Interaction of peristaltic flow with pulsatile flow in a circular cylindrical tube

The effect of pulsatile flow on peristaltic transport in a circular cylindrical tube is analysed. The flow of a Newtonian viscous incompressible fluid in a flexible circular cylindrical tube on which an axisymmetric travelling sinusoidal wave is imposed, is considered. The initial flow in the tube is induced by an arbitrary periodic pressure gradient. A perturbation solution with amplitude ratio (wave amplitude/tube radius) as a parameter is obtained when the frequency of the travelling wave and that of the imposed pressure gradient are equal. The interaction effects of periodic wall induced flow and periodic pressure imposed flow are visualized through the presence of substantially different components of steady and higher harmonic oscillating flow in the first order flow solution. Numerical results show a strong variation of steady state velocity profiles with boundary wave number and Reynolds number and a strong phase shift behaviour of the flow in the radial direction.     

Mathematical Description of Water and Solution Flows in Segments of Maize Roots and in Branches of White Birch

The need of the study of the transport of water molecules and of solutions in the biological system and shortcomings in the contemporary modelling of bioflows led us to the construction of a new mathematical model which would more precisely characterize the bioflows controlled by natural sources (for example the gradient of hydrostatic and osmotic pressure, of electric potential and of temperature) without limiting thermodynamic conditions. The model issues from the reality of the biosystem as a black box. It uses those input quantities which are attainable. It has been verified with white birch branches, the primary root and the roots of the first node of 24-day-old maize plants under conditions of the action of external force in the form of temperature gradient. The results obtained during the study of conductances, ultrafiltration and reflection properties of the above tissues suggest that these properties are dependent on the stage of tissue development. The osmotic flow is higher in white birch branches than the volume flow which is on the contrary higher in maize roots. The heat flow is higher in maize roots than in white birch branches and its course is synchronized with the volume flow. White birch branch tissues also show a higher reflection ability under these conditions than maize roots. The reflection abilities of all the above tissues decrease with increasing temperature gradient. Lower values of this gradient correspond to higher reflection abilities.     

Pulsatile flow in a catheterised artery

A model is presented for the physiological problem of a catheter which is inserted in a femoral artery to measure the pressure gradient. As the catheter will modify the pressure distribution in the artery, the pressure gradient which would be recorded by a perfect pressure transducer attached to it would differ from that in the uncatheterised artery. To estimate the magnitude of this error, it is assumed that the rates of flow of blood through the catheterised and the uncatheterised artery are described by the same known periodic function of time.     

Modulation of cellular rhythm and photoavoidance by oscillatory irradiation in the Physarum plasmodium

We studied responses of cellular rhythm and light-induced movement to periodic irradiation in a unicellular amoeboid organism, the Physarum plasmodium. The intrinsic frequency of the contraction rhythm, which is based on biochemical oscillations, became synchronized with the frequency of periodic irradiation with light when both frequencies were close enough. In order to study the role of the synchronization in light-induced movement, periodic irradiation was applied to only part of the plasmodium. The rate of avoidance of light was modulated in the frequency band in which the synchronization occurred. The synchronization property of the contraction oscillation underlies the regulation of tactic movement in plasmodium.     

Theoretical study of flow,pressure and solute concentration in double membrane systems

A model system consisting of two rigidly held membranes in series was investigated through the application of the Kedem and Katchalsky thermodynamic single membrane flow equations. This analysis results in predictions of the steady state flow properties as well as values for the solute concentration and pressure of the internal compartment when the system is under the influence of a constant solute concentration or hydrostatic pressure gradient. It is demonstrated that although the flow properties and internal compartment pressure are complicated functions of the membrane permeability coefficients and driving gradient across the system, the relationships are greatly simplified by the explicit appearance of the internal compartment steady state solute concentration in the equations. It is shown that the steady state volume flow rate depends on the absolute value of the solute concentration in the external compartments, as well as the solute concentration gradient across the system. The properties of non-linear dependence of volume flow on concentration gradient, and rectification of volume flow are discussed and shown to be independent properties of the system. For the system under the influence of a solute concentration gradient, the internal compartment pressure can be greater or less than the ambient pressure, and depends mainly on the order in which the membranes are encountered by the volume flow. These properties are qualitatively correlated with certain available experimental observations in biological systems.     

Effect of an anomalous broadening of the synchronization band after electric stimulation of heart tissues

Synchronization effects of the second order induced by a change of the action potential (AP) shape in relation to the frequency of periodic stimulation were studied. Mechanism of anomalous increase of the synchronization band at periodic stimulation of the heart fibers was explained. By means of a modified method of synchronization diagrams the synchronization bands were calculated for possible stimulation regimes taking into account a change in RP shape and dynamic threshold (DT) depending on the frequency of the initiated regimes. Regions of stimulating signals parameters (multiplicity regions or prolonging regions) were discovered, within the range of which the same stimulating signal may induce different synchronization regimes. Physiological meaning of the existence of anomalous synchronization regimes which significantly broaden the adaptation possibilities of the heart is discussed.     

Linear and nonlinear analyses of pulsatile blood flow in a cylindrical tube

A non-Newtonian shear-thinning constitutive relation is proposed to study pulsatile flow of whole blood in a cylindrical tube. The constitutive relation, which satisfies the principle of material frame indifference, is derived from viscometric data obtained from whole blood over a range of hematocrits. Assuming axisymmetric flow in a rigid cylindrical tube of constant diameter, a second-order, nonlinear partial differential equation governing the axial velocity component is obtained. Imposing a periodic pressure gradient, the governing equation was solved numerically using finite difference methods over a range of Stokes values and hematocrits. For a forcing frequency of 1 Hz, results are presented over tube diameters ranging between 0.1 and 2 cm and over hematocrits ranging between 10 and 80%. For a given hematocrit, velocity profiles predicted for the non-Newtonian model under sinusoidal forcing reveal attenuated volume flow rate and enhanced vorticity transport over the tube cross-section relative to a Newtonian fluid having a viscosity corresponding to the high shear-rate limit. For moderate to high Stokes numbers, consistent with flow in large arteries, our results revealed a viscosity distribution that was nearly time invariant. An analytic solution was obtained for a fluid having arbitrarily prescribed radially varying, temporally invariant viscosity and density distributions under arbitrary periodic pressure forcing. Close agreement was observed between our numerical and analytical results when the imposed viscosity distribution was chosen to approximate the time-averaged viscosity distribution predicted by the shear-thinning non-Newtonian model. For St > or approximately= 100, the disparity between our results and those of a Newtonian fluid of constant viscosity grows with a decreasing ratio of the DC to AC components of the pressure-gradient amplitude below 50%. In particular, for any purely oscillatory pressure-gradient (vanishing DC component), the Womersley solution is a particularly poor predictor of the amplitude and phase of wall shear rate for over half of the flow cycle. Under such circumstances, the analytical models presented here provide a simple and accurate means of estimating instantaneous wall shear rate, knowing only the pressure gradient and hematocrit.     

Interaction of Peristaltic Flow with Pulsatile Couple-Stress Fluid

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External compression increases forearm perfusion.

Application of compression stockings to the lower extremities is a widely used therapeutic intervention to improve venous return, but there is little information about the effects of compression on local arterial perfusion. Therefore, we tested the hypothesis that a positive external pressure increases forearm perfusion. The relation of increasing external pressure induced by standardized compression to the arterial inflow and arterial flow reserve of the forearm was critically evaluated in a group of healthy young men (n = 9). Flow was measured with venous occlusion plethysmography after a 10-min application of six different stockings with compression pressure increasing from 13 to 23 mmHg. During compression, the arterial inflow increased significantly from 3.7 +/- 0.85 to 8.8 +/- 2.01 ml.min(-1).100 ml tissue(-1) (P < 0.001) and the arterial flow reserve increased from 17.7 +/- 4.7 to 28.3 +/- 7.0 ml.min(-1).100 ml tissue(-1). The flow increase was persistent after 3 h of constant application of external pressure and also during simultaneous low-intensity hand grip. Similar results obtained with occlusion plethysmography were seen with MRI. During the interventions, forearm temperature was unchanged, and the volunteers reported no discomfort. In conclusion, 1) arterial perfusion of the human forearm increases more than twofold during application of external compression over a pressure range of 13-23 mmHg, and 2) the result is interpreted as an autoregulatory response following the decrease of the vascular transmural pressure gradient.     

Synchronization of oscillations of proliferation of keratinocytes in psoriatic skin by external periodic force: a mathematical model

A mathematical model of mitotic activity of epidermis in normal skin and skin afflicted with psoriasis is presented as a system of two autonomous nonlinear differential equations. Its qualitative analysis was carried out and numerical solutions were obtained at the parameter values corresponding to these states. It was shown that in the norm, a single stable equilibrium of a "focus" type exists in the system; whereas in psoriasis, owing to an increase in the growing fraction, hyperproliferation, and enhanced migration of interacting keratinocytes, a stable limit cycle arises from the state of unstable focus. In this paper we also report on the results of computer modeling of synchronization of self-excited oscillations of keratinocyte population density in psoriatic lesions by an external periodic force. This synchronization is viewed as a possible mechanism of the clinically observed dependence of psoriasis course on some natural factors of cyclic nature.     

A Zonal Density Gradient Centrifuge for Separating Cytoplasmic Granules from Trypanosoma brucei

SYNOPSIS. A small zonal density gradient centrifuge has been designed and constructed for the separation of cell granules from Trypanosoma brucei. Two distinct bands were obtained on a simple sucrose density gradient of the following granules which were found in corresponding fractions of the effluent by electron microscopy: Type I granules (lysosomes) which formed a clear-cut band toward the periphery of the rotor, and Type II (endoplasmic reticular) granules which formed a more diffuse band and showed great diversity of size, shape and state of aggregation. This aggregation is related to the structure of these granules which are formed in the endoplasmic reticular tubules and are therefore not easily dispersed during rupture of the cell body.     

Intrinsic pump-conduit behavior of lymphangions

Lymphangions, segments of lymphatic vessels bounded by valves, have characteristics of both ventricles and arteries. They can act primarily like pumps when actively transporting lymph against a pressure gradient. They also can act as conduit vessels when passively transporting lymph down a pressure gradient. This duality has implications for clinical treatment of several types of edema, since the strategy to optimize lymph flow may depend on whether it is most beneficial for lymphangions to act as pumps or conduits. To address this duality, we employed a simple computational model of a contracting lymphangion, predicted the flows at both positive and negative axial pressure gradients, and validated the results with in vitro experiments on bovine mesenteric vessels. This model illustrates that contraction increases flow for normal axial pressure gradients. With edema, limb elevation, or external compression, however, the pressure gradient might reverse, and lymph may flow passively down a pressure gradient. In such cases, the valves may be forced open during the entire contraction cycle. The vessel thus acts as a conduit, and contraction has the effect of increasing resistance to passive flow, thus inhibiting flow rather than promoting it. This analysis may explain a possible physiological benefit of the observed flow-mediated inhibition of the lymphatic pump at high flow rates.     

Studies on water vapor pressure gradient from external air through clothing to the skin in relation to external humidity and clothing conditions

Using a hygrometric capsule method developed by the authors, water vapor pressure was measured at each layer of clothing as well as at the skin surface on a human subject under actual wearing conditions. The pattern of vapor pressure gradient from the skin surface through clothing to the external air was examined in relation to the ambient vapor pressure and ths sort of textiles worn. The following findings were obtained. 1) Water vapor pressure gradient was greater between coat and external air than that between coat and underwear. The gradient became steeper again between underwear and the skin. 2) Under given clothing conditions, vapor pressure at each layer of clothing as well as at the skin varied according to the ambient humidity. However, the pattern of vapor pressure gradient from the skin through clothing to the external air was not greatly influenced by the external humidity. 3) The pattern of vapor pressure gradient from the skin through clothing to the external air was not greatly influenced by the external humidity. 3) The pattern of vapor pressure gradient through the clothing as a whole differed according to the kinds of textiles used for coat and underwear.     

Heat transfer mediated by coronary circulation in Langendorff-perfused isolated whole hearts

Although coronary flow is essential for oxygen supply, which is a prerequisite for cardiac electrical activity, energy metabolism and mechanical performance, the roles of coronary circulation on heat transfer to the heart have received less attention. This study investigated the effects of coronary circulation on epicardial temperature, the effects of temperature on coronary resistance, and the effects of ischemia on temperature fall, using isolated perfused rat or guinea pig hearts. Monophasic action potential (MAP) and epicardial temperature were recorded by a pair of suction electrodes and thermisters, while whole heart conductance (WHC) was estimated by a two-electrode instrument arranged in a diagonal array, under the alteration of the coronary flow rate of perfusate with different temperatures. MAP duration was sensitive to the local temperature, and lowering the temperature caused reduced WHC and increased coronary resistance calculated by dividing perfusion pressure by flow rate. After the onset of ischemia, WHC fell immediately in a single exponential manner, and MAP duration was abbreviated after transient behaviors explained well by the exquisite temperature gradient governed by coronary artery geometry. Epicardial temperature is maintained by coronary circulation in isolated perfused heart. Temperature-sensitive coronary tonus and MAP duration indicate that an exquisite temperature gradient underlies inhomogeneous distributions of coronary flow and electrical property. No-flow ischemia disturbs heat transfer and augments the temperature gradient transiently. Therefore, an isolated perfused heart can be considered as a heat transfer model where thermoregulation is maintained by warm coronary perfusion.     

Synchronizing a multicellular system by external input: an artificial control strategy

MOTIVATION: Although there are significant advances on elucidating the collective behaviors on biological organisms in recent years, the essential mechanisms by which the collective rhythms arise remain to be fully understood, and further how to synchronize multicellular networks by artificial control strategy has not yet been well explored. RESULTS: A control strategy is developed to synchronize gene regulatory networks in a multicellular system when spontaneous synchronization cannot be achieved. We first construct an impulsive control system to model the process of periodically injecting coupling substances with constant or random impulsive control amounts into the common extracellular medium, and further study its effects on the dynamics of individual cells. We derive the threshold of synchronization induced by the periodic substance input. Therefore, we can synchronize the multicellular network to a specific collective behavior by changing the frequency and amplitude of the periodic stimuli. Moreover, a two-stage scheme is proposed to facilitate the synchronization in this paper. We show that the presence of the external input may also initiate different dynamics. The multicellular network of coupled repressilators is used to show the effectiveness of the proposed method. The results not only provide a perspective to understand the interactions between external stimuli and intrinsic physiological rhythms, but also may lead to development of realistic artificial control strategy and medical therapy. AVAILABILITY: CONTACT: aihara@sat.t.u-tokyo.ac.jp.     

Biomechanics of Schlemm's canal endothelial cells: influence on F-actin architecture

Aqueous humor drains from the eye through Schlemm's canal, a small endothelial-lined collecting duct. Schlemm's canal endothelial cells may be important in controlling the pressure within the eye (and hence are of interest in glaucoma), and are subject to an unusual combination of shear stress and a basal-to-apical pressure gradient. We sought to characterize this biomechanical environment and determine its effects on F-actin architecture in situ. A theoretical model of flow in Schlemm's canal was used to estimate shear stresses applied to endothelial cells by flowing aqueous humor. Alignment of Schlemm's canal endothelial cells in human eyes was quantified by scanning electron microscopy. F-actin architecture was visualized by fluorescent labeling and compared for closely adjacent cells exposed to different biomechanical environments. We found that, despite the relatively low flow rate of aqueous humor, shear stresses experienced by Schlemm's canal endothelial cells could reach those in the arterial system. Schlemm's canal endothelial cells showed a statistically significant preferential alignment, consistent with a shear-mediated effect. Schlemm's canal endothelial cells subjected to a basal-to-apical pressure gradient due to transendothelial flow showed a prominent marginal band of F-actin with relatively few cytoplasmic filaments. Adjacent cells not subject to this gradient showed little marginal F-actin, with a denser cytoplasmic random network. We conclude that Schlemm's canal endothelial cells experience physiologically significant levels of shear stress, promoting cell alignment. We speculate that this may help control the calibre of Schlemm's canal. F-actin distribution depends critically on the presence or absence of transendothelial flow and its associated pressure gradient. In the case of this pressure gradient, mechanical reinforcement around the cell periphery by F-actin seems to be critical.     

Physiological factors affecting O2 transport by hemoglobin in an in vitro capillary system

O2 transport was examined by measuring the fractional saturation of concentrated hemoglobin solutions flowing through an artificial capillary that was approximately 27 micron in diameter and embedded in a silicone rubber film approximately 170 micron thick. The effects of pH, hemoglobin concentration, O2 tension, temperature, and organic phosphate were measured and analyzed quantitatively by a rigorous mathematical model that included the geometry of the capillary in the silicone film, parabolic flow velocity distributions inside the lumen, and cooperative O2 binding by hemoglobin. The rates of both oxygenation and deoxygenation were limited by diffusion and governed by the magnitude of the O2 gradient between the intracapillary fluid phase and the external gas space. In uptake experiments, O2 flux is determined primarily by the external O2 tension (16-160 mmHg in our experiments) because the internal O2 pressure is kept small due to chemical combination with hemoglobin. In release experiments, the external O2 tension is maintained at zero, and the transport rate is determined by the intracapillary partial pressure of O2 that is proportional to the O2 half-saturation pressure of hemoglobin value of the hemoglobin sample. As a result, factors that change the affinity of hemoglobin for O2, such as pH, temperature, and organic phosphate concentration, influence strongly the rate of O2 release but have little effect on the rate of O2 uptake. These properties are physiologically advantageous, since a decrease in pH or an increase in temperature during exercise increases both the rate and extent of deoxygenation while not altering the kinetics of oxygenation.     

Synchronization ability of coupled cell-cycle oscillators in changing environments

Background

The biochemical oscillator that controls periodic events during the Xenopus embryonic cell cycle is centered on the activity of CDKs, and the cell cycle is driven by a protein circuit that is centered on the cyclin-dependent protein kinase CDK1 and the anaphase-promoting complex (APC). Many studies have been conducted to confirm that the interactions in the cell cycle can produce oscillations and predict behaviors such as synchronization, but much less is known about how the various elaborations and collective behavior of the basic oscillators can affect the robustness of the system. Therefore, in this study, we investigate and model a multi-cell system of the Xenopus embryonic cell cycle oscillators that are coupled through a common complex protein, and then analyze their synchronization ability under four different external stimuli, including a constant input signal, a square-wave periodic signal, a sinusoidal signal and a noise signal.

Results

Through bifurcation analysis and numerical simulations, we obtain synchronization intervals of the sensitive parameters in the individual oscillator and the coupling parameters in the coupled oscillators. Then, we analyze the effects of these parameters on the synchronization period and amplitude, and find interesting phenomena, e.g., there are two synchronization intervals with activation coefficient in the Hill function of the activated CDK1 that activates the Plk1, and different synchronization intervals have distinct influences on the synchronization period and amplitude. To quantify the speediness and robustness of the synchronization, we use two quantities, the synchronization time and the robustness index, to evaluate the synchronization ability. More interestingly, we find that the coupled system has an optimal signal strength that maximizes the synchronization index under different external stimuli. Simulation results also show that the ability and robustness of the synchronization for the square-wave periodic signal of cyclin synthesis is strongest in comparison to the other three different signals.

Conclusions

These results suggest that the reaction process in which the activated cyclin-CDK1 activates the Plk1 has a very important influence on the synchronization ability of the coupled system, and the square-wave periodic signal of cyclin synthesis is more conducive to the synchronization and robustness of the coupled cell-cycle oscillators. Our study provides insight into the internal mechanisms of the cell cycle system and helps to generate hypotheses for further research.

     

Under what conditions signal transduction pathways are highly flexible in response to external forcing? A case study on calcium oscillations

Sensitivity and flexibility are typical properties of biological systems. These properties are here investigated in a model for simple and complex intracellular calcium oscillations. In particular, the influence of external periodic forcing is studied. The main point of the study is to compare responses of the system in a chaotic regime with those obtained in a regular periodic regime. We show that the response to external signals in terms of the range of synchronization is not significantly different in regular and chaotic Ca2+ oscillations. However, both types of oscillation are highly flexible in regimes with weak dissipation. Therefore, we conclude that dissipation of free energy is a suitable index characterizing flexibility. For biological systems this appears to be of special importance since for thermodynamic reasons, notably in view of low free energy consumption, dissipation should be minimized.     

Interaction of spiral and flat periodic autowaves in an active medium

Interaction between the rotating wave and a periodic external source in the model of Fitz Hugh--Nagumo type was computed. When the periods of the external source are longer than the rotation period of the spiral wave (T greater than Ts) the external source does not affect the spiral wave. At T less than Ts autowave synchronization effects are observed. The oscillation period predetermined by the external source is set in all the points of the medium except the neighbourhood of the spiral wave. The dislocation (wavebreak) persists in the medium drifting slowly at the angle to the wave vector of the flat waves. After the external source is eliminated, the spiral wave with the original period restores from this dislocation. When the dislocation reaches the interface, it disappears. In this case after the switching off of the external source the resting state is established. A theory of the drift is proposed which connects the drift velocity with the nucleus size and the rotation period of spiral wave.