The use of physiological models in medicine allows the evaluation of new hypotheses, development of diagnosis and clinical treatment applications, development of training and medical education tools, as well as medical device design. Although several mathematical models of physiological systems have been presented in the literature, few of them are able to predict the human cardiorespiratory response under physical exercise stimulus adequately. This paper aims to present the building and comparison of an integrated cardiorespiratory model focused on the prediction of the healthy human response under rest and aerobic exercise. The model comprises cardiovascular circulation, respiratory mechanics, gas exchange system, as well as cardiovascular and respiratory controllers. Every system is based on previously reported physiological models and incorporates reported mechanisms related to the aerobic exercise dynamics. Experimental data of thirty healthy male volunteers undergoing a cardiopulmonary exercise test and simulated data from two of the most current and complete cardiorespiratory models were used to evaluate the performance of the presented model. Experimental design, processing, and exploratory analysis are described in detail. The simulation results were compared against the experimental data in steady-state and in transient regime. The predictions of the proposed model closely mimic the experimental data, showing in overall the lowest prediction error (10.35%), the lowest settling times for cardiovascular and respiratory variables, and in general, the fastest and similar responses in transient regime. These results suggest that the proposed model is suitable to predict the cardiorespiratory response of healthy adult humans under rest and aerobic exercise conditions.

Respiratory system modeling has been extensively studied in steady-state conditions to simulate sleep disorders, to predict its behavior under ventilatory diseases or stimuli and to simulate its interaction with mechanical ventilation. Nevertheless, the studies focused on the instantaneous response are limited, which restricts its application in clinical practice. The aim of this study is double: firstly, to analyze both dynamic and static responses of two known respiratory models under exercise stimuli by using an incremental exercise stimulus sequence (to analyze the model responses when step inputs are applied) and experimental data (to assess prediction capability of each model). Secondly, to propose changes in the models' structures to improve their transient and stationary responses. The versatility of the resulting model vs. the other two is shown according to the ability to simulate ventilatory stimuli, like exercise, with a proper regulation of the arterial blood gases, suitable constant times and a better adjustment to experimental data. The proposed model adjusts the breathing pattern every respiratory cycle using an optimization criterion based on minimization of work of breathing through regulation of respiratory frequency.

One of the most complex physiological systems whose modeling is still an open study is the respiratory control system where different models have been proposed based on the criterion of minimizing the work of breathing (WOB). The aim of this study is twofold: to compare two known models of the respiratory control system which set the breathing pattern based on quantifying the respiratory work; and to assess the influence of using direct-search or evolutionary optimization algorithms on adjustment of model parameters. This study was carried out using experimental data from a group of healthy volunteers under CO2 incremental inhalation, which were used to adjust the model parameters and to evaluate how much the equations of WOB follow a real breathing pattern. This breathing pattern was characterized by the following variables: tidal volume, inspiratory and expiratory time duration and total minute ventilation. Different optimization algorithms were considered to determine the most appropriate model from physiological viewpoint. Algorithms were used for a double optimization: firstly, to minimize the WOB and secondly to adjust model parameters. The performance of optimization algorithms was also evaluated in terms of convergence rate, solution accuracy and precision. Results showed strong differences in the performance of optimization algorithms according to constraints and topological features of the function to be optimized. In breathing pattern optimization, the sequential quadratic programming technique (SQP) showed the best performance and convergence speed when respiratory work was low. In addition, SQP allowed to implement multiple non-linear constraints through mathematical expressions in the easiest way. Regarding parameter adjustment of the model to experimental data, the evolutionary strategy with covariance matrix and adaptation (CMA-ES) provided the best quality solutions with fast convergence and the best accuracy and precision in both models. CMAES reached the best adjustment because of its good performance on noise and multi-peaked fitness functions. Although one of the studied models has been much more commonly used to simulate respiratory response to CO2 inhalation, results showed that an alternative model has a more appropriate cost function to minimize WOB from a physiological viewpoint according to experimental data.Postprint (author's final draft

Applying complex mathematical models of physiological systems is challenging due to the large number of parameters. Identifying these parameters through experimentation is difficult, and although procedures for fitting and validating models are reported, no integrated strategy exists. Additionally, the complexity of optimization is generally neglected when the number of experimental observations is restricted, obtaining multiple solutions or results without physiological justification. This work proposes a fitting and validation strategy for physiological models with many parameters under various populations, stimuli, and experimental conditions. A cardiorespiratory system model is used as a case study, and the strategy, model, computational implementation, and data analysis are described. Using optimized parameter values, model simulations are compared to those obtained using nominal values, with experimental data as a reference. Overall, a reduction in prediction error is achieved compared to that reported for model building. Furthermore, the behavior and accuracy of all the predictions in the steady state were improved. The results validate the fitted model and provide evidence of the proposed strategy’s usefulness.