Biomimetic design of microfluidic manifolds based on a generalised Murray's law

The relationship governing the optimum ratio between the diameters of the parent and daughter branches in vascular systems was first discovered by Murray using the principle of minimum work. This relationship is now known as Murray's law and states that the cube of the diameter of the parent vessel must equal the sum of the cubes of the daughter vessels. For symmetric bifurcations, an important consequence of this geometric rule is that the tangential shear stress at the wall remains constant throughout the vascular network. In the present paper, we extend this important hydrodynamic concept to arbitrary cross-sections and provide a framework for constructing a simple but elegant biomimetic design rule for hierarchical microfluidic networks. The paper focuses specifically on constant-depth rectangular and trapezoidal channels often employed in lab-on-a-chip systems. To validate our biomimetic design rule and demonstrate the application of Murray's law to microfluidic manifolds, a comprehensive series of computational fluid dynamics simulations have been performed. The numerical predictions are shown to be in very good agreement with the theoretical analysis, confirming that the generalised version of Murray's law can be successfully applied to the design of constant-depth microfluidic devices.     

Voltammetry Under Microfluidic Control,a Flow Cell Aproach

A generic approach to the design, construction and experimental characterization of novel microelectrochemical reactors (MECR) is presented. Structurally well‐defined rectangular microchannels incorporating electrochemical sensors were fabricated using a propriety photosensitive glass and photolithographic techniques. Microelectrode sensors were produced via evaporation to yield, gold, silver or platinum bands of approximate lengths 10–50 μm. The approach outlined permits cells of dimensions in the range: height 50–100 μm, width 100–500 μm and length 1–3 cm to be accurately constructed, in single or array configurations and were characterized via a voltammetric study utilizing electrolyte solutions containing N,N,N′N′‐Tetramethyl‐1,4‐phenylenediamine. In all cases, the test cells were constructed so that the three dimensional hydrodynamic boundary layer within the cells would significantly influence the reagent transport and therefore the observed current density at the microelectrodes. The current/flow rate relationship observed was analogous to the response of the observed within the macroscopic channel flow cells, where typically the cell design is restricted to configurations where a two dimensional transport analysis can be performed.     

Passive recruitment of circulating leukocytes into capillary sprouts from existing capillaries in a microfluidic system

Recent evidence implicating leukocytes in angiogenesis raises the question of whether leukocytes and other cells circulating with the blood in microvascular networks can home to capillary sprouts intraluminally. This study describes an investigation of leukocyte trafficking in sprouting capillaries fabricated using soft lithography. The leukocytes passing with whole blood through existing capillaries were able to enter microfabricated capillary sprouts of variable length and sprouting angle due to the mechanical interaction with red blood cells (RBCs) at the sprouting bifurcation, in spite of the complete absence of blood flow through the blind-ended sprouts or any chemoattractants. The RBCs formed "comet tails" (the densely packed cellular trains forming behind leukocytes as they move through narrow capillaries) and effectively pushed leukocytes into the microfabricated sprouts while bypassing them at the sprouting bifurcation. Individual sprouts filled with several leukocytes, as wells as RBCs and platelets, were observed. The results of this study suggest that (i) blood cells are likely present in capillary sprouts throughout their development, (ii) leukocytes and other circulating cells may use this mechanism to home to capillary sprouts intraluminally for direct engraftment, and (iii) tissues may use this phenomenon as another mechanism for local recruitment of leukocytes from the blood stream.     

EOF using the Ritz method: application to superelliptic microchannels

An efficient Ritz method is developed from the variational principle to solve the Poisson-Boltzmann equation under the Debye-Hückel approximation for studying the EOF in microchannels. The method is applied to the family of superelliptic cross sections which includes the elliptic channel and the rectangular channel as limiting cases. Several accurate tables presented are useful for design of electroosmotic channels, especially rectangular channels with rounded corners. It is shown how the flow rate Q is a sophisticated consequence of the nondimensional electrokinetic width K, the aspect ratio b as well as the superelliptic exponent n.     

Circular, nanostructured and biofunctionalized hydrogel microchannels for dynamic cell adhesion studies

We report on a method to fabricate biofunctionalized polyethylene glycol hydrogel microchannels with adjustable circular cross-sections. The inner channel surfaces are decorated with Au-nanoparticle arrays of tunable density. These Au-nanoparticles are functionalized with biomolecules whereas the hydrogel material provides an inert and biocompatible background. This technology provides control over flow conditions, channel curvature and biomolecule density on the channel surface. It can be applied for biophysical studies of cell-surface interactions mimicking, for example, leukocyte interactions with the endothelial lining in small vessels.     

Dense colloid transport in a bifurcating fracture

In this work, the transport of dense colloids through a water-saturated, bifurcating fracture is investigated using a constant spatial step particle tracking technique. The size of the constituents of a colloid plume is an important factor affecting the partitioning of dense colloids at the bifurcation. While neutrally buoyant colloids partition between daughter fractures in proportion to flow rates, dense colloids will preferentially exit fractures that are gravitationally downgradient, notwithstanding that the majority of the interstitial fluid may flow through the upper fracture. Comparison of the partitioning ratio between daughter fractures with the ratios of characteristic settling, diffusion, and advection time reveal that these parameters control how colloids behave at fracture bifurcations.     

Biomimetic postcapillary expansions for enhancing rare blood cell separation on a microfluidic chip

Blood cells naturally auto-segregate in postcapillary venules, with the erythrocytes (red blood cells, RBCs) aggregating near the axis of flow and the nucleated cells (NCs)--which include leukocytes, progenitor cells and, in cancer patients, circulating tumor cells--marginating toward the vessel wall. We have used this principle to design a microfluidic device that extracts nucleated cells (NCs) from whole blood. Fabricated using polydimethylsiloxane (PDMS) soft lithography, the biomimetic cell extraction device consists of rectangular microchannels that are 20-400 μm wide, 11 μm deep and up to 2 cm long. The key design feature is the use of repeated expansions/contractions of triangular geometry mimicking postcapillary venules, which enhance margination and optimize the extraction. The device operates on unprocessed whole blood and is able to extract 94 ± 4.5% of NCs with 45.75 ± 2.5-fold enrichment in concentration at a rate of 5 nl s(-1). The device eliminates the need to preprocess blood via centrifugation or RBC lysis, and is ready to be implemented as the initial stage of lab-on-a-chip devices that require enriched nucleated cells. The potential downstream applications are numerous, encompassing all preclinical and clinical assays that operate on enriched NC populations and include on-chip flow cytometry (A. Y. Fu et al., Anal. Chem., 2002, 74, 2451-2457; A. Y. Fu et al., Nat. Biotechnol., 1999, 17, 1109-1111), genetic analyses (M. M. Wang et al., Nat. Biotechnol., 2005, 23, 83-87; L. C. Waters et al., Anal. Chem., 1998, 70, 5172-5176) and circulating tumor cell extraction (S. Nagrath et al., Nature, 2007, 450, 1235-1241; S. L. Stott et al., Proc. Natl. Acad. Sci. U. S. A., 2010, 18392-18397; H. K. Lin et al., Clin. Cancer Res., 2010, 16, 5011-5018).     

Effect of capillary cross-section geometry and size on the separation of proteins in gradient mode using monolithic poly(butyl methacrylate-co-ethylene dimethacrylate) columns

Porous polymer monoliths have been prepared in capillaries with circular or square cross-sections and lateral dimensions of 50, 75, 100 μm as well as in a rectangular 38 μm × 95 μm capillary. These capillaries have been used to determine the effect of the size and shape of their cross-section on the porous and hydrodynamic properties of poly(butyl methacrylate-co-ethylene dimethacrylate) monoliths. The capillaries were studied by scanning electron microscopy and evaluated for their permeability to flow and their performance in the liquid chromatographic separation of a protein mixture comprising ribonuclease A, cytochrome c, myoglobin, and ovalbumin using a linear gradient of acetonitrile in the mobile phase. No differences resulting from channel geometry were found for the various capillary columns. These results demonstrate that standard capillaries with circular geometry are a good and affordable alternative conduit for modeling the processes carried out in microfluidic chips with a variety of geometries.     

Targeting the leukocyte activation cascade: getting to the site of inflammation using microfabricated assays

This paper describes the use of microfabricated devices to study the leukocyte activation cascade (LAC). The devices consist of microchannels fabricated in polydimethylsiloxane using soft lithography. Microfluidics, used to generate physiologically relevant levels of shear flow, was achieved by the simple attachment of a syringe pump. Microchannel surfaces were modified by self-assembled monolayer (SAM) chemistries. The devices were adapted to standard 96-well tissue culture format with microchannels that could accommodate either a monolayer of endothelial cells or a SAM with immobilized chemokines. Chemotaxis was performed using linear gradients of chemokine set in a 3D matrix. Using this approach, we demonstrated robust chemotaxis of primary human leukocytes (PHLs) in response to a gradient of the chemokine CCL2. Rolling and adhesion assays performed under shear flow demonstrated that leukocyte recruitment to the substrate was highly sensitive to both biological and physical forces. CCL2 and CXCL12 treatment of PHLs dose dependently increased activation and adhesion. These actions could be inhibited by the use of peptide or small molecule antagonists. These devices provide a robust platform to perform LAC assays under in vivo-like conditions.     

A microfabricated electrical differential counter for the selective enumeration of CD4+ T lymphocytes

We have developed a microfabricated biochip that enumerates CD4+ T lymphocytes from leukocyte populations obtained from human blood samples using electrical impedance sensing and immunoaffinity chromatography. T cell counts are found by obtaining the difference between the number of leukocytes before and after depleting CD4+ T cells with immobilized antibodies in a capture chamber. This differential counting technique has been validated to analyze physiological concentrations of leukocytes with an accuracy of ～9 cells per μL by passivating the capture chamber with bovine serum albumin. In addition, the counter provided T cell counts which correlated closely with an optical control (R(2) = 0.997) for CD4 cell concentrations ranging from approximately 100 to 700 cells per μL. We believe that this approach can be a promising method for bringing quantitative HIV/AIDS diagnostics to resource-poor regions in the world.     

Fabrication of circular microfluidic channels by combining mechanical micromilling and soft lithography

The fabrication of microfluidic channels with complex three-dimensional (3D) geometries presents a major challenge to the field of microfluidics, because conventional lithography methods are mainly limited to rectangular cross-sections. In this paper, we demonstrate the use of mechanical micromachining to fabricate microfluidic channels with complex cross-sectional geometries. Micro-scale milling tools are first used to fabricate semi-circular patterns on planar metallic surfaces to create a master mold. The micromilled pattern is then transferred to polydimethylsiloxane (PDMS) through a two-step reverse molding process. Using these semi-circular PDMS channels, circular cross-sectioned microchannels are created by aligning and adhering two channels face-to-face. Straight and serpentine-shaped microchannels were fabricated, and the channel geometry and precision of the metallic master and PDMS molds were assessed through scanning electron microscopy and non-contact profilometry. Channel functionality was tested by perfusion of liquid through the channels. This work demonstrates that micromachining enabled soft lithography is capable of fabricating non-rectangular cross-section channels for microfluidic applications. We believe that this approach will be important for many fields from biomimetics and vascular engineering to microfabrication and microreactor technologies.     

Dendrite structure of electrolytic gold deposited from molten chlorides

The structure of gold deposits produced by electrolysis of molten eutectic NaCl-KCl-CsCl at 500–700°C in an inert atmosphere is studied. The initial process on the gold cathode is the epitaxial growth of a layer up to 3 μm thick with a smoothed surface and a considerably later growth of grain boundaries. Gradually, on the protruding parts of deposit, the growth of dendrites starts. The dendrites are the major form of gold deposits. Typical gold dendrites are two-dimensional 2D〈112〉 and 2D〈112〉–〈110〉 and three-dimensional 3D〈100〉. Upon supplying air into the atmosphere above the melt at high current densities at the initial period there appears a powder comprising particles of a rounded twisted shape. Probable mechanisms leading to the formation of the “rounded” powder are discussed.     

Interface motion of capillary-driven flow in rectangular microchannel

In microchannel flow, gas-liquid interface behavior is important for developing a wide range of microfluidic applications, especially in passive microfluidic systems. This paper presents a discussion of interface motion driven by capillary action in a microchannel. We have extended the theory beyond the previous theory of capillary rise problem for a circular tube, to a rectangular microchannel. The same formula for the relation between nondimensional time and interface position is obtained as for a circular tube. We examined rectangular microchannels with several sizes (about 50 to 100 microm square) of glass capillaries and 85 x 68 microm and 75 x 45 microm polydimethylsiloxane (PDMS) microchannels fabricated by photolithography technique, respectively. We observed movement of the gas-liquid interface position and compared it to the dimensionless relation. We obtained the value of a dimensionless variable of driving force that is related to dynamic contact angles for glass-water, glass-ethanol, and PDMS-ethanol. Using this variable, interface motion can be predicted for any size of rectangular channels.     

A microfluidic photolithography for controlled encapsulation of single cells inside hydrogel microstructures

A microfluidic approach to generate hydrogel microstructures inside microchannels for controlled encapsulation of single cells was developed. The method was based on a modified microscope projection photolithography which allowed for the photopolymerization of poly(ethylene glycol) diacrylate (PEG-DA) inside microchannels. Uniform-sized hydrogel microstructures (~50 μm in diameter) were generated one by one with determined positions to encapsulate single cells without losing the viability. Cells of interest could be identified by any kinds of visible labels to be selectively encapsulated inside the formed hydrogel microstructures. Large-scale encapsulation of single cells was achieved with a relatively high efficiency of 80% and the viability of encapsulated cells could be guaranteed by removing the dead cells identified with Trypan blue. This method is simple, fast and convenient to pattern the microchannels with single cells for a wide range of cell-based applications. For demonstration, two intracellular enzyme assays of carboxylesterase were performed to investigate the distribution of enzyme concentrations and the kinetic information within the encapsulated single HepG2 cells.     

A low-cost 2D fluorescence detection system for μm sized beads on-chip

In this paper we describe a compact fluorescence detection system for on-chip analysis of beads, comprising a low-cost optical HD-DVD pickup. The complete system consists of a fluorescence detection unit, a control unit and a microfluidic chip containing microchannels and optical markers. With these markers the laser beam of the optical pickup can be automatically focused at the centre of the microchannel. With the complete system a two-dimensional fluorescent profile across the channel width can be obtained such that there is no need for hydrodynamic or electrokinetic focusing of the particles in a specific part of the channel. Fluorescent μm sized beads suspended in medium have been detected with the system. Since on both sides of the main beam two additional laser beams at a known distance are generated, also the velocity of individual beads has been determined.     

High fidelity neuronal networks formed by plasma masking with a bilayer membrane: analysis of neurodegenerative and neuroprotective processes

Spatially defined neuronal networks have great potential to be used in a wide spectrum of neurobiology assays. We present an original technique for the precise and reproducible formation of neuronal networks. A PDMS membrane comprising through-holes aligned with interconnecting microchannels was used during oxygen plasma etching to dry mask a protein rejecting poly(ethylene glycol) (PEG) adlayer. Patterns were faithfully replicated to produce an oxidized interconnected array pattern which supported protein adsorption. Differentiated human SH-SY5Y neuron-like cells adhered to the array nodes with the micron-scale interconnecting tracks guiding neurite outgrowth to produce neuronal connections and establish a network. A 2.0 μm track width was optimal for high-level network formation and node compliance. These spatially standardized neuronal networks were used to analyse the dynamics of acrylamide-induced neurite degeneration and the protective effects of co-treatment with calpeptin or brain derived neurotrophic factor (BDNF).     

Integration of a macro/micro architectured compartmentalised neuronal culture device using a rapid prototyping moulding process

The rapid prototyping of a reversible and one step moulded compartmentalised neuron glass/PDMS device with a thin wall barrier directly adjacent to the reservoirs is presented. A simple moulding technique to produce these devices results in a barrier of 560 μm where the 3 μm deep by 8 μm wide channels can be reversibly fabricated in either the glass base or PDMS compartmentalised mould depending on the type of application required. Using glass substrates with commercially laser engraved microchannels, both the PDMS planar and PDMS channelled device can be easily fabricated in a standard laboratory. The compartmentalised device has several advantages including good experimental accessibility and versatility with a variety of end user applications.     

Analysis of a Monod–Haldene type food chain chemostat with seasonally variably pulsed input and washout

In this paper, we introduce and study a model of a Monod–Haldene type food chain chemostat with seasonally variably pulsed input and washout. We investigate the subsystem with substrate and prey and study the stability of the periodic solutions, which are the boundary periodic solutions of the system. The stability analysis of the boundary periodic solution yields an invasion threshold. By use of standard techniques of bifurcation theory, we prove that above this threshold there are periodic oscillations in substrate, prey and predator. Simple cycles may give way to chaos in a cascade of period-doubling bifurcations. Furthermore, bifurcation diagrams have shown that there exists complexity for the pulsed system including periodic doubling cascade, periodic halving cascade and Pitchfork bifurcations and tangent bifurcations.      

Validation of CE modeling with a contactless conductivity array detector

Dynamic computer simulation data are compared for the first time with CE data obtained with a laboratory made system comprising an array of 8 contactless conductivity detectors (C⁴Ds). The experimental setup featured a 50 μm id linear polyacrylamide (LPA) coated fused‐silica capillary of 70 cm length and a purpose built sequential injection analysis manifold for fluid handling of continuous or discontinuous buffer configurations and sample injection. The LPA coated capillary exhibits a low EOF and the manifold allows the placement of the first detector at about 2.7 cm from the sample inlet. Agreement of simulated electropherograms with experimental data was obtained for the migration and separation of cationic and anionic analyte and system zones in CZE configurations in which EOF and other column properties are constant. For configurations with discontinuous buffer systems, including ITP, experimental data obtained with the array detector revealed that the EOF is not constant. Comparison of simulation and experimental data of ITP systems provided the insight that the EOF can be estimated with an ionic strength dependent model similar to that previously used to describe EOF in fused‐silica capillaries dynamically double coated with Polybrene and poly(vinylsulfonate). For the LPA coated capillaries, the electroosmotic mobility was determined to be 17‐fold smaller compared to the case with the charged double coating. Simulation and array detection provide means for quickly investigating electrophoretic transport and separation properties. Without realistic input parameters, modeling alone is not providing data that match CE results.     

Dynamic Gradient Directed Molecular Transport and Concentration in Hydrogel Films

Materials which selectively transport molecules along defined paths offer new opportunities for concentrating, processing and sensing chemical and biological agents. Here, we present the use of traveling ionic waves to drive molecular transport and concentration of hydrophilic molecules entrained within a hydrogel. The traveling ionic wave is triggered by the spatially localized introduction of ions, which through a dissipative ion exchange process, converts quaternary ammonium groups in the hydrogel from hydrophilic to hydrophobic. Through a reaction–diffusion process, the hydrophobic region expands with a sharp transition at the leading edge; it is this sharp gradient in hydrophilicity that drives the transport of hydrophilic molecules dispersed within the film. The traveling wave moved up to 450 μm within 30 min, while the gradient length remained 20 μm over this time. As an example of the potential of molecular concentration using this approach, a 70‐fold concentration of a hydrophilic dye was demonstrated.