Generalized dispersion in a synovial fluid of human joints

An unsteady convective diffusion in a synovial fluid of human joints modeled as a power-law fluid is studied using the generalized dispersion model of Gill and Sankara-subramanian [12]. The contributions of convection and diffusion, and pure convection on the dispersion of nutrient are investigated in detail. It is shown that the effect of decrease in non-Newtonian parameter is to decrease the dispersion coefficient. The mean concentration distribution appears to increase as the non-Newtonian parameter decreases upto a certain value of the axial distance. Beyond this point, however, the reverse pattern is observed.     

Equations of heat distribution within the body

A vector integral equation describing heat distribution within the body has been derived. The factors considered are heat conduction, forced convection via the circulatory system, environmental exchange, metabolic heat production, and change in heat content. The vector partial differential equation and alternative forms incorporating boundary conditions were also developed. A difference equation based on a first-order approximation to the fundamental equations was derived to form the basis of a model for heat distribution within the body. It has been shown that factors involving conduction and convection must be considered independently unless the temperature of the blood flowing from a region of the body is equal to the average temperature of the tissue in that region. If this relation between tissue and blood temperature does exist, only a single temperature from each eleeent is needed to describe the heat distribution. In this latter case, models which ascribe all heat transfer to “equivalent” conduction or to convection can give valid predictions.     

Effect of tissue and atmosphere's parameters on human eye temperature distribution

A three dimensional finite element method analysis was employed to investigate the effect of tissue and atmosphere parameters namely, ambient temperature, ambient convection coefficient, local blood temperature, and blood convection coefficient upon temperature distribution of human eyes. As a matter of simplification, only eye ball and skull bone are considered as the system of eye modeling. Decreasing the local blood temperature and keeping it cool is one of the most important ways to control bleeding during surgeries. By lower temperature of body organs such as the eye, the need for oxygenated blood is reduced, allowing for an extension in time for surgery. With this in mind, this study is done to see which one of parameters, such as ambient temperature, ambient convection coefficient, local blood temperature, and blood convection coefficient, has an effective role in decreasing the temperature of the eye. To this end, 3 different paths were employed to find out about the temperature distribution through the eye. The analysis of the three paths demonstrates the interaction of ambient and blood temperature in modeling temperature changes in specific locations of the eye. These data will be important in applications such as eye surgery, relaxation, and sleep therapy.     

Millimeter‐Wave Heating in In Vitro Studies: Effect of Convection in Continuous and Pulse‐Modulated Regimes

Shallow penetration of millimeter waves (MMW) and non‐uniform illumination in in vitro experiments result in a non‐uniform distribution of the specific absorption rate (SAR). These SAR gradients trigger convective currents in liquids affecting transient and steady‐state temperature distributions. We analyzed the effect of convection on temperature dynamics during MMW exposure in continuous‐wave (CW) and pulsed‐wave (PW) amplitude‐modulated regimes using micro‐thermocouples. Temperature rise kinetics are characterized by the occurrence of a temperature peak that shifts to shorter times as the SAR of the MMW exposure increases and precedes initiation of convection in bulk. Furthermore, we demonstrate that the liquid volume impacts convection. Increasing the volume results in earlier triggering of convection and in a greater cooling rate after the end of the exposure. In PW regimes, convection strongly depends on the pulse duration that affects the heat pulse amplitude and cooling rate. The latter results in a change of the average temperature in PW regime. Bioelectromagnetics. 2019;40:553–568. © 2019 Bioelectromagnetics Society.     

The role of convection in the standard fluid-mechanical model for morphogenesis

The effect of convection on reaction-diffusion instabilities in a visco-elastic medium is studied by using the standard continuum theory of a fluid mixture. The medium is assumed to be in local mechanical equilibrium, and convection is generated by pressure forces which arise if the equilibrium density of the medium changes with its composition. A linear stability analysis shows that reaction-diffusion instabilities proceeding from homogeneous steady states at rest are unmodified by induced convection to first order in concentration changes. We suggest that a non-linear analysis would show convection produces no new instabilities, as a linear analysis of inhomogeneous non-convecting stationary states shows that reaction-diffusion growth rates are reduced by convection at long wavelengths and are otherwise unchanged. For applications in embryology, numerical estimates suggest that convection can be ignored in reaction-diffusion mechanisms for pattern formation, and this conclusion is supported by a dimensional analysis.On leave from Department of Physics, Monash University, Clayton, Victoria 3168, Australia     

Heat transfer in perfused biological tissue—II. The “macroscopic” temperature distribution in tissue

In Part I, the general solution of the heat transport equation was given for a medium of constant thermal properties, containing a general convection fieldv(r,t). Starting from this general solution, an average or “macroscopic” temperature distribution is calculated in this paper, since in most physiological problems only an average or “macroscopic” temperature is accessible to the measurement. It is shown that the averaged temperature distribution is influenced alone by the order of the local symmetries of the convection field. These local symmetries can be deduced from anatomical data on the vascular architecture. In order to perform the averaging process, a detailed discussion, and an estimate of the correlation between the microscopic temperature variation and the convection field is carried out. Hereby, great emphasis is put on the experimental consequences of these results. As an illustrative example, the calculation of the macroscopic temperature distribution in a medium traversed by parallel capillaries is outlined.     

Ventilation distribution in rats: Part I - The effect of gas composition as measured with electrical impedance tomography

ABSTRACT: The measurement of ventilation distribution is currently performed using inhaled tracer gases for multiple breath inhalation studies or imaging techniques to quantify spatial gas distribution. Most tracer gases used for these studies have properties different from that of air. The effect of gas density on regional ventilation distribution has not been studied. This study aimed to measure the effect of gas density on regional ventilation distribution. METHODS: Ventilation distribution was measured in seven rats using electrical impedance tomography (EIT) in supine, prone, left and right lateral positions while being mechanically ventilated with either air, heliox (30% oxygen, 70% helium) or sulfur hexafluoride (20% SF6, 20% oxygen, 60% air). The effect of gas density on regional ventilation distribution was assessed. RESULTS: Gas density did not impact on regional ventilation distribution. The non-dependent lung was better ventilated in all four body positions. Gas density had no further impact on regional filling characteristics. The filling characteristics followed an anatomical pattern with the anterior and left lung showing a greater impedance change during the initial phase of the inspiration. CONCLUSION: It was shown that gas density did not impact on convection dependent ventilation distribution in rats measured with EIT.     

Ion transport and the vibrating probe.

The theory of ion transport in the vicinity of a vibrating probe is developed. It is shown that the convection loops produced by the probe will not affect the electrical current density, assuming that the action of the probe does not affect the sources of the current in the biological system. However, the convection loops will significantly alter the ion concentration gradients in the unstirred layer near a tissue or cell surface. The concentration gradients within each convection loop will be reduced, while the concentration gradients between the loops and outside of the loops will be increased relative to the gradients existing without the probe. As a consequence, the electrical potential gradients can be changed relative to the potential gradients existing in the absence of the convection caused by the probe. If the mobility of the ion species carrying the electrical current is greater than the average ion mobility in the medium, then a decrease in ion concentration gradient will be accompanied by an increase in electrical potential gradient, while an increase in concentration gradient will be accompanied by a decrease or even a reversal of electrical potential gradient. Thus, the electrical potential gradient measured by the probe will depend on the concentration gradient in the vicinity of the probe, which will depend in turn on the spatial relation of the convection loops to the probe. An example of the effect of the convection loops on ion concentration and electrical potential is obtained from the theory via a numerical computer calculation. Experimental tests of this theory are discussed.     

Computer-based analysis of steady-state and transient heat transfer of small-sized leaves by free and mixed convection

In order to study convective heat transfer of small leaves, the steady‐state and transient heat flux of small leaf‐shaped model structures (area of one side = 1730 mm²) were studied under zero and low (= 100 mm s^?1) wind velocities by using a computer simulation method. The results show that: (1) distinct temperature gradients of several degrees develop over the surface of the model objects during free and mixed convection; and (2) the shape of the objects and onset of low wind velocities has a considerable effect on the resulting temperature pattern and on the time constant τ. Small leaves can thus show a temperature distribution which is far from uniform under zero and low wind conditions. The approach leads, however, to higher leaf temperatures than would be attained by ‘real’ leaves under identical conditions, because heat transfer by transpiration is neglected. The results demonstrate the fundamental importance of a completely controlled environment when measuring heat dissipation by free convection. As slight air breezes alter the temperature of leaves significantly, the existence of purely free convection appears to be questionable in the case of outdoor conditions. Contrary to the prognoses yielded by standard approximations, no quantitative effect of buoyancy on heat transfer under the considered conditions could be detected for small‐sized leaf shapes.     

A theoretical model to study the effect of convection and leaky junctions on macromolecule transport in artery walls

A mathematical model is presented herein to determine the effect of convection on macromolecular transport across an artery wall due to transmural or osmotic pressure differences. The model is based on an extension of the leaky junction-cell turnover model of Weinbaum et al. (1985) to take into account a combined transport mechanism of convection and diffusion and also to provide the leaky junctions in the model with a finite resistance, thus allowing the results to be extended to intercellular clefts with a retarding extracellular matrix or to macromolecules whose dimensions are nearly the same as the junctional width. The results from this improved model show that the effect of pressure on transarterial macromolecular transport is important especially for cell turnover rates greater than 1% and that significant changes in the equilibrium balance of the cholesterol carrying LDL molecules in the arterial wall can occur due to a very small fraction of leaky junctions. At very high turnover rates (large fraction of leaky junctions) the effect of convection on macromolecular transport becomes dramatic and explains the very large increases in uptake observed experimentally after artificially inducing extensive endothelial damage.     

Some factors affecting oxygen uptake by red blood cells in the pulmonary capillaries

In this study we investigate the equations governing the transport of oxygen in pulmonary capillaries. We use a mathematical model consisting of a red blood cell completely surrounded by plasma within a cylindrical pulmonary capillary. This model takes account of convection and diffusion of oxygen through plasma, diffusion of oxygen through the red blood cell, and the reaction between oxygen and haemoglobin molecules. The velocity field within the plasma is calculated by solving the slow flow equations. We investigate the effect on the solution of the governing equations of: (i) mixed-venous blood oxygen partial pressure (the initial conditions); (ii) alveolar gas oxygen partial pressure (the boundary conditions); (iii) neglecting the convection term; and (iv) assuming an instantaneous reaction between the oxygen and haemoglobin molecules. It is found that: (a) equilibrium is reached much more rapidly for high values of mixed-venous blood and alveolar gas oxygen partial pressure; (b) the convection term has a negligible effect on the time taken to reach a prescribed degree of equilibrium; and (c) an instantaneous reaction may be assumed. Explanations are given for each of these results.     

Estimation of hematocrit profile symmetry recovery length downstream from a bifurcation

Downstream from a microvascular bifurcation the distribution of blood cells in the vessel lumen is not symmetric. A diffusion process is used to model the rearrangement of red cells as blood flows between junctions in the microcirculation. A Fourier series approach is used to solve the model diffusion convection equation in slit geometry. Both flat and parabolic velocity profiles are considered. The eigenvalues, found using the Rayleigh-Ritz method, are used to find an upper bound on distance required for a symmetric red cell distribution to be obtained. The method has also been applied to cylindrical geometry and the computed symmetry recovery lengths are compared to distances between bifurcations measured in vivo. These estimates indicate that red cell distributions are frequently asymmetric in the microcirculation. Such asymmetries can have a strong effect on plasma skimming and material balance calculations.     

On the subnormal variance in the counts of randomly distributed particles: I. Approximate treatment of the three-dimensional case and discussion of experiments

The question is raised concerning the possible causes of abnormally small standard deviations found in counting samples in which particles are distributed at random (e.g., blood cells, fat globules in milk, etc.). The effect of discarding abnormal samples is discounted inasmuch as small standard deviations occur even when all samples are counted. An approximation method is used to calculate the effect of finite particle size, of known repulsive forces between particles and of convection currents. This calculation shows that neither finite size nor the known repulsive forces are sufficient to account for the observed abnormality of standard deviation, but that convection currents can possibly account for it. The possible presence of long-range repulsive forces cannot, however, be excluded. The main part of this work was done in the Committee on Mathematical Biology at the University of Chicago and originated with a suggestion by Dr. A. Rapoport.     

Thermal convection over East Antarctica: Potential microorganism dispersal

The Indian Antarctic station, Maitri is in the Schirmacher oasis of east Antarctica. The oasisis covered with snow/ice; except for the local summer season when it gets deglaciated and exposes the small hilly region. During summer, minute microorganisms are observed near water bodies of this rocky terrain. In the year 1996a monostatic acoustic sounder probed planetary boundary layer dynamics over this region. From the data it is observed that the thermal convection (both free and forced) persist for 5.63% of the time in the whole year. The occurrence of free convection predominates in the local summer season around midday, while sporadic cases of forced convection have been recorded during the autumn and winter seasons. The onset of convection is mainly at 0600 hrs to 1200 hrs, while the cessation period is limited within 1400 hrs to 1900 hrs. The cessation of convection is basically governed by the katabatic wind flow around the Schirmacher region and it indicates that the interior of Antarctica or the polar cap ice becomes cooler much faster than the rocky region of Schirmacher oasis.Examples taken from the literatures on atmospheric structure and their effects on dispersal of microorganisms and their distribution by the wind are discussed. The study of monostatic acoustic sounder for thermal convections/plumes may form input for the study of dispersal, survival, metabolicactivities and dispersion model of microorganisms. The application of convection/plume to aerobiology can also lead to improvements in forecasting, monitoring and understanding the various mechanisms of organism dispersal.     

Residence time distribution in the chromatographic column: Applications in the separation engineering of DNA

Experimental and theoretical works were performed for the separation of large polyelectrolyte, such as DNA, in a column packed with gel particles under the influence of an electric field. Since DNA quickly orient in the field direction through the pores, this paper presents how intraparticle convection affects the residence time distribution of DNAs in the column. The concept is further illustrated with examples from solid-liquid systems, for example, from chromatography showing how the column efficiency is improved by the use of an electric field. Dimensionless transient mass balance equations were derived, taking into consideration both diffusion and electrophoretic convection. The separation criteria are theoretically studied using two different Peclet numbers in the fluid and solid phases. These criteria were experimentally verified using two different DNAs via electrophoretic mobility measurements, which showed how the separation position of the DNAs varies in the column in relation to the Peg/Pef values of an individual DNA. The residence time distribution was solved by an operator theory and the characteristic method to yield the column response.     

The Onset of Double Diffusive Convection in a Viscoelastic Fluid-Saturated Porous Layer with Non-Equilibrium Model

The onset of double diffusive convection in a viscoelastic fluid-saturated porous layer is studied when the fluid and solid phase are not in local thermal equilibrium. The modified Darcy model is used for the momentum equation and a two-field model is used for energy equation each representing the fluid and solid phases separately. The effect of thermal non-equilibrium on the onset of double diffusive convection is discussed. The critical Rayleigh number and the corresponding wave number for the exchange of stability and over-stability are obtained, and the onset criterion for stationary and oscillatory convection is derived analytically and discussed numerically.     

Buoyancy effect on forced convection in the leaf boundary layer

Abstract. Mixed convection (forced convection plus free convection) in the leaf boundary layer was examined by air flow visualization and by evaluation of the boundary layer conductance at different leaf-air temperature differences ( T _L- T _A) under low wind velocities. The visualized air flow was found to become more unstable and buoyant at higher T _L- T _A. An ascending longitudinal plume was induced along the upper surface, and the air flow along the lower surface ascended after passing the trailing leaf edge. The air flow modified by buoyancy was considered to result in an increase in boundary layer conductance ( G _A) for mixed convection, which became higher with higher T _L- T _A as compared with the conductance for pure forced convection without buoyancy. This increase in G _A appeared larger at larger Grashof number (Gr) and at smaller Reynolds number (Re). The dependences of buoyancy effect on Gr and Re were related to 'edge-effects'.     

Nutrients of the Saronikos Gulf in relation to environmental characteristics (1973–1976)

The nutrient distribution in relation to environmental characteristics of the Saronikos Gulf was studied at two stations for the period 1973–1976. The distribution of measured values and their spatiotemporal variations were compared with previous data for the same area. Winter convection resulted in a very weak gradient of temperature, salinity, oxygen and nutrients. Stratification started to develop in May and persisted. for about six months. Little seasonal variation of nutrients appeared to occur, with higher values generally in winter. It was found that the station in the vicinity of the outfall contained more phosphate and ammonia than the station in the source water. Their levels of nutrients were similar in both years, except in the case of phosphate and nitrite, which were double at the station near the outfall in 1975. Of the nutrients controlling productivity in the photic layer of the examined stations in the Saronikos Gulf, phosphate had a stronger limiting effect on plant growth than inorganic nitrogen.     

Simulation of gentamicin delivery for the local treatment of osteomyelitis

In order to understand the effect of antibiotics delivery to bone tissue, by biodegradable polymeric drug disc, for the treatment of osteomyelitis, a three-dimensional simulation model is developed. The simulation investigates the effect of pressure-induced convection on drug distribution, by taking into account the pressure gradient that exists between capillaries and interstitial space, and also as a result of the surgical opening. The clotting process at the surgical opening is incorporated into the simulation, and the effect of clotting duration is investigated. The clotting duration for the baseline simulation is 2 days and it is observed that increasing this duration depresses the mean drug concentration in the marrow and cortical bone. The effect of double burst release profile is also studied and it is observed that drug concentration drops too rapidly after the first burst to provide any therapeutic effect. However, it is shown that the drug concentration after the second burst stays above the minimum inhibitory concentration of the bacteria for a longer period of time, than would have been observed for a mono-burst release. Inserting non-biodegradable polymethylmethacrylate (PMMA) beads into bone seems to cause a higher average concentration of drug in the marrow. However, this could be brought about by the difference in the geometry between the disc and the bead, and the amount of drug packed in each bead. Further simulations on the management of dead space shows the ineffectiveness of having the void filled up with surgical gel as it becomes an additional barrier to drug delivery to the infected tissues.     

Intratumour factors influencing the access of antibody to tumour cells

Summary The histological structure and biochemical composition of human tumours is very varied, as is the structure of the microvascular network. It can be expected, therefore, that the extravasation, diffusion and convection of macromolecules will vary between tumours — and also between areas in the same tumour. The major factors influencing the intratumour distribution of injected antibody are reviewed and an attempt made to identify the tumour types in which therapeutic antibody, with or without a cytotoxin, will distribute most effectively.