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.     

The pre-Bötzinger oscillator in the mouse embryo

Studies of the sites and mechanisms involved in mammalian respiratory rhythm generation point to two clusters of rhythmic neurons forming a coupled oscillator network within the brainstem. The location of these oscillators, the pre-Bötzinger complex (preBötC) at vagal level, and the para-facial respiratory group at facial level, probably result from regional patterning schemes specifying neural types in the hindbrain during embryogenesis. Here, we report evidence that the preBötC oscillator (i) is first active at embryonic stages, (ii) originates in the post-otic hindbrain neural tube and (iii) requires the glutamate vesicular transporter 2 for rhythm generation.     

Respiratory changes induced by kainic acid lesions in rostral ventral respiratory group of rabbits

The role played by the B?tzinger complex (B?tC), the pre-B?tzinger complex (pre-B?tC), and the more rostral extent of the inspiratory portion of the ventral respiratory group (iVRG) in the genesis of the eupneic pattern of breathing was investigated in anesthetized, vagotomized, paralyzed, and artificially ventilated rabbits by means of kainic acid (KA, 4.7 mM) microinjections (20-30 nl). Unilateral KA microinjections into all of the investigated VRG subregions caused increases in respiratory frequency associated with moderate decreases in peak phrenic amplitude in the B?tC and pre-B?tC regions. Bilateral KA microinjections into either the B?tC or pre-B?tC transiently eliminated respiratory rhythmicity and caused the appearance of tonic phrenic activity ("tonic apnea"), whereas injections into the rostral iVRG completely suppressed inspiratory activity. Rhythmic activity resumed as low-amplitude, high-frequency oscillations and displayed a progressive, although incomplete, recovery. Combined bilateral KA microinjections (B?tC and pre-B?tC) caused persistent (>3 h) tonic apnea. Results show that all of the investigated VRG subregions exert a potent control on both the intensity and frequency of inspiratory activity, thus suggesting that these areas play a major role in the genesis of the eupneic pattern of breathing.     

Interactions of persistent sodium and calcium-activated nonspecific cationic currents yield dynamically distinct bursting regimes in a model of respiratory neurons

The preBötzinger complex (preBötC) is a heterogeneous neuronal network within the mammalian brainstem that has been experimentally found to generate robust, synchronous bursts that drive the inspiratory phase of the respiratory rhythm. The persistent sodium (NaP) current is observed in every preBötC neuron, and significant modeling effort has characterized its contribution to square-wave bursting in the preBötC. Recent experimental work demonstrated that neurons within the preBötC are endowed with a calcium-activated nonspecific cationic (CAN) current that is activated by a signaling cascade initiated by glutamate. In a preBötC model, the CAN current was shown to promote robust bursts that experience depolarization block (DB bursts). We consider a self-coupled model neuron, which we represent as a single compartment based on our experimental finding of electrotonic compactness, under variation of g _NaP, the conductance of the NaP current, and g _CAN, the conductance of the CAN current. Varying these two conductances yields a spectrum of activity patterns, including quiescence, tonic activity, square-wave bursting, DB bursting, and a novel mixture of square-wave and DB bursts, which match well with activity that we observe in experimental preparations. We elucidate the mechanisms underlying these dynamics, as well as the transitions between these regimes and the occurrence of bistability, by applying the mathematical tools of bifurcation analysis and slow-fast decomposition. Based on the prevalence of NaP and CAN currents, we expect that the generalizable framework for modeling their interactions that we present may be relevant to the rhythmicity of other brain areas beyond the preBötC as well.     

Multiple timescale mixed bursting dynamics in a respiratory neuron model

Experimental results in rodent medullary slices containing the pre-Bötzinger complex (pre-BötC) have identified multiple bursting mechanisms based on persistent sodium current (I _NaP) and intracellular Ca²⁺. The classic two-timescale approach to the analysis of pre-BötC bursting treats the inactivation of I _NaP, the calcium concentration, as well as the Ca²⁺-dependent inactivation of IP ₃ as slow variables and considers other evolving quantities as fast variables. Based on its time course, however, it appears that a novel mixed bursting (MB) solution, observed both in recordings and in model pre-BötC neurons, involves at least three timescales. In this work, we consider a single-compartment model of a pre-BötC inspiratory neuron that can exhibit both I _NaP and Ca²⁺ oscillations and has the ability to produce MB solutions. We use methods of dynamical systems theory, such as phase plane analysis, fast-slow decomposition, and bifurcation analysis, to better understand the mechanisms underlying the MB solution pattern. Rather surprisingly, we discover that a third timescale is not actually required to generate mixed bursting solutions. Through our analysis of timescales, we also elucidate how the pre-BötC neuron model can be tuned to improve the robustness of the MB solution.     

The role of spiking and bursting pacemakers in the neuronal control of breathing

Breathing is controlled by a distributed network involving areas in the neocortex, cerebellum, pons, medulla, spinal cord, and various other subcortical regions. However, only one area seems to be essential and sufficient for generating the respiratory rhythm: the preBötzinger complex (preBötC). Lesioning this area abolishes breathing and following isolation in a brain slice the preBötC continues to generate different forms of respiratory activities. The use of slice preparations led to a thorough understanding of the cellular mechanisms that underlie the generation of inspiratory activity within this network. Two types of inward currents, the persistent sodium current (I_NaP) and the calcium-activated non-specific cation current (I_CAN), play important roles in respiratory rhythm generation. These currents give rise to autonomous pacemaker activity within respiratory neurons, leading to the generation of intrinsic spiking and bursting activity. These membrane properties amplify as well as activate synaptic mechanisms that are critical for the initiation and maintenance of inspiratory activity. In this review, we describe the dynamic interplay between synaptic and intrinsic membrane properties in the generation of the respiratory rhythm and we relate these mechanisms to rhythm generating networks involved in other behaviors.     

d-serine regulation of the timing and architecture of the inspiratory burst in neonatal mice

d-serine, released from mouse medullary astrocytes in response to increased CO₂ levels, boosts the respiratory frequency to adapt breathing to physiological demands. We analyzed in mouse neonates, the influence of d-serine upon inspiratory/expiratory durations and the architecture of the inspiratory burst, assessed by pwelch's power spectrum density (PSD) and continuous wavelet transform (CWT) analyses. Suction electrode recordings were performed in slices from the ventral respiratory column (VRC), site of generation of the respiratory rhythm, and in brainstem-spinal cord (en bloc) preparations, from the C5 ventral roots, containing phrenic fibers that in vivo innervate and drive the diaphragm, the main inspiratory muscle.In en bloc and slice preparations, d-serine (100 μM) reduced the expiratory, but not the inspiratory duration, and increased the frequency and the regularity of the respiratory rhythm. In en bloc preparations, d-serine (100 μM) also increased slightly the amplitude of the integrated inspiratory burst and the area under the curve of the integrated inspiratory burst, suggesting a change in the recruitment or the firing pattern of neurons within the burst. Time-frequency analyses revealed that d-serine changed the burst architecture of phrenic roots, widening their frequency spectrum and shifting the position of the core of firing frequencies towards the onset of the inspiratory burst. At the VRC, no clear d-serine induced changes in the frequency-time domain could be established. Our results show that d-serine not only regulates the timing of the respiratory cycle, but also the recruitment strategy of phrenic motoneurons within the inspiratory burst.     

Computational study on neuronal activities arising in the pre-Bötzinger complex

Experimental investigations have shown that the pre-Bötzinger complex (pre-BötC) within the mammalian brainstem generates the inspiratory phase of respiratory rhythm. Based on a single-compartment model of a pre-BötC inspiratory neuron, we, in this paper, use semi-analytical, numerical as well as fast-slow dynamical methods to investigate the effects of sodium conductance (\(g_{\text{Na}}\)) and potassium conductance (\(g_{{\text{K}}}\)) on the firing activities of pre-BötC and try to reveal the dynamical mechanisms behind them. We show how \(g_{{\text{Na}}}\) and \(g_{\text{K}}\) affect the bifurcations of the fast-subsystem and how the the firing patterns of pre-BötC transit according to the bifurcations.     

Chemical activation of pre-Bötzinger complex in vivo reduces respiratory network complexity

In the in vivo anesthetized adult cat model, multiple patterns of inspiratory motor discharge have been recorded in response to chemical stimulation and focal hypoxia of the pre-B?tzinger complex (pre-B?tC), suggesting that this region may participate in the generation of complex respiratory dynamics. The complexity of a signal can be quantified using approximate entropy (ApEn) and multiscale entropy (MSEn) methods, both of which measure the regularity (orderliness) in a time series, with the latter method taking into consideration temporal fluctuations in the underlying dynamics. The current investigation was undertaken to examine the effects of pre-B?tC-induced excitation of phasic phrenic nerve discharge, which is characterized by high-amplitude, rapid-rate-of-rise, short-duration bursts, on the complexity of the central inspiratory neural controller in the vagotomized, chloralose-anesthetized adult cat model. To assess inspiratory neural network complexity, we calculated the ApEn and MSEn of phrenic nerve bursts during eupneic (basal) discharge and during pre-B?tC-induced excitation of phasic inspiratory bursts. Chemical stimulation of the pre-B?tC using DL-homocysteic acid (DLH; 10 mM; 10-20 nl; n=10) significantly reduced the ApEn from 0.982+/-0.066 (mean+/-SE) to 0.664+/-0.067 (P<0.001) followed by recovery ( approximately 1-2 min after DLH) of the ApEn to 1.014+/-0.067; a slightly enhanced magnitude reduction in MSEn was observed. Focal pre-B?tC hypoxia (induced by sodium cyanide; NaCN; 1 mM; 20 nl; n=2) also elicited a reduction in both ApEn and MSEn, similar to those observed for the DLH-induced response. These observations demonstrate that activation of the pre-B?tC reduces inspiratory network complexity, suggesting a role for the pre-B?tC in regulation of complex respiratory dynamics.     

Cooperation of intrinsic bursting and calcium oscillations underlying activity patterns of model pre-Bötzinger complex neurons

Activity of neurons in the pre-Bötzinger complex (pre-BötC) within the mammalian brainstem drives the inspiratory phase of the respiratory rhythm. Experimental results have suggested that multiple bursting mechanisms based on a calcium-activated nonspecific cationic (CAN) current, a persistent sodium (NaP) current, and calcium dynamics may be incorporated within the pre-BötC. Previous modeling works have incorporated representations of some or all of these mechanisms. In this study, we consider a single-compartment model of a pre-BötC inspiratory neuron that encompasses particular aspects of all of these features. We present a novel mathematical analysis of the interaction of the corresponding rhythmic mechanisms arising in the model, including square-wave bursting and autonomous calcium oscillations, which requires treatment of a system of differential equations incorporating three slow variables.     

Dual oscillator model of the respiratory neuronal network generating quantal slowing of respiratory rhythm

We developed a dual oscillator model to facilitate the understanding of dynamic interactions between the parafacial respiratory group (pFRG) and the preBötzinger complex (preBötC) neurons in the respiratory rhythm generation. Both neuronal groups were modeled as groups of 81 interconnected pacemaker neurons; the bursting cell model described by Butera and others [model 1 in Butera et al. (J Neurophysiol 81:382–397, 1999a)] were used to model the pacemaker neurons. We assumed (1) both pFRG and preBötC networks are rhythm generators, (2) preBötC receives excitatory inputs from pFRG, and pFRG receives inhibitory inputs from preBötC, and (3) persistent Na⁺ current conductance and synaptic current conductances are randomly distributed within each population. Our model could reproduce 1:1 coupling of bursting rhythms between pFRG and preBötC with the characteristic biphasic firing pattern of pFRG neurons, i.e., firings during pre-inspiratory and post-inspiratory phases. Compatible with experimental results, the model predicted the changes in firing pattern of pFRG neurons from biphasic expiratory to monophasic inspiratory, synchronous with preBötC neurons. Quantal slowing, a phenomena of prolonged respiratory period that jumps non-deterministically to integer multiples of the control period, was observed when the excitability of preBötC network decreased while strengths of synaptic connections between the two groups remained unchanged, suggesting that, in contrast to the earlier suggestions (Mellen et al., Neuron 37:821–826, 2003; Wittmeier et al., Proc Natl Acad Sci USA 105(46):18000–18005, 2008), quantal slowing could occur without suppressed or stochastic excitatory synaptic transmission. With a reduced excitability of preBötC network, the breakdown of synchronous bursting of preBötC neurons was predicted by simulation. We suggest that quantal slowing could result from a breakdown of synchronized bursting within the preBötC.     

Dopamine Receptor 1 Modulates the Discharge Activities of Inspiratory and Biphasic Expiratory Neurons via cAMP-Dependent Pathways

Dopamine receptor 1 (D₁R) plays an essential role in regulating respiratory activity in mammals, however, little is known about how this receptor acts to modulate the basic respiratory rhythmogenesis. Here, by simultaneously recording the discharge activities of biphasic expiratory (biphasic E) neurons/inspiratory (I) neurons and the XII nerve rootlets from brainstem slices, we found that the application of D₁R agonist cis-(±)-1-(aminomethyl)-3,4-dihydro-3-phenyl-1H-2-benzopyran-5,6-diolhydrochloride (A68930, 5 μM), or forskolin, an intracellular cAMP-increasing agent, substantially decreased respiratory cycle and expiratory time of both types of neurons, and elevated the integral amplitude and frequency of XII nerve rootlets discharge. These changes were reversed by subsequent application of their antagonists SCH-23390 and Rp-Adenosine 3′,5′-cyclic monophosphorothioate triethylammonium salt hydrate (Rp-cAMPS), respectively. Importantly, after pretreatment with Rp-cAMPS, the effects of A68930 in both types of neurons were blocked, suggestive of a cAMP-dependent action of A68930. Thus, the current study indicates that D₁R may modulate basic breathing rhythmogenesis via cAMP-dependent mechanisms.     

Post-Hypoxic Recovery of Respiratory Rhythm Generation Is Gender Dependent

The preBötzinger complex (preBötC) is a critical neuronal network for the generation of breathing. Lesioning the preBötC abolishes respiration, while when isolated in vitro, the preBötC continues to generate respiratory rhythmic activity. Although several factors influence rhythmogenesis from this network, little is known about how gender may affect preBötC function. This study examines the influence of gender on respiratory activity and in vitro rhythmogenesis from the preBötC. Recordings of respiratory activity from neonatal mice (P10–13) show that sustained post-hypoxic depression occurs with greater frequency in males compared to females. Moreover, extracellular population recordings from the preBötC in neonatal brainstem slices (P10–13) reveal that the time to the first inspiratory burst following reoxygenation (TTFB) is significantly delayed in male rhythmogenesis when compared to the female rhythms. Altering activity of ATP sensitive potassium channels (K_ATP) with either the agonist, diazoxide, or the antagonist, tolbutamide, eliminates differences in TTFB. By contrast, glucose supplementation improves post-hypoxic recovery of female but not male rhythmogenesis. We conclude that post-hypoxic recovery of respiration is gender dependent, which is, in part, centrally manifested at the level of the preBötC. Moreover, these findings provide potential insight into the basis of increased male vulnerability in a variety of conditions such as Sudden Infant Death Syndrome (SIDS).     

Reflex control of inspiratory duration in newborn infants

We applied graded resistive and elastic loads and total airway occlusions to single inspirations in six full-term healthy infants on days 2-3 of life to investigate the effect on neural and mechanical inspiratory duration (TI). The infants breathed through a face mask and pneumotachograph, and flow, volume, airway pressure, and diaphragm electromyogram (EMG) were recorded. Loads were applied to the inspiratory outlet of a two-way respiratory valve using a manifold system. Application of all loads resulted in inspired volumes decreased from control (P less than 0.001), and changes were progressive with increasing loads. TI measured from the pattern of the diaphragm EMG (TIEMG) was prolonged from control by application of all elastic and resistive loads and by total airway occlusions, resulting in a single curvilinear relationship between inspired volume and TIEMG that was independent of inspired volume trajectory. In contrast, when TI was measured from the pattern of airflow, the effect of loading on the mechanical time constant of the respiratory system resulted in different inspired volume-TI relationships for elastic and resistive loads. Mechanical and neural inspired volume and duration of the following unloaded inspiration were unchanged from control values. These findings indicate that neural inspiratory timing in infants depends on magnitude of phasic volume change during inspiration. They are consistent with the hypothesis that termination of inspiration is accomplished by an "off-switch" mechanism and that inspired volume determines the level of vagally mediated inspiratory inhibition to trigger this mechanism.     

Modeling the effects of extracellular potassium on bursting properties in pre-Bötzinger complex neurons

There are many types of neurons that intrinsically generate rhythmic bursting activity, even when isolated, and these neurons underlie several specific motor behaviors. Rhythmic neurons that drive the inspiratory phase of respiration are located in the medullary pre-Bötzinger Complex (pre-BötC). However, it is not known if their rhythmic bursting is the result of intrinsic mechanisms or synaptic interactions. In many cases, for bursting to occur, the excitability of these neurons needs to be elevated. This excitation is provided in vitro (e.g. in slices), by increasing extracellular potassium concentration (K _out ) well beyond physiologic levels. Elevated K _out shifts the reversal potentials for all potassium currents including the potassium component of leakage to higher values. However, how an increase in K _out , and the resultant changes in potassium currents, induce bursting activity, have yet to be established. Moreover, it is not known if the endogenous bursting induced in vitro is representative of neural behavior in vivo. Our modeling study examines the interplay between K _out , excitability, and selected currents, as they relate to endogenous rhythmic bursting. Starting with a Hodgkin-Huxley formalization of a pre-BötC neuron, a potassium ion component was incorporated into the leakage current, and model behaviors were investigated at varying concentrations of K _out . Our simulations show that endogenous bursting activity, evoked in vitro by elevation of K _out , is the result of a specific relationship between the leakage and voltage-dependent, delayed rectifier potassium currents, which may not be observed at physiological levels of extracellular potassium.     

Respiration in energy-transducing membranes of the thermophilic cyanobacterium Mastigocladus laminosus: I. Relation of the respiratory and photosynthetic electron transport

The thermophilic cyanobacterium Mastigocladus laminosus was grown at different CO₂ concentrations and temperatures. Respiratory and photosynthetic electron transport in isolated membranes were measured and their activities were compared. Cells grown at low CO₂ concentration showed respiratory electron transport, whereas Photosystem-II-dependent transport was optimal in cells grown at high CO₂ concentrations. The respiratory electron transport from NADH and succinate were KCN-sensitive, whereas NADPH-dependent O₂ uptake was not. It could be shown that NADH and succinate donate electrons in the photosynthetic electron pathway via Photosystem I. In cytochrome-c-553-depleted membranes added cytochrome c-553 could stimulate photosynthetic and respiratory electron transport. A common electron transport pathway between the quinone and cytochrome c is postulated.     

Regulation of Dissimilatory Fe(III) Reduction Activity in Shewanella putrefaciens

Under anaerobic conditions, Shewanella putrefaciens is capable of respiratory-chain-linked, high-rate dissimilatory iron reduction via both a constitutive and inducible Fe(III)-reducing system. In the presence of low levels of dissolved oxygen, however, iron reduction by this microorganism is extremely slow. Fe(II)-trapping experiments in which Fe(III) and O₂ were presented simultaneously to batch cultures of S. putrefaciens indicated that autoxidation of Fe(II) was not responsible for the absence of Fe(III) reduction. Inhibition of cytochrome oxidase with CN⁻ resulted in a high rate of Fe(III) reduction in the presence of dissolved O₂, which suggested that respiratory control mechanisms did not involve inhibition of Fe(III) reductase activities or Fe(III) transport by molecular oxygen. Decreasing the intracellular ATP concentrations by using an uncoupler, 2,4-dinitrophenol, did not increase Fe(III) reduction, indicating that the reduction rate was not controlled by the energy status of the cell. Control of electron transport at branch points could account for the observed pattern of respiration in the presence of the competing electron acceptors Fe(III) and O₂.     

A model of the central and reflex inhibition of inspiration in the cat

An attempt is made to summarize the results obtained in previous work from this and other laboratories on the steady state and transient relationships between the mechanical and neural events in breathing and their precise timing in the breathing cycle at different blood chemical demands for ventilation and at different body temperatures, and to fit these results into a functional and realistic model of the bulbo-pontine inspiratory off-switch mechanisms. The experimentally based requirements for the model are briefly described and listed. After a presentation of the model in qualitative terms its functional properties are considered quantitatively and compared with the performance of the real, biological system. This has been achieved by assuming some simple mathematical approximations for the activities of the introduced physiological parameters and their chemical “drive” dependence. The gaps in our present knowledge are pointed out and some key experiments suggested. The proposed model is consistent with the main conclusions reached in previous work from this laboratory that there are three neural submechanisms which are mainly responsible for the effects of increased CO₂ on ventilation: 1) a rise in the inspiratory off-switch threshold, 2) an increased rate of rise of the centrally generated inspiratory activity that projects to the off-switch mechanism (and to the spinal respiratory motoneurons), and 3) the vagal volume feed-back. Of these 1) and 2) are mainly responsible for the increase in tidal volume, whereas the vagal volume feed-back is mainly responsible for the increase in respiratory rate. The comparison between the model behaviour and experimental data suggest that the slight CO₂ sensitivity of the pulmonary stretch receptors recently reported on, has to be taken into account. The model studies have suggested the increase in respiratory rate with increased temperature may be due either to an increased rate of rise of inspiratory activity or to a decreased off-switch threshold, or both in combination. The mechanism controlling the expiratory durations are briefly discussed.     

Pacemaker properties of respiratory neurons of the ventrolateral medullary regions in early postnatal rats

Spike activity of respiratory neurons of the ventrolateral medullary regions was studied under conditions of blocking of synaptic transmission. The experiments were carried out on superfusedin situ semi-isolated medullo-spinal preparations (SIMSP) of newborn (1st day of life) and 4- to 5-day-old rats. Part of the pre-inspiratory and (to a somewhat lesser extent) expiratory neurons of newborn rats appeared most resistive to superfusion of preparations with a low-Ca²⁺ (0.2 mM) and Mg²⁺-rich (5.0 mM) solution. Spike activity in some neurons of these groups was preserved up to 40 and 25 min, respectively, after mass inspiratory discharges in then. phrenicus had disappeared. Similar neurons in 4- to 5-day-old SIMSP were less resistive. Inspiratory neurons in animals of both age groups demonstrated no pacemaker properties. Coagulation of the regions where pre-inspiratory neurons are localized (the retrofacial zone) did not evoke irreversible blockade of respiratory rhythm in all SIMSP of 4- to-5-day-old rats and in most SIMSP of newborn animals. At the same time, coagulation of the zone where inspiratory neurons are concentrated (the pre-Bötzinger complex) resulted in the blockade of respiratory rhythm in all SIMSP, with no exceptions.Neirofiziologiya/Neurophysiology, Vol. 28, No. 6, pp. 273–284, November–December, 1996.