Red blood cell motions in high-hematocrit blood flowing through a stenosed microchannel

We investigated the behavior of red blood cells (RBCs) in a microchannel with stenosis using a confocal micro-PTV system. Individual trajectories of RBCs in a concentrated suspension of up to 20% hematocrit (Hct) were measured successfully. Results indicated that the trajectories of healthy RBCs became asymmetric before and after the stenosis, while the trajectories of tracer particles in pure water were almost symmetric. The asymmetry was greater in 10% Hct than in 20% Hct. We also investigated the effect of deformability of RBCs on the cell-free layer thickness by hardening RBCs using a glutaraldehyde treatment. The results indicated that deformability is the key factor in the asymmetry of cell-free layer thickness. Therefore, the motions of RBCs are influenced strongly by the Hct, the deformability, and the channel geometry. These results give fundamental knowledge for a better understanding of blood flow in microcirculation and biomedical microdevices.     

Residence time distributions of gas flowing through rotating drum bioreactors

Residence time distribution studies of gas through a rotating drum bioreactor for solid-state fermentation were performed using carbon monoxide as a tracer gas. The exit concentration as a function of time differed considerably from profiles expected for plug flow, plug flow with axial dispersion, and continuous stirred tank reactor (CSTR) models. The data were then fitted by least-squares analysis to mathematical models describing a central plug flow region surrounded by either one dead region (a three-parameter model) or two dead regions (a five-parameter model). Model parameters were the dispersion coefficient in the central plug flow region, the volumes of the dead regions, and the exchange rates between the different regions. The superficial velocity of the gas through the reactor has a large effect on parameter values. Increased superficial velocity tends to decrease dead region volumes, interregion transfer rates, and axial dispersion. The significant deviation from CSTR, plug flow, and plug flow with axial dispersion of the residence time distribution of gas within small-scale reactors can lead to underestimation of the calculation of mass and heat transfer coefficients and hence has implications for reactor design and scale-up.     

The influence of suspending phase viscosity on the passage of red blood cells through capillary-size micropores

Much attention has been paid to the study of blood flow in long, narrow tubes. While the influence of tube diameter and driving pressure have been examined in detail, the influence of suspending phase viscosity has generally been assumed only to affect the blood viscosity in a linearly proportional manner, hence the practice of normalizing apparent blood viscosity values by the suspending phase viscosity to give a relative viscosity (e.g., Pries et al., 1992). While this assumption is probably valid for long tubes, it apparently does not hold for blood flow in short tubes (and by extension also for flow in short or branching capillary segments in vivo) in which RBC deformation plays a more significant role. In this paper we present a series of experiments using the Cell Transit Analyzer (CTA) in which the influence of driving pressure and suspending phase viscosity on RBC passage through short, narrow tubes has been systematically evaluated. Over the range studied (1 to 10 cm water), the influence of driving pressure was found to be unremarkable, in that RBC velocity scaled directly and linearly with pressure. This finding is consistent with previous studies. However, a distinct intercept was observed in the linear relationship between RBC pore transit time and suspending phase viscosity, which presumably arises as a consequence of RBC deformation either at the pore entrance or within the pore. Two simple mathematical models for the suspending phase-viscosity/transit-time relationship were considered. The results show that making CTA measurements over a range of suspending medium viscosities is a simple and practical way to obtain additional information about RBC mechanical properties.     

Effects of inner solution viscosity and membrane stiffness on erythrocyte deformability on passing through a microchannel: prediction by two-dimensional simulation

We studied erythrocyte deformability in an effort to develop diagnostic methods based on its measurement and thus aid in the development of therapies for circulatory diseases. In the reported work, we performed two-dimensional numerical simulations of blood flow through a microchannel (MC) to evaluate erythrocyte deformability, applying the immersed boundary method to simulate erythrocyte movement and deformation. To evaluate deformability, MC transit capacity and shape recoverability were considered, defined as the time required to pass through the MC and the time constant during the shape-recovery process after exiting the MC, respectively. The simulation results showed that the erythrocyte MC transit time increased when the viscosity of the inner solution or the stiffness of the membrane increased. The time constant for erythrocyte shape recovery increased as the inner solution viscosity increased. In contrast, the time constant decreased as the erythrocyte membrane stiffness increased. These time-constant trends were in agreement with a theoretical equation derived using the Kelvin model and with previous experimental results. This diagnostic method of measuring erythrocyte shape recoverability and MC transit capacity is anticipated to have clinical application.     

Simulation of a tumor cell flowing through a symmetric bifurcated microvessel

Biomechanics and Modeling in Mechanobiology - Microvessel bifurcations serve as the major sites of tumor cell adhesion and further extravasation. In this study, the movement, deformation, and...     

Hematocrit,viscosity and velocity distributions of aggregating and non-aggregating blood in a bifurcating microchannel

Microscale blood flow is characterised by heterogeneous distributions of hematocrit, viscosity and velocity. In microvascular bifurcations, cells are unevenly distributed between the branches, and this effect can be amplified in subsequent branches depending on a number of parameters. We propose an approach to infer hematocrit profiles of human blood flowing through a bifurcating microchannel. The influence of aggregation, induced by the addition of Dextran 2000 to the samples, is also considered. Averaged values indicate plasma skimming, particularly in the presence of red blood cell (RBC) aggregation. Using an empirical model, the hematocrit profiles are used to estimate local relative viscosity distributions. Simulations are used to predict how the non-uniform viscosity influences the velocity profiles. Comparing these data to velocity profiles of RBCs measured using particle image velocimetry provides validation of the model. It is observed that aggregation blunts velocity profiles after a long straight section of channel. Downstream of the bifurcation, skewing of the velocity profiles is detected, which is enhanced by aggregation. The proposed methodology is capable of providing hitherto unreported information on important aspects of microscale blood rheology.     

First passage time problem for a drifted Ornstein-Uhlenbeck process

We consider a continuous stochastic process defined as a drifted Ornstein-Uhlenbeck, for which the first passage time is of interest. The process being non-homogeneous, the first passage time probability density function cannot be found analytically, but numerical methods enable to find its estimate. Estimating the first passage time implies solving an unsteady convection-diffusion equation, with variable coefficients, and we use an implicit Euler scheme to solve it. This work is applied to simulated data, and the continuous process is inspired from recent work on biological marker modelling for HIV-positive patients. The first passage time probability density function can be useful to compare the marker progression in different groups. Numerical results show that the first passage time is highly dependent from the process perturbation, and is then more relevant than methods not considering the stochastic process directly to compare the progression.     

The passage of an ion through a synthetic ion channel

The simulated system consisted of a fatty acid bilayer membrane dividing two electrolyte layers each containing ions, and a channel composed of linked 15-crown-5 ether rings. The Na⁺ and F^?  ions in the aqueous electrolyte layers were too large to enter the channel, but the Li⁺ ions entered and were transported. Conditions that optimised the passive, electric-field-induced transport of Li⁺ ions through the channel were investigated. It was calculated and rationalised that the higher the numerical value of the electrostatic charge on the oxygen atoms of the crown ether rings, the more easily does the channel convey the Li⁺ ions.     

Phosphorus absorption by intact maize plants from flowing solutions influenced by 2.4-dinitrophenol and viscosity of solution

The investigation of phosphorus absorption by intact plants during a short period has above all confirmed the validity of the results obtained in the foregoing study of the kinetics of absorption by excised roots. Further, the results show the unquestionably important role of mass flow in transporting ions to plant roots, mainly at lower and medium concentrations, that is, from about 0.1 to 10 mM. Under conditions of growth close to the optimum, the supply by means of mass flow can be sufficient even at lower concentrations of phosphorus, such as 1.47 mM KH₂PO₄, or the absorption of phosphorus by plants can be higher than in the case of ions being transported to roots by diffusion. With a higher absorption the phosphorus distribution somewhat changes as well, relatively more of it being accumulated in the roots. 2.4-DNP applied to the nutrient solution at a concentration of 10^-5 M reduces the phosphorus absorption.     

Estimation of causal effects of a time-varying exposure at multiple time points through multivariable mendelian randomization

Mendelian Randomisation (MR) is a powerful tool in epidemiology that can be used to estimate the causal effect of an exposure on an outcome in the presence of unobserved confounding, by utilising genetic variants as instrumental variables (IVs) for the exposure. The effect estimates obtained from MR studies are often interpreted as the lifetime effect of the exposure in question. However, the causal effects of some exposures are thought to vary throughout an individual’s lifetime with periods during which an exposure has a greater effect on a particular outcome. Multivariable MR (MVMR) is an extension of MR that allows for multiple, potentially highly related, exposures to be included in an MR estimation. MVMR estimates the direct effect of each exposure on the outcome conditional on all the other exposures included in the estimation. We explore the use of MVMR to estimate the direct effect of a single exposure at different time points in an individual’s lifetime on an outcome. We use simulations to illustrate the interpretation of the results from such analyses and the key assumptions required. We show that causal effects at different time periods can be estimated through MVMR when the association between the genetic variants used as instruments and the exposure measured at those time periods varies. However, this estimation will not necessarily identify exact time periods over which an exposure has the most effect on the outcome. Prior knowledge regarding the biological basis of exposure trajectories can help interpretation. We illustrate the method through estimation of the causal effects of childhood and adult BMI on C-Reactive protein and smoking behaviour.     

Estimation of the distribution of blood vessel diameters from the arteriovenous passage of microspheres

We present an estimator of the probability density of capillary diameters based on a simple probabilistic model of microsphere passage through a microvascular bed. With this model, an estimate of the density is obtained as the solution of an integral equation. The density is approximated by a linear combination of B-splines with the coefficients restricted to be nonnegative. Equations for maximum likelihood estimates of the coefficients are obtained. The proposed method is applied to data from the dog intestinal circulation.     

A computational model for the transit of a cancer cell through a constricted microchannel

We propose a three-dimensional computational model to simulate the transient deformation of suspended cancer cells flowing through a constricted microchannel. We model the cell as a liquid droplet enclosed by a viscoelastic membrane, and its nucleus as a smaller stiffer capsule. The cell deformation and its interaction with the suspending fluid are solved through a well-tested immersed boundary lattice Boltzmann method. To identify a minimal mechanical model that can quantitatively predict the transient cell deformation in a constricted channel, we conduct extensive parametric studies of the effects of the rheology of the cell membrane, cytoplasm and nucleus and compare the results with a recent experiment conducted on human leukaemia cells. We find that excellent agreement with the experiment can be achieved by employing a viscoelastic cell membrane model with the membrane viscosity depending on its mode of deformation (shear versus elongation). The cell nucleus limits the overall deformation of the whole cell, and its effect increases with the nucleus size. The present computational model may be used to guide the design of microfluidic devices to sort cancer cells, or to inversely infer cell mechanical properties from their flow-induced deformation.

     

Characteristics of current passage through plant tissue

Plant tissue connected in a d.c. circuit behaves as a capacitor, short-circuited through a resistor. Using a saw-tooth voltage (T = 2 ma, U_max = + 13 V), structural and physiological conditions in a plant tissue can be analyzed on the basis of changes in the current character.     

Diffusion approximation and first passage time problem for a model neuron

A diffusion equation for the transition p.d.f. describing the time evolution of the membrane potential for a model neuron, subjected to a Poisson input, is obtained, without breaking up the continuity of the underlying random function. The transition p.d.f. is calculated in a closed form and the average firing interval is determined by using the steady-state limiting expression of the transition p.d.f. The Laplace transform of the first passage time p.d.f. is then obtained in terms of Parabolic Cylinder Functions as solution of a Weber equation, satisfying suitable boundary conditions. A continuous input model is finally investigated.     

Estimation of time of divergence from phylogenetic studies.

Recent studies with comparative data on base sequences of homologous DNA's or amino acid sequences of homologous proteins indicate that simultaneous estimation of phylogenetic structure and time of divergence is often cumbersome and time consuming. On the other hand, when the topology of an evolutionary tree is known, it is shown in this paper that the least squares theory may be applied to obtain simple estimates of the relative time lengths for each segment of the tree under the assumption of uniform random substitutions in each segment. The method is illustrated with amino acid sequence data on various globin molecules and cytochrome c. The evolutionary significance of some of the estimates is also discussed.     

First passage time study of DNA strand displacement

DNA strand displacement, in which a single-stranded nucleic acid invades a DNA duplex, is pervasive in genomic processes and DNA engineering applications. The kinetics of strand displacement have been studied in bulk; however, the kinetics of the underlying strand exchange were obfuscated by a slow bimolecular association step. Here, we use a novel single-molecule fluorescence resonance energy transfer approach termed the “fission” assay to obtain the full distribution of first passage times of unimolecular strand displacement. At a frame time of 4.4 ms, the first passage time distribution for a 14-nucleotide displacement domain exhibited a nearly monotonic decay with little delay. Among the eight different sequences we tested, the mean displacement time was on average 35 ms and varied by up to a factor of 13. The measured displacement kinetics also varied between complementary invaders and between RNA and DNA invaders of the same base sequence, except for T → U substitution. However, displacement times were largely insensitive to the monovalent salt concentration in the range of 0.25–1 M. Using a one-dimensional random walk model, we infer that the single-step displacement time is in the range of ～30–300 μs, depending on the base identity. The framework presented here is broadly applicable to the kinetic analysis of multistep processes investigated at the single-molecule level.     

Differential passage time of mistletoe fruits through the gut of honeyeaters and flowerpeckers: effects on seedling establishment

McKey's (1975) hypothesis that avian dispersers with a specialized gut provide higher quality seed dispersal than unspecialized frugivores was tested using grey mistletoe (Amyema quandang) fruits, and captive mistletoebirds (Dicaeum hirundinaceum) and spinycheeked honeyeaters (Acanthagenys refogularis) in arid South Australia. Mistletoebirds have a specialized gut, unlike spiny-cheeked honeyeaters. The gut passage time of A. quandang fruits through mistletoebirds was 820±29 s (mean±SE, n=188), compared to 2434±36 s (n=436) for honeyeaters. The seeds defecated by both bird species were deployed on twigs of host trees. Despite the longer retention time of fruit in the gut of honeyeaters, the germination percentage of seeds defecated by mistletoebirds (85% of 485 seeds) and honeyeaters (81% of 485 seeds) did not differ significantly 1 week after deployment. However, after 5 months, a significantly greater proportion of seedlings had established from seeds passed by mistletoebirds (42.7%) than from seeds defecated by honeyeaters (31.1%). The data support the notion that the more gentle treatment of seeds in the gut of specialized dispersers translates into higher seedling establishment.