P Lasaygues
email: lasaygues@lma.cnrs-mrs.fr

E Franceschini

R Guillermin

J-P Lefebvre

N Salaud

P Petit

Two-dimensional ultrasonic computed tomography of growing bones

Keywords: Ultrasonic Computed Tomography, Bone imaging, Born approximation, iterative distorted method I

This study deals with the 2-D ultrasonic qualitative and quantitative imaging of child bone. The inverse problem is linearly and non-linearly solved via a Born-based procedure involving minimization of the discrepancies between measurements and modeling data. Inversions of experimental data are presented.

INTRODUCTION

Ultrasonography is the main first-line imaging technique used to diagnose various pediatric pathologies. Ultrasonography appeals to pediatric radiologists because it is a non-invasive, non-irradiant, painless, inexpensive imaging method, which is also practicable at the bedside. In patients with bone diseases, this technique has also proved to be a highly effective tool for assessing congenital disorders such as hip dysplasia, infectious processes such as sub-periostal abscesses, inflammatory diseases such as chronic arthritis, and even traumatic events such as ankle sprain. However, with standard devices, this method of examination is not suitable for diagnostic purposes or for monitoring bone tumors, with which other methods are more effective, although they have several disadvantages (cost, relatively low availability, and the irradiation and sedation risks involved).

Many authors have dealt with the ultrasonic imaging of bones. Their main aim has usually been to assess the thickness of the diaphysis [START_REF] Bossy | Effect of bone cortical thickness on velocity measurements using ultrasonic axial transmission: A 2D simulation study[END_REF] and to estimate the speed of sound of a wave crossing the structure [START_REF] Andre | Measurement of the velocity of ultrasound in the human femur in vivo[END_REF]. Our group has been focusing on the cross-sectional radial imaging process, using ultrasonic computed tomography. Although this method is known to provide a potentially valuable means of imaging objects with similar acoustical impedance, problems arise when it is proposed to obtain quantitative tomograms of more highly contrasted media (such as hard bone tissues). Finding solutions involves either using non-linear schemes and/or performing extensive studies to reduce the initial approximations. In this paper, we recall the advantages and limitations of ultrasonic computed tomography methods when dealing with highly contrasted scatterers, using a high-order iterative procedure method.

The performances and limitations of this method were then tested using an ultrasonic scanner on a single child fibula, with an adjacent thighbone and geometrical phantom mimicking child bone. The results obtained are promising and suggest that the geometrical and acoustical characteristics of children's bones can be efficiently determined using this ultrasonic computed tomography method.

II. ULTRASONIC COMPUTED TOMOGRAPHY -UCT

The aim of UCT is to perform scattered ultrasonic measurements to build a spatial picture of the distribution of some geometrical and physical parameters of an object. These measurements are carried out using variably densely spaced sets of transmitter and receiver positions and various interrogating wave frequencies. We are then faced with both a forward scattering problem, i.e., predicting the pressure field when the scattering medium and the incident field are assumed to be known, and the inverse scattering problem, i.e., retrieving the parameters of the medium from the incident and scattered fields measured. This inverse problem is non-linear and ill posed, and there generally exists no single solution. It is necessary to find a means of eliminating those solutions, which do not correspond to reality.

Basic UCT principles have by now been clearly established in the case of weakly varying media such as low-contrast structures, i.e. almost homogeneous media [START_REF] Norton | Ultrasonic reflectivity imaging in three dimensions : reconstruction with spherical transducer arrays[END_REF][START_REF] Mensah | Enhanced Compressibility Tomography[END_REF]. A constant reference medium can therefore be chosen (i.e., approximations will be made with a constant background). The scattering problem can be linearized by using the first-order Born approximation, and if the Green's function of the unperturbed problem (the background) is known, the forward problem can be solved with the Lippmann-Schwinger integral equation, and one method of solving this inverse problem will consist in performing a far field asymptotic development. The "classical" tomographic algorithm will yield the perturbation with respect to the reference problem. This leads to a linear relation between the object function (or contrast function) and the scattered field, particularly in the far-field (2-D or 3-D Fourier transform), which makes it possible in principle to reconstruct the object function in almost real time based on a sufficiently large set of scattering data [START_REF] Lefebvre | A linearized inverse problem: acoustic impedance tomography of biological media[END_REF].

In the case of hard biological tissues having larger acoustical impedances than those of the surrounding medium, however, the weak scattering hypothesis is not realistic. If the problem arising for example with the bone thickness imaging is how to identify a water-like cavity within an elastic cylinder, immersed in a water-like fluid, using the low frequency ultrasonic wave (≈ 3 MHz) propagation scheme will be the first solution because the penetration length of the wave increases. In this case, the Born approximation is still satisfied (the wavelengths will be large in comparison with the local acoustical assumptions adopted). The background can be defined in terms of the solid part without any hollow, surrounded by water, and the perturbation, i.e. the object to be reconstructed, namely the cavity. The algorithm of summation of the filtered back-projections can then be used with some signal processing refinements. Despite the artifacts and biases affecting the assessment of the shell thickness, the main result obtained will be a qualitative image of the cavity [START_REF] Lasaygues | Cancellous and cortical bone imaging by reflected tomography[END_REF][START_REF] Lasaygues | Assessing the cortical thickness of long bone shafts in children, using two-dimensional ultrasonic diffraction tomography[END_REF].

However, the first Born approximation will no longer be valid in cases of this kind and it will be necessary to resort to other non-linear strategies. The strategy adopted here involves performing the algebraic inversion of the scattered field, based on the distorted Born iterative (DBI) method, using iterative numerical steps [START_REF] Chew | Wave and fields in Inhomogeneous Media[END_REF]. The DBI method was developed to extend the applicability of the Born approximation to higher orders. Iterations are performed numerically by solving forward and inverse problems at every iteration. With this approach, the medium is modeled without any a priori knowledge by performing a simple discretization procedure and using various simulation techniques involving finite differences to calculate the forward diffraction problem. This inversion method consists in updating the medium by performing iterations and requires more computational time and resources, but the algorithm concomitantly determines the appropriate Green's function and the incident field. The previous iteration serves in each case to define the surrounding medium with a variable background, which gives the propagation properties of the medium at the previous iteration. DBI tomography has the advantage of working at a relatively low frequency (≈ 250 kHz). This procedure is based on a mean-square solution obtained via conjugate gradient and Tikhonov regularization methods. The DBI tomography requires only one series of experimental data and five frequencies were used here: 150 kHz, 180 kHz 250 kHz, 300 kHz and 350 kHz. The results thus obtained yield quantitative information about the scatterer, such as speed-of-sound. Very promising results have been obtained previously on synthetic data [START_REF] Lasaygues | Distorted Born Diffraction Tomography: limits and applications to inverse the ultrasonic field scattered by an non-circular infinite elastic tube[END_REF].

III. EXPERIMENTAL DEVICE

The experimental setup used here was designed for performing ultrasonic reflected and diffracted measurements. Six stepping motors sequentially driven by a programmable translator-indexer device fitted with a power multiplexer were used to perform all the movements. The transducers used for the data acquisition were broadband piezo-composite transducers with nominal frequencies of 250 kHz and 3 MHz.

IV. RESULTS

The validity of UCT was tested on experimental data obtained using the scanner on real child bones and a bonemimicking phantom.

A. Real child bone

The sample was a fresh fibula from a 12-year old child containing no marrow in the inner cavity. The mean crosssection of the bone was 17 ± 2 mm and that of the inner cavity was 6 ± 2 mm. This child bone was surrounding by a tubularshaped agar gel (30 mm) simulating soft tissues. Fig. 3 and Fig. 4 show respectively the sinogram and the reconstruction of the child bone surrounded by an agar gel shell. In this case, the UCT procedure adopted was the classical one: a first-order Born approximation and the algorithm for the summation of filtered projections [START_REF] Lasaygues | Circular antenna for breast ultrasonic diffraction tomography[END_REF] were used. No signal or image processing was performed. The dimensions and the shape of the bone could be readily distinguished on the tomogram, but it was difficult to discriminate between the inner cavity and the cortical area. This is a serious limitation, since the cortical thickness is an index to many bone diseases.

In the second case, the fibula was placed 6 mm from a thighbone so as to create a structure resembling two adjacent bones. This situation required a sufficiently high resolution to be able to detect the gap between the two bones. To check the resolution, we placed a small copper wire (0.6 mm) near the thighbone. In Fig. 7, it can be seen that the thighbone and the fibula show up particularly clearly. The copper rod is also visible. On the other hand, the zone between the thighbone and the fibula is not clearly imaged and it is impossible to measure the distance between the two bones. This was mainly due to the multiple diffusion occurring between the two objects.

B. Geometrical phantom

The transmitter used could be rotated step-wise around the target with an angular increment of 5° (72 emission positions). The receiver could be rotated from 40° to 320° with respect to the transmitter position with an angular increment of 10° (29 reception positions at every emission). Fig. 8 shows images reconstructed via the DBI inversion method. The experimental sample used here was a non-circular homogeneous isotropic tube made of artificial resin (Neukadur ProtoCast 113 TM ). The density of the resin was ρ 1 ≈ 1150 kg/ m 3 , and the mean velocity of the compressional wave was c 1 ≈ 2400 ± 50 m/s. Its maximum internal and external diameters were measured with a caliper and were respectively 6 and 12 mm. It should be noted that in these experiments, differences in the density were observed between the target and the surrounding medium that were not taken into account in the inversion scheme. With then resin of the kind used here to form the outer shell, the density contrast is quite small and can be treated as additional noise when interpreting the experimental data. In addition, it is very difficult to find a high-contrast material having same density as water; the resin adopted here gives the best compromise available. It can be seen here that the resolution and the quality of the modeled contrast improved gradually. The geometry was fairly accurate, whereas the velocity was less accurately assessed, with a relative error of about 5%. This inaccuracy was mainly due to the regularization parameter selected. CONCLUSION This paper deals with the two-dimensional imaging of growing bones and a bone-mimicking phantom using ultrasonic computed tomographic methods. The examples tested in this study involve non-canonical homogeneous real and artificial bone shapes. The results obtained are most promising, because the geometrical and physical parameters of the scatterer were accurately reconstructed. Various means of improving this method, especially the DBI tomography, will now be investigated. One important aspect of the inversion scheme used here is the choice of regularization procedure. Another point, which requires further attention, is the constant density hypothesis. Further studies are now required on methods of taking the density contrast into account in the inversion procedure.

Figure 1 .

 1 Figure 1. Diffraction/ reflection mode set-up

Figure 2 .Figure 3 .Figure 4 . 2 -

 2342 Figure 2. Child fibula sample embedded in an agar-gel shell

Figure 5 .

 5 Figure 5. Samples -femur and fibula -with an agar-gel shell

Figure 6 .Figure 7 .

 67 Figure 6. Ultrasonic sinogram; reflection mode, nominal frequency of 3 MHz, 180 signals / 360°

Figure 8 .

 8 Figure 8. Ultrasonic distorted Born iterative inversion of experimental data obtained on a geometrical phantom mimicking child bone, "Neukadur ProCast" resin, diffraction mode, tomogram 60 x 60 pixels (a) 11 iterations at 150 kHz (b) "a" + 9 iterations at 180 kHz (c) "b" + 14 iterations at 250 kHz (d) "c" + 13 iterations at 300 kHz + 11 iterations at 350 kHz


Toussaint Lucette
email: lucette.toussaint@univ-poitiers.fr

Wamain Yannick

Bidet-Ildei Christel

Coello Yann

Pr Lucette Toussaint

Short-term upper-limb immobilization alters peripersonal space representation

Keywords: Perception and action, Spatial perception, Peripersonal space, Limb immobilization

Peripersonal space is a multisensory interface between the environment and the body subserving motor interactions with the physical and social world. Although changing body properties has been shown to alter the functional processing of space, little is known about the effect of short-term limb immobilization specifically on the motor representation of peripersonal space. In the present study, we investigated the effect of a right upperlimb immobilization for a duration of 24 hours on a reachability judgment task and a brightness judgment task.

Analyses of perceptual thresholds revealed a reduction of peripersonal space representation after the immobilization period, which was not observed when there was no immobilization (control group). In contrast, no variation appeared in the brightness judgment task, suggesting no presence of specific visual perception or decisional deficits in the limb immobilization group. Considered together, the results confirm the crucial role of the motor system in the representation of peripersonal space. They also highlight the plasticity of the motor system resulting in a rapid change of its activity following limb immobilization, with a concomitant effect on motor-related perceptual and cognitive processes.

Introduction

The specific effect of the motor system on visual perception as a function of the location of objects in space has led to the conception of external space not as a continuum but rather as a series of nested functional regions defined by potentialities of action [START_REF] Previc | The neuropsychology of 3-D space[END_REF]. Accordingly, the brain dissociates the region in the environment where objects are accessible hic et nunc (namely the peripersonal space) from the region in space where the body must be transported to reach distant objects (namely the extrapersonal space). Dominant theoretical frameworks emphasize that the peripersonal space is a dynamic representation of the environment where object coding specifically involves a multisensory [START_REF] Graziano | Location of the polysensory zone in the precentral gyrus of anesthetized monkeys[END_REF][START_REF] Rizzolatti | Afferent properties of periarcuate neurons in macaque monkeys. II. Visual responses[END_REF] and body-part centred frame of reference in relation to the motor system [START_REF] Coello | Embodied perception of objects and people in space: towards a unified thoretical framework[END_REF][START_REF] Pellegrino | Peripersonal space in the brain[END_REF][START_REF] Cléry | Neuronal bases of peripersonal and extrapersonal spaces, their plasticity and their dynamics: knowns and unknowns[END_REF]. In line with this view, modifying arm length in the body schema through tool-use (Bourgeois, Farnè, Coello, 2014), or biasing the spatial outcome of a manual reaching action [START_REF] Bourgeois | Effect of visuomotor calibration and uncertainty on the perception of peripersonal space[END_REF] were found to modify the representation of the peripersonal space. The fact that the presence of threatening stimuli also modifies the representation of peripersonal space [START_REF] Coello | Embodied perception of reachable space: how do we manage threatening objects ?[END_REF] has led to the view that peripersonal space similarly represents a safety buffer zone protecting body integrity by prompting defensive/avoidance motor actions [START_REF] De Vignemont | How many peripersonal spaces?[END_REF]Di Pellegrino and Ladavas, 2015;Graziano and Cooke, 2006;[START_REF] Ruggiero | The effect of facial expressions on peripersonal and interpersonal spaces[END_REF]. Accordingly, peripersonal space underlies two functions: the guidance of non-defensive behaviours in relation to neutral, nonthreatening objects; and the guidance of defensive behaviours in relation to threatening or potentially harmful stimuli [START_REF] De Vignemont | How many peripersonal spaces?[END_REF][START_REF] Coello | Action space representation in social contexts[END_REF][START_REF] Hunley | What is peripersonal space? An examination of unresolved empirical issues and emerging findings[END_REF].

In agreement with previous statements, neural alteration of the motor system was found to produce alteration of the representation of peripersonal space. This is indeed what stroke patients with brain damage in motor-related regions suggested, by showing not only specific deficits in the control of motor actions, but also in their representation of peripersonal space [START_REF] Bartolo | The perception of peripersonal space in right and left brain damage hemiplegic patients[END_REF][START_REF] Bartolo | Reachability judgement in optic ataxia: Effect of peripheral vision on hand and target perception in depth[END_REF]. Another way of altering the normal functioning of the motor system is to prevent people to move by constraining their limb degree of freedom for a predefined duration. Neuroimaging studies have effectively shown that finger or arm immobilization by means of a cast or a rigid splint for a short time ranging from 10 hours to 4 days can decrease activity in the contralateral motor cortex [START_REF] Avanzino | Use-dependent hemispheric balance[END_REF][START_REF] Facchini | Time-related changes of excitability of the human motor system contingent upon immobilization of the ring and little fingers[END_REF][START_REF] Huber | Arm immobilization causes cortical plastic changes and locally decreases sleep slow wave activity[END_REF]. In the same vein, behavioural studies highlighted the negative impact of sensorimotor restriction on the sensorimotor and cognitive control of action. Overall, the immobilization-induced effects associated with the decrease of input/output signal processing were reflected in the less accurate aiming [START_REF] Huber | Arm immobilization causes cortical plastic changes and locally decreases sleep slow wave activity[END_REF], alteration of inter-joint coordination [START_REF] Moisello | Short-term limb immobilization affects motor performance[END_REF] and movement kinematics [START_REF] Bassolino | Functional effect of short-term immobilization: kinematic changes and recovery on reaching-to-grasp[END_REF], as well as by slowdown of motor simulation processes [START_REF] Meugnot | The embodied nature of motor imagery processes highlighted by short-term limb immobilization[END_REF]Meugnot and Toussaint, 2015;[START_REF] Toussaint | Short-term limb immobilization affects cognitive motor processes[END_REF].

Assuming that restricting upper-limb movements for even a short period of time alters cortical excitability of the motor regions dedicated to limb control [START_REF] Avanzino | Use-dependent hemispheric balance[END_REF][START_REF] Facchini | Time-related changes of excitability of the human motor system contingent upon immobilization of the ring and little fingers[END_REF][START_REF] Huber | Arm immobilization causes cortical plastic changes and locally decreases sleep slow wave activity[END_REF], and that idiosyncratic representation of peripersonal space relies on the sensorimotor system [START_REF] Coello | Embodied perception of objects and people in space: towards a unified thoretical framework[END_REF], one may expect those individuals prevented to use their arm to show a specific alteration of the representation of their peripersonal space leaving visual perception as a whole unaffected. Previous findings by Bassolino and collaborators (2015), who examined the effect of sensorimotor deprivation on the multisensorial representation of peripersonal space, reported a shrinkage of that space following a period of several hours of arm immobilization. Using an audio-tactile interaction task before and after a short period of arm immobilization, they indeed found that the space where multisensory processing occurred, based on response time variations, contracted for the non-used arm but not for the other arm. However, in this study peripersonal space representation was derived from multisensory processing of approaching and receding auditory stimuli, thereby emphasizing the defensive function of peripersonal space [START_REF] Cléry | Neuronal bases of peripersonal and extrapersonal spaces, their plasticity and their dynamics: knowns and unknowns[END_REF][START_REF] De Vignemont | How many peripersonal spaces?[END_REF][START_REF] Coello | Action space representation in social contexts[END_REF]Hunley and Lorenco, 2018). In the present experiment, we specifically examined the effect of movement restriction (i.e. 24 hours of arm immobilization) on the motor representation of peripersonal space. For that, we used a reachability judgment task thought to imply the motor system in the coding of visual objects in relation to peripersonal space [START_REF] Bartolo | The perception of peripersonal space in right and left brain damage hemiplegic patients[END_REF][START_REF] Coello | Perceiving what is reachable depends on motor representations: A study using transcranial magnetic stimulation[END_REF]. Our hypothesis was that if the motor function of peripersonal space was affected by movement restriction, then immobilizing the upper-limb for 24 hours would affect the perception of object's reachability, but would leave unchanged the perception of other object visual attributes assessed by means of a brightness judgement task.

Method

Participants

Forty right-handed French speaking students (29 women, 11 men, 18-24 years old, mean age = 21.3 years) were recruited in the University of Poitiers. Right hand dominance was estimated using the Edinburgh Inventory Scale (Oldfield 1991). The participants were separated randomly into 2 groups of 20 participants: a control group (14 women, 6 men, 18-24 years old, mean age = 22 years) and an immobilized group (15 women, 5 men, 18-24 years old, mean age = 20.5 years). In a survey, each participant indicated that he/she was healthy, had normal or corrected-to-normal vision and had no history of motor or neurological disorders. The study has been approved by the ethics committee for research in science of physical and sports activities and has therefore been performed in accordance with the ethical standards laid down in the 1964 Declaration of Helsinki and its later amendments. All participants gave their informed consent prior to their inclusion in the study and received course credits (for the control group) or money (for the immobilized group, €25) for their participation. Before testing, participants were naïve about the aims of the experiment.

Material and procedure

All participants were administered two experimental tasks: a reachability judgment task and a brightness discrimination task. Both tasks were identical to those proposed in the study of Bartolo and collaborators (2014). Stimuli consisted in the presentation of a picture created with a 3D graphic software (Blender 3D modeler under GNU General Public License) and represented a virtual scene with a mug (height: 7.5 cm, diameter: 4.2 cm) lying on a table (See Figure 1). The geometry of the visual scene was computed with advantage point at eye level 43 cm above the horizontal surface. The virtual surface on which the objects were presented was a 2m × 8m rectangular surface made with a homogenous texture. On the surface, a black dot was displayed 5 cm from the nearest side of the table on the sagittal axis. Participants (all right-handed) were instructed to imagine having their right index finger on the black dot while performing the perceptual task. The surface of the table was generated with a linear texture extracted from a picture of a piece of wood, which produced a realistic rendering using a ray-tracing algorithm with shadow calculation, but with no information about absolute distance [START_REF] Shirley | Realistic Ray Tracing[END_REF]. Due to the geometry of the virtual scene, the distance of the visible object could be estimated mainly on the basis of the relative size and perspective cues.

In the reachability judgment task, participants were required to estimate as fast as possible if the mug displayed was reachable or unreachable with their right-hand. The brightness of the mug (considering the average value between red, green, and blue channels using the 0 to 255RGB levels scale) was 66.33 during the entire task. The mug was placed in perspective at different distances with respect to the starting location (from 30 to 175 cm by step of 5 cm), providing thus 30 possible distances for the mug.

In the brightness discrimination task, participants were instructed to indicate as fast as possible whether the presented mug had a bright or dark brightness. The mug used in this task was identical to this one used in the reachability judgment task but it was placed consistently at 50 cm from the starting location. Here, the brightness of the mug (estimated through 0 to 255 RGB levels scale) varied along the task between bright (103.09) and dark (29.26), by step of 2.546, providing thus 30 levels of brightness for the mug.

For both tasks, the stimuli were presented on a 15'' CRT computer screen that was placed on a horizontal table at a viewing distance of 50 cm. The experiment was run using E-prime programme (Psychology Software Tools, Inc. www.pstnet.com). Each task offered two possible answers for the participants (reachable/unreachable for the reachability judgment task and bright/dark for the brightness discrimination task).

In both cases, responses were provided verbally. For each trial, the experimenter registered directly the nature of the response whereas verbal responses times were collected using a microphone connected with SR-BOX of Eprime software.

In each task, each trial started with the presentation of a picture with one of the stimuli. This picture stayed visible until the participant's response was provided, within a time window of maximum 4 seconds followed by another 2 seconds of black screen. The other stimuli were presented randomly according to the same temporal sequence. After 30 trials (1 block), participants could have a break of 2 minutes if they asked for. Each task contained 4 blocks where each possible distance or brightness was presented randomly. In total, participants performed 120 trials in each task, which lasted about 10-12 min leading to a total duration of about 20-24 minutes (2 tasks × 10-12 min). To assess the role of short-term upper-limb immobilization on the perception of peripersonal space, both the control and immobilized groups performed the reachability judgment and the brightness discrimination tasks in two experimental sessions with a 24-hr interval between sessions (session 1 and session 2). In our design, the brightness discrimination task served as a control task to evaluate whether the participants showed specific modifications in the perception of peripersonal space or general modifications concerning visual perception. Therefore, and also because the immobilization-induced effects can be masked when participants perform a non sensorimotor task first [START_REF] Toussaint | Short-term limb immobilization affects cognitive motor processes[END_REF], the reachability task was made before the brightness discrimination task in both sessions. It is worth noting that the brightness discrimination task contained a region of ambiguity according to the decision to make (transition area between bright and dark decision), as it is the case for the reachability judgment task (transition area between reachable and unreachable stimuli; [START_REF] Coello | Perceiving what is reachable depends on motor representations: A study using transcranial magnetic stimulation[END_REF]. Therefore, the two tasks had similar difficulties in relation to the decision process.

For the immobilized group, we used a rigid splint (model DONJOY "Comfort Digit"; DJO, Surrey, UK) to prevent the right wrist and fingers movements and an immobilization vest (model DONJOY "Immo Axmed") to restrain movement from the right shoulder, arm, and forearm. The participants were instructed to remove the immobilization vest for the night, but to never remove the splint during the 24 hours immobilization period. To ensure that participants followed the instructions to keep their right hand at rest as much as possible during immobilization, we monitored the physical activity of both hands through wrist actimeters, which provided continuous record of hands activity (i.e., changes in position and acceleration) during 24 hours, expressed as the number of counts per minute. Therefore, fewer counts per minutes for the immobilized hand should confirm compliance with the immobilization procedure. On average 578 counts/min were recorded for the immobilized right hand and 2822 counts/min for the non-immobilized left hand (see also [START_REF] Toussaint | Short-term limb immobilization affects cognitive motor processes[END_REF], for a similar procedure). The ANOVA performed on the actimeters values confirmed that the level of activity was higher for the left hand than for the right hand [F(1,19)=468.88, p<.0001, η²p=.96].

Data analyses

In the reachability judgment task and the brightness discrimination task, the transition between one type of response (reachable-bright) to the other (unreachable-dark) was computed using a maximum likelihood fit procedure based on the second-order derivatives (quasi-newton method) to obtain the logit regression model that best fitted the reachable (bright) / unreachable (dark) responses of the participants, using the equation: y = e (a+bX) / (1+ e (a+bX) ) in which y was the participant's response, X corresponded to the distance, (-a/b) was the critical value of X at which the transition from one type of response (reachable-bright) to the other type of response (unreachabledark) occurred, thus expressing the perceived maximum reachable distance or the brightness perceived mid-way between brightness and darkness. Note that quality of the fitting was measured for each participant thanks to Rsquared. We excluded data from one participant because R-squared estimate was below than 3 SD from the mean R-squared. After exclusion, the mean R-squared computed for the reachability judgment task was to 0.752 (SD = 0.124) before limb immobilization and 0.797 (SD = 0.102) after. For the brightness judgment task, the mean R-squared computed was to 0.730 (SD = 0.110) before limb immobilization and 0,744 (SD = 0.131) after.

ANOVA performed for each task on the R-squared values did not reveal any effect of session.

Response times were also analysed, but differentiating response times for the 5 most reachable (bright) and 5 most unreachable (dark) stimuli, as well as for the 5 stimuli at the boundary of reachable space or at the threshold between bright and dark brightness (corresponding hereafter to the Distance and Brightness factors).

Data above or below 2.5 SD from the mean response time in all condition were discarded for the statistical analysis (less than 3% of the data for Brightness judgment and Reachability judgment tasks). For the judgment performance, statistical analysis was performed in the two tasks using a Group (immobilized, control) x Session (session 1, session 2) ANOVA, with repeated measures on the last factor. Concerning response time, statistical analysis was performed using a Group (immobilized, control) x Session (session 1, session 2) x Space (peripersonal, boundary, extrapersonal) ANOVA in the reachability judgment task, and using a Group (immobilized, control) x Session (session 1, session 2) x Brightness (bright, boundary, dark) ANOVA in the brightness judgment task, with repeated measures on the two last factors. Local comparisons were performed using the post-hoc Bonferroni test with threshold corrections to account for multiple comparisons and measures of effect size were performed using generalized eta squared [START_REF] Olejnik | Generalized eta and omega squared statistics : measures of effect size for some common research designs[END_REF].

Results

Reachability judgment task

Estimation of maximum reachable distance

A Group (control, immobilized) x Session (session 1, session 2) ANOVA on reachability judgments revealed a significant effect of Session (F1,37 = 5.85; p = 0.021; h 2 = 0.14), and a significant Session x Group interaction (F1,37= 4.71, p = 0.036; h 2 = 0.11). Post-hoc comparisons revealed a reduction of perceived maximum reachable distance in session 2 compared to session 1, but only for the group with an immobilized limb. As depicted in Figure 2, perceived maximum reachable distance space decreased from 104.3 cm (SD = 3.5) before limb immobilization to 96.2 cm (SD = 4.1) after limb immobilization (p = 0.013), while perceived maximum reachable distance stayed unchanged between sessions in the control group (106.8 cm [SD = 3.3 cm] and 106.4 cm [SD = 3.4 cm] for session 1 and 2 respectively).

Response Time

A Group (control, immobilized) x Session (session 1, session 2) x Space (reachable, boundary, uneachable) ANOVA did not revealed any effect of the Group (F1,37 = 0.13; p = 0.72; h 2 = 0.004) on response time. However, a significant effect of Session (F1,37 = 33.96, p < 0.0001, h 2 = 0.48), with shorter response time in session 2 than in session 1, and a significant effect of Space (F2,74= 239.75, p < 0.0001, h 2 = 0.87) were observed on the response time. Post hoc comparisons revealed an increase of response time for stimuli at the boundary of reachability in comparison to reachable and unreachable stimuli (+162.92 ms and +115.14 ms respectively, both p < 0.001). Moreover, response time for reachable stimuli was shorter than for unreachable ones (-47.77 ms, p < 0.001). We also found a significant Group x Session interaction (F1,37= 6.17, p < 0.02, h 2 = 0.14, see Figure 3).

In fact, we observed that response time was shorter during the second session in comparison to the first one but only for the immobilized group (-65.86 ms, p < 0.001), not for the control group (-26.50 ms, p = 0.12). Note however that post hoc comparisons did not revealed significant differences in session 1 and in session 2 between both groups.

Brightness judgment task

Boundary of bright-dark discrimination

A Group (control, immobilized) x Session (session 1, session 2) ANOVA did not show any significant main effect of Group (F1,37 = 2.08; p = 0.15; h 2 = 0.05, see Figure 2) or Session (F1,37 = 0.13; p = 0.71; h 2 = 0.003) on brightness judgments. The Group x Session interaction was also not significant (F1,37 = 0.12; p = 0.73; h 2 = 0.003).

Response time

A Group (control, immobilized) x Session (session 1, session 2) x Brightness (bright, boundary, dark) ANOVA showed no effect of Group (F1,37 = 0.17; p = 0.68; h 2 = 0.005) on response time. However, a significant effect of Session (F1,37 = 16,03, p < 0.001, h 2 = 0.30) and a significant effect of Brightness (F2,74 = 129.15, p < 0.001, h 2 = 0.78) were observed, but the factors did not interacted (see Figure 3). We found that response time was shorter in session 2 than in session 1 (-30.21ms). Moreover, while no difference was observed in response time for bright and dark stimuli (p = 0.10), post hoc comparisons revealed an increase of response time for stimuli at the boundary in comparison to bright and dark stimuli (+99.40 ms and +112.26 ms respectively, both p < 0.001).

Discussion

The aim of the present study was to examine the effects of short-term upper-limb immobilization on the motor representation of the peripersonal space. For this purpose, immobilized and control (i.e. without immobilization) participants performed a reachability judgment task and a brightness judgment task in two experimental sessions with a 24-hr interval, corresponding to the duration of sensorimotor restriction in the immobilized group. In agreement with previous literature, it is surmised that reachability judgments implied processing motor-related properties of visual objects and depend on how peripersonal space is represented [START_REF] Coello | Embodied perception of objects and people in space: towards a unified thoretical framework[END_REF][START_REF] Grade | Evidence for the embodiment of space perception: concurrent hand but not arm action moderates reachability and egocentric distance perception[END_REF][START_REF] Patané | Cooperative tool-use reveals peripersonal and interpersonal spaces are dissociable[END_REF][START_REF] Valdés-Conroy | So far so good: emotion in the peripersonal/extrapersonal space[END_REF]. The brightness judgment task served as control task, as focusing essentially on the visual attributes of objects. The main outcome of the present study was that the maximum distance at which objects are perceived as reachable was altered by the upper-limb immobilization, suggesting shrinking of the motor representation of peripersonal space after the period of immobilization. No variation of reachability judgments was observed across sessions in the control group, which was not submitted to the limb immobilization. Moreover, no immobilization-induced effect appeared when judging the brightness of objects.

The sensitivity of the boundary of the peripersonal space to the individuals' sensorimotor abilities have been previously reported in the literature. Although different measures were used to probe the representation of peripersonal space (audio or visuo-tactile integration, line bisection, spatial alignment effect, reachability judgments), all results converged towards the finding that modifying the possibilities of interacting manually with the environment alters the representation of the peripersonal space. In audio-tactile interaction paradigms, that emphasize the defensive component of peripersonal space, the plasticity of the sensory peripersonal space has been highlighted following short-term tool use training [START_REF] Canzoneri | Tool-use reshapes the boundaries of body and peripersonal space representations[END_REF]) and short-term upper-limb movement restriction [START_REF] Bassolino | Dissociating effect of upper limb non-use and overuse on space and body representations[END_REF]. Interestingly, it has been shown that tool-used changed the body metric representation and extended the representation of the peripersonal space [START_REF] Cardinali | When action is not enough: tool-use reveals tactile-dependent access to body schema[END_REF][START_REF] Cardinali | Grab an object with a tool and change your body: tool-use-dependent changes of body representation for action[END_REF]. On the contrary, limb immobilization reduced the peripersonal space representation although no change in body metric representation was observed [START_REF] Bassolino | Dissociating effect of upper limb non-use and overuse on space and body representations[END_REF]. Likewise, in reachability judgment paradigms that emphasize the motor component of peripersonal space, modifying arm length through tool-use was found to alter the representation of peripersonal space due to the functional extension of action capabilities.

The present experiment extends this knowledge by showing that limb non-use influences reachability judgments and suggested a reduction of peripersonal space representation. This confirms that judging whether an object is reachable or not required the contribution of the sensorimotor system [START_REF] Bartolo | The perception of peripersonal space in right and left brain damage hemiplegic patients[END_REF][START_REF] Coello | Perceiving what is reachable depends on motor representations: A study using transcranial magnetic stimulation[END_REF][START_REF] Wamain | EEG µ rhythm in virtual reality reveals that motor coding of visual objects in peripersonal space is task dependent[END_REF], which could be altered as a consequence of action deprivation, even in healthy participants. This also shows that the representation of peripersonal space can be updated very quickly, a period of 24 hours of sensorimotor deprivation being sufficient to affect the reachability judgments.

Response time analyses in the reachability judgment task revealed that objects near the body (i.e., in the peripersonal space) are recognized faster as reachable than distant objects as unreachable (i.e., in the extrapersonal space), and objects at the boundary of peripersonal space led to the highest response time.

Considering brightness judgments, the longest response time appeared for stimuli located at the brightnessdarkness boundary, but no differences were observed for objects clearly bright or dark objects. These results confirmed previous experiment [START_REF] Bartolo | The perception of peripersonal space in right and left brain damage hemiplegic patients[END_REF][START_REF] Coello | Perceiving what is reachable depends on motor representations: A study using transcranial magnetic stimulation[END_REF]. In both tasks, the incertitude for stimuli at the threshold of reachability/brightness was at the origin of the longer time required to provide the response. With regard to the shorter response time in the reachability judgment task for reachable objects, this effect could be interpreted as resulting from the motor coding of object in peripersonal space, which was found to facilitate visual processing [START_REF] Costantini | Where does an object trigger an action? An investigation about affordances in space[END_REF]. A possible interpretation is also that, assuming that the participants look at the centre of the screen while waiting for the forthcoming stimulus, objects in peripersonal space projected predominantly on the upper retina (lower visual field) whereas objects in extrapersonal space projected predominantly on the lower retina (upper visual field). Lower and upper visual field differences have been observed across various tasks (Christman and Niebauer, 1997), with a lower visual field bias emerging in many instances. Anatomical disparity in the superior-inferior retinal axis [START_REF] Curcio | Topography and ganglion cells in the human retina[END_REF]) leads to a lower visual field advantage for attentional resolution [START_REF] Handy | Graspable objects grab attention when the potential for action is recognized[END_REF], motion segmentation [START_REF] Lakha | Lower visual field advantage for motion segmentation during high competition for selection[END_REF] and the control of goal-directed actions [START_REF] Danckert | Superior performance for visually guided pointing in the lower visual field[END_REF]. This difference in the processing of information in the upper and lower visual fields represents thus a potential explanation for the differences in the time required to process object in the peripersonal and extrapersonal space. Another possible interpretation for this effect is that taking the decision of unreachability might require more time than taking the decision of reachability. Previous studies indeed highlighted that, in 2alternative forced choice paradigms, time to respond "yes" is usually shorter than time to respond "no" [START_REF] Brouillet | The embodied cognition theory and the motor component of "yes" and "no" verbal responses[END_REF] and implies different processing [START_REF] Coltheart | DRC: A Dual Route Cascaded model of visual word recognition and reading aloud[END_REF][START_REF] Grainger | Orthographic processing in visual word recognition: A multiple readout model[END_REF]. The fact that reachable responses were still faster than unreachable responses after the immobilization period suggests that this difference in response time cannot unambiguously be related to the contribution of the motor system to the perceptual decision for reachable stimuli [START_REF] Coello | The mutual roles of action representations and spatial deictics in French language[END_REF]. Further experiments would be required to disentangle these different interpretations.

To sum up, the present study provided new evidence for the plasticity of the peripersonal space representation which was quickly updated in the presence of upper-limb perturbation. Twenty four hours of upper-limb immobilization was sufficient to affects the accuracy of reachability judgments thought to depend on the motor representation of peripersonal space. As a whole, these findings provide new evidence for the crucial requirement of a neurologically intact sensorimotor system in the representation of the peripersonal space.

Fig. 1 .

 1 Fig. 1. Examples of two trials in the reachability judgment task (on the left) and the brightness judgment task (on the right).

Fig. 2 .

 2 Fig. 2. Evolution of the reachability threshold (left) and brightness (right) as a function of experimental session and Group. Error bars represent standard error.

Fig. 3 .

 3 Fig. 3. Evolution of response time for the reachability judgment (left) and brightness judgment task (right) as a function of experimental session and Group. Error bars represent standard error.

Ethical standards

The study has been approved by the ethics committee for research in science of physical and sports activities and has therefore been performed in accordance with the ethical standards laid down in the 1964 Declaration of Helsinki and its later amendments.

All participants gave their informed consent prior to their inclusion in the study. Details that might disclose the identity of the participants have been omitted.

Conflict of interest

The authors declare that no conflict of interest exists. Moreover, they have full control of all primary data and they agree to allow the journal to review their data if requested.