Digital simulation of the ventilatory response to CO 2 inhalation and CSF perfusion

A mathematical model of ventilation response to inhaled carbon monoxide

A comprehensive mathematical model, describing the respiration, circulation, oxygen metabolism, and ventilatory control, is assembled for the purpose of predicting acute ventilation changes from exposure to carbon monoxide in both humans and animals. This Dynamic Physiological Model is based on previously published work, reformulated, extended, and combined into a single model. Model parameters are determined from literature values, fitted to experimental data, or allometrically scaled between species. The model predictions are compared with ventilation-time history data collected in goats exposed to carbon monoxide, with quantitatively good agreement. The model reaffirms the role of brain hypoxia on hyperventilation during carbon monoxide exposures. Improvement in the estimation of total ventilation, through a more complete knowledge of ventilation control mechanisms and validated by animal data, will increase the accuracy of inhalation toxicology estimates.

Multiple modeling in the study of interaction of hemodynamics and gas exchange

Circulation plays an important rule in gas exchange. Therefore, there is an interaction between circulation and gas exchange. To understand the dynamic effect of these two physiological systems, a computer simulation model of hemodynamics and gas exchange is established in this work. This model includes two physiological systems, namely the respiratory and circulatory systems. It consists of five parts: the model of gas transport, exchange and storage within the body, the multi-element nonlinear mathematical model of human circulatory system, an alveolar ventilation controller, a cardiac output controller, and a controller of breathing frequency. Model simulations provide results consistent with both dynamic and steady-state responses under hypoxia. Simulation results can reflect the interaction of hemodynamics and gas exchange. Using this model, the changes of pulmonary arterial pressure and right ventricular pressure in high altitude are studied. The optimal mode of breathing extra oxygen using nasal prongs or a facial mask is studied. This model may provide a useful tool to study reaction of hypoxia and the oxygen inhalation mode under hypoxia environments.

A mathematical model of the human respiratory system

A model of the human respiratory system is proposed which has a satisfactory performance under different physiological conditions. The model comprises a continuous plant and a discrete controller which generates and updates the drive signal to the plant at the end of every breath to represent the Hering-Breuer reflex. Arterial and central medullary sensors are included. The lung volume, dead space volume, cardiac output and cerebral blood flow are time varying. The respiratory work is minimized. The model is examined and simulation results of its performance in hypercapnia, hypoxia, periodic breathing and moderate exercise are presented. The responses presented include the relatively fast transients of Cheyne-Stokes breathing and the slower transients associated with carbon dioxide inhalation.

Transient CO2 elimination and storage as functions of the ventilatory response to CO2

The effect on CO2 storage and elimination of variations in the slope and intercept of the ventilatory response to CO2 curve was examined. Theoretical and experimental results show that although CO2 elimination rate following a transient ventilatory disturbance is decreased at low ventilatory response slopes, this decrease can be compensated by elevated PCO2 intercepts, or thresholds. Conversely, high CO2 elimination rate following a ventilatory disturbance due to a high ventilatory response slope can be off-set by a depressed PCO2 threshold. The results suggest that elevated thresholds which often accompany depressed ventilatory response slopes may be part of a compensatory mechanism for minimizing transient hypercapnia and acidosis.

[Mathematical simulation of the respiratory system (author's transl)]

The respiratory system is described as a feedback control system. The controller consists of the peripheral chemoreceptors and the central chemosensitive structures, the respiratory centre in the medulla oblongata and the thorax-lung pump which they drive. The controlled system is comprised of three compartments (lung, brain and the remaining tissue) connected by the blood circulation. The controlled values are arterial pH and arterial O2 partial pressure and cerebral extracellular pH. Earlier models have been improved by: (1) the dead space description, (2) the thermodynamic formulation of the CO2 dissociation equation and the simple but accurate O2 dissociation equation of the blood, (3) the alteration of the CO2 dissociation equation for the brain and the remaining tissue to accommodate recent results, (4) the application of the one-receptor-theory of central chemosensitivity, (5) the pH dependence of brain circulation, (6) the bicarbonate exchange between blood and extracellular fluid of the brain and (7) the introduction of variable circulation times. Respiratory and metabolic disturbances of the respiratory system are analyzed. The mathematical formulation of the respiratory system is a differential difference equation system. In the steady state the experimental results are reproduced fairly well. A slight discrepancy is found in the simulation of metabolic acidosis. Apparently we have assumed the sensitivity of the peripheral chemoreceptors to be too large so that the respiratory response is not correctly predicted. In the numerical solution there is an overshoot in the on-transient and a damped oscillation in the off-transient of the alveolar CO2 partial pressure during respiratory acidosis. We have varied the parameters to make deviations small. The best agreement seems to result, if the central threshold is near the normal extracellular pH of the brain. A further deviation from experimental findings is that the cerebral CO2 and H+ concentration, the blood circulation of the brain, the alveolar O2 partial tension and the ventilation show a slight oscillation in the off-transient. Except for these discrepancies the experimental results, especially the stability of the extracellular pH of the brain, are reproduced fairly well. During hypoxia there are deviations form the experimental results if the central residual activity is constant and the central threshold deviates from the normal extracellular pH of the brain. But if the central residual activity is pH dependent and if the central threshold is equal to the normal extracellular pH of the brain, then the time course of VE and the other variables agree fairly well with experimental results. There is also a good correspondence between the theoretical and experimental data during hyperoxia. During metabolic acidosis the time constant of the bicarbonate exchange between blood and extracellular fluid of the brain is important. If a time constant of one minute is assumed, then the predicted and the experimental results correspond sufficiently well.

Modeling static and dynamic human cardiovascular responses to exercise

A human performance model has been developed and described [9] which portrays the human circulatory, thermo regulatory and energy-exchange systems as an intercoupled set. In this model, steady state or static relationships are used to describe oxygen consumption and blood flow. For example, heart rate (HTRT) is calculated as a function of the oxygen and the thermo-regulatory requirements of each body compartment, using the steady state work values of cardiac output (CO, sum of all compartment blood flows) and stroke volume (SV, assumed maximal after 40% maximal oxygen consumption): HTRT=CO/SV. The steady state model has proven to be an acceptable first approximation, but the inclusion of transient characteristics are essential in describing the overall systems' adjustment to exercise stress. In the present study, the dynamic transient characteristics of heart rate, stroke volume and cardiac output were obtained from experiments utilizing step and sinusoidal forcing of work. The gain and phase relationships reveal a probable first order system with a six minute time constant, and are utilized to model the transient characteristics of these parameters. This approach leads to a more complex model but a more accurate representation of the physiology involved. The instrumentation and programming essential to these experiments are described.