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.     

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".     

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.     

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.     

Calculation of regional deposition of aerosol in the respiratory tract

The removal of air-borne particles in the respiratory tract is treated to enable regional deposition to be inferred from measurement of expired aerosol as well as predicted from theory of the primary removal processes. The analysis uses the analogy of a continuous tubular filter-bed and includes consideration of respiratory pauses and the mechanical mixing of gas flow. Derived equations relate regional deposition, distribution of aerosol in the expired air, and efficiency of removal at different depths in the respiratory tract.     

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 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.     

Quantitative deposition of ultrafine stable particles in the human respiratory tract

Theoretical models of particle deposition in the respiratory tract predict high fractional deposition for particles of less than 0.1 micron, but there are few confirming experimental data for those predictions. We have measured the deposition fraction of a nonhygroscopic aerosol in the human respiratory tract. The aerosol had a count mean diameter of 0.044 micron SD of 1.93, as measured with an electrical aerosol analyzer, and was produced from a 0.01% solution of bis(2-ethylhexyl) sebacate using a condensation generator. Subjects inhaled the aerosol using a controlled respiratory pattern of 1 liter tidal volume, 12/min. Deposition was calculated as the difference in concentration between inhaled and exhaled aerosol of five size fractions corrected for system deposition and dead-space constants. Three deposition studies were done on each of five normal male volunteers. Means (+/- SE) for the five size fractions were 0.024 micron, 0.71 +/- 0.06; 0.043 micron, 0.62 +/- 0.06; 0.075 micron, 0.53 +/- 0.05; 0.13 micron, 0.44 +/- 0.04; and 0.24 micron, 0.37 +/- 0.06. These data demonstrate that deposition of inhaled particles in the 0.024- to 0.24-micron size range is high and increases with decreasing size. These observations agree with and validate predictions of mathematical models.     

Use of ceftriaxone in urinary and respiratory tract infections

Efficiency of ceftriaxone (Rocephin Hoffman Laroche) was assessed in 16 children aged between 3 and 14 years and in 4 adults aged between 17 and 70 years with severe infections of the urinary and respiratory tracts caused by E. coli. S. pneumoniae, P. aeruginosa, P. mirabilis or enterococci. Pyelonephritis as a sole pathology was diagnosed in 10 patients whereas in further 8 patients it complicated other diseases (nephrotic syndrome, hepatitis, cholangitis, leukemia). Pneumonia complicated nephritis leukemia or lymphoma in 8 children. Peritonitis was diagnosed in 1 adult patient. Ceftriaxone was given in a single daily dose of 50 mg/kg to all children and 2.0 g to adult patients for 7-10 days. No adverse reactions were noted. Clinical improvement was achieved in all treated patients. Cultures became negative in 17 cases after the treatment. Significant bacteremia caused by P. aeruginosa persisted in 2 patients and by E. coli in 1 patient. No toxic effects on liver, renal, pancreatic and bone marrow functioning were seen. Ceftriaxone may be safely and efficiently used for the treatment of the urinary and respiratory infections.     

Determining the basic characteristics of aerosols suitable for studies of deposition in the respiratory tract

Studies of aerosol particle deposition in the respiratory tract requires experimental inhalation of artificial model aerosols. The paper formulates some of the most important requirements for the properties of such aerosols. Several suitable fractions were prepared as part of a research project dealing with the use of microporous polymers for diagnostic purposes. 5 fractions of the polymer designated G-gel 60 with the particle size as stated by the manufacturer, ranging from 3 to 7 micron were evaluated using a 16-channel particle dispersity analyzer HIAC/ROYCO MT 3210 with the sensor 1200 and operated by a microprocessor, the equipment being coupled to an APPLE IIe computer. G-gel 60 particles introduced into the aerosol were characterized by the parameters CMAD, MMAD and sg both numerically and graphically. The measurement procedure was found to be very sensitive with respect to all fractions in evaluating the subtile differences between different lot numbers of the aerosol. G-gel 60 fractions characterized both numerically and graphically were compared with the known aerosols from paraffin oil and atmospheric air. The equipment MT 3210 enables prompt determination of the percentages of aerosol particles distribution by size class. The authors conclude that the procedure, both in its numerical and graphical versions, is particularly suitable for the diagnosis of aerosol particles deposition in the respiratory tract, offering a new application for HIAC/ROYCO in the field of medicine. In evaluating atmospheric aerosol in exhaled air, the number of particles was found to be below that in inhaled air, the difference being dependent on the choice of investigation methods. Percentual distribution of deposited particles following one minute ventilation proved to be at its maximum, as regards atmospheric aerosol, in the 0.30-0.50 micron range. The deposition curve was similar to already published curves, being characterized by an S-shaped pattern with maximum deposition in the greater size classes. An analysis of inhaled, exhaled and deposited aerosol suggested that deposited aerosol is more polydisperse and has particles of greater sizes than inhaled aerosol. Investigation of the effect of apnoe on deposition indicated that deposition increased as a function of apnoeic pause.     

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.