Measurement of local mass transfer coefficients in a cast model of the human upper respiratory tract

Local mass transfer coefficients measured using the naphthalene sublimation technique in an acrylic cast model of the human upper respiratory tract are reported as the Sherwood numbers for the corresponding regions. A steady air flow rate of 12 L per min was used for all measurements. Values of the Sherwood number are seen to be highest in the nasal cavity and proximal nasopharynx while a minimum value occurs just downstream from the larynx. Local values of the Nusselt number obtained in the trachea and proximal nasal cavity assuming a complete heat and mass transfer analogy agree well with in-vivo physiological measurements. The mass transfer coefficients found can be incorporated into an analytical model of respiratory heat and water vapor transfer or into a model of pollutant gas uptake in the respiratory tract.     

Mathematical modeling of heat and water transport in human respiratory tract

Excessive heat and water losses from the airways are stimuli to asthma. To study heat and water vapor transport in the human respiratory tract, a time-dependent model, based on a single differential equation with an analytical solution, was developed that could predict the intra-airway temperatures and water vapor contents. The key feature is the dependence of the temperature and water vapor along the respiratory tract as a function of the air residence time at each location. The model assumes disturbed laminar flow leading to enhanced transport mechanisms and wall temperature profiles modeled according to experimental data (E. R. McFadden, Jr., B. M. Pichurko, H. F. Bowman, E. Ingenito, S. Burns, N. Dowling, and J. Soloway. J. Appl. Physiol. 58: 564-570, 1985). It predicts that 1) the air equilibrates with the wall before it reaches body conditions (37 degrees C, 99.5% relative humidity); 2) conditioning of the inspired air involves several generations, with the number depending on the respiratory conditions; and 3) the walls of the upper airways are unsaturated, although it is difficult to judge at this state the depth of the respiratory tract affected.     

Model simulation of heat and water transport dynamics in an airway

Heat and water transport processes in the respiratory tract depend on environmental conditions, breathing patterns, and the physiological state of the respiratory system. To study these processes, we have developed a mathematical model of the dynamics of temperature and water vapor in the radial and axial directions of an idealized trachea. The model is expressed as two implicit finite-difference equations and solved using an alternating-direction algorithm. Using these equations, we simulated the effects of inspired gas temperature and humidity, velocity profile, and flow rate on heat and water transport between the gas and airway wall. Under inspired gas conditions of low temperature or high relative humidity, supersaturation occurs. Increasing either the velocity gradient at the wall or the flow rate increases the heat and water transport rates. However, these rates change by only 10 percent when the velocity gradient is doubled, and by about 35 percent when flow rate undergoes a two-fold change. The model can be used with in-vivo data from the trachea to test hypotheses concerning normal and abnormal heat and water transport.     

Simulation of a steady-state mass-heat exchange in the respiratory tract

On the basis of Weibel respiratory tract model the mathematical model of mass and heat transfer in the lungs was solved for steady-state one-dimensional case. Coefficients of mass and heat transfer were taken from empirical expressions for canals. The model shows that independent water vapour or air heat saturation in the lungs occurs in 12-14 generations of the bronchial tree. The saturation site depends upon volume velocity of the air and functioning of the upper respiratory tract.     

A Model of Respiratory Heat Transfer in a Small Mammal

A steady-state model of the heat and water transfer occurring in the upper respiratory tract of the kangaroo rat, Dipodomys spectabilis, is developed and tested. The model is described by a steady-state energy balance equation in which the rate of energy transfer from a liquid stream (representing the flow of heat and blood from the body core to the nasal region) is equated with the rate of energy transfer by thermal conduction from the nose tip to the environment. All of the variables in the equation except the flow rate of the liquid stream can be either measured directly or estimated from physiological measurements, permitting the solution of the equation for the liquid stream flow rate. After solving for the liquid stream flow rate by using data from three animals, the energy balance equation is used to compute values of energy transfer, expired air temperature, rates of water loss, and efficiency of vapor recovery for a variety of ambient conditions. These computed values are compared with values measured or estimated from physiological measurements on the same three animals, and the equation is thus shown to be internally consistent. To evaluate the model's predictive value, calculated expired air temperatures are compared with measured expired air temperatures of eight additional animals. Finally, the model is used to examine the general dependence of expired air temperature, of rates of water loss, and of efficiency of vapor recovery on ambient conditions.     

A mathematical model of the dynamic heat transfer from the respiratory tract of a chicken

A mathematical model of the dynamic (periodic) heat exchange from the respiratory tract of a chicken is postulated and solved analytically. The model expresses the periodic respiratory heat loss as a function of respiration rate, respiratory air velocity, ambient temperature and humidity ratio, and body (trachea) temperature. It is unique in that previous models have been formulated for steady state heat transfer. The processes of sensible and latent heat exchange are considered as uncoupled processes.     

Heat and water rate transfer processes in the human respiratory tract at various altitudes

The process of the respiratory air conditioning as a process of heat and mass exchange at the interface inspired air-airways surface was studied. Using a model of airways (Olson et al., 1970) where the segments of the respiratory tract are like cylinders with a fixed length and diameter, the corresponding heat transfer equations, in the paper are founded basic rate exchange parameters-convective heat transfer coefficient h(c)(W m(-2) degrees C(-1)) and evaporative heat transfer coefficient h(e)(W m(-2)hPa(-1)). The rate transfer parameters assumed as sources with known heat power are connected to airflow rate in different airways segments. Relationships expressing warming rate of inspired air due to convection, warming rate of inspired air due to evaporation, water diffused in the inspired air from the airways wall, i.e. a system of air conditioning parameters, was composed. The altitude dynamics of the relations is studied. Every rate conditioning parameter is an increasing function of altitude. The process of diffusion in the peripheral bronchial generations as a basic transfer process is analysed. The following phenomenon is in effect: the diffusion coefficient increases with altitude and causes a compensation of simultaneous decreasing of O(2)and CO(2)densities in atmospheric air. Due to this compensation, the diffusion in the peripheral generations with altitude is approximately constant. The elements of the human anatomy optimality as well as the established dynamics are discussed and assumed. The square form of the airways after the trachea expressed in terms of transfer supposes (in view of maximum contact surface), that a maximum heat and water exchange is achieved, i.e. high degree of air condition at fixed environmental parameters and respiration regime.     

Analysis of a self-propelling sheet with heat transfer through non-isothermal fluid in an inclined human cervical canal

The present theoretical analysis deals with biomechanics of the self-propulsion of a swimming sheet with heat transfer through non-isothermal fluid filling an inclined human cervical canal. Partial differential equations arising from the mathematical modeling of the proposed model are solved analytically. Flow variables like pressure gradient, propulsive velocity, fluid velocity, time mean flow rate, fluid temperature, and heat-transfer coefficients are analyzed for the pertinent parameters. Striking features of the pumping characteristics are explored. Propulsive velocity of the swimming sheet becomes faster for lower Froude number, higher Reynolds number, and for a vertical channel. Temperature and peak value of the heat-transfer coefficients below the swimming sheet showed an increase by the increment of Brinkmann number, inclination, pressure difference over wavelength, and Reynolds number whereas these quantities decrease with increasing Froude number. Aforesaid parameters have shown opposite effects on the peak value of the heat-transfer coefficients below and above the swimming sheet. Relevance of the current results to the spermatozoa transport with heat transfer through non-isothermal cervical mucus filling an inclined human cervical canal is also explored.     

Water permeability of plant cuticles: permeance,diffusion and partition coefficients

Summary Using isolated cuticular membranes from ten woody and herbaceous plant species, permeance and diffusion coefficients for water were measured, and partition coefficients were calculated. The cuticular membranes of fruit had much higher permeance and diffusion coefficients than leaf cuticular membranes from either trees or herbs. Both diffusion and partition coefficients increased with increasing membrane thickness. Thin cuticles, therefore, tend to be better and more efficient water barriers than thick cuticles. We compared the diffusion coefficients and the water content of cuticles as calculated from transport measurements with those obtained from water vapor sorption. There is good to fair agreement for cuticular membranes with a low water content, but large discrepancies appear for polymer matrix membranes with high permeance. This is probably due to the fact that diffusion coefficients obtained from transport measurements on membranes with high permeance and water content are underestimated. Water permeabilities of polyethylene and polypropylene membranes are similar to those of leaf cuticular membranes. However, leaf cuticles have much lower diffusion coefficients and a much greater water content than these synthetic polymers. This suggests that cuticles are primarily mobility barriers as far as water transport is concerned.     

Use of a heat transfer analogy for a mathematical model of respiratory tract deposition

Mathematical models predicting the aerosol deposition in the respiratory tract are reviewed. Data in the literature indicated not only that the air flow in the trachea and major bronchi may not be laminar, but also that the entrance effect of the tube or airway has not been considered. A new approach to a mathematical model of respiratory tract deposition, based on the analogy of the heat and mass transfer, is discussed.     

Thermal history of reef-associated environments during a record cold-air outbreak event

Summary Several polar continental air masses intruding into the south Florida/northern Bahama Bank region during January 1981 caused record low air temperatures and rapid chilling of extensive shallow-water carbonate systems. Numerous coral kills along the Florida reef tract and massive fish mortalities in Florida Bay were attributable to unusually cold waters generated at this time. Thermal evolution of Florida Bay/Florida reef tract and northern Bahama Bank waters from 8 to 21 January was assessed from thermal infrared data acquired by the NOAA-6 environmental satellite, in situ water temperatures, local meteorological data, and a computerized heat flux model. Field observations and laboratory experiments identify 16°C as a thermal stress threshold for most reef corals (Mayor 1915; Davis 1981). Temperaturecorrected digital satellite data indicated that water temperatures below 16°C were generated in Florida Bay and on Little and Great Bahama Banks during a 10-day period in January. Lowest temperatures on the Florida reef tract resulted from offshelf transport of Florida Bay water through major tidal channels. Offshelf movement of bay water is driven primarily by strong northerly winds, density gradients, and tidal pumping. Absence of reef development opposite major tidal passes along the Florida reef tract (Ginsburg and Shinn 1964) and aperiodic coral kills along bank margins can be attributed to this process, which has probably had a limiting influence on Holocene reef development in these areas.     

Absorbed fractions for electrons and beta particles in sensitive regions of human respiratory tract

The absorbed fractions (AF) of electrons in sensitive layers of human respiratory tract were calculated in this paper. For that purpose the source code for simulation package PENELOPE, based on Monte Carlo method, was developed. The human respiratory tract was modeled according to ICRP66 publication, where AF of electrons was calculated using EGS4 simulation software. Some approximations used in ICRP66 were corrected in this work, and new values of AF for radon progeny are given. Minimal energy (EABS) that electron can have during transport through material is 1 keV in ICRP66, while it is set as low as 100 eV in the presented work. Lowering value of EABS gives more accurate results for AF when initial energy of electrons is below 50 keV. To represent tissue, water is used in ICRP66, while in this work epithelia tissue is used.     

The Effect of Thermophoresis on Unsteady Oldroyd-B Nanofluid Flow over Stretching Surface

There are currently only a few theoretical studies on convective heat transfer in polymer nanocomposites. In this paper, the unsteady incompressible flow of a polymer nanocomposite represented by an Oldroyd-B nanofluid along a stretching sheet is investigated. Recent studies have assumed that the nanoparticle fraction can be actively controlled on the boundary, similar to the temperature. However, in practice, such control presents significant challenges and in this study the nanoparticle flux at the boundary surface is assumed to be zero. We have used a relatively novel numerical scheme; the spectral relaxation method to solve the momentum, heat and mass transport equations. The accuracy of the solutions has been determined by benchmarking the results against the quasilinearisation method. We have conducted a parametric study to determine the influence of the fluid parameters on the heat and mass transfer coefficients.     

Heat transfer modeling of the tongue

The heat transfer mechanism of tongue was investigated on the basis of experimental and theoretical research. Firstly, the relationship between tongue temperature and blood perfusion was obtained from animal experiment that mainly carried out on porcine tongue, subordinate on human tongue. Secondly, a one-dimensional variable coefficients second-order inhomogeneous heat transfer equation is developed by simplifying tongue as fin cube and the analytical solution is got. The results show that the change regulations of temperature by blood perfusion rate are the same in human and porcine tongue, and also, there is a good agreement between calculation and experimental results. When checking the model with corresponding properties of human tongue, the result is also satisfied. In conclusion, predicting temperature distribution of tongue is feasible with the fin cube model.     

Linking influenza virus tissue tropism to population-level reproductive fitness

Influenza virus tissue tropism defines the host cells and tissues that support viral replication and contributes to determining which regions of the respiratory tract are infected in humans. The location of influenza virus infection along the respiratory tract is a key determinant of virus pathogenicity and transmissibility, which are at the basis of influenza burdens in the human population. As the pathogenicity and transmissibility of influenza virus ultimately determine its reproductive fitness at the population level, strong selective pressures will shape influenza virus tissue tropisms that maximize fitness. At present, the relationships between influenza virus tissue tropism within hosts and reproductive fitness at the population level are poorly understood. The selective pressures and constraints that shape tissue tropism and thereby influence the location of influenza virus infection along the respiratory tract are not well characterized. We use mathematical models that link within-host infection dynamics in a spatially-structured human respiratory tract to between-host transmission dynamics, with the aim of characterizing the possible selective pressures on influenza virus tissue tropism. The results indicate that spatial heterogeneities in virus clearance, virus pathogenicity or both, resulting from the unique structure of the respiratory tract, may drive optimal receptor binding affinity-that maximizes influenza virus reproductive fitness at the population level-towards sialic acids with α2,6 linkage to galactose. The expanding cell pool deeper down the respiratory tract, in association with lower clearance rates, may result in optimal infectivity rates-that likewise maximize influenza virus reproductive fitness at the population level-to exhibit a decreasing trend towards deeper regions of the respiratory tract. Lastly, pre-existing immunity may drive influenza virus tissue tropism towards upper regions of the respiratory tract. The proposed framework provides a new template for the cross-scale study of influenza virus evolutionary and epidemiological dynamics in humans.     

Evaporative losses of water by birds

1. Birds lose water in evaporation from the respiratory tract and, in many species, through the skin. Anatomical arrangements in the nasal passages to conservation of water and hear from the expired air in the absence of heat loads. However, most species still expend more water in evaporation than they produce in metabolism when either quiescent or vigorously active. Certain small birds, several of them associated with arid environments, represent exceptions to this and their more favorable situation appears in part to reflect as an ability to curtail cutaneous water loss. 2. Birds typically resort to panting in dealing with substantial heat loads developing in hot environments or accumulated over bouts of activity. In a number of species this form of evaporative cooling is supplemented by gular fluttering. 3. The ubiquitousness of active heat defense appears to reflect more the importance for birds of dealing with heat loads existing following flight or sustained running than any universal affinity for hot climates. Panting can be sustained for hours, despite progressive dehydration and, in some instances, hypocapnia and respiratory alkalosis. The prominent involvement of thermoreceptors in the spinal cord in its initiation is of considerable interest.     

Nitroxide radicals. Controlled release from and transport through biomimetic and hollow fibre membranes

Stable nitroxide radicals have found wide applications in chemistry and biology and they have some potential applications in medicine due to their antioxidant properties. Nitrocellulose filters impregnated with lipid-like substances are used as an imitation of biomembranes and could be used as a controlled drug release vehicle, while experiments with hollow fibres can be useful in the modelling of a drug delivery via blood vessels. This paper describes mechanisms of the nitroxide transport in four different model systems, i.e. a) exit of nitroxide into aqueous solution from porous nitrocellulose filters, impregnated with organic solvents, b) transport of nitroxides through the impregnated membrane from one into another aqueous solution, c) transport of nitroxides from bulk phase of organic solvents through the impregnated membrane into aqueous phase with ascorbic acid, and d) transport of nitroxides from liquid organic phase into aqueous solution through porous hollow fibres. The results are analysed in terms of mass transfer resistance of a membrane, organic and aqueous phase, based on nitroxide diffusion and distribution coefficients. Ascorbic acid reduced nitroxides in water and enhanced the rate of their transfer due to the decrease of transport resistance of unstirred aqueous layers. It is demonstrated that in the case of biomembranes the rate limiting step could be the transport through unstirred aqueous layers and membrane/water interface.     

Nitroxide radicals. Controlled release from and transport through biomimetic and hollow fibre membranes

Stable nitroxide radicals have found wide applications in chemistry and biology and they have some potential applications in medicine due to their antioxidant properties. Nitrocellulose filters impregnated with lipid-like substances are used as an imitation of biomembranes and could be used as a controlled drug release vehicle, while experiments with hollow fibres can be useful in the modelling of a drug delivery via blood vessels. This paper describes mechanisms of the nitroxide transport in four different model systems, i.e. a) exit of nitroxide into aqueous solution from porous nitrocellulose filters, impregnated with organic solvents, b) transport of nitroxides through the impregnated membrane from one into another aqueous solution, c) transport of nitroxides from bulk phase of organic solvents through the impregnated membrane into aqueous phase with ascorbic acid, and d) transport of nitroxides from liquid organic phase into aqueous solution through porous hollow fibres. The results are analysed in terms of mass transfer resistance of a membrane, organic and aqueous phase, based on nitroxide diffusion and distribution coefficients. Ascorbic acid reduced nitroxides in water and enhanced the rate of their transfer due to the decrease of transport resistance of unstirred aqueous layers. It is demonstrated that in the case of biomembranes the rate limiting step could be the transport through unstirred aqueous layers and membrane/water interface.     

Comments on “Modified wind chill temperatures determined by a whole body thermoregulation model and human-based convective coefficients” by Ben Shabat,Shitzer and Fiala (2013) and “Facial convective heat exchange coefficients in cold and windy environments estimated from human experiments” by Ben Shabat and Shitzer (2012)

Ben Shabat et al. (Int J Biometeorol 56(4):639-51, 2013) present revised charts for wind chill equivalent temperatures (WCET) and facial skin temperatures (FST) that differ significantly from currently accepted charts. They credit these differences to their more sophisticated calculation model and to the human-based equation that it used for finding the convective heat transfer coefficient (Ben Shabat and Shitzer, Int J Biometeorol 56:639-651, 2012). Because a version of the simple model that was used to create the current charts accurately reproduces their results when it uses the human-based equation, the differences that they found must be entirely due to this equation. In deriving it, Ben Shabat and Shitzer assumed that all of the heat transfer from the surface of their cylindrical model was due to forced convection alone. Because several modes of heat transfer were occurring in the human experiments they were attempting to simulate, notably radiation, their coefficients are actually total external heat transfer coefficients, not purely convective ones, as the calculation models assume. Data from the one human experiment that used heat flux sensors supports this conclusion and exposes the hazard of using a numerical model with several adjustable parameters that cannot be measured. Because the human-based equation is faulty, the values in the proposed charts are not correct. The equation that Ben Shabat et al. (Int J Biometeorol 56(4):639-51, 2013) propose to calculate WCET should not be used.