Kinetics of absorption atelectasis during anesthesia: a mathematical model

1999 ◽  
Vol 86 (4) ◽  
pp. 1116-1125 ◽  
Author(s):  
C. J. Joyce ◽  
A. B. Williams
Keyword(s):  
Mathematical Model ◽  
Gas Exchange ◽  
Main Parameter ◽  
Important Determinant ◽  
Gas Absorption ◽  
Gas Composition ◽  
Gas Uptake ◽  
Lung Compartment ◽  
Combined Models ◽  
Kinetics Of

Recent computed tomography studies show that inspired gas composition affects the development of anesthesia-related atelectasis. This suggests that gas absorption plays an important role in the genesis of the atelectasis. A mathematical model was developed that combined models of gas exchange from an ideal lung compartment, peripheral gas exchange, and gas uptake from a closed collapsible cavity. It was assumed that, initially, the lung functioned as an ideal lung compartment but that, with induction of anesthesia, the airways to dependent areas of lung closed and these areas of lung behaved as a closed collapsible cavity. The main parameter of interest was the time the unventilated area of lung took to collapse; the effects of preoxygenation and of different inspired gas mixtures during anesthesia were examined. Preoxygenation increased the rate of gas uptake from the unventilated area of lung and was the most important determinant of the time to collapse. Increasing the inspired O2 fraction during anesthesia reduced the time to collapse. Which inert gas (N2 or N2O) was breathed during anesthesia had minimal effect on the time to collapse.

Intertissue diffusion effect for inert fat-soluble gases

1965 ◽  
Vol 20 (4) ◽  
pp. 621-627 ◽  
Author(s):  
William Perl ◽  
Herbert Rackow ◽  
Ernest Salanitre ◽  
Gerald L. Wolf ◽  
Robert M. Epstein
Keyword(s):  
Adipose Tissue ◽  
Gas Exchange ◽  
Human Subjects ◽  
Compartment Model ◽  
Inert Gases ◽  
Gas Uptake ◽  
Model Generalization ◽  
Capillary Exchange ◽  
Uptake Measurement ◽  
Kinetics Of

An approximately constant 5% difference in alveolar concentration of nitrous oxide and cyclopropane exists when these two gases are administered simultaneously to human subjects. This difference in uptake cannot be fully explained within the traditional framework of a perfusion-limited, multi-compartment model of inert gas exchange. It is proposed that this difference reflects direct diffusion from lean to neighboring adipose tissue through distances of the order of 1 mm. The diffusional rate of cyclopropane uptake into adipose tissue is initially large relative to perfusional uptake. The two rates eventually become and remain comparable as both decrease to zero. Implications of these results for deduction of blood flow to body adipose tissue by gas uptake measurement, and for utilization of capillary exchange surface by fat-soluble gases in adipose tissue are discussed. compartment model generalization; gas uptake in body; inert, fat-soluble gas uptake; kinetics of gas exchange in body; body uptake of inert gases; fat-soluble gas uptake; distribution kinetics of gases in body Submitted on February 3, 1964

Estimation of cardiac output by analysis of respiratory gas exchange

1975 ◽  
Vol 39 (1) ◽  
pp. 159-165 ◽  
Author(s):  
L. D. Homer ◽  
B. Denysyk
Keyword(s):  
Mathematical Model ◽  
Cardiac Output ◽  
Standard Deviation ◽  
Gas Exchange ◽  
Simultaneous Estimation ◽  
Gas Composition ◽  
Central Venous ◽  
Blood Samples ◽  
Arterial Blood ◽  
Spontaneously Breathing

Cardiac output is estimated by least squares fitting of a model of pulmonary gas exchange to measurements of respiratory gas composition obtained with a mass spectrometer during a rebreathing maneuver. This new technique estimates cardiac output on spontaneously breathing subjects at rest and requires neither central venous nor arterial blood samples. Principal features of the technique are the use of multiple gases simultaneously in the analysis, the use of a mathematical model for breath-to-breath evaluation of gas exchange, and simultaneous estimation of gas exchange and alveolar gas tensions with the same instrumentation. The technique is compared with thermal dilution estimates in dogs before and during hemorrhagic shock. Two-thirds of these estimates were within 20% of one another. The standard deviation of replication was 15%. Shortcomings, possibilities for improvement, and possible applications are discussed.

Role of nitrogen in transmucosal gas exchange rate in the rat middle ear

2006 ◽  
Vol 101 (5) ◽  
pp. 1281-1287 ◽  
Author(s):  
Romain E. Kania ◽  
Philippe Herman ◽  
Patrice Tran Ba Huy ◽  
Amos Ar
Keyword(s):  
Mathematical Model ◽  
Steady State ◽  
Gas Exchange ◽  
Phase Ii ◽  
Middle Ear ◽  
Phase Iii ◽  
Gas Composition ◽  
Linear Decrease ◽  
Gas Volume

This study investigates the role of nitrogen (N2) in transmucosal gas exchange of the middle ear (ME). We used an experimental rat model to measure gas volume variations in the ME cavity at constant pressure. We disturbed the steady-state gas composition with either air or N2 to measure resulting changes in volume at ambient pressure. Changes in gas volume over time could be characterized by three phases: a primary transient increase with time (phase I), followed by a linear decrease (phase II), and then a gradual decrease (phase III). The mean slope of phase II was −0.128 μl/min (SD 0.023) in the air group ( n = 10) and −0.105 μl/min (SD 0.032) in the N2 group ( n = 10), but the difference was not significant ( P = 0.13), which suggests that the rate of gas loss can be attributed mainly to the same steady-state partial pressure gradient of N2 reached in this phase. Furthermore, a mathematical model was developed analyzing the transmucosal N2 exchange in phase II. The model takes gas diffusion into account, predicting that, in the absence of change in mucosal blood flow rate, gas volume in the ME should show a linear decrease with time after steady-state conditions and gas composition are established. In accordance with the experimental results, the mathematical model also suggested that transmucosal gas absorption of the rat ME during steady-state conditions is governed mainly by diffusive N2 exchange between the ME gas and its mucosal blood circulation.

scholarly journals A mathematical model for the process of gas exchange in lung capillaries using nth order one-step kinetics of oxygen uptake by haemoglobin

1988 ◽  
Vol 30 (2) ◽  
pp. 203-213 ◽  
Author(s):  
Maithili Sharan ◽  
M. P. Singh ◽  
Balbir Singh
Keyword(s):  
Mathematical Model ◽  
Gas Exchange ◽  
Oxygen Uptake ◽  
Empirical Relation ◽  
Diffusion Reaction ◽  
Facilitated Diffusion ◽  
One Step ◽  
Total Haemoglobin ◽  
Lung Capillaries ◽  
Kinetics Of

AbstractA mathematical model is developed for the process of gas exchange in lung capillaries, taking into account the transport mechanisms of molecular diffusion and the facilitated diffusion of the species due to haemoglobin. We have assumed here equilibrium conditions which enable us to neglect advection effects. The nth order one-step kinetics of oxygen uptake by haemoglobin, proposed by Sharan and Singh [8], have been incorporated. The solution of this coupled nonlinear facilitated diffusion-reaction problem together with the physiologically-relevant boundary conditions is obtained in the closed form.It is found that about 97.15% of total haemoglobin has combined with oxygen and 2.85% free pigment is left, which is present as carbaminohaemoglobin, met haemoglobin, carboxy haemoglobin etc. It is also shown that the percentage of free haemoglobin at a given PO2 and PCO2 is independent of total haemoglobin content present in the blood.The well-known Hill's empirical relation is deduced from our solution. The results obtained from our model, based on physical formulation, are in good agreement with the documented data [6] and those computed from the Kelman [3] empirical relation.

Kinetics of CO2 excretion and intravascular pH disequilibria during carbonic anhydrase inhibition

1998 ◽  
Vol 84 (2) ◽  
pp. 683-694 ◽  
Author(s):  
Victor Cardenas ◽  
Thomas A. Heming ◽  
Akhil Bidani
Keyword(s):  
Mathematical Model ◽  
Gas Exchange ◽  
Carbonic Anhydrase ◽  
Blood Cells ◽  
Venous Blood ◽  
Hysteresis Loops ◽  
Mixed Venous Blood ◽  
Carbonic Anhydrase Inhibition ◽  
Kinetics Of ◽  
Mixed Venous

Cardenas, Victor, Jr., Thomas A. Heming, and Akhil Bidani.Kinetics of CO2 excretion and intravascular pH disequilibria during carbonic anhydrase inhibition. J. Appl. Physiol. 84(2): 683–694, 1998.—Inhibition of carbonic anhydrase (CA) activity (activity in red blood cells and activity available on capillary endothelium) results in decrements in CO2 excretion (V˙co 2) and plasma-erythrocyte CO2-[Formula: see text]-H+disequilibrium as blood travels around the circulation. To investigate the kinetics of changes in blood [Formula: see text]and pH during progressive CA inhibition, we used our previously detailed mathematical model of capillary gas exchange to analyze experimental data of V˙co 2and blood-gas/pH parameters obtained from anesthetized, paralyzed, and mechanically ventilated dogs after treatment with acetazolamide (Actz, 0–100 mg/kg iv). Arterial and mixed venous blood samples were collected via indwelling femoral and pulmonary arterial catheters, respectively. Cardiac output was measured by thermodilution. End-tidal[Formula: see text], as a measure of alveolar[Formula: see text], was obtained from continuous records of airway [Formula: see text] above the carina. Experimental results were analyzed with the aid of a mathematical model of lung and tissue-gas exchange. Progressive CA inhibition was associated with stepwise increments in the equilibrated mixed venous-alveolar [Formula: see text] gradient (9, 19, and 26 Torr at 5, 20, and 100 mg/kg Actz, respectively). The maximum decrements in V˙co 2were 10, 24, and 26% with 5, 20, and 100 mg/kg Actz, respectively, without full recovery ofV˙co 2 at 1 h postinfusion. Equilibrated arterial [Formula: see text]overestimated alveolar [Formula: see text], and tissue [Formula: see text] was underestimated by the measured equilibrated mixed venous blood[Formula: see text]. Mathematical model computations predicted hysteresis loops of the instantaneous CO2-[Formula: see text]-H+relationship and in vivo blood[Formula: see text]-pH relationship due to the finite reaction times for CO2-[Formula: see text]-H+reactions. The shape of the hysteresis loops was affected by the extent of Actz inhibition of CA in red blood cells and plasma.

SENSITIVITY ANALYSIS AND IDENTIFIABILITY OF A MATHEMATICAL MODEL OF A CHEMICAL REACTION

2021 ◽  
pp. 14-18
Author(s):  
Л.Ф. Сафиуллина
Keyword(s):  
Mathematical Model ◽  
Inverse Problem ◽  
Sensitivity Analysis ◽  
Chemical Reaction ◽  
Reaction Model ◽  
Numerical Calculations ◽  
Specific Reaction ◽  
Uniqueness Of The Solution ◽  
The Mathematical Model ◽  
Kinetics Of

В статье рассмотрен вопрос идентифицируемости математической модели кинетики химической реакции. В процессе решения обратной задачи по оценке параметров модели, характеризующих процесс, нередко возникает вопрос неединственности решения. На примере конкретной реакции продемонстрирована необходимость проводить анализ идентифицируемости модели перед проведением численных расчетов по определению параметров модели химической реакции. The identifiability of the mathematical model of the kinetics of a chemical reaction is investigated in the article. In the process of solving the inverse problem of estimating the parameters of the model, the question arises of the non-uniqueness of the solution. On the example of a specific reaction, the need to analyze the identifiability of the model before carrying out numerical calculations to determine the parameters of the reaction model was demonstrated.

Final products and kinetics of biochemical and chemical sulfide oxidation under microaerobic conditions

2018 ◽  
Vol 78 (9) ◽  
pp. 1916-1924 ◽  
Author(s):  
Lucie Pokorna-Krayzelova ◽  
Dana Vejmelková ◽  
Lara Selan ◽  
Pavel Jenicek ◽  
Eveline I. P. Volcke ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Oxidation Rate ◽  
Elemental Sulfur ◽  
Sulfide Oxidation ◽  
Cost Effective ◽  
Anaerobic Treatment ◽  
Batch Experiments ◽  
Cost Effective Method ◽  
Microaerobic Conditions ◽  
Kinetics Of

Abstract Hydrogen sulfide is a toxic and usually undesirable by-product of the anaerobic treatment of sulfate-containing wastewater. It can be removed through microaeration, a simple and cost-effective method involving the application of oxygen-limiting conditions (i.e., dissolved oxygen below 0.1 mg L−1). However, the exact transformation pathways of sulfide under microaerobic conditions are still unclear. In this paper, batch experiments were performed to study biochemical and chemical sulfide oxidation under microaerobic conditions. The biochemical experiments were conducted using a strain of Sulfuricurvum kujiense. Under microaerobic conditions, the biochemical sulfide oxidation rate (in mg S L−1 d−1) was approximately 2.5 times faster than the chemical sulfide oxidation rate. Elemental sulfur was the major end-product of both biochemical and chemical sulfide oxidation. During biochemical sulfide oxidation elemental sulfur was in the form of white flakes, while during chemical sulfide oxidation elemental sulfur created a white suspension. Moreover, a mathematical model describing biochemical and chemical sulfide oxidation was developed and calibrated by the experimental results.

CH4 Direct Reduction of In-Flight Fe3O4 Concentrate Particles

2018 ◽  
Vol 14 (1) ◽  
Author(s):  
Bahador Abolpour ◽  
M. Mehdi Afsahi ◽  
Ataallah Soltani Goharrizi
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Fine Particles ◽  
Direct Reduction ◽  
Constant Heat Flux ◽  
Constant Heat ◽  
Dynamic Motion ◽  
Magnetite Ore ◽  
Model Predictions ◽  
Kinetics Of

Abstract In this study, reduction of in-flight fine particles of magnetite ore concentrate by methane at a constant heat flux has been investigated both experimentally and numerically. A 3D turbulent mathematical model was developed to simulate the dynamic motion of these particles in a methane content reactor and experiments were conducted to evaluate the model. The kinetics of the reaction were obtained using an optimizing method as: [-Ln(1-X)]1/2.91 = 1.02 × 10−2dP−2.07CCH40.16exp(−1.78 × 105/RT)t. The model predictions were compared with the experimental data and the data had an excellent agreement.

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