Modelling the Dynamic Ventilatory Response to Carbon Dioxide in Healthy Human Subjects During Normoxia

Abstract

The use of the dynamic end-tidal forcing technique (DEF technique) to estimate the contributions to total ventilation (V_E) of the peripheral and central chemoreflex loops following a CO₂ challenge was introduced by Swanson and Bellville¹. By use of feedback control of inspired gas tensions the end-tidal carbon dioxide tension (P_ET,CO₂) is forced dynamically, while holding the end-tidal oxygen tension (P_ET,O₂) constant. A simple model to analyse the resulting ventilatory response consists of two independent first order systems both driven by carbon dioxide, representing the peripheral and central chemoreflex loop (deterministic part of the model)^1,2. To date the DEF technique is the only non-invasive technique able to separate the contribution to V_E from each chemoreflex loop. This paper presents the results of a study of the ventilatory response to steps in P_ET,CO₂ in humans using the deterministic model by Bellville et al.². However, human breathing is noisy and irregular and little work has done to model the noise. We therefore modelled the noise in three different ways: as measurement white noise on the output (model 1); as measurement white noise on the output and process noise on the input of both chemoreflex loops (model 2 or process noise model); as measurement white noise on the output and independent first order noise on the output (model 3 or external noise model). This last model has been proposed but only used for analysing data of anesthetized cats³. To differentiate between models we compare the deterministic parameters, the auto-correlation function of the residuals, the cross-correlation between the input and the residual and the standard deviation of individual parameters.