ILP-Based Pin-Count Aware Design Methodology for Microfluidic Biochips

Chiung-Yu Lin and Yao-Wen Chang

Department of EE, NTU

DAC 2009

Outline

Introduction Pin demand and proposed flow Stage assignment Device assignment Placement and routing guideline Experimental results Conclusions

Introduction

Digital microfluidic biochips, also referred to as lab-on-a-chip, have emerged as an alternative for conventional laboratory experiments.

A biochip consists of a 2D electrode array and peripheral devices (optical detector, dispensing ports, etc.)

Movement of the droplets are controlled by the electrodes.

Introduction

Devices and reactions Reservoirs/Dispensing ports: droplet generation Optical detector: droplet detection Mixer: mixing two droplets

Introduction

The side view of the 2D array. A droplet moves to an adjacent electrode when this electrode

is activated. A droplet can stay at one cell if its neighboring electrodes are

not activated.

Introduction

Pin demand and proposed flow

Classify the demand of pins Np into three categories:

Pin demand and proposed flow

Stage assignment: This stage minimizes Preaction by enables the synchronous

control of the reactions.

Pin demand and proposed flow

Device assignment: This stage minimizes Pbranching by matching the reactions

to specific devices.

Stage assignment

Advantage of Synchronous Reactions

(a) Asynchronous: Mixers 1 and 2 are controlled separately and do not share a control pin. A shorter completion time is achieved.

(b) Synchronous: Mixers 1 and 2 are controlled together, the mixers must begin and cease their mixing reactions synchronously. Mixers 1 and 2 can share their control pins.

Stage assignment

The Stage Assignment Problem

Given a bioassay, stage assignment divides the reactions into a set of execution stages, and each stage is dedicated to a single category of reactions.

e.g., generation of certain sample/reagent, mixing, optical detection, etc.

Stage assignment

Following are the constraints for the stage assignment:

Capacity constraints: The number of reactions in a stage is upper-bounded by the

number of the devices belonging to the category of the stage.

Uniqueness constraints: A reaction exists in exactly one stage.

Duration constraints: The duration of a stage is the duration of the slowest reaction.

Stage assignment

Sequence constraints: Stages that belong to the same category are sorted and e

xecuted sequentially without overlapping.

Precedence constraints: If reaction Ri must happen before reaction Rj, then the sta

ge that includes Rj can begin only after the stage of Ri ends.

Problem Formulation for Stage Assignment

Given:

Problem Formulation for Stage Assignment

Find: A partitioning of Sr into independent stages Sm,1, Sm,2, …,

Sm,Im, where Sm,i represents the i-th stage for Dm, and Im represents the max number of stages for Dm.

Corresponding start time Bm,i and finish time Em,i for these stages.

Minimize:

ILP Formulation for Stage Assignment

ILP Formulation for Stage Assignment

Solution Space Reduction

Reaction Category Mapping All gn,m,i with m≠Vn can be removed.

Upper Bound for the Stage Number Bound the number of stages used by each device categor

y.

Lower Bound for Assay Completion Time Add a lower bound for the assay completion time into the I

LP formulation to speed up the runtime.

Device Assignment

Effect of Device Permutation Device assignment can affect the number of branchings. In (b), {1-1, 1-2, 2-1} three paths are used. In (c), {1-1, 2-1} only two paths are used and thus fewer el

ectrodes are needed for controlling the branchings.

Problem Formulation for Device Assignment

Given: Sr, Sd, Vn, Cm, Sp, Sm,i same as that from stage assignme

nt.

Find:

xn,z is the occurrence of that Rn is assigned to the z-th device of the category.

Minimize:

pm1,z1,m2,z2 denotes the existence of a path from the z1-th device of Dm1 to the z2-th device of Dm2.

ILP Formulation for Device Assignment

Solution-Space Reduction

Redundancy Pruning Reduce the solution space by removing the path

around universal peripheral reactions.

R1

R2

R3 R4

Placement and Routing Guideline

Pin-Count Saving Guidelines Provide guarding cells between two electrodes that work

in separate time spans. Electrodes E1 and E2 are turned on for different routing

paths in separate time slots, but they still cannot be controlled by the same pin because they are neighbors.

Placement and Routing Guideline

Propose the following placement and routing guidelines:

The placement and routing for the entire bioassay should be decided simultaneously on a 2D plane.

Routing paths should not touch each other, except for necessary crossings or branchings.

Guarding electrodes should be placed between devices and devices.

Experimental Results

Experimental Results

Experimental Results

Experimental Results

Conclusions

ILP-based algorithms have been proposed for the stage and device assignments with effective solution-space reductions.