Josselin Baumard
email: josselin.baumard@univ-rouen.fr

Frédérique Etcharry-Bouyx

Valérie Chauviré

Delphine Boussard

Mathieu Lesourd

Chrystelle Remigereau

Yves Rossetti

François Osiurak

Didier Le Gall

Repetitive reaching in optic ataxia EFFECT OF OBJECT SUBSTITUTION, SPONTANEOUS COMPENSATION AND REPETITIVE TRAINING ON REACHING MOVEMENTS IN A PATIENT WITH OPTIC ATAXIA

Keywords:

We report the case of M.B. who demonstrated severe optic ataxia with the right hand following stroke in the left hemisphere. The clinical picture may shed light on both the pathological characteristics of reaching and grasping actions, and potential rehabilitation strategies for optic ataxia. First, M.B. demonstrated a dissociation between severely impaired reaching and relatively spared grasping and tool use skills and knowledge, which confirms that grasping may be more intermingled with non-motoric cognitive mechanisms than reaching. Besides, M.B.'s reaching performance was sensitive to movement repetition. We observed a substitution effect:

Reaching time decreased if M.B. repeatedly reached toward the same object but increased when object identity changed. This may imply that not only object localization but also object identity, is integrated into movement programming in reach-to-grasp tasks. Second, studying M.B.'s spontaneous compensation strategies ascertained that the mere repetition of reaching movements had a positive effect, to the point M.B. almost recovered to normal level after an intensive one-day repetitive training session. This case study seems to provide one of the first examples of optic ataxia rehabilitation. Reaching skills can be trained by repetitive training even two years post-stroke and despite the presence of visuo-imitative apraxia.

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AIMS OF THE PRESENT STUDY

This study reports the case of M.B., a stroke patient who suffered from optic ataxia after unilateral lesions of the left occipitoparietal regions. M.B. demonstrated severely impaired reaching movements with his right hand but relatively spared grasping abilities and normal tool use skills and knowledge. Besides, clinical investigation showed a substitution effect: Changing the identity of the object had an adverse influence on reaching time whereas repeatedly reaching toward the same object improved performance -with object location being fixed. In an attempt to understand this phenomenon and infer potential rehabilitation methods we studied M.B.'s spontaneous compensation strategies and found that performance benefited from mere movement repetition. A few hours of repetitive reaching movements led to sustainable decrease in reaching time. So, this case study provides insight into the pathological characteristics of optic ataxia, and paves the way for future rehabilitations.

THEORETICAL BACKGROUND

Using a tool requires three steps: 1) reaching the tool (e.g., a hammer); 2) grasping the tool;

3) using the tool with an object (e.g., pounding a nail). Each of these steps may call for different motor and/or cognitive mechanisms.

REACHING, GRASPING AND USING COMPONENTS OF ACTION

Reaching

Reaching movements correspond to the hand trajectory toward the tool to be grasped, independently of how the tool is subsequently grasped. They are proximal-to-distal, fast movements with a straight line and a bell shape speed profile [START_REF] Karniel | A model for learning human reaching movements[END_REF]. In normal human activity, reaching movements rely mainly on visuo-motor connections [START_REF] Jeannerod | Mechanisms of visuomotor coordination: A study of normal and braindamaged subjects[END_REF].

They are thought to depend on characteristics of the body (e.g., proprioceptive input; [START_REF] Ghez | Impairments of reaching movements in patients without proprioception. II. Effects of visual information on accuracy[END_REF] rather than of the object (except for its position and orientation relative to the body) in that they connect the body and the object. While reaching movements are most frequently programmed on a top-down basis (i.e., the intention), they are also driven by bottomup real-time corrections [START_REF] Grea | A lesion of the posterior parietal cortex disrupts on-line adjustments during aiming movements[END_REF] seeing that rapid changes in target location modify movement kinematics [START_REF] Pisella | An 'automatic pilot' for the hand in human posterior parietal cortex: Toward reinterpreting optic ataxia[END_REF]. Therefore, reaching is automatically elicited but voluntarily activated. Reaching movements under visual control rely on the activity of the posterior parietal cortex (Rossetti, Pisella, & Vighetto, 2003).

Grasping

Grasping corresponds to the shaping of the hand while taking an object (e.g., a paper clip calls for a precision grip whereas a pencil holder calls for a power grip; e.g., [START_REF] Bongers | Hand apperture patterns in prehension[END_REF][START_REF] Castiello | The neuroscience of grasping[END_REF][START_REF] Jeannerod | Mechanisms of visuomotor coordination: A study of normal and braindamaged subjects[END_REF]. Graspable tools (in comparison with nongraspable tools) automatically attract visual attention (e.g., cup versus cactus; [START_REF] Garrido-Vásquez | Modulation of visual attention by object affordance[END_REF] and elicit activity in the left premotor and parietal cortex [START_REF] Grafton | Premotor cortex activation during observation and naming of familiar tools[END_REF]. That being said, the grasping component is in an intermediate position between reaching and using in that it can be viewed as a high-level perceptual-motor skill [START_REF] Rosenbaum | Cognition, action, and object manipulation[END_REF]. Indeed, grasping may depend not only on structural information (i.e., the shape or size of the object; [START_REF] Ellis | Micro-affordance: The potentiation of components of action by seen objects[END_REF] but also on functional information (i.e., knowledge about the function and the prototypical manipulation of an object; [START_REF] Buxbaum | Neural substrates of knowledge of hand postures for object grasping and functional object use: Evidence from fMRI[END_REF][START_REF] Jax | Deficits in movement planning and intrinsic coordinate control in ideomotor apraxia[END_REF]) and intentional/teleological information (i.e., the action to be done with the object; Osiurak et al., 2008;[START_REF] Rosenbaum | Cognition, action, and object manipulation[END_REF]. Function-based grasping may depend on the left inferior parietal lobe whereas structure-based grasping is associated with the left superior parietal lobe [START_REF] Buxbaum | Cognitive representations of hand posture in ideomotor apraxia[END_REF].

Using

Using a tool with an object corresponds to the final step of tool use actions. While both the reaching and grasping components of action have been observed with similar apparatus in humans and animals [START_REF] Rosenbaum | Cognition, action, and object manipulation[END_REF], tool use is very specific in humans (see Osiurak, Jarry, & Le Gall, 2010). There is still debate as to the underlying cognitive mechanisms [START_REF] Buxbaum | Reply: Apraxia: A gestural or a cognitive disorder?[END_REF]Osiurak & Le Gall, 2014) but it has been suggested that using a tool with an object may depend on planning skills [START_REF] Hartmann | It takes the whole brain to make a cup of coffee: The neuropsychology of naturalistic actions involving technical devices[END_REF], semantic knowledge about tool function and context of use (Osiurak, 2014;[START_REF] Rothi | A cognitive neuropsychological model of limb praxis[END_REF][START_REF] Roy | Common considerations in the study of limb, verbal and oral apraxia[END_REF] and technical reasoning about physical properties of tools and objects (Osiurak et al., 2010(Osiurak et al., , 2011; for a similar view, see [START_REF] Goldenberg | Tool use and mechanical problem solving in apraxia[END_REF]. For instance, if one intends to eat a slice of tomato, technical reasoning indicates him/her that a cutting action and an abrasive tool are needed, semantic knowledge provides information as to where these properties can be found in near spaces (e.g., a knife has these properties and can be found in a kitchen; Osiurak & Badets, 2016) and planning is required to organize the whole action sequence. Planning skills are frequently assessed with the Tower of London test [START_REF] Shallice | Specific impairments of planning[END_REF], in which performance has been associated with bilateral activations in prefrontal cortex and superior parietal cortex (Newman, Carpenter, Varma, & Just, 2003). Technical reasoning can be assessed by novel tool use and has been suggested to depend on the left inferior parietal lobe (Goldenberg, 2009; see also [START_REF] Reynaud | On the neurocognitive origins of human tool use: A critical review of neuroimaging data[END_REF]. Semantic memory can be assessed by picture matching tasks and relies on the activity of the ventral, temporal lobes (e.g., [START_REF] Mummery | A voxel-based morphometry study of semantic dementia: Relationship between temporal lobe atrophy and semantic memory[END_REF].

DIAGNOSIS AND DISSOCIATIONS IN OPTIC ATAXIA

Lesions in the posterior parietal cortex can result in optic ataxia, that is, inaccurate movement trajectories when reaching for visual objects. It is a specific visuo-motor disorder which can be observed despite normal visual and motor functions [START_REF] Perenin | Optic ataxia: A specific disruption in visuomotor mechanisms. I. Different aspects of the deficit for reaching for objects[END_REF]. [START_REF] Rossetti | Optic ataxia revisited: Visually guided action versus immediate visuomotor control[END_REF] reviewed exclusion criteria for the diagnosis of optic ataxia:

(1) the visual field should be spared in the area concerned by the visuomotor deficit; (2) proprioception should be spared so that the deficit is elicited under visual control only; (3) intrinsic motor or cerebellar deficits should be ruled out; (4) deficits in visual space perception may be observed but they should not be sufficient to account for severe misreaching errors.

The differential diagnosis between optic ataxia and apraxia (i.e., the inability to perform voluntary gestures in the absence of sensory or motor deficits; [START_REF] Rothi | A cognitive neuropsychological model of limb praxis[END_REF] is sometimes difficult. Optic ataxia can be unilateral -following left brain damage [START_REF] Revol | Pointing errors in immediate and delayed conditions in unilateral optic ataxia[END_REF][START_REF] Perenin | Optic ataxia: A specific disruption in visuomotor mechanisms. I. Different aspects of the deficit for reaching for objects[END_REF] -and affects the spatial accuracy of reaching and grasping movements performed under visual control, following contralateral lesions in the superior parietal lobule and precuneus (area 7). In contrast, apraxia is generally a bilateral symptom that impairs either tool use or gestures performed without visual control (e.g., imitation of reflexive configurations), and results from lesions in the left inferior parietal lobe and parieto-occipital junction (areas 39 and 40; Goldenberg, 2009).

Several dissociating functions have been described in patients with optic ataxia. The latter is frequently more severe in non-foveal vision [START_REF] Buxbaum | Subtypes of optic ataxia: Reframing the disconnection account[END_REF][START_REF] Garcin | Optic ataxia localized in 2 left homonymous visual hemifields[END_REF][START_REF] Perenin | Optic ataxia: A specific disruption in visuomotor mechanisms. I. Different aspects of the deficit for reaching for objects[END_REF] but both hand and field effects have been documented [START_REF] Perenin | Optic ataxia: A specific disruption in visuomotor mechanisms. I. Different aspects of the deficit for reaching for objects[END_REF][START_REF] Revol | Pointing errors in immediate and delayed conditions in unilateral optic ataxia[END_REF]. Also, optic ataxia has been interpreted as an impairment of real-time automatic adjustments rather than a complete inability to program reaching movements [START_REF] Rossetti | Optic ataxia revisited: Visually guided action versus immediate visuomotor control[END_REF][START_REF] Rossetti | Rise and fall of the two visual systems theory[END_REF]. Classically, patients with optic ataxia also have grasping deficit in that they demonstrate poorly scaled grip aperture, yet grasping can be selectively impaired (Jeannerod, Deceti, & Michel, 1994;[START_REF] Sirigu | A selective impairment of hand posture for object utilization in apraxia[END_REF], suggesting relative independence between the reaching and grasping components of action. Another famous dissociation is the one between impaired immediate and better delayed reaching, while healthy participants demonstrate the reverse pattern, especially in peripheral vision (e.g., [START_REF] Himmelbach | Dorsal and ventral stream interaction: Contributions from optic ataxia[END_REF]Rossetti et al., 2005). On ground of this paradoxical delay effect, Himmelbach et al. (2009) suggested that both immediate and delayed reaching movements may rely on occipitoparietal brain regions.

REHABILITATION OF OPTIC ATAXIA

The literature is sparse on optic ataxia rehabilitation, probably because it is a rare -yet probably overlooked -deficit [START_REF] Jacob | Balint's syndrome: Missed or mistaken?[END_REF]. The objective of a therapy should be the generalization of what has been learned to a variety of contexts, and the rehabilitation method should be to provide compensatory strategies allowing patients to correct their errors [START_REF] Perez | Balint's syndrome arising from bilateral posterior cortical atrophy or infarction: Rehabilitation strategies and their limitation[END_REF].

Previous single case studies suggested that starting 4-to-6 month therapies during the first year post-stroke with either unspecified outpatient rehabilitation [START_REF] Moscote-Salazar | Post-traumatic Balint's syndrome: A case report and review of the literature[END_REF] or learning of compensatory strategies, remediation exercises and activities of daily living [START_REF] Zgaljardic | Balint's syndrome and post-acute brain injury rehabilitation: A case report[END_REF]) may be effective in the treatment of Balint's syndrome (i.e., simultagnosia, ocular apraxia, optic ataxia) -but with no specific effect on reaching movements. However, it is usually accepted that spontaneous recovery mainly occurs during the first year following the stroke, therefore it is difficult to disentangle the relative effects of either spontaneous remission or rehabilitation. [START_REF] Rosselli | Rehabilitation of Balint's syndrome: A single case report[END_REF] started a 12-month rehabilitation program -based on visual tracking, convergence and reading exercises, and activities of daily living -more than a year after the brain embolism. This method led to significant improvement in tasks involving visual scanning, with probably low influence of spontaneous recovery, yet there was no available data regarding the specific effect of rehabilitation on reaching skills. Actually, the specific rehabilitation of reaching movements has received greater attention in patients with hemiparesis, in whom the study of spontaneous compensations has led to effective therapies (e.g., restraining trunk movements if the patient relies on the latter to compensate for upper limb deficits; [START_REF] Thielman | Rehabilitation of reaching after stroke: Comparing 2 training protocols utilizing trunk restraint[END_REF].

As can be seen, much remains to be done in this field. To our knowledge, the effect of mere movement repetition as well as the evolution of spontaneous compensation strategies have not been studied yet in the field of optic ataxia. Nevertheless, the "movement history effect" has been described in healthy adults whereby a prior grasping action reduces the planning time of a subsequent grasping action performed with the same hand (e.g., [START_REF] Valyear | Hand selection for object grasping is influenced by recent motor history[END_REF]. Since this effect is present in healthy adults, it might prove beneficial for patients with optic ataxia. Here, we present the case of a patient with optic ataxia, who spontaneously set up different compensation methods across time and benefited from a single training session consisting of repetitive reaching movements.

CASE REPORT

Figure 1 displays a timeline of the case study. M.B. was a 75 year-old, right-handed pensioner. His medical history included: Type 2 diabetes, high blood pressure, smoking, dyslipidemia, chronic renal failure treated by hemodialysis, and sleep apnea syndrome treated by positive pressure ventilation. In 2001, he sustained a first ischemic stroke which provoked lesions in the left middle cerebral artery territory. At that time, he recovered with little disability (see Figure 1). In 2014, M.B. suddenly became confused but he did not present any obvious language, motor or sensory deficits according to his wife. After three days, he eventually visited the emergency department. Brain imaging revealed large ischemic lesions in the left occipital, temporal and parietal lobes (Brodmann areas 18,19,21,22,37,39,40) but also in the cerebellum, the left caudate nucleus and the right thalamus (Figure 2).

At the 3-month follow-up, M.B. had various neuropsychological sequelae that were consistent with the presence of left parietal lesions, including tool use disorders (Figure 1). He spontaneously described a disabling reaching deficit with his right hand. For example, when he tried to reach and grasp his phone, he had to concentrate a lot to initiate the movement, then his hand wandered twenty centimeters above the phone and/or passed by it. Interestingly, he found a way to compensate this symptom: If he first reached the target with his left hand, then he could reach it with his right hand with considerably less hesitation. This strategy was very effective but also time-consuming, leading him to underutilize his right hand. It was decided to re-assess this phenomenon during long-term follow-up. M.B. returned home and received weekly speech therapy. One year later, he did not complain about tool use disorders anymore but his reaching deficit remained a disabling symptom so we started the following clinical investigation. M.B. gave his informed consent to this study.

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CLINICAL INVESTIGATION

GENERAL TESTING STRATEGY

M.B.'s gestures were investigated in order to answer the following questions: (1) Did the reaching deficit correspond to optic ataxia? (2) Which components of action were at stake among reaching, grasping and using? (3) Did reaching time depend on the target object? (4) Which compensation method was the most effective? (5) Did repetitive testing reduce optic ataxia?

DIAGNOSING OPTIC ATAXIA

Method. The aim of this testing session was to clarify the nature of M.B.'s reaching deficit.

To this end, M.B. was tested under three comparable conditions:

Test 1. Reaching (visual input). M.B. was asked to reach and touch (but not grasp) a wooden cube (3*3*3 cm) with his hand under visual control. Before starting a trial, M.B. was asked to replace his hand palm-down in a central starting position on the desk, about ten centimeters from his trunk.

Test 2. Reaching (proprioceptive input). Proprioceptive pointing may be impaired too in optic ataxia [START_REF] Blangero | Optic ataxia is not only 'optic': Impaired spatial integration of proprioceptive information[END_REF]. In order to disentangle the relative contributions of proprioceptive and visual inputs, M.B. was asked to close his eyes, then to reach the thumb of one of his hands with the other hand. Before starting a trial, the examiner placed M.B.'s target hand in the left, central or right visual field so as to make Test 1 and Test 2 comparable.

Test 3. Pointing (visual input).

The purpose of this test was to ascertain that the reaching deficit was indeed a reaching deficit and could not be accounted for by intrinsic visual disorders (e.g., hemianopia). M.B. was given a laser pointer and asked to point at targets presented in the left, central or right visual field. Targets were located in the reachable, peri-personal space so as to allow comparison with previous tests. The starting position was M.B.'s trunk so as to ensure that he stopped pointing at targets between items.

In each of these three tests, M.B. underwent the same 18 trials in the same order with either his left or his right hand (Table 1). The target was located about thirty centimeters from the starting point in either the left, central or right visual field with a 90-degree angle difference between each position. When targets were in either the left or right visual field, M.B. was urged to gaze at a central fixation cross drawn on the desk (which corresponded to the location of the target cube when it was in the central visual field); if he did not, the item was considered invalid and repeated. M.B. was instructed to either reach (Tests 1 and 2) or point (Test 3) the target at the "go" signal, then to come back to the starting position as quickly as possible and so on until the examiner interrupted the session. The session was filmed and coded afterwards. For each item, the score was the number of back-and-forth movements between the starting position and the target, in no more than 10 seconds from the "go" signal.

Results and conclusion.

Results are displayed in Figure 3. M.B.'s reaching deficit was not caused by somatosensory loss because he performed better in the "proprioceptive" condition than in the "visual" condition. The left hand/right hand difference was overall more important in Test 1 than in other tests, suggesting that the Hand effect was relatively specific to visually-driven reaching movements. Subsequently, the reaching deficit was probably not caused by intrinsic motor deficits because in that case, the Hand effect should have been constant across conditions. M.B. also demonstrated a field effect (i.e., severe misreaching in the right visual field) already documented in patients with optic ataxia (e.g., G.H.; [START_REF] Himmelbach | Dorsal and ventral stream interaction: Contributions from optic ataxia[END_REF]. Although this finding can be explained by right hemianopia in the case of M.B., errors were also frequent in the central visual field. On this ground, it seemed reasonable to conclude that M.B.'s reaching deficit with the right hand was the consequence of optic ataxia, at least in the left and central visual fields.

This conclusion was also consistent with M.B.'s spontaneous complaints about his reaching skills as the latter is not typical of mere hemianopia.

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REACHING, GRASPING AND USING COMPONENTS OF ACTION

Method. This testing session was designed to assess each component of action separately:

Reaching, grasping and using. The latter component was divided into planning skills, semantic memory and technical reasoning which are good predictors of tool use skills in daily life (see Section 2.1).

Test 4. Reach-to-grasp (reaching). M.B. was asked to reach and grasp six different objects presented in his central visual field with his right hand (Table 1). Objects were removed and reinstalled between trials. The starting and ending positions were the same as in previous tests.

Reaching time was measured with a stopwatch as the time taken to reach and touch the object, from a "go" signal to the hand/object contact.

Test 5. Reach-to-grasp (grasping). Tests 4 and 5 were actually one and the same testing session but it was coded twice in different ways based on video recordings. For each item, grip scale aperture was coded when the hand moved within ten centimeters of the object. The grasping component was considered normal and one point was given if grip aperture (i.e., the space between the thumb and the forefinger) fitted the size of the object: A precision grip (i.e., the object is grasped between the thumb, the forefinger and the middle finger) was expected for small objects (i.e., coin, paper clip) and medium objects (i.e., lighter, inhaler), whereas a power grip (i.e., the object is grasped with all the fingers) was expected for larger objects (i.e., pencil holder, large wooden cube; Table 1). Excessive anticipation or grip aperture as well as late corrections were worth 0 point. There were 18 items so the maximum score was 18.

Test 6. Tower of London. This test assessed planning skills and consisted in a modified, shorter version of the classical Tower of London test [START_REF] Jarry | Apraxia of tool use: More evidence for the technical reasoning hypothesis[END_REF]. In each item, M.B. was given 2 minutes to replicate a configuration of three colored beads arranged on three vertical sticks (short, medium, long). He was instructed to move only one bead at a time on the sticks, and to do as few moves as possible but he could use both hands. He had to solve six problems of increasing difficulty (i.e., two to seven moves). Performance was rated on a 3-point scale depending on the number of moves (maximum score = 18).

Test 7. Picture matching. The use of familiar tools calls for semantic knowledge about their function and context of use (Osiurak, 2014;[START_REF] Roy | Common considerations in the study of limb, verbal and oral apraxia[END_REF]. This component was assessed by asking M.B. to select among four pictures the one that matched the picture of a tool. Pictures could be matched on either a functional criterion (e.g., target = match; choice = lighter, pen, coffee maker, colander) or a contextual criterion (e.g., target = match; choice = anniversary, wedding, Christmas day, baptism) depending on items. There were ten items in each condition (plus two corrected, practice items). Each correct answer given within 20 seconds was worth 1 point (maximum score = 20).

Test 8. Mechanical Problem Solving. The final step of tool use actions is the interaction between the tool and the object, which may depend on technical reasoning about mechanical properties of both (Osiurak et al., 2010). Technical reasoning can be assessed using mechanical problem-solving tasks in which patients have to select and use tools for which there is no preexisting usage (e.g., choosing a tool to lever a cylinder; [START_REF] Goldenberg | Tool use and mechanical problem solving in apraxia[END_REF]. Here, M.B. was presented successively with three mechanical problem-solving tasks previously described by [START_REF] Lesourd | Mechanical problem-solving strategies in Alzheimer's disease and semantic dementia[END_REF] and [START_REF] Baumard | Tool use disorders in neurodegenerative diseases. Roles of semantic memory and technical reasoning[END_REF][START_REF] Baumard | Tool use in neurodegenerative diseases: Planning or technical reasoning[END_REF]; Supplementary Figure 1). He was asked to extract a red wooden cube out from a transparent box, using both hands and one or more tools to be selected among eight rods offering different mechanical properties (e.g., long/short, rigid/bendable). The time limit was set to 3 minutes per item and performance was scored on a 3-point scale: (3) The cube is extracted from the box; (2) The first step of the problem is completed; (1) The cube has been reached with a rod but the first step is not completed; (0) The participant does not reach the cube. The maximum total score was 9 (i.e., 3 problems x 3 points).

Results and conclusion.

Reaching movements were very slow and inaccurate whereas grasping was relatively spared (Table 2). In parallel, planning skills, semantic knowledge and technical reasoning were spared. This is consistent with clinical observation that in 2015, M.B. no longer reported tool use disorders. With regard to the distinction between reaching, grasping and using (Section 2.1), M.B.'s core symptom was the inability to initiate and guide fast reaching movements under visual control.

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RELATIONSHIP BETWEEN REACHING TIME AND OBJECT IDENTITY

Method. In order to determine whether characteristics of the object had an influence on reaching skills, performance in Test 4 was recoded with different criteria.

Test 9. Reach-to-grasp. This testing session was the same as Test 4 and Test 5 but it was coded -and named -differently. The sequence of items was important: In some cases, the same object was presented twice in a row whereas in other cases, the object was replaced by a new one of different shape or size. (Table 1). Objects were always presented in the central visual field. The measure was the time taken to reach and touch the object.

Results and conclusion.

As shown in Figure 4, M.B.'s reaching performance improved when he was presented consecutively with the same object but decreased when he was presented with a new one. This was the case even though object size and the expected grip remained unchanged. So, it was concluded that reaching skills were influenced by mere object substitution.

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COMPARISON OF TWO COMPENSATION METHODS

Method. M.B. spontaneously set up compensation methods that evolved between the postacute phase and the long-term follow-up consultation. Three months after the stroke, his method was to first reach objects with the left hand, then with the right hand. Clinically, this method appeared to be efficient. One year later, he did not engage in such behavior anymore. Instead, he grasped his right hand with his left hand so as to correct the movement trajectory of the right hand. From there, he became able to reach objects with his right hand only, but only for a few seconds, after which he had to start compensating again. Based on this clinical observation it was decided to test the effectiveness of the two aforementioned compensation methods.

Test 10. Unimanual compensation. As in Test 1, M.B. was asked to reach and touch a wooden cube which was placed either in the left, central or right visual field. There were six blocks of three items (Table 1). In the first item, M.B. was asked to reach the target only with his right hand. In the second item, he was asked to do the same but with his left hand. The third item was the same as the first one. The position of the target remained identical across the three items. There was no delay between the three items of a series but a pause of ten seconds between each series of items, during which M.B. let his hand rest at the starting position. The measure was the number of backand-forth reaching movements in 10 seconds.

Test 11. Bimanual compensation. This test was very similar to Test 10 except that during item 2, M.B. was asked to use his second compensation method, that is, reaching the target with his right hand while holding the latter with his left hand so as to correct the movement trajectory -of his right hand.

Results and conclusion.

As shown in Figure 5, the bimanual compensation method was more effective than the unimanual compensation method at the time of testing. For all that, none of the methods was more effective than the mere repetition of reaching movements (Test 1).

Likewise, repeating items in Test 4 was very helpful for M.B. (Figure 4). As a consequence, these results are interpreted in terms of repetition effect rather than compensation effect. M.B.'s reaching performance improved only if he successfully reached the target at least once with his right hand before subsequent tries.

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TRAINING EFFECT

Method. We met M.B. on June 13, 2014, then on December 17, 2015. He passed Tests 1 to 11 on January 8, 2016. On this occasion, after about one hour and a half of continuous testing, M.B.'s reaching performance slightly improved. After the lunch break, he spontaneously reported that using his right hand was easier, which became obvious after a few tries. Therefore, it was decided to compare different testing sessions performed with the right hand in the central visual field: (1) Test 1 (i.e., reaching a cube under visual control) had been conducted at 10 AM; (2) Test 4 (i.e., reaching different objects under visual control) had been administered at 11:30 AM; (3) Test 4 was renewed at 6 PM, after various reaching tasks that were not described in this study;

(4) Four new objects (i.e., stopwatch, pencil, glass, jug) were presented once each at 6 PM so as to determine whether improvement was object-dependent; (5) Test 4 was proposed again on June 3, 2016 to verify whether improvement was sustainable. At that time reaching was tested with his left hand too as a point of comparison; (6) On this occasion, we also repeated imitation of meaningless gestures in order to compare the effects of training on optic ataxia and apraxia and, on that basis, determine how specific was the improvement of reaching skills.

Test 12. Imitation of meaningless gestures. M.B. was asked to imitate ten reflexive hand configurations with each hand, "like in a mirror", without delay [START_REF] Goldenberg | Severity of neglect predicts accuracy of imitation in patients with right hemisphere lesions[END_REF]. Performance was scored on a 2-point scale: (2) correct imitation within the time limit (i.e., 10 seconds); (1) approximate imitation in less than 5 seconds or correct imitation in more than 5 seconds; (0) incorrect imitation. Scoring considered only the final position of the hand relative to the body. The maximum score was 20.

Results and conclusion.

Figure 6 shows a training effect for optic ataxia since the reaching performance improved across testing sessions, especially in the afternoon. Tests 1 to 9 were performed in the morning and hence this training effect was presumably low at that time. Besides, this effect was neither object-dependent -since generalization was observed with new objectsnor context-dependent -since the third training session (i.e., at 6 PM) took place in M.B.'s room rather than in the office. Likewise, the spatial location of the target relative to the body did not modify the reaching behavior: As long as M.B. was allowed to gaze at objects, he was able to grasp tools on both the left and the right sides. Actually, while leaving the unit M.B. demonstrated to caregivers how easy it was for him to grasp any object he found. This improvement persisted five months later although M.B. did not receive rehabilitation services during this period. On this occasion the repetition of imitation tasks did not induce a similar improvement, suggesting that repetitive training is efficient in the treatment of optic ataxia but not apraxia.

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GENERAL DISCUSSION

MAIN RESULTS

Optic ataxia was diagnosed in M.B. because he demonstrated severe reaching errors under visual control in both foveal and peripheral vision, which could not be accounted for by hemianopia, proprioceptive loss or intrinsic motor deficit (see criteria in [START_REF] Rossetti | Optic ataxia revisited: Visually guided action versus immediate visuomotor control[END_REF][START_REF] Rossetti | Optic ataxia: Beyond the dorsal stream cliché[END_REF]. Subsequent clinical studies demonstrated (1) a classical dissociation between reaching and grasping; (2) changes in reaching time after mere object substitution; (3) the efficacy of spontaneous compensation methods and mere movement repetition; (4) a clearcut improvement of reaching skills after an intensive one-day repetitive training session. Each of these findings may shed light on both the pathological characteristics of reaching and grasping actions, and potential rehabilitation strategies for optic ataxia.

PATHOLOGICAL CHARACTERISTICS OF OPTIC ATAXIA

Reaching versus grasping

Even though the coding system used to test the grasping component probably lacked sensitivity (i.e., correct/incorrect grasping based on video recordings), the first finding here is the dissociation between severely impaired reaching and relatively spared grasping -which corresponded to M.B.'s complaints. Presumably, M.B.'s grasping was slightly impaired as a secondary consequence of inaccurate reaching movements (Cavina-Pratesi, Ietswaart, Humphreys, Lestou, & Milner, 2010). The reverse dissociation -i.e., impaired grasping but spared reaching -has already been documented (e.g., [START_REF] Binkofski | Human anterior intraparietal area subserves prehension: A combined lesion and functional MRI activation study[END_REF][START_REF] Jeannerod | Impairment of grasping movements following a bilateral posterior lesion[END_REF][START_REF] Sirigu | A selective impairment of hand posture for object utilization in apraxia[END_REF]. This is consistent with neuroimaging data demonstrating that grasping may call for a dorsolateral circuit (i.e., from the anterior intraparietal sulcus to the ventral premotor cortex) whereas reaching may rely on a dorsomedial circuit (i.e., from the parieto-occipital transition zone to the dorsal premotor cortex; [START_REF] Vingerhoets | Contribution of the posterior parietal cortex in reaching, grasping, and using objects and tools[END_REF]. With regard to this functional organization, M.B.'s lesions in the occipito-parietal regions (Figure 2) may explain the relatively isolated reaching deficit.

Beyond dissociations between brain regions, why was grasping better than reaching? One way of answering this question is to look at the parameters that modulate reaching and grasping.

As regards reaching, demands in movement trajectory remain constant as long as the starting position of the hand and the end position of the object are fixed. The subsequent goal of the action once the object has been grasped, has only late influence on timing parameters (i.e., deceleration; [START_REF] Marteniuk | Contraints on human arm movement trajectories[END_REF] and spatial parameters (i.e., endpoint; [START_REF] Ambron | The effect of goals and vision on movements: A case study of optic ataxia and limb apraxia[END_REF]. In contrast, grip selection and scaling is much more dependent on the subsequent task (e.g., grabbing a spoon with full hands to dig in dry land versus holding it with three fingers to eat soup). Neurons in area F5 -which are thought to underlie grasping [START_REF] Himmelbach | Dorsal and ventral stream interaction: Contributions from optic ataxia[END_REF] -discharge in relation with goaldirected actions (Rizzolatti, Fogassi, & Gallese, 2001). From this point of view, grasping may be only the motor product of higher-level cognitive processes [START_REF] Ambron | The effect of goals and vision on movements: A case study of optic ataxia and limb apraxia[END_REF][START_REF] Jeannerod | Mechanisms of visuomotor coordination: A study of normal and braindamaged subjects[END_REF][START_REF] Rosenbaum | Cognition, action, and object manipulation[END_REF] and thus could be considered the "least motoric" of motor behaviors in the sense that the way we grasp tools may emerge on ground of any mechanism providing teleological information (see also [START_REF] Cisek | Cortical mechanisms of action selection: The affordance competition hypothesis[END_REF]. Besides object shape [START_REF] Ellis | Micro-affordance: The potentiation of components of action by seen objects[END_REF], task goal (Osiurak et al., 2008;[START_REF] Randerath | Grasping tools: Effects of task and apraxia[END_REF]) and precision demands [START_REF] Rosenbaum | Cognition, action, and object manipulation[END_REF], technical reasoning and semantic knowledge may also play a role by informing individuals on potential mechanical actions (e.g., a stone shall be grasped with a power grip in order to break a window but with a precision grip in order to write in the sand; Osiurak, 2014) and canonical actions leading to functional grasps (e.g., even an oversized pencil shall be grasped with the first three fingers because it corresponds to the way it is usually grasped, for writing; [START_REF] Buxbaum | Neural substrates of knowledge of hand postures for object grasping and functional object use: Evidence from fMRI[END_REF][START_REF] Jax | Response interference between functional and structural object-related actions is increased in patients with ideomotor apraxia[END_REF]. Overall, the common point between these sources of information is that they provide teleological information about which actions to perform and how, which in return allows grip selection [START_REF] Cisek | Cortical mechanisms of action selection: The affordance competition hypothesis[END_REF]. This "teleological" approach completes the classical dichotomy (see Binkofski & Buxbaum, 2012) between structural graspsbased on objects' structure -and functional grasps -based on object semantics -by extending the range of cognitive mechanisms potentially involved in affordance perception/selection and grasping. In all likelihood, M.B. was able to access teleological information since he performed mechanical problem solving and matching tasks in normal range. Subsequently, grasping was relatively spared. Conversely, it can be assumed that M.B.'s reaching deficit was not the consequence of a teleological deficit (i.e., the inability to identify the end and means of actions).

Future works on optic ataxia may focus on the relationships between reaching, grasping and different sources of teleological information, especially since recent experimental studies of healthy adults emphasized the influence of the abstract intention to use an object (i.e., distal, contextual goals rather than proximal hand-object interactions) on the prior reach-to-grasp action [START_REF] Bub | Switching between lift and use actions[END_REF].

Interpreting the substitution effect

M.B.'s reaching performance improved after two presentations of the same object, but decreased if the second object was different from the first one. So, it can be concluded that object substitution had an impact on the reaching component of action (i.e., the substitution effect). A similar object substitution effect has already been demonstrated on grasping in patient I.G. [START_REF] Milner | Grasping the past: Delay can improve visuomotor performance[END_REF]. Since object location was fixed, the question arises whether this effect was provoked either by object substitution per se or by repetitive reaching toward the same localization in peripersonal space.

Previous works documented the paradoxical delay effect (e.g., [START_REF] Himmelbach | Dorsal and ventral stream interaction: Contributions from optic ataxia[END_REF]: Introducing a delay between the presentation of the stimulus and the initiation of the reaching movement increases the reaching time in healthy subjects but decreases it in patients diagnosed with optic ataxia. In our design, items were necessarily separated by short 3-second delays (i.e., the time for the examiner to remove the object and place the next one), a delay that is sufficient to observe substantial improvement of reaching movements [START_REF] Himmelbach | Dorsal and ventral stream interaction: Contributions from optic ataxia[END_REF]. On this ground, one could assume that the first presentation of the object called for immediate reaching whereas the second presentation additionally elicited delayed reaching based on short-term representation of the spatial location of the target. In a sense, M.B. used a memory-based route to bypass his visuomotor deficit, as did I.G. for grasping [START_REF] Milner | Grasping the past: Delay can improve visuomotor performance[END_REF].

However, this explanation is not sufficient in itself because it is based on the assumption that object location, rather than object identity, is stored and reused in delayed reaching. Since object location was fixed -in the central visual field -the paradoxical delay effect should have led to progressive improvement across trials independently of object identity, yet this was not observed. Interestingly, [START_REF] Rossetti | Optic ataxia revisited: Visually guided action versus immediate visuomotor control[END_REF] suggested that optic ataxia is not due to a general impairment of visuomotor transformations but distinguished between intentional movement programming and real-time automatic adjustments [START_REF] Pisella | An 'automatic pilot' for the hand in human posterior parietal cortex: Toward reinterpreting optic ataxia[END_REF], with only the latter being dependent on the superior parietal lobes. Patients with lesions in the parietal lobes and optic ataxia are able to program movements and reach targets, but they need an unusual amount of time to adapt to target displacement as if they were acting in the past [START_REF] Milner | Grasping the past: Delay can improve visuomotor performance[END_REF]). The reverse pattern (i.e., involuntary object-hand magnetization without intentional programming) has already been documented in patients with anarchic hand syndrome following lesions of the corpus callosum and/or of the medial frontal cortex [START_REF] Della Sala | Right-sided anarchic (alien) hand: A longitudinal study[END_REF]Osiurak & Badets, 2016). Electrical stimulation of premotor areas also induces involuntary yet complex motor behaviors [START_REF] Desmurget | Movement intention after parietal cortex stimulation in humans[END_REF][START_REF] Luria | Higher cortical functions in man[END_REF]. These data fit well with a dissociation between automatic reaching supported by the parietal dorsomedial region [START_REF] Vingerhoets | Contribution of the posterior parietal cortex in reaching, grasping, and using objects and tools[END_REF] and voluntary motor programming supported by premotor regions as well as the inferior parietal region (e.g., [START_REF] Mattingley | Motor role of human inferior parietal lobe revealed in unilateral neglect patients[END_REF].

In this framework, M.B.'s reaching deficit can be understood as a deficit in automatic movement correction, contrasting with spared intentional programming. In support of this hypothesis, M.B. obviously made conscious efforts to reach the targets, suggesting he could not rely on automatic "object-hand magnetization" and hence had to constantly reset intentional movement programming at each target change. In contrast, the reaching time decreased when the identity of the target remained unchanged because it was not necessary to initiate new movement programming. This interpretation may suggest that not only object localization but also object identity, is integrated into movement programming in proximal-to-distal reach-to-grasp tasks.

The specific influence of object identity -already demonstrated on grip selection [START_REF] Dixon | Repetition effects in grasping[END_REF] -is plausible regarding fMRI findings that changes in either object identity or orientation elicit more activation in the temporo-occipital and parieto-occipital cortex, respectively [START_REF] Valyear | A double dissociation between sensitivity to changes in object identity and object orientation in the ventral and dorsal visual streams: A human fMRI study[END_REF]. It is also consistent with previous works demonstrating better grasping skills with familiar than with neutral objects [START_REF] Jeannerod | Impairment of grasping movements following a bilateral posterior lesion[END_REF]) -even though it should be noted that what we call "object identity" here does not necessarily refer to object familiarity or semantics but rather to the mere fact that the object remains the same across items. To sum up, the substitution effect can be reasonably interpreted as a consequence of two combined effects caused by occipito-parietal lesions, i.e., the immediate/delayed dissociation and the voluntary/automatic dissociation.

Alternatively, the repetition/substitution effects observed in M.B. may be well explained by -and actually correspond to -the movement history effect described by [START_REF] Valyear | Hand selection for object grasping is influenced by recent motor history[END_REF].

The latter effect is characterized by a reduction of movement time across successive reach-tograsp actions performed with the same hand. A critical issue in this field is to determine whether this improvement depends on characteristics of either the stimulus or the motor ouput. This issue was addressed by [START_REF] Randerath | Two routes to the same action: An action repetition priming study[END_REF] who observed an effect of both dimensions and hence concluded that "instead of attributing it to single aspects, repetition primingeffects are more likely predominantly induced by the facilitation of action selection through reactivation of stimulus bound action units" (pp. 10). The observation of both a repetition effect and a substitution effect in M.B.'s case fits well with this hypothesis: Presenting the same object twice in a row (i.e., same stimulus) at the same location of peripersonal space (i.e., same reaching movement) may have reinforced abnormally slow stimulus-action binding process whereas presenting different objects broke this bond and forced M.B. to start programming movements de novo. The movement history effect mostly studied in healthy adults seems to be relevant to understanding some clinical manifestations of optic ataxia. Future works may try to disentangle the impact of the abovementioned variables on reaching skills and movement training in patients with optic ataxia.

POTENTIAL IMPLICATIONS FOR OPTIC ATAXIA REHABILITATION

Interpreting the compensation effect

From the post-acute phase of stroke to the last follow-up consultation, M.B. demonstrated great adaptive resources. His first compensation method was to reach objects with his left hand, which improved subsequent reaching with the right hand. The paradoxical delay effect (see Section 5.2.1) may account for this pattern yet another explanation is plausible. Previous studies have found that unilateral brain activation tends to elicit activations in similar controlateral brain regions [START_REF] Belin | Hemispheric specialization versus inter-hemispheric communication[END_REF]. This may explain some cases of allochiria (i.e., erroneous localization of sensitive stimuli in the controlateral, non stimulated side of the body; [START_REF] Lhermitte | L'image de notre corps[END_REF]. So, perhaps visuo-motor connections in the right hemisphere elicited mirror activations in the left hemisphere, hence facilitating partial spontaneous recovery. In broad terms, M.B. may have intuitively set up his own brain stimulation therapy, which has already been found to be effective in post-stroke motor recovery [START_REF] Lindenberg | Bihemispheric brain stimulation facilitates motor recovery in chronic stroke patients[END_REF].

Although this first method appeared to be effective at the three-month follow-up, it was no longer the case at the one-year follow-up. At that time, M.B.'s second compensation method was to hold and guide his right hand with his left hand, which again improved subsequent reaching with the right hand. This evolution may reflect either brain reorganization during the recovery process, M.B.'s trial-and-error strategy toward a more effective compensation method, or both. In fact, the mere repetition of reaching movements pointed to the same results as this second compensation method whereas the first method was no longer efficient (Figure 5). So, the key for subsequent improvement was not delay in itself -as would predict the paradoxical delay effect (section 5.2.2) -but rather the experience of successfully reaching the target. It amounts to considering that in M.B.'s case, both trial-and-error learning (no compensation) and errorless learning (driving his right hand with his left hand) of movement trajectory were efficient. Perhaps M.B. unconsciously preferred the compensation strategy because it was a faster and less effortful way to attain the same result.

If a first successful reaching movement provided additional information useful for subsequent reaching movements, the question arises as to what information was gained across trials. In partial contradiction with the previous paragraph, it is also possible that repetition and compensation led to similar quantitative improvements (Figure 5) but on the basis of different qualitative information. With regard to compensation, a "somesthetic" hypothesis would be that left and right hand contact (when holding the right hand with the left hand) provided enhanced tactile and proprioceptive input, turning the expected visuo-motor reaching movement into a "somesthetic-motor" movement. For instance, both the left and right elbow angles may have helped M.B. recoding the position of his right hand relative to the object. In other words, the reaching movement performed with the right hand under control of the left hemisphere may have been programmed based on somesthetic information processed in the right hemisphere. With regard to mere repetition, another "tactile" hypothesis would be that touching the object just once provided enriched information about its structure that vision could not provide, thus enhancing affordance perception and the subsequent programming of the reaching movement. If this is correct, then touching the object should be more critical than reaching it. Even though the training effect did not allow us to disentangle these hypotheses, we hope this will be of interest to set up future research on optic ataxia assessment and rehabilitation.

Interpreting the training effect

M.B.'s reaching behavior greatly improved after a few hours of training. Before that, optic ataxia had remained a disabling symptom for almost two years post-stroke -whereas tool use disorders had spontaneously recovered in December 2015. Spontaneous recovery generally occurs within three to six months after the injury [START_REF] Kertesz | Aphasia and related disorders[END_REF] while rehabilitation may be efficient even if started more than a year after the acute phase [START_REF] Prigatano | Principles of neuropsychological rehabilitation[END_REF]. Therefore, the evolution from impaired to subnormal reaching performance -on a single day -is interpreted as a consequence of training rather than spontaneous recovery. This finding suggests that significant improvement of reaching skills can be obtained even after the typical period of spontaneous remission.

This finding raises a crucial issue: Which underlying process has been trained? It is unlikely that M.B. learned object locations -as would predict the paradoxical delay effect -because at the end of the day he was able to reach any object toward any location in its peripersonal space and in different contexts (i.e., office, room). The delay effect might explain successive improvements across items but not the generalization of this improvement to other objects and spatial locations.

With regard to the dichotomy between automatic reaching and intentional programming (section 5.2.1), another possibility would be that the repetition of reaching movements reinforced movement programming, thus allowing M.B. to compensate for the loss of automatic reaching mechanisms. Again, this is unlikely because reaching movements were very fast and totally effortless at the end of the day. In the framework of the movement history effect [START_REF] Randerath | Two routes to the same action: An action repetition priming study[END_REF] -according to which both the repetition of the stimulus and that of motor coordinates lead to a decrease in movement time -the training effect may have been induced by the repetition of motor outputs. Indeed, the facilitation of action selection by movement repetition has been explained by the reactivation of stimulus-action units. However, M.B. became able to reach objects for which he had received no training, meaning that he improved with untrained stimuli. This amounts to considering that training was due to the repetition of motor outputs themselves (i.e., the coordinates of reaching movements in the peripersonal space), yet in that case one may wonder why optic ataxia did not recover spontaneously for M.B. had to reach and grasp objects every day. Therefore, the observed decrease in reaching time may rather suggest that automatic visuo-motor conversion mechanisms recovered to subnormal levels. In line with the previously mentioned automatic/intentional dichotomy [START_REF] Pisella | An 'automatic pilot' for the hand in human posterior parietal cortex: Toward reinterpreting optic ataxia[END_REF][START_REF] Rossetti | Optic ataxia revisited: Visually guided action versus immediate visuomotor control[END_REF], it is proposed that objects elicited automatic object-hand magnetization in a more effective way after intensive training sessions. This contrast between controlled, effortful reaching before training and effortless reaching after training suggests that under normal conditions, a balance between intentional programming and automatic reaching allows individuals to reach tools without having to focus on their movement, thereby freeing attentional resources for tool use.

In contrast with optic ataxia, repetitive training had only little impact on visuo-imitative apraxia. Previous studies demonstrated that three training sessions per week with enriched feedback (i.e., verbal facilitations, demonstration of the correct gesture, passive positioning of the hand) did not allow significant improvement in imitation tasks [START_REF] Smania | The rehabilitation of limb apraxia: A study in left-brain-damaged patients[END_REF]. This differential effect of training on optic ataxia and apraxia may reflect the fact that optic ataxia is a deficit in automatic visuo-motor conversion mechanisms [START_REF] Rossetti | Optic ataxia revisited: Visually guided action versus immediate visuomotor control[END_REF] while imitation of meaningless gestures is thought to rely on "higher-level" cognitive mechanisms (e.g., body knowledge, categorical apprehension of body parts; [START_REF] Goldenberg | Imitating gestures and manipulating a manikin. The representation of the human body in ideomotor apraxia[END_REF]Goldenberg, , 2009)). Based on this distinction and M.B.'s results, it is proposed that rehabilitation of apraxia might call for complex compensation strategies -requiring the identification of specific underlying impairments (see [START_REF] Cantagallo | The cognitive rehabilitation of limb apraxia in patients with stroke[END_REF][START_REF] Rossetti | Perspectives in higher-order motor deficit rehabilitation: Which approach for which ecological result[END_REF] -whereas reaching behaviors that we share with animals can be trained through repetitive training in some instances.

CONCLUSION

To conclude, M.B.'s case provides insight into both the pathological characteristics of optic ataxia, and potential rehabilitation methods. As regards the former, integrating literature on optic ataxia (i.e., reaching, grasping) and apraxia (i.e., using) may enrich our understanding of motorlike deficits [START_REF] Ambron | The effect of goals and vision on movements: A case study of optic ataxia and limb apraxia[END_REF]. In this regard, the substitution effect observed in M.B. suggests that object identity is one of the multiple variables that affect the programming of reaching movements: In some patients, repeatedly reaching toward the same object may improve the reaching performance. Studying M.B.'s spontaneous compensation strategies allowed us to ascertain that the mere repetition of reaching movements had a positive effect, to the point M.B.

almost recovered to normal level. M.B.'s case seems to provide one of the first examples of optic ataxia rehabilitation, which is of particular interest in the light of famous patients extensively explored and tested in the laboratory over decades: AT and IG [START_REF] Pisella | An 'automatic pilot' for the hand in human posterior parietal cortex: Toward reinterpreting optic ataxia[END_REF]Rossetti et al. 2005), DF [START_REF] Rossetti | Rise and fall of the two visual systems theory[END_REF], U.S. and G.H. [START_REF] Himmelbach | Dorsal and ventral stream interaction: Contributions from optic ataxia[END_REF]. These findings imply that optic ataxia can be trained by repetitive training even two years post-stroke -and despite the presence of visuo-imitative apraxia. They might also encourage therapists to propose intensive training sessions -throughout an entire day when possible -instead of short treatment sessions several days apart. In terms of strategies, restoring automatic object-hand automatization through repetitive training may be a relevant therapeutic goal in the treatment of optic ataxia.

As a limit, the lack of substantial normative data in the present work makes it difficult to ascertain the normality of some performances -hence within-patient comparisons are more compelling. It can also be mentioned that M.B.'s reaching performance improved toward objects presented in the central visual field, yet reaching in peripheral vision -a classical characteristic of optic ataxia -may still be impaired. So, despite tangible benefits for M.B.'s daily life it cannot be concluded that training cured optic ataxia in itself. Besides, it is unlikely that training leads to such clear-cut improvement in all patients. The absence of severe aphasia or other higher-order cognitive impairments (i.e., technical reasoning, semantic memory, planning) was probably a facilitating factor. It should also be noticed that previous cases of optic ataxia were tested in the first days post-stroke (e.g., patients U.S. and G.H.; [START_REF] Himmelbach | Dorsal and ventral stream interaction: Contributions from optic ataxia[END_REF] whereas M.B. was tested more than a year after his stroke. Aside from intrinsic individual differences in brain and psychological organization, functional inhibition (i.e., diaschisis) in the acute phase, and functional reorganization in long-term follow-up, are likely to result in different clinical presentations and might explain the -atypical -training effect presented here. Newman, S.D., Carpenter, P.A., Varma, S., & Just, M.A. (2003).

FOOTNOTES

There is no footnote in the manuscript. visual fields, respectively). In contrast, the bimanual method appeared quite effective (+1, +3.5 and +0). In all likelihood, hemianopia accounts for the lack of improvement in the right visual field.

Mere repetition (Test 1) was effective too (+2, +3 and +1).

Repetitive reaching in optic ataxia

  Frontal and parietal participation in problem solving in the Tower of London: fMRI and computational modeling of planning and high-level perception. Neuropsychologia, 41(12), 1668-1682. Retrieved from https://www.ncbi.nlm.nih.gov/pubmed/12887991 Osiurak, F. (2014). What neuropsychology tells us about human tool use? The four constraints theory (4CT): mechanics, space, time, and effort. Neuropsychology Review, 24(2), 88-115. doi: 10.1007/s11065-014-9260-y Osiurak, F., Aubin, G., Allain, P., Jarry, C., Etcharry-Bouyx, F., Richard, I., & Le Gall, D. (2008). Different constraints on grip selection in brain-damaged patients. . & Badets, A. (2016). Tool use and affordance: Manipulation-based versus reasoning-based approaches. Psychological Review, 123(5), 534-568. doi: 10.1037/rev0000027 Osiurak, F., Jarry, C., & Le Gall, D. (2010). Grasping the affordances, understanding the reasoning: Toward a dialectical theory of human tool use. Psychological Review, 117(2), 517-540. doi: 10.1037/a0019004 Osiurak, F., Jarry, C., & Le Gall, D. (2011). Re-examining the gesture engram hypothesis. New perspectives on apraxia of tool use. Neuropsychologia, 49,299-312. doi: 10.1016/j.neuropsychologia.2010.12.041 Osiurak, F. & Le Gall, D. (2014). Apraxia: A gestural or a cognitive disorder? Brain, 138(3), e333. doi: 10.1093/brain/awu238

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Optic ataxia; reaching; grasping; rehabilitation; apraxia.

bimanual methods, respectively). Test 12 assessed visuo-imitative apraxia. VF: Visual field.

ACKNOWLEDGMENTS / FUNDING

This work was supported by grants from ANR (Agence Nationale pour la Recherche; Project Démences et Utilisation d'Outils/Dementia and Tool Use, N°ANR 2011 MALZ 006 03; D. Le Gall, F. Osiurak), and was performed within the framework of the LABEX CORTEX (ANR-11-LABX-0042; F. Osiurak) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007; F. Osiurak,) operated by the French National Research Agency (ANR).

DISCLOSURE STATEMENT

SUPPLEMENTARY FIGURE 1. MATERIALS FOR THE MECHANICAL PROBLEM SOLVING TASK 974

The rods (a) were as follows: For each box, the position of the target was clearly shown to participants and they were invited to examine carefully each side of the box. They were allowed to move and turn the boxes but not to tilt or lift them. As for other tests, they could use one or both hands. The test included one practice item: the participant was presented with a batten (23x3x3 cm) and a specific box (not to be used in experimental items) consisting of a transparent tunnel open at both ends (20x7x7 cm) and containing a red wooden bead. The participant was asked to extract the bead using the batten, which was possible by simply inserting the latter in the box and pushing the bead. In this item only, the examiner was allowed to demonstrate the solution for the participant to identify targets and to understand the purpose of the test.

Each box could be solved in two steps (a step was defined as a significant modification of the whole technical device that pointed towards the solution). For experimental box 1 (b), the solution was to insert a long rod into the "chimney" and to push the cube to bring it down (first stage). The second stage required pulling the cube out of the box. For box 2 (c), participants had to remove the lid by hand, then to create a hook with a flexible rod and

Repetitive reaching in optic ataxia to lift the target so as to disunite it from the bottom of the box (first stage). The second step was reached when the target was completely extracted from the box, which required the hook to be well shaped to avoid dropping the target. For box 3 (d), it was necessary to insert a rigid rod into the round hole and to use it as a lever to lift the mobile compartment contained inside the box. Then the bead rolled onto the entrance of the box (first step) and participants could retrieve it with a rod (second step).

For each box, two rods were critical to solve the problem (i.e., Box 1: A, C; Box 2: E, G; Box 3: A, C) but some other rods could be relevant depending on the status of the problem (i.e., Box 1: A, C, E, G; Box 2: only rods E and H were relevant; Box 3: A, C, E, G). None of the small rods were useful per se, however every rod could be actually relevant if combined with another rod.

975


Caroline Andriantsiferana

Marie-Hélène Manero

Edith Fardet-Lemaire

Henri Delmas

Anne-Marie Wilhelm

Adsorption of aqueous organic mixtures on activated carbon: experiments and modelling of competitive adsorption

come

ADSORPTION OF AQUEOUS ORGANIC MIXTURES ON ACTIVATED CARBON : EXPERIMENTS AND MODELLING OF COMPETITIVE ADSORPTION

An integrated process (AD-OX) has been developed for the treatment of waste water containing refractory or toxic organic compounds. This process couples adsorption and catalytic oxidation in the same apparatus and on the same material: activated carbon. The porous solid plays successively the role of adsorbent under ambient conditions then that of catalyst under air at higher pressure and temperature. The first step of adsorption of phenols and derivatives is presented in this work, including both experimental results and calculation model. The experimental study is carried out in batch reactor to obtain the kinetics of adsorption and the adsorption isotherms. The theoretical approach is based on the ideal model called "Ideal Adsorption Solution Theory" to obtain theoretical adsorption isotherms. Two binary mixtures were chosen to investigate the behaviour of the adsorbent in competitive adsorption : a mixture of para-hydroxy benzoic acid and dimethyl phenol (PBHA/2,4DMP) and a mixture of para-hydroxy benzoic acid and phenol (PBHA/Phenol). For each binary mixture, different molar proportions were used: equimolar (50%-50%) and unbalanced proportions (30%-70% and 70%-30%). Activated carbon was supplied by Merck. The solutions were analysed by HPLC.

Experimental dynamic adsorption of pure compounds was performed to compare the adsorption kinetics of the two compounds of the binary mixtures. The kinetics of adsorption of each component out of a binary mixture were similar to those observed for each pure compound.

Experimental adsorption isotherms showed that, for the molecule having the best affinity with active carbon, adsorption in competitive mode is roughly as efficient as in non-competitive mode. For a given mixture, according to the proportion of each component, an inversion in the behaviour of the system was found. The preferential adsorption could be inverted if the proportion of the two compounds was reversed. This behaviour was better observed for lower values of the equilibrium concentrations than for high concentrations.

Partial isotherms for competitive mode predicted by IAST model were in good agreement with the experimental results for equimolar mixtures. For non equimolar mixtures the thermodynamic model was in good agreement with the partial isotherms provided that selectivity does not change. Indeed, in the case of inversion of selectivity the IAST model was not able to predict this change. In these cases, the IAST model presents some limits: the mixture is no longer ideal; the RAST model (Real Adsorption Solution Theory) would be more convenient to predict interactions between the compounds.