**Lumped-Element Modeling for Rapid Design and Simulation of Digital Centrifugal Microfluidic Systems**

Mahdi Mohammadi, David J Kinahan and Jens Ducrée

Additional information is available at the end of the chapter

http://dx.doi.org/10.5772/62836

#### **Abstract**

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Since the 1990s, centrifugal microfluidic platforms have evolved into a mature technol‐ ogy for the automation of bioanalytical assays in decentralized settings. These "Lab-ona-Disc" (LoaD) systems have already implemented a range of laboratory unit operations (LUOs) such as sample loading, liquid transport, metering, aliquoting, routing, mixing, and washing. By assembling these LUOs in highly functional microfluidic networks, including sample preparation and detection, a sizable portfolio of common test formats such as general chemistry, immunoassays/ protein analysis, nucleic acid testing, and cell counting has been established. The availability of these bioanalytical assay types enables a broad range of applications in fields such as life-science research, biomedical point-ofcare testing and veterinary diagnostics, as well as agrifood, environmental, infrastruc‐ tural, and industrial monitoring.

Recently, a new method of the so-called "event-triggered" flow control has been developed which is independent of the spin rate. These valves, which function in a handshake mode as opposed to the typically batchwise liquid transfers on the "Lab-on-a-Disc" (LoaD) platform, assume a similarly pivotal role as relays and transistors in digital electronics, allowing conditional, logical (flow) control elements. This chapter will describe the modeling of this new generation of "digital" centrifugal microfluidic systems with lowdimensional, lumped-element simulations which have already been instrumental to the modern success story of modern microelectronics.

**Keywords:** lumped-element simulation, centrifugal microfluidics, lab-on-a-disc, event-triggered flow control, valving

© 2016 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

### **1. Introduction**

The centrifugal microfluidic platform has evolved into mature technology platform which has already proven to open significant market opportunity [1–5]. A large number of groups groups working on such LoaD systems in industry has already convincingly demonstrated the capability to integrate, automate, parallelize, and miniaturize a wide range of common bioanalytical test formats for detecting targets such as small molecules, proteins/antibodies, nucleic acids, and cells. Applications span from decentralized biomedical point-of-care diagnostics, veterinary medicine and agrifood, to the surveillance of the environment and infrastructures.

Based on the recently introduced, event-triggered flow control scheme [6, 7], highly functional microfluidic circuits can be assembled in a modular fashion from a limited set of LUOs to implement a broad repertoire of multi-step, multi-reagent bioassay protocols in a sample-toanswer fashion. Furthermore, it has been demonstrated that the chips could be progressively miniaturized to significantly enhance integration density (i.e., the number of assay steps and/ or tests per disc) and thus boost the overall cost efficiency and functionality of the LoaD platform.

Similar to integrated circuits in microelectronics, a microfluidic network can be modeled by lumped-element descriptors. Instead of a finely meshed 3-dimensional lattice, the Lab-on-a-Disc systems are described by a low number of parameters such as pressure head (voltage source), flow resistance (electric resistance), and compressibility (capacitance). This reduceddimension method can be utilized for fast design and simulation of microfluidic systems that are composed of a library of functional units.

After the introduction (Section 1), the hydrodynamic principles of centrifugal microfluidics are presented (Section 2) before outlining digital flow control schemes (Section 3). Next, the concept of lumped-element simulation in event-triggered centrifugal microfluidic networks is developed (Section 4).
