Daniele Sch Ön
email: daniele.schon@univ-amu.fr

Barbara Tillmann

Daniele Sch

Issue: The Neurosciences and Music V Short-and long-term rhythmic interventions: perspectives for language rehabilitation

Keywords: music, rhythm, language, rehabilitation, entrainment nyas12635 W3G-nyas.cls

This paper brings together different perspectives on the investigation and understanding of temporal processing and temporal expectations. We aim to bridge different temporal deficit hypotheses in dyslexia, dysphasia, or deafness in a larger framework, taking into account multiple nested temporal scales. We present data testing the hypothesis that temporal attention can be influenced by an external rhythmic auditory stimulation (i.e., musical rhythm) and benefits subsequent language processing, including syntax processing and speech production. We also present data testing the hypothesis that phonological awareness can be influenced by several months of musical training and, more particularly, rhythmic training, which in turn improves reading skills. Together, our data support the hypothesis of a causal role of rhythm-based processing for language processing and acquisition. These results open new avenues for music-based remediation of language and hearing impairment.

Dynamics of attending

Temporal expectations are linked to synchroniza-Q1 tion, entrainment, and phase coupling of exter-Q2 nal stimuli and internal oscillators. An illustrative example of phase coupling can be seen in a setup in which several metronomes set to the same tempo but with different phases, once placed on a moving table, will synchronize and end up sharing the same phase (see https://www.youtube.com/watch?v= Aaxw4zbULMs). Once energy can travel from one metronome to the other via the moving table, metronomes synchronize, and the minimal energy state of the system is reached. This example of phase coupling can be seen as a good metaphor of how music, that is, periodic and temporally structured sounds, can synchronize and entrain neural populations via traveling waves (first acoustic and then neuroelectric).

In regard to synchronization and entrainment, Jones [START_REF] Jones | Time, our lost dimension: toward a new theory of perception, attention, and memory[END_REF] has started to develop a theoretical framework of temporal attention. The hypothesis of this dynamic attending theory (DAT) is that attention is not evenly distributed over time, but rather fluctuates (or oscillates) in time via cycles. These oscillations would be driven by a phase coupling between internal (neuronal) oscillators and (external) periodicities in the environment (e.g., music). There can be different frequency relationships with that of the external regulator, leading to metric hierarchical structures in music. [START_REF] Jones | Musical time[END_REF] Thus, attentional energy would be maximal at most expected moments in time (that is, moments with high probability that an event would occur). The DAT was first described for and applied to music (see, in particular, Ref. 3), and then also to speech or movement. Large and Jones [START_REF] Large | The dynamics of attending: how we track time-varying events[END_REF] have proposed a mathematical model describing entrainment phenomena in music perception. In this model, the periodic music structure entrains the attentional oscillatory cycles. Moreover, the metrical structure (the organization of strong and weak beats) also affects these attentional fluctuations, engendering larger peaks at strong beats. [START_REF] Jones | Musical time[END_REF][START_REF] Large | The dynamics of attending: how we track time-varying events[END_REF] doi: 10.1111/nyas.12635 The DAT has been empirically tested in the auditory domain for musical material, speech material, as well as cross-modal perceptual setups to test for interactions with visual perception. The various data sets have shown that perception is enhanced for musical events (tones, chords) that are presented at highly expected moments in time, notably on the beat. [START_REF] Jones | Temporal aspects of stimulus-driven attending in dynamic arrays[END_REF][START_REF] Schmuckler | Harmonic and rhythmic influences on musical expectancy[END_REF][7] More recently, a series of cross-modal experiments has shown that this enhancement is not only limited to the auditory modality but can also benefit visual processing. Indeed, when one is listening to an auditory regular sequence (e.g., a metronome), processing of visual stimuli is facilitated when the stimulus is presented on the beat in comparison to when it is presented off the beat. [8][START_REF] Miller | When what you hear influences when you see: listening to an auditory rhythm influences the temporal allocation of visual attention[END_REF][START_REF] Brochard | Got rhythm . . . for better and for worse. Cross-modal effects of auditory rhythm on visual word recognition[END_REF] The facilitated processing is not limited to the comparison between presentations on the beat versus off the beat: it also depends on the structural hierarchy of beats. In a recent experiment, we presented visual or auditory targets simultaneously to a piece of music (e.g., a Bach Solo Sonata for violin). Presenting visual stimuli on the beat or off the beat had a relatively small effect. In contrast, targets presented on the strong beat or right before, showed shorter RT compared to those presented on or right before a weaker beat. [START_REF] Bolger | Rhythm implicitly affects temporal orienting of attention across modalities[END_REF] It thus seems that the rhythm of attention is locked to the occurrences of strong beat, with weak beats in the trough of the oscillation. With respect to neural substrates, this effect seems to rely on the left intraparietal lobule, a region that has been shown to be involved in the temporal orienting of attention, the ability to flexibly and voluntarily orient attention to moments in time. [START_REF] Coull | Dissociating explicit timing from temporal expectation with fMRI[END_REF] More precisely, the functional connectivity between this region and a motor network (premotor and motor regions) as well as a sensory network (auditory and visual cortices) seems to fluctuate over time, notably with peaks of connectivity strength at strong beats. This possibly reflects a top-down attentional mechanism (highly coupled to the motor network) that modulates the metabolic activity in auditory and visual areas and influences event processing. [START_REF] Bolger | Metrical rhythm implicitly orients attention in time as indexed by improved target detection and left inferior parietal activation[END_REF]

Extending the DAT from music to speech

The DAT framework was first developed for musical material for both pitch and time dimensions, that is, listeners' expectations for what kind of pitch will come next and when in time it will occur. This attentional framework (temporal expectations) has been also applied for speech material, even though the periodicity (isochrony) in the speech signal is less pronounced than the periodicity in the musical signal. [START_REF] Dalla Bella | Why movement is captured by music, but less by speech: role of temporal regularity[END_REF] Although quasi-isochronous beats are found across all music cultures (and allow motor synchronization), in conversational speech, and although rhythmic grouping certainly shapes speech perception, the degree of regularity is certainly weaker. [START_REF] Patel | Music, Language, and the Brain[END_REF] Nonetheless, when one is listening to speech, the temporal regularity of the alternating stressed and unstressed syllables would cause the listener's attention to time-lock (couple) to this temporal pattern going from one stress to the following. Interestingly, this effect goes beyond the physical salience of the phonemes and, rather, seems to rely on the fact that the perception of salient events, such as stressed syllables, generates expectancies concerning later events (position of the next stress). [START_REF] Martin | Rhythmic (hierarchical) versus serial structure in speech and other behavior[END_REF] Thus, similarly to what has been suggested above in the musical domain, attention is directed to points at which stressed syllables are expected to occur. In a similar manner, as pitches are better processed when they occur at expected time points, syllables and words are better processed when they occur at expected time points. Temporal regularity and predictability of speech can enhance different aspects of speech processing, going from phoneme perception over lexical processing to syntax and semantic processing. [START_REF] Pitt | The use of rhythm in attending to speech[END_REF][START_REF] Falk | When speech sounds like music[END_REF][START_REF] Schmidt-Kassow | Entrainment of syntactic processing? ERP-responses to predictable time intervals during syntactic reanalysis[END_REF][START_REF] Quené | Effects of timing regularity and metrical expectancy on spoken-word perception[END_REF] On the basis of these findings, namely the effects of temporal regularity and predictability on both music and speech processing, we now present three possible ways of combining music and speech in different experimental designs. The aim of these designs is to see whether, and to what extent, music can entrain attentional processes and affect speech (and language) perception and production and possibly explain the potential underlying mechanisms. These designs differ with respect to their time scale, going from short over medium to longer time periods, and with respect to the role of the participant with respect to the music (active or passive listening). The hypothesis that musical structures might boost temporal processing that benefits linguistic processing even in an impaired language system fits with the conclusion of Thomson and Goswami 21 stating, " . . . there is value in the use of rhythmic interventions for children with both developmental dyslexia and SLI."

Rhythmic speech cuing

We recently investigated whether complex metrical rhythms corresponding to the prosodic structure of sentences can enhance phonological processing via rhythmic expectations. In this paradigm, participants listen to a metrical sequence immediately followed by a word or a sentence and perform a phoneme detection task. Thus, the metrical sequence is a sort of cue to the temporal structure of the following speech, and we refer to this paradigm as rhythmic cuing, to distinguish it from rhythmic priming, which we describe in the next section. The cue's meter can either match or mismatch the prosody of the sentence with respect to both stress patterns and number of elements. We collected both behavioral and electrophysiological data using a phoneme detection task (e.g., "say whether the last syllable of the sentence contains the sound [a]").

Providing a matching rhythmic cue resulted in faster reaction times, thus revealing a cross-domain effect of the musical metrical structure on the phonological processing of speech. This effect was larger when participants received audiomotor training with the rhythmic sequences before the task. In this training, participants were asked to reproduce the rhythmic pattern several times. This possibly allowed them to internalize more finely the temporal structure of the cues. Electrophysiological data confirmed these behavioral effects, showing a mismatch-like negative component, possibly originating in the auditory associative cortices, clearly visible when the speech target did not match the metrical structure of the previous temporal sequence. [START_REF] Cason | Rhythmic priming enhances the phonological processing of speech[END_REF][START_REF] Cason | Under review. Bridging music and speech rhythm: rhythmic priming and audio-motor training affect speech perception[END_REF] Building on these findings on speech perception, we decided to study whether speech production may also benefit from rhythmic cuing, because this may have important implications about how rhythm can be used in speech therapies. More precisely, we studied whether metrical cuing has an effect on phonological production abilities in prelingually deaf children (wearing a hearing device). In our study, children listened to a rhythmical isochronous sequence (drum sounds) and had to reproduce it vocally (using two phonemes: ([ti] and [pa]). Then, they listened to a sentence and had to repeat it. The sentence either matched or mismatched the metrical structure of the rhythmical sequence (i.e., same number of syllables but with a different stress pattern). There was also a baseline condition wherein sentences were not preceded by a rhythmical sequence. Matching conditions resulted in a greater phonological accuracy of spoken sentences compared to baseline and mismatching conditions at several levels of phonological measurements (the production of vowels, consonants, syllables, and words), suggesting that rhythmic cuing can enhance phonological production. This facilitation may take place via an enhanced perception of the target sentence, similarly to the studies presented above. Nonetheless, on the basis of previous findings described above, [START_REF] Cason | Under review. Bridging music and speech rhythm: rhythmic priming and audio-motor training affect speech perception[END_REF] we suggest that both an enhanced entrainment of speech motor rhythms through rhythmic listening and a greater familiarity of speech motor rhythms through rhythmic training contribute to the greater accuracy in speech imitation.

Rhythmic priming of language processing

Another way of combining music and speech is to use the musical material as an auditory rhythmic stimulation to boost language processing, in particular language processing that requires temporal sequencing and segmentation (at local and/or global levels). In this case, in contrast to rhythmic cuing wherein the stimulation is short and mimics the temporal structure of the following sentence, the stimulation is typically longer and does not necessarily have a "precise" temporal relation with the following linguistic task.

Linguistic meter has been described as a good candidate to support segmentation, [START_REF] Cutler | The perception of rhythm in language[END_REF] and regular predictable presentation has been shown to influence syntax processing. [START_REF] Schmidt-Kassow | Entrainment of syntactic processing? ERP-responses to predictable time intervals during syntactic reanalysis[END_REF][START_REF] Schmidt-Kassow | Event-related brain potentials suggest a late interaction of meter and syntax in the P600[END_REF] As successful metric processing allows for the prediction of when a subsequent element will occur, a metric pattern serves as a "framework" enabling listeners to sequence linguistic input and to build up syntactic hierarchies. Kotz et al. [START_REF] Kotz | The basal ganglia are receptive to rhythmic compensation during auditory syntactic processing: ERP patient data[END_REF] have shown that metrical stimulation makes it possible to compensate for a sequencing deficit in sentence processing in patients with focal basal ganglia lesions, suggesting that metrical stimulation is likely to act as a therapeutic tool modulating sequencing capacities. The authors suggested a compensation of the basal ganglia impairment with the help of an overactivation in premotor areas. Kotz et al. [START_REF] Kotz | Nonmotor basal ganglia functions: a review and proposal for a model of sensory predictability in auditory language perception[END_REF] proposed that the basal ganglia (or more generally the medial pre-SMA-basal ganglia circuit) and the cerebellar-thalamic-pre-SMA pathway have important roles in the processing of timing in spoken sequences. They play a role in sequencing and segmentation of incoming information streams, in attention formation of sensory predictions, as well as in beat perception and syntax processing. When the contribution of the basal ganglia is impaired, nonlinguistic stimulation (via the metric prime) might stimulate the cerebellarthalamic-pre-SMA pathway and boost the development of internal oscillators and their synchronization to the external (stimulus) oscillations.

These findings suggest the use of external oscillators as compensatory mechanisms in patients with syntactic integration deficits or, more generally, in sequencing and segmentation deficits. In a recent work, [START_REF] Przybylski | Rhythmic auditory stimulation influences syntactic processing in children with developmental language disorders[END_REF] we have extended this benefit of a metrical prime to syntax processing in children with developmental language disorders: children with SLI and children with dyslexia (and their agematched and reading-age-matched control participants). Even though recent research has revealed that children with SLI and children with dyslexia have deficits in rhythm and meter processing, [START_REF] Thomson | Rhythmic processing in children with developmental dyslexia: auditory and motor rhythms link to reading and spelling[END_REF][START_REF] Weinert | Deficits in acquiring language structure: the importance of using prosodic cues[END_REF][START_REF] Corriveau | Rhythmic motor entrainment in children with speech and language impairment: tapping to the beat[END_REF][START_REF] Overy | Dyslexia and music: measuring musical timing skills[END_REF][START_REF] Muneaux | Deficits in beat perception and dyslexia: evidence from French[END_REF] we formed the hypothesis that these populations might benefit from the musical prime, as did the basal ganglia patients (for whom deficits in temporal processing have also been reported). [START_REF] Jones | Dynamic attending and responses to time[END_REF] In our study, we compared the influence of two rhythmic structures (played by two percussion instruments) on syntax processing: a regular prime and an irregular prime, for which meter extraction was easy and difficult, respectively. In the experimental paradigm, children listened for 30 seconds to the musical excerpt, and this music presentation was followed by a block of experimental trials of the language task requiring grammaticality judgments. Sentences (presented auditorily) were either syntactically correct or incorrect, and children indicated whether a given sentence was correct or not. Over the experimental session, blocks of the language task were preceded by either regular primes or irregular primes. The results showed an influence of the prime on the subsequent language task: children's performance in the grammaticality judgments was better after a regular prime than after an irregular prime.

In this first study we have compared the influence of regular and irregular musical primes to establish the potential effect of prior music on subsequent language processing. This comparison does not yet allow conclusions about compensatory benefits of the regular prime in comparison to children's performance without music. We have chosen this procedure as a first approach because the comparison of a regular prime with a no-music condition is inadequate for their unequal levels of arousal and the unknown temporal persistence (or carryover effects) of the regular prime. We have now started to introduce a baseline condition aiming to investigate whether the benefit observed for regular musical primes (in comparison to the irregular primes) actually represents a benefit in comparison to a normal/silent listening situation. The first results obtained with children with SLI showed better performance after the regular musical prime than after the baseline condition (here we used an environmental sound scene). These findings are encouraging for the use of musical primes to boost language processing, suggesting their potential use for rehabilitation purposes.

Along the same lines, we are now extending this research to reading performance, aiming to test whether the beneficial effect of a regular rhythmic prime extends to syllable segmentation in a reading task. Children were asked to read words and pseudowords. The items of both types of stimuli were constructed to differ in their syllabic complexity as instilled by sonority cues, which allowed us to manipulate the difficulty level of segmentation. [START_REF] Bedoin | Sonority and syllabic structure in reading: differences between French and English readers[END_REF][START_REF] Fabre | Sensitivity to sonority for print processing in normal readers and dyslexic children[END_REF] We tested dyslexic and SLI children and their matched controls by comparing regular and irregular contexts first. [START_REF] Bedoin | Sonority and syllabic structure in reading: differences between French and English readers[END_REF] Results showed some improvement for syllable segmentation in reading after regular primes. For the more difficult items (containing the ambiguous syllable boundaries), SLI children produced more correct syllable boundaries after regular than irregular primes. For SLI and dyslexic children, the quality of reading increased after the regular prime, for example, with reduced phoneme omissions (i.e., the entire stimulus was read; /vukti/ versus /vyki/ or /vyti/). This work now needs also to be completed with the addition of a neutral (baseline) context to further determine the beneficial effect of the regular prime.

Long-term rhythmic training

The third example of an experimental design assessing the links between musical rhythm and language processing is a long-term training of rhythmic skills. In contrast to the short-term effects described above, this type of design implies both an active involvement-with respect to training-and a long-term intervention, typically over several weeks, months, or, even better, years. In the case of clinical studies, this corresponds to randomized control trials, requiring a strict observance of several methodological issues. Although these studies are of utmost interest insofar as they speak of the causal role of music training on nonmusical abilities (e.g., language), they are rather difficult to carry out. This is why most literature on the effects of music training on language skills essentially relies on correlational or cross-sectional studies. However, more recently, various long-term approaches using musical training have been proposed, mainly confirming conclusions coming from cross-sectional studies comparing musicians and nonmusicians. [START_REF] Franc ¸ois | Music training for the development of speech segmentation[END_REF] Another difficulty of the long-term approach is linked to the choice of the content of musical activity. Indeed, most of the time a general music training is chosen, often barely defined and relying on all properties of a music activity: timbral, melodic, harmonic, rhythmic, emotional, social, and so on. Although this is done for the obvious reasons of maximizing the chances of success and to get close to a more realistic musical training, results cannot disentangle the contribution of each of these different musical features to speech processing. Thus, the ideal design should compare the effects of different types of music intervention, both with respect to effects on speech and language processing and to covariance of the different measures. In other terms, one should first show that rhythmic training has an impact on grammatical skills, for instance, and then also show that among other musical competences (e.g., harmonic, melodic skills) the changes in performance in rhythmic tasks are the best predictor of the changes in performance in language tasks.

We now briefly present an example of longterm rhythmic training on a population of children with developmental dyslexia. One explanation of the poor performance in rhythmic tasks described above is a deficit in processing the amplitude envelope and more precisely in processing rise time. 37 Rise times are critical in speech perception because they facilitate syllabic segmentation and prosodic processing. Poor auditory perception of slow temporal modulations may thus cause poor perception of speech rhythm and syllable stress. [START_REF] Goswami | A temporal sampling framework for developmental dyslexia[END_REF] Interestingly, phase locking between the speech envelope and low-frequency oscillations in the auditory cortex implements a mechanism for efficient sampling and segmentation of speech. [START_REF] Gross | Speech rhythms and multiplexed oscillatory sensory coding in the human brain[END_REF] Going back to the phase-coupling model described above with the DAT, one possibility would be that although a "normal" neural oscillatory activity will phase lock to speech modulation patterns, [START_REF] Ghitza | Linking speech perception and neurophysiology: speech decoding guided by cascaded oscillators locked to the input rhythm[END_REF][START_REF] Giraud | Cortical oscillations and speech processing: emerging computational principles and operations[END_REF] in developmental dyslexia there may be a poor phase alignment between speech and neural activity. [START_REF] Lehongre | Altered low-gamma sampling in auditory cortex accounts for the three main facets of dyslexia[END_REF] We recently collected data from a highly selected sample of Italian children with developmental dyslexia to investigate, on one hand, the relation among musical temporal, phonological, and decoding skills and, on the other hand, the causal effects of music rhythmic training on phonological and reading abilities. Results clearly show both a larger improvement in several phonological and reading abilities compared to the control group (here trained in visual arts) and a similar developmental trajectory of rhythmic and phonological abilities. [START_REF] Flaugnacco | Rhythm perception and production predict reading abilities in developmental dyslexia[END_REF][START_REF] Flaugnacco | Under review. Music training increases phonological awareness and reading skills in developmental dyslexia: a randomized control trial[END_REF] This adds evidence to previous studies showing a potential benefit of music training to improve phonological abilities. [START_REF] Cogo-Moreira | Effectiveness of music education for the improvement of reading skills and academic achievement in young poor readers: a pragmatic cluster-randomized, controlled clinical trial[END_REF][START_REF] Overy | Dyslexia, temporal processing and music: the potential of music as an early learning aid for dyslexic children[END_REF][START_REF] Bhide | A rhythmic musical intervention for poor readers: a comparison of efficacy with a letter-based intervention[END_REF][START_REF] Goswami | Perception of patterns of musical beat distribution in phonological developmental dyslexia: significant longitudinal relations with word reading and reading comprehension[END_REF]

Temporal scales and perspectives for rehabilitation

When we consider the use of music and rhythm to improve linguistic skills, it is important to keep in mind that several temporal scales come into play. These levels possibly rely on different neural circuitry and are affected to a certain extent in different language pathologies. Table 1 proposes an overview. This is not an exhaustive list of all possible temporal levels that may be relevant but is an overview to show the diversity and complexity of the processes involved and, possibly, to stimulate further research to better define these temporal levels and suggest new ones.

The shortest temporal scale (<3 ms) is important

Q3

to ensure a high consistency in neural responses to sounds in the brain stem. A low brain-stem response consistency has been observed in poor readers, [START_REF] Hornickel | Unstable representation of sound: a biological marker of dyslexia[END_REF] and a high-response consistency is typically associated with proficient sensorimotor synchronization skills. [START_REF] Tierney | The ability to move to a beat is linked to the consistency of neural responses to sound[END_REF] Next, we have a temporal scale (approximately 40 ms) that is important in perceiving consonantic contrasts that are known to be poorly perceived by children with developmental dyslexia, [START_REF] Tallal | Improving language and literacy is a matter of time[END_REF] whereas musician children discriminate similar consonants better than nonmusician children. We have described the next two levels concerning amplitude modulation, word segmentation, and prosodic boundaries (approximately from 50 ms to above 500 ms). These levels can be impaired in speech disorders [START_REF] Goswami | Perception of patterns of musical beat distribution in phonological developmental dyslexia: significant longitudinal relations with word reading and reading comprehension[END_REF] and are typically processed more efficiently by musicians than by nonmusicians. [START_REF] Francois | Musical expertise boosts implicit learning of both musical and linguistic structures[END_REF][START_REF] Franc ¸ois | Music training for the development of speech segmentation[END_REF] The last level is on a rather long time scale, above 1 second. Prediction as well as cognition based on Bayesian inference are what allow readers to decode "Aoccdrnig to rscheearch at Cmabrigde Uinervtisy" without difficulties. Actually, readers are not able to refrain from reading the correct words and imagining the correct sounds. Although this level is also impaired in developmental dyslexia, we are not aware of any study testing whether musicians have an advantage compared to a nonmusician population. Overall, one can predict that by improving these different levels of temporal processing via rhythmic stimulation, children with language disorders might also benefit to some extent and improve their language processing. This hypothesis, together with the rather encouraging set of findings presented above, can be integrated in the temporal sampling framework recently proposed by Goswami for dyslexia and by extension for SLI. [START_REF] Goswami | A temporal sampling framework for developmental dyslexia[END_REF] Together with the DAT, postulating internal oscillators guiding attention over time, Goswami suggests that an impaired rhythmic entrainment leads to difficulties in developing attention over time, engendering in turn deficits in syllabic segmentation and other sequential processes. [START_REF] Goswami | A temporal sampling framework for developmental dyslexia[END_REF] Goswami discusses the potential benefits of therapeutic interventions or educational practices based on rhythm and music (e.g., metrical poetry or singing nursery rhymes) as those might entrain the impaired oscillatory networks. In line with this framework, the data described above provide new grounds and motivations for further testing the benefit of rhythmic stimulation on language processing and its underlying mechanisms. The perspective of using music might also exploit the motivational advantages and pleasantness that musical material can provide in a rehabilitation setting beyond its stimulating effect for impaired temporal processing networks.

1

  Ann. N.Y. Acad. Sci. xxxx (2014) 1-8 C 2014 New York Academy of Sciences.

Q4Figure 1 .

 1 Figure 1. Example of four different matching rhythmical primes preceding a spoken sentence. The participant sees a target vowel on the screen and hears a rhythm followed by a sentence (matching or mismatching). The task is to say whether the vowel is present or not in the last word of the sentence.

52 5

 52 Ann. N.Y. Acad. Sci. xxxx (2014) 1-8 C 2014 New York Academy of Sciences.

	nyas12635	W3G-nyas.cls	November 30, 2014	11:10
		Rhythmic interventions for language rehabilitation	Sch ön & Tillmann

Table 1 . Nonexhaustive overview of different levels of analyses involved in speech and language comprehension and an approximate corresponding temporal scale

 1 Note: : The two columns on the right indicate whether there is evidence that music training benefits this level of processing (Ý indicates Yes) and whether this level may be impaired in individuals suffering language disorders (X indicates Yes, impaired).

	Function	Scale	Effect of music training Language disorders
	Consistency of spectrotemporal analysis	< 3 ms	Ý	X
	Consonantic contrasts	ß40 ms	Ý	X
	Amplitude modulation: speech rate and speech rhythm 50-500 ms	Ý	X
	Word segmentation and prosodic boundaries	> 500 ms	Ý	X
	Bayesian cognition and predictive coding	> 1 s	?	X

Ann. N.Y. Acad. Sci. xxxx (2014) 1-8 C 2014 New York Academy of Sciences.

Ann. N.Y. Acad. Sci. xxxx (2014) 1-8 C 2014 New York Academy of Sciences.

Conflicts of interest

The authors declare no conflicts of interest.


Serpa Ary

Luiz Neto

V Guilherme

Sabrine N T Da Costa

Jaume Hemmes

Goran Canet

Samir Hedenstierna

Michael Jaber

Markus Hiesmayr

Gary Hollmann

Marcos Vidal Mills

Melo

The LAS VEGAS risk score for prediction of postoperative pulmonary complications

de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


Laure Buhry
email: laure.buhry@loria.fr

Francesco Giovannini

Tonic inhibition mediates a synchronisation enhancement during propofol anaesthesia in a network of hippocampal interneurons: a modelling study

Keywords: general anesthesia, computational modeling, propofol, Hodgkin-Huxley model, extrasynaptic inhibition

Neural oscillations are thought to be correlated with the execution of cognitive functions. Indeed, gamma oscillations are often recorded in functionally-coupled brain regions for cooperation during memory tasks, and this rhythmic behaviour is thought to result from synaptic GABAergic interactions between interneurons. Interestingly, GABAergic synaptic and extrasynaptic receptors have been shown to be the preferred target of the most commonly used anaesthetic agents. We present a in-depth computational study of the action of anaesthesia on neural oscillations by introducing a new mathematical model which takes into account the four main effects of the anaesthetic agent propofol on GABAergic hippocampal interneurons. These are: the action on synaptic GABA A receptors, which includes an amplification and an extension of the duration of the synaptic currents, as well as an increase in current baseline, and the action on extrasynaptic GABA A receptors mediating a tonic inhibitory current. Our results indicate that propofol-mediated tonic inhibition contributes to an unexpected enhancement of synchronisation in the activity of a network of hippocampal interneurons. We speculate that this enhanced synchronisation could provide a possible mechanism supporting the occurrence of intraoperative awareness and explicit memory formationunder general anaesthesia, by transiently facilitating the communication between brain structures which should supposedly be not allowed to do so when anaesthetised.

Tonic inhibition mediates a synchronisation enhancement during propofol an aesthesia in a network of hippocampal interneurons: a modelling study

Résumé : Neural oscillations are thought to be correlated with the execution of cognitive functions. Indeed, gamma oscillations are often recorded in functionally-coupled brain regions for cooperation during memory tasks, and this rhythmic behaviour is thought to result from synaptic GABAergic interactions between interneurons. Interestingly, GABAergic synaptic and extrasynaptic receptors have been shown to be the preferred target of the most commonly used anaesthetic agents. We present a in-depth computational study of the action of anaesthesia on neural oscillations by introducing a new mathematical model which takes into account the four main effects of the anaesthetic agent propofol on GABAergic hippocampal interneurons. These are: the action on synaptic GABA A receptors, which includes an amplification and an extension of the duration of the synaptic currents, as well as an increase in current baseline, and the action on extrasynaptic GABA A receptors mediating a tonic inhibitory current. Our results indicate that propofol-mediated tonic inhibition contributes to an unexpected enhancement of synchronisation in the activity of a network of hippocampal interneurons. We speculate that this enhanced synchronisation could provide a possible mechanism supporting the occurrence of intraoperative awareness and explicit memory formationunder general anaesthesia, by transiently facilitating the communication between brain structures which should supposedly be not allowed to do so when anaesthetised.

Mots-clés : general anesthesia, computational modeling, propofol, Hodgkin-Huxley model, extrasynaptic inhibition

Introduction

General anaesthesia is a reversible drug-induced coma which is commonly administered to patients undergoing surgery due to its desirable properties, which are: loss of consciousness, analgesia, immobility, and amnesia, all obtained whilst preserving physiological stability [START_REF] Brown | General anesthesia, sleep, and coma[END_REF]. Indeed, after the induction of general anaesthesia, patients enter a state of sedation during which they are not aware of the surgery, they do not perceive nor react to the noxious stimuli deriving from it, and they do not remember undergoing it. These properties derive from the combined action of an hypnotic agent, an analgesic (to avoid pain), and a curariform skeletal muscle relaxant or neuromuscular blocker (to induce immobility). Although having become a standard operating procedure during surgery -in the United States alone, approximately 60000 patients undergo general anaesthesia every day [START_REF] Brown | General anesthesia, sleep, and coma[END_REF] -the chemical and neuronal mechanisms by which these effects are obtained are yet to be fully unravelled.

Loss of consciousness is achieved by the injection or gas inhalation of an hypnotic agent like the widely used propofol. Propofol, 2,6-di-isopropyl-phenol, [START_REF] Vanlersberghe | Modern Anesthetics: Handbook of Experimental Pharmacology[END_REF] is one of the main anaesthetic intravenous agents used in surgical operations for the induction and maintenance of general anaesthesia. Propofol-induced sedation is obtained by globally potentiating GABAergic inhibitory activity [START_REF] Adodra | Potentiation, activation and blockade of GABAA receptors of clonal murine hypothalamic GT1-7 neurones by propofol[END_REF], Bai et al., 1999, Bai et al., 2001, Kitamura et al., 2004, McDougall et al., 2008, Song et al., 2011], as the drug binds on GABA A receptors, both synaptic and extrasynaptic, enhancing their activation [START_REF] Garcia | General anesthetic actions on GABA(A) receptors[END_REF], Nelson et al., 2002, Rudolph and Antkowiak, 2004, Zhou et al., 2012]. Four main molecular mechanisms are thought to underlie propofol-induced general anaesthesia:

1. An enhancement of the amplitude of GABA A -mediated tonic currents by activating extrasynaptic GABA A receptors [START_REF] Bai | Distinct functional and pharmacological properties of tonic and quantal inhibitory postsynaptic currents mediated by g -aminobutyric acid(A) receptors in hippocampal neurons[END_REF], McDougall et al., 2008, Song et al., 2011] 2. A potentiation of GABA A -mediated synaptic currents by increasing the conductance of synaptic GABA A receptors [Adodra andHales, 1995, McDougall et al., 2008] 3. An increase in the baseline of GABA A -mediated synaptic currents by slowing the desensitisation of GABA A receptors [START_REF] Bai | The general anesthetic propofol slows deactivation and desensitization of GABA(A) receptors[END_REF], Bai et al., 2001, McDougall et al., 2008] 4. An extension in the duration of GABA A -mediated synaptic currents by increasing the closing time of synaptic GABA A receptors [START_REF] Bai | Distinct functional and pharmacological properties of tonic and quantal inhibitory postsynaptic currents mediated by g -aminobutyric acid(A) receptors in hippocampal neurons[END_REF], Kitamura et al., 2004, McDougall et al., 2008] Here, we present a novel detailed model of anaesthetic action, including all four of the afore-mentioned effects, on neural oscillations mediated by GABAergic transmission. Synaptic GABAergic interactions between interconnected inhibitory neurons are thought to play an important role in the generation and maintenance of rhythmic neural activity, in particular in the γ-band (20-80) Hz [START_REF] Bartos | Synaptic mechanisms of synchronized gamma oscillations in inhibitory interneuron networks[END_REF], Cobb et al., 1995, Jonas et al., 2004]. Oscillations arise because inhibitory neurons provide their postsynaptic targets with precise windows of reduced excitability, and consequently of increased excitability once the inhibition fades away. We model a network of interconnected inhibitory interneurons whose activity tends to display, in the absence of propofol, loosely synchronous activity in the gamma range [START_REF] Wang | Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model[END_REF]. Our results indicate that increasing the concentration of the anaesthetic agent yields a dosage-dependent enhancement of network synchronisation. This enhancement could facilitate the communication between brain structures [Fries, 2005] which, being anaesthetised, should supposedly be not allowed to do so. We hypothetise that this could provide a possible explanation for the emergence of unwanted behaviours under general anaesthesia, including intraoperative awareness and implicit memory formation.In addition, the transient characteristics of this phenomenon could explain the variability between different studies and patients.

Methods

We modelled the four afore-mentioned effects of propofol on a population of Hodgkin-Huxley hippocampal interneurons as follows.

Fast-Spiking Hippocampal Interneurons

We modelled fast-spiking hippocampal GABAergic interneurons using the Hodgkin-Huxley formalism, adapting the model described in [START_REF] Kopell | Gamma and theta rhythms in biophysical models of hippocampal circuits[END_REF] and [START_REF] Hutt | Study of GABAergic extra-synaptic tonic inhibition in single neurons and neural populations by traversing neural scales: application to propofol-induced anaesthesia[END_REF]. The current-balance equation takes the form:

C m • dV m dt = -I l -I K -I N a -I syn -I ton (1)
where I l is the leak current, I K is the potassium current, I N a is the sodium current, I syn is the inhibitory current deriving from synaptic GABAergic interactions, and I ton is the tonic inhibitory current mediated by extrasynaptic GABA A receptors.

The transmembranal ionic currents are described by the following equations:

I l = g l • (V m -E l ) I K = g K • n 4 • (V m -E K ) I N a = g N a • m 3 • h • (V m -E N a )
where, m, h and n are activation variables which obey the following rules:

dx dt = x ∞ -x τ x x ∞ = α x α x + β x τ x = 10 7 • (α x + β x )
for x ∈ { n, m, h }. The α and β functions for each activation variable are defined as:

α n = 0.01 • (V m + 34) 1 -exp(-0.1 • (V m + 34)) β n = 0.125 • exp - (V m + 44) 80 α m = 0.1 • (V m + 35) 1 -exp -(Vm+35) 10 β m = 4 • exp - (V m + 60) 18 α h = 0.07 • exp - (V m + 58) 20
β h = 1 exp(-0.1 • (V m + 28)) + 1 Inria 2.

Modelling the Effects of Anaesthetics on GABA A Receptors

Synaptic Phasic Inhibition

The equation for the synaptic takes the form:

I syn = I i = g i • (V m -E i ) + k bas (2)
where g i is the synaptic conductance which obeys the following rule, given its time decay constant τ i :

dg i dt = - g i τ i (3)
Whenever a postsynaptic neuron receives a presynaptic spike its conductance g i is increased as follows: g i ← g i + w i , where w i is the connection weight between the interneurons. Propofol binds on synaptic GABA A receptors enhancing their conductance [START_REF] Adodra | Potentiation, activation and blockade of GABAA receptors of clonal murine hypothalamic GT1-7 neurones by propofol[END_REF] and increasing their closing time [START_REF] Bai | The general anesthetic propofol slows deactivation and desensitization of GABA(A) receptors[END_REF]. We modelled this effect by acting on the inhibitory synaptic weights w i and decay time τ i parameters as in [START_REF] Mccarthy | Potential network mechanisms mediating electroencephalographic beta rhythm changes during propofolinduced paradoxical excitation[END_REF]. Increasing propofol dosage reflects in an increase in both of these values.

In addition, we modelled the slowing desensitisation of GABA A receptors caused by exposure to propofol [START_REF] Bai | The general anesthetic propofol slows deactivation and desensitization of GABA(A) receptors[END_REF], Bai et al., 2001, McDougall et al., 2008] by appropriately modifying the baseline of the postsynaptic current k bas etween 0 and 100 pA, the literature giving 0 ≥ k bas ≤ 60 [START_REF] Mcdougall | Propofol enhances both tonic and phasic inhibitory currents in second-order neurons of the solitary tract nucleus (NTS)[END_REF]). The baseline is the synaptic current received by neurons when all their presynaptic afferents are quiescent. In the absence of propofol this parameter was set to k bas = 0 pA. Since the synaptic conductance g i obeys the rule described in Equation 3, k bas = 0 pA indicates that the synaptic current decays to 0 pA as the ionic channel closes. However, increasing the value of k bas ensures that the synaptic current does not dip below the specified baseline. To the best of our knowledge, propofol-induced receptor desensitisation has never been modelled in existing computational studies. Let us note that concentrations of propofol higher than 1µM are not physiological.

Extrasynaptic Tonic Inhibition

The action of propofol on extrasynaptic GABAergic receptors was modelled by varying the conductance g ton of the tonic current I ton , which takes the form:

I ton = g ton • (V m -E i ) (4)
as described in [START_REF] Hutt | Study of GABAergic extra-synaptic tonic inhibition in single neurons and neural populations by traversing neural scales: application to propofol-induced anaesthesia[END_REF], where E i is the same reversal potential used for the synaptic inhibitory current I i to maintain the equivalence between tonic and shunting inhibition. Increasing propofol dosage reflects in an increase in the tonic conductance g ton , as described in the literature [START_REF] Mcdougall | Propofol enhances both tonic and phasic inhibitory currents in second-order neurons of the solitary tract nucleus (NTS)[END_REF], Song et al., 2011]. This produces a noninactivating tonic inhibitory current which is not governed by activation-deactivation kinetics, as is the case for its synaptic counterpart. phenomenon is probably comparable to the synchrony observed in inhibitory networks where the decay time of the inhibition is very long [START_REF] Rinzel | Analysis of neural excitability and oscillations[END_REF]] since here, the inhibitory conductance is kept constant.

Network Configuration

Our network model comprised 100 fast-spiking hippocampal inhibitory neurons, which were randomly connected with a certain probability p. p = 0 indicates that the neurons make zero synaptic contacts with other neurons, whereas p = 1 represents a fully connected network in which all neurons project on all other neurons (including themselves). The results presented in [START_REF] Wang | Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model[END_REF] identify a critical number of synaptic contacts ( 40) per neuron within a network, independently on the number of cells in the network, required for the emergence of synchronous activity. For 100 neurons, this would equate to a critical connection probability of p = 0.4. In our network, the connection probability was set to p = 0.6 so as to be higher than this critical probability, ensuring the presence of synchronous network activity.

External Current Stimulation

Throughout all our simulations, the network was stimulated with a constant current I stim = 0.4 nA. Heterogeneity was introduced in the form of Gaussian-distributed noise when initialising the resting potential and the synaptic conductance values of the neurons.

Model Parameters

Table 1 summarises the parameter values used for the hippocampal inhibitory neuron model, unless otherwise specified.

Network Synchronisation

The network synchronisation is computed using the coherence measure devised by [START_REF] Wang | Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model[END_REF].

The measure computes the pair-wise co-occurrence of neuron action potentials κ i,j (τ ) given a time windows of size τ . For any pair of neurons X and Y , given their spike trains represented as a series of ones and zeroes depending on whether the neuron spiked or did not in the time window respectively:

X i (l), Y j (l) ∈ {0, 1} l = 1, 2, ..., L L = t sim τ τ = 10 ms
where t sim = 2000 ms is the duration time of the simulation, and L is the number of time windows of size τ . Increasing the size of τ augments the probability of spike co-occurrence and allowing for larger synchronisation values which might be unrealistic. For all our computations Inria we used τ = 10 ms, which we deemed small enough to capture the dynamics of the network without compromising the reliability of the computed coherence values. The pair-wise coherence measure is quantified as:

κ i,j (τ ) = L l=1 X i (l) • Y j (l) L l=1 X i (l) • L l=1 Y j (l)
The network synchronisation measure is then computed as the average κ i,j (τ ) for a randomly sampled subset of neuron pairs in the network:

κ(τ ) = i,j∈P κ i,j (τ ) N
where P = { (0, 1), (3, 4), ... } is a subset of randomly sampled neuron pairs of size N . Unless otherwise specified, the network synchronisation is averaged over a subset containing 10% of the total neuron pairs in the network, without repetitions. κ(τ ) is comprised between 0 and 1, representing an asynchronous population firing and fully synchronised firing respectively.

Results -Studying Tonic Inhibition

We began by studying the effects of propofol-mediated tonic inhibition on network oscillations. This was done by acting solely on the tonic conductance g ton . The synaptic weight was fixed at w i = 1.6 nS, and the decay time constant was τ i = 10 ms.

Tonic Inhibition Improves Neural Synchronisation

In the absence of anaesthetic agent (g ton = 0 nS), the network synchronised its activity with κ(τ ) = 0.40 (Figure 1a) at a population frequency of f = 20.72 Hz (Figure 1b), and an oscillatory frequency of f osc = 42.67 Hz (Figure 1c). Increasing doses of propofol reduced the overall network activity and slowed down its oscillations, whilst the network synchronisation remained stable at an average value of κ(τ ) = 0.42 ± 0.01. When the tonic inhibition reached a critical value of g ton = 14 nS at which the synchronisation increased abruptly reaching κ(τ ) = 0.72, and the mean firing rate increased to f 18 Hz. The network synchronisation remained unchanged at an average plateau value of κ(τ ) = 0.76 ± 0.00 until further strengthening the effects of propofol g ton = 21 nS caused the overall network activity to drastically decrease (κ(τ ) = 0.02, f = 4.98 Hz and f osc = 13.04 Hz), until it faded away (κ(τ ) = 0, f = 0 Hz and f osc = 0 Hz for g ton ≥ 21.5 nS).

Figure 2 shows the activity of the network for increasing values of g ton , in the form of raster plots. Their corresponding computed LFP signals are shown in Figure 3. At g ton = 0 nS the network displayed gamma frequency oscillations (f osc = 42.67 Hz) with an average population frequency of f = 20.72 Hz and a synchronisation of κ(τ ) = 0.40. This indicates that, on average, approximately half of the neurons fire synchronously at any given time, as shown in Figure 2a. In addition, each individual neuron fired once every two cycles. Taken together, these two observations indicate that the intrinsic firing rate of each isolated neuron was f = 42.67 Hz, although the presence of synaptic inhibition halved it.

Increasing tonic inhibition above a threshold value of 14 nS produced slower population firing rates, and slower oscillations. At g ton = 15 nS, the network activity oscillated at f osc = 20.67 Hz with a population frequency of f = 17.27 Hz (Figure 2b). Similarly, at g ton = 18 nS, the network activity oscillated at f osc = 17.33 Hz with a population frequency of f = 14.08 Hz.

(Figure 2c). We observe that, although slower, the oscillatory activity was approximately twice as synchronised (κ(τ ) = 0.76 ± 0.00 for 14 nS ≤ g ton ≤ 19 nS) compared to the same network in the absence of tonic inhibition (g ton = 0 nS). As inhibition increased, the neurons in the network became less prone to discharging action potentials and the population frequency slowed down. In addition, stronger inhibition provided the neurons with tighter windows of increased excitability, ensuring that most of the neurons in the network (approximately 80%) would fire concurrently, which explains the enhanced network synchronisation.

Figure 2d shows weak, albeit synchronous activity at f osc = 12.67 Hz with a population frequency of f = 3.85 Hz for g ton = 21 nS. Further strengthening the tonic inhibition caused the neurons to emit fewer and fewer action potentials, until eventually the network activity faded away (g ton > 21 nS).

The LFP signal computed from the network activity reflected its synchronous behaviour (Figure 3). In the absence of propofol (g ton = 0 nS in Figure 3a) the LFP oscillated between -0.6 mV and 0.7 mV at f osc = 42.67 Hz. Increasing the effects of anaesthetics caused an increase in the amplitude of the LFP signal, which oscillated between -1 mV and 1.2 mV at f osc = 20.67 Hz for g ton = 15 nS (Figure 3b), and -0.95 mV and 1.3 mV at f osc = 17.33 Hz for g ton = 18 nS (Figure 3c). This increase in amplitude reflected the increase in network synchronisation as the more neurons fire concurrently at any given time the stronger the generated LFP signal will be. Similarly, the LFP amplitude decreased for g ton = 21 nS (Figure 3d) as less neurons fire due to the strong tonic inhibition, producing an LFP signal which oscillated between -0.32 mV and 0.47 mV at f osc = 12.67 Hz.

Results -Combining the Effects of Tonic and Phasic Inhibition

We then turned our attention towards analysing the joint effects of both synaptic and extrasynaptic propofol-enhanced inhibition. As previously explained, we modelled the action of propofol on synaptic GABA A receptors by increasing the inhibitory synaptic conductance, time constant, and current baseline. Our results show that solely the tonic inhibition was responsible for enhancing the network synchronisation in the presence of the anaesthetic agent.

Propofol-Enhanced Inhibitory Synaptic Conductance Does not Hinder Synchronisation

Increasing the inhibitory synaptic conductance did not hinder the synchronising properties of tonic inhibition (Figure 4). Figure 4a and Figure 4b depict the evolution of the average population frequency and synchronisation (κ(τ )) respectively (vertical z axis), as both the synaptic weight w i (y axis) and the tonic conductance g ton (x axis) are increased, for a fixed synaptic time constant τ i = 10 ms. Similarly, Figure 4c and Figure 4d illustrate the evolution of the average population frequency and synchronisation, for a fixed synaptic time constant τ i = 14 ms. Finally, Figure 4e and Figure 4f show the evolution of the average population frequency and synchronisation, for a fixed synaptic time constant τ i = 30 ms. The synaptic weights ranged between 1.4 nS ≤ w i ≤ 2.6 nS and the tonic conductance ranged between 0 nS ≤ g ton ≤ 20 nS.

The overall population frequency decelerated from a maximum of f = 21.97 ± 0.06 Hz to a minimum of f = 7.78 ± 0.25 Hz as both w i and g ton grew (Figure 4a). However, whilst the firing rate followed a generally decreasing trend as synaptic weights were strengthened, it showed an up-and-down profile as tonic inhibition was enhanced, similar to that described previously in the absence of propofol-enhanced synaptic activity. Indeed, given g ton = 0 nS, the frequency slowed from f = 21.97 ± 0.06 Hz for w i = 1.4 nS to f = 16.59 ± 0.14 Hz for w i = 2.6 nS. At g ton = 15 nS, the frequency slowed from f = 16.81 ± 0.18 Hz for w i = 1.4 nS to f = 13.46 ± 0.18 Hz for w i = 2.6 nS. At g ton = 20 nS, the frequency slowed from f = 10.53 ± 0.26 Hz for w i = 1.4 nS to f = 7.78 ± 0.25 Hz for w i = 2.6 nS. In contrast, we can observe a sharp increase in network frequency as tonic inhibition strengthens, given fixed synaptic weights. At w i = 1.4 nS, the frequency slowed from f = 21.97±0.06 Hz for g ton = 0 nS to f = 13.99±0.06 Hz for g ton = 12 nS, then accelerated to f = 16.81 ± 0.18 Hz for g ton = 15 nS, and finally dropped to f = 10.53 ± 0.26 Hz for g ton = 20 nS. A similar bump pattern can be seen at all other values of w i on Figure 4a. For example, at w i = 2.4 nS, the frequency slowed from f = 17.08 ± 0.12 Hz for g ton = 0 nS to f = 13.08 ± 0.35 Hz for g ton = 10 nS, then accelerated to f = 15.62 ± 0.25 Hz for g ton = 12 nS, and finally dropped to f = 8.14 ± 0.46 Hz for g ton = 20 nS.

A similar trend can be observed, having fixed g ton , on the evolution of the network synchronisation with respect to increasing values of w i (Figure 4b). For example, at g ton = 0 nS, the synchronisation was κ(τ ) = 0.34±0.02 for w i = 1.4 nS, and κ(τ ) = 0.36±0.01 for w i = 2.6 nS, with a mean value of κ(τ ) = 0.36±0.00. At g ton = 15 nS, the synchronisation was κ(τ ) = 0.70±0.01 for w i = 1.4 nS, and κ(τ ) = 0.63 ± 0.07 for w i = 2.6 nS, with a mean value of κ(τ ) = 0.67 ± 0.01. At g ton = 20 nS, the synchronisation was κ(τ ) = 0.65 ± 0.01 for w i = 1.4 nS, and κ(τ ) = 0.48 ± 0.04 for w i = 2.6 nS, with a mean value of κ(τ ) = 0.59±0.01. Comparing the stepwise synchronisation values with the average across all w i values for a fixed g ton indicated that synaptic inhibition accounts for little to no variability in the enhanced synchronous activity displayed by the network. Conversely, Figure 4b illustrates how the network synchronisation tightened for increasing values of g ton given fixed synaptic weights, as previously observed (Figure 1a). At w i = 1.4 nS, the synchronisation remained stable at an average value of κ(τ ) = 0.37 ± 0.01 for 0 nS ≤ g ton ≤ 12 nS, Inria then increased to an average value of κ(τ ) = 0.65 ± 0.04 for g ton > 12 nS. This synchronisation bump pattern was preserved across all values of w i . For example, at w i = 2.4 nS, the synchronisation stabilised at an average value of κ(τ ) = 0.36±0.01 for 0 nS ≤ g ton ≤ 10 nS, then increased to an average value of κ(τ ) = 0.57 ± 0.09 for g ton > 10 nS.

In addition, we observed that stronger synaptic inhibition had a tendency to shift the tonic inhibition-mediated frequency rebound peak towards lower values of g ton . Our results show that this seemed to be the sole effect of propofol-enhanced GABAergic phasic inhibition. For 1.4 nS ≤ w i ≤ 2 nS the peak was centred around g ton = 15 nS, with a maximum frequency value of 16.81 ± 0.18 Hz (Figure 5a), and a corresponding coherence value of κ(τ ) = 0.71 ± 0.01 (Figure 5b) at w i = 1.4 nS. Stronger synaptic weights (w i > 2 nS) moved the centre of the peak around g ton = 12 nS, with a maximum frequency value of 16.21 ± 0.27 Hz (Figure 5a), and a corresponding coherence value of κ(τ ) = 0.63 ± 0.02 (Figure 5b) at w i = 2.1 nS. Likewise, the peak of the tonic inhibition-mediated synchronisation rebound was also affected by stronger synaptic activity. For 1.4 nS ≤ w i ≤ 2.4 nS it remained centred around g ton = 15 nS, with a maximum coherence value of κ(τ ) = 0.72±0.01 (Figure 5b), and a corresponding frequency value of 16.66±0.21 Hz (Figure 5a) at w i = 1.5 nS. Stronger synaptic weights (w i > 2.4 nS) moved the centre of the peak around g ton = 12 nS, with a maximum coherence value of κ(τ ) = 0.63 ± 0.01 (Figure 5b), and a corresponding frequency value of 15.43 ± 0.17 Hz (Figure 5a) at w i = 2.6 nS. This behaviour is to be expected since the presence of stronger inhibition invariably caused a reduction in overall network activity thus producing slower firing rates.

Prolonged Synapse Closing Times Allow for Synchronisation with Weaker Tonic Inhibition

Propofol also enhances synaptic inhibitory currents by extending the closing time of the synapse [START_REF] Bai | Distinct functional and pharmacological properties of tonic and quantal inhibitory postsynaptic currents mediated by g -aminobutyric acid(A) receptors in hippocampal neurons[END_REF], Kitamura et al., 2004, McDougall et al., 2008], allowing for longer lasting currents. We modelled this effect by prolonging the synaptic time constant τ i . Figure 4a, Figure 4c and Figure 4e depict the relationship between the network frequency and the synaptic and tonic inhibition as τ i is increased, from 10 ms to 14 ms to 30 ms respectively. Intuitively, longer synaptic time constants should reduce the firing frequency of the network, as is reflected in our results. At τ i = 10 ms the maximum firing rate was f = 21.97 ± 1.24 Hz for w i = 1.4 nS and g ton = 0 nS (Figure 4a). A longer time constant τ i = 14 ms decelerated the maximum firing rate to f = 17.42 ± 0.14 Hz for w i = 1.4 nS and g ton = 0 nS (Figure 4c). Further extending τ i to 14 ms reduced the maximum firing rate to f = 9.28 ± 0.24 Hz for w i = 1.4 nS and g ton = 0 nS (Figure 4e). In general, the network frequency was slower at all values of w i and g ton as τ i was increased.

Longer synaptic time constants also affected the network synchronisation and its propofoldependent bump-like evolution. Figure 4b, Figure 4d and Figure 4f depict the relationship between the network synchronisation and the synaptic and tonic inhibition as τ i is increased, from 10 ms to 14 ms to 30 ms respectively. Interestingly, we observe that extending the duration of the inhibitory synaptic current enhanced the network synchronisation at lower g ton values, as longer time constants shifted the peak of the synchronisation bump towards the lower end of the x axis. At τ i = 14 ms (Figure 4d), given w i = 1.4nS the synchronisation stabilised at an average value of κ(τ ) = 0.29 ± 0.01 for 0 nS ≤ g ton ≤ 5 nS, then increased to an average value of κ(τ ) = 0.59 ± 0.02 for 5 < g ton ≤ 15 nS, and proceeded to drop to an average value of κ(τ ) = 0.31±0.01 for g ton > 15 nS. Once again, this synchronisation bump pattern was preserved across all values of w i . For example, a similar evolution can be observed at w i = 2.2 nS where the synchronisation stabilised at an average value of κ(τ ) = 0.34 ± 0.06 for 0 nS ≤ g ton ≤ 5 nS, then increased to an average value of κ(τ ) = 0.41 ± 0.02 for 5 < g ton ≤ 15 nS, and proceeded to drop to an average value of κ(τ ) = 0.18 ± 0.02 for g ton > 15 nS.

Further extending the synapse closing time caused further network frequency deceleration, as the number of spikes elicited were drastically reduced by the presence of stronger inhibition. Eventually, the network reverted to a slow, asynchronous firing regime. Figure 4e and Figure 4f illustrate the network frequency and synchronisation, respectively, for τ i = 30 ms. The maximum frequency was reduced to f = 9.28 ± 0.24 Hz for w i = 1.4 nS and g ton = 0 nS. Whereas the maximum network synchronisation was reduced to κ(τ ) = 0.18 ± 0.01. Both frequency and synchronisation followed decreasing trends as w i and g ton were increased, and the bump pattern was absent.

Tonic Inhibition-Mediated Synchronisation Is Unaffected by Potentiated Inhibitory Synaptic Baseline Currents

In vitro experimental studies [START_REF] Jin | Presynaptic actions of propofol enhance inhibitory synaptic transmission in isolated solitary tract nucleus neurons[END_REF], McDougall et al., 2008] have reported that exposure to propofol causes a concentration-dependent increase in GABAergic baseline currents in postsynaptic neurons. We modelled this effect by adding a constant 0 pA ≤ k bas ≤ 100 pA to the inhibitory synaptic current I i , where k bas = 0 pA indicates the absence of propofol. To our knowledge, ours is the first computational study to include propofol-induced receptor desensitisation in its model. Our results indicate that a propofol-mediate shift in inhibitory synaptic baseline current does not interfere with the enhanced synchronisation provided by tonic inhibition. Figure 6 illustrates the relationship between the network frequency (vertical z axis) and the combined effects of tonic and synaptic inhibition -namely, increasing tonic conductance (x axis), shifting the inhibitory synaptic current baseline (y axis), enhancing synaptic current amplitudes (horizontally distributed surface plots), and prolonging synaptic current duration (vertically distributed surface plots). In particular, the top row of surface plots in Figure 6 depict the network frequency for τ i = 10 ms and increasing values of w i i.e. 1.6 nS (Figure 6a), 1.9 nS (Figure 6b), and 1.9 nS (Figure 6c) respectively. The middle row of surface plots in Figure 6 depict the network frequency for τ i = 14 ms and increasing values of w i i.e. 1.6 nS (Figure 6d), 1.9 nS (Figure 6e), and 2.2 nS (Figure 6f) respectively. The bottom row of surface plots in Figure 6 depict the network frequency for τ i = 30 ms and increasing values of w i i.e. 1.6 nS (Figure 6g), 1.9 nS (Figure 6h), and 2.2 nS (Figure 6i) respectively. Similarly, Figure 7 illustrates the relationship between the network synchronisation (vertical z axis) and the combined effects of tonic and synaptic inhibition -namely, increasing tonic conductance (x axis), shifting the inhibitory synaptic current baseline (y axis), enhancing synaptic current amplitudes (horizontally distributed surface plots), and prolonging synaptic current duration (vertically distributed surface plots). In particular, the top row of surface plots in Figure 7 depict the network frequency for τ i = 10 ms and increasing values of w i i.e. 1.6 nS (Figure 7a), 1.9 nS (Figure 7b), and 1.9 nS (Figure 7c) respectively. The middle row of surface plots in Figure 7 depict the network frequency for τ i = 14 ms and increasing values of w i i.e. 1.6 nS (Figure 7d), 1.9 nS (Figure 7e), and 2.2 nS (Figure 7f) respectively. The bottom row of surface plots in Figure 7 depict the network frequency for τ i = 30 ms and increasing values of w i i.e. 1.6 nS (Figure 7g), 1.9 nS (Figure 7h), and 2.2 nS (Figure 7i) respectively.

The presence of a non-zero inhibitory baseline current had a general tendency to produce lower network firing rates. Indeed for g ton = 0 nS, w i = 1.6 nS, and τ i = 10 ms, the network frequency was 20.83 ± 0.07 Hz at k bas 0 = pA, and decelerated to 16.76 ± 0.07 Hz at k bas = 100 pA. Moreover, for g ton = 20 nS, w i = 1.6 nS, and τ i = 10 ms, the network frequency was 10.10 ± 0.18 Hz at k bas 0 = pA, and decelerated to 0.04 ± 0.00 Hz at k bas = 100 pA. However, the sharp acceleration of the network frequency caused by tonic inhibition remained unaffected, aside from increasing k bas values causing the peak of the acceleration bump to shift towards lower Inria g ton values. For example, in Figure 6a for w i = 1.6 nS, τ i = 10 ms, and k bas = 0 pA the peak of the acceleration was at g ton = 15 nS with a frequency of 16.28 ± 0.23 Hz. Increasing k bas to 40 pA shifted the peak to g ton = 12 nS with a frequency of 15.73 ± 0.25 Hz. Further increasing k bas to 90 pA shifted the peak to g ton = 10 nS with a frequency of 15.26 ± 0.17 Hz. This effect is comparable to that caused by stronger synaptic weights w i , in that both increasing k bas and w i effectively correspond to an enhancement of global network inhibition.

As expected, longer synaptic time constants shifted the acceleration peak towards lower tonic inhibition strengths, regardless of the increasing synaptic baseline current. This shift can be observed when comparing the surface plots in Figure 6 vertically. Taking the first column of Figure 6 as an example, w i = 1.6 nS, τ i = 10 ms, and k bas = 40 pA the peak of the acceleration was at g ton = 15 nS (Figure 6a). Extending the synaptic time constant to τ i = 14 ms shifts the peak to g ton = 5 nS for k bas = 40 pA (Figure 6d). A longer time constant τ i = 30 ms shifts the peak to g ton = 0 nS for k bas = 40 pA (Figure 6g). Finally, stronger inhibitory synaptic weights globally decelerated the network activity (Figure 6a, Figure 6b, and Figure 6c), whilst preserving the bump-like pattern in the population frequency. These behaviours are consistent with our previously reported findings within this Chapter.

In addition, the network tonic-inhibition mediated synchronisation seemed to remain unaffected as k bas increased (Figure 7). The network continued to display enhanced synchronisation in the presence of critical degrees of tonic inhibition. Intensifying shifts in inhibitory baseline currents solely slightly shifted the synchronisation peak towards lower tonic conductance values. For example, in Figure 7a the synchronisation peak for k bas = 0 pA was at g ton = 0 nS with a synchronisation of κ(τ ) = 0.70 ± 0.01 for w i = 1.6 nS, and τ i = 10 ms. Increasing k bas to 60 pA shifted the peak to g ton = 12 nS with a synchronisation of κ(τ ) = 0.72 ± 0.01.

Longer synaptic time constants shifted the synchronisation peak towards lower tonic inhibition strengths, regardless of the increasing synaptic baseline current. This shift can be observed when comparing the surface plots in Figure 7 vertically. Finally, stronger inhibitory synaptic weights globally decreased the maximum attainable network synchronisation (Figure 7a, Figure 7b, and Figure 7c), whilst preserving the enhanced synchronisation phenomenon observed in the presence of tonic inhibition.

Tonic Inhibition Allows for the Emergence of Elevated Network Synchronisation

Having isolated the two model parameters which were responsible for significantly affecting the synchronisation exhibited by the network activity -namely, the tonic conductance g ton and the synaptic time constant τ i -we simulated an experiment in which we varied both of these parameters concurrently. The purpose of this simulation was to study the effect of the absorption of increasing doses of anaesthetic agent over time on network activity. We increased g ton from 0 nS to 20 nS in steps of 2 nS, and τ i from 10 ms to 20 ms in steps of 1 ms, in 2 s intervals. Figure 8 depicts the raster plot of the network activity for the first 14 s of simulation time, and Figure 9 the last 6 s of simulation time. Each raster plot is divided into 6 s intervals with an overlap of 2 s between them i.e. Figure 8a shows the network spikes between 0 s and 6 s, Figure 8b shows the network spikes between 4 s and 10 s, Figure 8c shows the network spikes between 8 s and 14 s, Figure 9d shows the network spikes between 12 s and 18 s, and Figure 9e shows the network spikes between 16 s and 22 s.

We observe how the network activity was fast (f = 18.79 ± 0.03 Hz) but loosely synchronised (κ(τ ) = 0.41 ± 0.01) between 0 s ≤ t ≤ 6 s (Figure 8a), where 0 nS ≤ g ton ≤ 4 nS and 10 ms ≤ τ i ≤ 12 ms. During this period of time, the population frequency (Figure 10a) decelerated from f = 20.77±0.01 Hz to f = 17.14±0.12 Hz, whilst the network synchronisation remained centred around κ(τ ) = 0.41 ± 0.01 (Figure 10b), as g ton and τ i increased (Figure 10c and Figure 10d respectively). As the neurons began absorbing stronger doses of propofol (6 nS ≤ g ton ≤ 8 nS and 13 ms ≤ τ i ≤ 14 ms) tighter synchronous activity emerged increasing up to a maximum value of κ(τ ) = 0.63 ± 0.00 for g ton = 8 nS and τ i = 14 ms. Concurrently, the network frequency accelerated to a maximum of f = 19.13±0.17 Hz (g ton = 6 nS and τ i = 13 ms) and subsequently began decelerating. The enhanced synchronisation is reflected in the raster plots in Figure 8b showing its emergence at t 6.5 s and in Figure 8c illustrating how the synchronisation persisted.

g ton = 12 nS and τ i = 16 ms at t = 12 s (Figure 9d) marked the end of the synchronisation rebound with κ(τ ) decreasing from 0.63±0.00 to 0.42±0.00 and population frequency decelerating to f = 18.04±0.04 Hz. Finally, further increases in propofol dosage (Figure 9e) caused a gradual weakening of global network activity (g ton geq14 nS, τ i ≥ 17 ms, and t ≥ 14 s), whose frequency eventually decayed to f = 2.74±0.02 Hz with a synchronisation of κ(τ ) = 0.08±0.00 at t = 22 s.

Conclusions and Discussion

GABAergic inhibition is thought to play an important role in the generation of oscillatory rhythmic activity in neural populations [START_REF] Bartos | Fast synaptic inhibition promotes synchronized gamma oscillations in hippocampal interneuron networks[END_REF], Bartos et al., 2007, Buzsáki and Wang, 2012, Cobb et al., 1995, Colgin, 2016]. In addition, GABA receptors have been shown to be the primary target of anaesthetic agents [Mueller et al., 2011, Rudolph andAntkowiak, 2004] and in particular of propofol [START_REF] Vanlersberghe | Modern Anesthetics: Handbook of Experimental Pharmacology[END_REF]. Indeed, propofol has been shown to target both synaptic and extrasynaptic GABA receptors with the effect of amplifying and extending the duration of inhibitory postsynaptic currents [START_REF] Adodra | Potentiation, activation and blockade of GABAA receptors of clonal murine hypothalamic GT1-7 neurones by propofol[END_REF], Bai et al., 2001, Kitamura et al., 2004, McDougall et al., 2008], enhancing extrasynaptic tonic inhibition [START_REF] Bai | Distinct functional and pharmacological properties of tonic and quantal inhibitory postsynaptic currents mediated by g -aminobutyric acid(A) receptors in hippocampal neurons[END_REF], McDougall et al., 2008, Song et al., 2011], and slowing the receptor desensitisation [START_REF] Bai | The general anesthetic propofol slows deactivation and desensitization of GABA(A) receptors[END_REF], Bai et al., 2001, Jin et al., 2009, McDougall et al., 2008]. In this work we presented an in-depth study of the action of anaesthesia on neural oscillations by modelling all of the afore-mentioned effects on a network of hippocampal interneurons.

Tonic Inhibition Produces Tighter Synchronous Activity

Our results show how propofol-mediated tonic inhibition contributes to enhancing network synchronisation in a network of hippocampal interneurons. Whilst propofol does also act on the phasic inhibition mediated by synaptic GABA A receptors, neither the increase in the amplitude and duration of the synaptic response, nor the desensitisation due to propofol binding on these receptors seemed to account for an increase in network synchronisation. The sole significant effect of phasic inhibition was to lower the threshold of tonic conductance necessary for the emergence of enhanced network synchronisation, by prolonging the duration of inhibitory postsynaptic currents. Taken together, these observations allow us to conclude that the enhanced network synchronisation we observed was mostly dependent on tonic inhibition mediated by extrasynaptic GABA receptors.

Enhanced Synchronisation for Neuronal Communication under General Anaesthesia

The role of neural oscillations has been extensively described in the literature, giving rise to a number of stimulating theories. Neural oscillations may represent the stable, unperturbed state of the brain [START_REF] Buzsáki | Neuronal oscillations in cortical networks[END_REF] during sleep, and can also be used as indicators of certain sleep stages [START_REF] Llinas | Coherent 40-Hz oscillation characterizes dream state in humans[END_REF]]. In addition, experimental studies Inria have linked synchronous activity with perception [START_REF] Engel | Dynamic predictions: Oscillations and synchrony in top-down processing[END_REF] stimulus encoding and representation [START_REF] Gray | Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties[END_REF], information integration and memory [START_REF] Colgin | Gamma oscillations in the hippocampus[END_REF], Engel et al., 2001, Kahana et al., 2001, Lisman, 2010, Lisman and Jensen, 2013, Varela et al., 2001] The common denominator of all of these theories is the hypothesis of neuronal communication through coherence [Fries, 2005], according to which synchronous activity enables communication and cooperation between neural ensembles. Indeed, functionally-linked brain regions have been shown to synchronise their operational frequency when collaborating. These include, and are not limited to, parietal and occipital regions during visual attention tasks [START_REF] Fries | Modulation of Oscillatory Neuronal Synchronization by Selective Visual Attention[END_REF]; hippocampus and (pre) frontal cortex during memory tasks [START_REF] Fell | Human memory formation is accompanied by rhinal-hippocampal coupling and decoupling[END_REF] and consolidation during sleep [START_REF] Maingret | Hippocampo-cortical coupling mediates memory consolidation during sleep[END_REF]; motor cortex and spinal motor neurons during movement tasks [START_REF] Conway | Synchronization between motor cortex and spinal motoneuronal pool during the performance of a maintained motor task in man[END_REF].

Intraoperative Awareness

The enhanced synchronisation described here could provide a possible mechanism supporting the occurrence of intraoperative awareness, intended as the explicit recollection of perceived stimuli during sedation. Patients who report having experienced intraoperative awareness often describe their ability to hear voices and sounds, to perceive visual stimuli such as the surgical lighting, to feel touch, and sometimes discomfort or pain [START_REF] Ghoneim | Awareness during anesthesia: Risk factors, causes and sequelae: A review of reported cases in the literature[END_REF], Moerman et al., 1993, Ranta et al., 1998, Sandin et al., 2000, Schwender et al., 1998], accompanied by a feeling of helplessness and the inability to communicate. Although rarely occurring -0.1% to 0.3% of patients according to experimental studies [START_REF] Ghoneim | Awareness during anesthesia: Risk factors, causes and sequelae: A review of reported cases in the literature[END_REF], Jones, 1994, Ranta et al., 1998] which, if we consider that in the US alone approximately 60000 patients undergo general anaesthesia every day [START_REF] Brown | General anesthesia, sleep, and coma[END_REF], equates to 60 to 180 patients per day -, intraoperative awareness is a traumatic experience which engenders fear and mistrust towards surgery and general anaesthesia, and can even sometimes lead to post-traumatic stress disorder [Osterman and Van Der Kolk, 1998, Osterman et al., 2001, Schwender et al., 1998]. The commons causes of intraoperative awareness are thought to be: insufficient drug dosages, increased anaesthetic requirements, damaged of defective drug delivery systems [START_REF] Ghoneim | Awareness during anesthesia: Risk factors, causes and sequelae: A review of reported cases in the literature[END_REF], Mashour, 2010]. These findings indicate that the occurrence of intraoperative awareness is heavily dependent on the concentration of the anaesthetic agent administered to, and absorbed by, the patient. General anaesthetics inhibit the conscious perception of pain but fail to fully cut off the pain transmission pathways from the sympathetic to the central nervous system. This is reflected in the haematological and metabolical responses commonly recorded under general anaesthesia, showing prototypical indicators of the surgical stress response -namely, increased heart rate and blood flow, and changes in skin conductance [Longnecker David E et al., 2008, Storm, 2008] -as well as in the statistical analyses of postoperative patient reports indicating that up to 30% of intraoperatively aware patients recall experiencing pain [START_REF] Sebel | The incidence of awareness during anesthesia: a multicenter United States study[END_REF]. Taken together, these observations indicate that the sympathetic and central nervous of system anaesthetised patients are capable of processing noxious stimuli. This allows us to postulate that propofol-enhanced network synchronisation could provide the favourable conditions needed for the perception of pain under general anaesthesia. Precise timing between the surgical incision and the anaesthesiadependent improved synchronous activity could facilitate the transmission of pain stimuli to the central nervous system in anaesthetised patients.

Implicit Memory Formation

There is a large volume of published studies describing the formation of implicit memories under general anaesthesia [START_REF] Andrade | Unconscious memory formation during anaesthesia[END_REF], Bonett et al., 2014, Cork et al., 1996, Ghoneim and Block, 1997, Jones, 1994, Kihlstrom et al., 1990]. According to these, anaesthetised patients perceive and remember auditory stimuli, and are capable of recalling them in postoperative interviews, without being able to consciously identify when and how these stimuli were encoded. A recent study described how propofol enables a dose-dependent increase in synchronous activity within the human medio-temporal lobe under general anaesthesia [START_REF] Fell | Human mediotemporal EEG characteristics during propofol anesthesia[END_REF]. These results, coupled with the theory that neural synchronisation between the entorhinal cortex and the hippocampus correlates with memory formation in humans [START_REF] Fell | Human memory formation is accompanied by rhinal-hippocampal coupling and decoupling[END_REF], provide a possible neural substrate underlying mnemonic processes during anaesthesia. Our model supports this view by making the compelling prediction that anaesthetic agents could facilitate the communication between brain structures which should supposedly be not allowed to do so under general anaesthesia. Therefore, memory formation under general anaesthesia could be facilitated by a propofol-dependent enhancement in rhinal-hippocampal coherence.

The dosage-dependent synchronisation enhancement described here is a transient phenomenon that may depend on subject sensitivity. Moreover, its transient characteristics may render it hard to observe and monitor. This could explain why a recent study [START_REF] Bejjani | No Evidence of Memory Processing During Propofol-Remifentanil Target-Controlled Infusion Anesthesia With Bispectral Index Monitoring in Cardiac Surgery[END_REF] did not find statistically significant evidence for implicit memory formation under general anaesthesia. A possible explanation could be that memory consolidation probably requires the conjunction of several conditions, for example a strong external stimulation (such as the noxious stimulus caused by a surgical incision) concurrent with the induction of anaesthesia. Indeed, it is not clear if memory formation happens during unconsciousness or during short periods of intraoperative awareness [START_REF] Bailey | Patients' memories of events during general anaesthesia[END_REF], Bejjani et al., 2009, Deeprose et al., 2004, Kerssens et al., 2005, Lubke et al., 1999, Willems et al., 2005]. In addition, implicit memory formation could also depend on the interaction of anaesthetic agents with other perioperative drugs.

Paradoxical Excitation

Paradoxical excitation is a state of increased arousal which commonly occurs shortly during the initial phases of the induction of anaesthesia [START_REF] Brown | General anesthesia, sleep, and coma[END_REF]. Although the mechanisms behind have been extensively investigated [START_REF] Bevan | Midazolam premedication delays recovery after propofol without modifying involuntary movements[END_REF], Clark and Rosner, 1973, Gibbs et al., 1936, Kiersey et al., 1951, McCarthy et al., 2008, Rampil, 1998], these are far from being fully unravelled. This phenomenon is dubbed "paradoxical" since it is caused by the administration of drugs which are supposed to suppress excitation rather than fostering it. Paradoxical excitation manifests itself in the form of involuntary purposeless or defensive movements, the expression of incoherent speech, and sometimes euphoria or dysphoria [START_REF] Bevan | Midazolam premedication delays recovery after propofol without modifying involuntary movements[END_REF], Clark and Rosner, 1973, Gibbs et al., 1936, Kiersey et al., 1951, McCarthy et al., 2008, Rampil, 1998].

One possible explanation behind the emergence of paradoxical excitation under general anaesthesia is based on the circuit hypothesis [Schiff andPosner, 2007, Schiff, 2008]. This theorises that a dosage-dependent disinhibition of striatothalamic pathways may allow the reactivation of stimuli which were temporarily stored within the thalamus prior to the induction of sedation. Since thalamocortical circuits have been shown to be involved in arousal regulation [Schiff, 2008] it is conceivable that a temporary stimulation of the thalamus could awaken anaesthetised subjects. Indeed, this was demonstrated to be the case in various experimental studies [START_REF] Alkire | Thalamic Microinjection of Nicotine Reverses Sevoflurane-induced Loss of Righting Reflex in the Rat[END_REF], Schiff et al., 2007]. However, the mechanisms mediating this disinhibition under general anaesthesia remain unclear.

A theoretical model [START_REF] Mccarthy | Potential network mechanisms mediating electroencephalographic beta rhythm changes during propofolinduced paradoxical excitation[END_REF] attempted to provide another explanation for the occurrence of paradoxical excitation. Here, the authors investigated the cellular mechanisms underlying the changes in the EEG signal recorded from anaesthetised patients during paradoxical excitation events -namely an increase in beta power [START_REF] Gugino | Quantitative EEG changes associated with loss and return of consciousness in healthy adult volunteers anaesthetized with propofol or sevoflurane[END_REF]. Their results indicate that an interaction between the GABAergic synaptic current and an intrinsic Inria M-current produces a propofol-dependent switch in inhibitory network activity synchronisation, which enhances excitation in postsynaptic pyramidal neurons [START_REF] Mccarthy | Potential network mechanisms mediating electroencephalographic beta rhythm changes during propofolinduced paradoxical excitation[END_REF] leading to enhanced excitation. However, their model fails to account for the effects of propofol-mediated tonic inhibition. We suggest including these as an avenue for future work.

[ Willems et al., 2005] Willems, S. J., Forster, A., and Linden, M. V. D. (2005) a Given τ i = 10 ms and w i = 1.6 nS, the bump-like pattern caused by the tonic inhibition-mediated (x axis) deceleration followed by an acceleration of the network frequency is unaffected by the presence of a non-zero synaptic baseline current (y axis). These only slightly shift the peak of the acceleration towards lower g ton values. The acceleration bump is unaffected by stronger synaptic weightsw i = 1.9 nS in b, and w i = 1.6 nS in c. d Given τ i = 14 ms and w i = 1.6 nS, the peak of the acceleration shifts towards lower g ton values. This behaviour is unaffected by stronger synaptic weights -w i = 1.9 nS in e, and w i = 1.6 nS in f. g Given τ i = 30 ms and w i = 1.6 nS, the network acceleration follows a decreasing trend as g ton and k bas are increased. This behaviour is unaffected by stronger synaptic weights -w i = 1.9 nS in h, and w i = 1.6 nS in i. The network was stimulated with a constant current I stim = 0.4 nA. Figure 7: Propofol-enhanced tonic inhibition allows for tighter network synchronisation, regardless of the presence of a stronger inhibitory baseline current. a Given τ i = 10 ms and w i = 1.6 nS, the bump-like pattern caused by the tonic inhibition-mediated (x axis) enhanced synchronisation is unaffected by the presence of a non-zero synaptic baseline current (y axis). These only slightly shift the peak of the synchronisation towards lower g ton values. The synchronisation bump is unaffected by stronger synaptic weights -w i = 1.9 nS in b, and w i = 1.6 nS in c. d Given τ i = 14 ms and w i = 1.6 nS, the peak of the synchronisation shifts towards lower g ton values. This behaviour is unaffected by stronger synaptic weightsw i = 1.9 nS in e, and w i = 1.6 nS in f. g Given τ i = 30 ms and w i = 1.6 nS, the network synchronisation follows a decreasing trend as g ton and k bas are increased. This behaviour is unaffected by stronger synaptic weights -w i = 1.9 nS in h, and w i = 1.6 nS in i. The network was stimulated with a constant current I stim = 0.4 nA. The network synchronisation follows a bump-like pattern, increasing from a baseline of κ(τ ) = 0.41 ± 0.01 between 0 s ≤ t ≤ 6 s to a maximum of κ(τ ) = 0.63 ± 0.00 for g ton = 8 nS and τ i = 14 ms at 8 s ≤ t ≤ 10 s. Further anaesthetic dosages gradually lower the network synchronisation. b The network frequency follows a bump-like pattern, decelerating between 0 s ≤ t ≤ 6 s and then accelerating to a maximum of f = 19.13 ± 0.17 Hz for g ton = 6 nS and τ i = 13 ms at 6 s ≤ t ≤ 8 s. Further anaesthetic dosages gradually decelerate the network frequency. c g ton is increased from an initial value of 0 nS in steps of 2 nS every 2 s. d τ i is increased from an initial value of 10 ms in steps of 1 ms every 2 s.

Figure 1 :

 1 Figure1: Increasing propofol enhances network synchronisation. a At low values of propofol (0 nS ≤ g ton ≤ 13 nS) the network synchronisation is stable at an average value of κ(τ ) = 0.43 ± 0.01. Increasing the propofol dosage -by acting on the tonic conductance g ton -causes the overall activity of the network to decrease, until a critical value of g ton = 14 nS at which both the network synchronisation a, and the firing rate b increase to κ(τ ) = 0.72, and f = 16.57 Hz respectively. The oscillation frequency c follows a monotonically decelerating trend. When the concentration value reaches a value of g ton ≥ 21.5 nS the activity, synchronous or otherwise, fades out (κ(τ ) = 0, f = 0 Hz and f osc = 0 Hz for g ton >= 21.5 nS).

Figure 2 :

 2 Figure 2: Increasing propofol dosage enhances network synchronisation. a Raster plot for the 100-cell inhibitory network in the absence of propofol (g ton = 0 nS), showing f osc = 42.67 Hz oscillations with a synchronisation of κ(τ ) = 0.4, τ = 10 ms. b Raster plot for the same network with a higher dose of propofol (g ton = 15 nS), showing f osc = 20.67 Hz oscillations with a synchronisation of κ(τ ) = 0.8, τ = 10 ms. c Raster plot for the same network with a higher dose of propofol (g ton = 18 nS), showing f osc = 17.33 Hz oscillations with a synchronisation of κ(τ ) = 0.8, τ = 10 ms. d Raster plot for the same network with a higher dose of propofol (g ton = 21 nS), showing f osc = 12.67 Hz oscillations with a synchronisation of κ(τ ) = 0.8, τ = 10 ms. The network was stimulated with a constant current I stim = 0.4 nA.

Figure 3 :Figure 4 :Figure 5 :Figure 6 :

 3456 Figure3: The synchronous activity displayed by the interneuron network is reflected in the computed LFP signals. a LFP signal computed from the spiking activity of the inhibitory network in the absence of propofol shows f osc = 42.67 Hz oscillations with a synchronisation of κ(τ ) = 0.4, τ = 10 ms (one-second extract). b LFP signal computed from the spiking activity of the inhibitory network with a higher dose of propofol (g ton = 15 nS), showing f osc = 20.67 Hz oscillations with a synchronisation of κ(τ ) = 0.8, τ = 10 ms (one-second extract). c LFP signal computed from the spiking activity of the inhibitory network with a higher dose of propofol (g ton = 18 nS), showing f osc = 17.33 Hz oscillations with a synchronisation of κ(τ ) = 0.8, τ = 10 ms (one-second extract). d LFP signal computed from the spiking activity of the inhibitory network with a higher dose of propofol (g ton = 21 nS), showing f osc = 12.67 Hz oscillations with a synchronisation of κ(τ ) = 0.8, τ = 10 ms (one-second extract).

Figure 8 :Figure 9 :Figure 10 :

 8910 Figure8: Enhanced network synchronisation emerges as tonic inhibition is strengthened and synaptic time constants are prolonged. g ton and τ i are increased every 2 s in steps of 2 nS and 1 ms respectively. a Initially the network activity is fast (f = 18.79 ± 0.03 Hz) but loosely synchronised (κ(τ ) = 0.41 ± 0.01) between 0 s ≤ t ≤ 6 s, where 0 nS ≤ g ton ≤ 4 nS and 10 ms ≤ τ i ≤ 12 ms. b Enhanced synchronisation emerges at t 6.5 ms, and the network activity accelerates to a maximum of f = 19.13 ± 0.17 Hz for g ton = 6 nS and τ i = 13 ms. c The maximum synchronisation (κ(τ ) = 0.63 ± 0.00) occurs for g ton = 8 nS and τ i = 14 ms at 8 s ≤ t ≤ 10 s. The network was stimulated with a constant current I stim = 0.4 nA.

  -Rocquencourt BP 105 -78153 Le Chesnay Cedex inria.fr ISSN 0249-6399

Table 1 :

 1 Inhibitory neuron model parameters.

	Parameter	Value
	g l	0.1 mS cm -2
	E l	-65 mV
	g K	9 mS cm -2
	E K	-90 mV
	g N a	35 mS cm -2
	E N a	55 mV
	area	14000 µm 2
	C m	1 µF cm -2
	E i	-80 mV
	τ i	10 ms

  . Investigation of Implicit Memory during Isoflurane Anesthesia for Elective Surgery Using the Process. Fast-Spiking Hippocampal Interneurons . . . . . . . . . . . . . . . . . . . . . . . 4 2.2 Modelling the Effects of Anaesthetics on GABA A Receptors . . . . . . . . . . . . 5 2.2.1 Synaptic Phasic Inhibition . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.2.2 Extrasynaptic Tonic Inhibition . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Network Configuration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.4 External Current Stimulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.5 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.6 Network Synchronisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 Tonic Inhibition Improves Neural Synchronisation . . . . . . . . . . . . . . . . . 7 4 Results -Combining the Effects of Tonic and Phasic Inhibition 10 4.1 Propofol-Enhanced Inhibitory Synaptic Conductance Does not Hinder Synchronisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.2 Prolonged Synapse Closing Times Allow for Synchronisation with Weaker Tonic Inhibition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 4.3 Tonic Inhibition-Mediated Synchronisation Is Unaffected by Potentiated Inhibitory Synaptic Baseline Currents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 4.4 Tonic Inhibition Allows for the Emergence of Elevated Network Synchronisation 13 Tonic Inhibition Produces Tighter Synchronous Activity . . . . . . . . . . . . . . 14 5.2 Enhanced Synchronisation for Neuronal Communication under General Anaesthesia 14 5.2.1 Intraoperative Awareness . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5.2.2 Implicit Memory Formation . . . . . . . . . . . . . . . . . . . . . . . . . . 15 5.2.3 Paradoxical Excitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

	Contents
	Anes-
	thesiology, 103:925-933. 1 Introduction	3
	[Zhou et al., 2012] Zhou, C., Liu, J., and Chen, X.-D. (2012). General anesthesia mediated by 2 Methods	4
	effects on ion channels. World journal of critical care medicine, 1(3):80-93. 2.1 3 Results -Studying Tonic Inhibition	7
	3.1 5 Conclusions and Discussion	14
	5.1 Inria

RR n°9320

Buhry & Giovannini

Acknowledgements

Laure Buhry thanks the CNRS for its financial support under the PEPS INS2I 2016. Laure Buhry and Francesco Giovannini thank Jean-Baptiste Schneider for his internship work in the Neurosys team.