Finite Element Characteristic Methods Requiring no Quadrature

The characteristic methods are known to be very efficient for convection-diffusion problems including the Navier-Stokes equations. Convergence is established when the integrals are evaluated exactly, otherwise there are even cases where divergence has been shown to happen. The family of methods studied here applies Lagrangian convection to the gradients and the function as in Yabe (Comput. Phys. Commun. 66(2–3), 233–242, 1991); the method does not require an explicit knowledge of the equation of the gradients and can be applied whenever the gradients of the convection velocity are known numerically. We show that converge can be second order in space or more. Applications are given for the rotating bell problem.     

AC electroosmotic flow in a DNA concentrator

Experimental velocity measurements are conducted in an AC electrokinetic DNA concentrator. The DNA concentrator is based upon Wong et al. (Transducers 2003, Boston, pp 20–23, 2003a; Anal Chem 76(23):6908–6914, 2004)and consists of two concentric electrodes that generate AC electroosmotic flow to stir the fluid, and dielectrophoretic and electrophoretic force fields that trap DNA near the centre of the inside electrode. A two-colour micro-PIV technique is used to measure the fluid velocity without a priori knowledge of the electric field in the device or the electrical properties of the particles. The device is also simulated computationally. The results indicate that the numerical simulations agree with experimental data in predicting the velocity field structure, except that the velocity scale is an order of magnitude higher for the simulations. Simulation of the dielectrophoretic forces allows the motion of the DNA within the device to be studied. It is suggested that the simulations can be used to study the phenomena occurring in the device, but that experimental data is required to determine the practical conditions under which these phenomena occur.     

Algorithmic applications of XPCR

An emerging trend in DNA computing consists of the algorithmic analysis of new molecular biology technologies, and in general of more effective tools to tackle computational biology problems. An algorithmic understanding of the interaction between DNA molecules becomes the focus of some research which was initially addressed to solve mathematical problems by processing data within biomolecules. In this paper a novel mechanism of DNA recombination is discussed, that turned out to be a good implementation key to develop new procedures for DNA manipulation (Franco et al., DNA extraction by cross pairing PCR, 2005; Franco et al., DNA recombination by XPCR, 2006; Manca and Franco, Math Biosci 211:282–298, 2008). It is called XPCR as it is a variant of the polymerase chain reaction (PCR), which was a revolution in molecular biology as a technique for cyclic amplification of DNA segments. A few DNA algorithms are proposed, that were experimentally proven in different contexts, such as, mutagenesis (Franco, Biomolecular computing—combinatorial algorithms and laboratory experiments, 2006), multiple concatenation, gene driven DNA extraction (Franco et al., DNA extraction by cross pairing PCR, 2005), and generation of DNA libraries (Franco et al., DNA recombination by XPCR, 2006), and some related ongoing work is outlined.     

An integrated genetic analysis microfluidic platform with valves and a PCR chip reusability method to avoid contamination

Clinical diagnostics and genomic research often require performing numerous genetic tests. While microfluidic devices provide a low-cost alternative to such demands, integrated microfluidic devices are fabricated using expensive technology not always affordable for single use. However, carryover cross-contamination (CXC) concerns (i.e. either false positive or false negative PCR data) in PCR chips prevent reuse, defying much of the advantages of miniaturized systems developed using expensive MEMS processing. In this work, we present an integrated and reusable PCR–CE glass microfluidic chip capable of multi-chamber PCR and sequential CE, with emphasis on a unique chip reusability approach to avoid CXC. For reliable PCR, the surface of the chamber is re-configured from its virgin hydrophilic (CA < 20°) to hydrophobic (CA > 110°) by silanization. To then extend this silanization method as a chip reusability technique, the silanization coating is ‘stripped and re-silanized’ (SRS) to create a fresh coating prior to each successive PCR run. Experimental confirmation of the effectiveness of SRS method in avoiding the CXC is demonstrated using plasmid DNA and HIV-1 infected DNA samples. We also present passive plug microvalves incorporated in the chip to enable fluid/vapor retention during the PCR and controlled fluid flow from the PCR chamber to the CE section for further analysis.     

A new thermal cycling mechanism for effective polymerase chain reaction in microliter volumes

This study presents a new thermal cycler using infrared (IR) heating and water impingement cooling for polymerase chain reaction (PCR) amplification of 10 l samples in thin glass capillary tubes. The thermal cycling system can achieve a temperature ramping-up rate of 65 °C/s and a ramping-down rate of 80 °C/s. Two other cooling mechanisms, natural convection and forced air convection, can also be used in the present system to obtain a ramping-down rate of 2 °C/s and 6 °C/s, respectively. The amplification of the 439 fragment of hepatitis B virus (HBV) DNA was successful. The PCR amplified products were analyzed by agarose gel electrophoresis with ethidium bromide staining for visualization. A comparison of results of the amplification products at three different ramping-down rates was made and the rapid thermal cycling of the present system can run DNA required amplification in 29 min for 20 thermal cycles that is only 1/3 the time spent in the conventional PCR machine used in comparison.This work was supported by the National Taiwan University College of Medicine in preparing the HBV DNA samples. We thank our research assistance W. L. Chen and Dr. Chen for their technical advice. We gratefully acknowledge the financial support by the Nation Science Council, No. NSC-88–2212-E-002–025.     

Mathematical modeling and optimization of intratumor drug transport

A pseudohyperbolic problem of optimal control of intratumoral drug distribution is formulated. It takes into account the heterogeneity of tumor tissues and effects of convection diffusion in a fissured porous medium. A mathematical model constructed and the corresponding optimal control problem are shown to be correct. __________ Translated from Kibernetika i Sistemnyi Analiz, No. 6, pp. 147–154, November–December 2007.     

3D visualization of convection patterns in lab-on-chip with open microfluidic outlet

Open-outlet microfluidics is getting more and more attention, thanks to the generation of capillarity-driven flows which simplify the connection with the macro-world. It is known that convection flows are generated at the interface with air, i.e., the meniscus. Several works have investigated evaporation-induced convection, but its effect on particle position control in open-outlet biodevices is still not characterized. In this paper, we present the results of 3D measurement of particle traces near the meniscus in an open-outlet vertical 400 μm micro-channel filled with a water-based saline solution. Using a standard optical microscope and a system of mirrors, we observe the 3D position of individual micro-beads floating in the solution, in a way akin to particle image velocimetry technique. A single vortex is generated at the meniscus and occupies the whole region under observation at a distance of 1.5–2.7 mm from the meniscus. The generation of the convection pattern and the vortex rotational speed are described. The convection patterns disappear when evaporation is inhibited, while both the vortex generation and the rotational speed are faster for highly saline solutions. These results are relevant to the design of biochips which require control of the particle position in a fluid since they emphasize that in open-outlet microfluidic systems not only the gravitational fall but also the convection drag must be counteracted.     

A Dynamic Penalty or Projection Method for Incompressible Fluids

In a previous work (Angot et al. in J. Comput. Appl. Math. 226:228–245, 2009), some penalty–projection methods have been tested for the numerical analysis of the Navier-Stokes equations. The purpose of this study is to introduce a variant of the penalty–projection method which allows us to compute the solutions faster than by using the previous solver. This new variant combines dynamically and alternatively a penalty procedure and a projection procedure according to the size of the divergence of the velocity. In other words, this study aims to prove that it is possible to project the intermediate velocity, computed by the first step of the penalty–projection method, only if its divergence is larger than a specified threshold. Theoretical estimates for the new method are given, which are in accordance with the numerical results provided.     

Three-dimensional finite element method for the filling simulation of injection molding

With the development of molding techniques, molded parts have more complex and larger geometry with nonuniform thickness. In this case, the velocity and the variation of parameters in the gapwise direction are considerable and cannot be neglected. A three-dimensional (3D) simulation model can predict the filling process more accurately than a 2.5D model based on the Hele–Shaw approximation. This paper gives a mathematical model and numeric method based on 3D model to perform more accurate simulations of a fully flow. The model employs an equal-order velocity–pressure interpolation method. The relation between velocity and pressure is obtained from the discretized momentum equations in order to derive the pressure equation. A 3D control volume scheme is used to track the flow front. During calculating the temperature field, the influence of convection items in three directions is considered. The software based on this 3D model can calculate the pressure field, velocity field and temperature field in filling process. The validity of the model has been tested through the analysis of the flow in cavities.     

Effects of planar inlet plenums on the hydrodynamically developing flows in rectangular microchannels of complementary aspect ratios

The effects of planar inlet plenum geometry on the developing flow fields in two rectangular microchannels of reciprocal aspect ratios (H/W ∼2.75 and ∼0.40) were investigated for Re _D =  1–100 using micro particle image velocimetry (μPIV). These two microchannels were made by a precision sawing and silicon microfabrication techniques. Both the velocity profiles and centerline velocity developments were clearly resolved and extracted along the axial distance from μPIV results. The entrance lengths were found from the centerline velocities using a decaying exponential fitting function where the centerline velocity reaches 99% of the fully developed centerline velocity. The proposed fitting function showed excellent agreement with the experimental results. The planar plenum was shown to cause an upstream predevelopment resulting in the significant reductions in the entrance lengths. Two entrance length correlations were proposed in the forms of Atkinson et al.’s (AIChE J 15:548–553, 1969) and Chen’s (J Fluids Eng 95:153–158, 1973) correlations. The proposed entrance length correlations showed that acquired constant portion and slope of the entrance lengths showed 23–27 and 70–81% reductions for H/W =  2.75 while the entrance length correlation for H/W =  0.40 showed 69–73% increase and 41–63% decrease in the constant portion and slope, respectively.     

A magnetic bead-based DNA extraction and purification microfluidic device

This article introduces a novel magnetic bead-based DNA extraction and purification device using active magnetic mixing approach. Mixing and separation steps are performed using functionalised superparamagnetic beads suspended in cell lysis buffer in a circular chamber that is sandwiched between two external magnetic coils. Non-uniform nature of magnetic field causes temporal and spatial distribution of beads within the chamber. This process efficiently mixes the lysis buffer and whole blood in order to extract DNA from target cells. Functionalized surface of the magnetic beads then attract the exposed DNA molecules. Finally, DNA-attached magnetic beads are attracted to the bottom of the chamber by activating the bottom magnetic coil. DNA molecules are extracted from magnetic beads by washing and re-suspension processes. In this study, a circular PMMA microchamber, 25 μL in volume, 500 μm in depth and 8 mm in diameter was fabricated to purify DNA from spiked bacterial cell cultures into the whole blood sample using Promega Magazorb DNA extraction kit. The lysis efficiency was evaluated using a panel of Gram-positive (Bacillus subtilis) and Gram-negative (Escherichia coli) bacterial cells cultures into the blood sample to achieve approximately 100,000 copy levels inside the chip. Manufacturer’s standard extraction protocol was modified to a more simplified process suitable for chip-based extraction. The lysis step was performed using 5 min incubation at 56 °C followed by 5 min incubation at room temperature for binding process. Temperature rise was generated and maintained by the same external magnetic coils used for active mixing. The yield/purity and recovery levels of the extracted DNA were evaluated using quantitative UV spectrophotometer and real-time PCR assay, respectively. Real-time PCR results indicated efficient chip-based bacterial DNA extraction using modified extraction protocol comparable to the standard bench-top extraction process.     

Thinking About Evolution in Terms of Cellular Computing

The past five decades of molecular genetics have produced many discoveries about genome structure and function that can only be understood from an informatic perspective: – distinct sequence codes to mark the individual steps in packaging, expression, replication, transmission, repair and restructuring of DNA molecules; – modularity of data files for RNA and protein products; – combinatoric organization of signals to format the genome for differential functioning during cellular and organismal cycles; – direct participation of DNA in the execution of biological algorithms (formation of highly structured nucleoprotein complexes); – hierarchical organization of genomic subsystems to form higher level system architectures. This review will discuss aspects of genome organization and genome change that require a more formal computational analysis. We will see how modern results indicate that genome evolution has many similarities to computer system engineering. The ability of cells to control the function of natural genetic engineering systems is central to the genome’s potential as a Read–Write information storage system.     

Padlock probe-mediated qRT-PCR for DNA computing answer determination

Padlock probe-mediated quantitative real time PCR (PLP-qRT-PCR) was adapted to quantify the abundance of sequential 10mer DNA sequences for use in DNA computing to identify optimal answers of traveling salesman problems. The protocol involves: (i) hybridization of a linear PLP with a target DNA sequence; (ii) PLP circularization through enzymatic ligation; and (iii) qRT-PCR amplification of the circularized PLP after removal of non-circularized templates. The linear PLP was designed to consist of two 10-mer sequence-detection arms at the 5′ and 3′ ends separated by a core sequence composed of universal PCR primers, and a qRT-PCR reporter binding site. Circularization of each PLP molecule is dependent upon hybridization with target sequence and high-fidelity ligation. Thus, the number of PLP circularized is determined by the abundance of target in solution. The amplification efficiency of the PLP was 98.7% within a 0.2 pg–20 ng linear detection range between thermal cycle threshold (C_t value) and target content. The C_t values derived from multiplex qRT-PCR upon three targets did not differ significantly from those obtained with singleplex assays. The protocol provides a highly sensitive and efficient means for the simultaneous quantification of multiple short nucleic acid sequences that has a wide range of applications in biotechnology.     

Remote Visual Servoing of a Robot Manipulator via Internet2

Visual servoing is a powerful approach to enlarge the applications of robotic systems by incorporating visual information into the control system. On the other hand, teleoperation – the use of machines in a remote way – is increasing the number of applications in many domains. This paper presents a remote visual servoing system using only partial camera calibration and exploiting the high bandwidth of Internet2 to stream video information. The underlying control scheme is based on the image-based philosophy for direct visual servoing – computing the applied torque inputs to the robot based in error signals defined in the image plane – and evoking a velocity field strategy for guidance. The novelty of this paper is a remote visual servoing with the following features: (1) full camera calibration is unnecessary, (2) direct visual servoing does not neglect the robot nonlinear dynamics, and (3) the novel velocity field control approach is utilized. Experiments carried out between two laboratories demonstrated the effectiveness of the application. Work partially supported by CONACyT grant 45826 and CUDI.     

Capillary filling with the effect of pneumatic pressure of trapped air

This article presents an investigation into the effects of pneumatic pressure of trapped air on the dynamics of capillary filling. Controlled experiments were carried out in horizontal closed-end capillaries with diameters of 200–700 μm. Glycerol–DI water mixture solutions having viscosities ranging from 8 to 80 mPa s were used as the filling liquids. The pneumatic air backpressure is built up as a result of the air compressed at the closed end of the capillary. A model is presented based on the conventional theory of capillary filling (i.e., Washburn’s equation) with consideration of the effect of air backpressure force on the advancing meniscus. The molecular kinetics theory of Blake and De Coninck’s model (Adv Colloid Interface Sci 96:21–36, 2002) is also incorporated in the model to account for the dependence of dynamic contact angle on wetting velocity. The model predictions agree reasonably well with the experimental data. It is observed that due to the presence of air backpressure, the smaller the capillary diameter, the longer the length that the liquid fills the capillary, regardless of the liquid viscosity. It is also shown that the increased pneumatic air backpressure reduces the equilibrium contact angle (θ ⁰). A relation is then proposed among liquid penetration, capillary length and radius, and contact angle. In addition, a dimensionless analysis is performed on experimental data, and the power law dependence of dimensionless meniscus position on dimensionless time is obtained.     

DNA computation simulator based on abstract bases

 We developed a simulator to aid those who design algorithms and protocols for DNA computing. In this simulator, abstract sequences instead of real DNA sequences are used to represent molecules in order to increase efficiency of simulations. Two approaches for simulation are available: threshold and stochastic. The simulator consists of two main parts, one for finding reactions among existing molecules and generating new ones, and the other for numerically solving differential equations to calculate the concentration of each molecule. The two parts rely on each other. In particular for the threshold approach, the former avoids a combinatorial explosion by setting a threshold on concentrations of molecules that can take part in reactions. In addition, the stochastic approach is also available for simulations which are hard by the threshold approach. Some simulation results by the approaches are also presented: computation of Boolean circuits, whiplash PCR, formation of DNA tiles and polymerase chain reaction (PCR). We also integrate simulating DNA computation and fitting parameters by the genetic algorithm (GA), where simulation results are used as evaluation functions for the genetic algorithm. The integration is applied to find good protocols for PCR amplification. A trial to refine the reaction model for hybridization is also described before the final discussion on the simulator.     

Identification of respiratory pathogen Bordetella Pertussis using integrated microfluidic chip technology

Integrated PCR–CE chip technology has immense potential to be applied in clinical diagnostics. In this work we demonstrate the application of our integrated PCR–CE chip for the detection of the respiratory pathogen Bordetella pertussis. A series of experiments with varying cell concentrations (200,000–2 cfu) were performed to obtain the analytical detection limits of the chip. We find that the chip technology is well suited for sensitive detection of Bordetella pertussis, using genetic material from less than even 2 cfu. We also utilized an off-chip real-time PCR method to compare and validate our on-chip approach.     

On the application of the minimum polynomial extrapolation method to incompressible flows with heat transfer

In this paper, the Minimum Polynomial Extrapolation method (MPE) is used to accelerate the convergence of the Characteristic–Based–Split (CBS) scheme for the numerical solution of steady state incompressible flows with heat transfer. The CBS scheme is a fractional step method for the solution of the Navier–Stokes equations while the MPE method is a vector extrapolation method which transforms the original sequence into another sequence converging to the same limit faster then the original one without the explicit knowledge of the sequence generator. The developed algorithm is tested on a two-dimensional benchmark problem (buoyancy–driven convection problem) where the Navier–Stokes equations are coupled with the temperature equation. The obtained results show the feature of the extrapolation procedure to the CBS scheme and the reduction of the computational time of the simulation.     

Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for?Conservation Laws on Triangular Meshes

In Zhang and Shu (J. Comput. Phys. 229:3091–3120, 2010), two of the authors constructed uniformly high order accurate finite volume and discontinuous Galerkin (DG) schemes satisfying a strict maximum principle for scalar conservation laws on rectangular meshes. The technique is generalized to positivity preserving (of density and pressure) high order DG or finite volume schemes for compressible Euler equations in Zhang and Shu (J. Comput. Phys. 229:8918–8934, 2010). The extension of these schemes to triangular meshes is conceptually plausible but highly nontrivial. In this paper, we first introduce a special quadrature rule which is exact for two-variable polynomials over a triangle of a given degree and satisfy a few other conditions, by which we can construct high order maximum principle satisfying finite volume schemes (e.g. essentially non-oscillatory (ENO) or weighted ENO (WENO) schemes) or DG method solving two dimensional scalar conservation laws on triangular meshes. The same method can preserve the maximum principle for DG or finite volume schemes solving two-dimensional incompressible Euler equations in the vorticity stream-function formulation, or any passive convection equation with an incompressible velocity field. We also obtain positivity preserving (for density and pressure) high order DG or finite volume schemes solving compressible Euler equations on triangular meshes. Numerical tests for the third order Runge-Kutta DG (RKDG) method on unstructured meshes are reported.     

Boundedness analysis for open Chemical Reaction Networks with mass-action kinetics

This paper describes the working principles of an algorithm for boundedness analysis of open Chemical Reaction Networks endowed with mass-action kinetics. Such models can be thought of both as a special class of compartmental systems or a particular type of continuous Petri Nets, in which the firing rates of transitions are not constant or preassigned, but expressed as a function of the continuous marking of the network (function which in chemistry is referred to as the “kinetics”). The algorithm can be applied to a broad class of such open networks, and returns, as an outcome, a classification of the possible dynamical behaviors that are compatible with the network structure, by classifying each variable either as bounded, converging to 0 or diverging to ∞. This can be viewed as a qualitative study of Input–Output Stability for chemical networks, or more precisely, as a classification of its possible I–O instability patterns. Our goal is to analyze the system irrespectively of values of kinetic parameters. More precisely, we attempt to analyze it simultaneously for all possible values. Remarkably, tests on non-trivial examples (one of which is discussed in this paper) showed that, as the kinetic constants of the network are varied, all the compatible behaviors could be observed in simulations. Finally, we discuss and illustrate how the results relate to previous works on the qualitative dynamics of closed reaction networks.