Waste-aware dilution and mixing of biochemical samples with digital microfluidic biochips

A key challenge in design automation of digital microfluidic biochips is to carry out on-chip dilution/mixing of biochemical samples/reagents for achieving a desired concentration factor (CF). In a bioassay, reducing the waste is crucial because the waste droplet handling is cumbersome and the number of waste reservoirs on-chip needs to be minimized to use limited volume of sample and expensive reagents and hence to reduce the cost of a biochip. The existing dilution algorithms attempt to reduce the number of mix/split steps required in the process but focus little on minimization of sample requirement or waste droplets. In this work, we characterize the underlying combinatorial properties of waste generation and identify the inherent limitations of two earlier mixing algorithms (BS algorithm by Thies et al., Natural Computing 2008; DMRW algorithm by Roy et al., IEEE TCAD 2010) in addressing this issue. Based on these properties, we design an improved dilution/mixing algorithm (IDMA) that optimizes the usage of intermediate droplets generated during the dilution process, which in turn, reduces the demand of sample/reagent and production of waste. The algorithm terminates in O(n) steps for producing a target CF with a precision of 1/2n. Based on simulation results for all CF values ranging from 1/1024 to 1023/1024 using a sample (100% concentration) and a buffer solution (0% concentration), we present an integrated scheme of choosing the best waste-aware dilution algorithm among BS, DMRW, and IDMA for any given value of CF. Finally, an architectural layout of a DMF biochip that supports the proposed scheme is designed.