A model for control of breathing in mammals: Coupling neural dynamics to peripheral gas exchange and transport

Abstract

A new model for aspects of the control of respiration in mammals has been developed. The model integrates a reduced representation of the brainstem respiratory neural controller together with peripheral gas exchange and transport mechanisms. The neural controller consists of two components. One component represents the inspiratory oscillator in the pre-Bötzinger complex (preBötC) incorporating bio-physical mechanisms for rhythm generation. The other component represents the ventral respiratory group (VRG), which is driven by the pre-BötC for generation of inspiratory (pre)motor output. The neural model was coupled to simplified models of the lungs incorporating oxygen and carbon dioxide transport. The simplified representation of the brainstem neural circuitry has regulation of both frequency and amplitude of respiration and is done in response to partial pressures of oxygen and carbon dioxide in the blood using proportional (P) and proportional plus integral (PI) controllers. We have studied the coupled system under open and closed loop control. We show that two breathing regimes can exist in the model. In one regime an increase in the inspiratory frequency is accompanied by an increase in amplitude. In the second regime an increase in frequency is accompanied by a decrease in amplitude. The dynamic response of the model to changes in the concentration of inspired O 2 or inspired CO 2 was compared qualitatively with experimental data reported in the physiological literature. We show that the dynamic response with a PI-controller fits the experimental data better but suggests that when high levels of CO 2 are inspired the respiratory system cannot reach steady state. Our model also predicts that there could be two possible mechanisms for apnea appearance when 100% O 2 is inspired following a period of 5% inspired O 2 . This paper represents a novel attempt to link neural control and gas transport mechanisms, highlights important issues in amplitude and frequency control and sets the stage for more complete neurophysiological control models.

Central regulation of heart rate and the appearance of respiratory sinus arrhythmia: New insights from mathematical modeling

“…We therefore decided to exclude the cardiac chemoreflex from the model. On the other hand, we have previously incorporated ventilatory control [68] into the model, and although this aspect is “switched off” for the present study, by enabling ventilatory control we should obtain the observed tachycardia due to mechanical feedback, as found experimentally in spontaneously breathing man.…”

“…The two differential equations (1) & (2) are coupled to a model of the lungs (also referred to in Figure 1) which is based on [68] and is described for convenience in Appendix A. The differential equations of the lung and heart-rate models are solved together: lung volume from the lung model acts as input to the heart rate model and the heart beat period from the heart rate model serves as input in the lung model.…”

“…Note that this formula is equivalent to the one given in equation (5) of [68] when Δ t is fixed. But while in [68] I l depends on Δ t there is no such dependency in the formula we use here. In all of our simulations T r 1 = 0.35.…”

“…represent an average subject) and are used as the default if an explicit value is not mentioned when specific results are presented. All values are taken from [68]. …”

Recent advances in theoretical models of respiratory mechanics

“…1 Schematic drawing of typical respiratory mechanics models. a The respiratory system and blood circulation system, in which the arrows and circles show the position concerned with the corresponding model (RA, right atrium; RV, right ventricle; LA, left atrium; LV, left ventricle); b A macroscopic model that merely considers the oxygen consumption and carbon dioxide production of a mobile human body in a chamber; c A typical inflation P-V curve in a patient with ARDS, including the parameters in a sigmoidal model [10]; d A generated 1D centerline airway tree containing the 3D CT-resolved upper airway, central airway tree, and central airway skeleton [20]; e A two-compartment lumped parameter model, in which the spring and dashpot represent the static elasticity and the resistance, and a module comprising a dashpot and a spring reflect the tissue viscoelasticity [14]; f A model showing the process of oxygen uptake of blood flowing through the pulmonary capillaries [29]; g A lung-heart coupling model that includes gas exchange between alveolar gas and blood, as well as blood gas transport [40] the heart was thus investigated [41,42]. One recent study combined a ventilatory neuromuscular model and a cardiovascular model [43].…”