Minimum Resource Characterization of Biochemical Analyses for Digital Microfluidic Biochip Design

Digital microfluidic systems (DMFS) are a class of lab-on-a-chip systems that manipulate individual droplets of chemicals on an array of electrodes. The biochemical analyses are performed by repeatedly moving, mixing, and splitting droplets on the electrodes. In this paper, we characterize the tree structure of biochemical analyses and identify their minimum resource requirements, towards the design of cost and space-efficient biochips. Mixers and storage units are two primary functional resources on a DMFS biochip; mixers mix and split droplets while storage units store droplets on the chip for subsequent processing. Additional DMFS resources include input and output units and transportation paths. We present an algorithm to compute, for a given number of mixers M , the minimum number of storage units f(M) for an input analysis using its tree structure, and design a corresponding scheduling algorithm to perform the analysis. We characterize the variation of the M -depth of a tree (i.e., its minimum number of storage units f(M)) with M , and use it to calculate the minimum total size (the number of electrodes) of mixers and storage units. We prove that the smallest chip for an arbitrary analysis uses one mixer and f(1) storage units. Finally, we demonstrate our results on two example biochemical analyses and design the smallest chip for a biochemical analysis with a complete tree structure of depth 4. These are the first results on the least resource requirements of DMFS for biochemical analyses, and can be used for the design and selection of chips for arbitrary biochemical analyses.