biomechanics design lab presentation final (2)
DESCRIPTION
BiomechanicsTRANSCRIPT
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Biomechanics Design Lab: Viscoelasticity of Chicken Femoral
Cartilage
Group 7Priyanka Parajuli, Hemali Patel, Catherine Porter, Shri Rajan, Linh Phan
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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
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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
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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
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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
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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
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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
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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.)
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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.
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OBJECTIVE:To assess the mechanical and viscoelastic properties of chicken femoral cartilage and model its viscoelastic behavior as a mathematical equation.
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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)
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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
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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
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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
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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
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RESULTS: STRESS-RELAXATION TEST
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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:
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DATA ANALYSIS: WIECHERT MODEL
Use Matrix to Solve E coefficients:
System of Equations:
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RESULTS: STRESS-RELAXATION TEST MODELEDWiechert
Parameters:0.203
Correlation Coefficient R =
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RESULTS: WIECHERT MODEL APPLIED TO ALL GROUPS
R = 0 R = 0.939
R = 0 R = 0
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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
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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
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RESULTS: GROUP ELASTIC MODULIGroup
NumberElastic Moduli
(Pa)Group 6 2.42E+04Group 7 8.37E+04Group 8 2.05E+04Group 9 3.92E+04
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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
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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
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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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REFERENCES:1. Ahearne, M., Siamantouras, E., Yang, Y., & Liu, K.-K. (2009). Mechanical
characterization of biomimetic membranes by micro-shaft poking. Journal of the Royal Society Interface, 6(34), 471–478. http://doi.org/10.1098/rsif.2008.0317
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.