Computing Bounds for Linear Functionals of Exact Weak Solutions to Poisson’s Equation

We present a method for Poisson’s equation that computes guaranteed upper and lower bounds for the values of linear functional outputs of the exact weak solution of the infinite dimensional continuum problem using traditional finite element approximations. The guarantee holds uniformly for any level of refinement, not just in the asymptotic limit of refinement. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity which is linear in the number of elements in the finite element discretization.Singapore-MIT Alliance (SMA

Computing bounds for linear functionals of exact weak solutions to Poisson's equation

We present a method for Poisson’s equation that computes guaranteed upper and lower bounds for the values of piecewise-polynomial linear functional outputs of the exact weak solution of the infinite-dimensional continuum problem with piecewise-polynomial forcing. The method results from exploiting the Lagrangian saddle point property engendered by recasting the output problem as a constrained minimization problem. Localization is achieved by Lagrangian relaxation and the bounds are computed by appeal to a local dual problem. The proposed method computes approximate Lagrange multipliers using traditional finite element approximations to calculate a primal and an adjoint solution along with well known hybridization techniques to calculate interelement continuity multipliers. The computed bounds hold uniformly for any level of refinement, and in the asymptotic convergence regime of the finite element method, the bound gap decreases at twice the rate of the energy norm measure of the error in the finite element solution. Given a finite element solution and its output adjoint solution, the method can be used to provide a certificate of precision for the output with an asymptotic complexity that is linear in the number of elements in the finite element discretization. The elemental contributions to the bound gap are always positive and hence lend themselves to be used as adaptive indicators, as we demonstrate with a numerical example

Fast DNA translocation through a solid-state nanopore

We report translocation experiments on double-strand DNA through a silicon oxide nanopore. Samples containing DNA fragments with seven different lengths between 2000 to 96000 basepairs have been electrophoretically driven through a 10 nm pore. We find a power-law scaling of the translocation time versus length, with an exponent of 1.26 $\pm$ 0.07. This behavior is qualitatively different from the linear behavior observed in similar experiments performed with protein pores. We address the observed nonlinear scaling in a theoretical model that describes experiments where hydrodynamic drag on the section of the polymer outside the pore is the dominant force counteracting the driving. We show that this is the case in our experiments and derive a power-law scaling with an exponent of 1.18, in excellent agreement with our data.Comment: 5 pages, 2 figures. Submitted to PR

Unzipping Kinetics of Double-Stranded DNA in a Nanopore

We studied the unzipping kinetics of single molecules of double-stranded DNA by pulling one of their two strands through a narrow protein pore. PCR analysis yielded the first direct proof of DNA unzipping in such a system. The time to unzip each molecule was inferred from the ionic current signature of DNA traversal. The distribution of times to unzip under various experimental conditions fit a simple kinetic model. Using this model, we estimated the enthalpy barriers to unzipping and the effective charge of a nucleotide in the pore, which was considerably smaller than previously assumed.Comment: 10 pages, 5 figures, Accepted: Physics Review Letter

UV activation of polymeric high aspect ratio microstructures: Ramifications in antibody surface loading for circulating tumor cell selection

The need to activate thermoplastic surfaces using robust and efficient methods has been driven by the fact that replication techniques can be used to produce microfluidic devices in a high production mode and at low cost, making polymer microfluidics invaluable for in vitro diagnostics, such as circulating tumor cell (CTC) analysis, where device disposability is critical to mitigate artifacts associated with sample carryover. Modifying the surface chemistry of thermoplastic devices through activation techniques can be used to increase the wettability of the surface or to produce functional scaffolds to allow for the covalent attachment of biologics, such as antibodies for CTC recognition. Extensive surface characterization tools were used to investigate UV activation of various surfaces to produce uniform and high surface coverage of functional groups, such as carboxylic acids in microchannels of different aspect ratios. We found that the efficiency of the UV activation process is highly dependent on the microchannel aspect ratio and the identity of the thermoplastic substrate. Colorimetric assays and fluorescence imaging of UV-activated microchannels following EDC/NHS coupling of Cy3-labeled oligonucleotides indicated that UV-activation of a PMMA microchannel with an aspect ratio of ???3 was significantly less efficient toward the bottom of the channel compared to the upper sections. This effect was a consequence of the bulk polymer's damping of the modifying UV radiation due to absorption artifacts. In contrast, this effect was less pronounced for COC. Moreover, we observed that after thermal fusion bonding of the device's cover plate to the substrate, many of the generated functional groups buried into the bulk rendering them inaccessible. The propensity of this surface reorganization was found to be higher for PMMA compared to COC. As an example of the effects of material and microchannel aspect ratios on device functionality, thermoplastic devices for the selection of CTCs from whole blood were evaluated, which required the immobilization of monoclonal antibodies to channel walls. From our results, we concluded the CTC yield and purity of isolated CTCs were dependent on the substrate material with COC producing the highest clinical yields for CTCs as well as better purities compared to PMMA.close9

Microfluidic Chip for Molecular Amplification of Influenza A RNA in Human Respiratory Specimens

A rapid, low cost, accurate point-of-care (POC) device to detect influenza virus is needed for effective treatment and control of both seasonal and pandemic strains. We developed a single-use microfluidic chip that integrates solid phase extraction (SPE) and molecular amplification via a reverse transcription polymerase chain reaction (RT-PCR) to amplify influenza virus type A RNA. We demonstrated the ability of the chip to amplify influenza A RNA in human nasopharyngeal aspirate (NPA) and nasopharyngeal swab (NPS) specimens collected at two clinical sites from 2008–2010. The microfluidic test was dramatically more sensitive than two currently used rapid immunoassays and had high specificity that was essentially equivalent to the rapid assays and direct fluorescent antigen (DFA) testing. We report 96% (CI 89%,99%) sensitivity and 100% (CI 95%,100%) specificity compared to conventional (bench top) RT-PCR based on the testing of n = 146 specimens (positive predictive value = 100%(CI 94%,100%) and negative predictive value = 96%(CI 88%,98%)). These results compare well with DFA performed on samples taken during the same time period (98% (CI 91%,100%) sensitivity and 96%(CI 86%,99%) specificity compared to our gold standard testing). Rapid immunoassay tests on samples taken during the enrollment period were less reliable (49%(CI 38%,61%) sensitivity and 98%(CI 98%,100%) specificity). The microfluidic test extracted and amplified influenza A RNA directly from clinical specimens with viral loads down to 103 copies/ml in 3 h or less. The new test represents a major improvement over viral culture in terms of turn around time, over rapid immunoassay tests in terms of sensitivity, and over bench top RT-PCR and DFA in terms of ease of use and portability

The Potential and Challenges of Nanopore Sequencing

A nanopore-based device provides single-molecule detection and analytical capabilities that are achieved by electrophoretically driving molecules in solution through a nano-scale pore. The nanopore provides a highly confined space within which single nucleic acid polymers can be analyzed at high throughput by one of a variety of means, and the perfect processivity that can be enforced in a narrow pore ensures that the native order of the nucleobases in a polynucleotide is reflected in the sequence of signals that is detected. Kilobase length polymers (single-stranded genomic DNA or RNA) or small molecules (e.g., nucleosides) can be identified and characterized without amplification or labeling, a unique analytical capability that makes inexpensive, rapid DNA sequencing a possibility. Further research and development to overcome current challenges to nanopore identification of each successive nucleotide in a DNA strand offers the prospect of ‘third generation’ instruments that will sequence a diploid mammalian genome for ~$1,000 in ~24 h.Molecular and Cellular BiologyPhysic

An automated low cost instrument for simultaneous multi-sample tissue homogenization

Tissue homogenization is a common sample preparation procedure in the analysis of clinical samples, but to date there has been no good way to incorporate it into high throughput assays. The classic mortar and pestle is still in common use in laboratories for homogenizing small samples in low quantities. Blenders and high pressure valve processors are used when large quantities of tissue must be homogenized. There are two technologies in the market that process multiple samples simultaneously: bead beating and sonication. Both have been implemented on a standard microplate form factor, but have their drawbacks. Bead beating requires the careful addition and subsequent removal and sanitizing of the beads, which can be a costly and time-intensive process. Sonication works well only with very small samples and does not always give consistent results. This paper describes the development of a new instrument that is capable of quickly homogenizing an array of unique tissue sa mples directly in a microplate. The instrument requires no special training to achieve uniform, repeatable results, and is thus adaptable to semi- and fully automated equipment. Additionally, the system is easy to clean and sterilize, has adjustable speed and force to control shear and unwanted heating, and is useful for sample sizes ranging the entire breadth needed for clinical samples (microliters to milliliters)

Computing Bounds for Linear Functionals of Exact Weak Solutions to the Advection-Diffusion-Reaction Equation

We present a cost e#ective method for computing quantitative upper and lower bounds on linear functional outputs of exact weak solutions to the advection-di#usion-reaction equation and we demonstrate a simple adaptive strategy by which such outputs can be computed to a prescribed precision. The bounds are computed from independent local subproblems resulting from a standard finite element approximation to the problem. At the heart of the method lies a local dual problem by which we transform an infinite dimensional minimization problem into a finite dimensional feasibility problem. The bounds hold for all levels of refinement on polygonal domains with piecewise polynomial forcing, and the bound gap converges at twice the rate of the -norm of the error in the finite element solution

A wearable optical device for continuous monitoring during neoadjuvant chemotherapy infusions

We present a new continuous-wave (CW) wearable diffuse optical device aimed at investigating the hemodynamic response of locally advanced breast cancer patients during a patient’s first neoadjuvant chemotherapy infusion. The system consists of a flexible substrate that supports an array of surface-mount LED and photodiode pairs (i.e. optodes). Probe performance was evaluated using solid tissue-simulating phantoms. Measurements revealed high SNR (65dB), low source-detector crosstalk (-59 dB), high measurement precision (0.17%), and good thermal stability (0.2% Vrms/°C). A cuff occlusion experiment was performed on the forearm of a healthy volunteer to demonstrate the ability to track rapid hemodynamic changes