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

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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

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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?