Youcef Bouchekioua

Holly C Miller

Paul Craddock

Aaron P Blaisdell

Mikael Molet
email: mikael.molet@univ-lille3.fr

Spatial integration of boundaries in a 3D virtual environment

Keywords:

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

Introduction

Spatial integration refers to an organism's capacity for linking independently acquired spatial information that shares a common element. [START_REF] Ellen | Problem solving in the rat: Piecemeal acquisition of cognitive maps[END_REF] provided one of the first observations of such a phenomenon. They showed that rats were able to integrate individually and separately acquired spatial relationships into a unified cognitive representation. Such an integration of fragmentary maps into a whole map should allow an organism to follow the direct route from one part of the environment to another [START_REF] Gallistel | The organization of learning[END_REF][START_REF] Poucet | Spatial cognitive maps in animals: New hypotheses on their structure and neural mechanisms[END_REF][START_REF] Worden | Navigation by fragment fitting: A theory of hippocampal function[END_REF]. This ability is one basic tenet of the cognitive map theory proposed by [START_REF] Tolman | Cognitive maps in rats and men[END_REF] and developed by O' Keefe and Nadel (1978). The latter proposed that a cognitive map allows organisms to conceptually link parts of an environment that have never been experienced at the same time [START_REF] O'keefe | The hippocampus as a cognitive map[END_REF].

A growing body of literature suggests that spatial integration is ruled by associative mechanisms of high-order conditioning [START_REF] Leising | Associative basis of landmark learning and integration in vertebrates[END_REF]. A classic example of high-order conditioning is sensory preconditioning (SPC, Brogden, 1939). A conventional SPC procedure consists of pairing two neutral stimuli (S2-S1) in Phase 1 and then pairing S1 with an unconditioned stimulus (US; S1-US) in Phase 2. When testing S2, a conditioned response (CR) appropriate to the US is observed, even though S2 itself has never been paired directly with the US. The same result (i.e. a CR to the S2) is observed following a second-order conditioning procedure (SOC; [START_REF] Pavlov | Conditioned reflexes (G. V. Anrep[END_REF] that consists of an SPC procedure with Phases 1 and 2 reversed. Within the timing literature, Miller and colleagues provided evidence that the integration of temporal maps is based on the associative process of SPC (see [START_REF] Savastano | Time as content in Pavlovian conditioning[END_REF] for a review). For example, [START_REF] Matzel | Information and expression of simultaneous and backward associations: Implications for contiguity theory[END_REF] initially trained rats with S2-S1 pairings with a trace interval followed by backward pairings of S1 with an aversive US (i.e., US-S1). Conditioned responding was not observed following presentation of S1 (consistent with the backward conditioning response deficit; [START_REF] Pavlov | Conditioned reflexes (G. V. Anrep[END_REF]. However, S2 evoked strong conditioned responding. The authors interpreted this result as indicative of temporal integration of associative memories acquired during Phase 1 and 2 of training that shared a common element (S1). Through temporal integration, the rats seemingly retrieved a representation of the US upon presentation of S2. [START_REF] Leising | Temporal integration in Pavlovian appetitive conditioning in rats[END_REF] reported similar findings in an appetitive conditioning procedure with rats. In addition to Matzell et al.'s (1988) findings on SPC, Miller and colleagues reported a few years later evidence for temporal integration in second-order conditioning (SOC; e.g., [START_REF] Barnet | Temporal integration in second-order conditioning and sensory preconditioning[END_REF][START_REF] Barnet | Second-order excitation mediated by a backward conditioned inhibitor[END_REF][START_REF] Cole | Temporal encoding in trace conditioning[END_REF].

Within the spatial literature, [START_REF] Sawa | Sensory preconditioning in spatial learning using a touch screen task in pigeons[END_REF] explored the integration of spatial maps in a two-dimensional spatialsearch task presented on a touchscreen to pigeons. In phase 1, pigeons were presented with two visual landmarks (X and A) that had a consistent spatial relationship to each other. The pigeons were then reinforced for pecking at an unmarked goal location, which bore a constant spatial relationship to first-order A, which was presented in the absence of X. Subsequent test trials on which X alone was presented revealed that the pigeons were able to infer a spatial relationship between X and the goal (seemingly, an X-A-goal associative chain). This suggests that pigeons have the ability to combine two independently learned spatial maps into a single spatial map by a common linking element (i.e., A) in a two-dimensional setting. Using an open-field procedure with pigeons, [START_REF] Blaisdell | Integration of spatial maps in pigeons[END_REF] reported spatial integration similar to that found by [START_REF] Sawa | Sensory preconditioning in spatial learning using a touch screen task in pigeons[END_REF]. Similarly, [START_REF] Molet | Integration of spatila relationships and temporal relationships in humans[END_REF] showed integration, in humans, of independently acquired spatial relationships in a 2-D, computer, landmark-based search task. Using a dynamic 3-D virtual environment, [START_REF] Molet | Spatial integration using a 3D virtual environment with humans[END_REF] extended this result by providing evidence that humans can integrate two spatial relationships between landmarks into a new spatial relationship that guides spatial navigation.

Data in the literature supportive of spatial integration in twodimensional environments with pigeons and humans [START_REF] Molet | Integration of spatila relationships and temporal relationships in humans[END_REF][START_REF] Sawa | Sensory preconditioning in spatial learning using a touch screen task in pigeons[END_REF], in conjunction with results observing spatial integration in three-dimensional environments with pigeons and humans [START_REF] Blaisdell | Integration of spatial maps in pigeons[END_REF][START_REF] Molet | Spatial integration using a 3D virtual environment with humans[END_REF] support the hypothesis that the processes that integrate information concerning separate but related associations between landmarks when using spatial information work in a way that is similar to the processes involving temporal information in experiments from the timing literature (e.g., [START_REF] Savastano | Time as content in Pavlovian conditioning[END_REF].

While these studies focused on landmark-based spatial learning, [START_REF] Prados | Spatial integration in human geometry learning[END_REF] provided evidence suggesting that spatial integration could be extended to geometric cues and compound stimuli containing both geometric and non-geometric information, by using SOC and SPC procedures in a 2D computer based search task with humans (see also [START_REF] Rhodes | Integration of geometric with luminance information in the rat: Evidence from withincompound associations[END_REF] for a similar experiment in rats). However, a closer look at their data reveals that the evidence is rather modest. In Experiment 2 (SOC), two groups of participants (Experimental and Control) first learned to use triangle shapes to locate a goal. Subsequent to this, the Experimental group received compound exposure in which the trained triangle was associated with a second triangle for a number of trials. The two triangles were aligned such that the vertex indicating the goal in one triangle (CS1) overlapped with the other (CS2); whereas the Control group did not receive any compound exposure. During testing with CS2, both groups were tested with an untrained triangle. The participants choosing the vertex that overlapped with CS1 indicated integration, whereas, those choosing the vertex that matched the reinforced angle of CS1 from training indicated generalization. Though more participants chose a strategy based on integration in the Experiment group (30%) in comparison to the Control group (10%), the data revealed that the dominant strategy adopted by the participants in both groups was not integration but rather generalization (50% in the Experimental group and 70% in the Control group). The integration strategy was indicated when the choice occurred as if the participants inferred the spatial relationship between the untrained triangle and the goal through the trained triangle from Phase 1. The generalization strategy was indicated when the choice occurred as if the test-trial triangle was the trained triangle from Phase 1 (see also [START_REF] Sawa | Sensory preconditioning in spatial learning using a touch screen task in pigeons[END_REF], for a similar result in pigeons). Experiment 4 (SPC) that reversed the order of place preference training and the compound exposure training phases reproduced the results observed in Experiment 2.

The data reported by [START_REF] Prados | Spatial integration in human geometry learning[END_REF] provide some indication that spatial integration between geometric cues is possible; yet leave a need for more solid demonstrations that minimize generalization effects. First, it would be more convincing to observe that spatial integration is the dominant strategy. Second, it would be more relevant to observe spatial integration of geometric cues in a three-dimensional environment to mimic real-world situations. This is potentially important because real-world events involve physical settings that often differ from one another by geometry that can be used in spatial navigation. Some have argued that geometric features of the environment are processed with a dedicated geometric module that utilizes specific rules that differ from those governing landmark-based learning [START_REF] Cheng | A purely geometric module in the rat's spatial representation[END_REF][START_REF] Döeller | Distinct error-correcting and incidental learning of location relative to landmarks and boundaries[END_REF][START_REF] Gallistel | The organization of learning[END_REF]. Even though doubt has been cast upon this geometric module hypothesis [START_REF] Cheng | Whither geometry? Troubles of the geometric module[END_REF][START_REF] Pearce | An associative analysis of spatial learning[END_REF], the idea from which it originated, that geometric features of the environment should be of a greater biological importance for organisms than landmarks, is not inconsistent with an associative analysis of spatial learning [START_REF] Miller | Learning about environmental geometry: An associative model[END_REF].

According to the cognitive map theory, there is a clear distinction between the taxon system, based on associative learning, and the local system, based on place learning [START_REF] O'keefe | The hippocampus as a cognitive map[END_REF]. These two systems make reference respectively to what [START_REF] Tolman | Cognitive maps in rats and men[END_REF] called the narrow strip-map, and the broader and more flexible comprehensive map. The discovery of place cells, hippocampal neurons that increase firing rate only at a particular location of the animal environment (O' Keefe & Dostrovsky, 1971), led to the assumption that the hippocampus is the neural substrate of the cognitive map (O' Keefe & Nadel, 1978). At that time, progress in neuroscience reinforced the hypothesis of two neural systems dedicated to spatial learning, the hippocampus being allocated to the local system, while the extra-hippocampal areas being involved in the taxon system. One major distinction between these two systems lies in the fact that, unlike the taxon system, the local system is involved in situations where landmarks are absent or made unusable. The local system is also known to automatically update new information of the explored environment into the cognitive map, while the taxon system is subject to cue-competition phenomena. A recent two-system account of spatial learning comes from [START_REF] Burgess | Spatial memory: how egocentric and allocentric combine[END_REF][START_REF] Burgess | Spatial cognition and the brain[END_REF] who posits that allocentric spatial coding, that is to say the local system, is limited to the boundaries of the environment, whereas egocentric coding, that is to say the taxon system, is allocated to associations between the animal and landmarks of its environment. From an associative learning perspective, the rules involved in spatial learning based on boundaries or shapes of the environment, and the rules that govern landmarkbased spatial learning should be the same, so that spatial integration without any landmark should also follow associative learning rules.

The aim of the present research was to assess the possibility of spatial integration in a navigation task, following associative learning principles with the geometric information of a virtual maze as the only available and relevant stimulus. In Experiment 1 (using SPC) and Experiment 2 (using SOC), we asked whether human participants would be capable of integrating separately learned geometric information to locate a goal within a three-dimensional (3D) virtual environment.

Experiment 1

The participants were assigned to one of two groups: Common Element and No Common Element. The Common Element group assessed the potential integration of spatial relationships sharing common elements between learning Phases 1 and 2. The No Common Element group served as a control condition that precluded integration of spatial relationships by not having common elements between Phases 1 and 2 of learning.

Both groups explored a 3D virtual environment modelled on a kite-shaped maze by using an SPC procedure (see Fig. 1). They first explored two separate pathways (A and X, see Fig. 2, screenshots 3 and 4 respectively) that both originated from a starting room (see Fig. 2, screenshots 1 and 2), and ended in two different adjoining rooms (B and Y, see Fig. 2, screenshots 5 and 6 respectively). A and X can be easily discriminated by the spatial relationship they share with the starting room. More specifically, when the participants start in the starting room, the entry of A is always at the left corner, providing a left diagonal path, while the entry X is always at the right corner, providing a right diagonal path. The symmetrically opposite spatial relationship between the first alleys (A and X) and their adjoining rooms (B and Y respectively) constitutes the crucial information that emerges from the boundaries of the walls and the angles they form.

In Euclid terms, a boundary can be defined as the extremity of anything and the angles as an inclination of two lines in a plane which meet one another and do not lie in a straight line [START_REF] Tommasi | From natural geometry to spatial cognition[END_REF]. We hypothesized that navigation through these parts of the maze would automatically elicit the formation of two spatial associations of the environment (i.e., A → B and X → Y). Subsequent to this, the participants in the Common Element group explored two additional pathways (C and Z, see Fig. 2, screenshots 7 and 8 respectively) that each originated from their respective adjoining rooms (i.e., B and Y) and ended in two different goal rooms. The path Z led to a room containing a treasure chest (+) whereas the path C led to an empty room (-) (see Fig. 2, screenshots 10 and 9 respectively). The color of the walls and doors of rooms B and Y were exactly the same. The only available cue to discriminate between these two rooms was the position of the sharp angles formed by the connecting rooms (B and Y) with the final pathways (C and Z), from the starting position of the participants during this second Phase. Although unnecessary to this discrimination, the differently colored doors could have also been used to disambiguate the two rooms B and Y. When starting in room B, the black door was on the left and the blue one on the right, contrary to the room Y. It is worth noting that alone, associations between colors could not have been used to resolve the task, since the association chains were the same for the two possible pathways of the maze (i.e. Yellow → Black → Blue → Empty and Yellow → Black → Blue → Treasure chest). Back to the starting point, the participants were then asked to take the route that led to the treasure. If participants in the Common Element group integrated the independently learned geometric information of their environment by means of the common elements (i.e., adjoining rooms B and Y), then one would expect them to take the path X to reach the room containing the treasure chest despite the fact that the two pathways X and Z had never been experienced through a continuous exploration. We hypothesized that this result would reflect the establishment of two associative chains: X → Y → Z+ and A → B → C-.

The participants in the No Common Element group also explored two additional pathways (C and Z) that ended in two different goal rooms. The path Z led to a room containing a treasure chest (+) whereas the path C led to an empty room (-). However, they did not originate from the adjoining rooms (i.e., B and Y). Instead, they started at the bottom end of Pathway C or Z. In test, it was expected that participants in the No Common Element group would not integrate the independently learned geometric information because no common elements (i.e., no adjoining rooms B and Y) were experienced in the second phase to connect the learned information with the first phase.

Method

Participants

Thirty-two students from the University of Lille, between 18 and 30 years old and without any previous experience with this task participated in Experiment 1 (16 women and 16 men). They were randomly assigned to one of two groups (Common Element and No Common Element, both n = 16) with an equal sex ratio.

Apparatus

The experiment was conducted in a cubicle containing a table, a chair, and a computer for the participant placed in the centre of the cubicle. The dynamic 3D virtual environment was implemented using the 3DVIA Virtools software (Dassault Systemes).

The 3D virtual environment consisted of a kite-shaped maze (see Panel 1 in Fig. 1). Dimensions of length × width × height were measured in virtual units (vu). The starting room (40 × 20 × 10 vu) was flat gray in color with dark walls and was connected to two pathways (A and X; 60 × 10 × 10 vu each). Each pathway was identical, with blue walls and a dark red floor; and was separated from the starting room by a yellow door that was either open or closed. Pathway A led to Room B (26.5 × 10 × 10 vu) through a black door, and Pathway X led to Room Y (26.5 × 10 × 10 vu) also through a black door. It took approximately 5-6 s to reach the end of Room B or Y from the starting point in a straightforward journey. Rooms B and Y are also described as the small rooms in the text due to their small dimension. A blue door separated Room B from Pathway C (60 × 10 × 10 vu) that led to a goal room (10.7 × 7.5 × 10 vu) with a treasure chest (5 × 5 × 5 vu). In like manner, Room Y was separated by a blue door from Pathway Z (60 x 10 x 10 vu) that led to the second goal room (10.7 × 7.5 × 10 vu). It took approximately 4-5 s to reach the end of the Room B or Y from the starting point in a straightforward journey. The adjoining rooms B and Y were identical: both had white walls and dark red floors. Both end rooms were also identical, with yellow walls and dark red floors. All doors could either be open or closed (the thick dark lines in Panel 1 of Fig. 1 indicate that the door is closed). For half of the participants the goal room on the right contained the treasure and for the remaining half it was reversed. For the sake of clarity, only the condition in which the treasure was placed in the room on the right will be further described.

Procedure

Participants moved through virtual space by pressing keyboard keys: ↑ (forward), ↓ (backward), ← (left rotation), and →(right rotation). Participants navigated from a first-person perspective, at a constant velocity. The computer screen displayed a view from the perspective of the participant within the 3D virtual environment so that the arrangement was analogous to an individual's view of the natural environment (see Fig. 2).

Participants were run individually. The experiment was conducted in 3 phases.

Training phase 1

Phase 1 consisted of a semi-randomized sequence of three A → B trials and three X → Y trials (see Panels 2 and 3 in Fig. 1) that were counterbalanced across participants for order. Before start, the participant was presented the following information (screen 1) "You will always be in the same maze throughout the experiment. You can move by using the arrow keys of the keyboard. Press SPACEBAR to contin-ue…" (screen 2) "For the moment, only one part of the maze will be open to you. You will start from the starting room. For each trial, only one of two paths will be available. Your task is to walk along the open pathway from the starting room to the end. There will be several trials to explore your environment. Press ENTER to contin-ue…" After reading and responding, half of the participants began the first trial with Pathway A being the only available pathway. A closed door blocked the entrance to Pathway X. The trial ended when the participants reached Room B. The next trial began with the participants being repositioned in the starting room with Pathway A being closed and Pathway X that led to room Y being open. This trial ended when the participants reached room Y. The doors separating Room B and Room Y from Pathways C and Z were closed during this phase. For the remaining participants the trial order was reversed.

Training Phase 2

During Phase 2, participants were assigned to one of two conditions: Common Element and No Common Element. The Common Element condition consisted of a semi-randomized sequence of three B → Ctrials and three Y → Z + trials (see Panels 4 and 5 in Fig. 1) that were counterbalanced across participants for order. Before start, the participant was presented the following information "From now on, the blue doors will be open. The unexplored part of the maze is available to you. You will now start from the small rooms. For each trial, only one of two paths will be available. Explore the pathway that is open until you reach its end. Press ENTER to continue…" After reading and responding, half of the participants began the first trial in Room B where only Pathway C leading to the left goal room was open. A black door blocked the exit to Pathway A. Participants were verbally instructed to make a 360°rotation before the first trial. When participants reached the right goal room containing the treasure chest a pleasant sound (corresponding to the discovery of a treasure in Zelda's, Ocarina of Time) was produced as reinforcement.

In the No Common Element condition, participants started at the bottom end of Pathway C or Z, the blue doors separating these pathways from the small rooms being closed. Thus the participants in the No Common Element condition did not experience the adjoining rooms (B and Y). This was the critical difference with the Common Element condition that was expected to preclude integration of spatial relationships. Their task was to progress along the pathway until they reached the goal room. Participants explored the last part of the maze through a semi-randomized sequence of three Ctrials and three Z+ trials that were counterbalanced across participants for order. The instructions were adapted as follow: "The unexplored part of the maze is available to you. For each trial, only one of two paths will be available. Explore the pathway that is open until you reach its end. Press ENTER to continue…"

Test trial

Before completing the test trial the following instructions were displayed on the screen, "The entire maze is now available, and you have the key that allows you to open the treasure chest and discover its contents. You will start from the starting room of the maze. To open the closed doors, you have to press SPACEBAR. But, CAREFUL!! Once you make a choice, you cannot go back. There is no time limit. Press ENTER to start." Once the instructions were understood, participants found themselves in the starting room and were allowed to choose between opening one of the two doors (see Panel 6 in Fig. 1).

Results and discussion

The majority of the participants in the Common Element group (14 out of 16, 87.5%) chose to take the pathways leading to the treasure. This result was anticipated on the basis of the integration of spatial relationships between pathways X → Y and Y → Z +, and between pathways A → B and B → C -. A binomial test indicated that this was significantly different from chance (50%), p = .005. In the No Common Element group, only 6 out of 16 participants (37.5%) made the same choice. A binomial test indicated that this was not significantly different from chance (50%), p = .4. The Pearson Chi-square test also supported the finding that the choice strategy significantly differed between groups χ 2 (1, 32) = 8.53, p = .003 (Cramer's V = 0.52, p = .003). The results of this study provide clear evidence that human participants have the ability to integrate two separate experiences with spatial geometry when boundaries overlapped. The integrated spatial information presumably resulted in a unified higher-order spatial map that was based on the superimposition of the associations in memory that shared common elements (rooms B and Y). Importantly, the use of intra-maze cues to resolve the task was neutralized since the two pathways of the maze were identical. Moreover, no extra-maze cue was present. It is worth noting that while instructions in the present experiment, (i.e., "you will always be in the same maze throughout the experiment"), might have increased attention to common and overlapping spatial features of the maze, this directed attention was not sufficient to produce spatial integration. Rather, actual experience of the common, overlapping features (rooms B and Y), was necessary for participants to show evidence of higher-order integration at test (as in the Common Element group but not the No Common Element group). Importantly, all participants were interviewed after completion of the experiment, and none of the participants that showed spatial integration were able to clearly verbalize the reasons for his/her choice (i.e., use of a spatial integration strategy). Therefore, responding presumably depended on simple associations that encoded spatial relationships rather than on higher-order cognitive processes based on the use of linguistic labels such as "left and right". As far as we know, this is the first clear demonstration of spatial integration of boundaries of a threedimensional environment in a human navigation task, without any relevant landmark.

Experiment 2

Given the similarity of the procedures for SPC and SOC, it appears highly plausible that the spatial integration of boundaries of an environment also applies to SOC. However, there have been some reports questioning the similarity of the underlying associative structures of SPC and SOC (e.g., [START_REF] Rizley | Associations in second-order conditioning and sensory preconditioning[END_REF]. As opposed to the SPC procedure of Experiment 1 in which participants learned the maze's parts separately in a forward pattern (i.e. exploring the first part, and then the last part of the maze), the SOC procedure of Experiment 2, assigned the participants to a backward pattern (i.e. exploring the last part before the first part of the maze). Hence, we sought to investigate the generality of the findings of Experiment 1 by determining whether a SOC procedure would also indicate spatial integration of boundaries of the environment. The design was identical to that used in Experiment 1 with the exception that Phases 1 and 2 were reversed.

Method

Participants

Thirty-two students from the University of Lille, between 18 and 30 years old and without any previous experience with this task, participated in Experiment 2 (16 women and 16 men). They were assigned to one of two groups (Common Element and No Common Element (both n = 16) with an equal sex ratio.

Apparatus and procedure

The apparatus and procedure were the same as those used in Experiment 1 except that Phases 1 and 2 of training were reversed.

Results and discussion

The results of Experiment 2 extend the results of Experiment 1. The majority of the participants in the Common Element group (13 out of 16, 81.25%) chose the correct pathway that led to the treasure. A binomial test indicated that this was significantly different from chance (50%), p = .02. In the No Common Element group, only 7 out of 16 participants (43.75%) made the same choice, which did not differ significantly from chance (50%), p N .8. The Pearson Chi-square test revealed that the choice strategy significantly differed between groups χ 2 (1, 32) = 4.80, p = .03 (Cramer's V = 0.39, p = .03). We interpret this result as indicative of spatial integration of associations acquired during Phase 1 (Y → Z+; B → C-) and Phase 2 (X → Y; A → B) of training based on the element common to both experiences (i.e., Y; B). Through spatial integration, the participants seemingly retrieved a representation of X as the pathway leading to the treasure. Fig. 2. Screenshots from the first-person perspective within the 3D virtual environment taken at each part of the maze.. Panels 1 and 2 have been taken at the beginning of phase 1 and test phase respectively, in the starting room. Panels 3 and 4 have been taken in the entrance of alleys A and X of phase 1. Panels 5 and 6 have been taken in the beginning of phase 2 (experimental group), respectively in room B and Y. Panels 7 and 8 have been taken in the 2nd phase, in the entrance of alleys C and Z respectively. Panels 9 and 10 have been taken at the end of the second phase, when participants face the end rooms of alleys C and Z respectively. In this condition, the treasure was at the end of alley X, as in Fig. 1. This is consistent with the idea that participants encoded associative chains X → Y → Z+ and A → B → C -.

General discussion

We found evidence in both SPC and SOC that human subjects navigating a virtual maze can integrate separately learned geometric information that are joined by a common element, in a landmarkfree environment (i.e. with neutralized extra-maze and intra-maze cues). The unique nature of the SPC and SOC procedures used in the present navigational task involving pathways and small rooms deserve attention, as it differs from previous research relying on discrete stimuli. Our demonstrations of spatial integration using a navigation task with boundaries of a 3D environment as the only available stimuli are readily explained by high-order associative principles, and argue against the claim that the rules governing geometric information are different from those governing landmark-based spatial learning [START_REF] Cheng | A purely geometric module in the rat's spatial representation[END_REF][START_REF] Döeller | Distinct error-correcting and incidental learning of location relative to landmarks and boundaries[END_REF][START_REF] Gallistel | The organization of learning[END_REF]. The results we report here extend associative learning theory to situations involving spatial integration of boundaries of the subject's navigational 3D environment, which is consonant with the growing evidence that associative learning can be conceived as a general theory of learning [START_REF] Pearce | An associative analysis of spatial learning[END_REF]. Our results also add to the growing body of work revealing a role of associative processes in integrating spatial information across separate experiences [START_REF] Blaisdell | Integration of spatial maps in pigeons[END_REF][START_REF] Chamizo | Spatial integration with rats[END_REF][START_REF] Leising | Factors that influence negative summation in a spatial-search task with pigeons[END_REF][START_REF] Sawa | Sensory preconditioning in spatial learning using a touch screen task in pigeons[END_REF].

As animals have to navigate through the same environment in different seasons, the general shape of environment is important. It is, after all, more likely to remain constant, while physical information (e.g. color or texture) is more likely to change. [START_REF] Gallistel | The organization of learning[END_REF] proposed this hypothesis to theoretically justify the claim that the brain contains a geometric module capable of only processing geometric information [START_REF] Cheng | A purely geometric module in the rat's spatial representation[END_REF][START_REF] Gallistel | The organization of learning[END_REF]. Recently, [START_REF] Prados | Spatial integration in human geometry learning[END_REF] challenged this view but, as we mentioned in the introduction, the demonstration was modest. Nevertheless, his results suggested that (1) geometric information can interact with non-geometric information (Experiment 1 and Experiment 3) and that (2) spatial integration could be extended to geometric cues by means of SOC (Experiment 2) and SPC (Experiment 4) procedures in a 2D computer based search task with humans. We extended these findings by using a 3D environment without any discriminative landmarks, and evidencing spatial integration that more closely resembles realworld situations where the most relevant information for reaching a goal is provided by the boundaries of pathways in a given environment. This is particularly important in humans, as boundaries or shapes of streets are less likely to change than building facades that can quickly and unpredictably be renovated and repainted. Consonant with this idea, empirical evidence of the primacy of extended surfaces over landmarks has been found in human children under 5 years of age and in rats (see [START_REF] Tommasi | From natural geometry to spatial cognition[END_REF], for a review). Moreover, it has been shown in rodents that neurons in the hippocampus [START_REF] O'keefe | Geometric determinants of the place fields of hippocampal neurons[END_REF][START_REF] Wills | Attractor dynamics in the hippocampal representation of the local environment[END_REF] and the medial enthorinal cortex [START_REF] Barry | Experience-dependent rescaling of entorhinal grids[END_REF][START_REF] Fyhn | Hippocampal remapping and grid realignment in entorhinal cortex[END_REF] are strongly responsive to the macroscopic surface layout of an environment, suggesting a primacy in the treatment of geometric information. The fact that physically disparate stimuli are processed in different neural networks, also called neural modules, has been used to suggest a modularity of learning rules [START_REF] Jeffery | Theoretical accounts of spatial learning -A neurobiological view (commentary on Pearce 2009)[END_REF]. That said, it deserves noting that [START_REF] Pecchia | Spatial reorientation by geometry with freestanding objects and extended surfaces: A unifying view[END_REF] demonstrated that chicks rely solely on discrete objects to find a reward site in a rectangular shaped arena. Their performance was not different than chance as soon as they were provided only with the geometric information of the arena. This discrepancy might be explained in terms of stimulus saliency, which could be the determinant factor for using only one type of information (i.e. geometric or non-geometric information) when both are available. Such an assumption remains to be experimentaly tested.

In support of the view that associative learning mechanisms have general applicability are all the studies that report evidence of temporal integration, a phenomena that has been extensively investigated by the Miller laboratory (see review by [START_REF] Savastano | Time as content in Pavlovian conditioning[END_REF]. For example, [START_REF] Arcediano | Temporal integration and temporal backward associations in humans and nonhuman subjects[END_REF] trained human participants in a computer-based sensory preconditioning task. Subjects observed the temporal relations between visual cues presented on the screen. After viewing a sequence between A and B (A → B) in Phase 1, and a sequence between B and an outcome (B → O) in Phase 2, subjects were presented with event A and asked to press a key when they thought O would occur. Different groups of subjects experienced different temporal arrangements of events. Only those subjects for whom a linking element was common across the two phases showed temporal integration, and pressed the button most frequently at the time O would be predicted to occur based on temporal integration (see also [START_REF] Molet | Integration of spatila relationships and temporal relationships in humans[END_REF].

In addition to the encoding of spatial and temporal information between events, there is evidence that causal relationships or causal maps can be encoded and integrated during conditioning procedures. For instance, rats appear to be capable of learning cause-effect relationships between paired events, and of integrating them into a coherent causal map that guides causal inference [START_REF] Blaisdell | Causal reasoning in rats[END_REF][START_REF] Leising | The special status of actions in causal reasoning in rats[END_REF]. The catalog of paradigms, procedures, motivational systems, and species in which spatial, temporal, and causal information are encoded and integrated suggests that associative processes are fundamental for binding together independently acquired perceptions and memories [START_REF] Blaisdell | The role of associative processes in spatial, temporal, and causal cognition[END_REF].

Fig. 1 .

 1 Fig. 1. Schematic representations of the virtual environment used in the present research (never seen by the participants). The colors of the doors are symmetrically identical.

  When the participants reached the empty goal room an aversive sound corresponding to the opening of an empty treasure chest in Zelda's, Ocarina of Time (Nintendo) was produced. The next trial began by repositioning participants in Room Y with Pathway Z being open and the exit to Pathway X being blocked by a closed door.

Y. Bouchekioua et al. / Acta Psychologica 144 (2013) 316-323

Supported by an F+ fellowship by KU Leuven financed by the Center for Excellence on Generalization Research (GRIP.TT; KU Leuven grant PF/10/005).


Noel Zahr
email: noel.zahr@aphp.fr

Saïk Urien

Benoit Llopis

Valerie Pourcher

Olivier Paccoud

Alexandre Bleibtreu

Julien Mayaux

Estelle Gandjbakhch

Guillaume Hekemian

Alain Combes

Noël Zahr

Saik Urien

Valérie Pourcher

Olivier Benveniste

David Saadoun

Yves Allenbach

Bruno Pinna

Patrice Cacoub

Christian Funck-Brentano

Joe-Elie Salem

Dr Noël Zahr

Pharmacokinetics and pharmacodynamics of hydroxychloroquine in hospitalized patients with COVID-19

Keywords: Hydroxychloroquine, Covid-19, Pharmacokinetics, Pharmacodynamics

Introduction

A new human respiratory-tropic coronavirus, SARS-CoV-2, has spread rapidly worldwide. COVID-19, the disease caused by this virus, has a very variable clinical presentation, ranging from pauci-symptomatic to acute respiratory distress syndrome. Several drugs are being evaluated for the treatment of covid-19 including hydroxychloroquine (C18H26ClN3O) (HCQ). Some observational, non-randomized studies have suggested the possible efficacy of HCQ associated or not with azithromycin in COVID 19 patients contrasting with other studies [START_REF] Arshad | Treatment with hydroxychloroquine, azithromycin, and combination in patients hospitalized with COVID-19[END_REF][START_REF] Gautret | Hydroxychloroquine and azithromycin as a treatment of COVID-19: results of an open-label non-randomized clinical trial[END_REF][START_REF] Gautret | Clinical and microbiological effect of a combination of hydroxychloroquine and azithromycin in 80 COVID-19 patients with at least a six-day follow up: A pilot observational study[END_REF][START_REF] Mikami | Risk Factors for Mortality in Patients with COVID-19 in New York City[END_REF][START_REF] Million | Early treatment of COVID-19 patients with hydroxychloroquine and azithromycin: A retrospective analysis of 1061 cases in Marseille, France[END_REF]. Recent randomized controlled trials showed that HCQ was not effective in hospitalized or non-hospitalized patients with Covid-19 [START_REF] Geleris | Observational Study of Hydroxychloroquine in Hospitalized Patients with Covid-19[END_REF][START_REF] Rosenberg | Association of Treatment With Hydroxychloroquine or Azithromycin With In-Hospital Mortality in Patients With COVID-19 in New York State[END_REF][START_REF] Boulware | A Randomized Trial of Hydroxychloroquine as Postexposure Prophylaxis for Covid-19[END_REF][START_REF] Tang | Hydroxychloroquine in patients with mainly mild to moderate coronavirus disease 2019: open label, randomised controlled trial[END_REF]. The results of over 120 randomized controlled trials for the treatment and prevention of COVID-19 are pending. Doses of HCQ tested were highly variable, ranging from 400mg/day for few weeks up to 2.4g on day 1 as a loading dose followed by 400 mg/day for few days, based on extrapolation from pharmacokinetics properties of HCQ derived from its approved indications (malaria, auto-immune diseases) [START_REF] Le | Rationale of a loading dose initiation for hydroxychloroquine treatment in COVID-19 infection in the DisCoVeRy trial[END_REF]. Yao et al. reported that HCQ possesses anti-viral activity, against SARS-CoV2 in vitro [START_REF] Yao | In Vitro Antiviral Activity and Projection of Optimized Dosing Design of Hydroxychloroquine for the Treatment of Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2)[END_REF] with an EC50 (half maximal effective concentration) of 0.72μM (240ng/mL) of HCQ on Vero-cells. The antiviral effect of HCQ, has been suggested to result from increasing intracellular pH leading to decreased phago-lysosome fusion, and impaired viral receptor glycosylation. Moreover, HCQ has immune-modulating effect by inhibiting toll-like receptor signaling, decreasing production of cytokines, especially IL-1 and IL-6, potentially mitigating the cytokine release syndrome induced by SARS-CoV-2 infection [START_REF] Akpovwa | Chloroquine could be used for the treatment of filoviral infections and other viral infections that emerge or emerged from viruses requiring an acidic pH for infectivity[END_REF][START_REF] Savarino | Effects of chloroquine on viral infections: an old drug against today's diseases?[END_REF][START_REF] Rossi | Effect of Tocilizumab in Hospitalized Patients with Severe COVID-19 Pneumonia: A Case-Control Cohort Study[END_REF].

Steady-state pharmacokinetics of HCQ has previously been reported in healthy volunteers, adult patients with malaria [START_REF] Lim | Pharmacokinetics of hydroxychloroquine and its clinical implications in chemoprophylaxis against malaria caused by Plasmodium vivax[END_REF], systemic lupus erythematosus (SLE) [START_REF] Morita | Population Pharmacokinetics of Hydroxychloroquine in Japanese Patients With Cutaneous or Systemic Lupus Erythematosus[END_REF][START_REF] Costedoat-Chalumeau | Low blood concentration of hydroxychloroquine is a marker for and predictor of disease exacerbations in patients with systemic lupus erythematosus[END_REF] and rheumatoid arthritis (RA) [START_REF] Tett | Concentration-effect relationship of hydroxychloroquine in patients with rheumatoid arthritis--a prospective, dose ranging study[END_REF][START_REF] Munster | Hydroxychloroquine concentration-response relationships in patients with rheumatoid arthritis[END_REF][START_REF] Carmichael | Population pharmacokinetics of hydroxychloroquine in patients with rheumatoid arthritis[END_REF] and are summarized in Table-1. Herein, we analyzed plasma and blood concentration data in a cohort of consecutive patients hospitalized with COVID-19 who received HCQ. The aim of this work was to characterize HCQ pharmacokinetics in the setting of COVID-19 and to identify its main influencing covariates. The pharmacokinetic model developed from COVID-19 patients then allowed us to determine the best HCQ dosing regimen to rapidly reach relevant theoretical antiviral concentrations, i.e. higher than HCQ EC50 on SARS-CoV-2. We finally analyzed if there was any HCQ dose-efficacy relationship on SARS-CoV-2 clearance and inflammation parameters.

Materials and Methods

We conducted a monocenter study in consecutive patients with confirmed COVID-19 (positive for SARS-CoV-2 with reverse transcription polymerase chain reaction (RT-PCR), sampled for HCQ therapeutic drug monitoring left at the discretion of the treating physicians. Patients were treated with oral hydroxychloroquine sulfate (Plaquenil, Sanofi-Winthrop, Paris, France). Concentrations of HCQ and its metabolites in whole blood and plasma were assayed by Ultra-High Performance Liquid Chromatography (U-HPLC) with fluorometric detection [START_REF] Noe | Development and Validation of a Fast Ultra-High Performance Liquid Chromatography-Fluorescent Method for the Quantification of Hydroxychloroquine and Its Metabolites in Patients With Lupus[END_REF]. This retrospective study was based on data extracted from medical records, in strict compliance with the French reference methodology MR-004, established by French National Commission on Informatics and Liberties (CNIL) and was approved by Sorbonne University ethics Committee (CER-2020-14-JOCOVID).

Pharmacokinetic-dynamic modelling

Hydroxychloroquine time-courses were analyzed using the nonlinear mixed effect modelling software program Monolix 2019R2 (www.lixoft.eu). To ensure full convergence of the program, the iteration number was fixed to 1000 with 50 Markov Chain Monte Carlo. The effect of the demographic and clinical characteristics which were thought to influence pharmacokinetics were evaluated for the following covariates: bodyweight (BW), height, age, sex, hepatic function using ALAT (alanine aminotransferase), creatinine clearance using MDRD (modification of diet in renal disease equation), CRP (c-reactive protein) level, serum albumin, co-prescription with azithromycin or other macrolides, intensive care unit vs. medical wards patients, platelets/white cells counts and hematocrit. Parameter estimates were standardized for a mean standard covariate using an allometric model:

Pi = PSTD x (COVi/COVSTD) PWR
where PSTD is the standard value of parameter and Pi and COVi are the parameter and covariate values of the i th individual. The superscript PWR denotes an exponent power.

For bodyweight, allometric scaling theory dictates that PWR are typically 1 and 0.75 for volumes and clearance terms, respectively [START_REF] Anderson | Mechanism-based concepts of size and maturity in pharmacokinetics[END_REF]. The goodness-of-fit of each model was evaluated by the observed-predicted (population and individual) concentration scatter plots, by the visual inspection of the individual concentration-time courses, and the prediction-corrected visual predictive checks.

A one-compartment open model best described HCQ pharmacokinetics, whatever the sampling reference, blood or plasma. The parameters of the model were the elimination oral clearance (CL/F), the apparent volume of distribution (V/F) and the absorption rate constant, Ka (with F, as the unknown bioavailability). Given the lack of data on the absorption phase, Ka was fixed to 0.75 and 1.15 h -1 in blood and plasma respectively as previously reported [START_REF] Anderson | Mechanism-based concepts of size and maturity in pharmacokinetics[END_REF]. Between-subject variabilities were estimated for CL/F and V/F parameters and the residual variability was described by a proportional model. F stands for unknown bioavailability.

HCQ and Viral clearance

Different covariates, including HCQ concentration, thought to influence the time-to-PCR negativation were tested using the R-program [START_REF] Team | R: A language and environment for statistical computing[END_REF] and the survival package [START_REF] Therneau | A Package for Survival Analysis in S. version 2.38[END_REF]. The Kaplan-Meier method and log-Rank test were used for this purpose. Patients were split according to their individual model-predicted HCQ plasma concentration at 48h using the 1 st , 50 th or 75 th quartile.

Thereafter, two Kaplan-Meyer curves were generated for each splitting factor. The time to negativation was the first occurrence when two successive RT-PCR were negative.

HCQ effect on CRP

The CRP time-courses were modelled as a function of time and plasma HCQ Concentration (Cp) as:

CRP = CRP0*{1 -fHCQ*Cp/(Cp50 + Cp) -(1 -fHCQ)*t/(t + t50) }
where CRP0, fHCQ, Cp50 and t50 denote the initial CRP concentration, fractional effect of HCQ, HCQ concentration or time that produce a 50% decrease in the CRP0 level. The model stands for the effect of HCQ (fHCQ and Cp50) plus an independent time-related effect ([1 -fHCQ] and t50) which simultaneously decrease the initial CRP0 level.

Results

Demographic and biological characteristics

A total of 149 plasma samples were obtained from 104 COVID-19 patients, (n=31 in intensive care units and n=73 in medical wards). Dosing schedules represented are 800mg/12h (total 1600 mg) the 1 st day, then 400mg/12h (RED); 800mg/12h (total 1600 mg) the 1 st day, then 200mg/8h (ORANGE); 400mg/8h (total 1200mg) loading dose the 1 st day, then 400mg/12h (BLUE); 600mg/8h (total 1800mg) loading dose the 1 st day, then 200mg/8h (GREEN).

Pharmacodynamic effects of HCQ in COVID-19

A total of 75 patients were available for a SARS-CoV-2 viral status analysis using nasopharyngeal swab. PCR follow-up was negative in 40 (53%). To assess the effect of plasma HCQ concentration on time-to-PCR negativation, patients were grouped as follows: individual predicted plasma HCQ concentration at 48h below versus above 25th (72 ng/mL), 50th (95.5 ng/mL), 75th quantile (129 ng/mL). There were no significant differences in time-to-PCR negativation for all tested comparisons (Figure -6). In our cohort, only 4 and 16 patients among 104 had observed or imputed (in patients with data available after 72 hours) HCQ plasma levels >240ng/mL, the in-vitro half maximal effective concentration of HCQ against SARS-CoV-2, at 48 and 72 hours, respectively.

There was also no significant effect of HCQ plasma concentration on the CRP time-course. All attempts gave non-significant values for fHCQ, or Cp50 parameters that stand for the effect of HCQ on CRP time-course, meaning that the effect of HCQ on the inflammation status could not be demonstrated. hours of HCQ start. Blue and red curves represent patients with an HCQ plasma concentration at 48 h below or above the 1 st HCQ plasma concentration quartile observed in our cohort, respectively (72 ng/mL, A), median (95 ng/mL, B) and 3 rd quartile (129 ng/mL, C).

Discussion

In this study, we developed a plasma and blood population pharmacokinetics models of HCQ based on data obtained in hospitalized COVID-19 patients in intensive care units and in medical wards. The blood and plasma pharmacokinetics were described by a one-compartment model with first-order absorption. Body weight had a significant effect on CL and Vd in both matrices. HCQ pharmacokinetic parameters in COVID-19 patients are different from those of other pathologies (lupus, malaria, rheumatoid arthritis) and healthy volunteers [START_REF] Lim | Pharmacokinetics of hydroxychloroquine and its clinical implications in chemoprophylaxis against malaria caused by Plasmodium vivax[END_REF][START_REF] Morita | Population Pharmacokinetics of Hydroxychloroquine in Japanese Patients With Cutaneous or Systemic Lupus Erythematosus[END_REF][START_REF] Carmichael | Population pharmacokinetics of hydroxychloroquine in patients with rheumatoid arthritis[END_REF]. The theoretical ideal lowest dose to achieve a target plasma concentration >EC50 (240ng/ml) within 48/72 hours in most patients was 1600mg as a loading dose, followed by 200mg/8h thereafter. Nevertheless, plasma concentrations of HCQ showed a high interindividual variability (see Figure -1) mainly influenced by body weight. In COVID 19, either HCQ dosage adjusted on body weight or HCQ plasma therapeutic drug monitoring may be useful options if HCQ is clinically effective on COVID-19.

However, in our cohort study, there was no significant influence of HCQ plasma concentrations on inflammation (CRP) or on viral clearance (RT-PCR).

Interestingly, recent studies used HCQ pharmacokinetics parameters derived from autoimmune diseases, to propose dosing regimen of HCQ to be used in COVID-19 patients [START_REF] Martin-Blondel | Hydroxychloroquine in COVID-19 patients: what still needs to be known about the kinetics[END_REF][START_REF] Funck-Brentano | Response to the editorial "COVID-19 in patients with cardiovascular diseases": Covid-19 treatment with hydroxychloroquine or chloroquine and azithromycin: A potential risk of Torsades de Pointes[END_REF][START_REF] Garcia-Cremades | Optimizing Hydroxychloroquine Dosing for Patients With COVID-19: An Integrative Modeling Approach for Effective Drug Repurposing[END_REF].

Thus, our data suggest that relevance of these type of modelling might be toned down given the importance of difference observed between HCQ pharmacokinetic parameters in COVID-19 versus other settings (Table -1). Supporting our findings, preliminary pharmacokinetics data from a small cohort of 7 hospitalized COVID-19 patients treated with HCQ as part of the RECOVERY trial (2.4g as loading dose then 400 mg/12h) have recently been pre-published [START_REF] Macgowan | Hydroxychloroquine serum concentrations in non-critical care patients infected with SARS CoV 2[END_REF]. The results indicate that HCQ concentrations are lower than those expected based on previous modelling, even though a high dose regimen was used.

Of note, our PK blood parameters estimates were concordant with those estimated by Thémans et al [START_REF] Themans | Population Pharmacokinetics of Hydroxychloroquine in COVID-19 Patients: Implications for Dose Optimization[END_REF] and other groups [START_REF] Garcia-Cremades | Optimizing Hydroxychloroquine Dosing for Patients With COVID-19: An Integrative Modeling Approach for Effective Drug Repurposing[END_REF][START_REF] Themans | Population Pharmacokinetics of Hydroxychloroquine in COVID-19 Patients: Implications for Dose Optimization[END_REF][START_REF] Karatza | Optimization of hydroxychloroquine dosing scheme based on COVID-19 patients' characteristics: a review of the literature and simulations[END_REF] providing evidence that a high HCQ loading dose is needed to reach circulating levels in COVID-19 patients theoretically relevant as compared to in-vitro SARS-CoV-2 inhibitory concentrations.

In our cohort including over 100 COVID-19 patients, subjects had different profiles ranging from hospitalization in medicine to intensive care unit, with variable renal and hepatic functions, as well as co-prescription with macrolides, most of which are cytochrome P-450 inhibitors [START_REF] Von Rosensteil | Macrolide antibacterials. Drug interactions of clinical significance[END_REF]. None influenced HCQ plasma and blood pharmacokinetics in COVID-19 except weight, or weight and platelet count, respectively. This finding is concordant with other HCQ pharmacokinetic studies in lupus and malaria settings, in which body mass index and platelet count were also significant contributing covariates in the model [START_REF] Morita | Population Pharmacokinetics of Hydroxychloroquine in Japanese Patients With Cutaneous or Systemic Lupus Erythematosus[END_REF][START_REF] Jallouli | Determinants of hydroxychloroquine blood concentration variations in systemic lupus erythematosus[END_REF].

Of note, the relationship between circulating concentrations of HCQ and clinical efficacy has been demonstrated in rheumatoid arthritis and systemic lupus erythematosus [START_REF] Costedoat-Chalumeau | Low blood concentration of hydroxychloroquine is a marker for and predictor of disease exacerbations in patients with systemic lupus erythematosus[END_REF][START_REF] Tett | Concentration-effect relationship of hydroxychloroquine in patients with rheumatoid arthritis--a prospective, dose ranging study[END_REF][START_REF] Munster | Hydroxychloroquine concentration-response relationships in patients with rheumatoid arthritis[END_REF][START_REF] Chasset | The effect of increasing the dose of hydroxychloroquine (HCQ) in patients with refractory cutaneous lupus erythematosus (CLE): An open-label prospective pilot study[END_REF]. However, our study did not show any association between plasma HCQ concentration and time to negativation of SARS-CoV-2 viral load in hospitalized patients, or resolution of inflammation (assessed by CRP). We are currently studying the association between the blood and plasma concentration of HCQ and QTc (i.e the duration of ventricular repolarization corrected for heart rate, a predictor of ventricular arrhythmias) [START_REF] Funck-Brentano | Response to the editorial "COVID-19 in patients with cardiovascular diseases": Covid-19 treatment with hydroxychloroquine or chloroquine and azithromycin: A potential risk of Torsades de Pointes[END_REF] in patients with COVID-19 to further assess cardiovascular safety of HCQ in COVID-19 setting [START_REF] Nguyen | Cardiovascular Toxicities Associated With Hydroxychloroquine and Azithromycin: An Analysis of the World Health Organization Pharmacovigilance Database[END_REF]. Indeed, the risks of cardiotoxicity associated with HCQ during the COVID-19 pandemic might increase for several reasons. Patients with COVID-19 have multiple risk factors for drug-induced QT prolongation and proarrhythmia: hypokalemia; fever amplifying drug-induced IKr blockade; and an increase in interleukin-6, as seen in COVID-19 infection which has been suggested as a mechanism of the QT prolongation associated with inflammation [START_REF] Funck-Brentano | Retraction and republication: cardiac toxicity of hydroxychloroquine in COVID-19[END_REF]. The French Pharmacovigilance Network has reported 103 notifications of cardiac adverse drug reactions associated with "off-label" use of hydroxychloroquine since March 2020 up to April 2020 [START_REF] Gerard | Off-label" use of hydroxychloroquine, azithromycin, lopinavir-ritonavir and chloroquine in COVID-19: A survey of cardiac adverse drug reactions by the French Network of Pharmacovigilance Centers[END_REF]. These observations, on top of its lack of efficacy, justified limiting the prescription of HCQ in COVID-19 patients [START_REF] Roustit | Chloroquine and hydroxychloroquine in the management of COVID-19: Much kerfuffle but little evidence[END_REF].

The retrospective, observational design of our work is the main limitation. The blood and nasopharyngeal samples were not systematically assessed for all patients during the treatment period. This may have biased our results by precluding to demonstrate that there was an association between plasma HCQ levels and negative viral loads. Unfortunately, the detailed time course of viral load was unknot available, precluding further analysis. However, multiple lines of evidence are emerging against HCQ efficacy in hospitalized COVID-19, even with theoretically effective high dosing regimen such as in the RECOVERY randomized controlled trial [START_REF] Cavalcanti | Hydroxychloroquine with or without Azithromycin in Mild-to-Moderate Covid-19[END_REF][START_REF] Skipper | Hydroxychloroquine in Nonhospitalized Adults With Early COVID-19: A Randomized Trial[END_REF][START_REF] Mitja | Hydroxychloroquine for Early Treatment of Adults with Mild Covid-19: A Randomized-Controlled Trial[END_REF]. In that study, patients received a loading dose of 2.4g then 400mg every 12 hours. HCQ was not associated with reduced mortality but was associated with an increased length of hospital stay and a trend towards increased risk of progression to invasive mechanical ventilation or death. [START_REF] Funck-Brentano | Retraction and republication: cardiac toxicity of hydroxychloroquine in COVID-19[END_REF][START_REF] Horby | Effect of Hydroxychloroquine in Hospitalized Patients with COVID-19: Preliminary results from a multi-centre, randomized, controlled trial[END_REF] Indeed, the dosing regimen used in the RECOVERY trial was even higher than the adapted dosing regimen that we can recommend based on in vitro HCQ EC50 on SARS-CoV-2 and HCQ human pharmacokinetic parameters in COVID-19, identified in this work.

Conclusions

Interindividual variability of HCQ pharmacokinetics parameters in hospitalized COVID-19 patients was important and parameters differed from those identified in non-COVID-19 patients. No effect of HCQ was found on SARS-CoV-2 (nasopharyngeal) viral clearance nor on inflammation resolution. Loading doses of 1600mg HCQ followed by 600mg daily doses reached within 72 hours, concentrations relevant to SARS-CoV-2 inhibition in ≥60% (95% confidence-interval: 49.5-69.0%) of COVID-19 patients. platelets count, i.e., for the i th patient CL/Fi = CL/F*(BWi/70) 0.75 and V/Fi = V/F*(BWi/70)*(PLATi/300,000) -0.726

213Figure 1 .

 1 Figure 1. Observed blood (red) and plasma (green) hydroxychloroquine concentrations. Numbers

216 3 . 2 .

 32 Pharmacokinetic modelling 217The population plasma and blood HCQ pharmacokinetic parameter estimates and their 218 influencing covariates are summarized in

  221 checks for the HCQ plasma final model in COVID-19 (for blood final model, see Figure-2B). The 222 observed concentrations percentiles are well included in the corresponding model-predicted 90% 223 confidence interval bands. Among the tested covariates (age, bodyweight, gender, hepatic and renal 224 function, CRP, intensive care vs. medical wards care, macrolide/azithromycin co-prescription, 225 platelet count), bodyweight (based on allometry principles) was the sole variable having an effect on 226 plasma or blood HCQ CL/F and V/F prediction that improved the model. Platelet count had an 227 additional significant effect on V/F estimation for blood HCQ (supplementary Table-1).

Figure 2 .

 2 Figure 2. Prediction-corrected visual predictive check for plasma (A) and blood (B) hydroxychloroquine population pharmacokinetics. Plain (•) and green lines stand for prediction-corrected observed concentrations and their 5 th , 50 th and 95 th percentiles. Light blue and red bands stand for the corresponding model predicted 90% confidence intervals.

Figure 3 .

 3 Figure 3. Representative predicted plasma HCQ concentrations-time courses as a function of the dosing regimen evaluated in major prospective trials testing HCQ for COVID-19. Curves are drawn according to our final parameters for a typical patient weight (WT) of 79 kg (observed median).

A

  mg/8h (SANOFI), 200mg/8h (IHU.Marseille) and 800 mg loading dose then 400 mg/24h (DISCOVERY). Curves shown are using Covid-19 patients (A), lupus patients (B), malaria patients (C), and healthy subjects (D) parameters.

Figure 4 .

 4 Figure 4. Possible dosing regimen in COVID-19 patients (weighing 79 kg) according to our final model.

Figure 5 .

 5 Figure 5. Mean plasma hydroxychloroquine concentration-time courses for a patient with bodyweight (WT) <58Kg or >103Kg and half-life >70h, red and blue curves, respectively (A) and for typical patients with 79kg WT and clearance (CL) ranging between 30-68 L/h and volume of distribution (Vd) between 4765-13470 L, black curves drawn from variable CL and Vd Bayesian estimates (B). Dosing regimen is 200 mg HCQ/8h, with no loading dose.

Figure 6 .

 6 Figure 6. Time-to-Sars-Cov-2 PCR negativation curves as a function of HCQ plasma levels within 48

Table 1 .

 1 Median plasma and blood pharmacokinetics parameters of HCQ in several pathologies. HCQ sulfate 400 mg/day[START_REF] Morita | Population Pharmacokinetics of Hydroxychloroquine in Japanese Patients With Cutaneous or Systemic Lupus Erythematosus[END_REF], § HCQ sulfate 400, 800, or 1,200 mg/day[START_REF] Munster | Hydroxychloroquine concentration-response relationships in patients with rheumatoid arthritis[END_REF], ¥ HCQ sulfate 200 or 400mg/day[START_REF] Carmichael | Population pharmacokinetics of hydroxychloroquine in patients with rheumatoid arthritis[END_REF], ¤ HCQ sulfate dose 800mg then 400 mg at 6, 24, and 48 h afterward[START_REF] Lim | Pharmacokinetics of hydroxychloroquine and its clinical implications in chemoprophylaxis against malaria caused by Plasmodium vivax[END_REF], ** 96 patients (135 samples), *** 104 patients (149 samples) in our study were assessed.

	Plasma	COVID-19***	Lupus*	Malaria¤	Healthy+
	V/F, L	6696	2440	2363	2851
	CL/F, L/h	45.5	68.2	15.5	12.0
	t1/2, h	102	19.5	106	172.3
	Blood	COVID-19**	LUPUS*	RA¥	RA §
	V/F, L	1990	903	605	2283
	CL/F, L/h	14.7	18.6	9.9	15
	t1/2, h	93.8	25.9	43.3	124.3

Time point of drug sampling was performed at various times after HCQ dosing, i.e., mean 16.2 h (SD 30 h). Characteristics of included COVID-19 patients are detailed in Table-2. At the time of HCQ blood sampling, 10/104 patients (9.6%) had severe renal failure with a glomerular filtration rate <30 mL/min/1.73m2 and 34/104 (32.7%) had ALAT levels 3 times higher than the upper normal limit. In all patients, SARS-CoV-2 was confirmed by a positive (RT-PCR) assay on a nasopharyngeal sample. All patients were treated with HCQ and 75/104 (72%) had a post-treatment follow-up with RT-PCR on nasopharyngeal samples. HCQ was combined with a macrolide antibiotic in 29 patients (n=6 with azithromycin). The mean time between the introduction of HCQ and the onset of symptoms was 8.6 ± 5 days. The usual HCQ dosage was 200mg t.i.d (78/104 patients) for 1 to 11 days (3 patients received an 800mg loading dose). Figure

-1

shows plasma and blood HCQ concentrations available in our cohort.

*

Table 2 .

 2 Demographic and biological characteristics of 104 patients. Body Mass Index, NA: non-applicable, MDRD: (modification of diet in renal disease equation), HT: hematocrit, ALAT: alanine aminotransferase, ASAT: aspartate aminotransferase, HCQ: hydroxychloroquine. All data were collected at the time of HCQ sampling.

	Mean	Minimum	Maximum
	± standard deviation

  Table-3, and supplementary Table-1, respectively. These

	219
	220	parameters estimates were different from those reported in other diseases (lupus, malaria,
		rheumatoid arthritis) or in healthy volunteers (Table-1). Figure-2A shows the visual predictive

Table 3 .

 3 Median plasma hydroxychloroquine population pharmacokinetic parameters in 104 COVID-19 adult patients.

	Parameter	Estimate	%res
	ka, h-1	1.15	fixed
	V/F, L	6690	16.1
	β, V/F*(BW/70) β	1	fixed
	CL/F	45.9	21.2
	β, CL/F*(BW/70) β	0.75	fixed
	ηV/F	0.61	18.9
	ηCL/F	0.69	25.1
	σ, ng/mL	64.1	9.76

CL/F, apparent elimination clearance; V/F, apparent volume of distribution; Ka, absorption rate constant; F, unknown bioavailability; , covariate effect parameter; , between-subject variability; σ, proportional residual variability; BW, bodyweight (CL/F and V/F estimates are normalized to a 70 kg BW, i.e., for the i th patient CL/Fi = CL/F*(BWi/70) 0.75.

Table S1 .

 S1 Median blood Hydroxychloroquine population pharmacokinetic parameters in 98 COVID-19 adult

	patients
	Parameter	Estimate	%res
	ka, h-1	0.75	fixed
	V/F, L	1,990	15.9
	β, V/F*(BW/70) β	1	fixed
	β, V/F*(PLAT/300,000) β	-0.726	37
	CL/F	14.7	13.5
	β, CL/F*(BW/70) β	0.75	fixed
	ηV/F
	ηCL/F
	σ, proportional	0.272	12.2

CL/F, apparent elimination clearance; V/F , apparent volume of distribution; Ka, absorption rate constant; F, unknown bioavailability; , covariate effect parameter; , between-subject variability; σ, proportional residual variability; BW, bodyweight (CL/F and V/F estimates are normalized to a 70 kg BW plus V/F to a 300,000

Funding: This research received no external funding

Acknowledgments: NA

Abbreviations

ALAT

Alanine aminotransferase ASAT Aspartate aminotransferase β

Covariate effect parameter

Conflicts of Interest:

The authors declare no conflict of interest.