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.     

A mathematical model of electron transfer within the mitochondrial respiratory cytochromes

A simple mathematical model of electron flow along the mitochondrial respiratory cytochrome assembly and the transfer of electrons to molecular oxygen is presented. First, an expression for the current-voltage relationship for a biological oxygen electrode is derived, and from this the relationship between oxygen consumption rate and oxygen partial pressure is determined. An independent relationship between mitochondrial oxygen partial pressure and oxygen supply rate is then derived. By eliminating oxygen partial pressure from these two expressions, we may obtain a relationship between oxygen supply rate and oxygen consumption rate. This model is then used to investigate the effects of tissue dysoxia, uncoupling of oxidative phosphorylation, increased cellular diffusional resistance and inhomogeneities in oxygen supply on oxygen consumption. It is concluded that each of the above contribute in varying degrees to the phenomenon of "pathological oxygen supply dependency".     

A dynamic mathematical model of the chemostat

A number of experimental studies on the dynamic, behavior of the chemostat have shown that the specific growth rate does not, instantaneously adjust to changes in the concentration of limiting substrate in the chemostat following disturbances in the steady state input limiting substrate concentration or in the steady state dilution rate. Instead of an instantaneous response, as would be predicted by the Monod equation, experimental studies have shown that the specific growth rate experiences a dynamic lag in responding to the changes in the concentration of limiting substrate in the culture vessel. The observed dynamic lag has been recognized by researchers in such terms as an inertial phenomenon and as a hysteresis effect, but as yet a systems engineering approach has not been applied to the observed data. The present paper criticizes the use of the Monod equation as a dynamic relationship and offers as an alternative a dynamic equation relating specific growth rate to the limiting substrate concentration in the chemostat. Following the development of equations, experimental methods of evaluating parameters are discussed. Dynamic responses of analog simulations (incorporating the newly derived equations) are compared with the dynamic responses predicted by the Monod equation and with the dynamic responses of experimental chemostats.     

A theoretical model of localized heat and water vapor transport in the human respiratory tract

A steady-state, one-dimensional theoretical model of human respiratory heat and water vapor transport is developed. Local mass transfer coefficients measured in a cast replica of the upper respiratory tract are incorporated into the model along with heat transfer coefficients determined from the Chilton-Colburn analogy and from data in the literature. The model agrees well with reported experimental measurements and predicts that the two most important parameters of the human air-conditioning process are: the blood temperature distribution along the airway walls, and the total cross-sectional area and perimeter of the nasal cavity. The model also shows that the larynx and pharynx can actually gain water over a respiratory cycle and are the regions of the respiratory tract most subject to drying. With slight modification, the model can be used to investigate respiratory heat and water vapor transport in high stress environments, pollutant gas uptake in the respiratory tract, and the connection between respiratory air-conditioning and the function of the mucociliary escalator.     

A dynamic mathematical model for microbial removal of pyritic sulfur from coal

A dynamic mathematical model has been developed to describe microbial desulfurization of coal by Thiobacillus ferrooxidans. The model considers adsorption and desorption of cells on coal particles and microbial oxidation of pyritic sulfur on particle surfaces. The influence of certain parameters, such as microbial growth rate constants, adsorption-descrption constants, pulp density, coal particle size, initial cell and solid phase substrate concentration on the maximum rate of pyritic sulfur removal, have been elucidated. The maximum rate of pyritic sulfur removal was strongly dependent upon the number of attached cells per coal particle. At sufficiently high initial cell concentrations, the surfaces of coal particles are nearly saturated by the cells and the maximum leaching rate is limited either by total external surface area of coal particles or by the concentration of pyritic sulfur in the coal phase. The maximum volumetric rate of pyritic sulfur removal (mg S/h cm(3) mixture) increases with the pulp density of coal and reaches a saturation level at high pulp densities (e.g. 45%). The maximum rate also increases with decreasing particle diameter in a hyperbolic form. Increases in adsorption coefficient or decreases in the desorption coefficient also result in considerable improvements in this rate. The model can be applied to other systems consisting of suspended solid substrate particles in liquid medium with microbial oxidation occurring on the particle surfaces (e.g., bacterial ore leaching). The results obtained from this model are in good agreement with published experimental data on microbial desulfurization of coal and bacterial ore leaching.     

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.     

A mathematical model to describe the dynamic response of a spruce tree to the wind

 A mathematical, computer-based, dynamic sway model of a Sitka spruce (Picea sitchensis) tree was developed and tested against measurements of the movement of a tree within a forest. The model tree was divided into segments each with a stiffness, mass and damping parameter. Equations were formulated to describe the response of every segment which together form a system of coupled differential equations. These were solved with the aid of matrices and from the resulting modes, the transfer function of the tree was found and used to calculate the movement of the tree in the wind. Comparison of the modelled movement of a tree in response to the measured wind speed above a forest canopy gave good agreement with the measured movement of the top of the tree but less satisfactory agreement close to the base. The comparison also pointed to the complexity of tree response to the wind and inadequacies in the model. In particular, the branches need to be treated as coupled cantilevers attached to the stem rather than simply as masses lumped together. Received: 18 February 1997 / Accepted: 16 December 1997     

A mathematical model for the aerobic growth of Saccharomyces cerevisiae with a saturated respiratory capacity

A mathematical model for the aerobic growth of Saccharomyces cerevisiae in both batch and continuous culture is described. It was based on the experimental observation that the respiratory capacity of organism may become saturated and exhibit a maximum specific oxygen uptake rate after suitable adaptation. This experimental observation led to the possibility that transport into and out of the mitochondrion was of major importance in the overall metabolism of S. cerevisiae and was subject to long-term adaptation. Consistent with this observation a distributed model was proposed which. as its basis, assumed the control of repression or inhibition of the uptake rates of other substrates. No other regulation of fermentation and respiration was assumed. The model provided a suitable structure allowing precise quantification of the changes in rate and stoichiometry of energy production. The model clearly indicated that growth under the wide range of experimental conditions reported could not be predicted using constant values for the maximum specific respiratory rate of constant values of Y_ATP (g biomass/mol ATP) and PO ratio of (mol ATP/atom oxygen). The causes of the variation in the respiratory rate were not determined and it was concluded that a more detailed analysis (reported subsequently) was required. The variation of Y_ATP and PO ratio with specific growth rate implied that the efficiency of ATP generation or ATP utilization decreased with increasing specific growth rate. It was concluded that it was not possible to quantify the individual effect of Y_ATP and PO ratio until independent means for their reliable estimation is available.     

Isolation and characterization of protease producing bacteria from upper respiratory tract of wild chicken

Bacterial samples isolated from the upper respiratory tract of a healthy broiler chicken and a wild chicken suffering from influenza which were collected locally revealed proteolytic activity as detected by sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) and zymogram analysis. Among five protease producing strains screened, one was selected as promising protease producer. The activity of the protease produced by this organism is stable up to 620C. Optimum yield was achieved after 19 hours of culture, at pH 9.0 and 450C. The desired protein was precipitated from the crude extract by using ammonium sulfate (60%) followed by dialysis and purified by Ion-exchange chromatography. Further investigations are needed to know about the structure elucidation of the purified protein for industrial exploitation.     

Finite difference analysis of respiratory heat transfer

A numerical computer model of heat and water transfer within the tracheobronchial tree of humans was developed based on an integral formulation of the first law of thermodynamics. Simulation results were compared with directly measured intraluminal airway temperature profiles previously obtained in normal human subjects, and a good correlation was demonstrated. The model was used to study aspects of regional pulmonary heat transfer and to predict the outcomes of experiments not yet performed. The results of these simulations show that a decrease in inspired air temperature and water content at fixed minute ventilation produces a proportionately larger increase in heat loss from extrathoracic airways relative to intrathoracic, whereas an increase in minute ventilation at fixed inspired air conditions produces the opposite pattern, with cold dry air penetrating further into the lung, and that changes in breathing pattern (tidal volume and frequency) at fixed minute ventilation and fixed inspiratory-to-expiratory (I/E) ratio do not affect local air temperature profiles and heat loss, whereas changes in I/E ratio at fixed minute ventilation do cause a significant change.     

Exploring transgene transfer from the transgenic chicken model to its offspring through a nonviral vector

There is much interest in using chickens as “bioreactors” to produce large quantities of biopharmaceuticals. However, transient expression of foreign genes have been known to cause low efficiency of obtaining transgenic offspring, especially when using nonviral vectors. In present study, a transgenic chicken model was investigated to determine whether an exogenous gene can be expressed stably and transferred to its offspring through a matrix attachment region (MAR)-mediated non-viral vector using the eGFP marker gene. The eukaryotic expression vector pEGFP-N1-MAR, which contains the eGFP gene and MAR, was constructed and transfected into a chicken stage-X blastoderm to produce a G0 generation of transgenic chickens. The hatchabilities of different injection regions were tested; 18 of the 40 eggs injected with pEGFPN1- MAR in the area opaca hatched after 21 days of incubation, and had a hatchability rate of 45%. By contrast, eggs injected at the area pellucida did not hatch. Results from the fluorescence signal detection and polymerase chain reaction (PCR) verified that four hatched chicks from the G0 generation expressed the eGFP gene. Furthermore, fluorescence signal detection results indicated that 2 of the 65 chicks from the G1 generation expressed the eGFP gene. We conclude that MAR facilitates the production of transgenic chickens; pEGFP-N1-MAR application is a novel approach that can produce transgenic chicken offspring.     

Direct cooling of the human brain by heat loss from the upper respiratory tract.

This study is the first report on human intracranial temperature in conscious patients during and after an upper respiratory bypass. Temperatures were measured in four subjects subdurally between the frontal lobes and cribriform plate (T(cr)) and on the vault of the skull (T(sd)). Further measurements were taken in the esophagus (T(es)) and on the tympanic membrane. Reinstitution of airflow in the upper respiratory tract under conditions of mild hyperthermia gave a rapid drop in T(cr) of 0.4-0.8 degrees C. In three patients the intracranial temperature at the basal aspect of the frontal lobes fell below T(es). Thus local selective cooling of the brain surface below that of the trunk temperature was shown to occur. Intensive breathing by the patients after extubation for a 3-min period produced a cooling at the site of T(cr) measurement at a rate of up to 0.1 degrees C/min, and this response could be evoked on demand. The results support the view that cooling of the upper airway can directly influence human brain temperature.     

A tracheal culture model of respiratory tract infection withPseudomonas Aeruginosa

Summary The pathogenesis ofPseudomonas aeruginosa for the respiratory tract has been examined using hamster tracheal organ cultures. Tracheal rings prepared from male Syrian hamsters, strain LSH/LAK, were infected withP. aeruginosa for 4 h and processed at 4-h intervals for 24 h for examination by light- and electron microscopy. Tissue destruction was observed within 8 h after infection with 10⁸ colony-forming units (cfu)/ml and within 12 h after infection with 10⁴ or 10⁶ cfu/ml. Ciliated cells that contained abnormal subcellular organelles were expelled from the epithelium. By 20 h the epithelial borders were composed primarily of nonciliated cells. Transmission- and scanning electron microscopy revealed details of the cellular destruction and attachment ofP. aeruginosa to the ciliated epithelium.Pseudomonas aeruginosa causes a rapid destruction of the epithelium of hamster trachea in cultures. Hamster tracheal organ cultures have been shown to be useful in studying the pathogenesis ofP. aeruginosa for the respiratory tract. This work was supported by Grants G-430B and G-431B from the Cystic Fibrosis Foundation.