Neural network implementation of a three-phase model of respiratory rhythm generation

A mathematical model of the central neural mechanisms of respiratory rhythm generation is developed. This model assumes that the respiratory cycle consists of three phases: inspiration, post-inspiration, and expiration. Five respiratory neuronal groups are included: inspiratory, late-inspiratory, post-inspiratory, expiratory, and early-inspiratory neurons. Proposed interconnections among these groups are based substantially on previous physiological findings. The model produces a stable limit cycle and generally reproduces the features of the firing patterns of the 5 neuronal groups. When simulated feedback from pulmonary stretch receptors is made to excite late-inspiratory neurons and inhibit early-inspiratory neurons, the model quantitatively reproduces previous observations of the expiratory-prolonging effects of pulses and steps of vagal afferent activity presented in expiration. In addition the model reproduces expected respiratory cycle timing and amplitude responses to change of chemical drive both in the absence and in the presence of simulated stretch receptor feedback. These results demonstrate the feasibility of generating the respiratory rhythm with a simple neural network based on observed respiratory neuronal groups. Other neuronal groups not included in the model may be more important for shaping the waveforms than for generating the basic oscillation.     

A network model for control of inspiratory cutoff by the pneumotaxic center with supportive experimental data in cats

A network model for the control of inspiratory cutoff by the pneumotaxic center (PC) in cats, based on a previously described anatomical model, is proposed. It is postulated that in vagotomized cats early expiratory cells in the PC produce the inspiratory cutoff. The firing patterns of neurons derived from the model were similar to those observed in the PC. Systematic changes in any one of several parameters in the model resulted in a marked change in inspiratory amplitude with no significant change in inspiratory duration; this response is similar to that already observed in vagotomized cats during changes in ventilatory drive. The basic conformation of the model was tested experimentally in the isolated respiratory center preparation of the cat. Discharges of 48 cells in the PC were recorded and the firing patterns analyzed to determine the change in frequency and temporal pattern of activity associated with spontaneous changes in the amplitude and/or duration of inspiration. 47 of the 48 cells exhibited changes in firing pattern that were consistent with the model.     

Respiratory rhythmicity in the cat.

Brain stem respiratory neuron activity in the cat was studied in relation to efferent outflow (phrenic discharge) under the influence of several forcing inputs: 1) CO2 tension: hypocapnia produces disappearance of firing in some neurons, and conversion of respiratory-modulated to continuous (tonic) firing in others. 2) Lung inflation: during the Bruer-Hering reflex, some neurons have "classical" responses and others have "paradoxical" responses (i.e., opposite in direction to peripheral discharge). 3) Electrical stimulation: stimulus trains to the pneumotaxic center region (rostral lateral pons) produce phase-switching, whose threshold is: a) sharp (indicating action of positive-feedback mechanisms), and b) dependent on timing of stimulus delivery (indicating continuous excitability changes during each respiratory phase). Auto- and crosscorrelation analysis revealed the existence of short-term interactions between: a) medullary inspiratory (I) neurons and phrenic motoneurons; b) pairs of medullary I neurons; c) medullary I neurons and expiratory (E) neurons. A model of the respiratory oscillator is presented, in which the processes of conversion of tonic to phasic activity and switching of the respiratory phases are explained by recurrent excitatory and inhibitory loops.     

Evidence that glycine and GABA mediate postsynaptic inhibition of bulbar respiratory neurons in the cat.

Experiments were carried out on decerebrate cats to identify transsynaptic mediators of spontaneous postsynaptic inhibition of bulbar inspiratory and postinspiratory neurons. Somatic membrane potentials were recorded through the central micropipette of a coaxial multibarreled electrode. Blockers of type A gamma-aminobutyric acid (GABA-A) and glycine receptors were iontophoresed extracellularly from peripheral micropipettes surrounding the central pipette. Effective antagonism was demonstrated by iontophoresis of agonists with antagonists; application of strychnine antagonized the action of glycine but not GABA, and application of bicuculline antagonized the action of GABA but not glycine. In both types of neurons, iontophoresis of either antagonist depolarized the somatic membrane and increased input resistance throughout the respiratory cycle. Bicuculline preferentially depolarized the somatic membrane in both types of neurons during inactive phases. Strychnine increased the firing rate of inspiratory neurons during inspiration despite maintenance of somatic membrane potential at preiontophoresis levels. Tetrodotoxin reduced the effects of iontophoresed bicuculline and strychnine, suggesting that the action of the antagonists required presynaptic axonal conduction. The present results suggest that presynaptic release of both GABA and glycine contributes to tonic postsynaptic inhibition of bulbar respiratory neurons. GABA-A receptors appear to contribute to inhibition during inactive phases in inspiratory and postinspiratory neurons, whereas glycinergic mechanisms appear to contribute to inspiratory inhibition in inspiratory neurons.     

昆虫脑中央复合体的结构与功能研究进展

中央复合体是昆虫脑内具有显著特征的一个重要结构,它位于昆虫脑的中央,主要包括四个亚结构,相互间形成高度组织化的网络连接。中央复合体通过大范围神经元与多种感觉神经元和运动神经元相连,是一个控制脑的高级功能的中心。近年来的研究表明中央复合体参与了记忆的形成、运动的协调与控制以及处理偏振光进行导航等多种功能。揭示中央复合体参与以及调控这些复杂功能的神经机制,必将会极大地促进我们在神经回路层次上理解脑的高级复杂功能。     

Hyperoxia, reactive oxygen species, and hyperventilation: oxygen sensitivity of brain stem neurons.

Hyperoxia is a popular model of oxidative stress. However, hyperoxic gas mixtures are routinely used for chemical denervation of peripheral O2 receptors in in vivo studies of respiratory control. The underlying assumption whenever using hyperoxia is that there are no direct effects of molecular O2 and reactive O2 species (ROS) on brain stem function. In addition, control superfusates used routinely for in vitro studies of neurons in brain slices are, in fact, hyperoxic. Again, the assumption is that there are no direct effects of O2 and ROS on neuronal activity. Research contradicts this assumption by demonstrating that O2 has central effects on the brain stem respiratory centers and several effects on neurons in respiratory control areas; these need to be considered whenever hyperoxia is used. This mini-review summarizes the long-recognized, but seldom acknowledged, paradox of respiratory control known as hyperoxic hyperventilation. Several proposed mechanisms are discussed, including the recent hypothesis that hyperoxic hyperventilation is initiated by increased production of ROS during hyperoxia, which directly stimulates central CO2 chemoreceptors in the solitary complex. Hyperoxic hyperventilation may provide clues into the fundamental role of redox signaling and ROS in central control of breathing; moreover, oxidative stress may play a role in respiratory control dysfunction. The practical implications of brain stem O2 and ROS sensitivity are also considered relative to the present uses of hyperoxia in respiratory control research in humans, animals, and brain stem tissues. Recommendations for future research are also proposed.     

Temperature dependence of monoamine-induced pulmonary respiration of mollusc Lymnaea stagnalis

Pulmonary respiration of molluscs (spontaneous and mediated by intracavital injection of monoamines) was studied at different environmental temperatures (5, 15, and 25 degrees C). It was established that monoamines (dopamine, serotonin, adrenalin) did not enlarge the temperature diapason, in which the respiratory behavior was realized. Microelectrode studies of spontaneous electrical activity of neurons from the respiratory network of Lymnaea stagnalis (RPeD1, VD4, cells of the Vi cluster) have shown that the respiratory program, both spontaneous and the monoamine-induced, is terminated in hypothermia. The indicated effects are suggested to be due to temperature dependence of the chemical, predominantly peptidergical, transmission of signal between neurons of the central pattern generator of respiratory pattern in Lymnaea.     

Development of respiratory function in perinatal ontogenesis

In development of respiratory function in rats, mice, and other representatives of placental animals there exists the general plan of formation of rhythm: from single contraction of respiratory musculature to formation of bursts and complexes alternating periodically with pauses and apnea intervals and subsequent rhythm stabilization. These peculiarities are closely connected with the states of sleep and consciousness. A concept is put forward about a certain sequence of functional maturation and ways of regulation of activity of the respiratory rhythm central pacemaker. At the first stage the autogenic rhythmical activity is determined by pacemaker properties of a part of neurons of the medulla rostral ventrolateral part. It is not ruled out that the first respiratory discharges in spinal cord ventral roots might have been a manifestation of the nervous network rhythmogenic properties. The direct sensitivity of central neurons to chemical composition if the medium and to some neutomodulators serves as the first regulatory mechanism. Somewhat later, inhibitory control is established from supramedullary structures, with an increase of role of peripheral receptors in regulation of respiration.     

Temperature dependence of monoamine-induced pulmonary respiration in the mollusc <Emphasis Type="Italic">Lymnaea stagnalis</Emphasis>

Pulmonary respiration (spontaneous and mediated by intracavitary administration of monoamines) has been studied in molluscs at different ambient temperatures (5, 15, and 25°C). Monoamines (dopamine, serotonin, and adrenaline) were established not to broaden the temperature diapason realization of the respiratory behavior. Microelectrode studies of the spontaneous electrical activity of the Lymnaea stagnalis respiratory network neurons (RPeD1, VD4, and Vi-cluster cells) revealed that both spontaneous and monoamine-induced respiration programs had been terminated under hypothermia conditions. The indicated effects are suggested to be due to the temperature dependence of the chemical, predominantly peptidergic, transmission of signal between neurons of the central respiratory rhythm generator in Lymnaea.     

Model-Based Analysis of Mechanisms Responsible for Sleep-Induced Carbon Dioxide Differences

This work describes a comprehensive mathematical model of the human respiratory control system which incorporates the central mechanisms for predicting sleep-induced changes in chemical regulation of ventilation. The model integrates four individual compartments for gas storage and exchange, namely alveolar air, pulmonary blood, tissue capillary blood, body tissues, and gas transport between them. An essential mechanism in the carbon dioxide transport is its dissociation into bicarbonate and acid, where a buffering mechanism through hemoglobin is used to prevent harmfully low pH levels. In the current model, we assume high oxygen levels and consider intracellular hydrogen ion concentration as the principal respiratory control variable. The resulting system of delayed differential equations is solved numerically. With an appropriate choice of key parameters, such as velocity of blood flow and gain of a non-linear controller function, the model provides steady-state results consistent with our experimental observations measured in subjects across sleep onset. Dynamic predictions from the model give new insights into the behaviour of the system in subjects with different buffering capacities and suggest novel hypotheses for future experimental and clinical studies.     

The effect of leu-enkephalin on membrane potential and activity of the rat respiratory center neurons in vitro

In frontal brainstem slices of Wistar rats, the whole-cell patch-clamp recordings showed the effect of opioid peptide leu-enkephalin (10 nM-1 microM) on membrane potential and spontaneous activity pattern of neurons in two divisions of the respiratory center, ventro-lateral area of the solitary tract nucleus, and the pre-B?tzinger complex. Leu-enkephalin induced a membrane hyperpolarization of the respiratory centre neurons and reduction of the spike activity level in spontaneously active units. After administration of leu-enkephalin, a decrease in frequency of bursts was found in bursting cells of the pro-B?tzinger complex; in two cases, there was a transition of bursting activity to tonic one. The data suggest that the mechanism of the central respiratory activity of leu-enkephalin is based on its direct action at the level of membrane of the respiratory centre neurons.     

Entrainment, Instability, Quasi-periodicity, and Chaos in a Compound Neural Oscillator

We studied the dynamical behavior of a class of compound central pattern generator (CPG) models consisting of a simple neural network oscillator driven by both constant and periodic inputs of varying amplitudes, frequencies, and phases. We focused on a specific oscillator composed of two mutually inhibiting types of neuron (inspiratory and expiratory neurons) that may be considered as a minimal model of the mammalian respiratory rhythm generator. The simulation results demonstrated how a simple CPG model— with a minimum number of neurons and mild nonlinearities— may reproduce a host of complex dynamical behaviors under various periodic inputs. In particular, the network oscillated spontaneously only when both neurons received adequate and proportionate constant excitations. In the presence of a periodic source, the spontaneous rhythm was overriden by an entrained oscillation of varying forms depending on the nature of the source. Stable entrained oscillations were inducible by two types of inputs: (1) anti-phase periodic inputs with alternating agonist-antagonist drives to both neurons and (2) a single periodic drive to only one of the neurons. In-phase inputs, which exert periodic drives of similar magnitude and phase relationships to both neurons, resulted in varying disruptions of the entrained oscillations including magnitude attenuation, harmonic and phase distortions, and quasi-periodic interference. In the absence of significant phasic feedback, chaotic motion developed only when the CPG was driven by multiple periodic inputs. Apneic episodes with repetitive alternation of active (intrinsic oscillation) and inactive (cessation of oscillation) states developed when the network was driven by a moderate periodic input of low frequency. %and amplitudes of intermediate strength, Similar results were demonstrated in other, more complex oscillator models (that is, half-center oscillator and three-phase respiratory network model). These theoretical results may have important implications in elucidating the mechanisms of rhythmogenesis in the mature and developing respiratory CPG as well as other compound CPGs in mammalian and invertebrate nervous systems.     

An integrate-and-fire model for synchronized bursting in a network of cultured cortical neurons

It has been suggested that spontaneous synchronous neuronal activity is an essential step in the formation of functional networks in the central nervous system. The key features of this type of activity consist of bursts of action potentials with associated spikes of elevated cytoplasmic calcium. These features are also observed in networks of rat cortical neurons that have been formed in culture. Experimental studies of these cultured networks have led to several hypotheses for the mechanisms underlying the observed synchronized oscillations. In this paper, bursting integrate-and-fire type mathematical models for regular spiking (RS) and intrinsic bursting (IB) neurons are introduced and incorporated through a small-world connection scheme into a two-dimensional excitatory network similar to those in the cultured network. This computer model exhibits spontaneous synchronous activity through mechanisms similar to those hypothesized for the cultured experimental networks. Traces of the membrane potential and cytoplasmic calcium from the model closely match those obtained from experiments. We also consider the impact on network behavior of the IB neurons, the geometry and the small world connection scheme. Action Editor: David Golomb     

Central complex substructures are required for the maintenance of locomotor activity in Drosophila melanogaster

In Drosophila melanogaster, former studies based on structural brain mutants have suggested that the central complex is a higher control center of locomotor behavior. Continuing this investigation we studied the effect of the central complex on the temporal structure of spontaneous locomotor activity in the time domain of a few hours. In an attempt to dissect the internal circuitry of the central complex we perturbed a putative local neuronal network connecting the four neuropil regions of the central complex, the protocerebral bridge, the fan-shape body, the noduli and the ellipsoid body. Two independent and non-invasive methods were applied: mutations affecting the neuroarchitecture of the protocerebral bridge, and the targeted expression of tetanus toxin in small subsets of central complex neurons using the binary enhancer trap P[GAL4] system. All groups of flies with a disturbed component of this network exhibited a common phenotype: a drastic decrease in locomotor activity. While locomotor activity was still clustered in bouts and these were initiated at the normal rate, their duration was reduced. This finding suggests that the bridge and some of its neural connections to the other neuropil regions of the central complex are required for the maintenance but not the initiation of walking. Accepted: 21 June 1999     

Expression and developmental regulation of the Hydra-RFamide and Hydra-LWamide preprohormone genes in Hydra: evidence for transient phases of head formation

Hydra magnipapillata has three distinct genes coding for preprohormones A, B, and C, each yielding a characteristic set of Hydra-RFamide (Arg-Phe-NH2) neuropeptides, and a fourth gene coding for a preprohormone that yields various Hydra-LWamide (Leu-Trp-NH2) neuropeptides. Using a whole-mount double-labeling in situ hybridization technique, we found that each of the four genes is specifically expressed in a different subset of neurons in the ectoderm of adult Hydra. The preprohormone A gene is expressed in neurons of the tentacles, hypostome (a region between tentacles and mouth opening), upper gastric region, and peduncle (an area just above the foot). The preprohormone B gene is exclusively expressed in neurons of the hypostome, whereas the preprohormone C gene is exclusively expressed in neurons of the tentacles. The Hydra-LWamide preprohormone gene is expressed in neurons located in all parts of Hydra with maxima in tentacles, hypostome, and basal disk (foot). Studies on animals regenerating a head showed that the prepro-Hydra-LWamide gene is expressed first, followed by the preprohormone A and subsequently the preprohormone C and the preprohormone B genes. This sequence of events could be explained by a model based on positional values in a morphogen gradient. Our head-regeneration experiments also give support for transient phases of head formation: first tentacle-specific preprohormone C neurons (frequently associated with a small tentacle bud) appear at the center of the regenerating tip, which they are then replaced by hypostome-specific preprohormone B neurons. Thus, the regenerating tip first attains a tentacle-like appearance and only later this tip develops into a hypostome. In a developing bud of Hydra, tentacle-specific preprohormone C neurons and hypostome-specific preprohormone B neurons appear about simultaneously in their correct positions, but during a later phase of head development, additional tentacle-specific preprohormone C neurons appear as a ring at the center of the hypostome and then disappear again. Nerve-free Hydra consisting of only epithelial cells do not express the preprohormone A, B, or C or the LWamide preprohormone genes. These animals, however, have a normal phenotype, showing that the preprohormone A, B, and C and the LWamide genes are not essential for the basic pattern formation of Hydra.     

Development of respiratory function in perinatal ontogenesis

In development of respiratory function in rats, mice, and other representatives of placental animals there exists the general plan of formation of rhythm: from single contractions of respiratory musculature to formation of bursts and complexes alternating periodically with pauses and apnea intervals and subsequent rhythm stabilization. These peculiarities are closely connected with the states of sleep and wakefulness. A concept is put forward about a certain sequence of functional maturation and ways of regulation of activity of the breathing rhythm pacemaker. At the first stage the autogenic rhythmical activity is determined by pacemaker properties of a part of neurons of the medulla rostral ventrolateral part. It cannot be ruled out that the first respiratory discharges in spinal cord ventral roots might have been a manifestation of the nervous network rhythmogenic properties. The direct sensitivity of central neurons to chemical composition of the medium and to some neuromodulators serves as the first regulatory mechanism. Somewhat later, inhibitory control is established from supramedullary structures, with an increase of the role of peripheral receptors in regulation of respiration.     

Pattern association and retrieval in a continuous neural system

This paper studies the behavior of a large body of neurons in the continuum limit. A mathematical characterization of such systems is obtained by approximating the inverse input-output nonlinearity of a cell (or an assembly of cells) by three adjustable linearized sections. The associative spatio-temporal patterns for storage in the neural system are obtained by using approaches analogous to solving space-time field equations in physics. A noise-reducing equation is also derived from this neural model. In addition, conditions that make a noisy pattern retrievable are identified. Based on these analyses, a visual cortex model is proposed and an exact characterization of the patterns that are storable in this cortex is obtained. Furthermore, we show that this model achieves pattern association that is invariant to scaling, translation, rotation and mirror-reflection.     

Optimization behavior of brainstem respiratory neurons

A recent model of respiratory control suggested that the steady-state respiratory responses to CO₂ and exercise may be governed by an optimal control law in the brainstem respiratory neurons. It was not certain, however, whether such complex optimization behavior could be accomplished by a realistic biological neural network. To test this hypothesis, we developed a hybrid computer-neural model in which the dynamics of the lung, brain and other tissue compartments were simulated on a digital computer. Mimicking the controller was a human subject who pedalled on a bicycle with varying speed (analog of ventilatory output) with a view to minimize an analog signal of the total cost of breathing (chemical and mechanical) which was computed interactively and displayed on an oscilloscope. In this manner, the visuomotor cortex served as a proxy (homolog) of the brainstem respiratory neurons in the model. Results in 4 subjects showed a linear steady-state ventilatory CO₂ response to arterial PCO₂ during simulated CO₂ inhalation and a nearly isocapnic steady-state response during simulated exercise. Thus, neural optimization is a plausible mechanism for respiratory control during exercise and can be achieved by a neural network with cognitive computational ability without the need for an exercise stimulus.     

Limiting models for calcification in fibrous tissues adjacent to orthopedic implants: Variational indicator functions and influences of implant stiffness

Calcification and eventual integration of orthopedic implants into bone is important to many load-bearing devices, and the influence of load and implant stiffness on this process are assessed in this mathematical modelling study. Three research questions are posed in this study. First, can limiting material models provide useful information on the overall behavior of the tissue adjacent to a loaded orthopedic implant? Second, can the limiting models lead to optimization criteria? Third, can an optimization approach be used to differentiate between the four prospective remodeling rate equations which are proposed? The answers are yes, yes, and no, respectively. A two degree of freedom lumped parameter model for axial loading of an intramedullary implant is considered. Two limiting composite material models are used, and the strain energy density in the calcified and non-calcified phases are assessed as stimuli for calcification. The rate equations posed here assume that the calcified material volume fraction decreases at high strain-energy densities, and increases at small strain-energy densities. In all four cases (both models, both phases) the steady states for these rate equations find equilibrium points of indicator functions which are a weighted sum of total strain energy and the mass of calcified tissue in the layer considered. The weights on strain-energy density and mass differ in each case. This shows that for appropriate choices of parameters, all four models can yield the same results, and it also shows that an optimization approach does not uniquely determine the appropriate rate equation in these cases. The rate equations showed complicated dynamic behavior and a phase-plane analysis was used which led to upper bounds on load, which depended on implant stiffness and distal support. The predictions of the four cases studied are compared.