1. Summarized by Ji-Yeon Lee & Soo-Yong Shin
Using three-dimensional microfluidic networks for solving computationally hard problems
PNAS March 13, 2001 vol. 98 no ~2966
Daniel T. Chiu, Elena Pezzoli, Hongkai Wu, Abraham D. Stroock, and George M. Whitesies
Harvard University
Summarized by Ji-Yeon Lee & Soo-Yong Shin

2. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Abstract
Solving Maximal clique problem
3-MCP, 6-MCP
Algorithm
parallel fabrication of the microfluidic system
parallel searching of all potential solutions by using fluid flow
parallel optical readout of all solutions
(C) 2001, SNU Biointelligence Lab, 

3. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Algorithm
Four steps
1) for every edge [i,j] of G, label (tag) every subgraph of G that contains vertices i and j
2) for every subgraph, count the number of tags
3) decide whether there are enough tags (edges) in each subgraph to be a clique
4) return the size and identity of the largest clique
(C) 2001, SNU Biointelligence Lab, 

4. Implementation of algorithm
Fig A : schematic diagram of 3-vertex graph
subgraph well
edge reservoir
3D microfluidic system
 to avoid the crossover
 three vertices & four layers
Quantitation of the connectivity
 measure the flow from reservoir into well
 use liquid containing a uniform suspension of fluorescent beads (filter membrane was used)
connected
by channel
(C) 2001, SNU Biointelligence Lab, 

5. putting a calibrated number of beads into each reservoir
Step 1
putting a calibrated number of beads into each reservoir
(parallel operation)
spilts and flows simultaneously into both channels
Step 2
exploit the optical systems to read out the relative
amount of fluorescence in each well (parallel)
Step 3
setting the appropriate optical detection threshold
for each clique size
Step 4
observing the position of the clique along
the x and y axes in microfluidic device
the size of a clique can be easily derived by knowing
its relative displacement along the y axis
(C) 2001, SNU Biointelligence Lab, 

6. Schematic of the microfluidic device
(C) 2001, SNU Biointelligence Lab, 

7. Quntitation with fluorescence
(C) 2001, SNU Biointelligence Lab, 
[1,2][1,3][2,3] introduced
[1,2][2,3] introduced

8. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Materials and Methods
PDMS
REM
Small sizes of fluorescent beads (400nm or smaller)
(C) 2001, SNU Biointelligence Lab, 

9. Results and Discussion
Needed layer (= edges layer + bottom layer)
n(n-1)/2 for edges
in six vertex problem, = 16 layer
Subgraphs with k vertices
must have k(k-1)/2 units of fluorescence to be clique
 threshold criterion
More relaxed criterion
to account for errors
set a threshold halfway between the intensities expected for a k clique and a k-1 clique
must have [(k-1)(k-2)/2 + (k-1)/2] fluorescence intensities
(C) 2001, SNU Biointelligence Lab, 

10. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Even splitting
the pressure drop along the two branches is identical
cross section and the total length of each channel pathway from reservoir to waste are the same!
 flow rate in each channel are indistinguishable
(C) 2001, SNU Biointelligence Lab, 

11. Experimental solution to a Three-Vertex Graph
exactly
three times!!
(C) 2001, SNU Biointelligence Lab, 

12. Experimental solution to a Six-Vertex Graph I
(C) 2001, SNU Biointelligence Lab, 

13. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Experimental solution to a Six-Vertex Graph II
(C) 2001, SNU Biointelligence Lab, 

14. Discussion and Conclusions I
Analog computation device
Parallel operation
Microfluidic channel
Multi-layer structure
Fluorescent beads
strength
high parallelism vs
space-time tradeoff
weakness
exponential increase in its physical size
(C) 2001, SNU Biointelligence Lab, 

15. Discussion and Conclusions II
Potential sources of error
1) biased splitting of fluorescent beads at each channel branching
2) misalighment between layers that results in error in the integrated fluorescence intensities
 main cause of misalignment between layers is differential shrinkage of PDMS in different layers during fabrication
To overcome errors
1) implement error-correction step before integrating the intensities from each layer (reset to zero)
2) use exactly the same procedures (using the same amount of catalyst and curing at the same temperature)
(C) 2001, SNU Biointelligence Lab, 

16. Discussion and Conclusions III
Limitation
largest graph : 20 vertices or 40 vertices
impractical
Advantages to using microfluidic system
using parallel optical system
different color beads (fluorescent)
no requirement in power
Personal thinking
scale-up : both device and fluorescence
(C) 2001, SNU Biointelligence Lab, 

17. Using Microfluidic Systems as Analog Devices for Solving Computational Problems
D. R. Reyes, G. M. Whitesides, and A. Manz
TAS 2001
Summarized by Soo-Yong Shin

18. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Abstract
Solving shortest path problems using microfluidic chip.
Maze searches
(C) 2001, SNU Biointelligence Lab, 

19. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Algorithms
Graphical representation of the problems were generated.
The graphical representations were fabricated on glass chips
Helium gas was used.
(C) 2001, SNU Biointelligence Lab, 

20. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Results
Small problems
(C) 2001, SNU Biointelligence Lab, 

21. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Results
A segment of a map of London
From Traflagar Square to Victoria Station
(C) 2001, SNU Biointelligence Lab, 

22. (C) 2001, SNU Biointelligence Lab, http://bi.snu.ac.kr/
Results
Solutions of the problems were obtained in less than 250ms.
(C) 2001, SNU Biointelligence Lab,