Digital Computer Simulation of Respiratory Response to Cerebrospinal Fluid PCO2 in the Cat

Horgan, James D.; Lange, Ramon L.

doi:10.1016/s0006-3495(65)86760-1

Cited by 21 publications

(4 citation statements)

References 11 publications

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“…First Defares et al (1960) added a brain compartment where measurement of PCO2 levels took place for the feedback loop. Then Horgan and Lange (1963) added in an independent P02 control loop and time lags between the lung and brain compartments, later expanding the model by dividing the brain compartment into 3 sections representing cerebrospinal fluid, the brain CO2 reservoir, and the ventrolateral surface where Pa,C02 was detected by the controller (Horgan and Lange, 1965). The controller also responded to the level of P02 and PCO2 in the arterial blood, and the various time constants were derived from data collected in cats.…”

Section: The Use Of Models In Respiratory Physiologymentioning

confidence: 99%

Modelling the Dynamic Ventilatory Response to Hypoxia in Normal Subjects

Kirby

Wraith

Cort

et al. 1994

Journal of Theoretical Biology

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We have developed a mathematical model to describe the dynamic ventilatory response to hypoxia. The ventilatory response to both transient (two to three breaths nitrogen) and 3 min step change hypoxic stimuli were measured in ten normal subjects during moderate exercise (oxygen consumption 0.96 +/- 0.08 1 min-1). The simplest model relating ventilation to ear oxygen saturation which adequately described the responses in all subjects consisted of two linear differential equations in parallel; both using the fall in oxygen saturation as input, and with the outputs summed to give the rise in ventilation. One equation had a fast time constant (< 3 sec), and the other a slow time constant. Non-linear terms included were (i) a "saturating" effect, similar to that described by the Michaelis-Menten equation, reducing the gain of the equation with the slow time constant as oxygen saturation falls, and (ii) "inhibition" or "potentiation" of the gain of the equation with a slow time constant as the output of the fast time constant equation increased. Repeated measurements in four subjects showed intra- and inter-subject variability for all parameters, with significant between-subject variability for the gain of the fast time constant equation. The final model structure is similar to that describing the peripheral chemoreceptor-mediated hypoxic ventilatory response in anaesthetized cats.

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Section: The Use Of Models In Respiratory Physiologymentioning

confidence: 99%

Modelling the Dynamic Ventilatory Response to Hypoxia in Normal Subjects

Kirby

Wraith

Cort

et al. 1994

Journal of Theoretical Biology

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“…Detailed derivations have been published by Horgan and Lange and associates.12' 15 The parameters expressed are based upon reasonable estimates of coefficients and dynamic response characteristics obtained in human and animal investigation. Following the development reported previously,9 the chemoreceptor block relates Pco2, pH, and Po2 to alveolar ven-Circulation, Volume XXXVII, March 1968 Since Paco,0 is desired, the following expression of the CO2 dissociation curve is applied8: Ca0O2 = 48 + 0.45 (Paco2-39).…”

Section: Appendixmentioning

confidence: 99%

Observation and Simulation of the Circulation, Acid-Base Balance, and Response to CO ₂ in Cheyne-Stokes Respiration

et al. 1968

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Circulatory, chemical, and ventilatory response factors in Cheyne-Stokes respiration (CSR) were studied by experimental procedures and by mathematical analysis. Hemodynamic, ventilatory, and blood gas patterns in 16 patients with heart disease and CSR (group A) and 16 patients with congestive heart failure (CHF) without CSR (group B) were compared. CO2 and oxygen were administered to group A. The phenomena exhibited by patients with CSR were simulated by a mathematical model.The following conclusions were drawn: (1) Reduced blood flow and respiratory alkalosis were similar in both groups; (2) circulation times, lung to artery, were 29 sec greater than normal in patients with CSR but only 8 sec greater than normal in group B patients; (3) the abnormal CO2 response in CSR, a reduction in threshold and sensitivity, was similar to that in CHF, suggesting that abnormal respiratory mechanics were responsible; (4) mathematical simulation of CSR was possible by appropriate prolongation of circulation time alone; the CO2 response (reduction in threshold and sensitivity) had no significant effect on stability; (5) damping of oscillatory ventilation by CO2 inhalation could be efficiently simulated; (6) CSR with cycle periods less than 50 sec suggests increased neural or chemoreceptor excitability, anemia, or hypoxemia as contributory factors, whereas longer periods suggest primary circulatory factors.

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“…In previous mathematical models, either of the entire respiratory system or of the controlled plant per se, the body is lumped into one or more compartments and described by a set of ordinary differential equations (Cherniack et al, 1966(Cherniack et al, , 1968Defares et al, 1960;Farhi and Rahn, 1960;Fowle and Campbell, 1964;Grodins et al, 1954Grodins et al, , 1967Horgan and Lange, 1965;Longobardo et al, 1966Longobardo et al, , 1967Matthews et al, 1968;Milhorn et al, 1965;Staw, 1968;Tenney and Lamb, 1964). For example, in Grodins' classic model of the respiratory system (Grodins et al, 1954), the total body CO2 is treated as though it were confined to a single venous compartment and the functional residual capacity of the lung.…”

Section: Introductionmentioning

confidence: 99%

A Mathematical Model of the Controlled Plant of the Réspiratory System

Trueb¹,

Cherniack²,

D’Souza³

et al. 1971

Biophysical Journal

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Ability to predict the dynamic response of oxygen, carbon dioxide tensions, and pH in blood and tissues to abrupt changes in ventilation is important in the mathematical modeling of the respiratory system. In this study, the controlled plant (the amount and distribution of O(2) and CO(2)) of the respiratory system is modeled. Although the body tissues are divided into a finite number of "compartments" (three tissue groups), in contrast to earlier models, the blood and tissue gas tensions within each compartment are considered to be continuously distributed in time and in one spatial coordinate. The mass conservation equations for oxygen and carbon dioxide involved in the blood-tissue gas exchange are described by a set of partial differential equations which take into account convection of O(2) and CO(2) caused by the flow of blood as well as diffusion due to local tension gradients. Nonlinear algebraic equations for the dissociation curves, which take into account the Haldane and Bohr effects in blood, are used to obtain the relationships between concentrations and partial pressures. Time-variable delays caused by the arterial and venous transport of the respiratory gases are also included. The model so constructed successfully reproduced actual O(2) and CO(2) tensions in arterial blood, and in muscle venous and mixed venous blood when ventilation was abruptly changed.

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Digital Computer Simulation of Respiratory Response to Cerebrospinal Fluid PCO2 in the Cat

Cited by 21 publications

References 11 publications

Modelling the Dynamic Ventilatory Response to Hypoxia in Normal Subjects

Modelling the Dynamic Ventilatory Response to Hypoxia in Normal Subjects

Observation and Simulation of the Circulation, Acid-Base Balance, and Response to CO ₂ in Cheyne-Stokes Respiration

A Mathematical Model of the Controlled Plant of the Réspiratory System

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Digital Computer Simulation of Respiratory Response to Cerebrospinal Fluid PCO2 in the Cat

Cited by 21 publications

References 11 publications

Modelling the Dynamic Ventilatory Response to Hypoxia in Normal Subjects

Modelling the Dynamic Ventilatory Response to Hypoxia in Normal Subjects

Observation and Simulation of the Circulation, Acid-Base Balance, and Response to CO 2 in Cheyne-Stokes Respiration

A Mathematical Model of the Controlled Plant of the Réspiratory System

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Product

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Observation and Simulation of the Circulation, Acid-Base Balance, and Response to CO ₂ in Cheyne-Stokes Respiration