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WIREs Syst Biol Med
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Computational models of the neural control of breathing

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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 This article is categorized under: Analytical and Computational Methods > Computational Methods Physiology > Mammalian Physiology in Health and Disease
Interactions between Bötzinger complex/pre‐Bötzinger complex (BötC/pre‐BötC) and retrotrapezoid nucleus/ parafacial respiratory group (RTN/pFRG) affect timing of late‐E neuron activation in hypercapnia. (a) Lumped schematic illustration of the relation between the BötC/pre‐BötC (encompassing pre‐I/I, early‐I, post‐I, and aug‐E populations) and RTN/pFRG components of the respiratory network. RTN/pFRG activity can be recruited by hypercapnia, implemented as a direct excitation in computational models, or by hypoxia, implemented as a reduction of pontine drive yielding an effective drop in post‐I inhibitory output (maroon arrows). Red arrows denote excitatory pathways, while connections ending in circles represent inhibitory interactions. (Reprinted with permission from Ref . Copyright 2010) (b) In an activity‐based, nonspiking computational model, starting from simulated hypercapnia with monophasic activation of RTN/pFRG (labeled as late‐E on the y‐axis) in the late‐E phase of each respiratory cycle (compare late‐E timing to pre‐I, early‐I, post‐I, and aug‐E), hypoxia simulated by progressive reduction of pontine drive (bottom) yields a gradual shift in the timing of RTN/pFRG activation. With partial reduction of drive, activation shifts to the post‐I phase (middle), while additional loss of drive results in biphasic activation. Note as well the loss of post‐I activity and change in aug‐E activity profile with decreased drive. (Reprinted with permission from Ref . Copyright 2011)
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Augmented respiratory central pattern generator (CPG) model produces experimentally observed quantal acceleration of late‐E activity in hypercapnia. (a) Model schematic. In addition to components shown in Figure (a), a late‐E population with oscillatory capabilities supported by INaP is included. This population makes and receives a variety of synaptic connections as shown. In particular, it excites a caudal ventral respiratory group (cVRG) population that drives motor output via the abdominal nerve (AbN). Note that hypercapnia is implemented as an additional drive to the late‐E population while hypoxia is simulated as a decrease in the output from the pons. In a perfused rat brainstem‐spinal cord preparation, increased perfusate CO2 yields quantal acceleration of late‐E AbN activity. (b1)–(b4) Simultaneously recoded raw activity (bottom) and integrated activity (top) of phrenic nerve (PN) and AbN during normocapnia ((b1), 5% CO2) characterized by the absence of activity in the AbN, and with the development of hypercapnia, during which the ratio between the AbN and PN frequencies steps from 1:3 to 1:2 ((b2), (b3); 7% CO2) to 1:1 ((b4) 10% CO2). (bottom) Oscillation periods in the PN (red squares) and AbN (black circles) shown as functions of time throughout the experiment. The AbN late‐E bursts were phase‐locked to the PN bursts with a ratio that increased quantally from 1:5 to 1:1. The CO2 in the perfusate was changed at the times indicated by short arrows and vertical dashed lines. The episodes shown in (b1)–(b4) occurred at the times indicated by large arrows. (c1)–(c3) Increasing hypercapnic drive to the late‐E neuron yields quantal acceleration of late‐E activity in the activity‐based, nonspiking model. Outputs from model components at particular levels of hypercapnic drive show integer ratios of late‐E activations to full respiratory cycles as well as phase‐locking of late‐E activity to occur at the transition between expiration and inspiration marked by decaying post‐I activity and maximal aug‐E activity. (c4) Analogously to the experimental results, the time courses of late‐E (black dots) and early‐I (red dots) periods (defined as durations between successive activations) show a quantal acceleration from 1:5 to 1:1 with progressive increases in drive to the late‐E neuron, and the early‐I period remains approximately constant throughout. Arrows indicate drive levels used in (c1)–(c3). (Figure (a) and (b1)–(b4, bottom)—Reprinted with permission from Ref . Copyright 2010; Figure (c1)–(c4)—Reprinted with permission from Ref . Copyright 2011)
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Organization of the brainstem respiratory CPG and activities of the main respiratory populations. (a) Schematic representation of the spatial and functional organization of key neural structures and core circuits of the mammalian brainstem respiratory CPG distributed rostrocaudally within the lateral pons and medulla oblongata. These structures are contained on each side of the brainstem with bilateral interconnections (not shown). The critical populations of excitatory and inhibitory neurons are located within three anatomically defined compartments (gray regions): the BötC, pre‐BötC, and rVRG. These populations receive tonic excitatory inputs (‘tonic drives’) from sources/compartments located more rostrally in the dorsolateral pons and ventral RTN, as well as in the raphé, which control the excitation state of all neuron populations. These drive sources are shown as green triangles with drives indicated by green arrows. The drives from pontine and RTN sources affect all neuron populations in the model but with different weights. Most of these connections are not shown in this and following figures (only outgoing rays are shown) in order not to overcrowd the figures. Inspiratory pre‐I/I and early‐I interneurons in the pre‐BötC compartment, and expiratory post‐I and aug‐E neurons in the adjacent, more rostral BötC compartment, form the core microcircuits generating the rhythmic three‐phase respiratory pattern. In the pre‐BötC, the pre‐I/I excitatory neurons, with INaP functioning as an important conductance mechanism, constitute the circuit generating the inspiratory rhythm and excitatory synaptic drive, which is transmitted to other inspiratory neurons including to the bulbospinal excitatory neurons (ramp‐I) in the rVRG compartment. These rVRG neurons excite phrenic and other spinal inspiratory motoneurons to produce inspiratory motor output. The BötC inhibitory circuits with mutual interconnections to the pre‐BötC early‐I inhibitory neuron population constitute the core circuit interactions coordinating generation of the three respiratory phases. The BötC and pre‐BötC inhibitory neurons also have synaptic connections to the ramp‐I neurons in rVRG: the inhibitory input from early‐I neurons is involved in shaping the ramping pattern of inspiratory activity in these neurons, whereas the inhibitory inputs from post‐I and aug‐E suppress ramp‐I population activity during the expiratory phases. aug‐E, augmenting expiratory neurons; early‐I, early inspiratory neurons; pre‐I/I, pre‐inspiratory/inspiratory neurons; post‐I, post‐inspiratory neurons; ramp‐I, ramp inspiratory neurons. Nomenclature used for each population is based on the phase in which the neurons start generating spikes (pre‐I/I, early‐I, post‐I) and/or by the spiking frequency profile (ramp‐I, aug‐E) (refer to Table ). (b) Representative integrated activities of the main neuronal populations of the BötC, pre‐BötC, and rVRG during the three‐phase respiratory cycle simulated with the conductance‐based population model with the core excitatory and inhibitory circuit configuration as depicted in the schematic shown in (a). The three phases are indicated as I, P‐I (post‐I), and E‐2. Integrated population activities are the total number of spikes per second/number of neurons (50 neurons per population in this example). In the simulations, all of these circuit components received tonic excitatory synaptic drive. Descriptions of the model components and their interactions are given in the text. (Reprinted with permission from Ref . Copyright 2009)
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Respiratory baroreflex. Expiration resetting by transient baroreceptor stimulation simulated in the Baekey et al. model (a) and as experimentally recorded in situ (b). In (a), barostimulus activates the post‐I population, which inhibits aug‐E neurons. After the stimulus ends, the aug‐E neurons activate for the second time. (b) Shows corresponding extracellular recordings and firing rate histograms from post‐I and aug‐E neurons in the BötC. (Reprinted with permission from Ref . Copyright 2010)
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Central chemoreflex. (a) Experimental recordings of respiratory (abdominal and phrenic) and sympathetic motor outputs in an in situ arterially perfused rat brainstem‐spinal cord preparation at different CO2 levels in the perfusate. (b) Simulations of progressive change in CO2 content from hypocapnia to hypercapnia in the control model and the CIH model. Note hypocapnic shifts (toward lower CO2 levels) produce changes in the emergence of late‐expiratory activity in the abdominal nerve (AbN), and in the onset of respiratory activity of the phrenic nerve (PN, apneic threshold) in the CIH model. CIH, chronic intermittent hypoxia; tSN, thoracic sympathetic nerve. (Reprinted with permission from Ref . Copyright 2012)
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Respiratory‐autonomic system interactions. A network diagram representing a combination of models from Baekey et al. and Barnett et al. An excitatory population in the rostral ventrolateral medulla (RVLM) is a pre‐sympathetic population receiving inputs from various respiratory populations that mediate respiratory modulation in the thoracic sympathetic nerve (tSN). Second order baroreceptors in the nucleus of solitary tract (NTS) project to a population of GABAergic neurons in the caudal ventrolateral medulla (CVLM), which in turn inhibit presympathetic RVLM neurons (classical baroreflex). In addition, NTS baroreceptors excite post‐I neurons in Bötzinger complex (BötC, respiratory baroreflex). Second order peripheral chemoreceptors in the NTS excite pre‐BötC pre‐I/I neurons (providing an increase in respiratory frequency), central chemoreceptors in the retrotrapezoid nucleus [RTN, emergence of late‐E activity in the abdominal nerve (AbN) and tSN], and premotor post‐I population in the cVRG (not shown).
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Schematic of the closed‐loop respiratory system model. AbN, abdominal nerve; aug‐E, augmenting expiratory neuron; BötC, Bötzinger complex; cVRG, caudal ventral respiratory group; early‐I, early‐inspiratory neuron; late‐E, late‐expiratory neuron; NTS, nucleus of the tractus solitarius; P(e), excitatory pump cells; P(i), inhibitory pump cells; pFRG, parafacial respiratory group; PN, phrenic nerve; post‐I, post‐inspiratory neuron; pre‐BötC, pre‐Bötzinger complex; pre‐I/I, pre‐inspiratory/inspiratory neuron; PSRs, pulmonary stretch receptors; ramp‐I, ramp‐inspiratory neuron; RTN, retrotrapezoid nucleus; rVRG, rostral ventral respiratory group; VRC, ventral respiratory column. (Reprinted with permission from Ref . Copyright 2014)
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Simulation of progressive hypercapnia with the closed‐loop respiratory system model. (a) Model performance. The top 6 traces represent output activity (normalized firing rate) of the corresponding neurons. The bottom two traces represent the end capillary blood pc (pce) just before the next heartbeat and the retrotrapezoid nucleus (RTN) drive, respectively. The continuous increase of hypercapnia (the gray ramp at the bottom) was induced by increasing CO2 content in the mouth (fcm) from 0 to 10%. Active expiration starts with the first appearance of late‐E discharges (indicated by the left vertical dot‐dashed line at fcm = 2.6%) and reaches the regime with a 1:1 ratio of late‐E to ramp‐I activations at fcm = 7.2% (right dot‐dashed line). As described in the text, each late‐E discharge, representing the activity of abdominal nerve (AbN) output, actuates the abdominal pump that reduces the baseline level of lung volume (see in the VA trace). (b) Changes in tidal volume, breathing rate, and ventilation (relative to normocapnia) with the development of hypercapnia. CO2 content in the mouth fcm was linearly increased from 0 to 10%. Changes in three major breathing characteristics (tidal volume, breathing rate, and ventilation) that would occur without active expiration (simulated by setting AbN = 0) are shown by the corresponding dashed lines. The vertical dot‐dashed lines bound the development (quantal acceleration) of active expiration. (Reprinted with permission from Ref . Copyright 2014)
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