Mixing Models as Integer Factorization: A Key to Sample Preparation With Microfluidic Biochips

Abstract

Microfluidic biochips have recently emerged with significant promise and versatility in automating a variety of biochemical protocols on a tiny chip. Sample preparation, which involves the mixing of fluids with a specified target ratio in the minuscule scale, is an essential component of these protocols. Algorithms that optimize on-chip sample-preparation cost and time are closely intertwined with the underlying mixing model, mixing sequence, and fluidic architecture. Although numerous mixing models have been studied in the literature, their impact on the dynamics of mixing steps is hitherto not fully understood. In this article, we show that various mixing models can be envisaged in the light of prime factorization of integers thus establishing a connection among mixing algorithms, chip architectures, and performance. This insight has led to the development of the proposed factorization-based dilution algorithm ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FacDA</i> ) considering a generalized mixing model suitable for micro-electrode-dot-array (MEDA) biochips. It further leads to target volume oriented dilution algorithm ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TVODA</i> ) to cater to user’s demand for an output with a given volume. We formulate the optimization problem on the fabric of the satisfiability modulo theory (SMT) while determining mixing sequences. Simulation results on a large number of test-cases reveal that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FacDA</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">TVODA</i> outperform the state-of-the-art dilution algorithms for MEDA biochips with respect to reactant cost, mixing time, and waste production.