A Novel Strategy to Fit and Validate Physiological Models: A Case Study of a Cardiorespiratory Model for Simulation of Incremental Aerobic Exercise

Figures

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  Figure 1. Schematic diagram of the fitting and validation strategy. The dotted lines divide the diagram into the main procedures and their respective stages: the first procedure is at the top and corresponds to the classification and selection of parameters; the second is in the middle and corresponds to model fitting, and the third one is at the bottom and corresponds to model validation.

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  Figure 2. Top ten positions in the rankings of classification techniques: (a) correspond to the results for subset selection and (b) to the results for sensitivity analysis techniques. The light gray bars correspond to the selected base setting parameters, and the dark gray bars correspond to the parameters that will remain fixed at the nominal values.

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  Figure 3. Relative sensitivity rankings after removing the parameters selected for the base fitting approach. The light gray bars correspond to the selected parameters for the specific fitting approach, and the dark gray bars correspond to the parameters that remain fixed at nominal values. The subfigures from (a) to (i) correspond to the result for each of the variables evaluated.

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  Figure 4. Steady-state model predictions for each cardiorespiratory variable evaluated. Results are shown as a function of V˙CO2 values. Gray dots denote the experimental data limited at each subject’s AT; the black dot-line the experimental data average; the square marker the model predictions under nominal conditions (Nominal); the cross marker the predictions of the model at the first fitting stage (Base); the plus sign marker the model predictions at the second fitting stage (Specific); and the diamond marker the model predictions at the third fitting stage (Stimulus). The subfigures from (a) to (j) correspond to the result for each of the variables evaluated.

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  Figure 5. PE results for steady-state predictions under nominal conditions and at each fitting stage. The bar graph represents the errors’ median values, and the whiskers represent the interquartile distance. The gray bars represent the PE under nominal conditions (Nominal), the line pattern bars the results at the first fitting stage (Base), the dots pattern bars the results at the second fitting stage (Specific), and the white bars represent the results at the third fitting stage (Stimulus). Symbols (*) and (**) highlight the statistically significant differences found between the obtained PE values (ρ < 0.05 and ρ < 0.01, respectively).

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  Figure 6. Transient results for a single load step. Model inputs correspond to variations of V˙O2 and V˙CO2 from 0.64 to 0.82 L/min and 0.58 to 0.76 L/min, respectively. They were obtained from the experimental mean values at the beginning and end of the first exercise load step. The dotted lines are the simulation results under nominal conditions (Nominal); the dashed lines are the simulation results at the first fitting stage (Base); the dash-dot lines are the simulation results at the second fitting stage (Specific); and the dotted lines with cross marker are the simulation results at the third fitting stage (Stimulus). The simulation results are compared with the corresponding experimental data. The solid gray and black lines represent the subject-by-subject experimental data restricted at AT, and their total mean value. The subfigures from (a) to (i) correspond to the result for each of the variables evaluated.