Miguel Coviello Gonzalez

arXiv2019

A Waste-Efficient Algorithm for Single-Droplet Sample Preparation on Microfluidic Chips

We address the problem of designing micro-fluidic chips for sample preparation, which is a crucial step in many experimental processes in chemical and biological sciences. One of the objectives of sample preparation is to dilute the sample fluid, called reactant, using another fluid called buffer, to produce desired volumes of fluid with prespecified reactant concentrations. In the model we adopt, these fluids are manipulated in discrete volumes called droplets. The dilution process is represented by a mixing graph whose nodes represent 1-1 micro-mixers and edges represent channels for transporting fluids. In this work we focus on designing such mixing graphs when the given sample (also referred to as the target) consists of a single-droplet, and the objective is to minimize total fluid waste. Our main contribution is an efficient algorithm called RPRIS that guarantees a better provable worst-case bound on waste and significantly outperforms state-of-the-art algorithms in experimental comparison.

cs.DS↗

arXiv2019

Towards a Theory of Mixing Graphs: A Characterization of Perfect Mixability

Some microfluidic lab-on-chip devices contain modules whose function is to mix two fluids, called reactant and buffer, in desired proportions. In one of the technologies for fluid mixing the process can be represented by a directed acyclic graph whose nodes represent micro-mixers and edges represent micro-channels. A micro-mixer has two input channels and two output channels; it receives two fluid droplets, one from each input, mixes them perfectly, and produces two droplets of the mixed fluid on its output channels. Such a mixing graph converts a set I of input droplets into a set T of output droplets, where the droplets are specified by their reactant concentrations. The most fundamental algorithmic question related to mixing graphs is to determine, given an input set I and a target set T, whether there is a mixing graph that converts I into T. We refer to this decision problem as mix-reachability. While the complexity of this problem remains open, we provide a solution to its natural sub-problem, called perfect mixability, in which we ask whether, given a collection C of droplets, there is a mixing graph that mixes C perfectly, producing only droplets whose concentration is the average concentration of C. We provide a complete characterization of such perfectly mixable sets and an efficient algorithm for testing perfect mixability. Further, we prove that any perfectly mixable set has a perfect-mixing graph of polynomial size, and that this graph can be computed in polynomial time.

cs.DM↗