Geometrically Optimized Geometrically Optimized mPAD Device for Cell mPAD Device for Cell
AdhesionAdhesion
Professor Horacio Espinosa – ME 381 Final Project
Richard BesenAlbert Leung
Feng YuYan Zhao
Fall 2006
Fall 2006 ME 381 2
IntroductionIntroduction
Cellular Adhesion Force
For a cell to move, it must adhere to a substrate and exert traction
Traction forces are concentrated at focal points between the cell and substrate
Cellular Functions
Biological Mechanism
Fall 2006 ME 381 3
Cellular Adhesion VideoCellular Adhesion Video
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Literature ReviewLiterature Review
Continuous Substrate Method
Wrinkle Method Sensitive to nano-Newton forces Force calculations difficult because of
complexity of wrinkle pattern Model does not show adhesion force focal
points
Adhesion Force Measurement
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Literature ReviewLiterature Review
Continuous Substrate Method
Gel imbedded with fluorescent markers Highly sensitive to adhesion forces Markers aid in optical detection of
surface deformation Difficult to manufacture uniform
fluorescent marker pattern
Adhesion Force Measurement
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Proposed DesignProposed Design
mPADs (micro Pillar Array Detectors) Discrete individual force sensors Direct calculations from cantilever deflection theory Highly detailed force vector field Precise and simple manufacturing
Adhesion Force Measurement
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Proposed DesignProposed Design
CustomizationmPAD design depends on the type of cell being usedVariable Parameters: Material Selection Aspect ratio Pillar density Cell to pillar contact area
Adhesion Force Measurement
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Proposed DesignProposed Design
mPAD Sensing Pillar is modeled as a cantilever beam with uniform diameter Pillar geometry, quantity of pillars per area, material choice
can be modified to match known ranges of a cell’s adhesion force
Force vector field shows magnitude and direction of discrete forces exerted by the cell on the array
Adhesion Force Measurement
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Geometric and Mechanical AnalysisGeometric and Mechanical Analysis Force and Displacement
Area Percentage
F k 4
3
3
64
E Dk
H
2
24
DAP
L
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Geometric and Mechanical AnalysisGeometric and Mechanical Analysis
Bending Stress
Bending Moment
My
I
( )M F H x
H
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Optimization Optimization Material: 1. Flexible to cell adhesion forces2. Optically measurable displacements Geometry and Spatial Arrangement: 1. Minimize cell flow down sides of posts2. Detailed vector field representation 3. Manufacturable
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Optimization CriterionOptimization Criterion
Maximization of post density
Minimization of spring constant
21
LDN
3
4
64
ED3
HK
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Optimization TheoryOptimization Theory Cost function:
Optimization Problem:
Lagrangean:
KCLDCHLDJ 22
1),,(
subject to)(min ixJ
nkxh
mjxg
ik
ij
,...,1,0)(
,...,1,0)(
)()()()( ikkijjii xhxgxJxL
C1, C2- Weighting Coefficients
Fall 2006 ME 381 14
ConstraintsConstraints
3
4
64
ED3
HK
KF )(
464121
2D
FDLGPay
System Dynamics:
Material:1. Properties:
2. Yield Stress:
MPaEPDMS ]2,1[
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Constraints continuedConstraints continued
Spatial & Geometric Parameters:
Optical Resolution: R=50nm
Height (H) 4 μm -150 μm
Diameter (D) 100 nm – 5 μm
Distance between posts (L) >2Δmax
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Optimization trendsOptimization trends
Density as a function of diameter holding height constant at 4m
21
LDN
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Optimization trends continuedOptimization trends continued
Density as a function of the distance between adjacent posts holding diameter constant at 1.2141 m
21
LDN
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Optimization trends continuedOptimization trends continuedSpring constant as a function of diameter holding height constant at 4m
3
4
64
ED3
HK
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Optimization trends continuedOptimization trends continued
3
4
64
ED3
HK
Spring constant as a function of post height holding diameter constant at 1.2141m
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Optimization trends continuedOptimization trends continued
L
FK
max2
Spring constant as a function of distance between adjacent posts where K=2Fmax/L and Fmax=10nN
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ResultsResults
Canine Kidney Cell Forces F 1-10nN
Young’s Modulus EPDMS 2MPa
Spring constant K .0100 N/m
Minimum deflection Δmin .1 m
Maximum deflection Δ max 1 m
Diameter D 1.2141 m
Height H 4 m
Distance between posts L 2 m
Aspect ratio 3.2945
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MaterialsMaterials PDMS - polydimethylsiloxane
Desirable chemical, physical, and economic properties
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Chemical PropertiesChemical Properties
Cell friendly Chemically inert Thermally stable Non-toxic Can be made hydrophilic for adhesion
purposes
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Physical PropertiesPhysical Properties
Extremely flexible (.87MPa < E < 3.6MPa)
Scalability Conforms to nano-scale structures Necessary for micro-molding
Transparent within visible spectrum
Cheap! Around $50 per pound to process
Adjustable stiffness and aspect ratio based on mixing ratio and curing time
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Mask and pattern 1 μm photoresist using UV lithography
UV light
Photoresist
MicrofabricationMicrofabrication
Deposit mask oxide with LPCVD(SiO2)
Mask Oxide
Si substrate
Transfer pattern to mask oxide with HF isotropic etching
Mask 1 – quartz plate with 800Å chromium layer
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Microfabrication (cont’d)Microfabrication (cont’d)
First deep anisotropic silicon etch (DRIE) with Cl2/BCl3
Bosch Process
Passivation oxide
Deposit .3 μm passivation oxide with PECVD
After vertical oxide etch, deep Si etch alternating with passivation
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Microfabrication (cont’d)Microfabrication (cont’d)
Micromolding
Liquid PDMS poured into silanized micromold
Liquid PDMS prepolymer
Cured PDMS structure soft bonded to mono-silicon substrate (E ~ 100 GPa), removed from mold
mono-Si base substrate
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DefectsDefects
Scalloping from imperfect etch selectivity in DRIE (~100 nm)
Variable diameter (conic shape)
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Preparation and Fluorescent LabelingPreparation and Fluorescent Labeling Oxidize structure in air-plasma to
make hydrophilic Create flat PDMS stamps for top of
each pillar Microcontact print fluorescent label Coat pillars and stamps in adhesive
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Spring Constant (K) AFM Curves
Young’s Modulus (E) Compression
Height/Diameter SEM analysis
mPAD CalibrationmPAD Calibration
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Optical SensingOptical Sensing Phase-Contrast Microscopy
Epifluroescence Microscopy
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Pillar Deflection Detection
Force Analysis Package
Optical Sensing (cont’d)Optical Sensing (cont’d)
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Future StudiesFuture Studies
3D Analysis – Software improvements
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Thank You!Thank You!
Questions?