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 N p into three categories:

Pin demand and proposed flow Stage assignment:  This stage minimizes P reaction by enables the synchronous control of the reactions.

Pin demand and proposed flow Device assignment:  This stage minimizes P branching 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 executed sequentially without overlapping. Precedence constraints:  If reaction R i must happen before reaction R j, then the stage that includes R j can begin only after the stage of R i ends.

Problem Formulation for Stage Assignment Given:

Problem Formulation for Stage Assignment Find:  A partitioning of S r into independent stages S m,1, S m,2, …, S m,Im, where S m,i represents the i-th stage for D m, and I m represents the max number of stages for D m.  Corresponding start time B m,i and finish time E m,i for these stages. Minimize:

ILP Formulation for Stage Assignment

Solution Space Reduction Reaction Category Mapping  All g n,m,i with m≠V n can be removed. Upper Bound for the Stage Number  Bound the number of stages used by each device category. Lower Bound for Assay Completion Time  Add a lower bound for the assay completion time into the ILP 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 electrodes are needed for controlling the branchings.

Problem Formulation for Device Assignment Given:  S r, S d, V n, C m, S p, S m,i same as that from stage assignment. Find:  x n,z is the occurrence of that R n is assigned to the z-th device of the category. Minimize:  p m1,z1,m2,z2 denotes the existence of a path from the z 1 -th device of D m1 to the z 2 -th device of D m2.

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

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