Electrokinetics of the silica and aqueous electrolyte solution interface: Viscoelectric effects.

The manipulation of biomolecules, fluid and ionic current in a new breed of integrated nanofluidic devices requires a quantitative understanding of electrokinetics at the silica/water interface. The conventional capacitor-based electrokinetic Electric Double Layer (EDL) models for this interface have some known shortcomings, as evidenced by a lack of consistency within the literature for the (i) equilibrium constants of surface silanol groups, (ii) Stern layer capacitance, (iii) zeta (ζ) potential measured by various electrokinetic methods, and (iv) surface conductivity. In this study, we consider how the experimentally observable viscoelectric effect - that is, the increase of the local viscosity due to the polarisation of polar solvents - affects electrokinetcs at the silica/water interface. Specifically we consider how a model that considers viscoelectric effects (the VE model) performs against two conventional electrokinetic models, namely the Gouy-Chapman (GC) and Basic Stern capacitance (BS) models, in predicting four fundamental electrokinetic phenomena: electrophoresis, electroosmosis, streaming current and streaming potential. It is found that at moderate to high salt concentrations (>5×10(-3)M) predictions from the VE model are in quantitative agreement with experimental electrokinetic measurements when the sole additional adjustable parameter, the viscoelectric coefficient, is set equal to a value given by a previous independent measurement. In contrast neither the GS nor BS models is able to reproduce all experimental data over the same concentration range using a single, robust set of parameters. Significantly, we also show that the streaming current and potential in the moderate to high surface charge range are insensitive to surface charge behaviour (including capacitances) when viscoelectric effects are considered, in difference to models that do not consider these effects. This strongly questions the validity of using pressure based electrokinetic experiments to measure surface charge characteristics within this experimentally relevant high pH and moderate to high salt concentration range. At low salt concentrations (<5×10(-3)M) we find that there is a lack of consistency in previously measured channel conductivities conducted under similar solution conditions (pH, salt concentration), preventing a conclusive assessment of any model suitability in this regime.

Electrokinetics of isolated electrified drops.

Using a recently developed multiphase electrokinetic model, we simulate the transient electrohydrodynamic response of a liquid drop containing ions, to both small and large values of electric field. The temporal evolution is found to be governed primarily by two dimensionless groups: (i) Ohnesorge number (Oh), a ratio of viscous to inertio-capillary effects, and (ii) inverse dimensionless Debye length (κ), a measure of the diffuse regions of charge that develop in the drop. The effects of dielectric polarization dominate at low Oh, while effects of separated charge gain importance with increase in Oh. For small values of electric field, the deformation behaviour of a drop is shown to be accurately described by a simple analytical expression. At large electric fields, the drops are unstable and eject progeny drops. Depending on Oh and κ this occurs via dripping or jetting; the regime transitions are shown by a Oh-κ phase map. In contrast to previous studies, we find universal scaling relations to predict size and charge of progeny drops. Our simulations suggest charge transport plays a significant role in drop dynamics for 0.1 ≤ Oh ≤ 10, a parameter range of interest in microscale flows.

Isoelectric focusing in a silica nanofluidic channel: effects of electromigration and electroosmosis.

Isoelectric focusing of proteins in a silica nanofluidic channel filled with citric acid and disodium phosphate buffers is investigated via numerical simulation. Ions in the channel migrate in response to (i) the electric field acting on their charge and (ii) the bulk electroosmotic flow (which is directed toward the cathode). Proteins are focused near the low pH (anode) end when the electromigration effect is more significant and closer to the high pH (cathode) end when the electroosmotic effect dominates. We simulate the focusing behavior of Dylight labeled streptavidin (Dyl-Strep) proteins in the channel, using a relationship between the protein's charge and pH measured in a previous experiment. Protein focusing results compare well to previous experimental measurements. The effect of some key parameters, such as applied voltage, isoelectric point (pI), bulk pH, and bulk conductivity, on the protein trapping behavior in a nanofluidic channel is examined.

Concentration gradient focusing and separation in a silica nanofluidic channel with a non-uniform electroosmotic flow.

The simultaneous concentration gradient focusing and separation of proteins in a silica nanofluidic channel of various geometries is investigated experimentally and theoretically. Previous modelling of a similar device [Inglis et al., Angew. Chem. Int. Ed., 2011, 50, 7546] assumed a uniform velocity profile along the length of the nanochannel. Using detailed numerical analysis incorporating charge regulation and viscoelectric effects, we show that in reality the varying axial electric field and varying electric double layer thickness caused by the concentration gradient, induce a highly non-uniform velocity profile, fundamentally altering the protein trapping mechanism: the direction of the local electroosmotic flow reverses and two local vortices are formed near the centreline of the nanochannel at the low salt concentration end, enhancing trapping efficiency. Simulation results for yellow/red fluorescent protein R-PE concentration enhancement, peak focusing position and peak focusing width are in good agreement with experimental measurements, validating the model. The predicted separation of yellow/red (R-PE) from green (Dyl-Strep) fluorescent proteins mimics that from a previous experiment [Inglis et al., Angew. Chem. Int. Ed., 2011, 50, 7546] conducted in a slightly different geometry. The results will inform the design of new class of matrix-free particle focusing and separation devices.

Stationary chemical gradients for concentration gradient-based separation and focusing in nanofluidic channels.

Previous work has demonstrated the simultaneous concentration and separation of proteins via a stable ion concentration gradient established within a nanochannel (Inglis Angew. Chem., Int. Ed. 2001, 50, 7546-7550). To gain a better understanding of how this novel technique works, we here examine experimentally and numerically how the underlying electric potential controlled ion concentration gradients can be formed and controlled. Four nanochannel geometries are considered. Measured fluorescence profiles, a direct indicator of ion concentrations within the Tris-fluorescein buffer solution, closely match depth-averaged fluorescence profiles calculated from the simulations. The simulations include multiple reacting species within the fluid bulk and surface wall charge regulation whereby the deprotonation of silica-bound silanol groups is governed by the local pH. The three-dimensional system is simulated in two dimensions by averaging the governing equations across the (varying) nanochannel width, allowing accurate numerical results to be generated for the computationally challenging high aspect ratio nanochannel geometries. An electrokinetic circuit analysis is incorporated to directly relate the potential drop across the (simulated) nanochannel to that applied across the experimental chip device (which includes serially connected microchannels). The merit of the thick double layer, potential-controlled concentration gradient as a particle focusing and separation tool is discussed, linking this work to the previously presented protein trapping experiments. We explain why stable traps are formed when the flow is in the opposite direction to the concentration gradient, allowing particle separation near the low concentration end of the nanochannel. We predict that tapered, rather than straight nanochannels are better at separating particles of different electrophoretic mobilities.

Non-linear separation of pressure, velocity and wave intensity into forward and backward components.

Separating pressure, flow/velocity and wave intensity signals into forward and backward components provide insights about arterial wave propagation and reflection. A linear wave separation is normally used, but ignores the pressure-dependence of wave speed. While a non-linear separation could incorporate this pressure-dependence, no such method exists for wave intensity decomposition. Moreover, although linear separation errors for pressure (5-10 %) have been quantified previously, errors for velocity and wave intensity have not. Accordingly, we describe a non-linear wave separation technique based on the method of characteristics. Data from a computer model suggest that the percentage linear separation errors for velocity and wave intensity are approximately one-half and twice that for pressure, respectively. Although comparable to measurement uncertainty in many instances, linear separation errors may become more significant: (1) if wave speed varies substantially over the cardiac cycle, e.g. if pulse pressure or vessel compliance is high, (2) if the degree of wave reflection in the arterial system is large, or (3) if the constant wave speed used for the linear separation is closer to the minimum or maximum pressure-dependent value rather than the mean. Consideration of linear separation errors may therefore be important in some physiological settings.

The reservoir-wave paradigm introduces error into arterial wave analysis: a computer modelling and in-vivo study.

OBJECTIVES: Arterial wave reflection has traditionally been quantified from pressure and flow measurements using wave separation and wave intensity (WI) analysis. In the recently proposed reservoir-wave paradigm, these analyses are performed after dividing pressure into 'reservoir' and 'excess' components, yielding a modified wave intensity (WI(RW)). This new approach has led to controversial conclusions about the nature and significance of arterial wave reflection. Our aim was to assess whether WI or WI(RW) more accurately represent wave phenomena. METHODS: We studied two computer models (a simple network and a full model of the systemic arterial tree) in which all systolic forward waves and reflection properties were known a priori. Results of these models were compared with haemodynamic measurements in the ascending aorta of five adult sheep at baseline and after incremental arterial constriction. RESULTS: The key findings of model studies were that the reservoir-wave approach markedly underestimated or eliminated reflected compression waves, overestimated or artefactually introduced forward and backward expansion waves, and displayed nonphysical interactions between distal reflection sites and early systolic waves. These errors arose because, contrary to a key assumption of the reservoir-wave approach, reservoir pressure was not spatially uniform during systole. In-vivo results were qualitatively similar to model results, with baseline WI and WI(RW) suggesting that the arterial network was dominated by positive and negative wave reflection, respectively, while under all conditions, reflected WI(RW) compression waves were substantially smaller than corresponding WI waves. CONCLUSION: We conclude that the reservoir-wave paradigm introduces error into arterial wave analyses.

Microfluidic circuit analysis II: implications of ion conservation for microchannels connected in series.

A mathematical framework for analysing electrokinetic flow in microchannel networks is outlined. The model is based on conservation of volume and total charge at network junctions, but in contrast to earlier theories also incorporates conservation of ion charge there. The model is applied to mixed pressure-driven/electro-osmotic flows of binary electrolytes through homogeneous microchannels as well as a 4:1:4 contraction-expansion series network. Under conditions of specified volumetric flow rate and ion currents, non-linear steady-state phenomena may arise: when the direction of the net co-ion flux is opposite to the direction of the net volumetric flow, two different fully developed, steady-state flow solutions may be obtained. Model predictions are compared with two-dimensional computational fluid dynamics (CFD) simulations. For systems where two steady states are realisable, the ultimate steady behaviour is shown to depend in part upon the initial state of the system.

Microfluidic circuit analysis I: ion current relationships for thin slits and pipes.

Existing microfluidic circuit theories consider conservation of volume and conservation of total charge at each channel intersection (node) that exists within a circuit. However, in a strict sense conservation of number (or charge) for each ion species that is present should also be applied. To be able to perform such a conservation the currents due to the movement of each ion species (electrokinetic ion currents) that occur within each channel need to be known. Hence, we here present analytical and numerical methods for calculating these ion currents (and fluid flowrates) in Newtonian binary electrolyte solutions flowing within two-dimensional thin slits and pipes. Analytical results are derived in the limits of low potential, high potential, and thin double layers. We show that irrespective of double layer overlap, the Boltzmann distribution is valid provided that a local geometric mean is used for the reference ion concentration. While the real significance of the work lies in its application to multi-channel microfluidic circuit theory (see the accompanying paper of Biscombe et al. [1]), the present results show that even in single channels, ion current behaviour can be surprisingly complex.

Robustness of the P-U and lnD-U loop wave speed estimation methods: effects of the diastolic pressure decay and vessel wall non-linearities.

Arterial wave speed estimated invasively from pressure (P) and velocity (U) measurements using the P-U loop method, or non-invasively from diameter (D) and U measurements using the lnD-U loop method, assume that during early systole 1) backward-running waves are absent and 2) wave speed is constant. These assumptions also form the basis of a method for correcting time lags between P (or lnD) and U in which the R(2) of the early-systolic linear regression is maximized. However, neither of the two assumptions are strictly valid in vivo, where the diastolic pressure decay from the previous beat may give rise to some non-zero backward-running P, U and wave intensity (WI) components, and the pressure-dependency of wave speed may lead to curvilinearity in the early-systolic P-U and lnD-U relations. Accordingly, this study assessed the robustness of three phase correction algorithms, (including two that are not dependent on the two assumptions stated above, i.e., aligning the times of the peak 2nd derivative or peak signal curvature) and of the P-U and lnD-U loop wave speed estimation methods under a range of diastolic decay rates and degrees of vessel wall non-linearity. Results from a simple computer model of the arterial circulation suggested that although an apparent phase lag may be introduced by assuming linearity, the magnitude of this phase lag is likely to be small considering the sample intervals normally used in experimental studies; however, under highly non-linear flow conditions, the apparent lag may be comparable to hardware-related lags. Predicted errors in estimated wave speed using the P-U loop method were generally less than 10%, while somewhat higher errors were found in the lnD-U loop method (up to 15-20%). In both, higher diastolic pressure decay rates were associated with higher wave speed errors, although this effect was eliminated by subtracting the extrapolated diastolic pressure curve from the measured pressure. Overall, each of the time lag correction algorithms and wave speed estimation methods were generally satisfactory, although further experimental work is required to assess the curvature-based phase correction method and pressure adjustment in vivo.

Mechanism underlying accelerated arterial oxygen desaturation during recurrent apnea.

RATIONALE: Brief recurrent apneas in preterm infants and adults can precipitate rapid and severe arterial O(2) desaturation for reasons that remain unclear. OBJECTIVES: We tested a mathematically derived hypothesis that when breathing terminates apnea, mixed-venous hypoxemia continues into the subsequent apnea; as a result, there is a surge in pulmonary O(2) uptake that rapidly depletes the finite alveolar O(2) store, thereby accelerating arterial O(2) desaturation. METHODS: Recurrent apneas were simulated in an experimental lamb model. Pulmonary O(2) uptake was calculated from continuously measured arterial and mixed-venous O(2) saturation and cardiac output. MEASUREMENTS AND MAIN RESULTS: Direct measurements revealed that asynchrony in the desaturation and resaturation of arterial and venous blood gave rise to dips and surges in O(2) uptake. After desaturation to 50%, a typical nadir in preterm infants, O(2) uptake surged to a peak of 176.9 ± 7.8% of metabolic rate. During subsequent apneas, desaturation rate was increased two- to threefold greater than during isolated apneas, in direct proportion to the magnitude of the surge in O(2) uptake (P < 0.001; R(2) = 0.897). Application of our mathematical model to a published recording of cyclic apneas in a preterm infant precisely reproduced the accelerated desaturation rates of up to 15% · s(-1) observed clinically. CONCLUSIONS: Rapid depletion of alveolar O(2) stores by surges in O(2) uptake almost completely explains the acceleration of desaturation that occurs during recurrent apnea. This powerful mechanism is likely to explain the severity of intermittent hypoxemia that is associated with neurocognitive and cardiovascular morbidities in preterm infants and adults.

A dynamic model for assessing the impact of diffusing capacity on arterial oxygenation during apnea.

Preterm infants have a reduced pulmonary diffusing capacity that has been invoked to explain rapid arterial O(2)-desaturation during apnea, despite little evidence to support this view. We explored the role of diffusion limitation on O(2)-desaturation during apnea by developing a mathematical model of gas exchange in which O(2) dynamically loads the blood traversing the pulmonary capillary. While normal diffusing capacity DL((O(2)) had negligible impact on apneic desaturation, reduced DL((O(2)) advanced the onset of desaturation during apnea. Unexpectedly, despite considerable diffusion limitation, its influence on O(2)-desaturation disappeared within 15s, because its impact in slowing alveolar O(2) depletion maintained a higher driving pressure for diffusion. In contrast, reduced DL((O(2)) substantially slowed reoxygenation following apnea. Our findings do not support the hypothesis that reduced DL((O(2)) explains the rapid apneic desaturation observed in preterm infants. Instead, the signature of reduced DL((O(2)) is a prolonged hypoxemia following apnea, potentially causing a persistence of hypoxic conditions when heart rate and cardiac workload reach a peak.

A model investigation of the impact of ventilation-perfusion mismatch on oxygenation during apnea in preterm infants.

Ventilation-perfusion (V/Q) mismatch is a prominent feature of preterm infants and adults with lung disease. V/Q mismatch is known to cause arterial hypoxemia under steady-state conditions, and has been proposed as the cause of rapid arterial oxygen desaturation during apnea. However, there is little evidence to support a role for V/Q mismatch in the dynamic changes in arterial oxygenation that occur during apnea. Using a mathematical model, we quantified the effect of V/Q mismatch on the rate of desaturation during apnea to ascertain whether it could lead to rates of up to 10%s(-1) as observed in preterm infants. We used a lung-body model for the preterm infant that incorporated 50 parallel alveolar-capillary units that were ventilated and perfused with the severity of V/Q mismatch (sigma) defined conventionally according to sigma=S.D. of the distribution of V/Q ratios. Average desaturation rate 10s from apnea onset was strongly elevated with worsening V/Q mismatch as a result of an earlier desaturation of low V/Q units compared with high V/Q units. However, V/Q mismatch had little impact after apnea onset, with peak desaturation rate only substantially increased if mismatching caused a lowered resting arterial O(2) saturation. In conclusion, V/Q mismatch causes a more immediate onset of desaturation during apnea, and therefore places preterm infants and adults with lung disease at risk of hypoxemic dips. However, V/Q mismatch does not accelerate desaturation rate beyond apnea onset and cannot, therefore, explain the rapid desaturation observed during recurrent apnea in preterm infants.

A model analysis of arterial oxygen desaturation during apnea in preterm infants.

Rapid arterial O(2) desaturation during apnea in the preterm infant has obvious clinical implications but to date no adequate explanation for why it exists. Understanding the factors influencing the rate of arterial O(2) desaturation during apnea (Sa(O)2) is complicated by the non-linear O(2) dissociation curve, falling pulmonary O(2) uptake, and by the fact that O(2) desaturation is biphasic, exhibiting a rapid phase (stage 1) followed by a slower phase when severe desaturation develops (stage 2). Using a mathematical model incorporating pulmonary uptake dynamics, we found that elevated metabolic O(2) consumption accelerates Sa(O)2throughout the entire desaturation process. By contrast, the remaining factors have a restricted temporal influence: low pre-apneic alveolar P(O)2causes an early onset of desaturation, but thereafter has little impact; reduced lung volume, hemoglobin content or cardiac output, accelerates Sa(O)2during stage 1, and finally, total blood O(2) capacity (blood volume and hemoglobin content) alone determines Sa(O)2during stage 2. Preterm infants with elevated metabolic rate, respiratory depression, low lung volume, impaired cardiac reserve, anemia, or hypovolemia, are at risk for rapid and profound apneic hypoxemia. Our insights provide a basic physiological framework that may guide clinical interpretation and design of interventions for preventing sudden apneic hypoxemia.

Architecture control of three-dimensional polymeric scaffolds for soft tissue engineering. I. Establishment and validation of numerical models.

One of the most important functions of artificial three-dimensional (3D) polymeric scaffolds is to serve as a physical support to provide tissues with an appropriate architecture for in vitro cell culture as well as in vivo tissue regeneration. The production of three-dimensional (3D) polymeric scaffolds with tailored macroporous architecture is thus a crucial step in promoting controlled vascularization and tissue growth within host environments. In this study, 3D poly(lactic-co-glycolic acid) (PLGA) scaffolds were manufactured by a thermally induced phase-separation (TIPS) technique. By controlling the quenching strategy, 3D interconnected PLGA scaffolds with tunable pore size and alignment were obtained and characterized with the use of scanning electron microscopy (SEM). A series of numerical heat-transfer models were established in an effort to describe the cooling process within the PLGA freezing regime. Among them, a two-dimensional (2D) solidification model has proved to be the most successful in describing the quenching of the polymer solution and has the potential to be used to infer the various 3D macroporous architectures created from different quenching conditions.