femur• Pour cement

in cylinder until ¾ full

• Position distal side of femur vertically in bone cement

Allow cement to solidify • Hold femur

straight while cement cures

• Keep cartilage moist with saline and gauze

Mark Test Locations• Use marker

to indicate locations for stress relaxation and load-to-failure tests

METHODS: STRESS-RELAXATION TEST

Initial Thickness Measurement• Use needle

and caliper to measure thickness of cartilage at marked spot

Cartilage Placement for Testing• Align

cartilage perpendicular to the indenter

• Indenter is 2.5mm

Calibration of Load Cell• Calibrate

15kN load cell to 1.5kN total load

Indentation• Use MTS 858

MiniBionix to indent 2mm

• Hold for 2 minutes while sampling at a rate of 100Hz

Relaxation• Remove load• Let cartilage

relax to initial thickness

METHODS: LOAD-TO-FAILURE TEST

Initial Thickness Measurement• Use needle and

caliper to measure thickness of cartilage at marked spot

Cartilage Placement for Testing• Align cartilage

perpendicular to the indenter

• Indenter is 2.5mm

Calibration of Load Cell• Calibrate 15kN

load cell to 1.5kN total load

Indentation• Use MTS 858

MiniBionix to indent until failure

• Indent at 2mm/min. while sampling at a rate of 100Hz

DATA ANALYSIS: STRESS-RELAXATION TEST Stress Equation:

Area = cross-sectional area of indenter = Forces given by machine

Example Calculation at 60 Seconds:

MATLAB was used to calculate the stresses Plot σ vs. time

RESULTS: STRESS-RELAXATION TEST

DATA ANALYSIS: WIECHERT MODEL

Wiechert Model:

Relaxation Modulus:

http://www.ncbi.nlm.nih.gov/pubmed/19615781

Strain Equation:

axial displacement original thickness of cartilage new thickness

Calculation at 70 Seconds:

DATA ANALYSIS: WIECHERT MODEL

Use Matrix to Solve E coefficients:

System of Equations:

RESULTS: STRESS-RELAXATION TEST MODELEDWiechert

Parameters:0.203

Correlation Coefficient R =

RESULTS: WIECHERT MODEL APPLIED TO ALL GROUPS

R = 0 R = 0.939

R = 0 R = 0

DATA ANALYSIS: LOAD-TO-FAILURE TEST

Strain Equation:

axial displacement original thickness of cartilage new thickness

Example Calculation at 70 Seconds:

Stress Equation:

Area = cross-sectional area of indenter =

Example Calculation at 70 Seconds:

MATLAB was used to calculate the stresses and strain

Plot σ vs. ε

RESULTS: LOAD-TO-FAILURE TEST

Group Number

Ultimate Stress (Pa)

Group 6 1.55E+07Group 7 2.24E+07Group 8 1.96E+07Group 9 1.40E+07

RESULTS: GROUP ELASTIC MODULIGroup

NumberElastic Moduli

(Pa)Group 6 2.42E+04Group 7 8.37E+04Group 8 2.05E+04Group 9 3.92E+04

DISCUSSIONDifference between Stress-Relaxation Graphs•Various chicken cartilage samples

Different thicknesses Different properties

Wiechert Model Processing•R= 0.939 for our Wiechert model•Coefficients are dependent on • Trial and error method

Need to alter and per group manually Not a standardized model-fitting tool

Difference between Load-to-Failure Graphs•Our sample exhibited higher mechanical properties: High ultimate strength (strong) High elastic modulus (stiff)

•Other samples exhibited lower mechanical properties: Lower ultimate strengths Low elastic moduli (ductile)

Possible Sources of Variance:• Chicken age• Cartilage moisture• Chicken gender• Chicken physical activity and health

DISCUSSION (CONT.)Wiechert Model Best Fit Line

9th Degree Polynomial Best Fit Line (MATLAB Curve

Fitting Tool)

Correlation Coefficient = 0.987

Correlation Coefficient = 0.939

DISCUSSION (CONT.)Statistical Analysis

Mechanical

PropertiesAverage

(Pa)Standard Deviation

(Pa)Failure Stress 1.79E+07 ±

3.85E+06Elastic

Modulus 4.19E+04 ± 2.90E+04

Possible Sources of Error:

• Thickness measurement• Machine error• Bone alignment• Overlap of stress- relaxation and load-to-failure test locations

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2. Bonifasi-Lista, C., Lakez, S. P., Small, M. S. and Weiss, J. A. (2005), Viscoelastic properties of the human medial collateral ligament under longitudinal, transverse and shear loading. J. Orthop. Res., 23: 67–76. doi: 10.1016/j.orthres.2004.06.002

3. Kaufman, J. D., Miller, G. J., Morgan, E. F., & Klapperich, C. M. (2008). Time-dependent mechanical characterization of poly(2-hydroxyethyl methacrylate) hydrogels using nanoindentation and unconfined compression. Journal of Materials Research, 23(5), 1472–1481. http://doi.org/10.1557/JMR.2008.0185

4. Machiraju, C., Phan, A. -V., Pearsall, A. W., & Madanagopal, S. (2006). Viscoelastic studies of human subscapularis tendon: Relaxation test and a Wiechert model. Computer Methods and Programs in Biomedicine, 83(1), 29-33.

5. Ozkaya, N., Nordin, M., Goldsheyder, D., & Leger, D. (2012). Fundamentals of biomechanics: Equilibrium, motion, and deformation (3rd ed.). New York: Springer.