Extracting nonlinear material parameters from AFM indentation data'

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Extracting nonlinear material parameters from AFM
indentation data.
S Tripathy EJ Berger K Vemaganti
University of Virginia, Charlottesville, VA.
University of Cincinnati, Cincinnati, OH.
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Cellular Biomechanics

• Small Scale Cell-Biomechanics, (Zhu et. al. ,
  Humphrey et. al.)
• Experimental Methods used today
• Cell Poking (Daily et. al.)
• Micropipette Aspiration (Thoumine et. al.)
• Magnetic Twisting Cytometry (Chen et. al.)
• Optical Tweezers (Hénon et. al.)
• AFM (Radmacher et. al.)
• Atomic Force Microscopy.

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Cellular Biomechanics

• Hertz Contact Theory ( Hertz et. al. , Radmacher
  et. al. , Hassan et. al.)
• Non-Hertzian Effects
• Finite Thickness Hayes et. al., Dimitriadis et.
  al.
• Large Strains Costa et. al., Simha et. al.
• Material Systems
• Cells
• Bio-Gels like PVA, Agarose etc.

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AFM Imaging and Indentation Tests

• 1 Agarose Gel.
• Standard V-Shaped cantilever (Nominal k 0.06
  N/m)
• PicoForce Scanner
• Contact Mode
• Avg. Roughness
• 100 nm

Source Mikromasch
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AFM Indentation Tests
Noise 30 - 40 pN
? 0.5
E 20kPa
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FE Reconstructions
Boundary Conditions
Stress Profile
Source Abaqus
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Material Modeling

• Hyperelastic Material Elastic materials for
  which the work done by the stresses in
  independent of the load path Strain energy
• Exponential Model
• E 6b1b2 ( Beatty et. Al. , Costa et. al.)
• Parameter Study
• b1 1, 5, 10, 50, 100 x 109 Pa
• b2 0.1, 0.25, 0.5, 0.75, 1.0, 2.5,
  5.0,7.5,10.0
• R 125, 250, 500, 1000 nm

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Material Modeling

• Softening and Hardening
• Indentation Dependent Stiffness

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Indentation Dependent Stiffness

• Curve fit over 3 points
• (Moving Window Sense)
• Linear correction to the stiffness
• Linear dependence of the slope, m on the
  parameter, b1

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Extraction of parameters

• A 5th Order polynomial proposed for g(b2)
• Error Function used
• fminsearch in MATLAB

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Extraction of parameters
Max error b1 12 b2 14
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Experimental Data

• 3 different indentation ranges
• 1µm indenter radius
• 1 Agarose
• Contact Mode
• V-shaped tips
• Extraction protocol on the data

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Conclusion

• Parameter Extraction Protocol tested on FE data.
• Hyperelastic Material model for large scale
  deformation.
• b1 is the elastic part and b2 controls the
  nonlinearity

Future Work

• Extraction of parameters from AFM data on
  Agarose Gels.
• Detailed parameter analysis
• Effect of Gel Concentration and Indenter Radius
  
• Thin Film and Substrate Effects.
• Spin Coating
• Diff Concentration
• Indenter Radius
• Contact point analysis.
• Effect on Parameter ID

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Thank You
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Contact Point Analysis
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Inverse FE Problem.