Charles-Henri Malbert

Eric Bobillier-Chaumont

Chloé Picq

Jean-Louis Divoux

David Guiraud

Christine Henry

Eric Bobillier

Effects of

Keywords: Vagal stimulation, bariatric surgery, pulson, PET imaging, animal model

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24 pigs. After two weeks of chronic stimulation, food intake and brain metabolism were investigated. The electrical characteristics and histology of the vagus nerve were also studied.

Results

S3 stimulation required a lower amount of charges to trigger an action potential.

Chronically applied S2 & S3 activated the dorsal vagal complex and increased the metabolism of its afferent cortical structures. They also reduced energy intake together with a reduced ingestion of high fat and high sugar diets. All these effects were not observed for the S1 group. The vagal histology for the S1, S2 and S3 groups was not different from that of the sham.

Introduction

Obesity is an international public health issue that affects quality of life, increases the risk of illness, and raises health-care costs. Bariatric surgery remains the most effective treatment for obese patients [START_REF] Acosta | Recent advances in clinical practice challenges and opportunities in the management of obesity[END_REF]. However, these procedures could be associated with major adverse-effects [START_REF] Andrés | Roux-en-Y gastric bypass: major complications[END_REF]. There is an urgent need for alternative therapeutics.

Chronic vagal stimulation has the potential for weight control [START_REF] De Lartigue | Role of the vagus nerve in the development and treatment of diet-induced obesity[END_REF], but the animal and human data are ambiguous [START_REF] Koren | Vagus nerve stimulation does not lead to significant changes in body weight in patients with epilepsy[END_REF][START_REF] Pardo | Weight loss during chronic, cervical vagus nerve stimulation in depressed patients with obesity: an observation[END_REF][START_REF] Val-Laillet | Chronic vagus nerve stimulation decreased weight gain, food consumption and sweet craving in adult obese minipigs[END_REF]. This might relate to the different modalities of stimulation, including the location of the stimulating electrodes [START_REF] Królczyk | Effects of continuous microchip (MC) vagal neuromodulation on gastrointestinal function in rats[END_REF], the number of electrodes for bilateral or unilateral stimulation [START_REF] Laskiewicz | Effects of vagal neuromodulation and vagotomy on control of food intake and body weight in rats[END_REF], the stimulation profile and current intensity [START_REF] Burneo | Weight loss associated with vagus nerve stimulation[END_REF][START_REF] Sobocki | Does vagal nerve stimulation affect body composition and metabolism? Experimental study of a new potential technique in bariatric surgery[END_REF]. In addition, body mass index [START_REF] Bodenlos | Vagus nerve stimulation and food intake: effect of body mass index[END_REF] and diets [START_REF] Bugajski | Effect of long-term vagal stimulation on food intake and body weight during diet induced obesity in rats[END_REF] are confounding factors.

Retrospectively, the most efficient stimulation strategy was close to that used for epilepsy, e.g., 500 millisecond pulses of 2.5 to 5 mA for 30 sec every 5 minutes [START_REF] Biraben | Central activation after chronic vagus nerve stimulation in pigs: contribution of functional imaging[END_REF], applied on both abdominal or thoracic vagal trunks. However, the optimal stimulation parameters need to be investigated [START_REF] De Lartigue | Role of the vagus nerve in the development and treatment of diet-induced obesity[END_REF].

At the abdominal level, most vagal neurons located either in the dorsal or ventral vagal trunks are small diameter myelinated and un-myelinated neurons, i.e., A∂ or C type [START_REF] Mei | The composition of the vagus nerve of the cat[END_REF]. Therefore, large current pulses are required for depolarizing the axon membrane and thus generating an action potential. To do so, more than 20 mA may be needed at this level [START_REF] Guiraud | Vagus nerve stimulation: state of the art of stimulation and recording strategies to address autonomic function neuromodulation[END_REF]. While they proved to be effective in an acute set-up, these currents are unrealistic in a chronic implant since they generate damages both to the electrode and to the tissues [START_REF] Merrill | Electrical stimulation of excitable tissue: design of efficacious and safe protocols[END_REF].

Recently, Qing et al. [START_REF] Qing | Burst-Modulated Waveforms Optimize Electrical Stimuli for Charge Efficiency and Fiber Selectivity[END_REF] proposed to chop rectangular based waveforms into shorter rectangular waves lasting between 40 to 80 µsec, called pulsons. While individual pulsons were unable to trigger an action potential, they appear collectively to be effective in anaesthetized rats for stimulating C fibres at the cervical level. Furthermore, they achieved this with less charge injection than with a long lasting rectangular waveform. However, the efficacy of this method has never been tested in chronic conditions, and its capability to trigger action potentials in small diameter neurons at the abdominal or thoracic level remains to be proven.

Our hypothesis was that the classical stimulation scheme using low intensity, long-lasting current pulses (1-5 mA, 500 to 1000 µs) is unable to activate a large number of abdominal vagal neurons [START_REF] Guiraud | Vagus nerve stimulation: state of the art of stimulation and recording strategies to address autonomic function neuromodulation[END_REF]. This, in turn, might recruit only a limited number of neurons in the dorsal vagal complex (DVC). The extend of activated DVC neurons might be so small that it impossible to identify a DVC activation (versus background noise) because of the intrinsic limitations of our present imaging methods [START_REF] Ridgway | Ten simple rules for reporting voxel-based morphometry studies[END_REF]. Hence the reported absence of activation of the DVC in individuals with vagal stimulation irrespective of the brain imaging method used [START_REF] Guiraud | Vagus nerve stimulation: state of the art of stimulation and recording strategies to address autonomic function neuromodulation[END_REF][START_REF] Arle | Essential neuromodulation[END_REF][START_REF] Bari | Brain imaging correlates of peripheral nerve stimulation[END_REF][START_REF] Henry | Brain blood-flow alterations induced by therapeutic vagus nerve stimulation in partial epilepsy: II. prolonged effects at high and low levels of stimulation[END_REF][START_REF] O'reardon | Vagus Nerve Stimulation (VNS) and Treatment of Depression: To the Brainstem and Beyond[END_REF]. Conversely, using pulsons, large intensity currents could be applied to the nerve trunk, allowing effective triggering of a neuronal response through a larger amount of small diameter neurons being recruited.

Our primary objective was to demonstrate that, in anaesthetized animals, pulsons of large current intensity applied bilaterally on both abdominal vagal trunks are able to trigger action potentials in small diameter neurons (C and A∂ types), while their activities were recorded at the cervical level using the single fibre method. Our secondary objective was to investigate the long-lasting consequences on brain metabolism of chronic vagal stimulation using pulsons. Our third objective was to evaluate the capability of this stimulation pattern to modify food intake and to correlate these changes with the alterations in brain metabolism measured by PET imaging. These objectives were carried out using the large white pig as a large animal model of normal human physiology [START_REF] Sauleau | The pig model in brain imaging and neurosurgery[END_REF]. Furthermore, the size of the animal is well suited for laparoscopic surgery and for brain imaging using high end clinical PET scanners [START_REF] Malbert | Obesity-Associated Alterations in Glucose Metabolism are Reversed by Chronic Bilateral Stimulation of the Abdominal Vagus Nerve[END_REF].

In this study, we assessed, first in an acute set-up, the capability of three vagal stimulation schemes to trigger action potentials on slow adapting gastric and intestinal mechanosensitive vagal neurons (A∂ and C types). One stimulation pattern reproduced the classical long lasting pulse (S1) while the others (S2 and S3) integrated pulsons. The same stimulation patterns were also compared, in a chronic experiment, for their capabilities to modify brain metabolism and food intake behaviour.

Methods

The experimental procedures were conducted in accordance with the current ethical standards of the European and French legislation (Agreement number A35-622 and Authorization number 01894, Ethical approval R-2012-CHM-03 and 00341.01).

Experimental paradigm

Acute experiment

The experiment consisted of recording evoked action potentials at the cervical level on the left vagal nerve after careful microdissection of the nerve bundle to obtain single neuron action potentials. Evoked action potentials were generated by applying current pulses on two cuff electrodes implanted on the anterior and posterior vagus nerve at the entrance of the diaphragm using a lateral thoracic approach. This terminal procedure was performed on 5 animals. Two to three neurons per animal were analysed for the entire range of stimulation, while 4 to 8 neurons were unable to be studied for all current/stimulation scheme combinations, as a consequence of mechanical stress on the bundle or perineurium bleeding.

The stimulation pulses are presented in Figure 1 and consisted of a long lasting 1000 µsec pulse (S1), 14 constant amplitude pulsons forming a pattern lasting 1000 µsec (S2) and 14 pulsons of rising amplitude (S3) with a total duration identical to the two former patterns.

Current increments in amplitude used in the last stimulation pattern were following a onefourth sinusoidal series. The stimulating patterns were applied in a sequential manner, but the order was randomly selected. One minute without stimulation was allowed between each stimulation pattern.

Chronic experiment

The procedure was performed on 24 growing pigs (50% sex ratio and age-matched) distributed in 4 experimental groups consisting of sham, S1, S2 or S3 stimulation patterns (Figure 1). The experiment started with the application of one of the three stimulation patterns (Figure 1) or a sham stimulation immediately after the surgical procedure used to insert the stimulating electrodes (see supplementary material). The animals were placed for the entire experimental period in a robotic feed dispenser to evaluate their food intake. At the end of this period, the brain metabolism was mapped using PET-FDG imaging and the animal was euthanized afterwards. The vagal trunks were sampled for histological assessment of potential damage due to the stimulation.

We selected purposely different current amplitudes for S1 and for S2/S3 with the aim to inject the same amount of electrical charges per unit of time irrespective of the stimulation pattern. As a consequence, the S1 current was set to the maximal current used during unilateral vagal stimulation at the cervical level for epilepsy therapy, i.e., 5 mA supplying 5 µC. This value was also proven to be effective when applied bilaterally at the juxta-diaphragmatic level to alter food intake in pigs [START_REF] Val-Laillet | Chronic vagus nerve stimulation decreased weight gain, food consumption and sweet craving in adult obese minipigs[END_REF][START_REF] Biraben | Central activation after chronic vagus nerve stimulation in pigs: contribution of functional imaging[END_REF]. For the S2 stimulation pattern, the current required to inject the same 5 µC charge was 15 mA. Therefore, this current was selected for the S2 and S3 stimulation patterns. Consequently, S3 stimulation pattern injected 3.52 µC, i.e., approximately one third less charges than the S2 or S1 stimulation patterns.

Animals

All experiments were performed on young Large-White pigs weighing 32 ± 4 kg at the time of surgery. The animals were housed in individual cages, one week before the beginning of the experiment to allow adaptation to their new environment, and subjected to standard 12 : 12 h light dark cycle. During this period, the animals used in the acute experiment were fed daily between 08.00 h and 09.00 h with 1 kg of granulated porcine meal (3.63 kcal/g)..

The animals used for the chronic experiment were placed in special cages that include a robotic feeder, during the same time period and until the completion of the experiment 15 days after the surgery. Within this device, they had simultaneous access to three types of test feeds during 30 minutes at 9:00, 12:30 and 17:00 (see food intake and analysis below). Water was provided ad libitum.

Stimulating electrodes and device

Acute experiment

The animals were anaesthetized and surgically prepared for a dissection of the cervical vagus as previously described [START_REF] Cuche | Desensitization of ileal vagal receptors by short-chain fatty acids in pigs[END_REF]. A surgical access to the mediastinal area allowed the insertion of the cuff electrodes around both vagal trunks. They comprised two pairs of Pt-Ir 10% half-circular contacts (4 in total), short-circuited together to form a bipolar configuration. The overall dimension of the cuff was 25 ± 0.1 mm. The stimulation pattern was created using a D/A card (National instrument, USA) running a custom made software written using Labview. The voltage output of the D/A card was connected to a batteryoperated buffer amplifier that created a mirror current output while allowing electrical insulation with an optical coupling between the computer and the animal.

Chronic experiment

Two sets of cuff electrodes were fixed on the dorsal and ventral trunks using laparoscopy as described in the supplementary material. The electrode leads exited in the interscapular space and were connected to an external portable stimulator placed between the shoulders and held in position by a harness. The stimulators used were custom built either at the INRA (S1 pattern) or Axonic (S2 and S3 patterns) laboratories.

Recordings and data analysis

Vagal recording and analysis Electrical activity from single vagal afferent neurons was recorded by classical neurophysiological methods adapted to the pig [START_REF] Cuche | Desensitization of ileal vagal receptors by short-chain fatty acids in pigs[END_REF] and described in the supplementary material. Evoked potentials were recorded on characterized gastric or duodenal afferent neurons. Neurons with increased firing frequency during light distension of either the stomach or the proximal duodenum were selected by microdissection of the vagal bundle.

To achieve bowel distensions, a mid-line laparotomy was performed prior to nerve dissection to insert an inflatable balloon in the stomach and another one in the proximal duodenum. The balloons were connected to a home-made inflator/deflator capable of inflating the gastric or the duodenal balloon to a set pressure (20 mmHg) within 2 to 3 seconds.

Evoked potentials were analysed using dedicated software that allowed the identification of the occurrence or the absence of an action potential in three dimensions: time of occurrence during the sweep, sweep number and amplitude of the action potential. The conduction speed was calculated knowing the time of occurrence of the action potential and the distance between the stimulating and recording electrodes.

Impedance measurements

The impedance of the stimulating electrodes was recorded periodically using the method described elsewhere [START_REF] Wei | Impedance characteristics of deep brain stimulation electrodes in vitroand in vivo[END_REF] and detailed in the supplemental material. PET imaging After 15 days of chronic stimulation or sham procedure, a PET imaging with 18 Fluorodeoxyglucose was performed in anaesthetized animals as already described [START_REF] Clouard | Exposures to conditioned flavours with different hedonic values induce contrasted behavioural and brain responses in pigs[END_REF].

The 3D images were spatially normalized according to a porcine template (28) using PMod (Pmod Switzerland). They were analysed afterward with statistical parametric mapping (SPM8, Wellcome Trust Centre for Neuroimaging, London, UK).

Food intake measurement and analysis

The pigs received all their food from a robotic feeder comprising three troughs placed side by side. The animals had simultaneous access to the control (balanced), high lipids and high glucose test feeds at 9:00, 12:30 and 17:00, 30 minutes each, to assess their food preferences and food intake patterns. Details of the robotic feeder and data analysis were given in the supplementary material section.

Histological preparation and measurements

For histological analysis, 6-cm segments were collected from the ventral and dorsal vagus at the level of the cuffs and prepared as already described [START_REF] Val-Laillet | Chronic vagus nerve stimulation decreased weight gain, food consumption and sweet craving in adult obese minipigs[END_REF]. The number of the nerve bundles and the nerve area were calculated manually.

Statistics

Brain PET first-level analysis was performed as a series of paired t-tests (S1 > S0, S2 > S0 and S3 > S0) with a provision for type II error cancellation. These analyses were thresholded at p < 0.001 (false discovery rate -FDR). A conjunction analysis with a 3*6 full factorial analysis of variance with the study as an independent factor, and the effect (stimulation) as a dependent factor, was performed to identify the areas activated in all stimulation patterns versus sham. Other continuous dependent variables were analysed with ANOVA using Stata software.

Results

Effect of the stimulating patterns on current threshold in anaesthetized animals

Based on their conduction speed, seven neurons were identified as A∂ type while the remaining were C type. Seven of them had their receptor field located in the duodenum while the remaining 8 had their receptor field located in the stomach. The mechanical half adaptation time equalled 4.8 ± 0.08 sec for the duodenal projecting neurons, and 3.2 ± 0.04 sec for the gastric ones. The firing threshold of the gastric neurons was higher than the duodenal ones: 20 ± 2.8 vs 13 ± 3.1 mmHg, respectively.

The most efficient stimulating pattern to elicit an action potential was the rising burst pattern (S3) without differences between gastric versus duodenal neurons (Table 1, Figure 2). Indeed, the quantity of charges required to trigger action potentials was 18.7 ± 0.50, 6.8 ± 0.23 and 4.8 ± 0.16 µC for S1, S2 and S3, respectively (p<0.001 from each other).

Effects of the stimulating patterns on brain activity and food intake behaviour

We did not identify any clinically relevant deleterious side-effects during the experimental period irrespective of the stimulation pattern group.

Large differences in brain metabolism were observed between stimulation patterns compared to sham stimulation (Figure 3). S1 stimulation was unable to activate the DVC, unlike the S2 and S3 stimulation patterns. These two stimulation patterns were equally effective to increase the metabolism of the posterolateral region of the medulla including the solitary tract and the parabrachial area. However, due to the PET's spatial resolution, it was impossible to identify the exact nucleus involved. All primary or secondary afferent structures of the DVC were also activated with S2 or S3 stimulations (thalamus, insular cortex, superior colliculus, cingular cortex; Table 3 and4). Both S2 and S3 stimulation patterns had an impact on the prefrontal cortex, which was unaltered with S1 stimulation.

Unlike S2 or S3 stimulations, S1 was able to activate the ventral segmental area (Table 2).

Conjunction analysis allowed us to identify the area(s) that were activated by the three stimulation patterns. Surprisingly, only the medial hypothalamic area was found to be activated in all stimulation conditions compared to the sham group (P FWE = 0.001, Figure 4). Food intake was significantly modified 14 and 15 days after the onset of the stimulation.

The S2 and S3 stimulation patterns only reduced the overall daily intake (p<0.05) compared to sham, without any significant difference between S2 and S3. This reduction was due to (1) a change in diet preferences and (2) a reduction in the duration of the eating bouts within a single meal: (1) The high-fat diet and high sugar diet intake were both significantly reduced, while the ingestion of the balanced diet was unchanged compared to sham group (Figure 5). ( 2) The duration of eating bouts was also significantly reduced within the 30 minutes of diet access for S2 and S3 groups compared to sham (101 ± 8.2; 94 ± 18.5; 61 ± 3.3 and 62 ± 5.1 sec for Sham, S1, S2 and S3, p = 0.919; 0.036 and 0.044 for Sham vs S1; Sham vs S2 and Sham vs S3 respectively). However, this reduction was not significantly different depending on the diet. Furthermore, the ingestion speed and the daily number of eating bouts were unchanged in S1, S2 and S3 groups compared to sham (Figure 6). Finally, most of these changes in food intake pattern were observed during the last meal of the day and they were not spread over the three-daily food distribution.

Impedance and histological consequences of the stimulating patterns on abdominal vagal nerve structure

There was no significant difference between dorsal and ventral nerve bundles, which were pooled later. Rf (in parallel resistor with the capacitive load) was increased in the S2 and S3 groups compared to sham group. Rs (in series resistor) was also significantly larger in the S2 group (Figure 7).

There was a large quantity of connective tissue around the electrode cuffs that doubled the size of the vagus irrespective of the experimental group. The number of neuron bundles within the nerve was not significantly different between the groups: 39 ± 2.9, 37 ± 1.7, 36 ± 2.5 and 38 ± 2.7 for sham, S1, S2 and S3, respectively (Figure 8). The area of the nerve was altered for sham versus all the other groups, but it was not possible to identify a significant difference between sham and each of the stimulation groups using post hoc multiple comparisons test: 2.0 ± 0.15, 2.8 ± 0.38, 2.8 ± 0.37 and 2.6 ± 0.20 µm 2 *1E 5 for sham, S1, S2 and S3, respectively.

Discussion

We demonstrated that pulson-type stimulation applied to the abdominal vagus has the capability to evoke action potentials on small-diameter C and A∂ neurons, which represent the majority of abdominal vagal neurons. Similarly, it had the capability to increase the metabolism of the DVC and other brain areas that are primary or secondary afferent projections from the DVC. Finally, pulson stimulation was able to alter food intake, within two weeks, unlike the classical millisecond stimulation pattern that takes several weeks to be effective [START_REF] Val-Laillet | Chronic vagus nerve stimulation decreased weight gain, food consumption and sweet craving in adult obese minipigs[END_REF][START_REF] Biraben | Central activation after chronic vagus nerve stimulation in pigs: contribution of functional imaging[END_REF]. Since this stimulation pattern required approximately one-third of the charge needed for a classical long lasting pulse to evoke an action potential, it has the potential to be used chronically without altering the integrity of the nerve. Indeed, we could not find a difference in the histological remodelling of the nerve between stimulation groups.

Several limitations should be acknowledged. First, we did not evaluate different amplitudes for the pulsons stimulation (S2 and S3 groups) during our chronic experiment. This was the consequence of the difficulty to handle a large animal model, including brain imaging sequences and behavioural recordings, over several weeks. Using growing pigs instead of miniature pigs made it difficult to extend the experiment over several months, which would have been the optimal experimental design. However, at the time of study, we were not able to have an implantable stimulator capable of suppling S2 or S3 stimulations over several months, and an external stimulator would have been unethical for such an extended period of time. Second, we did not compare the same current amplitude in S1 and in S2/S3 groups. However, this was done on purpose because currents up to 15 mA for the S1 pattern were unrealistic due to safety and nerve damage concerns [START_REF] Guiraud | Vagus nerve stimulation: state of the art of stimulation and recording strategies to address autonomic function neuromodulation[END_REF][START_REF] Arle | Essential neuromodulation[END_REF].

While our initial end-point was to elicit brain metabolism changes with the pulson stimulation that was different from those observed with the classical pulse-type stimulation, we were able to identify altered food intake as early as 14 to 15 days after the onset of very high frequency stimulation. This delay is sharply less than the 5 weeks one demonstrated in prior experiments using S1 stimulation either in growing lean or morbid obese minipigs [START_REF] Val-Laillet | Chronic vagus nerve stimulation decreased weight gain, food consumption and sweet craving in adult obese minipigs[END_REF][START_REF] Biraben | Central activation after chronic vagus nerve stimulation in pigs: contribution of functional imaging[END_REF]. To our knowledge, this is the first demonstration of such early (e.g occurring 2 weeks only after the onset of the stimulation instead 5 weeks) behavioural effect of chronic vagal stimulation [START_REF] De Lartigue | Role of the vagus nerve in the development and treatment of diet-induced obesity[END_REF][START_REF] Pardo | Weight loss during chronic, cervical vagus nerve stimulation in depressed patients with obesity: an observation[END_REF][START_REF] Sobocki | Does vagal nerve stimulation affect body composition and metabolism? Experimental study of a new potential technique in bariatric surgery[END_REF][START_REF] Yuan | Vagus Nerve and Vagus Nerve Stimulation, a Comprehensive Review: Part I[END_REF], and it is a strong argument in favour of the efficacy of pulsons stimulation. Furthermore, the comprehensive use of a robotic feeder together with the development of algorithms for precise evaluation of food intake behavior allowed to identify the origin of the overall reduction in food intake. It relates both on a decreased duration of eating bouts and a reduced preference for high fat and high sugar diets.

PET data demonstrated that all stimulation patterns activated the insular cortex as already demonstrated with unilateral cervical VNS in humans and animals [START_REF] O'reardon | Vagus Nerve Stimulation (VNS) and Treatment of Depression: To the Brainstem and Beyond[END_REF][START_REF] Yuan | Vagus Nerve and Vagus Nerve Stimulation, a Comprehensive Review: Part I[END_REF]. Furthermore, we also observed an activation of the cingular cortex irrespective of the stimulation pattern, which is compatible with DVC projection [START_REF] Bari | Brain imaging correlates of peripheral nerve stimulation[END_REF][START_REF] O'reardon | Vagus Nerve Stimulation (VNS) and Treatment of Depression: To the Brainstem and Beyond[END_REF]. Finally, the activation of the prefrontal cortex could reflect its connectivity with the thalamo-insular pathway, which is altered during VNS-dependent alterations in synaptic plasticity [START_REF] Hays | Enhancing Rehabilitative Therapies with Vagus Nerve Stimulation[END_REF]. Undoubtedly, the activation of the medulla in the vicinity of the DVC was an important observation that was found with the S2 and S3 stimulation patterns only. To our best knowledge, we are not aware of animal or human imaging data demonstrating activation of the DVC during cervical or abdominal VNS [START_REF] Val-Laillet | Neuroimaging and neuromodulation approaches to study eating behavior and prevent and treat eating disorders and obesity[END_REF], while neuroanatomical studies provided extensive evidence that the sensory vagus projects to the NTS or, more liberally, to the DVC [START_REF] Berthoud | Brainstem mechanisms integrating gut-derived satiety signals and descending forebrain information in the control of meal size[END_REF]. A recent study was able to observe a widespread activation of the NTS by cymbal conchae stimulation in human. However, the parameters used for brainstem analysis were insufficiently conservative [START_REF] Frangos | Non-invasive Access to the Vagus Nerve Central Projections via Electrical Stimulation of the External Ear: fMRI Evidence in Humans[END_REF]. In contrast, we used highly conservative parameters [START_REF] Ridgway | Ten simple rules for reporting voxel-based morphometry studies[END_REF] and consequently the number and size of the activated areas are robust. Most likely, the best demonstration of the adequacy of our analysis workflow was the absence of activation of the medulla in S1 group compared to S2 or S3 groups versus S0 group. Since the activation of the DVC occurred concurrently with a significant change in food intake behaviour, it is tempting to speculate a causal relationship.

While using a conservative brain analysis workflow, the hypothalamus was not found to have an increased metabolism in all three stimulated groups compared to S0 group. Conjunction analysis, because of its statistical power, identified the hypothalamus as a key activated area common for all the VNS groups. This is not surprising since unilateral stimulation of the cervical vagus has been shown to increase the activity within the hypothalamus, measured using radioactive water PET imaging [START_REF] Henry | Brain blood-flow alterations induced by therapeutic vagus nerve stimulation in partial epilepsy: II. prolonged effects at high and low levels of stimulation[END_REF]. While it is tempting to speculate that hypothalamic activation might reflect the involvement of the homeostatic network controlling food intake [START_REF] Zheng | Eating for pleasure or calories[END_REF], such extrapolation must take into account the actual limited PET spatial resolution and the intricacy of the hypothalamic blood supply.

Both acute and chronic results demonstrated that pulsons stimulations evoked action potentials and that they were responsible for activation of the DVC, then the insula and prefrontal cortex, via the thalamo-insular pathway. It is likely that an identical cascade is also involved with the S1 stimulation pattern, but to a lesser extent as a consequence of the small number of axons actually stimulated [START_REF] Guiraud | Vagus nerve stimulation: state of the art of stimulation and recording strategies to address autonomic function neuromodulation[END_REF]. Since the number of axons involved in the generation of action potentials during S1 stimulation represents only a small fraction of the nerve, the activation of the primary brain integrator, i.e., the DVC, may not be strong enough to be detected with PET imaging [START_REF] Buchholz | Construction and comparative evaluation of different activity detection methods in brain FDG-PET[END_REF]. Such phenomena have already been noticed during vagal stimulation performed at the cervical vagus level [START_REF] Bari | Brain imaging correlates of peripheral nerve stimulation[END_REF].

The most effective stimulation pattern to trigger action potentials had a frequency of approximately 13 kHz. High frequency alternating current (HFAC) of approximately 5 kHz is known to inhibit action potentials [START_REF] Waataja | Effects of high-frequency alternating current on axonal conduction through the vagus nerve[END_REF] and has been used on the vagus nerve to improve weight control in obese individuals [START_REF] Sarr | The EMPOWER study: randomized, prospective, double-blind, multicenter trial of vagal blockade to induce weight loss in morbid obesity[END_REF]. While the therapeutic success of the latter is still to be proven (3), the differences between the two strategies encompassed (i) the duty cycle 25/50 vs 50/50, (ii) the pulse frequency 13 vs 5 kHz, (iii) the current amplitude 15 mA vs 6 mA, positive pulses follow by passive discharge for our strategy vs pure alternative pulses for the VBLOC solution.

We were not able to study the impact of the electrode placement itself on the nerve integrity since the cuffs were implanted in all experimental groups. However, the macroscopic observation of the electrode area during necropsy confirmed the presence of important connective tissue growth as already described in pigs [START_REF] Martin-Portugues | Histopathologic features of the vagus nerve after electrical stimulation in swine[END_REF]. While there were no significant changes in the number of neurons bundles or in the nerve area, we observed a significant increase in resistance in parallel and in series for S2 and S3 compared to sham group. These could be early signs of a more profound alteration in the nerve structure. Indeed, the 2 week stimulation protocol might be too short for the reorganization of the microstructure of the nerve. In contrast, despite the large currents injected in the S2 and S3

groups, one could have expected a large reorganization of the nerve [START_REF] Arle | Essential neuromodulation[END_REF], a situation that was not observed in our experiment.

Conclusions

The present findings demonstrate that very high-frequency pulsons applied bilaterally at the abdominal vagus were capable to activate brainstem and, subsequently, several higher order areas connected to the DVC. These changes in brain metabolism are associated with reduced daily food intake. All the former changes were likely the consequence of the induction of action potentials in small diameter neurons, which are extremely difficult to activate using the classical millisecond-lasting low intensity electrical pulses. The absence of deleterious effects observed after several days of chronic stimulation suggests that pulson stimulation might be worthwhile to investigate in the long term.

Figure 2 -

 2 Figure 2 -Single fibre action potentials triggered by the three different patterns of the stimulating pulses. Note the spread of the onset of the action potentials for S2 and S3patterns. The vertical arrow represents the stimulation onset. The neuron presented was neuron 7 of Table1

Figure 3 -

 3 Figure 3 -Results from voxel-based statistical parametric mapping analysis showing the differences in glucose metabolism between stimulated animals versus the sham-stimulated animals. p <0.005 cluster level FDR corrected. To improve reading, panel labelling refers to stimulation pattern only while the contrast was actually S1 > S0, S2 > S0 and S3 > S0.

Figure 4 -

 4 Figure 4 -Results from conjunction analysis showing the area(s) that have identical metabolism for all stimulation groups versus sham group. Threshold level was set to 0.05 at cluster level -cluster size = 100 voxels.

Figure 5 -

 5 Figure 5 -Food intake pattern recorded 14 and 15 days after the onset of stimulation. Top left panel -total number of calories ingested irrespective of the nature of the diet. The quantities of food ingested during the three daily meals were summed. Bottom left panelnumber of calories ingested during the 17:00 meal. The number of calories corresponded to the sum of the three different diets ingested. Top right and bottom right panel -energy ingested during the last daily meal as the consequence of high lipids and high glucose diet preference. * indicates a significant difference compared to sham (p<0.05).

Figure 6 -

 6 Figure 6 -Characteristics of the microstructure of the meals recorded 14 and 15 daysafter the onset of stimulation. Data from the three troughs/diets and from the three daily meals were concatenated to increase statistical power. Ingestion speed was calculated during eating bouts and the periods of no ingestion during the meal were not taken into account for the measurement. Eating bouts were defined on the basis of the ingestion speed evaluated every 30 seconds. Note that daily ingestion is reduced for S2 and S3 groups only due to a reduced duration of the eating bouts. On the contrary, the ingestion speed within

Figure 7 -

 7 Figure 7 -Changes in impedance 15 days after implantation and chronic stimulation for S1, S2 and S3 groups. Transient pulse responses were analysed according to a Randles equivalent circuit. Dorsal and ventral electrodes data were pooled for the analysis. * denotes a significant difference from sham group.

Figure 8 -

 8 Figure 8 -Cross section of the vagus nerve immediately at the exit of the stimulating cuff. Note the slight alteration in the repartition of the nerve bundles for S1, S2 and S3 groups compared to sham group. Improvements in the stimulating cuff design together with the minimally invasive surgical procedure reduced the impact on the connective tissue development around the nerve bundle.

Table 1 -

 1 Charge injection threshold (in µCoulombs) for triggering an action potential in a single neuron depending on the pattern of the stimulating pulses.

	Neuron Conduction	Receptive	Pulse	Constant	Rising
		speed (m.s -1 )	field	pattern	burst pattern	burst
				(S1)	(S2)	pattern
						(S3)
	1	2.3	Stomach	20.4	8.6	5.9
	2	2.3	Stomach	20.4	8.0	5.5
	3	2.4	Stomach	18.1	6.2	4.3
	4	6.8	Stomach	16.0	5.6	3.9
	5	3.5	Stomach	16.2	5.5	4.1
	6	4.8	Stomach	17.5	6.7	4.8
	7	3.9	Stomach	16.6	6.2	4.3
	8	4.0	Stomach	18.2	6.4	4.7
	9	2.3	Duodenum	18.9	7.2	5.0
	10	2.9	Duodenum	16.2	5.7	4.0
	11	2.9	Duodenum	18.1	6.8	4.9
	12	3.0	Duodenum	21.2	7.8	5.6
	13	3.1	Duodenum	20.6	6.9	4.9
	14	3.2	Duodenum	20.8	6.9	5.1
	15	3.5	Duodenum	21.3	7.8	5.8

Table 2 -

 2 Statistical parameter mapping analysis of activation patterns (local maxima) in S1 stimulated animals compared to sham group.

	Coordinates of local	Tentative	T Value	P FWE
	maximum (x, y, z in mm)	anatomical	(voxel	corrected
		localization	level)
	-6, 9, 15	Dorsal posterior	4.98	0.003
		cingular cortex
	-2, 0, -8	Ventral tegmental area	4.70	0.003
	-24, 6, 10	Insular cortex	4.27	0.004
	2, 11, -4	Anterior hypothalamic	4.02	0.004
		area

Table 3 -

 3 Statistical parameter mapping analysis of activation patterns (local maxima) in S2 stimulated animals compared to sham group.

	Coordinates of local	Tentative	T Value	P FWE
	maximum (x, y, z in mm)	anatomical	(voxel	corrected
		localization	level)
	-4, 20, -8	Rostral medulla	8.22	0.002
	-2, 0, 14	Ventral anterior	7.45	0.003
		cingular cortex
	11, -9, 1	Superior colliculus	5.21	0.004
	7, 19, -1	Putamen	4.66	0.004
	-4, 6, -3	Ventral anterior	3.94	0.005
		thalamic nucleus
	-10, 36, -1	Anterior prefrontal	3.85	0.005
		cortex

Table 4 -

 4 Statistical parameter mapping analysis of activation patterns (local maxima) in S3 stimulated animals compared to sham group. Stimulation patterns used during acute (line C only) and chronic experiments (lines A, B and C). For example, for stimulation pattern S2 applied chronically, the 1 msec pulse is chopped into 14 pulsons of 25 µsec duration each. The 1 ms composite waves occurred at 30 Hz for 30 seconds to create a train of pulses that were applied to the vagus every 5 minutes.

	Coordinates of local	Tentative	T Value	P FWE
	maximum (x, y, z in mm)	anatomical	(voxel	corrected
		localization	level)
	-24, 8, 12	Insular cortex	9.62	0.002
	-2, 6, 18	Dorsal posterior	7.73	0.002
		cingular cortex
	-11, -13, 7	Superior colliculus	7.01	0.002
	-5, -18, -8	Rostral medulla	4.45	0.004
	-5, 8, 2	Ventral anterior	4.32	0.005
		thalamic nucleus
	-5, 33, 14	Dorsal prefrontal cortex 4.3	0.005

Acknowledgements

The study was conducted within the Aniscan imaging centre (Aniscan, INRA, 35590 Saint-Gilles, France) and the animal facilities of Pegase unit (UMR Pegase, INRA, 35590 Saint-Gilles, France) at Saint-Gilles. No potential conflicts of interests relevant to this article were reported by C.H.M., E.B, C.P., J.L.D, D.G. and C.H. C-H.M. D.G. and C.P. planned the experiments, conducted the studies, analysed the data and wrote the manuscript. E.B designed one of the stimulators and the interface used for acute studies. J-L.D. designed the stimulating electrodes and the stimulator for chronic experiments. C.H. was responsible of the integration of the work in the grant. C-H.M. is the guarantor of this work and, as such, had full access to all the data in the study and takes responsibility for the integrity of the data and the accuracy of the data analysis. The authors thank the staff of the animal facilities of Pegase unit for animal care: Mickael Genissel, Julien Georges, Alain Chauvin, Francis Le Gouevec and Vincent Piedvache. The authors thank Gwenaelle Randuineau (ADNC, INRA, 35590 Saint-Gilles) for the histological analyses. The authors also thank the members of Aniscan imaging centre for data collection.

Funding sources

This work was supported by BPI France within the "Investments for the Future" programme through the INTENSE grant.


Lina Yuan

Simon Clevers

Antoine Burel

Philippe Négrier

Bacem Maria Del Barrio

Ben Hassine

Denise Mondieig

Valérie Dupray

Josep Ll Tamarit

Gérard Coquerel
email: gerard.coquerel@univrouen.fr.

Philippe Negrier

Maria Del Barrio

§ Bacem

Valeŕie Dupray

Josep Ll

Tamarit

Geŕard Coquerel

Lina Orcid

Yuan

New Intermediate Polymorph of 1-Fluoro-adamantane and Its Second-Order-like Transition toward the Low Temperature Phase

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

INTRODUCTION

Diamondoids formed by carbon cages have received much interest, in particular, for building up organic crystals with large cavities and specific physical and chemical properties. [1][2][3][4][5] The simplest diamondoids, adamantane and its derivatives, exhibit an orientationally disordered (OD) phase (plastic phase) and show rich polymorphic transitions upon temperature or pressure changes. [6][7][8][9][10][11] 1 Fluoro adamantane (1 F A hereafter, Figure 1) is one of the 1 substituted adamantanes, and thus far, two polymorphs have been revealed: one OD phase at high temperature (HT) and a less disordered low temperature (LT) phase.

The phase transition HT ↔ LT was first detected by differential scanning calorimetry (DSC) at 222 K (upon heating) with an enthalpy of 1.5 kJ/mol. 12 Later, Kawai et al. 13 reported the transition occurs at 227 K with an enthalpy of 1.7 kJ/mol upon cooling and at 231 K with an enthalpy of 1.6 kJ/mol upon heating. The transition displays a hysteresis which indicates a first order behavior in the Ehrenfest classification. 14 The HT phase has been widely studied by thermal analysis, 12 X ray diffraction, 15 NMR, 8 single crystal Raman scattering, 16 dielectric analysis, 17 and incoherent quasi elastic neutron scattering. 18 The structure of the HT phase was determined as face centered cubic (Fm3m) by single crystal X ray diffraction 15 and by X ray powder diffraction (XRPD). 19 However, less was known about the LT phase before the recent publication by Ben Hassine et al., 19 in which was reported the resolution of the crystal structure of the LT phase at 100 K by XRPD in the tetragonal noncentrosymmetric P42 1 c space group (Z = 2)CCDC number 1455093. 19 The variation of cell parameters and the cell volume of 1 F A were also monitored by temperature resolved XRPD from 90 K to 360 K, and a sole discontinuity of the lattice parameters across the HT ↔ LT transition was observed. Based on these results, it was presumed in the work of Ben Hassine et al. 19 that only two polymorphs exist and, consequently, that the structure of 1 F A could be resolved in the P42 1 c space group from 90 K until the phase transition toward the HT phase. As the LT polymorph is still disordered (as assessed by NMR and BDS 8,19 ), 1 F A is a perfect candidate to go deeper into the study of molecular motions in the solid states and across polymorphic transitions.

In this mater, temperature resolved second harmonic generation (TR SHG) can be used to gather valuable information. SHG (second harmonic generation) refers to an optical process in which an electromagnetic wave gives rise to a new wave at half the initial wavelength while traveling through a noncentrosymmetric material. [20][21][22][23][START_REF] Sutherland | Handbook of Nonlinear Optics[END_REF][START_REF] Bloembergen | Nonlinear Optics[END_REF] The variation of the second harmonic (SH) signal versus temperature can be obtained by TR SHG. Vogt [START_REF] Vogt | [END_REF]27 detailed that the temperature dependence of higher rank tensors describing SHG is related to variations of long and short range order. Moreover, Dougherty and Kurtz 21 mentioned that dynamic disorder possibly couples with local polarization fluctuations and then can induce modification in the SH signal. These make TR SHG a useful tool to detect phase transitions and polymorphs for systems involving symmetry changes in crystalline structures and molecular motions in noncentrosymmetric crystalline phases. TR SHG has already been applied to monitor transitions between monotropically or enantiotropically related solid phases, [28][29][30][31] and to track ferroelectric-paraelectric phase transitions 32,33 and order-disorder phase transitions 27,34,35 with as a required condition that at least one noncentrosymmetric crystalline structure is involved. 20,21,[36][START_REF] Sutherland | Handbook of Nonlinear Optic[END_REF][START_REF] Miller | [END_REF][39] In 1 F A, the HT phase is centrosymmetric and consequently generates no SH signal. The LT phase resolved in a noncentrosymmetric space group generates a SH signal. Thus, the phase transition between the HT phase and the LT phase can be studied by TR SHG. Through a careful investigation of phase transitions in 1 F A (especially at low temperatures) by the synergistic approach of combining TR SHG and XRPD, not only a new polymorph was ascertained in this work but also the knowledge on the mechanism of ordered-disordered transitions was improved.

■ EXPERIMENTAL SECTION

Materials. 1 Fluoro adamantane (CAS registry number: 768 92 3) was purchased from ABCR in Germany (98.3% purity, 1.7% impurity of 1 adamantanol). Crystals used in this work were purified by recrystallization from methanol (HPLC grade), and the average crystal size was 200 μm. The purity was checked by GC MS (higher than 99.9%). See SI 1: (a) the purification procedure of commercial 1 F A and (b) the purity checking process by GC MS.

Methods. Temperature-Resolved Second Harmonic Generation (TR-SHG). The nonlinear optical method has been introduced in our previous papers. 28,34,[40][41][42][43] Powder sample (50 mg) was placed in a computer controlled thermal stage (Linkam THMS 600). The sample was scanned at 1 K/min between 100 and 293 K. The number and the duration of the TR SHG analyses were chosen to ensure the best stability of the laser beam and the best stability of the compound under the laser irradiation. Therefore, the points on the TR SHG curve were recorded every 2 K and each point corresponds to the average value of the SH signal recorded over 3 s (the temperature variation during the recording is 0.05 K). For each SH signal versus temperature plot, the SH data were normalized using the maximum SH intensity, which was obtained by fitting the SH curve of the raw values.

The SH intensity generated by a given sample depends on numerous parameters (molecular nature, quality of the long range order, i.e. the crystallinity, crystal structures, size, and orientation of the crystals). 20,21 Therefore, in order to get reproducible results, we ensured that the laser irradiates the same area of the sample (40 mm 2 ) all along the experiments. The standard deviation of the SH signal was estimated to be ca. 3%, which is mainly due to energy fluctuations of the laser beams.

Differential Scanning Calorimetry (DSC). Thermal analyses were conducted in a Netzsch 204 F 1 DSC apparatus equipped with liquid nitrogen as the coolant. Both the temperature and the enthalpy changes of the calorimeter were calibrated by using the phase transition of cyclohexane and mercury. Samples with a mass of ca. 8 mg (with a maximum deviation of 0.05 mg) were sealed in a 25 μL aluminum crucible. Thermograms were obtained at a scanning rate of 1 K/min. The atmosphere during the measurements was regulated by a nitrogen flux (40 mL/min). Data treatment was performed with Netzsch TA Proteus V4.8.4 software.

Cold-Stage Microscope. Samples were loaded into an amorphous quartz crucible and set in a THMS 600 temperature stage setup (Linkam, the same as that used in TR SHG method). Liquid nitrogen was used as the coolant, and the nitrogen flux was regulated via an automatic pump. The setup was coupled with a Nikon Eclipse LV100 microscope and connected to a computer for image captures by a CCD camera.

Note that the temperature accuracy of the Linkam at low temperatures was checked. The melting points of o xylene (249 K) and tetrahydrofuran (165 K) in HPLC grade were observed by cold stage microscope. Different heating/cooling rates were used (0.5 K/ min, 1 K/min, 2 K/min, 4 and 5 K/min) and compared with DSC results. The temperature difference between cold stage microscopy and DSC was observed to be lower than 1 K.

Curve Fitting. Data were fitted to specific expressions by application of the Levenberg-Marquardt (least squares method) algorithm using the program Origin 10.

X-ray Powder Diffraction (XRPD). X ray powder diffraction data were collected by means of a horizontally mounted INEL cylindrical position sensitive detector (CPS 120) to pursue a careful structural determination from the HT to LT phases. The detector constituted by 4096 channels was used in Debye-Scherrer geometry. External calibration using the Na 2 Ca 2 Al 2 F 14 (NAC) cubic phase mixed with silver behenate was performed by means of cubic spline fittings providing an angular step of 0.029°(2θ) between 4°and 120°. Monochromatic Cu Kα1 radiation (λ = 1.5406 Å) was selected with an asymmetric focusing incident beam curved quartz monochromator. The samples were introduced into 0.5 mm diameter Lindemann capillaries which were rotated perpendicular to the X ray beam direction in order to decrease as much as possible the effects of preferred orientations. Temperature was controlled with an accuracy of 0.1K by means of a liquid nitrogen 600 series cryostream cooler from Oxford Cryosystems.

■ RESULTS AND DISCUSSION

Characterization of 1-F-A Phase Transitions by DSC. A single detectable thermal event was observed by DSC between 120 and 300 K for a heating rate of 1 K/min (Figure 2). Upon cooling, the onset temperature is 226.0 ± 0.3 K with an enthalpy of 1.9 ± 0.1 kJ/mol. Upon heating, a hysteresis is observed, with an onset temperature at 231.0 ± 0.2 K and an enthalpy of 1.8 ± 0.1 kJ/mol. This thermal event obviously corresponds to a first order phase transition. These values are consistent with previously reported values from the liter ature. 12,13,19 Note that the use of a higher heating rate (5 K/ min) led to a similar result (see SI 2).

TR-SHG Measurements. It is first necessary to mention that, in the present case, the intensity of the measured SH signal can be generated only by the noncentrosymmetric crystalline LT phase of 1 F A. Based on Kurtz and Perry, 20 SH intensity can be considered proportional to the mass fraction (or molar fraction) of the LT phase.

The thermal evolution of 1 F A was monitored by TR SHG through tracking the SH signal generated by the LT phase versus temperature (Figure 3). Apparently, the sample exhibits a positive SH signal at 100 K, which proves the structure is noncentrosymmetric at this low temperature and confirms the reliability of the XRPD crystal structure determination. 19 Surprisingly, the SH signal was observed to appear only at 178 K (upon cooling) while the transition temperature was detected at 226 K by DSC (black curve in Figure 2). The temperature difference is 48 K. Obviously, this difference is too large to be caused by the thermal gradient between the sample and the heating plate. Possible reasons for this phenomenon were investigated. First, we supposed that the SH signal generated by 1 F A between 178 and 226 K could have fallen under the detection threshold. Even though the detection threshold of our TR SHG apparatus can be considered as good (evaluated at ca. 1/100 compared to the SH intensity of the quartz standard, 45 μm), the sample was annealed at 213 K, a temperature between 178 and 226 K in order to obtain a better crystallization of the sample (i.e., to possibly enhance the SH signal). After 10 h, no SH signal was detected (see SI 3), which strongly suggests that no LT phase crystallized in the range of 178 and 226 K. Second, it was supposed that the transition kinetics might be low and the thermodynamic equilibrium was not reached in this temperature range. So, the sample was annealed at 167 K to possibly reach the thermodynamic equilibrium. Nevertheless, after 10 h, no variation of the SH signal was observed, indicating that the maximum amount of LT phase was already reached under the conditions used for the TR SHG experiments (see SI 4).

Finally, these results led us to envisage that 1 F A exhibits an intermediate phase between the HT and LT phases in the temperature range 178 K to 226 K. In the following, this intermediate phase is referred to as MT (for medium temperature). Since no SH signal was detected between 178 and 226 K, the MT phase probably exhibits a centrosymmetric crystalline structure (confidence higher than 99% 36 ).

Another interesting result is that no hysteresis was observed for the SH signal upon heating and cooling. That is to say, the SH intensity profile is thus completely reversible (i.e., thermal cycles after cycles or after stopping and restarting the heating/ cooling process). Consequently, a second order transition between MT ↔ LT can be suspected, complementary with the following observations:

(i) no detectable enthalpy change detected by DSC around 178 K; (ii) no transition front propagation observed by cold stage microscope (see SI 5); (iii) no change of the cell volume at the presumed transition temperature (178 K) in the work of Ben Hassine et al. 19 A thorough reinvestigation of the structures resolved from XRPD at various low temperatures confirmed this hypothesis as described in the following.

Crystal Structure of MT Phase Determined from XRPD. When cooling down from HT phase to the LT phase, single crystals break, and thus, powder diffraction is the only way to determine the structure of the low temperature phases. Therefore, powder X ray patterns obtained at 90 K and 190 K were submitted to a Rietveld refinement, 44 with the same rigid body constraints that are depicted in the work of Ben Hassine et al. 19 A single overall isotropic displacement parameter and preferred orientation by using the Rietveld-Toraya function were refined. The final refined patterns together with the experimental and refined pattern differences are shown in Figure 4. The Rietveld refinement converged for the LT phase and the MT phase to a final R wp value of 6.60% and 6.32%, respectively. The determined crystallographic data of both phases are summarized in Table 1.

A crystal structure validation by Platon 45 was performed on the two resolved space groups. For the LT crystal structure at 90 K, Platon results showed that no space group change is needed. While, if the MT phase is resolved in the space group of the LT phase (at 190 K), missed or additional symmetry is reported and Platon suggested the space group of P4 2 /nmc. These results proved that the resolutions of the space group in the MT and LT phases are robust.

Mechanism of the MT ↔ LT Phase Transition. The presumed second order phase transition of MT ↔ LT can be confirmed and interpreted microscopically by means of analysis of thermally induced structural changes. The structure of the LT phase is shown in Figure 5(a). The angle (ψ) defined between the C-F bond of the four equilibrium positions for the statistically disordered fluorine atoms (i.e., the molecular dipole direction) with the a (or b) tetragonal axis is ca. 6.8°at 90 K. Increasing the temperature, such angle continuously decreases, and at ca. 180 K, it vanishes and remains null until the phase transition to the HT phase. Such changes provide two new mirror planes perpendicular to the a and b tetragonal axes. Thus, the noncentrosymmetric space group P42 1 c (Z = 2) transforms to the centrosymmetric space group P4 2 /nmc (Z = 2), giving rise to the so called MT phase, which represents a group-subgroup transition. In addition, lattice parameters as well as volume as a function of temperature do not show any discontinuity (see SI 6). Therefore, the group-subgroup relation, the continuity of the lattice parameters and volume through the LT to the MT phase transition are in agreement with the continuity of the dynamic properties across this second order phase transition. 19 Figure 5(b) depicts a structural projection of the MT phase along the c plane at 190 K. It is worth noting that the fractional occupancy of 1/4 of the fluorine atoms remains unchanged across the group-subgroup transition (MT ↔ LT). Therefore, it is probable that the phase transition does not change the type of molecular reorientation and that the dynamics and frequency of molecular motions in the solid state are not (or slightly) modified at the transition temperature (178 K). This could be an explanation of why this group-subgroup transition was not highlighted by other techniques such as BDS or solid state NMR. 8,19 To summarize, at 178 K, a second order transition from the MT to the LT phase starts by a tilt of the angle ψ, resulting in an immediate change in the crystal structure. Then this angle ψ increases continuously with decreasing temperature but the crystal structure remains in the LT phase. The above explanations fit well with the TR SHG results. In Figure 3, the SH signal increases continuously from 178 to 100 K. Because SHG is intrinsically related to the crystal structure and molecular fluctuations, 36 it suggests that each SH signal corresponds to a LT form in which 1 F A molecules are tilted at a certain angle (e.g., ψ = 6.8°at 90 K) by thermal agitation.

Variation of the Order Parameter with Temperature. The order parameter η describes the extent of order or disorder in a material. It is equal to unity in the perfectly ordered state and zero in the completely disordered state. [START_REF] Rao | Phase Transitions in Solids: An Approach to the Study of the Chemistry and Physics of Solids[END_REF] TR SHG was used to track the variation of the order parameter η (according to the Landau theory) versus temperature and to determine the critical exponent β characteristic of this variation.

The temperature dependence of the SH intensity can be expressed as 47

χ δ δ ∝ • ⎡ ⎣ ⎢ ⎤ ⎦ ⎥ I T T l T n T n T T ( ) ( ( )) ( ) ( ) (T) sin ( ( )) ( ( )) SHG (2) 2 2 1 2 2 2 2 ( 1
)
where l is the thickness of the crystals, and n 1 and n 2 are the indices of refraction for λ 1 = 1.064 μm (fundamental beam) and λ 2 = 0.532 μm (second harmonic beam), respectively. χ (2) is the nonlinear susceptibility tensor, and δ = .

The term within brackets in eq 1 is generally responsible for a sin square modulation (sin c 2 ) of the SH intensity for single crystals. Considering that, for powders, the orientations of the crystals are random (averaging over all crystallographic directions) and the particle size (mean value ca. 200 μm in the present study) is likely to exceed the coherence length, 20 this modulation term can be neglected. Thus, in the following, we assume that the SH intensity is proportional to (χ (2) (T)) 2 . χ (2) (T) is a third rank tensor with 27 coefficients, but the number of independent coefficients can be reduced to 3 in the Taking into account the previous simplifications, I SHG (T) can be considered proportional to d eff 2 (T), where d eff is the effective coefficient of the nonlinear susceptibility. In the present case, d eff is proportional to the d 14 coefficient (using Voigt's convention). [START_REF] Dmitriev | Handbook of Nonlinear Optical Crystals[END_REF] Moreover, d 14 has already been shown to be a linear function of the order parameter η SHG 35,36 in single crystals. In the present study, measurements are performed on powder samples with random crystallographic orientations, but that does not modify the fact that χ (2) (T) depends only on one coefficient. Therefore, we can assume that the SH signal variations will be the same in all crystallographic directions. Hence, the square root the SH intensity can be taken as an order parameter:

η ∝ ∝ I T d T ( ) ( ) SHG eff (2)
The evolution of the order parameter η with temperature can be described by a simple critical power law derived from Landau theory: 35,[START_REF] Bruins | [END_REF] η = -

β ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ A T T 1 c (3)
where A is a prefactor, T c is the transition temperature, and β is the critical exponent.

Based on eqs 2 and 3, T c and β values can be extracted from SHG results using

η = = - β ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ I T A T T ( ) 1 SHG c (4)
The fitting procedure performed from eq 4 with A, T c , and β as free parameters returns upon cooling a β value of 0.255 ± 0.008 with T c = 178.8 ± 0.3 K. Upon heating, β is 0.263 ± 0.008 with T c = 179.1 ± 0.3 K (Figure 6). The experimental transition temperature (T c : 178 K to 180 K) is thus consistent with the temperature determined by the fitting.

The order parameter η can also be obtained from XRPD by recording ψ (the angle between the molecular dipole C-F bond and the crystallographic a axis) versus temperature (see Figure 6). The XRPD data is fitted according to the power law (eq 4), in which A corresponds to ψ (T 0K) and gives rise to β = 0.250 ± 0.027 and T c = 180.0 ± 0.1 K. It should be noticed here that the lowest temperature at which the structure was solved was 90 K, close to the temperature (92 K) at which reorientational motions are characterized by a relaxation time of the order of 100 s. 19 Below such temperature, reorientational motions are frozen, according to the previous dynamic study, 19 and thus, the LT phase becomes a low dimensional glass. [53][54][55] It is obvious that such a LT phase cannot be the stable phase at 0 K (the frozen disorder would confer a nonzero entropy) and the true stable phase remains, at present, elusive. Despite such thermodynamic evidence, for both TR SHG and ψ angle data from XRPD, we have assumed a continuous variation with temperature below 90 K and renormalization was performed under the hypothesis that the order parameter equals unity at 0 K. Under such assumptions, Figure 6 clearly shows that both TR SHG and the ψ angle from XRPD describe the second order transition.

■ CONCLUSIONS

Phase transitions of 1 F A were thoroughly investigated by using TR SHG and XRPD. The combination of both techniques unveiled a new phase with a stability domain between 178 and 231 K. A second order transition occurs at 178 K between the LT phase (P42 1 c) and the intermediate temperature phase (MT, P4 2 /nmc), which arises from a continuous tilt of the molecules by thermal agitation. A first order transition occurs at 231 K between the MT phase and the high temperature cubic phase HT (Fm3m). Moreover, variation of the order parameter versus temperature for the second order transition was monitored by TR SHG and XRPD, and results are in good agreement to support the proposed second order transition mechanism.

In this work, the hint of a second order phase transition might arouse certain debate, as in the literature, for several compounds, second order transitions finally turned out to be first order transitions. [START_REF] Mnyukh | Fundamentals of Solid State Phase Transitions, Ferromagnetism and Ferroelectricity[END_REF] For instance, the undetectable thermal signature of theses transitions might be interpreted as inconsistent with thermodynamics. In fact, the structure differences between LT and MT phases are very subtle and the phase transition arises from a slight tilt of the 1 F A molecule. Neither lattice parameters nor volume show discontinuity at the transition temperature (178 K). Con sequently, transition between both phases should be difficult, even impossible, to be detected by usual DSC measurements. Measurement of heat capacity (C p ) at low temperature might give some indications of the MT ↔ LT transition. So, further study of this second order transition combining other techniques could be suitable. For example, X ray absorption near edge structure (XANES) might provide certain information about the change of the local symmetry. Finally, this work underlines that the study of polymorphs and phase transitions should be carried out carefully. The combination of TR SHG and XRPD seems a suitable tool to monitor subtle symmetry changes when noncentrosymmetric structures are involved, such as, in diamondoids. In light of the present study, a thorough reinvestigation of phase transitions in adamantane derivatives could be envisaged.

Figure 1 .

 1 Figure 1. Molecular structure of 1 fluoro adamantane (1 F A).

Figure 2 .

 2 Figure 2. DSC measuring curves obtained for the phase transitions of 1 F A. Black line, upon cooling (1 K/min); red line, upon heating (1 K/min).

Figure 3 .

 3 Figure 3. TR SHG curves obtained for the phase transition of 1 F A. Black square, upon cooling (1 K/min); red spot, upon heating (1 K/ min). The signal appears/disappears at 178 K and increases with lowering the temperature down to 100 K.

4 .

 4 Experimental (red circles) and Rietveld refined (black line) diffraction patterns along with the difference profile (blue line) and Bragg reflections (vertical black sticks) of (a) the LT phase at 90 K and the (b) MT phase at 190 K. The insets show the high angle portion of each pattern (scaled to enhance their visibility).

Figure 5 .

 5 Figure 5. Crystal structure of 1 F A: (a) LT phase (P42 1 c, Z = 2) at 90 K and (b) MT phase (P4 2 /nmc, Z = 2) at 190 K. The fractional occupancy of 1/4 of the fluorine atoms (blue) remains unchanged across the MT ↔ LT transition.

Figure 6 .

 6 Figure 6. Order parameters determined from normalized values of the TR SHG data and the angle ψ between the C-F bond and the a (or b) crystallographic axis from XRPD. The black line corresponds to the fit of eq 4 for the TR SHG data on cooling (β is 0.255 ± 0.008 with T c = 178.8 ± 0.3 K). The red line corresponds to the fit on heating (β is 0.263 ± 0.008 with T c = 179.1 ± 0.3 K). The blue line corresponds to the fit of XRPD data (β is 0.250 ± 0.027 with T c = 180.0 ± 0.1 K).

Table 1 .

 1 Crystallographic Data Determined for the MT Phase and the LT Phase

		MT phase	LT phase
	temperature (K)	190	90
	crystal system	tetragonal	tetragonal
	space group	P4 2 /nmc	P4̅ 2 1 c
	a = b (Å)	6.8145 (5)	6.7696 (4)
	c (Å)	8.9232 (9)	8.8211 (9)
	Z	2	2
	volume (Å 3 )	414.37 (7)	404.25 (6)
	density (g/cm 3 )	1.236	1.267

This work was partially supported by the CICyT (Spain) Project FIS2011 24439, and by DGU (Catalonia) project 2014SGR00581.


Marek Penhaker
email: marek.penhaker@vsb.cz

Petr Klimes
email: petr.klimes@vsb.cz

Jakub Pindor
email: jakub.pindor@vsb.cz

David Korpas
email: david.korpas@seznam.cz

Advanced Intracardial Biosignal Processing

Keywords: iECG, Detection, Filtering, Processing

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

Introduction

By entering this work was, among other things, analysis and detection of significant characters in the intracardiac ECG recordings with subsequent processing of such information. Data from measurements of intracardiac ECG was provided in a hospital Podlesi Třinec. These are the signals measured at different types of system operations and subsequently Exported Cardiolab in *. txt. Each data set is also associated *. inf file that contains additional information about the record length, sampling frequency, number of leads, etc. The development application was trying to get signals of various parameters from different places with varying degrees of heart hampering to determine a success or approximate boundaries of functionality algorithm.

Source Intracardial Data

Data is stored in a file with the extension *. txt, and can therefore be viewed as a classic notepad in Windows. After the opening we see that this is a table of numbers, where each column represents a seduction. The measured signals were recorded with a sampling frequency of 977Hz. It follows that for such a long signal for 30 seconds for each lead-recorded 29310 samples. If recorded three intracardiac leads, for example, the first of the CS catheter ablation, and two, that the total surface leads recorded with 15 leads, it means that the file of the thirty-second measurement has 439,650 samples, or figures in the table. This comprehensive text file on your computer takes up about 5MB of memory.

The benefits file with the *. txt is the fact that it is very easy to load into MATLAB as a multidimensional variable. Indexing, we were able to separate each lead, respectively. vector and store it as a separate variable. Thus it can be done with all leads and each store separately under its own pre-chosen name. This prepared data from individual leads are ready for further processing.

Signal Preprocessing

In this work, the data are processed intracardiac leads see. Figure 1 shows the loaded signal from the ablation catheter accurately record the first 2.5 seconds. Signals from the chambers, which are clearly visible sign precedes the P wave, a signal from the hall. This wave, along with other manifestations of tissue, however, at this point redundant information. Our goal is to become independent and to detect ventricular signal.

For recognition of deformed QRS complex need to adjust the signal first. In the first phase of minor cropping potential and then using the wavelet transform.

Setting the threshold at the loaded signal seen in Figure 2 Red lines show the threshold values that are set both in positive terms and in the negative. Everything in this limited area is then ignored and reset the chart. However, it is necessary for this operation to maintain an identical length of the signal. It is therefore a direct replacement of values below the threshold at zero.

In the algorithm shown below is copied into a variable with a length of the original signal is modified in the wake. The next step is transformation modified signal using wavelets. Specifically, the selected wavelet bior1.5. As explained in section 4.3, determine the type of waves preceded the experimental procedure is based on knowledge parameters of wavelets and its use in other applications. Subsequent levels of decomposition setting, or scale, using this formula was based on wavelets for detecting QRS complexes in the surface ECG 02.05.

Finishing the signal is conducted continuous wavelet transform (CWT), wavelets bior1.5, with the fourth level of decomposition. The result of this transform shown in Figure 2.

Finding three significant characters in the intracardiac recordings

Trimming curve prepared in advance and continuous wavelet transform is now available for the final stage of detection. This is a clear target indication of significant peaks that are detected primarily ventricular cycles and finding the beginnings and ends of these impulses. As already mentioned in Chapters 3 and 4, our task is not interested to follow more closely the morphology of the curve. Valuable data are kept in the information exactly where on the timeline is detected peak of excitement, when the excitement begins and ends, respectively. length and its relationship to neighboring vzruchům detected. First of all, we must clearly identify the detected peak of excitement.

Finding the detected peak impulse

After adjusting signal quality before building a relatively simple task. The signal is free from all the surrounding potentials which are not interesting for us as well is wavelet transform rid of sharp transitions and changed into a form that presents Figure 3. So the only thing left, and find places where the transformed curve intersects the zero. We know that at the same time when the original curve reaches its local maximum, then the detected peak of excitement.

The problem with this procedure is the possibility of intersection of two lines of zeros. The signal zero crossing can be upward or downward, or may go from negative to positive and vice versa. Is needed in this algorithm into account, otherwise it will only detect one case of two and a high probability of excitation peak detect. Another complication lies in the multiple detection. Figure 28 shows that the zero passage of the transformed signal below the top of the original passage is not only zero in the area. Algorithm to actually detect several peaks and is not clearly determined which of them is described as the pinnacle of the impulse, ie as a global summit. Assuming that it would be a simple curve with really only one local maximum to avoid the multiple detection. With this, however, can not count, especially with intracardiac leads that may have a completely unexpected

The solution to this problem is the second part of the displayed code, which provides only the label is always the highest, that is the most prominent peak, which will ensure compliance with the requirement to detect a global peak of excitement. S_cwt variable represents the signal after processing the first part of the code and wavelet transforms. In the first phase will split the signal into sections that define the detected impulses. With a condition that can be detected only one peak in each such segment, the algorithm looks for the one with the highest amplitude relative to other peaks found. The definition of this section is based on sampling frequency, while the assumption of a distribution of excitation. As a limit value for setting limits for cropping signal, this value may be modified according to user needs and current signal parameters.

In this way, peaks are detected, or excitation peaks, which are used in the subsequent detection of the beginning and end of the impulse as a starting point, clearly defining where the peak is located.

Finding the beginning and end of the detected impulse

The next phase of the effort comes reliable indication of the place where the detected excitation begins and ends. Early attempts to design this part of the algorithm contributed to the final solution with satisfactory results. To better understand the description and the impasse of development.

The original idea comes from practice. The doctor looks at the curve and just see the place where the excitement begins. Identifies it as that of the relatively flat line curve begins to rise suddenly to higher values. Likewise, it is also able to detect an algorithm to detect the beginning of excitement, but it has to be defined in accordance with these requirements. It is not possible based on the projected shape of the curve, as is the case with the surface ECG. The shape can take various forms, it is necessary to build on this basic premise: excitement begins where the curve starts from a relatively flat line of steep climb to higher values.

To find this place is first necessary to map the section signal. Rather it is a section from the detected peak before the beginning of oscillation. The signals are then backward from this point marked points that are stored in a matrix for subsequent calculations. Not only do we know their coordinates, or location on the timeline, we also represent the value of the signal amplitude at a given point. This section mapped signal was then subjected to search for the smallest difference in amplitude between two neighboring points. The result of this comparison should be to find a flat end and the beginning of the steep climb. However, faced several problems. First and foremost was the smallest difference between points are often found at large distances from the actual beginning of the impulse, ie before it even began to stir. This was mainly due to the fact that the smallest difference amplitudes are often located away from the beginning of the excitement and not directly at him. The second complication occurred when the two adjacent points lie in the steep part, but one on the ascending and descending on the second, at about the same level. The algorithm then evaluate this case as a flat surface and named it as the beginning of excitement, but he saw a local maximum or minimum between these points and was unable to recognize that the points lie on a steep curve. Including more surrounding pixels into these calculations, the problem is solved.

To ensure a really steep marking the beginning of excitation, respectively. place before the start of the steep change was designed additional code, to ensure early recognition steep based on a predetermined level, the signal must exceed before the impulse. Points are mapped in the first phase of this calculation converted to their absolute values. It is not conclusive, if the beginning is in positive or negative values. Elements are among the neighboring points. Subsequently, the detected maximum value of the matrix marked points. This value is then determined the level of 0.1%.

In the detection of all impulses to proceed similarly, but on the opposite side of the detected peak. At the same time there is an effort to find the sharp end, because the impulses are usually sharply terminated. In most cases disappear more slowly than the rise. The algorithm was therefore counted the detected displacement of the point which was found in the same manner as at the beginning of excitation.

In this way the algorithm was developed to detect peaks, start and end of detected impulses. Beginnings and endings are detected based on detecting peaks. Without a mark on top of the algorithm is able to delimit excitement. The experimental part of the algorithm was able to recognize signs and Q and S waves detected in the chamber complex. Due to the nature of the intracardiac signals, however, from this expansion was abandoned and attention was paid to quality notably through the detection of peaks of individual impulses.

Analysis Result

The algorithm was tested on approximately 75 different intracardiac signals from 15 different operations. This was how the signals from the diagnostic catheters, which provide about the best possible signal, measured directly in the heart, as well as therapeutic catheters, especially ablation, which is more therapeutic than hampering because of almost constant motion after cardiac walls.

Detection of peaks achieved when the correct setting of limits almost total success even in noisy signals. In cases where the algorithm does not detect any peaks or, conversely, create false points, the curve was so hampering that there were doubts about the actual value of the information curve. Identifying the beginnings and ends of the excitation peaks detected in the header pipes from the CS catheter almost flawless. For noisy signals success begins to deteriorate, and to mark the beginning is always the case. Only the position of determining the beginning point is not exactly at the point of beginning of excitation.

By classifying peaks, start and end of each detected impulse was obtained by specific dates, which carry information about the amplitude of excitation, the frequency, duration, etc. The processing of this information is not targeted to any particular application. This is a demonstration of versatility of use of the algorithm. Analyzed intracardiac ECG curve has been described and this allows the subsequent use of these data for experimental and other purposes.

Of all ten measured parameters were selected to assess three basic parameters of the signal and then three time intervals for cross checking the accuracy of detection.

Table 1 are measured values from the analysis of the fifteen intracardiac signals. The upper part is shown on the measurement of diagnostic catheters, the lower part presents the signals of therapeutic catheters. HR heart rate indicates the heart rate of total recording time. It is therefore an average value in units of beats / min. The amplitude of the detected impulse Amp informs about the average height of the signal amplitude in mV units.

The following three values of PP, BB, EE is dedicated to time intervals to assess the mutual time between detected points. This is the time interval between two adjacent peaks, the time interval between the starts of two adjacent impulses, and the interval between the end in units of ms. The last column lists the values of hit rate achieved success at the individual signals. Word of success in this case think successfully found and marked points of the beginning, peak and end of detected impulses. This value was calculated based on detection by visual inspection for each of the records. The number of unsuccessfully marked or completely unmarked points and the total number of impulses detected catheter has been derived detection rate as a percentage. This value has a major impact on all previous calculations. If success is very small, we mean below 50%, does not have a previous column, too deal with. Measured and calculated data in such a case would probably not representative. Values above 90% success rate on the contrary we affirm the accuracy of the calculated parameters.

Table 1. THE MEASURED VALUES

Signals from a diagnostic catheter EN HR [bpm] Amp [mV] P -P [ms] B -B [ms] E -E [ms] Hit

Percentage success was calculated based on visual inspection of each detected impulse. In the event that the detector has not identified any excitement, the points were its peak, the beginning and end labeled as defective. Likewise, if the detector is evaluated as a potential suitable to describe excitement, while the excitement was not in effect, create a false detection, and also this point is marked as defective. Subsequently, the bad points of detection compared with the total number of impulses, which had a detector to recognize and label.

In the event that marked all the impulses in the signal, its peaks, starts and ends at the same time did not create any false detection, the program has reached the maximum, a 100% success rate. In case of omission of some important points, or marking the wrong places, the success rate has declined in the worst case up to 75%.

Overall, the table shows that the measured signal quality diagnostic catheters is generally achieved a higher success rate, while the ablation catheter, which is often hard to read the signal, detection rate was worse.

Simultaneously with this measurement was performed peak detection statistics of success and detection of beginnings and endings, which is not included in the table. In this measurement is not take into account the type of signal. It did not matter then whether the signal from the therapeutic or diagnostic catheter is taken into account only well or poorly marked points under visual control again seen as successful or faulty. The resulting, average values of success are as follows:

The success of the algorithm for detection of significant characters in the intracardiac signals. Detection rate peaks: 98.85%, The success of detection of beginnings and endings: 95.05%, The success rate in detecting signals from diagnostic catheters: 99.22%, The success rate in detecting signals of therapeutic catheters: 93.55%.

Conclusion

The benefit of this work is a new approach to detect points in the ECG signals nonstandard shapes. It introduced an efficient method to recognize, label and border impulses, which are directly from the heart wall observed invasive catheters. This project was created to continue work to further improve the algorithm to detect and use this system to find deposits of arrhythmia in the heart, using calculations of intervals between impulses of two different signals in real time. For processing and design of detection algorithms were used MATLAB, in which they were implemented as mathematical signal processing operations, so statistical analysis of test results.

Fig. 1 .

 1 Fig. 1. From the loaded signal is displayed intracardiac catheter ablation of seduction.

Fig. 2 .

 2 Fig. 2. Adjustment signal continuous wavelet transform -CWT, bior1.5. For clarity, only the first pick was detected excitation signal. It is clearer and shows how the signal continuous wavelet transform based on original changed shape.

Fig. 3 .

 3 Fig. 3. Detected peaks intracardiac ECG electrical activity generated by ventricular

Fig. 4 .

 4 Fig. 4. Marking the beginnings of impulses detected by intracardiac ECG

Fig. 5 .

 5 Fig. 5. Slightly hampering signal ablation catheter. Detection of peaks was flawlessly, beginnings and ends are detected for the second excitation reliably identified.

Acknowledgment

The work and the contribution were supported by the project: Ministry of Education of the Czech Republic under Project 1M0567 "Centre of Applied Cybernetics", Student grant agency SV 4501141 "Biomedical engineering systems VII" and TACR TA01010632 "SCADA system for control and measurement of process in real time". Also supported by project MSM6198910027 Consuming Computer Simulation and Optimization. This paper has been elaborated in the framework of the IT4Innovations Centre of Excellence project, reg. no. CZ.1.05/1.1.00/02.0070 supported by Operational Programme 'Research and Development for Innovations' funded by Structural Funds of the European Union and state budget of the Czech Republic.