statistical design of position-encoded 3d microarrayspinakisa/img/dissertation/talk.pdf ·...

Center for Sensor Signal and Information Processing

Ph.D. Dissertation Defense

Statistical Design of Position-Encoded3D Microarrays

Pinaki SarderAdvisor: Prof. Arye Nehorai

Department of Electrical and Systems Engineering

Washington University in St. Louis

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Outline Background

Performance analysis

Statistical design

Estimation

Results

Future work

Other research

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Background

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Existing 3D MicroarraysBackground:

Microarrays detect, identify, and quantify targets (proteins, antibodies, mRNAetc.) in a solution [1].

Conventional microarrays are 2D.

3D microarrays:

Contain multiple polystyrene microspheres (5-6m in diameter) sensitive toindividual targets [1], [2].

Microspheres are randomly placed on a substrate [2].

Microspheres employ color-codedquantum-dots (QDs) [3].

Color-codes identify targets.

Microspheres

[1] A. Mathur, Image Analysis of Ultra-High Density, Multiplexed, Microsphere-Based Assays, Ph.D. thesis, Northwestern University, IL., 2006.[2] K. D. Bake and D. R. Walt, Multiplexed Spectroscopic Detections, Annu. Rev. Anal. Chem., vol. 1, pp. 15-47, 2008.[3] M. Han, X. Gao, J. Z. Su, and S. Nie, Quantum-dot-tagged microbeads for multiplexed optical coding of biomolecules, Nat. Biotechnol.,

vol. 19, pp. 631-635, 2001.

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Existing 3D Microarrays (Cont.)

Advantages of 3D microarrays:

High sensitivity. Directional binding. Fast reaction (high surface-to-volume ratio).

However, 2D microarrays have position encoding:

Avoid target identification errors.

Potential applications:

Versatile screening. Drug discovery. Gene sequencing. Environmental monitoring. Home-tests (pregnancy tests, glucose meters, cholesterol meters, etc.).

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Target-Captured Microsphere

Microsphere

Target molecule

Receptor sites

QDs

Active sites

Nanosphere

Receptors on the microsphere react to target molecules.

Nanospheres: Diameter100nm. Indicate reaction (yes-no). Enhance detection.

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Microarray Solution Flow

Target solution inlet Outlet

Microspheres Substrate

Side view of a microarray.

To create reaction, the target solution:

Flows tangentially.

Encounters all the microspheres.

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How Does 3D Microarray Work?Targets:

Antibody, protein, mRNA, etc.

Free of labels (e.g., fluorescent dyes).

Unknown concentrations.Targets

: Target a

: Target b

: Target c

Targets:

Orange microsphere: Receptor A

Green microsphere: Receptor B

Blue microsphere: Receptor C

Capture probes:

Microarray

Receptor-target

interactions: A-a,

B-b, and C-c.

Inferences

Inferences:

Identify targets using the light spectra from the microsphere QDs.

Estimate target concentrations using the light levels from the nanosphere QDs.

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How Does 3D Microarray Work? (Cont.)

Adding nanospheres:

Microspheres with

receptor A, receptor B,

receptor CTargets

Microarray

Microspheres and

targets

Microspheres, targets,

and nanospheres

Adding nanospheres

Detection is label-free. Hence, target molecule structures and chemicalproperties are not modified.

QDs do not suffer from saturation or photo-disintegration under intenseillumination. Hence, the detection sensitivity enhances.

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Microarray Imaging

UV light

To obtain the measurement:

Ultra-violet (UV) light is applied to excite the QDs.

A fluorescence microscope (e.g., non-confocal) and an image sensor (e.g.,CCD/CMOS) capture cross-section images of the microarray.

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Microscopy

Out of

focus lightPlane of

focus

Sample

Epi-illumination

objective

Dichroic mirror

CC

DC

am

era

Light source

z

x

Non-confocal fluorescence microscope.

Camera acquisition

of optical sections

x y Optical sections

Focal

change

( z)

Microsphere

Focal plane

Microscope

objective

z axis

Image plane

Op

tica

laxis

Microscope provides 2D cross-section images.

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Ideal Microsphere and Nanosphere Images

QD light from the microsphere.QD light from the nanospheres.

2D cross-section intensity image (ideal).

Microsphere QD light:

Spherical source.

Cross-section images result in 2D discs.

Nanosphere QD light around each microsphere:

Spherical-shell source.

Cross-section images result in 2D rings.

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Real Microscope Image

Focal-plane quantum-dot intensity image of microspheres without targets.

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Drawbacks of Existing 3D Microarrays

Random placement of microspheres results in: Inefficient packing. Complex image processing. Suboptimal detectibility (close proximity of microspheres).

Microsphere QD color spectra are noisy which results in error in identifyingtargets.

Sensors require high cooling in imaging, hence expensive.

Optical cross-talking in target-concentration profilesof two neighboring microspheres (schematic).

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Our Research

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Our Research

Goal:

Design a compact 3D microarray device without target identification errors.

Minimize the error in estimating the target concentrations.

Our solution:

Place the microspheres at controllable positions, to avoid the identification error.

Use statistical analysis to select the optimal (minimal) distance betweenmicrospheres for a desired imaging performance, at a given temperature.

We:

Analyze the statistical performance using posterior Cramr-Rao bound.

Select the optimal distance.

Estimate the image parameter using maximum-likelihood.

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Proposed 3D Microarray Layout

dopt

Microspheres

Uniform 2D grid layout of the microarray.

Positioning of microspheres is realized using microfluidics or magnetics.

Advantages: Position encoding (no QD encoding of the microspheres). Error-free target identifiability. Higher sensitivity. Efficient packing. Simplified imaging.

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Statistical Performance Analysis

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Performance Analysis Overview

Performance measure: Error in estimating the unknown target concentrationsfrom two neighboring microspheres.

Analysis through computing the posterior Cramr-Rao bound (PCRB) on thiserror.

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Measurement Model

( , , ; )s x y z

ObjectMicroscope

PSF

CCD/

CMOS +

Background noise

( , , )h x y z( , , ; )s x y z

b ( , , )w x y z

( , , ; )x y z g

ccd ( ; )

(1/ ) ( ( , , ; ))

x, y,z

s x y z

!

!

g

P( , , ; ) (1/ ) ( ( , , ; ))

Block diagram of the imaging.

s(x, y, z;) =

z

y

x

h(x x, y y, z, z)s(x, y, z; )dxdydz[4].

h(x, y, z) : Microscope PSF.

s(x, y, z,) : Target-concentration profile.

: Unknown target-concentration levels.

[4] P. Sarder and A. Nehorai, Deconvolution methods for 3D fluorescence microscopy images: An overview, IEEE Signal ProcessingMagazine, vol. 23, pp. 32-45, 2006.

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Measurement Model (Cont.)

( , , ; )s x y z

ObjectMicroscope

PSF

CCD/

CMOS +

Background noise

( , , )h x y z( , , ; )s x y z

b ( , , )w x y z

( , , ; )x y z g

ccd ( ; )

(1/ ) ( ( , , ; ))

x, y,z

s x y z

!

!

g

P( , , ; ) (1/ ) ( ( , , ; ))

Block diagram of the imaging.

Measurement:g(x, y, z; ) = gccd(x, y, z;) + wb(x, y, z).

gccd(x, y, z; ) P(s(x, y, z;)).

: Photon conversion factor of the image sensor.

P() : Poisson random variable with mean-rate .

wb(x, y, z) : Background (thermal) noise, i.i.d. from voxel to voxel.

Gaussian distributed with mean zero and variance 2b. Independent of gccd(x, y, z; ) at each voxel.

x {x1, x2, . . . , xK}, y {y1, y2, . . . , yL}, and z {z1, z2, . . . , zM}.

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Measurement Model (Cont.)

Assuming high signal-to-noise ratio (SNR) imaging of QDs:

g(x, y, z; ) = gccd

(x, y, z; ) + wb(x, y, z),

s(x, y, z;) + wP(x, y, z;) + w

b(x, y, z),

where wP(x, y, z; ) is:

Gaussian distributed with zero mean and variance s(x, y, z; )/. Independent from voxel to voxel.

Measurement in vector form:

g = s+wP+w

b.

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Object Model: Full Shell

Assumptions:

Microspheres are completely surrounded by intended targets. Targets are attached to nanospheres.

Nanosphere QD lights from two neighboring microspheres, in shell shapes:

s(x, y, z; ) = ssh(x, y, z; 1) + ssh(x d, y, z; 2),

where (for i = 1, 2)

ssh(x, y, z; i) =

{i if r1

x2 + y2 + z2 r2,

0 otherwise.

d : Distance between shells. = [1, 2]

T : Unknown parameters. i Uniform(0, MAX) : Target-concentration level per measured voxel. MAX : User-chosen constant.

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Ideal Nanosphere QD Light Images: Full Shell

Full shell:

Microsphere

Nanospheres


Full-shell shape fits:

High target concentration.

Sufficiently long sensing duration.

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Object Model: Sparse Shell

Assumptions: Same as for full shell, except that microspheres are partiallysurrounded by intended targets.

Nanosphere QD lights from two neighboring microspheres, in shell shapes:

s(x, y, z; ) = ssh(x, y, z;1) + ssh(x d, y, z; 2),

where (for i = 1, 2)

ssh(x, y, z; i) =

{i(x, y, z) if r1

x2 + y2 + z2 r2,

0 otherwise.

d : Distance between shells. = [T1 ,

T2 ]

T : Unknown parameters. i : Vector form of i(x, y, z) from the measured voxels. i() Exp() [5] : Sparse target-concentration level in a measured voxel. : Inversely proportional to sparsity.

[5] S. Ji, Y. Xue, and L. Carin, Bayesian compressive sensing, IEEE Trans. Signal Processing, vol. 56, pp. 2346-2356, 2008.

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Ideal Nanosphere QD Light Images: Sparse Shell

Sparse shell:

Microsphere

Nanospheres


Sparse-shell shape fits:

Low target concentration.

Short sensing duration.

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Microscope PSF Model

Microscope PSF model (for a point source at a depth z in the specimen) [6]:

h(x, y, z) =

1

0

J0(2Nax2 + y2/M ) exp(j2(z, z, Na, , no, ns)/)d

2

.

J0() : Bessel function of the first kind.

Na : Microscope numerical aperture.

: Normalized radius in the back focal plane.

M : Lens magnification.

: QD emission wavelength.

() : Optical path difference function.

no and ns : Refractive indexes of the immersion oil and specimen.

[6] S. F. Gibson and F. Lanni, Experimental test of an analytical model of aberration in an oil-immersion objective lens used inthree-dimensional light microscopy, J. Opt. Soc. Am. A., vol. 8, pp. 1601-1612, 1991.

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Posterior Cramr-Rao Bound Joint data-parameter log-likelihood:

log pG,

(g,)

x

y

z

[(g() s()

)2

2(s()

+ 2b) +

1

2log

(s()

+ 2b

)]

Data likelihood

+ log(p())

Prior likelihood

.

Information matrix J has elements Jij = E

[

2 log pG,

(g,)

i

j

].

PCRBs on estimation errors correspond to the diagonal entries of J1 [7].

[7] H. L. van Trees, Detection, Estimation, and Modulation Theory, New York: Wiley, 1968.

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Statistical Design

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Design Approach

Goal: Use the statistical performance of the imaging to select the minimaldistance between the microspheres, for a desired estimation error and a giventemperature.

Design variables:

Distance between the microspheres. Temperature in imaging.

Performance measure: p = Trace(PCRB).

Trade offs: Higher temperature (i.e., reducing cost) and/or smaller distance vs.higher estimation accuracy.

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Sensor Temperature Effect

Estimation error depends on the image sensor temperature T .

Background noise variance 2b varies with T [8]:

2b(T ) = B exp(Eg/2kBT ),

where B : Constant. Eg : Bandgap of the detector material. kB : Boltzmann constant.

[8] J. Ohta, Smart CMOS Image Sensors and Applications, CRC Press, 2007.

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Minimal Distance Selection

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Motivation

Tra

ce (

PC

RB

)

Distance

As we increase the distance between the microspheres:

Their lights do not interfere with each other.

The performance measure flattens.

PCRB matrix becomes block-diagonal.

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Minimal Distance Selection

Goal: For a given temperature, select the minimal distance at which the performancemeasure starts to flatten.

Approach:

Substitute estimates of B and in the performance measure.

Fit a parametric curve to the estimated performance measure.

Find the minimal distance at which the performance measure starts to flattenusing least-squares estimation.

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Performance Measure: Parametric Model

Parametric model of the performance measure as a function of d:

p(d) = c exp(d)I[0,d0)(d) + p0,

where I[0,d0)(d) is an indicator function:

I[0,d0)(d) =

{1 if 0 d < d0,

0 otherwise.

c, , d0, and p0 are unknown parameters,

Performance measure starts to flatten at d0.

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Performance Parametric Model Example

Example of the parametric model for the performance measure.

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Selecting the Minimal Distance

Compute p(d) at increasing values of d at d1 d2 dN .

In vector form:p = A()x+ e,

where p = [p(d1), p(d2), . . . , p(dN )]

T .

A() : Matrix with jth row as [exp(dj)I[0,d0)(dj), 1]. e : Error vector. = [, d0]

T .

x = [c, p0]T .

,x : Unknown parameters.

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Selecting the Minimal Distance (Cont.)

Least-squares estimates [9]:

= argmax

{pT()p},

x = [AT ()A()]1AT ()p,

where() = A()[AT ()A()]1AT ().

Select the minimal distance as d0.

[9] S. M. Kay, Fundamentals of Statistical Signal Processing, Estimation Theory, Englewood Cliffs, NJ: PTR Prentice Hall, 1993.

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Estimating B and

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Estimation Overview

Goal: Estimate B and using a pilot experiment with existing 3D microarray.

Approach:

Image multiple QD-embedded microspheres [10] at temperature T0.

Estimate B using the noise-only sections of the captured image.

Estimate from each microsphere image.

[10] http://www.crystalplex.com.

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Measurement Model

Measurement from a single microsphere:

g(x, y, z; , , 2b) =

z

y

x

h(x x, y y, z, z)s(x, y, z; )dxdydz

+ wP(x, y, z; , ) + w

b(x, y, z;2b).

s(x, y, z; ) : QD intensity profile of a single microsphere, in spherical shape,

s(x, y, z; ) =

{ if

x2 + y2 + z2 r,

0 otherwise.

: Microsphere QD intensity level per voxel.

r : Radius of the microsphere.

, 2b, and (nuisance) : Unknown parameters.

x {x1, x2, . . . , xK}, y {y1, y2, . . . , yL}, and z {z1, z2, . . . , zM}.

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Estimating

Goal: Estimate from each microsphere image Un (n {1, 2, . . . , N }).

Assumption: Large (highly sensitive imaging).

Hence, neglecting wP() :

g(x, y, z; , 2b)

z

y

x

h(x x, y y, z, z)f(x, y, z)dxdydz+wb(x, y, z;2b),

where f(x, y, z) = s(x, y, z; )/.

Define, s(x, y, z) =z

y

xh(x x, y y, z, z)f(x, y, z)dxdydz.

In vector form:g = s +w

b,

s and wb

are the vector forms of s() and wb(), respectively.

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Estimating (Cont.)

Log-likelihood:

C0(, 2b) =

KLM

2ln 2b

||g s||2

22b.

Maximum likelihood (ML) estimates [11]:

= [sTs]1s

Tg,

2b = (KLM)1

gTP

sg,

where

Ps

= I s[sTs]1s

T.

[11] P. Sarder and A. Nehorai, Estimating locations of quantum-dotencoded microparticles from ultra-high density 3D microarrays, IEEETrans. on NanoBioscience, vol. 7, pp. 284-297, 2008.

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Estimating B

Estimate B using the estimate of 2b :

Estimate 2b from the noise only sections of the captured image, employing theclassical ML estimation method discussed in [12, Ch. 6].

Use a large number of measurement to ensure consistency.

Compute B by fitting the estimated 2b with B exp(Eg/2kBT0).

[12] R. V. Hogg and A. T. Craig, Introduction to Mathematical Statistics, 5th Ed., Prentice Hall, 1995.

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Estimating

Goal: Estimate from each microsphere image Un (n {1, 2, . . . , N }).

Method-of-moments estimate:

=

x

y

z s(x, y, z; )

x

y

z

[(g(x, y, z) s(x, y, z; )

)2 2b

] ,

where : Estimate of .

2b : Estimate of 2b.

Note: Conventionally is computed using detectors physical parameters [12].

[13] P. J. Verveer, Computational and Optical Methods for Improving Resolution and Signal Quality in Fluorescence Microscopy, Ph. D. thesis,Delft Technical University, Delft, The Netherlands, 1998.

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Estimation Summary

Estimating 2b( , , )n ng x y z !U

( {1,2,....., })n N ! "

n !

2

b

Individual object images

Capturing Image U

Maximum likelihood estimation

Estimating

Method of moments estimation

Estimating

{1,2,....., }

{1,2,....., }

n

n

n N

n N

!"

"

# $" "% &' (

" "% &' () *

!

Maximum likelihood estimation

Estimating B

B

2

b

Note: The estimated histograms of the imaging parameters from multiple microsphereimages can be employed as prior information for any next step estimation usingmaximum a posteriori (MAP) techniques.

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Results

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Estimating B, , and Using Existing Microarray

We imaged microspheres (r = 2.5m), placed on a PDMS substrate.

Used non-confocal microscope for image acquisition, with (partial) set-up: Na = 1.3, M

= 40X, = 535nm, no = 1.334, ns = 1.3.

Resolution: z = 1m and x = y = 0.654m. Temperature: T0 = 100C.

Microspheres (without targets) image using focal-plane quantum-dot intensity.

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Estimating B, , and Using Real Data

Histograms of the estimated and from 65 individual microsphere images.

Parameters Estimated values

B 7.29 106

305 (median)

0.0053 (median)

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Numerical Design Set-Up: Full-Shell Case

Set-up:

Object: QD light intensity from two target-captured microspheres. r1 = 2.774m and r2 = 2.874m. Protein targets (diameter 250nm). MAX 0.0053.

Microscope parameters: Na = 1.3, M = 40X, = 535nm, no = 1.334, ns = 1.3.

CCD parameter: = 305 (median of the estimates).

Noise level 2b : B = 7.29 106, Eg = 1.15eV (Si), T 10 to 200C.

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Effect of Microspheres Distance on Performance

Result at T = 00C.

Observation: Optimal (minimal) distance is 17m.

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Effect of Maximum Light Level on Design

Result at T = 00C for varying MAX.

Observation: Optimal distance is robust with respect to the maximum possibletarget-concentration level.

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Effect of Temperature on Performance

Result at d = 13m.

Observation: Performance degrades with higher temperature at a fixed distance.

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Distance and Temperature Effects on Performance

Performance as a function of temperature and distance.

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Numerical Design Set-Up: Sparse-Shell Case

Set-up:

Object: QD light intensity from two target-captured microspheres. r1 = 2.774m and r2 = 2.874m. Protein targets (diameter 250nm). = 1 (more sparsity) or = 5 (less sparsity).

Microscope parameters: Na = 1.3, M = 40X, = 535nm, no = 1.334, ns = 1.3.

CCD parameter: = 305 (median of the estimates).

Noise level 2b : B = 7.29 106, Eg = 1.15eV (Si), T 10 to 200C.

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Effect of Microspheres Distance on Performance

Result at T = 100C with = 1.

Observation: Optimal (minimal) distance is 11m.

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Effect of Sparsity on Design

Result at T = 100C with = 1 and = 5.

Observation: Optimal distance is robust with respect to the sparsity level.

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Effect of Temperature on Performance

Result at d = 7.5m with = 1.

Observation: Performance degrades with higher temperature at a fixed distance.

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Distance and Temperature Effects on Performance

Performance as a function of temperature and distance with = 1.

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Implementing the Microarrays

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Overview

Goal: Implement the proposed microarray based on the proposed statistical design.

Microfluidic approach:

Fabricate PDMS traps (in a microfluidic channel) using lithography.

Separate the traps based on the computed minimal microsphere distance.

Place microspheres in traps using microfluidic hydrodynamic trapping.

Acknowledgement: This implementation is done by our collaborators Drs. AxelScherer and Zhenyu Li of the Caltech Nanofabrication Group.

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Microfluidic Hydrodynamic Trapping

18 m

11 m

5 m 6 m

120 m

Inlet

Outlet

Microfluidic channel

PDMS trap

Microsphere trapping device based on a microfluidic hydrodynamic trapping

(separations are not yet optimal).

Microspheres in liquid flow from the inlet to outlet through vertically alignedmicrofluidic channels containing the traps.

Microspheres are trapped in the determined positions.

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Trapping

P1

P2

P1: Path 1

P2: Path 2

Microsphere

Trap

Trapping:

Fluidic resistance through P1 is smaller than P2.

Hence, microsphere moves through P1 into the empty trap.

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Bypassing

P2P2

Microsphere

Trap

Bypassing: Second microsphere bypasses first trap through P2 and fills the secondtrap.

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Bypassing (Cont.)

P2

Microsphere

Trap

Microsphere trapping through P2.

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Real Trapping Demonstration

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Conclusion We proposed a 3D microarray with position-controlled microspheres, and

discussed its advantages.

This research is multidisciplinary, involving optimal statistical design of thedevice, and implementing using microfluidics.

We derived the posterior Cramr-Rao bounds on the errors in estimating thetarget concentrations, for uniform or sparse profiles.

Estimated the unknown imaging parameters using maximum-likelihood.

Showed quantitatively the effects of distance and temperature on the imagingperformance.

Computed the optimal distance between the microspheres for a giventemperature.

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Future Work

Implement the proposed position-encoded 3D microarray:

Use minimal microsphere distance. Optimize microfluidic hydrodynamic trapping. Employ chambers with micromechanical valves for position encoding. Load chambers with respective microspheres sensitive to specific targets.

Derive tighter bounds for low SNR (sparse shell models).

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Other Research

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Topics

cDNA microarray image segmentation.

Sparse gene regulatory network (GRN) estimation.

Gene reachability analysis.

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cDNA Microarray Image Segmentation

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Overview

Goal: Segment and estimate gene signals for the noisy cDNA microarray images.

Research [14]:

Model cDNA microarray spots using parametric ellipses and circles.

Segment the foreground signals and estimate the noisy spot images using theGibbs sampling based Markov Chain Monte Carlo (MCMC) method.

Clinical application: Identify diseases by detecting gene signals of the protozoanhuman gut parasite Entamoeba histolytica.

[14] P. Sarder, A. Nehorai, P. H. Davis, and S. Stanley, Estimating gene signals from noisy microarray images, IEEE Trans. on

NanoBioscience, vol. 7, pp. 284-297, 2008.

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Results and Future Work

(a) (b)

(a) Noisy cDNA microarray spot image. (b) Estimation result using MCMC.Spots were printed by the Washington University Microarray Core Facility [15].

Future work:

Develop a fast algorithm.

Apply our analysis to clinical data and experiments.

[15] http://www.genome.wustl.edu/services/microarray.cgi.

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Sparse GRN Estimation

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Overview

Goal: Estimate sparse GRN from time-series microarray datasets.

Research [16]:

Estimate regulatory relationships between genes using a Bayesian linearregression method [17] for sparse parameter vectors.

Obtain a consensus GRN using our proposed method, a correlation-coefficientmethod [18], and a database method [19].

Clinical applications: Diagnose diseases and discover drugs.

[16] P. Sarder, W. Schierding, J. P. Cobb, and A. Nehorai, Estimating sparse gene regulatory networks using a Bayesian regression, to

appear in IEEE Trans. on NanoBioscience.

[17] E. G. Larsson and Y. Selen, Linear regression with a sparse parameter vector, IEEE Trans. on Signal Processing, vol. 55, pp. 451-460,

2007.[18] J. Ruan and W. Zhang, Identification and evaluation of functional modules in gene co-expression networks, RECOMB Satellite

Conferences on Systems Biology and Computational Proteomics, San Diego, CA, Dec. 2006.

[19] URL: http://www.ingenuity.com/products/pathwayanalysis.html.

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Results and Future Work

Result: Demonstrated that our proposed method outperforms or performscompetitively with NIR (TSNI) [20], [21] and BANJO [22], the twowell-established approaches in the community.

Result: Generated four biologically meaningful and consensus sub-networks fora human buffy-coat microarray expression profile dataset ofventilator-associated pneumonia (VAP).

Future work: Analyze the VAP sub-networks using conventional molecularanalysis.

[20] G. Della Gatta et. al, Direct targets of the TRP63 transcription factor revealed by a combination of gene expression profiling and reverse

engineering, Genome Research, vol. 18, pp. 939-948, 2008.

[21] T. S. Gardner et. al, Inferring genetic networks and identifying compound mode of action via expression profiling, Science, vol. 301,

pp. 102-105, 2003.

[22] J. Yu et. al, Advances to Bayesian network inference for generating causal networks from observational biological data, Bioinformatics,

vol. 20, pp. 3594-3603, 2004.

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Gene Reachability Analysis

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Overview

Goal: Analyze gene reachability in complex gene co-expression (CoE) networks.

Research [23]:

Compute the average connections per gene in a gene CoE network, inspired bythe Google Page-Rank algorithm [24].

Modify the Google Page-Rank algorithm [24], based on this average.

Compute this average as eight for human and three to seven for yeast. (Thesenumbers agree well with other published results [25], [26].)

Analyze the gene reachability in gene CoE networks, and cluster genes.

Clinical application: Select genes.

[23] P. Sarder, W. Zhang, J. P. Cobb, and A. Nehorai, Gene reachability using Page ranking on gene co-expression networks, in revision for

Link Mining: Models, Algorithms, and Applications, Ch. 11, P. S. Yu, C. Faloutsos, and J. Han, Eds., Springer.

[24] S. Brin and L. Page, The anatomy of a large-scale hypertextual Web search engine (http://www-db.stanford.edu/ backrub/google.html),

Proc. of Seventh Intl. Conf. of World Wide Web 7, pp. 107-117, 1998.

[25] A. K. Ramani, R. C. Bunescu, R. J. Mooney, and E. M. Marcotte, Consolidating the set of known human protein-protein interactions inpreparation for large-scale mapping of the human interactome, Genome Biol., vol. 6, 2005.

[26] G. T. Hart, A. K. Ramani, and E. M. Marcotte, How complete are current yeast and human protein-interaction networks? Genome Biol.,

vol. 7:I20, 2006.

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Acknowledgement

Advisor: Prof. Arye Nehorai (ESE, WUSTL)

Committee Members:

Prof. Hiro Mukai (ESE, WUSTL) Prof. Jr-Shin Li (ESE, WUSTL) Prof. Richard Martin Arthur (ESE, WUSTL) Prof. Dibyen Majumdar (Stats, UIC) Prof. Samuel Achilefu (Radiology, WUSTL)

Collaborators:

Dr. Zhenyu Li (EE, Caltech) Dr. Paul Davis (Biology, U Penn) Prof. Samuel L. Stanley (Stoney Brook) Dr. J. Perren Cobb (Anesthesia, Critical Care and Pain Medicine, MGH) Mr. William Schierding (Genome Center, WUSTL) Prof. Weixiong Zhang (CSE, WUSTL)

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PublicationsBook chapter:

1. P. Sarder, W. Zhang, J. P. Cobb, and A. Nehorai, Gene reachability using Page ranking on gene co-expression networks, inrevision for Link Mining: Models, Algorithms, and Applications, Ch. 11, P. S. Yu, C. Faloutsos, and J. Han, Eds., Springer.

Journal papers:

1. P. Sarder and A. Nehorai, Deconvolution methods for 3D fluorescence microscopy images: An overview, IEEE SignalProcessing Magazine, vol. 23, no. 3, pp. 3245, May 2006.

2. P. Sarder, A. Nehorai, P. H. Davis, and S. Stanley, Estimating gene signals from noisy microarray images, IEEE Trans. onNanoBioscience, vol. 7, no. 2, pp. 142153, June 2008.

3. P. Sarder and A. Nehorai, Estimating locations of quantum-dotencoded microparticles from ultra-high density 3Dmicroarrays, IEEE Trans. on NanoBioscience, vol. 7, no. 4, pp. 284-297, Dec. 2008.

4. P. Sarder, W. Schierding, J. P. Cobb, and A. Nehorai, Estimating sparse gene regulatory networks using a Baysianregression, to appear in IEEE Trans. on NanoBioscience.

5. P. Sarder and A. Nehorai, Statistical design of position-encoded 3D microarrays, submitted to IEEE Sensors Journal.

Conference papers:

1. P. Sarder and A. Nehorai, Performance analysis of quantifying fluorescence of target-captured microparticles frommicroscopy images, Proc. Fourth IEEE Workshop on Sensor Array and Multi-channel Processing, pp. 289-293, Waltham,Massachusetts, USA, Jul. 2006.

2. P. Sarder and A. Nehorai, Statistical design of a 3D microarray with position-encoded microspheres, Proc. Third InternationalWorkshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP), pp. 161-164, Aruba, Dutch Antilles,Dec. 2009.

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Thank You!

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Outlineextcolor {red}{Background}Existing 3D MicroarraysExisting 3D Microarrays (Cont.)Target-Captured MicrosphereMicroarray Solution FlowHow Does 3D Microarray Work?How Does 3D Microarray Work? (Cont.)Microarray ImagingMicroscopyIdeal Microsphere and Nanosphere ImagesReal Microscope ImageDrawbacks of Existing 3D Microarraysextcolor {red}{Our Research}Our ResearchProposed 3D Microarray Layoutextcolor {red}{Statistical Performance Analysis}Performance Analysis OverviewMeasurement ModelMeasurement Model (Cont.)Measurement Model (Cont.)Object Model: Full ShellIdeal Nanosphere QD Light Images: Full ShellObject Model: Sparse ShellIdeal Nanosphere QD Light Images: Sparse ShellMicroscope PSF ModelPosterior Cram{'{e}}r-Rao Boundextcolor {red}{Statistical Design}Design ApproachSensor Temperature Effectextcolor {red}{Minimal Distance Selection}MotivationMinimal Distance SelectionPerformance Measure: Parametric ModelPerformance Parametric Model ExampleSelecting the Minimal DistanceSelecting the Minimal Distance (Cont.)extcolor {red}{Estimating $B$ and $eta $}Estimation OverviewMeasurement ModelEstimating $heta $Estimating $heta $ (Cont.)Estimating $B$Estimating $eta $Estimation Summaryextcolor {red}{Results}Estimating $B,$ $eta ,$ and $heta $ Using Existing MicroarrayEstimating $B,$ $eta ,$ and $heta $ Using Real DataNumerical Design Set-Up: Full-Shell CaseEffect of Microspheres' Distance on PerformanceEffect of Maximum Light Level on DesignEffect of Temperature on PerformanceDistance and Temperature Effects on PerformanceNumerical Design Set-Up: Sparse-Shell CaseEffect of Microspheres' Distance on PerformanceEffect of Sparsity on DesignEffect of Temperature on PerformanceDistance and Temperature Effects on Performanceextcolor {red}{Implementing the Microarrays}OverviewMicrofluidic Hydrodynamic TrappingTrappingBypassingBypassing (Cont.)Real Trapping DemonstrationConclusionFuture Workextcolor {red}{Other Research}Topicsextcolor {red}{cDNA Microarray Image Segmentation}OverviewResults and Future Workextcolor {red}{Sparse GRN Estimation}OverviewResults and Future Workextcolor {red}{Gene Reachability Analysis}OverviewAcknowledgementPublicationsextcolor {red}{extit {Thank You!}}

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