Due to the ability of dynamic reconfiguration, the synthesis and routing problems of digital microfluidic biochips are different from traditional ones. First, an operation executed on a biochip needs a certain area and lasts for a period of time. Therefore, we model each operation as a 3D box with its width and height (X and Y dimensions) representing the physical dimensions occupied by the operation and its duration (T dimension) being the execution time required for the operation, as shown in Figure 1.10. Second, besides only determining the locations of each operation, the starting time of them must be determined; that is, it is needed to perform scheduling on operations.
In this dissertation, we first present the 3D modeling of the execution of a bioassay on a biochip. This 3D modeling maps the execution of a bioassay to a 3D floorplan. Therefore, to determine the placement/schedule of all operations of a bioassay is equivalent to the temporal floorplanning problem. Second, based on
the 3D floorplan, we present a placement algorithm of digital microfluidic biochips.
This algorithm is based on the T-tree representation, which is the first tree-based 3D floorplan representation. We also propose a clustering algorithm to make use of the property of a bioassay for better solution quality and less CPU time. Then we propose two droplet routing algorithms, one for general biochips and the other one for cross-referencing biochips. The first one is a network-flow based method. The min-cost max-flow algorithm is used for global routing while a negotiation based approach is used for detailed routing. The second one is the progressive-ILP based approach, where we determine the locations of droplets progressively, one time step at a time.
The topic of each chapter is briefly introduced in the following subsections.
1.4.1 Modeling of Bioassay Execution
In chapter 3, we first describe the execution of a bioassay on a biochip. Then, based on the characteristic of biochips, we model the execution of a bioassay as a 3D floorplan, where the X (Y ) dimension represents the width (height) of a biochip and the T dimension represents the duration of the bioassay. Each operation, such as droplets mix, is modeled as a 3D box in a 3D floorplan. With this modeling, we use a 3D floorplan to represent a placement/schedule of a bioassay. Besides, we apply the temporal floorplanning techniques to determine the execution of a bioassay.
1.4.2 Placement of Digital Microfluidic Biochips
In Chapter 4, we present the proposed placement algorithm for the place-ment problem of digital microfluidic biochips. Since T-tree is the core technology for the proposed algorithm, we first present the T-tree 3D floorplan representation.
We present the structure of T-tree, the method to transform a compacted placement to its corresponding T-tree, and the packing algorithm. We also derive the solution space and the reachability of T-tree. Next we present the T-tree based algorithm.
There are three challenges of the placement problem. First, to guarantee the cor-rect execution of a bioassay, there exists temporal orderings for all fundamental operations. A placement solution must satisfy these temporal orderings. Second,
in a digital microfluidic biochip, there are different types of operations with differ-ent characteristics. Differdiffer-ent modelings is needed for differdiffer-ent types of operations.
Third, the number and location of storage units are needed to be determined , where a storage unit is used to store the intermediate result between two data-dependent operations. Based on the structure of T-tree, we develop an efficient and effective algorithm to solve the placement problem. We also propose a clustering algorithm based on the property of a bioassay. Experimental results show that this method is more efficient and effective than previous unified synthesis and placement approach.
1.4.3 Droplet Routing on General Biochips
In Chapter 5, we present a network-flow based droplet routing algorithm on biochips. The main challenge is to satisfy the unique fluidic property of biochips to avoid unexpected mixing among droplets. This algorithm is divided into global and detailed routing stages. In global routing, we first determine a set of independent nets that can be freely routed without interfering other nets. Then, a network-flow based algorithm is used to optimally find the rough routing path of the independent nets. In detailed routing, we iteratively route and schedule each droplet based on the result of global routing stage. The objective is to minimize the number of cells used for routing for better fault tolerance or the maximum droplet transportation time for fast bioassay execution or better bioassay integrity. Routing results on a set of real-world bioassays show the efficiency and robustness of the proposed algorithm.
1.4.4 Droplet Routing on Cross-referencing Biochips
The previous two chapters handles placement and routing problems on gen-eral biochips. In Chapter 6, we target at cross-referencing biochips, a more scalable architecture that uses row/column addressing to activate electrodes. The main challenge of routing droplet on this type of architecture is the electrode interference which prevents simultaneous droplet movement. Therefore, the time for bioassay execution is potentially increased. In order to solve the droplet routing problem, we first propose a basic integer linear programming (ILP) formulation that minimizes the maximum droplet transportation time. Due to its high complexity, we propose
the progressive ILP routing scheme that determines min-cost droplet position pro-gressively, one time step at a time. Therefore, the complexity of solving ILP can be significantly reduced. Moreover, this scheme maximizes the number of droplets that can simultaneously move at the same time, which results in a routing solution with lower droplet transportation time. We also propose some implementation strategies to obtain a reasonable solution within reasonable CPU time. Experimental results show that the progressive ILP routing scheme can obtain a near-optimal solution.
Compared with previous droplet manipulation methods, the proposed algorithm can effectively minimize the droplet transportation time.