Towards a Theory of Droplet-Mixing Graphs in Microfluidics

In this work, we study the problem of fluid mixing in microfluidic chips. The motivation for studying this problem comes from the process of sample preparation for chemical, biological, medical and environmental experiments, which often require preparation of fluid mixtures with desired concentrations. We assume that fluids are manipulated in discrete units called droplets. The input set of droplets consist of two distinct fluids: the reactant, which is the fluid of interest, and the buffer fluid that is used to dilute it. The goal is to produce a target set of droplets with prespecified reactant concentrations. In the model we study, the mixing process in a microfluidic chip can be abstractly represented as a mixing graph. A mixing graph is a collection of micro-mixers (nodes) connected by micro-channels (edges) that converts an input set of droplets I into a set of output droplets T, by applying a sequence of 1:1 mixing operations. This graph may also produce some waste, which are superfluous droplets of fluid not used in the target set. Computational complexity of most natural questions regarding such mixing graphs remain open. For example, it is not even known whether it is decidable for a given target set to be produced without waste. Current work in the literature contains only heuristic approaches that compute mixing graphs while attempting to optimize certain objectives, including minimizing waste, reactant usage, the depth of the graphs, and more.Our first contribution is an efficient algorithm for computing mixing graphs for single-droplet targets. Our algorithm produces significantly less waste than state-of-the-art algorithms in an experimental comparison. We also provide a bound on its worst-case performance that is significantly better than those for earlier algorithms. Our second result concerns the variant of the problem where the objective is to design a mixing graph that perfectly mixes a collection of input droplets with arbitrary concentrations. We provide a complete characterization of input sets for which such graphs exist, and an efficient algorithm to construct these graphs. In addition, we provide several other results about properties of mixing graphs and the computational complexity of computing mixing graphs of fixed depth

Design and Optimization Methods for Pin-Limited and Cyberphysical Digital Microfluidic Biochips

<p>Microfluidic biochips have now come of age, with applications to biomolecular recognition for high-throughput DNA sequencing, immunoassays, and point-of-care clinical diagnostics. In particular, digital microfluidic biochips, which use electrowetting-on-dielectric to manipulate discrete droplets (or "packets of biochemical payload") of picoliter volumes under clock control, are especially promising. The potential applications of biochips include real-time analysis for biochemical reagents, clinical diagnostics, flash chemistry, and on-chip DNA sequencing. The ease of reconfigurability and software-based control in digital microfluidics has motivated research on various aspects of automated chip design and optimization.</p><p>This thesis research is focused on facilitating advances in on-chip bioassays, enhancing the automated use of digital microfluidic biochips, and developing an "intelligent" microfluidic system that has the capability of making on-line re-synthesis while a bioassay is being executed. This thesis includes the concept of a "cyberphysical microfluidic biochip" based on the digital microfluidics hardware platform and on-chip sensing technique. In such a biochip, the control software, on-chip sensing, and the microfluidic operations are tightly coupled. The status of the droplets is dynamically monitored by on-chip sensors. If an error is detected, the control software performs dynamic re-synthesis procedure and error recovery.</p><p>In order to minimize the size and cost of the system, a hardware-assisted error-recovery method, which relies on an error dictionary for rapid error recovery, is also presented. The error-recovery procedure is controlled by a finite-state-machine implemented on a field-programmable gate array (FPGA) instead of a software running on a separate computer. Each state of the FSM represents a possible error that may occur on the biochip; for each of these errors, the corresponding sequence of error-recovery signals is stored inside the memory of the FPGA before the bioassay is conducted. When an error occurs, the FSM transitions from one state to another, and the corresponding control signals are updated. Therefore, by using inexpensive FPGA, a portable cyberphysical system can be implemented.</p><p>In addition to errors in fluid-handling operations, bioassay outcomes can also be erroneous due the uncertainty in the completion time for fluidic operations. Due to the inherent randomness of biochemical reactions, the time required to complete each step of the bioassay is a random variable. To address this issue, a new "operation-interdependence-aware" synthesis algorithm is proposed in this thesis. The start and stop time of each operation are dynamically determined based on feedback from the on-chip sensors. Unlike previous synthesis algorithms that execute bioassays based on pre-determined start and end times of each operation, the proposed method facilitates "self-adaptive" bioassays on cyberphysical microfluidic biochips.</p><p>Another design problem addressed in this thesis is the development of a layout-design algorithm that can minimize the interference between devices on a biochip. A probabilistic model for the polymerase chain reaction (PCR) has been developed; based on the model, the control software can make on-line decisions regarding the number of thermal cycles that must be performed during PCR. Therefore, PCR can be controlled more precisely using cyberphysical integration.</p><p>To reduce the fabrication cost of biochips, yet maintain application flexibility, the concept of a "general-purpose pin-limited biochip" is proposed. Using a graph model for pin-assignment, we develop the theoretical basis and a heuristic algorithm to generate optimized pin-assignment configurations. The associated scheduling algorithm for on-chip biochemistry synthesis has also been developed. Based on the theoretical framework, a complete design flow for pin-limited cyberphysical microfluidic biochips is presented.</p><p>In summary, this thesis research has led to an algorithmic infrastructure and optimization tools for cyberphysical system design and technology demonstrations. The results of this thesis research are expected to enable the hardware/software co-design of a new class of digital microfluidic biochips with tight coupling between microfluidics, sensors, and control software.</p>Dissertatio

Confocal laser scanning microscopy of nanoparticles applied to immunosorbent assays

The aim of this project was to demonstrate and develop a confocal readout method for fluorescent immunosorbent assays and investigate its potential advantages in comparison to traditional immunoassays. The key point of a confocal immunosorbent assay is the ability to detect the thin layer of immunoassay in the presence of unbound fluorescent reagents without washing the overlayer. Heterogeneous and homogeneous sandwich immunoassays of human IgG model were demonstrated successfully followed by the use of an empirical decomposition method for quantitative separation of the signals of the thin fluorescent assay layer from the overlayer. The detection limits for the homogeneous and heterogeneous formats of the model were 2.2 and 5.5 ng/ml, respectively. The application of confocal microscopy in kinetic analysis of the antigen-antibody reaction of the human IgG model was studied for homogeneous and heterogeneous formats and two fluorescent labels antibodies (FITC and QDs)

Doctor of Philosophy

dissertationA majority of the functions in biological systems are mediated by specific interactions of cellular proteins. Such interactions also involve other biomolecules like antibodies, RNA and DNA, small molecules sometimes referred to as drugs, etc. A detailed understanding of functional proteomics necessitates the need for detection and quantification of such specific biochemical reactions with greater speed and precision. The primary biosensing technology that is employed for detecting these biological interactions optically and with good sensitivity and reproducibility is based on Surface Plasmon Resonance (SPR). In this work, we aim at utilization of chemical signal processing techniques in microfluidic chips to produce SPR measurements with higher signal-to-noise ratio (SNR), shorter measurement times, and lower reagent volumes than those of conventional SPR systems like BIAcore, ProteOn, etc. The drawbacks of conventional methods are discussed and schemes based on signal processing in frequency domain are applied to minimize the influence of spurious signals that affect the measurement accuracy. With the choice of applied excitation signal, a 100-fold improvement in SNR has been achieved. Similarly, with alteration of signal postprocessing methodology, we have reported a 10-fold faster dual-slope method that can be employed for a variety of methods are discussed and schemes based on signal processing in frequency domain are applied to minimize the influence of spurious signals that affect the measurement accuracy. With the choice of applied excitation signal, a 100-fold improvement in SNR has been achieved. Similarly, with alteration of signal postprocessing methodology, we have reported a 10-fold faster dual-slope method that can be employed for a variety of the microchip that uses less than a hundred nanoliter of reagent volume for bio-characterization. Discrete liquid droplets are synthesized in an ordered fashion to carry out the bioreaction that conventionally utilizes reagent volumes ranging from a few hundred microliters to a few milliliters