An Improved Dynamic Model for the Respiratory Response to Exercise

Figures

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  Figure 1. Experimental data distribution in function of time. (Left) Experimental exercise stimuli used to simulate the models under study: ventilated values of CO2 (V˙CO2) and O2 (V˙O2). Rest and moderate exercise levels are also marked in both variables. (Right) Experimental data of the cardiorespiratory variables analyzed: inspiratory time (TI), respiratory frequency (fR), tidal volume (VT), minute ventilation (V˙E), arterial partial pressure of CO2 (PaCO2) and O2 (PaO2), and heart rate (HR). Gray dots show original experimental data, bar plots and red lines display the median values obtained in 50-s consecutive time intervals and error bars show the interquartile ranges calculated in each interval.

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  Figure 2. Schematic diagram of the proposed respiratory system model RS3. A model based on RS2 (Cheng et al., 2010; Cheng and Khoo, 2012) that integrates key features of RS1 (Fincham and Tehrani, 1983). The changes introduced in RS2 have been highlighted in orange. In the model, mean values of P′aCO2, P′aO2 and PbCO2 (Pm) and a metabolically related neural drive component to the ventilation (MRV) are used by the central neural control system to compute the alveolar ventilation (V˙A) and the total ventilatory drive (DT≡V˙E=V˙A+V˙D). Then, V˙A is used to adjust the respiratory frequency (fR) each breathing cycle following the optimization principle set in Otis et al. (1950). A detailed description of model variables is provided in the Supplementary Material Section (Table S1).

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  Figure 3. Time series breath-to-breath of airflow signal at the onset of exercise when a step input was used to simulate the respiratory system models RS1, RS2, and RS3 (see text).

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  Figure 4. Transient responses of analyzed variables—ventilation (V˙E), inspiratory time (TI), respiratory frequency (fR), tidal volume (VT), arterial CO2 pressure (PaCO2), arterial O2 pressure (PaO2), and heart rate (HR)—when a step exercise input (V˙CO2= 1.20 L/min and V˙O2 =1.50 L/min) was used to simulate RS1, RS2, and RS3. Variations of each variable are showing regarding their respective values in rest.

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  Figure 5. Steady state values obtained when step inputs of exercise from 0.25 to 2.50 L/min of V˙CO2 were used to simulate the respiratory system models under study.

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  Figure 6. Response of RS3 to a step exercise input under two conditions: firstly, with all mechanism of respiratory control operative and, secondly, without the neurogenic mechanism MRV (see Equation 3). Results are compared with those obtained in RS2 for the same stimulus. Variations of each variable are showing regarding their respective rest values.

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  Figure 7. Contribution of each controller component of RS3 on ventilatory response (see Equation 3). Results are shown regarding their respective rest values.

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  Figure 8. Transient responses of models analyzed in this study. Median values and interquartile distance of experimental and simulated data are presented for each variable and model. Gray shadows show the IQR of experimental data and error bars the IQR of simulated data obtained by each model.

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  Figure 9. Prediction errors (PE) obtained by each one of analyzed models. Bars graph shows median values and error bars indicate interquartile distance (range of values from 25 to 75% quartile). Wilcoxon signed-rank test was used to find statistically significant differences between the obtained PE. (*) for ρ < 0.05 and (**) for ρ < 0.01.