Are the dynamic response characteristics of brachial artery flow-mediated dilation sensitive to the magnitude of increase in shear stimulus?

The purpose of this study was to determine the dynamic characteristics of brachial artery dilation in response to step increases in shear stress [flow-mediated dilation (FMD)]. Brachial artery diameter (BAD) and mean blood velocity (MBV) (Doppler ultrasound) were obtained in 15 healthy subjects. Step increases in MBV at two shear stimulus magnitudes were investigated: large (L; maximal MBV attainable), and small (S; MBV at 50% of the large step). Increase in shear rate (estimate of shear stress: MBV/BAD) was 76.8 +/- 15.6 s(-1) for L and 41.4 +/- 8.7 s(-1) for S. The peak %FMD was 14.5 +/- 3.8% for L and 5.7 +/- 2.1% for S (P < 0.001). Both the L (all subjects) and the S step trials (12 of 15 subjects) elicited a biphasic diameter response with a fast initial phase (phase I) followed by a slower final phase. Relative contribution of phase I to total FMD when two phases occurred was not sensitive to shear rate magnitude (r(2) = 0.003, slope P = 0.775). Parameters quantifying the dynamics of the FMD response [time delay (TD), time constant (tau)] were also not sensitive to shear rate magnitude for both phases (phase I: TD r(2) = 0.03, slope P = 0.376, tau r(2) = 0.04, slope P = 0.261; final phase: TD r(2) = 0.07, slope P = 0.169, tau r(2) = 0.07, slope P = 0.996). These data support the existence of two distinct mechanisms, or sets of mechanisms, in the human conduit artery FMD response that are proportionally sensitive to shear stimulus magnitude and whose dynamic response is not sensitive to shear stimulus magnitude.     

The role of the periciliary fluid in mucociliary flows: flow velocity profiles in frog palate mucus

Observations of flow velocity profiles over frog mucociliated palate are used to estimate viscosity, shear rate and shear stress in the periciliary flow field. The ability of cilia to generate significant shear stress at long distances and their utility as rhoeometers are examined. It is proposed that the depth of significant ciliary shear penetration into the periciliary fluid is sufficient to move mucus masses well beyond the ciliary tips, obviating the need for tip penetration where anchoring phenomena are sufficiently reduced.     

Flow behaviour of a POSS biopolymer solution

A non-biodegradable polyhedral oligomeric silsesquioxane (POSS) nanocomposite biopolymer has been developed for fabrication of medical devices and for tissue engineering human organs. The polymer in solution, containing 2 wt% of POSS, has been synthesized, characterized and investigated to determine its key rheological properties. Thus, the variation of shear stress and viscosity as a function of shear rate has been determined at ambient temperature to estimate yield stress and the index of pseudoplasticity, respectively. The temperature dependence of viscosity and the effect of ageing on the viscosity of the polymer have also been investigated. Results are compared with those of a conventional polycarbonate urethane (PCU) polymer solution. The POSS-PCU polymer solution shows near-Newtonian behaviour in the shear rate range to 1000 s(-1), having an apparent viscosity of approximately 3000 mPa s and a pseudoplasticity index of 0.90, decreasing slightly as the polymer solution is aged over 9 months. The temperature dependence of viscosity of the POSS polymer is extremely low and does not change with ageing but the yield strength increases from 2.7 Pa to 8.3 Pa.     

Effects of an anatomically detailed erector spinae model on L4/L5 disc compression and shear

Biomechanical models utilized for analysis of tasks that load the lumbar spine often predict the resultant moment, disc compression and sometimes shear. Usually the extensor muscular and ligament forces of the lumbar spine are assumed to act 5 cm posterior to a disc centre of rotation. This study has re-examined the generation and pathways of muscular force transmission within the extensor musculature. The effects on L4/L5 disc compression and shear estimates of an anatomically and biomechanically justifiable range of tissue moment arms, lines of force and force generating capacity of muscle, input to a computer model, have been determined. Results indicated that L4/L5 compression estimates could be reduced by up to 35% when the output from a more realistic anatomical model of the erector spinae muscle group was compared with that from the frequently reported and simplified single muscle equivalent with a 5 cm moment arm. The shear force estimates could be altered from more than 500 N (L4 tending to shear anteriorly on L5) to less than 200 N with L4 tending to shear posteriorly on L5. Using the combination of input variables considered by the authors to be most feasible to estimate compression, a single 'equivalent' extensor soft tissue moment arm of 7.5 rather than 5 cm would be needed to equate the compression. This simplification of course, does not accommodate the shear force estimate problem.     

Slow molecular clocks in Old World monkeys,apes, and humans

Two longstanding issues on the molecular clock hypothesis are studied in this article. First, is there a global molecular clock in mammals? Although many authors have observed unequal rates of nucleotide substitution among mammalian lineages, some authors have proposed a global clock for all eutherians, i.e., a single global rate of 2.2 x 10(-9) substitutions per nucleotide site per year. We reexamine this issue using noncoding, nonrepetitive DNA from Old World monkeys (OWMs), chimpanzee, and human. First, using the minimal date of 6 MYA for the human-chimpanzee divergence and more than 2.5 million base pairs of genomic sequences from human and chimpanzee, we estimate a maximal rate of 0.99 x 10(-9) for noncoding, nonrepetitive genomic regions for these two species. This estimate is less than half of the proposed global rate and much smaller than the commonly used rate (3.5 x 10(-9)) for eutherians. Further, using a minimal date of 23 MYA for the human-OWM divergence, we estimate a maximal rate of 1.5 x 10(-9) for both introns and fourfold degenerate sites in humans and OWMs. In addition, with the New World monkey (NWM) lineage as an outgroup, we estimate that the rate of substitution in introns is 30% higher in the OWM lineage than in the human lineage. Clearly, there is no global molecular clock in eutherians. Second, although many studies have indicated considerable variation in the mutation rate among regions of the mammalian genome, a recent study proposed a uniform rate. Using new and existing intron sequence data from higher primates, we find significant rate variation among genomic regions and a positive correlation between the rate of substitution and the GC content, refuting the claim of a uniform rate.     

Estimating mutation rates in low-replication experiments

Since mutation rate is a key biological parameter, its proper estimation has received great attention for decades. However, instead of the mutation rate, many authors opt for reporting the average mutant frequency, a less meaningful quantity. This is because the standard methods to estimate the mutation rate, derived from the Luria and Delbrück's fluctuation analysis, ideally require high-replication experiments to be applied; a requirement often unattainable due to constraints of time, budget or sample availability. But the main problem with mutant frequency, apart from being less informative, is its poor reproducibility; an especially marked defect when the chosen average is the arithmetic mean. Several authors tried to avoid this by employing other averages (such as the median or the geometric mean) or discarding outliers, though as far as we know nobody has evaluated which method performs best under low-replication settings. Here we use computer simulations to compare the performance of different methods used in low-replication experiments (≤4 cultures). Besides the customary averages of mutant frequency, we also tested two well-known fluctuation methods. Contrary to common practice, our results support that fluctuation methods should be applied in such circumstances, as they perform as well as or better than any average of mutant frequency. In particular, experimentalists will benefit from using MSS maximum likelihood in low-replication experiments because it: (i) provides more reproducible results, (ii) allows for direct estimation of mutation rate and (iii) allows for the application of conventional statistics.     

Estimate of the sticking probability for cells in uniform shear flow with adhesion caused by specific bonds

A theory is developed for the aggregation rate of cells in uniform shear flow when the cell-cell adhesion is mediated by bonds between specific molecules on the cell surfaces such as antigen and antibody or lectin and carbohydrate. The theory is based on estimates of the frequency and duration of cell-cell collisions and of the number of bonds formed and required to hold the cells together. For high shear rates, the sticking probability is a function of a single dimensionless parameter, A, that is proportional to G-2, with G the shear rate. For low shear rates, the sticking probability is a function of a second dimensionless parameter, A' proportional to G-1. In either case the rate of cell-cell sticking is a maximum when A (or A') congruent to 1.0. For small values of A (or A') the cells collide frequently, but do not stick, whereas for large values of A (or A') the cells collide infrequently, but stick with larger probability. Studies in Couette viscometer or other flow having approximately uniform shear can test these models.     

Concentration polarization of atherogenic lipids in the arterial system

Nomenclature c, Normalized LDL concentration (C*/C0); C0, incoming (bulk) LDL concentration (gr/cm3); Cw, LDL concentration on the luminal surface (gr/cm3); ,wC time average value of LDL concentration on the luminal surface (gr/cm3); D, diffusion coef-ficient of LDL (cm2/s); Q, blood flow rate (mL/s); 0R, average internal radius of the artery (cm); Re, Reynolds number (002/Run); Sc, Schmidt number (/Dn); t, normalized time (00*/tuR); u, normalized axial velocity (0*/uu); 0u, time a…     

Hydrodynamic effects and receptor interactions of platelets and their aggregates in linear shear flow.

We have modeled platelet aggregation in a linear shear flow by accounting for two body collision hydrodynamics, platelet activation and receptor biology. Considering platelets and their aggregates as unequal-sized spheres with DLVO interactions (psi(platelet) = -15 mV, Hamaker constant = 10(-19) J), detailed hydrodynamics provided the flow field around the colliding platelets. Trajectory calculations were performed to obtain the far upstream cross-sectional area and the particle flux through this area provided the collision frequency. Only a fraction of platelets brought together by a shearing fluid flow were held together if successfully bound by fibrinogen cross-bridging GPIIb/IIIa receptors on the platelet surfaces. This fraction was calculated by modeling receptor-mediated aggregation using the formalism of Bell (Bell, G. I. 1979. A theoretical model for adhesion between cells mediated by multivalent ligands. Cell Biophys. 1:133-147) where the forward rate of bond formation dictated aggregation during collision and was estimated from the diffusional limited rate of lateral association of receptors multiplied by an effectiveness factor, eta, to give an apparent rate. For a value of eta = 0.0178, we calculated the overall efficiency (including both receptor binding and hydrodynamics effects) for equal-sized platelets with 50,000 receptors/platelet to be 0.206 for G = 41.9 s(-1), 0.05 for G = 335 s(-1), and 0.0086 for G = 1920 s(-1), values which are in agreement with efficiencies determined from initial platelet singlet consumption rates in flow through a tube. From our analysis, we predict that bond formation proceeds at a rate of approximately 0.1925 bonds/microm2 per ms, which is approximately 50-fold slower than the diffusion limited rate of association. This value of eta is also consistent with a colloidal stability of unactivated platelets at low shear rates. Fibrinogen was calculated to mediate aggregation quite efficiently at low shear rates but not at high shear rates. Although secondary collisions (an orbitlike trajectory) form only a small fraction of the total number of collisions, they become important at high shear rates (>750 s(-1)), as these are the only collisions that provide enough time to result in successful aggregate formation mediated by fibrinogen. The overall method provides a hydrodynamic and receptor correction of the Smoluchowski collision kernel and gives a first estimate of eta for the fibrinogen-GPIIb/IIIa cross-bridging of platelets. We also predict that secondary collisions extend the shear rate range at which fibrinogen can mediate successful aggregation.     

Shear modulation of intercellular contact area between two deformable cells colliding under flow

Shear rate has been shown to critically affect the kinetics and receptor specificity of cell-cell interactions. In this study, the collision process between two modeled cells interacting in a linear shear flow is numerically investigated. The two identical biological or artificial cells are modeled as deformable capsules composed of an elastic membrane. The cell deformation and trajectories are computed using the immersed boundary method (IBM) for shear rates of 100-400s(-1). As the two cells collide under hydrodynamic shear, large local cell deformations develop. The effective contact area between the two cells is modulated by the shear rate, and reaches a maximum value at intermediate levels of shear. At relatively low shear rate, the contact area is an enclosed region. As the shear rate increases, dimples form on the membrane surface, and the contact region becomes annular. The nonmonotonic increase of the contact area with the increase of shear rate from computational results implies that there is a maximum effective receptor-ligand binding area for cell adhesion. This finding suggests the existence of possible hydrodynamic mechanism that could be used to interpret the observed maximum leukocyte aggregation in shear flow. The critical shear rate for maximum intercellular contact area is shown to vary with cell properties such as radius and membrane elastic modulus.     

Propagation of shear waves in muscle tissue

A mathematical model of the propagation of acoustic shear waves in muscle tissue is considered. Muscle is modeled as an incompressible transversely isotropic viscoelastic continuum with quasi-one-dimensional active tension. There are two types of shear waves in an infinite medium. Waves of the second type (transverse) propagate without decay even when myofibril viscosity is taken into account. A problem of standing transverse waves in a rectangular layer was investigated numerically. The values of the problem parameters are found for which one can easily estimate the active tension (or muscle tone) from the characteristics of standing waves. This value is informative for diagnostics of the muscle state.     

The effect of compliance on wall shear in casts of a human aortic bifurcation

Rigid and compliant casts of a human aortic bifurcation were subjected to physiologically realistic pulsatile fluid flows. At a number of sites near the wall in the approximate median plane of the bifurcation of these models, fluid velocity was measured with a laser Doppler velocimeter, and wall motion (in the case of the compliant cast) was determined with a Reticon linescan camera. The velocity and wall motion data were combined to estimate the instantaneous shear rates at the cast wall. Analysis showed that at the outer walls the cast compliance reduced shear rates, while at the walls of the flow divider the shear rate was increased.     

A free-drifting mimic of vertically migrating zooplankton

Many zooplankton species perform diel vertical migrations (DVM) which, in conjunction with vertical current shear, complicate the use of conventional fixed-depth drifters to account for advection. Here we illustrate the first use of an autonomous Vertically Migrating Drifter (VMD) to mimic DVM behavior. The vehicle resides within different subsurface layers at different times of day through either active hover cycles or passive drifts. It moves vertically between these layers at speeds comparable to those recorded for migratory populations. In this mode, it can be utilized as a tool to estimate the advection of migratory zooplankton in regions of high vertical current shear and can be employed as a Lagrangian tracer when attempting to sample the same population repeatedly over time.      

A numerical study on the effect of side hole number and arrangement in venous cannulae

Insertion of cannulae into vessels may apply non-physiological load and stress on blood cells, such that adenosine diphosphate may increase and result in hemolysis. Authors used the computational method to simulate the blood flow inside of the cannula. We limited the research to within the drainage cannulae. Nine different cannulae categorized by the number of side holes of 4, 12, and 20, and also categorized by the array type as staggered array, in-line array, and alternative in-line array were studied and compared to the cannulae with no side holes by using computational fluid dynamics. We evaluated the flow rate, the wall shear stress, and the shear rate, and compared them with one another to estimate the effect of the side holes. The flow rate is not proportional to the number of the side holes. However, larger number of side holes can reduce the mean shear rate.     

Concentration polarization of atherogenic lipids in the arterial system

The transport of atherogenic lipids (LDL) in a straight segment of an artery with a semi-permeable wall was simulated numerically. The numerical analysis predicted that a mass transport phenomenon called ’concentration polarization’ of LDL might occur in the arterial system. Under normal physiological flow conditions, the luminal surface LDL concentration was 5%–14% greater than the bulk concentration in a straight segment of an artery. The luminal surface LDL concentration at the arterial wall was flow-dependent, varying linearly with the filtration rate across the arterial wall and inversely with wall shear rate. At low wall shear rate, the luminal surface LDL concentration was very sensitive to changes in flow conditions, decreasing sharply as wall shear rate increased. In order to verify the numerical analysis, the luminal surface concentration of bovine serum albumin (as a tracer macromolecule) in the canine carotid artery was measured in vitro by directly taking liquid samples from the luminal surface of the artery. The experimental result was in very good agreement with the numerical analysis. The authors believe that the mass transport phenomenon of ‘concentration polarization’ may indeed exist in the human circulation and play an important role in the localization of atherosclerosis.     

Effects of shear rate on rouleau formation in simple shear flow

A kinetic equation for rouleau formation in a simple shear flow is derived, based on several assumptions. These are (a) colliding rouleaux stick to one another with a certain probability to form a single rouleau; (b) simultaneous collisions between more than two rouleaux are negligible; (c) rouleaux are broken by a viscous force exerted by the suspending fluid on the surfaces of rouleaux; (d) when a rouleau is broken by viscous forces, only two fragments are formed. Based on a simple mathematical model, collision rate, sticking probability and degradation rate are obtained as functions of applied shear rate. From the solution of the kinetic equation, the average size of rouleaux is obtained as a function of time with shear rate as a parameter. It is shown that the average size of rouleaux increases monotonically with increasing time and tends to an equilibrium size. The average size of rouleaux in a dynamical equilibrium decreases monotonically with increasing shear rate and tends to one cell as shear rate approaches infinity. It is also found that the initial rate of rouleau formation increases with increasing shear rate at very low shear rate, but this trend is reversed at higher shear rates. The theoretical results are compared quantitatively with experimental data.     

Physio-chemical properties of polymyxan 88A–water system

The system exopolysaccharide polymyxan 88A–water was studied at several temperatures. The temperature dependence of viscosity at cooling and heating was obtained in order to estimate the phase separation temperature (T_s) and the gelation temperature (T_g). The experimental values of T_s and T_g were used to plot the phase diagram of the system under study at polymer concentrations below 1.5 wt%. Viscous flow in the system was examined by the cylinder–cylinder rotation method. It has been found that: (i) at shear rates within 1–100 s⁻¹ the dependence of viscosity on shear rate can be fairly expressed by the power low; (ii) the activation enthalpy of viscous flow practically does not depend on shear rate; and (iii) the activation entropy of viscous flow is negative, most likely due to an orienting action of mechanical field.     

Effect of hematocrit on wall shear rate in oscillatory flow: do the elastic properties of blood play a role?

Porcine blood was used to examine the relationship between hematocrit levels and wall shear rate patterns in straight and curved artery models under fixed oscillatory flow conditions characteristic of larger arteries. It is demonstrated that porcine blood models both the viscous and elastic components of the 2 Hz complex viscosity of human blood quite accurately over a broad range of shear rates (1-1000 s-1) and hematocrits (20%-80%). For a fixed oscillatory flow waveform (Poiseuille peak shear rate = 168 s-1; mean shear rate 84 s-1), increases in hematocrit produced a decrease in the peak wall shear rate in both the straight and curved artery models and a corresponding decrease in wall shear rate reversal on the inside wall of the curved artery model. The same trends were also observed for oscillatory flows of aqueous glycerin solutions of increasing viscosity in the range of viscosity of the blood samples tested. Aqueous glycerin solutions produced wall shear rate waveforms of the same magnitude and shape as the porcine blood. This indicates that variations in the shear rate, and therefore the shear stress, were caused primarily by changes in the viscous and not the elastic properties of blood. The results suggest that simple Newtonian fluids may be sufficient for in vitro determination of the first order effects to be expected of human blood flow in large vessels having complex geometries and shear rates in or above the range of the present study.     

Sedimentation Coefficient and Fragility under Hydrodynamic Shear as Measures of Molecular Weight of the DNA of Phage T5

T5 DNA molecules resemble fragments of T2 DNA of molecular weight 84 × 10⁶ with respect to sedimentation coefficient and susceptibility to breakage under hydrodynamic shear. The sedimentation coefficient falls by the same factor when either T2 or T5 DNA is broken at its characteristic critical shear rate. At a given high rate of shear, both DNA's are broken into fragments exhibiting the same sedimentation coefficient. It follows that 84 × 10⁶ is a proper estimate of the molecular weight of T5 DNA, and that particles of phage T5, like those of T2, contain a single DNA molecule.     

Shear sensitivity of hybridoma cells in batch, fed-batch, and continuous cultures.

Previously, we observed that CRL-8018 hybridoma cells were more sensitive to well-defined viscometric shear during the lag and stationary phases than during the exponential phase of batch cultures. Some potential hypotheses for explaining the increase in shear sensitivity are (1) nutrient limitations that result in a decrease in production of specific cellular components responsible for the mechanical strength of the cell, (2) nutrient limitations that lead to synchronization of the culture in a cell cycle phase that is more sensitive to shear, or (3) a link between cell growth and shear sensitivity, such that slowly growing cells are more sensitive to shear. Here, the duration of the exponential phase was increased with use of fed-batch, and the effect on shear sensitivity of the cultures was measured with a viscometric technique. Extension of exponential growth resulted in an increased period during which the cells were insensitive to shear. Additionally, the shear sensitivity of the cells was constant over a wide range of growth rates and metabolic yields in chemostat cultures. These observations suggest that as long as the cells are actively (exponentially) growing, their shear sensitivity does not depend on the growth rate or metabolic state of the cell as expressed by metabolic yields. Thus, hypothesis 3 above can be dismissed.