Dilution and Mixing Algorithms for Flow-Based Microfluidic Biochips

Albeit sample preparation is well-studied for digital microfluidic biochips, very few prior work addressed this problem in the context of continuous-flow microfluidics from an algorithmic perspective. In the latter class of chips, microvalves and micropumps are used to manipulate on-chip fluid flow through microchannels in order to execute a biochemical protocol. Dilution of a sample fluid is a special case of sample preparation, where only two input reagents (commonly known as sample and buffer) are mixed in a desired volumetric ratio. In this paper, we propose a satisfiability-based dilution algorithm assuming the generalized mixing models supported by an { \boldsymbol {N}}-segment, continuous-flow, rotary mixer. Given a target concentration and an error limit, the proposed algorithm first minimizes the number of mixing operations, and subsequently, reduces reagent-usage. Simulation results demonstrate that the proposed method outperforms existing dilution algorithms in terms of mixing steps (assay time) and waste production, and compares favorably with respect to reagent-usage (cost) when 4-and 8-segment rotary mixers are used. Next, we propose two variants of an algorithm for handling the open problem of {k}-reagent mixture-preparation ( {k\geq 3} ) with an {N}-segment continuous-flow rotary mixer, and report experimental results to evaluate their performance. A software tool called flow-based sample preparation algorithm has also been developed that can be readily used for running the proposed algorithms.