Transport-Free Placement of Mixers for Realizing Bioprotocol on Programmable Microfluidic Devices

A Programmable Microfluidic Device (PMD) is one of the promising biochip platforms. On a PMD having a two-dimensional array of cells, fluids are mixed by a module called a mixer. We can configure various kinds of mixers, such as a $2\times 2$ mixer and a $2\times 3$ mixer consisting of $2\times 2$ and $2\times 3$ arrays of cells, respectively. Unlike other biochip platforms, it is difficult to precisely move a fluid from one cell to another in a PMD without any contamination. Thus, recently a “No Transport Mixing (NTM)’ method has been proposed, which binds and schedules the mixers without fluid transportation. However, NTM works with only $2\times 2$ mixers on a PMD biochip. In this paper, we propose an efficient method to bind and schedule the mixing operations using $2\times 3$ mixers as well as $2\times 2$ mixers. The proposed method is based on the transformation of a mixing tree into another one based on the “Placement Priority’ values as estimated. Simulation results confirm that this transformation indeed is useful to decrease the number of washing operations (‘flushing’) required during the implementation of a bioprotocol on a PMD biochip, which, in turn, reduces the consumption of expensive biochemical fluids in the bioprotocol.