Dilution and Mixing Algorithms for Flow-Based Microfluidic Biochips
01 Apr 2017-IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems (Institute of Electrical and Electronics Engineers Inc.)-Vol. 36, Iss: 4, pp 614-627
TL;DR: The proposed satisfiability-based dilution algorithm outperforms existing dilution algorithms in terms of mixing steps and waste production, and compares favorably with respect to reagent-usage (cost) when 4- and 8-segment rotary mixers are used.
Abstract: Albeit sample preparation is well-studied for digital microfluidic biochips, very few prior work addressed this problem in the context of continuous-flow microfluidics from an algorithmic perspective. In the latter class of chips, microvalves and micropumps are used to manipulate on-chip fluid flow through microchannels in order to execute a biochemical protocol. Dilution of a sample fluid is a special case of sample preparation, where only two input reagents (commonly known as sample and buffer ) are mixed in a desired volumetric ratio. In this paper, we propose a satisfiability-based dilution algorithm assuming the generalized mixing models supported by an ${ \boldsymbol {N}}$ -segment, continuous-flow, rotary mixer. Given a target concentration and an error limit, the proposed algorithm first minimizes the number of mixing operations, and subsequently, reduces reagent-usage. Simulation results demonstrate that the proposed method outperforms existing dilution algorithms in terms of mixing steps (assay time) and waste production, and compares favorably with respect to reagent-usage (cost) when 4- and 8-segment rotary mixers are used. Next, we propose two variants of an algorithm for handling the open problem of ${k}$ -reagent mixture-preparation ( ${k\geq 3}$ ) with an ${N}$ -segment continuous-flow rotary mixer, and report experimental results to evaluate their performance. A software tool called flow-based sample preparation algorithm has also been developed that can be readily used for running the proposed algorithms.
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29 Jun 2018
TL;DR: This work proposes to “lock” biochemical assays through random insertion of dummy mix-split operations, subject to several design rules, and experimentally evaluates the proposed locking mechanism, and shows how a high level of protection can be achieved even on bioassays with low complexity.
Abstract: It is expected that as digital microfluidic biochips (DMFBs) mature, the hardware design flow will begin to resemble the current practice in the semiconductor industry: design teams send chip layouts to third party foundries for fabrication. These foundries are untrusted, and threaten to steal valuable intellectual property (IP). In a DMFB, the IP consists of not only hardware layouts, but also of the biochemical assays (bioassays) that are intended to be executed on-chip. DMFB designers therefore must defend these protocols against theft. We propose to “lock” biochemical assays through random insertion of dummy mix-split operations, subject to several design rules. We experimentally evaluate the proposed locking mechanism, and show how a high level of protection can be achieved even on bioassays with low complexity. We offer guidance on the number of dummy mixsplits required to secure a bioassay for the lifetime of a patent.
27 citations
Cites background or methods from "Dilution and Mixing Algorithms for ..."
...Since O is a mixing ratio, it must satisfy ∑k i=1 ci = 1 [19]....
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...This process is called sample preparation [17], [18], [19], and in a DMFB it is typically implemented by repeatedly mixing two droplets of equal volume and splitting the resultant droplet into two equal size droplets (i....
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TL;DR: This work adopts a next generation DMFB platform, referred to as micro-electrode-dot-array (MEDA), for sample preparation, and proposes the first sample-preparation method that exploits the MEDA-specific advantages of fine-grained control of droplet sizes and real-time droplet sensing.
Abstract: Sample preparation in digital microfluidics refers to the generation of droplets with target concentrations for on-chip biochemical applications In recent years, digital microfluidic biochips (DMFBs) have been adopted as a platform for sample preparation However, there remain two major problems associated with sample preparation on a conventional DMFB First, only a (1:1) mixing/splitting model can be used, leading to an increase in the number of fluidic operations required for sample preparation Second, only a limited number of sensors can be integrated on a conventional DMFB; as a result, the latency for error detection during sample preparation is significant To overcome these drawbacks, we adopt a next generation DMFB platform, referred to as micro-electrode-dot-array (MEDA), for sample preparation We propose the first sample-preparation method that exploits the MEDA-specific advantages of fine-grained control of droplet sizes and real-time droplet sensing Experimental demonstration using a fabricated MEDA biochip and simulation results highlight the effectiveness of the proposed sample-preparation method
23 citations
TL;DR: A new approach to accurate dilution preparation on a DMFB that is oblivious to volumetric split-errors, which does not need any sensor and can handle multiple split- errors, deterministically is proposed.
Abstract: Microfluidic chips are now being increasingly used for fast and cost-effective implementation of biochemical protocols. Sample preparation involves dilution and mixing of fluids in certain ratios, which are needed for most of the protocols. On a digital microfluidic biochip (DMFB), these tasks are usually automated as a sequence of droplet mix-split steps. In the most widely used (1:1) mix-split operation for DMFBs, two equal-volume droplets are mixed followed by a split operation, which, ideally, should produce two daughter-droplets of equal volume (balanced splitting). However, because of uncertain variabilities in fluidic operations, the outcome of droplet-split operations often becomes erroneous, i.e., they may cause unbalanced splitting. As a result, the concentration factor (CF) of each constituent fluid in the mixture may become erroneous during sample preparation. All traditional approaches aimed to recover from such errors deploy on-chip sensors to detect possible volumetric imbalance, and adopt either checkpointing-based rollback or roll-forward techniques. Most of them suffer from significant overhead in terms of assay-completion time, reactant-cost, and uncertainties in termination due to randomly occurring split-errors. In this paper, we propose a new approach to accurate dilution preparation on a DMFB that is oblivious to volumetric split-errors. It does not need any sensor and can handle multiple split-errors, deterministically. The proposed method is customized for each target-CF based on the criticality of split-errors in each mix-split step. Simulation experiments on various test-cases demonstrate the effectiveness of the proposed method.
17 citations
Cites background from "Dilution and Mixing Algorithms for ..."
...5 2n [8], [9], each CF is represented as an n-bit binary fractional number x 2n , where x ∈ N, 0 ≤ x ≤ 2, and n ∈ N [29]....
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TL;DR: Simulation results for several target sets demonstrate the superiority of the proposed techniques over prior art in terms of the number of mix-split steps, waste droplets, and reactant usage when the on-chip reservoirs are preloaded with source-CFs using a customized droplet-streaming engine.
Abstract: Sample preparation is a fundamental preprocessing step needed in almost all biochemical assays and is conveniently automated on a microfluidic lab-on-chip. In digital microfluidics, it is accomplished by a sequence of droplet-mix-split steps on a biochip. Many real-life applications require a sample with multiple concentration factors (CFs). Existing algorithms, while producing multi-CF targets, attempt to share the mix-split steps in order to reduce reactant-cost and sample-preparation time. However, all prior approaches have two limitations: 1) sharing of intermediate droplets can be best effected only when all required target CFs are known a priori and 2) the processing time may vary depending on the allowable error-tolerance in target-CFs. In this paper, we present a cost-effective solution to multi-CF-dilution on-demand, by using only one (or two) mix-split step(s). In order to service dynamically arriving requests of multiple CFs quickly, we prepare dilutions of the sample with a few CFs in advance (called source-CFs), and fill on-chip reservoirs with these fluids. For minimizing the number of such preprocessed CFs, we present an integer linear programming-based method, an approximation algorithm, and a heuristic algorithm. The proposed methods also allow the users to tradeoff the number of on-chip reservoirs against service time for various applications. Simulation results for several target sets demonstrate the superiority of the proposed techniques over prior art in terms of the number of mix-split steps, waste droplets, and reactant usage when the on-chip reservoirs are preloaded with source-CFs using a customized droplet-streaming engine.
15 citations
Cites background from "Dilution and Mixing Algorithms for ..."
...Because of the (1:1) inherent mixing model supported by DMFB platform, each CF is required to be approximated as n-bit binary fractional number (x/2n), depending on ; where x ∈ N, 0 ≤ x ≤ 2n, and n ∈ N [19]....
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...Efficient sample preparation is thus a basic step in a biochemical protocol, where the objective is to prepare a homogeneous solution of two or more biochemical fluidic reagents in a given volumetric ratio with minimum reagent-cost and time [19]....
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TL;DR: This article presents a generic multiple-reactant sample preparation algorithm that exploits the novel fluidic operations on MEDA biochips and proposes an enhanced algorithm that increases the operation-sharing opportunities when multiple target concentrations are needed, and therefore the usage of reactants can be further reduced.
Abstract: Sample preparation, as a key procedure in many biochemical protocols, mixes various samples, and/or reagents into solutions that contain the target concentrations. Digital microfluidic biochips (DMFBs) have been adopted as a platform for sample preparation because they provide automatic procedures that require less reactant consumption and reduce human-induced errors. However, the most existing methods only consider two-reactant sample preparation, and they cannot be used for many biochemical applications that involve multiple reactants. In addition, the existing methods that can be used for multiple-reactant sample preparation were proposed on traditional DMFBs where only the (1:1) mixing model is available. In the (1:1) mixing model, only two droplets of the same volume can be mixed at a time, which results in higher completion time and the wastage of valuable reactants. To overcome this limitation, the micro-electrode-dot-array (MEDA) architecture has been introduced; it provides the flexibility of mixing multiple droplets of different volumes in a single operation. In this article, we present a generic multiple-reactant sample preparation algorithm that exploits the novel fluidic operations on MEDA biochips. We also propose an enhanced algorithm that increases the operation-sharing opportunities when multiple target concentrations are needed, and therefore the usage of reactants can be further reduced. The simulated experiments show that the proposed method outperforms existing methods in terms of saving reactant cost, minimizing the number of operations, and reducing the amount of waste.
15 citations
Cites background from "Dilution and Mixing Algorithms for ..."
...Previous work on flow-based microfluidic biochips (FMFBs), on the other hand, exploits the use of a rotary mixer that can blend more-than-two solutions in a single mixing operation [29], [30]....
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References
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29 Mar 2008
TL;DR: Z3 is a new and efficient SMT Solver freely available from Microsoft Research that is used in various software verification and analysis applications.
Abstract: Satisfiability Modulo Theories (SMT) problem is a decision problem for logical first order formulas with respect to combinations of background theories such as: arithmetic, bit-vectors, arrays, and uninterpreted functions. Z3 is a new and efficient SMT Solver freely available from Microsoft Research. It is used in various software verification and analysis applications.
6,859 citations
"Dilution and Mixing Algorithms for ..." refers methods in this paper
...We use a modeling that solves the dilution problem based on decision procedures over linear arithmetic, i.e., by utilizing the deductive power of solvers for SMT [25]....
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...Note that decision procedures of the SMT-over-linear-arithmetic is sound and complete [26]....
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...Next, we invoke the SMT(LA) solver [22] to check whether there exists a satisfiable assignment of underlying variables that can generate the target CF using only one unit of sample....
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...Therefore, the consistency conditions at depth j are given by xj + yj + d∑ i=j+1 wi,j = N, j−1∑ i=1 wj,i ≤ N. (3) Algorithm 2: FloSPA-D(Ct, , N) Input: Ct : target CF, : accuracy, N: mixer-N Output: Dilution Graph 1 Approximate Ct by choosing the smallest d ∈ N such that | xx+y − Ct | < ; Target ratio is {x : y}, where x + y = Nd and 1 ≤ x ≤ Nd − 1; /* Detailed modeling is discussed in Section VI-B */ 2 M = SMT instance generated from a dilution graph of depth d and{x : y}; /* one sample_unit is equal to the volume of ‘reagent’ in one segment of rotary mixer */ 3 sample_unit = 1; 4 M′ = M ∧ (∑di=1 xi = sample_unit); 5 checkSAT(M′); 6 while M′ is unsatisfiable do 7 sample_unit = sample_unit + 1; 8 M′ = M ∧ (∑di=1 xi = sample_unit); 9 checkSAT(M′); 10 Obtain dilution graph from satisfiable assignments of M′; 11 return dilution graph; Finally, all weights must satisfy 0 ≤ wi,j ≤ N −1, for 1 ≤ j < i ≤ d. Similarly, 0 ≤ xi, yi ≤ N − 1 for 1 ≤ i ≤ d....
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...In this section, we discuss how an SMT-based approach can be extended to implement the more general problem of mixture-preparation....
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TL;DR: This critical review summarizes developments in microfluidic platforms that enable the miniaturization, integration, automation and parallelization of (bio-)chemical assays and attempts to provide a selection scheme based on key requirements of different applications and market segments.
Abstract: This critical review summarizes developments in microfluidic platforms that enable the miniaturization, integration, automation and parallelization of (bio-)chemical assays (see S. Haeberle and R. Zengerle, Lab Chip, 2007, 7, 1094–1110, for an earlier review). In contrast to isolated application-specific solutions, a microfluidic platform provides a set of fluidic unit operations, which are designed for easy combination within a well-defined fabrication technology. This allows the easy, fast, and cost-efficient implementation of different application-specific (bio-)chemical processes. In our review we focus on recent developments from the last decade (2000s). We start with a brief introduction into technical advances, major market segments and promising applications. We continue with a detailed characterization of different microfluidic platforms, comprising a short definition, the functional principle, microfluidic unit operations, application examples as well as strengths and limitations of every platform. The microfluidic platforms in focus are lateral flow tests, linear actuated devices, pressure driven laminar flow, microfluidic large scale integration, segmented flow microfluidics, centrifugal microfluidics, electrokinetics, electrowetting, surface acoustic waves, and dedicated systems for massively parallel analysis. This review concludes with the attempt to provide a selection scheme for microfluidic platforms which is based on their characteristics according to key requirements of different applications and market segments. Applied selection criteria comprise portability, costs of instrument and disposability, sample throughput, number of parameters per sample, reagent consumption, precision, diversity of microfluidic unit operations and the flexibility in programming different liquid handling protocols (295 references).
1,536 citations
"Dilution and Mixing Algorithms for ..." refers background in this paper
..., dropletbased [1]–[8], digital [2], [9], and continuous flow-based microfluidics [10]....
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...More complex units such as mixers, micropumps, and multiplexers can be built with several hundreds of such units accommodated on a single chip [10]....
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TL;DR: Current work in commercializing microfluidic technologies is reviewed, with a focus on point-of-care diagnostics applications, and the need to strike a balance between achieving real-world impact with integrated devices versus design of novel single microfluidity components is discussed.
Abstract: A large part of the excitement behind microfluidics is in its potential for producing practical devices, but surprisingly few lab-on-a-chip based technologies have been successfully introduced into the market. Here, we review current work in commercializing microfluidic technologies, with a focus on point-of-care diagnostics applications. We will also identify challenges to commercialization, including lessons drawn from our experience in Claros Diagnostics. Moving forward, we discuss the need to strike a balance between achieving real-world impact with integrated devices versus design of novel single microfluidic components.
1,016 citations
"Dilution and Mixing Algorithms for ..." refers background in this paper
...CFMBs are quite popular in the biochemistry community because of their simplicity of fabrication, flexibility in reagent-volume control, and versatility of applications such as automation of assays and point-of-care diagnosis [11]....
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TL;DR: A high level overview of the field of microfluidic mixing devices is provided before describing some of the more significant proposals for active and passive mixers.
Abstract: The aim of microfluidic mixing is to achieve a thorough and rapid mixing of multiple samples in microscale devices. In such devices, sample mixing is essentially achieved by enhancing the diffusion effect between the different species flows. Broadly speaking, microfluidic mixing schemes can be categorized as either “active”, where an external energy force is applied to perturb the sample species, or “passive”, where the contact area and contact time of the species samples are increased through specially-designed microchannel configurations. Many mixers have been proposed to facilitate this task over the past 10 years. Accordingly, this paper commences by providing a high level overview of the field of microfluidic mixing devices before describing some of the more significant proposals for active and passive mixers.
910 citations
"Dilution and Mixing Algorithms for ..." refers background in this paper
...flow-based microfluidic mixing operations are quite slow [21],...
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TL;DR: Extensive experimental evidence shows that DPLL(T) systems can significantly outperform the other state-of-the-art tools, frequently even in orders of magnitude, and have better scaling properties.
Abstract: We first introduce Abstract DPLL, a rule-based formulation of the Davis--Putnam--Logemann--Loveland (DPLL) procedure for propositional satisfiability. This abstract framework allows one to cleanly express practical DPLL algorithms and to formally reason about them in a simple way. Its properties, such as soundness, completeness or termination, immediately carry over to the modern DPLL implementations with features such as backjumping or clause learning.We then extend the framework to Satisfiability Modulo background Theories (SMT) and use it to model several variants of the so-called lazy approach for SMT. In particular, we use it to introduce a few variants of a new, efficient and modular approach for SMT based on a general DPLL(X) engine, whose parameter X can be instantiated with a specialized solver SolverT for a given theory T, thus producing a DPLL(T) system. We describe the high-level design of DPLL(X) and its cooperation with SolverT, discuss the role of theory propagation, and describe different DPLL(T) strategies for some theories arising in industrial applications.Our extensive experimental evidence, summarized in this article, shows that DPLL(T) systems can significantly outperform the other state-of-the-art tools, frequently even in orders of magnitude, and have better scaling properties.
900 citations
"Dilution and Mixing Algorithms for ..." refers background or methods in this paper
...The SMT(LA) problem is to determine an assignment to the variables of , if there exists a satisfiable assignment, otherwise to prove that no such assignment exists [26]....
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...The SMT over linear arithmetic [SMT(LA)] problem is defined as follows....
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...The proposed algorithms utilize an SMT-based solving engine that is capable of handling both dilution and mixing problems within the same framework....
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...Although SMT-solvers are used to solve a decision problem, an optimization problem can be formulated as a sequence of decision problems....
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...Next, we invoke the SMT(LA) solver [22] to check whether there exists a satisfiable assignment of underlying variables that can generate the target CF using only one unit of sample....
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