Optimization techniques in respiratory control system models
Graphical abstract
Introduction
The primary function of respiratory system is to regulate the homeostasis of arterial blood gases and pH, through supplying oxygen to the blood and removing carbon dioxide (CO2) produced by metabolic activities. From a modeling viewpoint, the respiratory system can be considered as a neurodynamic feedback system, nonlinear, multivariable with delays and continuously affected by physiological and pathological disturbances. Its behavior can be defined by a continuous interaction between the controller and peripheral processes are being controlled (respiratory mechanics and pulmonary gas exchange). The peripheral processes have been extensively studied in previous research [1], [2], [3], [4], [5], [6], [7]. Nevertheless, respiratory controller behavior and how the controller processes different afferent inputs are not completely inferred yet [8].
One of the most interesting issues concerning respiratory system modeling is the possibility of forecasting the respiratory system response of a critical patient connected to a mechanical ventilator. However, mathematical models are still far from allowing this, mainly because of the complexity of the respiratory control system that adjusts the breathing pattern according to mechanical and chemical components minimizing the work of breathing (WOB) and the system response can be affected either by the cost function or by the optimization technique.
The aim of this study is twofold: firstly, to compare two known mechanical cost functions to quantify the WOB [9] and, secondly, to assess the influence of several known optimization techniques, such as direct search and evolutionary algorithms [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], on the adjustment of the breathing pattern (by the controller) and the model parameters (in the identification process).
Two nested optimizations were carried out for this purpose: the first one in the controller that minimizes the WOB by using both mechanical cost estimations proposed in [9] and the second one in the search of the model parameters associated with the response that better matched with experimental data. These data were recorded from a group of subjects under different levels of ventilation () produced by hypercapnic stimulation. Hypercapnia is characterized by changes in partial pressure of CO2 in arterial blood () above the normal value (40 mmHg), so the neural control center respond adjusting and, therefore, breathing pattern subject, in order to keep near physiological values. In this study, hypercapnia was produced increasing partial inspiratory pressure of CO2 ().
Known evolutionary and deterministic optimization algorithms are applied in order to identify the best option for this kind of optimization problems and to guarantee that the model parameter adjustment allows to reproduce real situations with physiological meaning. The performance of these optimization algorithms are evaluated regarding the goodness of fit to experimental data, the convergence rate and the dispersion of the found solutions.
The paper is organized as follows. Section 2 presents previous studies about modeling of respiratory control system response and concerning optimization procedures used in biomedical applications. Section 3 presents a general description of the algorithms addressed in this study and their selected parameter values. Section 4 presents a mathematical description of the analyzed model and its variables of interest. Afterwards, Section 5 shows the optimization problem to be solved: experimental data for the model adjustment, the two nested optimizations solved in this approach (the breathing pattern fitting and the model fitting to experimental data), and finally, statistical tests and validation procedure to select the best algorithms and to compare the found solutions. Section 6 presents the results associated to the both fittings. Finally, Section 7 discusses and concludes the results found in the optimization problem and provides their interpretation in the respiratory model from a physiological point of view. A step by step description about how this approach was carried out is presented in Fig. 1.
Section snippets
Respiratory control system modeling
The respiratory controller may be seen as a central pattern generator in which rhythmic respiratory activity is produced in response to different afferent pathways [20]. Following this hypothesis, several approaches have been used to simulate this control law in respiratory control modeling. In this sense, some authors consider respiratory control system as a reflex-mechanism where breathing pattern is adjusted, from mathematical relationships obtained empirically, in order to meet a
Optimization algorithms
Optimization techniques involve the selection of the best element, regarding some criteria, from a set of available alternatives. In this sense, optimization algorithms are tools which try to minimize (sometimes maximize) a cost function or error by systematically choosing input parameters within a search space. These input parameters involve variables which are often restricted or constrained. There is not a universal optimization algorithm, so the choice of an appropriate algorithm for a
Model description
The model used in this work was proposed by Poon et al. [9] to describe the stationary response of respiratory system under hypercapnia and exercise stimuli. This model presents an optimal control that adjusts and breathing pattern as a function of minimization of WOB and includes dynamic elements that relate neural activity to ventilatory mechanics [75]. The model discriminates between the mechanical work carried out during inspiration and expiration, so that not only adjusts but also
Optimization problem
The model response to ventilatory stimuli has to guarantee both the minimum respiratory cost (J) (Eq. (1)) and a good fit to the study population. Therefore, two nested optimization processes were involved in the analyzed model: the optimization of breathing pattern by minimizing J in function of [t1, t2, a1, a2, τ] and the fitting model response to experimental data by minimizing differences between experimental and simulated variables by fitting the parameters [λ1, λ2, n]. A description of
Breathing pattern fitting
The values of J resulting obtained from simulations of RSM1 and RSM2 with the eight analyzed optimization algorithms as a function of number of evaluations (N) are shown in Fig. 8. It can be seen that the lowest J and its corresponding value N were obtained by SQP in both models. Statistical differences were found between SQP and the others algorithms using WMW (p-value < 0.001). Thus, this algorithm was statically more appropriated for the optimization of breathing pattern, so it was selected to
Optimization problem
Two approaches for the respiratory control system modeling based on simultaneous optimization of ventilation and breathing pattern, which were called in this study RSM1 and RSM2, have been analyzed [9]. Such optimization was performed by minimizing a respiratory cost function (J) that reflects the balance of chemical (Jc) and mechanical (Jm) costs of breathing. Differences between both approaches were determined by the equations proposed to quantify Jm during inspiratory and expiratory phases
Acknowledgements
This study was partially funded by the Spanish government MINECO (DPI2014-59049-R), the Technical University of Catalonia (FPU-707.707), the University of Antioquia – Colombia (CODI-E01539-MDC11-1-07). Authors want to thank the Unitat de Semicrítics of Hospital de la Santa Creu i Sant Pau, led by Dr. Salvador Benito, for its help in designing experimental protocol and in the signal recording.
References (88)
- et al.
An integrative model of respiratory and cardiovascular control in sleep-disordered breathing
Central Cardiorespir. Regul.: Physiol. Pathol.
(2010) - et al.
On the regulation of cardiac output and cerebral blood flow
J. Biomed. Eng.
(1983) - et al.
A model of the chemoreflex control of breathing in humans: model parameters measurement
Respir. Physiol.
(2000) The role of the central chemoreceptors: a modeling perspective
Respir. Physiol. Neurobiol.
(2010)- et al.
Homeostasis of exercise hyperpnea and optimal sensorimotor integration: the internal model paradigm
Respir. Physiol. Neurobiol.
(2007) Optimal interaction of respiratory and thermal regulation at rest and during exercise: role of a serotonin-gated spinoparabrachial thermoafferent pathway
Respir. Physiol. Neurobiol.
(2009)Evolving paradigms in H+ control of breathing: from homeostatic regulation to homeostatic competition
Respir. Physiol. Neurobiol.
(2011)- et al.
Neonatal maternal separation and neuroendocrine programming of the respiratory control system in rats
Biol. Psychol.
(2010) A control system for mechanical ventilation of passive and active subjects
Comput. Methods Programs Biomed.
(2013)- et al.
Closed-loop ventilation: an emerging standard of care?
Crit. Care Clin.
(2007)
Genetic algorithm based {NARX} model identification for evaluation of insulin sensitivity
Appl. Soft Comput.
A differential evolution based approach for estimating minimal model parameters from IVGTT data
Comput. Biol. Med.
Supervised pattern recognition for the prediction of contrast-enhancement appearance in brain tumors from multivariate magnetic resonance imaging and spectroscopy
Artif. Intell. Med.
Modelling adrenaline secretion during counterregulatory response in Type 1 diabetes for improved hypoglycaemia prediction
IFAC-PapersOnLine
Applying evolution strategies to preprocessing EEG signals for brain–computer interfaces
Inform. Sci.
Optimization of mechanical ventilator settings
Constrained optimization of an idealized Y-shaped baffle for the Fontan surgery at rest and exercise
Comput. Methods Appl. Mech. Eng.
Adaptive filtering of EEG/ERP through noise cancellers using an improved PSO algorithm
Swarm Evol. Comput.
Comparison of approaches for parameter estimation on stochastic models: generic least squares versus specialized approaches
Comput. Biol. Chem.
Direct search methods: then and now
J. Comput. Appl. Math.
Hypercapnia attenuates inspiratory amplitude and expiratory time responsiveness to hypoxia in vagotomized and vagal-intact rats
Respir. Physiol. Neurobiol.
Equation discovery for model identification in ventilated human lung
Discovery
A computational model of the human respiratory control system: responses to hypoxia and hypercapnia
Ann. Biomed. Eng.
Mathematical analysis and computer simulation of the respiratory system in the newborn infant
IEEE Trans. Biomed. Eng.
A general mathematical model for respiratory dynamics relevant to the clinical setting
Am. Rev. Respir. Dis.
Respiratory muscle energetics
Handb. Physiol., Sect. 3, Respir.
Cardiovascular and Respiratory Systems: Modeling, Analysis, and Control
Optimization character of inspiratory neural drive
J. Appl. Physiol.
Procedures for optimization problems with a mixture of bounds and general linear constraints
ACM Trans. Math. Softw.
On the convergence of pattern search algorithms
SIAM J. Optim.
Pattern search algorithms for bound constrained minimization
SIAM J. Optim.
Mesh adaptive direct search algorithms for constrained optimization
SIAM J. Optim.
The CHC adaptive search algorithm
Macroevolutionary algorithms: a new optimization method on fitness landscapes
IEEE Trans. Evol. Comput.
Differential evolution – a simple and efficient heuristic for global optimization over continuous spaces
J. Glob. Optim.
Particle swarm optimization
Completely derandomized self-adaptation in evolution strategies
Evol. Comput.
Respiratory models and control
Biomed. Eng. Handb.
Mechanics of breathing in man
J. Appl. Physiol.
Optimal control of inspiratory airflow in breathing
Optim. Control Appl. Methods
Ventilatory control in hypercapnia and exercise: optimization hypothesis
J. Appl. Physiol.
Optimal control of respiration in exercise
Eng. Med. Biol.
Function of brainstem neurons in optimal control of respiratory mechanics
Biol. Cybern.
Cited by (8)
Regional Resistance Value Optimization of Cerebral Blood Circulation
2021, 2021 8th International Conference on Electrical and Electronics Engineering, ICEEE 2021Dynamic Model of the Cardiorespiratory System in Healthy Humans by using Electrocardiogram signals as Input
2021, 2021 19th Workshop on Information Processing and Control, RPIC 2021What you feel may not be what you experience: a psychophysiological study on flow in VR travel experiences
2020, Asia Pacific Journal of Tourism ResearchMetabolic Modeling in Altered Gravity
2020, IEEE Aerospace Conference Proceedings