Hend Omara-Reda

Omar Ouachikh

Dhouha Hamdi

Mohamed Lashin

Aziz Hafidi

Reinforcing effect of tramadol in the rat

Tramadol induced both behavioral (CPP) and motor (total movement) sensitizations in the rat.

•Tramadol promoted different molecular marker changes in the anterior cingulate cortex.

•All tramadol effects were significantly decreased by the administration of naltrexone, a µ opioid receptors antagonist.

•Tramadol constitutes a reinforcing substance in the rat.

Introduction

Tramadol is an opioid agonist that is often used alone or in combination with other medications to treat chronic pain. It is one of the most commonly prescribed analgesic opioids in various pharmacopeias due to its lower risk of addiction [START_REF] Grond | Sablotzki Clinical pharma-cology of tramadol[END_REF]. It delivers analgesia by two mechanisms: one, activation of opioid receptors, and the other, inhibition of central monoaminergic reuptake, which elevates monoaminergic neurotransmitter levels in the brain [ [START_REF] Codd | Serotonin and norepinephrine uptake inhibiting activity of centrally acting analgesics: structural determinants and role in antinociception[END_REF], [START_REF] Bloms-Funke | Tzschentke Tramadol increases extracellular levels of serotonin and noradrenaline as measured by in vivo microdialysis in the ventral hippocampus of freely-moving rats[END_REF]]. Tramadol acts on different receptors and ion channels (GABAA, glycine, NMDA, adrenergic, nicotinic acetylcholine, sodium channels) [ [START_REF] Faron-Gorecka | Dziedzicka-Wasylewska Long-termexposure of rats to tramadol alters brain dopamine and α1adrenoceptor function that may be related to antidepressant potency[END_REF], [START_REF] Shiraishi | Inhibition by tramadol of muscarinic receptor-induced responses in cultured adrenal medullary cells and in Xenopus laevis oocytes expressing cloned M1 receptors[END_REF], [START_REF] Hara | Sata The effects of tramadol and its metabolite on glycine, gamma-aminobutyric acidA, and N-methyl-D-aspartate receptors expressed in Xenopus oocytes[END_REF], [7], [8]]. There are differences in tramadol abuse effects in clinical research. Some studies showed a weak or no abuse liability for tramadol [34]]. These discrepancies have been attributed to different doses, tramadol use in non-opioid dependent versus drug-dependent people, oral versus injectable administrations or its interaction with other drugs or medication. Preclinical research on tramadol's potential for abuse have various discrepancies. Tramadol has a mild reinforcing effect in rhesus monkeys [35], but a strong reinforcing effect in mice and rats [36], according to a self-administration studies. In rodents, tramadol causes conditioned place preference (CPP) [[36], [37], [38], [39]]. The CPP is a test that measure the motivational effects of a drug. Tramadol induces CPP via mu-opioid receptor [39], and an increase in dopamine release within the nucleus accumbens [37]. However, studies did not report that tramadol induces motor sensitization in rats [38]. This lack of motor sensitization during CPP test suggests that tramadol is not devoid of reinforcing effect but it has only limited abuse potential. Based on its interactions with morphine and buprenorphine, tramadol was found to cause CPP in rats [40]. The purpose of this study was to explore how tramadol affected behavioral sensitizations (CPP and actimetry). Both sensitizations must be present for a molecule to be classified as an abuse drug [[38], [41]]. Sensitization is defined generally as an amplification of the response to a specific repeated stimulus. After repeated exposure to addictive substances, rodents frequently experience locomotor sensitization, a common and important behavioral alteration that causes the animal to become noticeably more hyperactive in response to an acute drug challenge. The effects of tramadol on cellular and molecular alterations in the rat brain, were also studied. In addition, the opioid antagonist naltrexone was used to counteract the effects of tramadol. The anterior cingulate cortex (ACC) constitutes an essential component of the limbic system, which is involved in a range of cognitive and emotional processing. The ACC plays major roles in pain [80] and drug reward [81]. The ACC processes both acute and chronic pain, which makes this region hyperactive [[44], [80]]. Contrarily, it has been reported that addiction causes an ACC hypoactivity [81,82]. For each of these reasons, the ACC has been investigated in this study.

Materials and methods

Animals

Fifty-one adult male Sprague Dawley rats (Charles Rivers, L'Arbresle, France) were used. Rats were maintained in a controlled environment (lights on 07:00-19:00 h, 22 °C) with ad libitum access to food and water. The experiments followed the ethical guidelines of the animal ethics committee of the University of Auvergne (APAFIS#19965-20190325052285). The CPP test was conducted as previously indicated [[42], [43]]. A software application (Imetronic, Pessac, France) was used to analyze rat movements within each compartment of the apparatus, and measure the number of entries and the time the rats spent in each compartment. Briefly, for habituation, the rats were placed in the central alley and were free to explore the entire apparatus for 15 min. During the pretest day, rats received only vehicle injection then placed in the central alley and the time spent in each compartment during a15 min session was recorded. The conditioning period consisted of a session of 30 min per day for 8 days. Each animal had one session with a tramadol (10 mg/kg) intraperitoneal injection (15 min before the CPP session) alternated on the second day by an injection of a vehicle (saline). During the conditioning phase of the CPP, the rats received four tramadol (10 mg/kg)-paired sessions and four vehicles paired sessions (Fig. 1). This procedure ruled out that place preference would result from response bias. By doing this, one group had its last tramadol injection 24 h before the test day while the other had it 48 h before the test day. In the test day, rats were introduced (during 15 min) into the apparatus by placing them in the central alley and did not receive any drug or vehicle. This group is referred to as tramadol-group. This group was continuously tested until the extinction of the tramadol-induced CPP. A second group was tramadol sensitized during the CPP and received naltrexone (1 mg/kg) intraperitoneal injection just before the test in the test day. This group is referred to as naltrexone group. This group continued to be naltrexone administered each day until the extinction of the CPP. The time spent in each compartment during a 15 min session was measured. Data were presented as means of individual differences between times spent in the drug-paired compartment during the pretest phase and the test day. Positive values reflected a CPP. To mention that the CPP experimenter was unaware of the treatment given to the animals. The rats were divided into two groups: tramadol group, which was conditioned with tramadol and had been CPP-tested after the test day for 7 additional days until the extinction of the behavioral sensitization (CPP) was obtained. The second group named the naltrexone group, which has been conditioned with tramadol and after the test was daily administered a naltrexone for additional 7 days. During the conditioning, the rats were split into two groups, one receiving tramadol while the other receiving a saline administration and there were switched the next day. As a result, one group had their last tramadol injection 24 h before the test, whereas the other received it 48 h before the test.

Software from the CPP apparatus gave information's on the number of entries on each compartment, the movement made at the back, front, and back and forth in each compartment. Locomotors activity performance (actimetry) represents the sum of movements performed in each compartment for each animal (mean ± SD) in 15 min. The input number is the sum of entries in the compartments made for each animal (mean ± SD) in 15 min.

Immunohistochemistry

At the end of behavioral studies (CPP extinction), rats were deeply anesthetized with 1 % ketamine and Xylazine. Rats were perfused through the heart with saline followed by 4 % paraformaldehyde in phosphate-buffered saline (PBS). The brains were then removed and placed in 30 % sucrose and 0.05 % sodium azide solution overnight at 4 °C. Coronal sections (30 µm) were obtained using a freezing microtome and collected in 0.05 M Tris-buffered saline (TBS). Free-floating sections were placed in 1 % normal goat serum for 1 h before overnight incubation in primary monoclonal antibody solution (1:5000 mouse anti-PKCγ, Sigma-Aldrich, France; anti-phosphoPKMζ 1/1000, rabbit, Clinisciences, France; anti-GAD67,1/1000, rabbit, Cell-Signaling, Netherland; anti-Δ-FosB, 1/1000, rabbit, Clinisciences, France) at 4 °C. After several rinses, sections were incubated with a corresponding secondary antibody (1:400 for goat anti-mouse Cy2or Cy3; Vector Lab, France) for 3 h at room temperature. All antibodies were diluted in TBS containing 0.25 % bovine serum albumin and 0.3 % TritonX-100. The sections were finally rinsed in TBS, mounted onto gelatin-coated slides, dehydrated in alcohol, cleared in xylene, and cover-slipped with distyrene-plasticizer-xylene. The specificity of the immunostaining was assessed by omitting the primary antibody or protein pre-adsorbed antibody, which resulted in the absence of a signal. Photomicrographs of immuno-stained sections were captured and image intensity analysis was completed using ImageJ software (ImageJ v1.41, National Institute of Health, USA).

The number of Δ-FosB positive cells or the intensity of the labeling were counted using ImageJ software as previousely reported [[42], [43], [44]]. For each animal group, data were the total number of cells or the labeling intensity per identical used square of the sections (n = 12 per animal).

Statistics

Data analysis and statistical comparisons were performed using GraphPad Prism 8 (GraphPad Software Inc.). The results are expressed as mean ± SEM. Level of significance was set as P ≤ 0.05. Brown Forsythe ANOVA one way and Bartlett's test were used to compare between three and more groups. Otherwise, Student's ttest was used for comparing pretest and test results (Fig. 3). The naltrexone effect was highly significant (p < 0.001) (C). Tramadol also induced a significant motor (total movements) sensitization (D) when compared to the pretest day. However, naltrexone administration did not result in a significant difference in motor sensitization (E) when compared to the pretest day, while it did reduce motor sensitization generated by tramadol considerably (p < 0.05) (F). Data are means ± SEM.

Results

Tramadol effect on behavioral (CPP) and motor (actimetry) sensitizations

The ANOVA one way revealed a very significant difference (p < 0.001) between groups during conditioning (Fig. 2). Tramadol produced a significant (p < 0.01) CPP starting with the third injection and became more significant (p < 0.001) at the fourth tramadol injection. After the conditioning period, tramadol induced a significant (p < 0.01) CPP (as evidenced by the time spent in the tramadol related compartment as compared to the pretest) (Fig. 3A). Naltrexone decreased significantly (p < 0.05) the CPP induced by tramadol conditioning (Fig. 3B). The naltrexone effect on tramadol induced conditioning was highly significant (p < 0.001) (Fig. 3C). In addition, when compared to the pretest total movement within the apparatus room, tramadol had a significant (p < 0.01) motor sensitization (actimetry, total movement within the apparatus room) (Fig. 3D). Although naltrexone treatment reduced overall movement, the difference was not significant when compared to the baseline (pretest) (Fig. 3E). When compared to tramadol, however, naltrexone had a significant (p < 0.05) effect on motor sensitization (Fig. 3F). When compared to the pretest, motor sensitization became non-significant after the fifth day after naltrexone injection, indicating that naltrexone had an effect on tramadol-induced activity.

CPP extinction and naltrexone effect (effect of NTX on tramadol induced-CPP)

From the first test day to the extinction of behavioral sensitization, tramadolinduced CPP was assessed (Fig. 4A). It is worth noting that the rats were not given tramadol beyond the first test day (eighth day after the pretest). The tramadolinduced CPP remained significant (p < 0.01) for four days following the test day, declined by the fifth day although still significant (p < 0.05), and subsequently became non-significant. Tramadol re-induced a substantial (p < 0.01) CPP when injected 7 days following the last test day.

1. Download : Download high-res image (498KB) 2. Download : Download full-size image Fig. 4. The figure represents the extinction of tramadol-induced CPP and the naltrexone effect on this CPP. Tramadol-induced behavior was significant for up to 7 days after the test day (A). Tramadol injections on day 7 after the test resulted in a significant (p < 0.01) increase in CPP. The tramadol-induced CPP was reduced significantly (p < 0.01) by naltrexone treatment in the first three days after the test day, and it was blocked after that (B). A CPP was not induced by tramadol injection 24 h after naltrexone injection on day 7 after the test. Tramadol-induced motor sensitization was considerable 6 days following the test day, but not by the 7th day (C).When tramadol was administered on the eighth day after the test, it caused a significant (p < 0.001) increase in CPP. For the first four days after the test day, naltrexone reduced tramadol-induced motor sensitization (D) and ultimately blocked it. Tramadol did not cause motor sensitization in this animal group on the eighth day after the test day (naltrexone-treated). Data are means ± SEM.

From the day of the CPP test, the Naltrexone group received naltrexone injections every day. Naltrexone administration reduced the CPP generated by tramadol considerably (p < 0.01) for the first three days after the test day (Fig. 4B) and then blocked it. There was no significant tramadol-induced CPP behavior in the naltrexone group when tramadol was reinjected 7 days after the test day. A significant tramadol-induced motor sensitization paralleled that of the CPP behavior, lasted for 6 days after the test day, and subsequently disappeared (Fig. 4C). The injection of tramadol eight days after the test day re-induced a significant (p < 0.01) motor sensitization. After the test day, naltrexone was given every day until the CPP behavior was no longer present. The first four days of tramadol-induced motor sensitization were reduced by naltrexone, but the motor sensitization was still significant when compared to the pretest. When compared to the pretest, motor sensitization became non-significant after the fifth day after naltrexone injection, indicating that naltrexone had an effect on tramadol-induced motor activity (Fig. 4D). There was no substantial motor sensitization when tramadol was re-injected on day 8 after the test day in the naltrexone group.

Molecular changes induced by tramadol in the anterior cingulate cortex

GAD67 staining:

In tramadol-(Fig. 5A), naltrexone-(Fig. 5B), and control rats, a comparable pattern of GAD67 immunostaining (Fig. 5) was found in cell bodies and processes within the ACC (Fig. 5C). In tramadol-treated ACC, the intensity of GAD67 staining was more higher, particularly within cell processes, than in naltrexone-treated and control ACC. Quantification of GAD67 immunostaining revealed a significant (p < 0.001) difference between tramadol-treated and naltrexone-treated or control ACC (Fig. 5D). Although the GAD67 staining intensity was higher in naltrexonetreated rats than in control rats, this difference was not significant.

PKMζ staining

PKMζ immunostaining in the ACC (Fig. 6) was primarily observed in neuronal cell bodies and processes in the tramadol-(Fig. 6A-B), naltrexone-(Fig. 6C-D) and control rats (Fig. 6E-F). The intensity of staining was more important in tramadol and naltrexone-treated when compared to control ACC. PKMζ staining quantification (Fig. 7) revealed a significant staining difference between tramadol, naltrexone (p < 0.01) and control (p < 0.001) rats. There was also a significant (p < 0.01) PKMζ staining difference between naltrexone-treated and control ACC. Bar represents 50 µm in A, C and E and 110 µm in B, D, and F. 1. Download : Download high-res image (958KB) 2. Download : Download full-size image Fig. 6. Represents phospho-PKMζ staining in the ACC. The staining can be seen in neuronal cell bodies and processes within the ACC of tramadol-treated rats at low magnification (A). The staining can be seen throughout somata and processes across the width of the cortex of tramadol-treated rats at high magnification (B). The intensity of the staining was decreased in naltrexone-treated animals (C, D), but it can be seen at high magnification in neuronal somata and processes inside the ACC (D). Similar staining is observed in the ACC (E) in the control, where it is localized in neuronal cell bodies (F). The bar represents 200 µm in A, C and E; and 50 µm in B, D and F.

1. Download : Download high-res image (125KB) 2. Download : Download full-size image Fig. 7. phospho-PKMζ intensity of staining quantification revealed a significant staining difference between tramadol treated and naltrexone-treated (p < 0.01) or control (p < 0.001) ACC. There was also a significant (p < 0.01) staining difference between naltrexone-treated and control ACC. Data are means ± SEM.

PKCγ staining

In tramadol (Fig. 8A-B), naltrexone (Fig. 9C-D), and control (Fig. 8 E-F) groups, PKCγ labeling (Fig. 8) was found in cell bodies and processes across the ACC. The processes were thick and resembled the dendritic subtype in appearance. In the ACC, PKCγ immunostaining quantification revealed a significant (p < 0.001) difference between tramadol and naltrexone or control (Fig. 9). Although the intensity of PKCγ staining in naltrexone was higher than in control ACC, the difference was not significant. Δ-FosB staining (Fig. 10) was observed in cell nuclei within the ACC of tramadol-(Fig. 10A,B), naltrexone-(Fig. 10C,D) and control (Fig. 10E,F) rats. There was a more cell staining in tramadol and naltrexone-treated ACC than in control. Cell count (Fig. 11) reveals a significant difference in the positive cell number between tramadol (p < 0.01), naltrexone (p < 0.05) and control rat. There is also a significant (p < 0.05) difference in cell number between tramadol and naltrexone ACC.

Discussion

The main results of the present study were that tramadol administration promoted both behavioral (CPP) and motor (actimetry) sensitizations making it a drug of abuse in the rat. Tramadol administration caused a high level of excitation in the ACC, as evidenced by an increase in markers such PKCγ, phospho-PKMζ, and Δ-FosB.

CPP caused by tramadol has already been demonstrated [[36],

[37], [38]]. Only one study, however, shows a minor motor sensitivity [38]. During the conditioning period in the current investigation, motor sensitization mirrored behavioral sensitization. During the conditioning, tramadol caused significant motor sensitization after the third injection. Also, motor sensitization followed behavioral sensitization in the tramadol-group (rats get tramadol under CPP training) after the test day (CPP). Furthermore, on the day of CPP extinction, motor sensitization was still evident and significant (behavior). In the naltrexone group, similar results were obtained. These findings support the fact that tramadol causes both motor and behavioral sensitization. Tramadol delivery-two weeks after CPP extinction resulted in an increase in both behavioral and motor sensitizations (unpublished data), while the differences were not statistically significant when compared to the pretest. The ACC is a structure that is important for cognitive control of decision-making, in reward [46], learning, emotion, and memory [48]. In drug addicts, there is a decrease in ACC activity [49]. These characteristics make the ACC an ideal structure for studying tramadol's molecular and cellular effects. The ΔFosB finding is consistent with a recent study that found that tramadol enhanced ΔFosB in the nucleus accumbens and prefrontal cortex after both acute and chronic treatment [50]. This effect is due to the tramadol activation of muopioid receptors as well as an increase in their expression The CPP generated by tramadol was dramatically reduced by naltrexone, a muopioid antagonist. It reduces behavioral as well as motor sensitizations. Furthermore, naltrexone accelerated the extinction of the tramadol-induced CPP by two days (at four days following the test day instead of 6 days in tramadol-treated rats). Tramadol-induced CPP (reinstatement) was totally prevented by continuous naltrexone (8 days after the test day) treatment. Both motor and behavioral sensitization were inhibited (Fig. 5A andB). Furthermore, naltrexone reduced all of the studied markers. Although, naltrexone decreased significantly most of tramadol effects it did not reverse them at the control levels. This revealed that some of tramadol's effects are due to its activity other than through mu-opioid receptors [ [START_REF] Codd | Serotonin and norepinephrine uptake inhibiting activity of centrally acting analgesics: structural determinants and role in antinociception[END_REF], [START_REF] Bloms-Funke | Tzschentke Tramadol increases extracellular levels of serotonin and noradrenaline as measured by in vivo microdialysis in the ventral hippocampus of freely-moving rats[END_REF], [START_REF] Faron-Gorecka | Dziedzicka-Wasylewska Long-termexposure of rats to tramadol alters brain dopamine and α1adrenoceptor function that may be related to antidepressant potency[END_REF], [START_REF] Shiraishi | Inhibition by tramadol of muscarinic receptor-induced responses in cultured adrenal medullary cells and in Xenopus laevis oocytes expressing cloned M1 receptors[END_REF], [START_REF] Hara | Sata The effects of tramadol and its metabolite on glycine, gamma-aminobutyric acidA, and N-methyl-D-aspartate receptors expressed in Xenopus oocytes[END_REF], [7], [8]] may be at central serotoninergic transmission level [79].

  [[8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18]]. Conversely, other studies linked an abuse effect to tramadol [[9], [19], [20], [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32], [3 3],

Fig. 1 .

 1 Fig. 1. The figure represents the time course of the CPP experiments.The rats were divided into two groups: tramadol group, which was conditioned with tramadol and had been CPP-tested after the test day for 7 additional days until the extinction of the behavioral sensitization (CPP) was obtained. The second group named the naltrexone group, which has been conditioned with tramadol and after the test was daily administered a naltrexone for additional 7 days. During the conditioning, the rats were split into two groups, one receiving tramadol while the other receiving a saline administration and there were switched the next day. As a result, one group had their last tramadol injection 24 h before the test, whereas the other received it 48 h before the test.

  Fig. 2. The diagram illustrates how tramadol's impact on motor sensitization during conditioning changed over time. Tramadol generated a considerable (p < 0.01) increase in motor sensitization after the third injection, and this increase became significantly more pronounced (p < 0.001) by the fourth dosage. Data are means ± SEM.

Fig. 3 .

 3 Fig.3. The figure represents the tramadol effect on the CPP and the motor sensitization (actimetry) as well as the effect of naltrexone on the CPP-induced by tramadol. Tramadol significantly (p < 0.01) induces a CPP (A) as revealed by the time spent in the tramadol associated compartment when compared to the pretest one. The injection of naltrexone significantly (p < 0.05) decreased the CPP induced by tramadol (B). The naltrexone effect was highly significant (p < 0.001) (C). Tramadol also induced a significant motor (total movements) sensitization (D) when compared to the pretest day. However, naltrexone administration did not result in a significant difference in motor sensitization (E) when compared to the pretest day, while it did reduce motor sensitization generated by tramadol considerably (p < 0.05) (F). Data are means ± SEM.

1 .

 1 Fig. 5. The figure represents the effect of tramadol and naltrexone on GAD67 expression in the ACC. Within the ACC of tramadol-(A), naltrexone-treated (B), and control rats, GAD67 staining can be seen in various cell bodies and processes (C). The GAD67 staining quantification indicated a significant (p < 0.001) difference in staining between tramadol and control rats, as well as tramadol and naltrexone treated rats. There is no significant change in staining between the naltrexone-treated and control rats. The bar represents 200 µm in A, C and E; and 50 µm in B, D and F. Data are means ± SEM.

1 .

 1 Download : Download high-res image (1MB) 2. Download : Download full-size image

Fig. 8 .

 8 Fig. 8. PKCγ staining within the ACC in tramadol-(A, B), naltrexone-treated (C, D) and control rats (E, F). PKCγ staining is observed in cell bodies and processes. The intensity of staining is high in tramadol and naltrexone-treated rats when compared to control. The bar represents 200 µm in A, C and E; and 50 µm in B, D and F.

Fig. 9 .

 9 Fig. 9. PKCγ intensity of staining quantification in the ACC revealed a significant (p < 0.001) staining difference between tramadol-treated when compared to naltrexone-treated or control. No significant staining difference is observed between naltrexone-treated and control ACC. Data are means ± SEM.

1 .

 1 Download : Download high-res image (1MB) 2. Download : Download full-size image

Fig. 10

 10 Fig. 10. Δ-FosB staining in the ACC. Δ-FosB staining is observed in cell nuclei of the cortex in tramadol-(A, B), naltrexone-(C, D) and control (E, F) rats. The bar represents 200 µm in A, C and E; and 50 µm in B, D and F.

  [[39], [50]]. ΔFosB is known to be elevated during chronic exposure to drug abuse and to play a key role in the neuroplasticity that underlay addiction [51]. Increased psychomotor sensitivity to psychostimulants is promoted by ΔFosB expression [[52], [53]]. As a result, the current study's rise in ΔFosB expression provides more evidence of tramadol's misuse potential in rats. ΔFosB may have a role in tramadol-induced behavioral and motor sensitizations by modulating the expression of Glutamate receptor subunits [[52], [54], [55]]. In both CPP and self-administration paradigms, inducing ΔFosB expression in the striatum's medium spiny neurons improves locomotor sensitivity and reward responses to cocaine [[52], [56], [57]]. In addition, tramadol administration increased two important synaptic plasticity proteins, PKCγ and PKMζ [[58], [59]]. Within the brain, synaptic plasticity occurs at glutamatergic synapses. Tramadol induces an increase in glutamate release and a decrease in GABA system [[60], [61]] causing seizure [[62], [63]]. Tramadol may suppress this cell type by acting on mu-opioid receptors, which are only found in GABA-ergic interneurons [[64], [65], [66], [67], [68]]. Within the ACC, this can help excitatory inputs to pyramidal cells or GABAergic afferent target cells. In addition, mu-opioid stimulation inhibits GABA release [69]. This decrease in GABA inhibition is most likely reflected in the current study by an increase in PKCγ [70] and PKMζ expression in the tramadol-treated group's ACC. Both of these markers are found in excitatory cells, including pyramidal cells. Also, tramadol inhibits GABA receptors [[71], [72]]. The fact that GAD67 increased in the ACC of the tramadol group is probably due to an increase in general excitation within the cortex. GAD67 expression is regulated by activity [[73], [74], [75], [76]]. It could be due also to disinhibition within GABAergic circuitry within the ACC [77]. The expression of GAD67 is highly correlated with the amount of intracellular GABA [78].

Acknowledgments

This study was funded by Clermont Auvergne University and all authors declare that there is no conflict of interest.

Data availability

The data that has been used is confidential.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.


Kendric Ruiz

Stéphane Victor

Pierre Melchior

Serge A Chaumette

A new dynamical attractive and repulsive fractional potential for UAV in 3D dynamical environment

In recent years, applications for drones have multiplied, from surveillance, exploration, rescue and transport applications.

UAVs are more and more autonomous, therefore real-time trajectory planning is necessary and can be achieved with potential fields. A quick study is proposed to better scale attractive and repulsive forces which has always been problematic when dealing with artificial potential fields. The purpose of this article is to develop a new dynamical fractional potential attractive and repulsive field usable in a dynamical 3D environment by taking into account the obstacle dynamics (position and speed) and theirs dangerousness. This makes it possible to avoid the obstacle in a more robust way, both from a safety point of view and from a trajectory optimization point of view. The potential fields are based on the relative position and speed of the drone in relation to the target for the attractive potential field or to the obstacle for the repulsive one.

A new dynamical attractive and repulsive fractional potential for UAV in 3D dynamical environment

Introduction

Path planning is used to find a suitable path between two points (mostly provided by the GPS) while avoiding obstacles in the environment. These obstacles can be dynamical or static. The notion of danger is therefore necessary to avoid a type of obstacle in the most harmonious way. Research on potential field methods has been extensively studied [START_REF] Khatib | Real-time obstacle avoidance for manipulators and mobile robots[END_REF][START_REF] Hwang | A potential field approach to path planning[END_REF][START_REF] Krogh | Integrated path planning and dynamic steering control for autonomous vehicles[END_REF][START_REF] Sfeir | An improved artificial potential field approach to real-time mobile robot path planning in an unknown environment[END_REF][START_REF] Receveur | New interpretation of fractional potential fields for robust path planning[END_REF]. However, most methods are generally adapted for a static environment or do not take into account the type of obstacle (see e.g. [START_REF] Li | Improved artificial potential field-based simultaneous forward search method for robot path planning in complex environment[END_REF][START_REF] Mac | Improved potential field method for unknown obstacle avoidance using uav in indoor environment[END_REF]). [START_REF] Ge | Dynamic motion planning for mobile robots using potential field method[END_REF] have improved work on artificial potential fields by taking into account the obstacle dynamics. In this sense, [START_REF] Poty | Dynamic path planning for mobile robots using fractional potential field[END_REF] and [START_REF] Metoui | Robust path planning for dynamic environment based on fractional attractive force[END_REF] have interpreted the attractive field as a control loop ensuring stability degree robustness of the trajectory towards mass variations of the ego-vehicle and disturbances by taking into account the position and speed of the target as defined by [START_REF] Ge | Dynamic motion planning for mobile robots using potential field method[END_REF] (see Fig. 1). Also, a novel interpretation of robust control is proposed in [START_REF] Receveur | New interpretation of fractional potential fields for robust path planning[END_REF] for autonomous vehicle. The objective of this article is to present a new potential attractive and repulsive field adapted to a dynamical 3D environment that ensures the robustness of the trajectory. Potential fields are well adapted for drone applications because its holonomic model can be identified by a point mass. The potential field method allows this mass to be taken into account for both attractive and repulsive. The concept of danger will also be taken into account, the obstacles will be considered as known and the method makes it possible to avoid the obstacle with a softer trajectory according to the obstacle type, in other words, its dangerousness (pedestrian, buildings, bicycle, car etc.). In Ge & Cui, no distinction is proposed to differentiate the dangerousness of obstacles (it is safer to go nearer a wall than a human). Therefore, Weyl repulsive potential definition has introduced a fractional degree to distinguish obstacles with their dangerousness. By gaining on differentiating obstacle danger, the dynamical behaviors of obstacle has been lost. Therefore, the paper proposes a new definition of attractive and repulsive field that takes into account both dangerousness and dynamics of the obstacles. Moreover, it is often difficult to scale the attractive and repulsive potential forces. A methodology is proposed to efficiently scale them.

A fractional attractive force is presented in section 2. Section 3 presents a new dynamical fractional repulsive force. To finally conclude in section 4.

Fractional Attractive Force

In [START_REF] Metoui | Robust path planning for dynamic environment based on fractional attractive force[END_REF], the [START_REF] Ge | Dynamic motion planning for mobile robots using potential field method[END_REF] method has been reinterpreted as a control loop, see Figure 1. This virtual attractive force is defined by: where p tar and p ego respectively are the real-time positions of the target and the ego-vehicle (EGV). v tar and v ego respectively are the real-time speeds of the target and the ego-vehicle. α p and α v are positive constants that define a lead-phase controller.

F att = α p (p tar -p ego ) + α v (v tar -v ego ) (1)
Introducing the error e(t) = p tar -p ego , and considering the fractional derivating of the velocity, it then comes:

F att = α p e(t) + α v d n e(t) dt n , (2)
where a tar and a ego respectively are the real-time acceleration of the target and the ego-vehicle and m ego is the mass of the ego-vehicle. Under zero initial conditions, the Laplace transform of relation [START_REF] Hwang | A potential field approach to path planning[END_REF] gives:

F att (s) = (α p + α v s n ) E(s), (3)
where E(s) is the transform Laplace of e(t).

Fractional Repulsive Force

Ge & Cui potential field definition depends both on the distance ρ between the EGV and the obstacle, and their relative velocities v RO . Weyl potential field solely depends on the distance while distinguishing obstacle dangerousness with order n. Therefore, it is proposed to differentiate the obstacle dangerousness by keeping the order n in the Weyl repulsive field definition, and by adding distance and relative speed to add reactivity to the obstacle. The new fractional repulsive potential becomes:

U rep (p, v) = (ρ s (p, p obs ) -ρ m (v RO )) n-2 -ρ n-2 max ρ n-2 min -ρ n-2 max , (4)
from where one draws the following repulsive forces:

Frepv = η (n -2) (ρs (p, p obs ) -ρm (vRO)) n-3 vRO ρs (p, p obs ) amax ρ n-2 min -ρ n-2 max v RO⊥ n RO⊥ (5)
and

Frepp = η (n -2) (ρs (p, p obs ) -ρm (vRO)) n-3 1 + v RO amax ρ n-2 min -ρ n-2 max nRO. (6)
Now, the repulsive potential field function takes into account an order n to manage obstacle avoidance according to its dangerousness and the obstacle speed to operate in a dynamical environment.

Conclusion

In trajectory planning, artificial potential fields provide good results for trajectory planning in dynamical environments. It remains essential for real-time application and allows a good reactivity of the EGV. The Ge & Cui force allows taking into account the velocity of obstacles but it is not robust to a change in mass. The Weyl potential force associates a degree of danger with an obstacle. A new dynamical fractional attractive and repulsive field is presented allying both advantages and guarantees robustness due to mass variations. This method takes into account the obstacle dynamical aspects such as positions and speeds, and associates dangerousness to a fractional order. The fractional regulator in an attractive form, which allows robustness in terms of EGV mass variations.

Figure 1 :

 1 Figure 1: Dynamical interpretation of Ge and Cui attractive and repulsive forces