Transcript Geometrically Optimized mPAD Device for Cell Adhesion

Geometrically Optimized mPAD
Device for Cell Adhesion
Professor Horacio Espinosa – ME 381 Final Project
Richard Besen
Albert Leung
Feng Yu
Yan Zhao
Fall 2006
Introduction
Cellular Adhesion Force
Cellular Functions
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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
Biological Mechanism
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Cellular Adhesion Video
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Literature Review
Adhesion Force Measurement
Continuous Substrate Method
Wrinkle Method
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Sensitive to nano-Newton forces
Force calculations difficult because of
complexity of wrinkle pattern
Model does not show adhesion force focal
points
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Literature Review
Adhesion Force Measurement
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
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Proposed Design
Adhesion Force Measurement
mPADs (micro Pillar Array Detectors)
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Discrete individual force sensors
Direct calculations from cantilever deflection theory
Highly detailed force vector field
Precise and simple manufacturing
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Proposed Design
Adhesion Force Measurement
Customization
mPAD design depends on the type of cell being used
Variable Parameters:
 Material Selection
 Aspect ratio
 Pillar density
 Cell to pillar contact area
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Proposed Design
Adhesion Force Measurement
mPAD Sensing
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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
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Geometric and Mechanical Analysis
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Force and Displacement
F    k
3E D
k
3
64 H
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Area Percentage
AP 
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 D2
4 L2
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Geometric and Mechanical Analysis
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Bending Stress
My

I
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Bending Moment
M  F ( H  x)
H
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Optimization
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1.
2.
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1.
2.
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Material:
Flexible to cell adhesion forces
Optically measurable displacements
Geometry and Spatial Arrangement:
Minimize cell flow down sides of posts
Detailed vector field representation
Manufacturable
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Optimization Criterion
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Maximization of post density
1
N
D  L 2
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Minimization of spring constant
3ED
K
3
64H
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Optimization Theory
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Cost function:
J ( D, L, H )  C1  D  L  C2  K
2
C1, C2- Weighting Coefficients
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Optimization Problem:
min J ( xi ) subject to g j ( xi )  0, j  1,...,m
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hk ( xi )  0, k  1,...,n
Lagrangean:
L( xi )  J ( xi )   j g j ( xi )   k hk ( xi )
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Constraints
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System Dynamics:
F ()  K
3ED
K
3
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Material:
1. Properties:
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EPDMS [1,2]MPa
1
L  D  F 
2. Yield Stress:   2GPa  2
y
1
  D4
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Constraints continued
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Spatial & Geometric Parameters:
Height (H)
4 μm -150 μm
Diameter (D)
Distance between posts (L)
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100 nm – 5
μm
>2Δmax
Optical Resolution:
R=50nm
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Optimization trends
Density as a function of diameter holding height constant at 4m
N
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D  L 2
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Optimization trends continued
Density as a function of the distance between adjacent posts
holding diameter constant at 1.2141 m
N
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D  L 2
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Optimization trends continued
Spring constant as a function of diameter holding height
constant at 4m
3ED4
K
64H 3
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Optimization trends continued
Spring constant as a function of post height holding diameter
constant at 1.2141m
3ED4
K
64H 3
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Optimization trends continued
Spring constant as a function of distance between adjacent
posts where K=2Fmax/L and Fmax=10nN
K
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2  F max
L
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Results
Canine Kidney Cell Forces F
Young’s Modulus EPDMS
2MPa
Spring constant K
.0100 N/m
Minimum deflection Δmin
Maximum deflection Δ
max
.1 m
1 m
1.2141 m
Diameter D
Height H
4 m
Distance between posts L
2 m
Aspect ratio
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1-10nN
3.2945
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Materials
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PDMS - polydimethylsiloxane
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Desirable chemical, physical, and economic
properties
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Chemical Properties
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Cell friendly
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Chemically inert
Thermally stable
Non-toxic
Can be made hydrophilic for adhesion
purposes
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Physical Properties
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Extremely flexible
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Scalability
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(.87MPa < E < 3.6MPa)
Conforms to nano-scale structures
Necessary for micro-molding
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Transparent within visible spectrum
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Cheap! Around $50 per pound to process
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Adjustable stiffness and aspect ratio based on
mixing ratio and curing time
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Microfabrication
Mask Oxide
Si substrate
Deposit mask oxide with LPCVD
(SiO2)
UV light
Photoresist
Mask
pattern
1 μm
Mask and
1 – quartz
plate
with 800Å
photoresist
using UV
chromium layer
lithography
Transfer pattern to mask oxide
with HF isotropic etching
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Microfabrication (cont’d)
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Bosch Process
First deep anisotropic silicon
etch (DRIE) with Cl2/BCl3
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)
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Micromolding
Liquid PDMS prepolymer
Liquid PDMS poured into
silanized micromold
mono-Si base substrate
Cured PDMS structure soft
bonded to mono-silicon
substrate (E ~ 100 GPa),
removed from mold
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Defects
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Scalloping from imperfect etch
selectivity in DRIE (~100 nm)
Variable diameter (conic shape)
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Preparation and Fluorescent Labeling
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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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mPAD Calibration
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Spring Constant (K)
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Young’s Modulus (E)
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Compression
Height/Diameter
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AFM Curves
SEM analysis
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Optical Sensing
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Phase-Contrast Microscopy
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Epifluroescence Microscopy
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Optical Sensing (cont’d)
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Pillar Deflection Detection
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Force Analysis Package
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Future Studies
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3D Analysis – Software improvements
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Thank You!
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Questions?
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