Introduction of respiratory pattern generators into models of respiratory control

Modulation-demodulation hypothesis of periodic breathing in human respiration

Periodic breathing (PB) is a diseased condition of the cardiorespiratory system, and mathematically it is modelled as an oscillation. Modeling approaches replicate periodic oscillation in the minute ventilation due to a higher than normal gain of the feedback signals from the chemoreceptors coupled with a longer than normal latency in feedback, and do not consider the waxing-waning pattern of the oronasal airflow. In this work, a noted regulation model is extended by integrating respiratory mechanics and respiratory central pattern generator (rCPG) model, using modulation-demodulation¹ hypothesis. This is a top-down modeling approach, and it is assumed that the sensory feedback signal from the chemoreceptors modulates the output of the rCPG model. It is also assumed that the brainstem network is responsible for the demodulation process. The respiratory mechanics is modeled as a multi-input multi-output (MIMO) system, where modulated and demodulated neural signals are applied as input and the minute ventilation and the oronasal airflow are specified as output. The minute ventilation signal drives the regulation model, completing the feedback loop. The proposed model is validated by comparing the model output with the clinical data. Using the modulation-demodulation hypothesis, a respiratory mechanics model is formulated in the form of a linear state-space model, which can be useful for providing assisted ventilation in clinical conditions.

Eupnea, tachypnea, and autoresuscitation in a closed-loop respiratory control model

How sensory information influences the dynamics of rhythm generation varies across systems, and general principles for understanding this aspect of motor control are lacking. Determining the origin of respiratory rhythm generation is challenging because the mechanisms in a central circuit considered in isolation may be different from those in the intact organism. We analyze a closed-loop respiratory control model incorporating a central pattern generator (CPG), the Butera-Rinzel-Smith (BRS) model, together with lung mechanics, oxygen handling, and chemosensory components. We show that 1) embedding the BRS model neuron in a control loop creates a bistable system; 2) although closed-loop and open-loop (isolated) CPG systems both support eupnea-like bursting activity, they do so via distinct mechanisms; 3) chemosensory feedback in the closed loop improves robustness to variable metabolic demand; 4) the BRS model conductances provide an autoresuscitation mechanism for recovery from transient interruption of chemosensory feedback; and 5) the in vitro brain stem CPG slice responds to hypoxia with transient bursting that is qualitatively similar to in silico autoresuscitation. Bistability of bursting and tonic spiking in the closed-loop system corresponds to coexistence of eupnea-like breathing, with normal minute ventilation and blood oxygen level and a tachypnea-like state, with pathologically reduced minute ventilation and critically low blood oxygen. Disruption of the normal breathing rhythm, through either imposition of hypoxia or interruption of chemosensory feedback, can push the system from the eupneic state into the tachypneic state. We use geometric singular perturbation theory to analyze the system dynamics at the boundary separating eupnea-like and tachypnea-like outcomes.NEW & NOTEWORTHY A common challenge facing rhythmic biological processes is the adaptive regulation of central pattern generator (CPG) activity in response to sensory feedback. We apply dynamical systems tools to understand several properties of a closed-loop respiratory control model, including the coexistence of normal and pathological breathing, robustness to changes in metabolic demand, spontaneous autoresuscitation in response to hypoxia, and the distinct mechanisms that underlie rhythmogenesis in the intact control circuit vs. the isolated, open-loop CPG.

Computational models of the neural control of breathing

The ongoing process of breathing underlies the gas exchange essential for mammalian life. Each respiratory cycle ensues from the activity of rhythmic neural circuits in the brainstem, shaped by various modulatory signals, including mechanoreceptor feedback sensitive to lung inflation and chemoreceptor feedback dependent on gas composition in blood and tissues. This paper reviews a variety of computational models designed to reproduce experimental findings related to the neural control of breathing and generate predictions for future experimental testing. The review starts from the description of the core respiratory network in the brainstem, representing the central pattern generator (CPG) responsible for producing rhythmic respiratory activity, and progresses to encompass additional complexities needed to simulate different metabolic challenges, closed-loop feedback control including the lungs, and interactions between the respiratory and autonomic nervous systems. The integrated models considered in this review share a common framework including a distributed CPG core network responsible for generating the baseline three-phase pattern of rhythmic neural activity underlying normal breathing. WIREs Syst Biol Med 2017, 9:e1371. doi: 10.1002/wsbm.1371 For further resources related to this article, please visit the WIREs website.

A closed-loop model of the respiratory system: focus on hypercapnia and active expiration

Breathing is a vital process providing the exchange of gases between the lungs and atmosphere. During quiet breathing, pumping air from the lungs is mostly performed by contraction of the diaphragm during inspiration, and muscle contraction during expiration does not play a significant role in ventilation. In contrast, during intense exercise or severe hypercapnia forced or active expiration occurs in which the abdominal “expiratory” muscles become actively involved in breathing. The mechanisms of this transition remain unknown. To study these mechanisms, we developed a computational model of the closed-loop respiratory system that describes the brainstem respiratory network controlling the pulmonary subsystem representing lung biomechanics and gas (O₂ and CO₂) exchange and transport. The lung subsystem provides two types of feedback to the neural subsystem: a mechanical one from pulmonary stretch receptors and a chemical one from central chemoreceptors. The neural component of the model simulates the respiratory network that includes several interacting respiratory neuron types within the Bötzinger and pre-Bötzinger complexes, as well as the retrotrapezoid nucleus/parafacial respiratory group (RTN/pFRG) representing the central chemoreception module targeted by chemical feedback. The RTN/pFRG compartment contains an independent neural generator that is activated at an increased CO₂ level and controls the abdominal motor output. The lung volume is controlled by two pumps, a major one driven by the diaphragm and an additional one activated by abdominal muscles and involved in active expiration. The model represents the first attempt to model the transition from quiet breathing to breathing with active expiration. The model suggests that the closed-loop respiratory control system switches to active expiration via a quantal acceleration of expiratory activity, when increases in breathing rate and phrenic amplitude no longer provide sufficient ventilation. The model can be used for simulation of closed-loop control of breathing under different conditions including respiratory disorders.

Integrative approaches for modeling regulation and function of the respiratory system

Mathematical models have been central to understanding the interaction between neural control and breathing. Models of the entire respiratory system-which comprises the lungs and the neural circuitry that controls their ventilation-have been derived using simplifying assumptions to compartmentalize each component of the system and to define the interactions between components. These full system models often rely-through necessity-on empirically derived relationships or parameters, in addition to physiological values. In parallel with the development of whole respiratory system models are mathematical models that focus on furthering a detailed understanding of the neural control network, or of the several functions that contribute to gas exchange within the lung. These models are biophysically based, and rely on physiological parameters. They include single-unit models for a breathing lung or neural circuit, through to spatially distributed models of ventilation and perfusion, or multicircuit models for neural control. The challenge is to bring together these more recent advances in models of neural control with models of lung function, into a full simulation for the respiratory system that builds upon the more detailed models but remains computationally tractable. This requires first understanding the mathematical models that have been developed for the respiratory system at different levels, and which could be used to study how physiological levels of O2 and CO2 in the blood are maintained.

Spontaneous autoresuscitation in a model of respiratory control

We introduce a closed-loop model of respiratory control incorporating a conductance-based central pattern generator (CPG), low-pass filtering of CPG output by the respiratory musculature, gas exchange in the lung, metabolic oxygen demand, and chemosensation. The CPG incorporates Butera, Rinzel and Smith (BRS)'s (1999) conditional pacemaker model. BRS model cells can support quiescent, bursting, or beating activity depending on the level of excitatory drive; we identify these activity modes with apnea (cessation of breathing), eupnea (normal breathing), and tachypnea (excessively rapid breathing). We demonstrate the coexistence of two dynamically stable behaviors in the closed-loop model, corresponding respectively to eupnea and tachypnea. The latter state represents a novel failure mode within a respiratory control model. In addition, the closed-loop system exhibits a form of autoresuscitation: conductances intrinsic to the BRS model buffer the CPG against brief episodes of hypoxia, steering the system away from catastrophic collapse as can occur with tachypnea.

Computational models and emergent properties of respiratory neural networks

Computational models of the neural control system for breathing in mammals provide a theoretical and computational framework bringing together experimental data obtained from different animal preparations under various experimental conditions. Many of these models were developed in parallel and iteratively with experimental studies and provided predictions guiding new experiments. This data-driven modeling approach has advanced our understanding of respiratory network architecture and neural mechanisms underlying generation of the respiratory rhythm and pattern, including their functional reorganization under different physiological conditions. Models reviewed here vary in neurobiological details and computational complexity and span multiple spatiotemporal scales of respiratory control mechanisms. Recent models describe interacting populations of respiratory neurons spatially distributed within the Bötzinger and pre-Bötzinger complexes and rostral ventrolateral medulla that contain core circuits of the respiratory central pattern generator (CPG). Network interactions within these circuits along with intrinsic rhythmogenic properties of neurons form a hierarchy of multiple rhythm generation mechanisms. The functional expression of these mechanisms is controlled by input drives from other brainstem components,including the retrotrapezoid nucleus and pons, which regulate the dynamic behavior of the core circuitry. The emerging view is that the brainstem respiratory network has rhythmogenic capabilities at multiple levels of circuit organization. This allows flexible, state-dependent expression of different neural pattern-generation mechanisms under various physiological conditions,enabling a wide repertoire of respiratory behaviors. Some models consider control of the respiratory CPG by pulmonary feedback and network reconfiguration during defensive behaviors such as cough. Future directions in modeling of the respiratory CPG are considered.

Influence of arousal threshold and depth of sleep on respiratory stability in man: analysis using a mathematical model

We examined the effect of arousals (shifts from sleep to wakefulness) on breathing during sleep using a mathematical model. The model consisted of a description of the fluid dynamics and mechanical properties of the upper airways and lungs, as well as a controller sensitive to arterial and brain changes in CO(2), changes in arterial oxygen, and a neural input, alertness. The body was divided into multiple gas store compartments connected by the circulation. Cardiac output was constant, and cerebral blood flows were sensitive to changes in O(2) and CO(2) levels. Arousal was considered to occur instantaneously when afferent respiratory chemical and neural stimulation reached a threshold value, while sleep occurred when stimulation fell below that value. In the case of rigid and nearly incompressible upper airways, lowering arousal threshold decreased the stability of breathing and led to the occurrence of repeated apnoeas. In more compressible upper airways, to maintain stability, increasing arousal thresholds and decreasing elasticity were linked approximately linearly, until at low elastances arousal thresholds had no effect on stability. Increased controller gain promoted instability. The architecture of apnoeas during unstable sleep changed with the arousal threshold and decreases in elasticity. With rigid airways, apnoeas were central. With lower elastances, apnoeas were mixed even with higher arousal thresholds. With very low elastances and still higher arousal thresholds, sleep consisted totally of obstructed apnoeas. Cycle lengths shortened as the sleep architecture changed from mixed apnoeas to total obstruction. Deeper sleep also tended to promote instability by increasing plant gain. These instabilities could be countered by arousal threshold increases which were tied to deeper sleep or accumulated aroused time, or by decreased controller gains.

A model for control of breathing in mammals: coupling neural dynamics to peripheral gas exchange and transport

A new model for aspects of the control of respiration in mammals has been developed. The model integrates a reduced representation of the brainstem respiratory neural controller together with peripheral gas exchange and transport mechanisms. The neural controller consists of two components. One component represents the inspiratory oscillator in the pre-Bötzinger complex (pre-BötC) incorporating biophysical mechanisms for rhythm generation. The other component represents the ventral respiratory group (VRG), which is driven by the pre-BötC for generation of inspiratory (pre)motor output. The neural model was coupled to simplified models of the lungs incorporating oxygen and carbon dioxide transport. The simplified representation of the brainstem neural circuitry has regulation of both frequency and amplitude of respiration and is done in response to partial pressures of oxygen and carbon dioxide in the blood using proportional (P) and proportional plus integral (PI) controllers. We have studied the coupled system under open and closed loop control. We show that two breathing regimes can exist in the model. In one regime an increase in the inspiratory frequency is accompanied by an increase in amplitude. In the second regime an increase in frequency is accompanied by a decrease in amplitude. The dynamic response of the model to changes in the concentration of inspired O2 or inspired CO2 was compared qualitatively with experimental data reported in the physiological literature. We show that the dynamic response with a PI-controller fits the experimental data better but suggests that when high levels of CO2 are inspired the respiratory system cannot reach steady state. Our model also predicts that there could be two possible mechanisms for apnea appearance when 100% O2 is inspired following a period of 5% inspired O2. This paper represents a novel attempt to link neural control and gas transport mechanisms, highlights important issues in amplitude and frequency control and sets the stage for more complete neurophysiological control models.

Analysis of the interplay between neurochemical control of respiration and upper airway mechanics producing upper airway obstruction during sleep in humans

Increased loop gain (a function of both controller gain and plant gain), which results in instability in feedback control, is of major importance in producing recurrent central apnoeas during sleep but its role in causing obstructive apnoeas is not clear. The purpose of this study was to investigate the role of loop gain in producing obstructive sleep apnoeas. Owing to the complexity of factors that may operate to produce obstruction during sleep, we used a mathematical model to sort them out. The model used was based on our previous model of neurochemical control of breathing, which included the effects of chemical stimuli and changes in alertness on respiratory pattern generator activity. To this we added a model of the upper airways that contained a narrowed section which behaved as a compressible elastic tube and was tethered during inspiration by the contraction of the upper airway dilator muscles. These muscles in the model, as in life, responded to changes in hypoxia, hypercapnia and alertness in a manner similar to the action of the chest wall muscles, opposing the compressive action caused by the negative intraluminal pressure generated during inspiration which was magnified by the Bernoulli Effect. As the velocity of inspiratory airflow increased, with sufficiently large increase in airflow velocity, obstruction occurred. Changes in breathing after sleep onset were simulated. The simulations showed that increases in controller gain caused the more rapid onset of obstructive apnoeas. Apnoea episodes were terminated by arousal. With a constant controller gain, as stiffness decreased, obstructed breaths appeared and periods of obstruction recurred longer after sleep onset before disappearing. Decreased controller gain produced, for example, by breathing oxygen eliminated the obstructive apnoeas resulting from moderate reductions in constricted segment stiffness. This became less effective as stiffness was reduced more. Contraction of the upper airway muscles with hypercapnia and hypoxia could prevent obstructed apnoeas with moderate but not with severe reductions in stiffness. Increases in controller gain, as might occur with hypoxia, converted obstructive to central apnoeas. Breathing CO2 eliminated apnoeas when the activity of the upper airway muscles was considered to change as a function of CO2 to some exponent. Low arousal thresholds and increased upper airway resistance are two factors that promoted the occurrence and persistence of obstructive sleep apnoeas.

Insights from models of rhythmic motor systems

Computational models of rhythmic motor systems are valuable tools for the study of motor pattern generation and control. Recent modeling advances, together with experimental results, suggest that rhythmic behaviors, such as breathing or walking, are influenced by complex interactions among motor system components. Such interactions occur at all levels of organization, from the subcellular through to the cellular, synaptic, and network levels to the level of neuromuscular interactions and that of the whole organism. Simultaneously, safety mechanisms at all levels contribute to network stability and the generation of robust motor patterns.

Mathematical models of periodic breathing and their usefulness in understanding cardiovascular and respiratory disorders

Periodic breathing is an unusual form of breathing with oscillations in minute ventilations and with repetitive apnoeas or near apnoeas. Reported initially in patients with heart failure or stroke, it was later recognized to occur especially during sleep. The recurrent hypoxia and surges of sympathetic activity that often occur during the apnoeas have serious health consequences. Mathematical models have helped greatly in the understanding of the causes of recurrent apnoeas. It is unlikely that every instance of periodic breathing has the same cause, but many result from instability in the feedback control involved in the chemical regulation of breathing caused by increased controller and plant gains and delays in information transfer. Even when it is not the main cause of the periodic breathing, unstable control modifies the ventilatory pattern and sometimes intensifies the recurrent apnoeas. The characteristics of disturbances to breathing and their interaction with the control system can be critical in determining ventilation responses and the occurrence of periodic breathing. Large abrupt changes in ventilation produced, for example, in the transition from waking to sleep and vice versa, or in the transition from breathing to apnoea, are potent factors causing periodic breathing. Mathematical models show that periodic breathing is a 'systems disorder' produced by the interplay of multiple factors. Multiple factors contribute to the occurrence of periodic breathing in congestive heart failure and cerebrovascular disease, increasing treatment options.