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

Mathieu Lesourd

Chrystelle Remigereau

Laetitia Laurent

Christophe Jarry

Frédérique Etcharry-Bouyx

Valérie Chauviré

François Osiurak

Didier Le Gall

Midline Crossing

Emile Blondel

Imitation in neurodegenerative diseases 1 MEANINGLESS IMITATION IN NEURODEGENERATIVE DISEASES: EFFECTS OF BODY PART, BIMANUAL IMITATION, ASYMMETRY, AND

Keywords: bimanual imitation, asymmetry, and body midline crossing 1; Tables: 6 Alzheimer's disease, dementia, imitation, apraxia, laterality

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GOALS OF THE PRESENT STUDY

Limb apraxia is the inability to perform intentional motor actions following brain lesions, in the absence of elementary motor disorders, sensory loss, lack of coordination, incomprehension of or inattention to commands [START_REF] Geschwind | The apraxias. Neural mechanisms of disorders of learned movement[END_REF][START_REF] Rothi | A Cognitive Neuropsychological Model of Limb Praxis[END_REF][START_REF] Rothi | A cognitive neuropsychological model of limb praxis and apraxia[END_REF][START_REF] Signoret | Les apraxies gestuelles. Rapport au 127e congrès de psychiatrie et de neurologie de langue française[END_REF]. Limb apraxia covers a wide range of impairments [START_REF] Butler | How comparable are tests of apraxia?[END_REF][START_REF] Buxbaum | IDEATIONAL APRAXIA AND NATURALISTIC ACTION[END_REF][START_REF] Buxbaum | The Role of Semantic Memory in Object Use[END_REF][START_REF] Negri | What is the role of motor simulation in action and object recognition? Evidence from apraxia[END_REF][START_REF] Schwartz | The Quantitative Description of Action Disorganisation after Brain Damage : A Case Study[END_REF][START_REF] Schwartz | Analysis of a disorder of everyday action[END_REF][START_REF] Wheaton | Ideomotor apraxia : A review[END_REF] including visuo-imitative apraxia [START_REF] Mehler | Visuo-imitative apraxia[END_REF], characterized by defective imitation of meaningless gestures [START_REF] De Renzi | Imitating Gestures : A Quantitative Approach to Ideomotor Apraxia[END_REF]. A diversity of error types has been documented to characterize visuo-imitative apraxia (e.g., wrong distance to the body; body side errors; finger selection errors; [START_REF] Bekkering | Goal-directed imitation in patients with Ideomotor Apraxia[END_REF][START_REF] Goldenberg | The meaning of meaningless gestures : A study of visuo-imitative apraxia[END_REF][START_REF] Goldenberg | The Neural Basis of Imitation is Body Part Specific[END_REF][START_REF] Goldenberg | Hemisphere asymmetries for imitation of novel gestures[END_REF][START_REF] Goldenberg | Matching and imitation of hand and finger postures in patients with damage in the left or right hemispheres[END_REF][START_REF] Goldenberg | Apraxia and the parietal lobes[END_REF]. Rothi et al's influential model of apraxia, and its further development, has proposed two routes for imitation: An indirect, semantic route to imitate meaningful gestures (e.g., military salute), and a direct, non-semantic route to imitate meaningful but also meaningless gestures (e.g., thumb on the ear; [START_REF] Achilles | Effect of meaning on apraxic finger imitation deficits[END_REF][START_REF] Rothi | A Cognitive Neuropsychological Model of Limb Praxis[END_REF][START_REF] Rumiati | Common and Differential Neural Mechanisms Supporting Imitation of Meaningful and Meaningless Actions[END_REF][START_REF] Rumiati | Neuropsychological perspectives on the mechanisms of imitation[END_REF][START_REF] Rumiati | Neuropsychological perspectives on the mechanisms of imitation[END_REF][START_REF] Tessari | Neuropsychological evidence for a strategic control of multiple routes in imitation[END_REF][START_REF] Tessari | The Strategic Control of Multiple Routes in Imitation of Actions[END_REF]; see also [START_REF] Bernardis | Behavioural and neurophysiological evidence of semantic interaction between iconic gestures and words[END_REF][START_REF] Ishibashi | The neural network for tool-related cognition : An activation likelihood estimation meta-analysis of 70 neuroimaging contrasts[END_REF]. Clinical double dissociations have confirmed that meaningful and meaningless imitation tap different processes [START_REF] Bartolo | Double Dissociation between Meaningful and Meaningless Gesture Reproduction in Apraxia[END_REF][START_REF] Tessari | Neuropsychological evidence for a strategic control of multiple routes in imitation[END_REF]; see also [START_REF] Mengotti | Selective imitation impairments differentially interact with language processing[END_REF]. They also depend on different brain regions. Disrupted imitation of intransitive (not tool-related) meaningful gestures has been associated with lesions of the anterior temporal and left inferior frontal lobes; [START_REF] Dressing | Distinct Contributions of Dorsal and Ventral Streams to Imitation of Tool-Use and Communicative Gestures[END_REF][START_REF] Weiss | Where language meets meaningful action : A combined behavior and lesion analysis of aphasia and apraxia[END_REF]; but see also [START_REF] Buxbaum | Critical brain regions for tool-related and imitative actions : A componential analysis[END_REF][START_REF] Lesourd | Cerebral correlates of imitation of intransitive gestures : An integrative review of neuroimaging data and brain lesion studies[END_REF], while defective imitation of meaningless gestures has been associated with lesions of the temporo-parietal junction, posterior intraparietal sulcus, superior parietal lobule, and premotor areas; [START_REF] Achilles | Neural correlates of differential finger gesture imitation deficits in left hemisphere stroke[END_REF][START_REF] Binkofski | Two action systems in the human brain[END_REF][START_REF] Goldenberg | The neural basis of tool use[END_REF][START_REF] Goldenberg | Apraxia and the parietal lobes[END_REF][START_REF] Goldenberg | Facets of Pantomime[END_REF][START_REF] Hoeren | Neural bases of imitation and pantomime in acute stroke patients : Distinct streams for praxis[END_REF] see also [START_REF] Rumiati | Common and Differential Neural Mechanisms Supporting Imitation of Meaningful and Meaningless Actions[END_REF][START_REF] Bekkering | Goal-directed imitation in patients with Ideomotor Apraxia[END_REF]. The present study focused on the imitation of meaningless gestures only.

Test of the ability of patients to imitate meaningless actions have recently proven sensitive to dementia [START_REF] Dobigny-Roman | Ideomotor apraxia test : A new test of imitation of gestures for elderly people[END_REF][START_REF] Lesourd | Apraxia and Alzheimer's Disease : Review and Perspectives[END_REF][START_REF] Li | The Gesture Imitation in Alzheimer's Disease Dementia and Amnestic Mild Cognitive Impairment[END_REF][START_REF] Nagahama | Impaired imitation of gestures in mild dementia : Comparison of dementia with Lewy bodies, Alzheimer's disease and vascular dementia[END_REF][START_REF] Ozkan | Apraxia for differentiating Alzheimer's disease from subcortical vascular dementia and mild cognitive impairment[END_REF][START_REF] Sanin | Bimanual Gesture Imitation in Alzheimer's Disease[END_REF][START_REF] Souza | The interlocking finger test in patients with Parkinson's disease and healthy subjects[END_REF][START_REF] Yamaguchi | Yamaguchi Fox-Pigeon Imitation Test : A Rapid Test for Dementia[END_REF].

Previous studies have stressed that dementia may be associated with marked difficulties in the imitation of bimanual gestures, as compared to unimanual gestures (e.g., [START_REF] Lesourd | Apraxia and Alzheimer's Disease : Review and Perspectives[END_REF][START_REF] Sanin | Bimanual Gesture Imitation in Alzheimer's Disease[END_REF][START_REF] Yamaguchi | Yamaguchi Fox-Pigeon Imitation Test : A Rapid Test for Dementia[END_REF]. Nevertheless, there have been substantial methodological discrepancies among studies. On the one hand, little is known about how different neurodegenerative diseases, associated with different patterns of cortical atrophy, may affect imitation. On the other hand, there have been slight yet potentially critical differences between the gestures used until now (i.e., hand Vs. finger postures; Uni-Vs. bimanual postures; Asymmetrical Vs. symmetrical postures; Crossed Vs. uncrossed postures). The influence of these dimensions on imitation has not been systematically addressed, which may have led to misleading conclusions on the imitation skills of patients with dementia. As a result, when a patient fails the meaningless imitation test, it is usually not possible to infer which dimension of the test was at the source of the failure. In addition, there is still debate as to the nature of the direct route for imitation. Multiple, sometimes competing hypotheses have been put forward to explain visuo-imitative apraxia (see discussion below). Therefore, our goal was to study specific imitation deficits in groups of patients who have been selected and assigned to a group solely based on clinical criteria. This study aimed at determining which dimensions of meaningless imitation are at the origin of visuo-imitative apraxia (i.e., finger/hand, uni-/bimanual, asymmetrical/symmetrical, crossed/uncrossed postures), in patients with cortical atrophy of temporal lobes (i.e., semantic dementia), frontalparietal lobes (i.e., corticobasal syndrome, posterior cortical atrophy), or both (i.e., Alzheimer's disease). Our secondary goal was to infer the cognitive correlates of meaningless imitation impairments in this population, in the light of the hypotheses available in the apraxia literature.

THEORETICAL BACKGROUND

LIMB APRAXIA IN NEURODEGENERATIVE DISEASES

Limb apraxia is a frequent condition in neurodegenerative diseases (e.g., [START_REF] Buchmann | Limb apraxia profiles in different clinical samples[END_REF], like posterior cortical atrophy (PCA; [START_REF] Benson | Posterior cortical atrophy[END_REF][START_REF] Crutch | Consensus classification of posterior cortical atrophy[END_REF] and corticobasal syndrome (CBS; [START_REF] Armstrong | Criteria for the diagnosis of corticobasal degeneration[END_REF][START_REF] Litvan | Accuracy of the Clinical Diagnosis of Corticobasal Degeneration : A Clinicopathologic Study[END_REF]. The emergence of non-amnestic cognitive phenotypes of Alzheimer's disease (AD) in recent criteria [START_REF] Mckhann | The diagnosis of dementia due to Alzheimer's disease : Recommendations from the National Institute on Aging-Alzheimer's Association workgroups on diagnostic guidelines for Alzheimer's disease[END_REF] has raised the importance of a thorough examination of higher-order motor symptoms in neurodegenerative diseases. Literature on this topic is, however, sparse in comparison with other cognitive domains [START_REF] Lesourd | Apraxia and Alzheimer's Disease : Review and Perspectives[END_REF]. Posterior cortical atrophy is clinically characterized by a progressive decline of visual-spatial skills, sometimes associated with limb apraxia but contrasting with the relative preservation of memory [START_REF] Benson | Posterior cortical atrophy[END_REF][START_REF] Crutch | Posterior cortical atrophy[END_REF][START_REF] Crutch | Shining a light on posterior cortical atrophy[END_REF]McMonagle et al., 2006). Whereas episodic memory impairments dominate the clinical picture in "typical" AD, PCA patients with AD pathology fail neuropsychological tasks that test functions that depend on fronto-parietal areas. Corticobasal degeneration is an atypical parkinsonian syndrome that is characterized by extrapyramidal (e.g., limb rigidity, bradykinesia, abnormal gait, postural instability, falls, tremor) as well as higher cortical signs typically associated with lesions of frontal and parietal networks, like limb apraxia [START_REF] Armstrong | Criteria for the diagnosis of corticobasal degeneration[END_REF]) executive dysfunction (Pillon et al., 1995), or visual-spatial impairments (Possin, 2010). Limb-kinetic apraxia is a form of apraxia affecting finger dexterity, which may differentially hamper finger imitation; Denes et al., 1998;Gross & Grossman, 2008;[START_REF] Leiguarda | Limb-kinetic apraxia in corticobasal degeneration : Clinical and kinematic features: Limb-Kinetic Apraxia[END_REF][START_REF] M293 Luria | Les fonctions corticales supérieures de l'homme[END_REF]. So, PCA and CBS have been associated with both lesions of parietal lobes and limb apraxia. In contrast, visuo-imitative apraxia is generally not observed in patients with semantic dementia (SD; [START_REF] Neary | Frontotemporal lobar degeneration[END_REF]; see also "semantic variant of primary progressive aphasia", [START_REF] Gorno-Tempini | Classification of primary progressive aphasia and its variants[END_REF]. The latter typically have bilateral anterior temporal lobe lesions resulting in marked impairments of semantic memory (e.g., loss of word or object meaning and comprehension, impaired naming, surface dyslexia or dysgraphia, semantic paraphasias, associative agnosia, prosopagnosia), contrasting with relative sparing of linguistic abilities and episodic memory; [START_REF] Gorno-Tempini | Classification of primary progressive aphasia and its variants[END_REF][START_REF] Neary | Frontotemporal lobar degeneration[END_REF][START_REF] Snowden | Semantic dementia and the left and right temporal lobes[END_REF]; see also [START_REF] Blundo | Category-specific knowledge deficit for animals in a patient with herpes simplex encephalitis[END_REF].

Given the clinical characteristics of the abovementioned groupings of patients (Felician et al., 2003;[START_REF] Seeley | Neurodegenerative Diseases Target Large-Scale Human Brain Networks[END_REF], we combined the patients with either posterior cortical atrophy, or corticobasal syndrome, into a Frontal-Parietal Network (FPN) group. Those individuals were expected to demonstrate imitation deficits. In contrast, patients with semantic dementia were expected to perform in normal range assuming that parietal and frontal brain regions and functions are spared in most patients [START_REF] Hodges | PROGRESSIVE FLUENT APHASIA WITH TEMPORAL LOBE A TROPHY[END_REF][START_REF] Kramer | Distinctive Neuropsychological Patterns in Frontotemporal Dementia, Semantic Dementia[END_REF]. The performance of patients with Alzheimer's disease was expected to be in an intermediate position between the two abovementioned groups, for these patients generally have temporal lobe lesions with or without marked parietal lobe lesions depending on cases [START_REF] Braak | Neuropathological stageing of Alzheimer-related changes[END_REF], 1997;[START_REF] Seeley | Neurodegenerative Diseases Target Large-Scale Human Brain Networks[END_REF]. So, as a group, they were expected to show less severe imitation impairments than patients with CBS or PCA.

THE MOTOR AND COGNITIVE BASES OF MEANINGLESS IMITATION

Previous studies have documented at least four dissociable aspects of meaningless imitation that might reveal different underlying motor-cognitive impairments. Table 1 summarizes the core hypotheses that may account for these effects, as well as the related predictions.

The body part effect

The body part effect corresponds to behavioral dissociations between finger and hand postures [START_REF] Goldenberg | The Neural Basis of Imitation is Body Part Specific[END_REF][START_REF] Goldenberg | Hemisphere asymmetries for imitation of novel gestures[END_REF][START_REF] Goldenberg | Matching and imitation of hand and finger postures in patients with damage in the left or right hemispheres[END_REF][START_REF] Goldenberg | Matching and imitation of hand and finger postures in patients with damage in the left or right hemispheres[END_REF]Goldenberg et al., 2009; see also [START_REF] Rumiati | Common and Differential Neural Mechanisms Supporting Imitation of Meaningful and Meaningless Actions[END_REF][START_REF] Tessari | Neuropsychological evidence for a strategic control of multiple routes in imitation[END_REF]. Fingers and hands are part of body representations, and are represented by both differences between body structures (e.g., the nose differs from the chin, the index finger differs from the little finger), and differences in their relative localization (e.g., nose over the chin, index finger of the right hand to the left of the little finger). Yet, clinical studies have suggested that finger and hand imitation may put different loads on cognitive functions. Goldenberg and colleagues have provided three empirical arguments for this dissociation. First, there are clinical dissociations between hand and finger postures in patients with stroke [START_REF] Goldenberg | Matching and imitation of hand and finger postures in patients with damage in the left or right hemispheres[END_REF][START_REF] Goldenberg | Hemisphere asymmetries for imitation of novel gestures[END_REF]. Second, patients with imitation impairments may also fail to reproduce configurations on a manikin, suggesting an involvement of body representations in the coding of body parts in both the first and third person perspective [START_REF] Goldenberg | Matching and imitation of hand and finger postures in patients with damage in the left or right hemispheres[END_REF]. Third, there is a positive association between impaired imitation of finger configurations, and impaired visualspatial skills (Goldenberg et al., 2009). So, even though both fingers and hands are represented in the body map, imitating finger or hand configurations may put different loads on different cognitive processes, as explained by Goldenberg (2001): "Hand postures are determined by relationships between a considerable number of different body parts, like lips, nose, ear, chin, cheek, back of hand, or palm of hand. Knowledge about the classification and boundaries of all of these parts is needed for coding of hand postures. In contrast, finger postures concern only a uniform set of five body parts, and the conceptual distinction between them is largely exhausted by an appreciation of their serial position. Body-part coding of hand postures may therefore […] demand more knowledge about the structure of the human body than coding of finger postures. […] Fingers are perceptually similar, and their identity is mainly determined by their spatial position with respect to other fingers. A distinction between, for example, the middle and the ring finger is likely to put higher demands on visuospatial exploration than a distinction between the edge and the palm of the hand or between the cheek and the forehead.

Thus, perceptual analysis is probably more difficult for finger than for hand postures" (Goldenberg, 2001, p. S134).

In this framework, imitation of hand postures directed toward the body, performed without visual control, relies on the perceptual discrimination of body parts (e.g., chin, lips, nose, ears) and hence may call for body representations (i.e., the body representation hypothesis; [START_REF] Goldenberg | Matching and imitation of hand and finger postures in patients with damage in the left or right hemispheres[END_REF]. Body representations encompass both body image (i.e., general knowledge about the structure of the body; [START_REF] Goldenberg | Matching and imitation of hand and finger postures in patients with damage in the left or right hemispheres[END_REF] and body schema (i.e., the tridimensional representation of the body personal and peripersonal space during action; [START_REF] Buxbaum | Ideomotor apraxia : A call to action[END_REF][START_REF] Schwoebel | Evidence for Multiple, Distinct Representations of the Human Body[END_REF][START_REF] Sirigu | MULTIPLE REPRESENTATIONS CONTRIBUTE TO BODY KNOWLEDGE PROCESSING : EVIDENCE FROM A CASE OF AUTOTOPAGNOSIA[END_REF]. According to the body representation hypothesis [START_REF] Goldenberg | Matching and imitation of hand and finger postures in patients with damage in the left or right hemispheres[END_REF][START_REF] Schwoebel | Representations of the human body in the production and imitation of complex movements[END_REF][START_REF] Schwoebel | Evidence for Multiple, Distinct Representations of the Human Body[END_REF][START_REF] Sirigu | MULTIPLE REPRESENTATIONS CONTRIBUTE TO BODY KNOWLEDGE PROCESSING : EVIDENCE FROM A CASE OF AUTOTOPAGNOSIA[END_REF], marked difficulties to imitate hand, but not finger postures, may reveal disorganization of body representations.

In contrast, imitation of finger configurations may put higher demands on visual-spatial and executive control due to the visual similarity of fingers, suggesting that finger imitation is similar to classical visuoconstructive tests (i.e., the visuo-constructive hypothesis; Goldenberg, 2001;[START_REF] Lesourd | Apraxia and Alzheimer's Disease : Review and Perspectives[END_REF]. In line with this proposal, finger imitation is particularly impaired in patients with right parietal lobe lesions causing visual-spatial impairments and neglect [START_REF] Goldenberg | Hemisphere asymmetries for imitation of novel gestures[END_REF][START_REF] Goldenberg | Matching and imitation of hand and finger postures in patients with damage in the left or right hemispheres[END_REF]. According to the visuo-constructive hypothesis, marked difficulties to imitate finger but not hand postures should be observed and may reveal either visual-spatial or executive dysfunction (or both). If the visuo-constructive hypothesis is correct, the imitation performance should also be a function of the number and spatial complexity of visual elements. It is expected that bimanual and asymmetrical postures are more difficult to imitate than unimanual and symmetrical postures. We further assume that visual-spatial processing contributes to imitation, especially of bimanual and asymmetrical postures. Subsequently, bimanual and asymmetrical postures were expected to be more difficult to imitate than unimanual and symmetrical postures, respectively. Finally, positive correlations were expected between classical visual-spatial and executive tests on the one hand, and imitation of finger, bimanual and/or asymmetrical postures on the other hand.

The bimanual effect

In dementia studies, emphasis has been placed on bimanual imitation. The bimanual effect manifests itself in the higher difficulty of bimanual postures as compared with unimanual postures, documented in Alzheimer's disease, mild cognitive impairments, or dementia with Lewy bodies [START_REF] Lesourd | Apraxia and Alzheimer's Disease : Review and Perspectives[END_REF][START_REF] Li | The Gesture Imitation in Alzheimer's Disease Dementia and Amnestic Mild Cognitive Impairment[END_REF][START_REF] Nagahama | Impaired imitation of gestures in mild dementia : Comparison of dementia with Lewy bodies, Alzheimer's disease and vascular dementia[END_REF][START_REF] Sanin | Bimanual Gesture Imitation in Alzheimer's Disease[END_REF][START_REF] Yamaguchi | Yamaguchi Fox-Pigeon Imitation Test : A Rapid Test for Dementia[END_REF]. This pattern has resulted in the creation of a new "bimanual apraxia" category [START_REF] Sanin | Bimanual Gesture Imitation in Alzheimer's Disease[END_REF] characterized by combined motor, spatial, and executive impairments of bimanual gesture imitation in patients with Alzheimer's disease.

Whether bimanual apraxia is specific to Alzheimer's disease, or can also be observed in focal cortical atrophy syndromes, remains an open question. More importantly, it is not known whether bimanual apraxia arises from bimanual activity per se, because there has not been systematic comparison of uni-and bimanual imitation skills, controlling for other dimensions of the test (i.e., body part, asymmetry, or midline-crossing). For example, most studies on bimanual imitation have used either finger configurations only, or mixed lists of hand and finger items. The heterogeneity of evaluation methods may explain why there is still controversy as to whether patients with dementia do have early bimanual imitation impairments [START_REF] Li | The Gesture Imitation in Alzheimer's Disease Dementia and Amnestic Mild Cognitive Impairment[END_REF][START_REF] Sanin | Bimanual Gesture Imitation in Alzheimer's Disease[END_REF][START_REF] Yamaguchi | Yamaguchi Fox-Pigeon Imitation Test : A Rapid Test for Dementia[END_REF]. Thus, one of the goals of the study was to verify the prevalence of bimanual apraxia (i.e., "unimanual > bimanual" dissociations) while controlling for other dimensions of the test.

The asymmetry effect

The asymmetry effect corresponds to the increased difficulty of asymmetrical gestures, in comparison with symmetrical ones [START_REF] Ajuriaguerra | Quelques aspects de la désintégration des praxies idéomotrices dans les démences de grand âge[END_REF][START_REF] Huhn | Symmetries in action : On the interactive nature of planning constraints for bimanual object manipulation[END_REF][START_REF] Kelso | On the coordination of two-handed movements[END_REF]. Some early studies have reported it in patients with Alzheimer's disease [START_REF] Ajuriaguerra | A propos de quelques problèmes posés par l'apraxie dans les démences[END_REF][START_REF] Ajuriaguerra | Quelques aspects de la désintégration des praxies idéomotrices dans les démences de grand âge[END_REF], but there are no data on other syndromes. Asymmetrical gestures can be defined as gestures for which motor patterns (e.g., the selected fingers) or goals (e.g., the hand-body contact point) are not the same for each hand. Humans have a natural preference for functional (goal) and timing symmetry during bimanual tasks [START_REF] Huhn | Symmetries in action : On the interactive nature of planning constraints for bimanual object manipulation[END_REF][START_REF] Kelso | On the coordination of two-handed movements[END_REF] while the spatial parameters and motor innervation patterns of each upper limb may vary. This has suggested that large groups of muscles act as functional units (thus simplifying movement control), reflecting the existence of a bilateral motor control system [START_REF] Brinkman | CEREBRAL CONTROL OF CONTRALATERAL AND IPSILATERAL ARM, HAND AND FINGER MOVEMENTS IN THE SPLIT-BRAIN RHESUS MONKEY[END_REF][START_REF] Kinsbourne | The corpus callosum equilibrates the cerebral hemispheres[END_REF]. Healthy adults, however, are able to break bimanual synergies -an ability needed to play a musical instrument or drive a car -through initiation strategies (i.e., delaying limb activations) or inhibitory neural networks [START_REF] Baumard | Imitation of meaningless gestures in normal aging[END_REF][START_REF] Swinnen | Control of asymmetrical bimanual movements[END_REF]; see also [START_REF] Wallon | Espace postural et espace environnant (le schéma corporel)[END_REF]. This in turn suggests that difficulties in desynchronizing hand movements to imitate asymmetrical configurations may reveal abnormal motor cognition.

Performing asymmetrical gestures requires selection and organization of the parameters governing the action across both effectors. According to the goal-directed theory of imitation [START_REF] Bekkering | Imitation of Gestures in Children is Goal-directed[END_REF][START_REF] Bekkering | Goal-directed imitation in patients with Ideomotor Apraxia[END_REF][START_REF] Gleissner | Children's coding of human action : Cognitive factors influencing imitaation in 3-year-old[END_REF], imitation results from the combination of elementary action patterns (subgoals) into more general action patterns (goals), with hierarchically organized goal structure dissociating means and ends (e.g., one must identify the end goal "reaching the ear" before identifying the subgoal "reaching the left ear", and the mean "with the left hand"). Left hemisphere lesions have been proposed to affect the ability to bind and maintain goals into such a hierarchical structure, resulting in simplifications of the model [START_REF] Bekkering | Goal-directed imitation in patients with Ideomotor Apraxia[END_REF]. This theory suggests that the activity of each hand is bound into one and the same general goal during bimanual imitation of symmetrical gestures (e.g., both hands target the ears), while it cannot be the case regarding asymmetrical gestures (e.g., one hand targets the ear while the other one targets the neck). In this framework, impaired imitation of asymmetrical gestures (i.e., different goals for each hand) but not of symmetrical gestures (i.e., similar goals) may be interpreted as a disruption of the hierarchical goal structure. In this view, one should also observe simplifications, i.e. a tendency to make symmetrical postures when presented with an asymmetrical model. To our knowledge, the available literature does not allow one to predict the reverse "asymmetrical > symmetrical" pattern.

The midline-crossing inhibition effect

Healthy individuals have a natural tendency to use the hand of the same body side as the target [START_REF] Furlanetto | Effects of Arm Crossing on Spatial Perspective-Taking[END_REF][START_REF] Yamamoto | Reversal of subjective temporal order due to arm crossing[END_REF]), yet they still have the ability to override this left-right organization of the reaching space. The midline crossing inhibition effect manifests itself in difficulties to reach, step, or look across the body midline, thus resulting in difficulties to imitate contralateral gestures (e.g., touching the left ear with the right index finger). It has been documented in stroke patients (Head, 1920, 1926, cited by Bekkering et al., 2000), in typically developing children ("crosslateral" or "contralateral" inhibition effect; [START_REF] Bekkering | Imitation of Gestures in Children is Goal-directed[END_REF][START_REF] Gleissner | Children's coding of human action : Cognitive factors influencing imitaation in 3-year-old[END_REF]Gordon, 1923;[START_REF] Lombardi | Age Differences and Changes in Midline-Crossing Inhibition in the Lower Extremities[END_REF]Schofield, 1976;Wagner & Cirillo, 1968;[START_REF] Wallon | Espace postural et espace environnant (le schéma corporel)[END_REF], as well as in healthy adults [START_REF] Baumard | Imitation of meaningless gestures in normal aging[END_REF][START_REF] Pedersen | Ageing and midline crossing inhibition. Laterality: Asymmetries of Body[END_REF], but barely described in patients with dementia, to our knowledge. Previous reports have suggested (but not demonstrated) that crossed hand configurations (i.e., one or both hands cross the body-midline axis and encroach(s) on the contralateral space) may be more difficult to imitate than uncrossed configurations (i.e., each hand remaining in the ipsilateral side; [START_REF] Ajuriaguerra | A propos de quelques problèmes posés par l'apraxie dans les démences[END_REF][START_REF] Yamaguchi | Yamaguchi Fox-Pigeon Imitation Test : A Rapid Test for Dementia[END_REF] for patients with dementia. In the framework of the body representation hypothesis, midline-crossing inhibition has been proposed to reflect insufficient perceptual-motor conversion mechanisms underlying body representation [START_REF] Ajuriaguerra | A propos de quelques problèmes posés par l'apraxie dans les démences[END_REF][START_REF] Ajuriaguerra | Quelques aspects de la désintégration des praxies idéomotrices dans les démences de grand âge[END_REF][START_REF] Buxbaum | Ideomotor apraxia : A call to action[END_REF][START_REF] Gooddy | SOME ASPECTS OF HUMAN ORIENTATION IN SPACE : (I) SENSATION AND MOVEMENT[END_REF]Kephart, 1971). In the framework of the goal-directed theory of imitation, [START_REF] Gleissner | Children's coding of human action : Cognitive factors influencing imitaation in 3-year-old[END_REF] have rather assumed that midline crossing is coded at a low level of movement goal hierarchy. In this view, the end-point of the action (e.g., hand on the ear) is more important than other parameters like the hand used (i.e., left/right) or the need to cross the body midline. This may explain simplification errors (e.g., reaching the correct target "ear" but without crossing the midline). Both hypotheses predicted that performance with imitation of crossed gestures would be more impaired than imitation of uncrossed gestures, while the available literature does not allow the reverse prediction to our knowledge.

MATERIALS AND METHODS

PARTICIPANTS

Thirty-two healthy controls and 63 patients diagnosed with Alzheimer's disease (AD), semantic dementia (SD), posterior cortical atrophy (PCA), or corticobasal syndrome (CBS) took part in the study (Table 2). All patients were recruited in four French outpatient neurological units (i.e., Angers, Rennes, Lyon, Grenoble). Patients were diagnosed by experienced neurologists with neurological examination, neuropsychological assessment, imaging data and biomarker analysis. They met criteria for probable Alzheimer's disease of the amnestic form [START_REF] Mckhann | The diagnosis of dementia due to Alzheimer's disease : Recommendations from the National Institute on Aging-Alzheimer's Association workgroups on diagnostic guidelines for Alzheimer's disease[END_REF], semantic dementia [START_REF] Gorno-Tempini | Classification of primary progressive aphasia and its variants[END_REF][START_REF] Neary | Frontotemporal lobar degeneration[END_REF], posterior cortical atrophy [START_REF] Benson | Posterior cortical atrophy[END_REF][START_REF] Crutch | Consensus classification of posterior cortical atrophy[END_REF][START_REF] Renner | Progressive posterior cortical dysfunction. A clinicopathologic series[END_REF][START_REF] Tang-Wai | Clinical, genetic, and neuropathologic characteristics of posterior cortical atrophy[END_REF], and corticobasal syndrome [START_REF] Armstrong | Criteria for the diagnosis of corticobasal degeneration[END_REF][START_REF] Litvan | Accuracy of the Clinical Diagnosis of Corticobasal Degeneration : A Clinicopathologic Study[END_REF]. Exclusion criteria included having a history of either neurological or major psychiatric illness; having a rheumatologic condition, mood disorder, medical treatment or cognitive state incompatible with the protocol; or a MMSE score below 10. Two PCA patients and one CBS patient were finally excluded from the sample because of depressive symptoms (n = 2) or diagnostic uncertainty (n = 1). In order to avoid exaggerating deficits by comparing older patients to young adults, healthy controls were matched on age and sex only to the oldest patients that is, patients with Alzheimer's disease. The study followed the guidelines of the Declaration of Helsinki and was approved by local ethics committee (Western Protection to Persons Committee II, n° 2012/32). There was substantial sample overlap with previous tool use studies [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]. The healthy control group was part of a larger sample (n = 103) from a previous imitation study [START_REF] Baumard | Imitation of meaningless gestures in normal aging[END_REF] while the clinical data on imitation are original.

NEUROPSYCHOLOGICAL ASSESSMENT

In addition to routine cognitive tests, all patients underwent neuropsychological assessment. General cognitive functioning was tested using the French Battery of Cognitive Efficacy [START_REF] Signoret | Batterie d'Evaluation Cognitive -BEC 96[END_REF]. This battery consists of eight tests of working memory (i.e., listing the days of the week in reverse order), orientation (i.e., questions on age, year, month, date, name of the president of the republic), verbal learning (i.e., immediate recall of eight concrete words across 3 trials), visual recognition (i.e., immediate and delayed recall, then recognition of six black and white pictures among three foils each), verbal reasoning (i.e., similarities, arithmetic problem, and proverb definition), verbal animal fluency, naming of 12 black and white pictures, and visuoconstructive skills (i.e., copying a 3-D cube, and three 2-D overlapping triangles). Each subtest is scored on a 12-point scale with any score below 9 being suggestive of cognitive impairment. The maximum score is 96 (i.e., 12 points x 8 subtests = 96) with a cut-off score of 80 -corresponding to -1.96 standard deviations from the mean. These values are based on French normative data (control sample, n = 30 participants 65 to 89 years of age).

Executive functioning was measured using the fast Frontal Assessment Battery (FAB; [START_REF] Dubois | The FAB: A Frontal Assessment Battery at bedside[END_REF] that tests conceptualization (i.e., similarities), mental flexibility (i.e., letter fluency), programming (i.e., motor series of Luria), sensitivity to interference (i.e., conflicting instructions), inhibitory control (i.e., go-no-go), environmental autonomy (i.e., prehension behavior). Each subtest is scored on a 3-point scale for a maximum score of 18 (i.e., 3 points x 6 subtests). Any score below or equal to 15 (corresponding to -1.96 standard deviations from the mean) may indicate cognitive impairment based on French normative data (control sample, n = 42 participants, mean age 58, standard deviation 14.4).

The results were consistent with the diagnosis as the core symptoms were orientation and memory disorders in Alzheimer's disease, verbal-semantic impairments in semantic dementia, and visuoperceptive deficits in posterior cortical atrophy (Table 2). Patients with corticobasal syndrome had relatively spared cognitive functioning and were diagnosed on the basis of extrapyramidal symptoms and upper limb apraxia (e.g., limb-kinetic apraxia). The imitation tasks described below were not used to establish the diagnosis.

IMITATION OF MEANINGLESS GESTURES

Materials and procedure

This task was inspired from the ones used by Goldenberg [START_REF] Goldenberg | The meaning of meaningless gestures : A study of visuo-imitative apraxia[END_REF][START_REF] Goldenberg | Matching and imitation of hand and finger postures in patients with damage in the left or right hemispheres[END_REF] and [START_REF] Peigneux | Présentation d'une batterie neuropsychologique et cognitive pour l'évaluation de l'apraxie gestuelle[END_REF]. Unimanual postures were the same as in [START_REF] Goldenberg | The meaning of meaningless gestures : A study of visuo-imitative apraxia[END_REF] with the exception of one item, because of a ceiling effect found in pretests (i.e., "palm down over the head" became "hand vertical on the head, thumb oriented downward"). The full list of gestures is available in Figure 1 and Supplementary Figure 1. Participants sat in front of the examiner, and were asked to successively imitate 45 meaningless configurations in a mirror-like fashion (i.e., axial rather than central symmetry).

They used their dominant hand, and they could see the model as they imitated (i.e., concurrent imitation). Gestures varied on the following criteria: body parts (i.e., finger/hand), number of hands (i.e., unimanual/bimanual), symmetry of configurations (i.e., symmetrical/asymmetrical), and body-midline crossing (i.e., crossed/uncrossed). Importantly, gestures were selected or created so that they varied only on the abovementioned independent variables, when possible (i.e., when it was consistent with biomechanical constraints and when it allowed creating unambiguous items). So, bimanual symmetrical configurations were derived from unimanual configurations by duplicating the initial posture (e.g., thumb-index ring became two thumb-index rings interlaced). Bimanual asymmetrical configurations consisted of slight alterations of symmetrical ones. The same rationale was applied to crossed and uncrossed configurations. As in previous studies, the participants could see their own hand during the imitation of finger configurations, whereas hand configurations were directed toward the head and neck so that the participant could not rely on visual control [START_REF] Goldenberg | The meaning of meaningless gestures : A study of visuo-imitative apraxia[END_REF]. The task order was fixed and was the same as in Figure 1 (the exact sequence is available in Supplementary Figure 1). The item order within each task was also the same for all participants. Bimanual postures may be more difficult to imitate than unimanual postures for healthy controls, based on previous studies [START_REF] Baumard | Imitation of meaningless gestures in normal aging[END_REF]. Therefore, we set different time limits for unimanual and bimanual postures to control for intrinsic task difficulty and avoid floor effects. Based on our data (n = 103), healthy adults needed less than 10 seconds to imitate unimanual postures in 99.9% of observations, and less than 20 seconds to imitate bimanual postures in 99.5% of observations. Therefore, the time limit was set to 10 seconds for unimanual postures and 20 seconds for bimanual postures, to avoid a floor effect in the latter condition.

For the same reason, two practice items preceded each series of bimanual postures (i.e., one finger configuration and one hand configuration, both symmetrical).

Quantitative data

Performance was video-recorded and later coded on a 2-point scale similar to those used in previous studies (e.g., [START_REF] Baumard | Imitation of meaningless gestures in normal aging[END_REF][START_REF] Goldenberg | The meaning of meaningless gestures : A study of visuo-imitative apraxia[END_REF][START_REF] Souza | The interlocking finger test in patients with Parkinson's disease and healthy subjects[END_REF]. Perfect imitation of the model within the time limit was worth 2 points, while approximate imitation within the time limit was worth 1 point (e.g., correct hand position on the body but incorrect hand orientation). No point was awarded in the absence of performance or if the imitation obviously differed from the model. Hesitations and self-corrections were accepted because they were frequent in healthy adults. Thereby performance was scored only when participants stopped trying new configurations and held the gesture for at least two seconds. The coding system focused on the position of fingers in the "finger" items, and on the position and orientation of the hand relative to the body in the "hand" items. This coding system has been used to test dissociations between the imitation of hand and finger configurations in stroke patients [START_REF] Goldenberg | The meaning of meaningless gestures : A study of visuo-imitative apraxia[END_REF]. As in previous studies, finger postures were expected to put higher loads on visual-spatial skills whereas hand postures were expected to put higher loads on body representations (see the rationale behind this in section 2.2.1). We used a similar coding system because our goal was to test how the body part effect documented in stroke patients would apply to patients with neurodegenerative diseases. The maximum total score was 90 (i.e., 45 items x 2 points).

Two coders tested the scoring system on 4 videos (1 participant from each group). Then, they coded separately 30% of the videos (i.e., 10 HC, 10 AD, 5 SD, and 5 FPN participants).

One of the coders was unaware of the hypotheses and of the clinical status of the participants.

The two raters agreed on 1109 out of 1350 observations (i.e., 45 observations x 30 participants) so the mean percentage of agreement at the item level was 82.2%. The correlation based on the total imitation score was high (r = 0.96, p < .001) and similar to the ones found in previous studies (e.g., [START_REF] Li | The Gesture Imitation in Alzheimer's Disease Dementia and Amnestic Mild Cognitive Impairment[END_REF][START_REF] Sanin | Bimanual Gesture Imitation in Alzheimer's Disease[END_REF]). Cohen's Kappa was calculated (with scores of 2, 1, or 0 considered as categories) since it adjusts for the level of agreement that would occur by chance. With this method, inter-rater reliability was moderate (K = 0.59).

Error analysis

In an attempt to better describe the performance (see also [START_REF] Bekkering | Goal-directed imitation in patients with Ideomotor Apraxia[END_REF], we defined two possible errors in bimanual subtests: Symmetry errors and body-midline crossing errors.

Symmetry errors were counted only in the 10 asymmetrical items and were defined as follows: At any moment of the performance, the participant generates a symmetrical configuration, whether it concerns either the selection of fingers (in the "finger" items) or the position of the hands on the body (in the "hand" items). This type of error was thought to reflect difficulties in inhibiting bimanual synchronization. There were 10 items (5 "finger" and 5

"hand" items). One point was given for each error (1 max. per item). Therefore, the maximum number of errors was 10 (5 for "finger" items and 5 for "hand" items).

Body-midline crossing errors were taken into account only in the 10 bimanual "crossed" items. They were defined as follows: At any moment of the performance, the participant generates a bimanual configuration directed toward the body, that does not cross the body midline. This type of error was thought to reflect difficulties in overriding the left-right organization of the peripersonal space. There were 10 items (all of which were "hand" items).

One point was given for each error (1 max. per item). Therefore, the maximum number of errors was 10.

STATISTICS

Raw imitation scores (but not error counts) were converted into percentages of the maximum score for the sake of clarity (e.g., a score of 7/10 was converted into 70%). Since the different imitation conditions varied in difficulty [START_REF] Baumard | Imitation of meaningless gestures in normal aging[END_REF], raw scores were also converted into t-scores. Individual deficits and dissociations were tested using modified t-tests (with a two-tailed probability) controlling for the mean, standard deviation and between-task correlations observed in healthy controls (Crawford & Garthwaite, 2002, 2005; Singlims_ES.exe and Dissocs_ES.exe softwares). This method allows the detection of dissociations between tasks that are rare in the control population. As a result, the dissociations observed in individual patients can be interpreted as an effect of the patient's clinical/cognitive status. The frequency of these dissociations was compared between groups with Chi-square tests, or Fisher tests in case of low values. Unless otherwise specified, p-values are corrected pvalues using Holm's method for multiple tests. "Tendencies toward significance" were reported if p-value was no longer significant after p-value adjustment. Finally, we performed a multiple regression analysis of the cognitive scores contributing to the variance of imitation scores.

RESULTS

FREQUENCY AND SEVERITY OF IMITATION IMPAIRMENTS

Individual raw scores and t-scores are available in Supplementary tables 1 and 2. We found 19 different patterns of imitation performance (Supplementary Table 3). Given this large number of profiles, we first studied how the presence/absence of imitation deficits mapped the clinical groups. As shown in Table 3, 31% of SD cases (5/16), 47% of AD cases (15/32), and 87% of FPN cases (13/15) failed at least one of the imitation tests. The difference of distribution was significant between the SD and FPN groups (χ² = 7.62, df = 1, p = .017), between the AD and FPN groups (χ² = 5.16, df = 1, p = .046), but not between the SD and AD groups (χ² = 0.52, df = 1, p = .469).

We also studied the severity of the imitation deficit, by studying the distribution of cases as a function of the number of imitation conditions impaired (i.e., 0, 1-2, 3-4, 5-6, 7). The distribution, shown in Table 3, varied between the SD and FPN groups (Fisher test, p < .001), as well as between the AD and FPN groups (p < .001), but not between the SD and AD groups (Fisher test, p = .080). Failure to imitate any of the seven conditions was observed only in the FPN group. Failure to imitate at least one of the two unimanual conditions (i.e., the easiest conditions for healthy controls, see Table 4) was observed in 6% of SD cases (1/16), 28% of AD cases (9/32), and 87% of FPN cases (13/15). Again, the distribution was different between the SD and FPN groups (χ² = 17.10, df = 1, p = <.001), between the AD and FPN groups (χ² = 11.80, df = 1, p = .001), but not between the SD and AD groups (Fisher test, p = .132).

IMITATION DEFICITS AS A FUNCTION OF GROUP AND CONDITION

Table 4 emphasizes significant control/patient differences as a function of imitation conditions (see also Supplementary Figure 2). To sum up, patients from the SD group had normal to subnormal imitation performance, whereas patients from the FPN group had frequent and important imitation impairments. Difficulties to imitate unimanual postures were particularly frequent and pronounced in the FPN group. Patients from the AD group either resembled SD patients, or were in an intermediate position between the SD and FPN groups (Supplementary Table 3). They showed imitation impairments mainly with bimanual finger asymmetrical postures as well as with bimanual hand configurations that were asymmetrical and required midline crossing.

DISSOCIATIONS BETWEEN CONDITIONS

Given the presence of both group effects and within-group heterogeneity, condition effects should be studied group by group, but also in individual cases, because opposite dissociations may exist in different patients from the same clinical group (e.g., case X may perform better with finger than hand postures while case Y may show the reverse pattern). Therefore, we studied dissociations in individual cases independently from the clinical group of origin, and then we tested whether the expected dissociations were more frequent in some clinical groups than in others (Table 5; Supplementary Table 4). Of note, we tested dissociations based on raw scores, but we concluded on the direction of the dissociation (i.e., score X < Y or score X > Y) based on t-scores, in order to control for intrinsic task difficulty. As a result, a patient may have a higher raw score in condition X than in condition Y, and yet show an "X < Y" dissociation based on the variance observed in the healthy control group. This method allows controlling for variations in difficulty across imitation conditions.

Overall, 54% of the patient sample (34/63) showed at least one of the expected dissociations: 5 SD cases (31%), 18 AD cases (56%), and 11 FPN cases (73%). Each of the four effects of interest are reported below.

The body part effect

We found 18 dissociations (observed in 13 cases) between finger and hand postures (either uni-or bimanual): 17 "Finger < Hand" dissociations (among which 8 were strong dissociations), and 1 "Finger > Hand" dissociation. There were more cases showing a "Finger < Hand" dissociation in the FPN group (n = 7/15) than in the SD group (n = 1/16; Fisher test, p = .046).

The bimanual effect

We found 28 dissociations (observed in 21 cases) between unimanual and bimanual postures (either finger or hand): 21 "Unimanual < Bimanual" dissociations (among which 12 were strong dissociations), and 7 "Unimanual > Bimanual" dissociations (among which one was a strong dissociation). The "Unimanual > Bimanual" dissociation was observed in 5/32 AD cases (i.e., 16%) and 2/16 SD cases (13%), and there was no difference between the SD and FPN group (p = 0.484). The unexpected "Unimanual < Bimanual" dissociation was more frequent in the FPN group (n = 10/15) than in the SD group (n = 1/16, Fisher test, p = .008).

Since only one hand was tested in the unimanual condition, one could argue that rightleft asymmetry of motor functions, which is frequent in patients with corticobasal syndrome, may have exaggerated this dissociation between unimanual and bimanual imitation in the FPN group. Nevertheless, this dissociation was found in 6 cases with posterior cortical atrophy, who do not have motor symptoms. In the 4 remaining CBS cases, imitation scores were available for both the right and left hand. We calculated the raw difference between the imitation scores obtained with the right and left hands (e.g., if a patient has a score of 80/100 with the right hand, and 70/100 with the left hand, the difference score is +10). In the control sample, the raw difference between the score obtained with the right and left hands ranged from -10 to +5 for finger configurations, and from -5 to +5 for hand configurations (on a 0-100 scale). Two cases showed an abnormal right-left difference, with hand configurations only (CBS.02: -10; CBS.08: -10).

Yet, neither of these two cases showed the abovementioned dissociation between unimanual and bimanual imitation. In contrast, 2 CBS cases showed dissociations between unimanual and bimanual imitation, but no dissociation between the right and left hand (CBS.01 and 06). This suggests that differences between imitation scores of the right and left hands did not exaggerate the prevalence of the dissociation between unimanual and bimanual dissociation.

The asymmetry effect

We found 14 dissociations (observed in 14 cases) between asymmetrical and symmetrical postures (either finger or hand): 11 "Asymmetrical < Symmetrical" dissociations (classical dissociations only), and 3 "Asymmetrical > Symmetrical" dissociations (among which 2 were strong dissociations; Table 5, Supplementary Table 4). The distribution of dissociations did not vary across the SD and FPN groups (p = .452).

The midline crossing inhibition effect

We found 11 dissociations (observed in 11 cases) between crossed and uncrossed postures. There were only "Crossed < Uncrossed" dissociations (among which 2 were strong dissociations). There were more cases showing the "Crossed < Uncrossed" dissociation in the FPN group (n = 7/15) than in the SD group (n = 0/16; Fisher test, p = .009).

ERROR ANALYSIS

The number of symmetry errors (finger configurations) was virtually the same in the HC (mean = 1.6, sd = 0.8), SD (mean = 1.9, sd = 1.2), AD (mean = 2.1, sd = 1.2), or FPN groups (mean = 1.9, sd = 1.3; F(3, 90) = 1.01, p = .39). The same was found with hand configurations (HC mean = 0.9, sd = 0.8; SD mean = 0.9, sd = 0.6; AD mean = 1.3, sd = 1.0; FPN mean = 1.0, sd = 1.2; F(3, 91) = 1.03, p = .38).

HC participants committed fewer midline crossing errors (mean = 0.2, sd = 0.5) than SD (mean = 0.9, sd = 1.1), AD (mean = 0.8, sd = 1.0), or FPN patients (mean = 1.7, sd = 1.6). There was a main effect of GROUP (F(3, 91) = 6.99, p < .001). Post-hoc analyses confirmed the HC/FPN difference (t(15.1) = -3.36, p < .001) only. One HC participant made 2 errors, 5 participants made 1 error, and 26 made no error. In contrast, 8 FPN participants made 2 or more errors, 2 participants made 1 error, and 5 participants made no error.

RELATIONS OF IMITATION TO NEUROPSYCHOLOGICAL SCORES

In order to infer predictors of imitation, we compared subgroups of patients as a function of the number of imitation conditions impaired (Table 3). We used the following dependent variables: the MMSE score as a measure of global cognitive decline; the FAB score as a measure of executive functioning; and the visuoconstructive test of the BEC96 battery as a measure of visuoconstructive skills. We selected these variables with regard to the visuoconstructive hypothesis, and to control for global cognitive decline. We performed these analyses regardless of the clinical group. As displayed in Table 3, the higher the number of imitation conditions impaired, the lower the cognitive scoresespecially the visuoconstructive score. We used the same method to study the cognitive scores of cases showing the dissociations of interest (Table 5). Based on data observation, cases with a "Finger < Hand" dissociation had lower visuoconstructive scores than other cases (a Mann-Whitney U test was preferred given the low number of cases; U = 85.0, p < .001).

The results of the multiple regression analysis (Table 5) also confirm that the visuoconstruction score is overall a better predictor of imitation scores than the MMSE and executive (FAB) score. Plots are available in Supplementary Figure 3. We could not confirm that this relation was due to the performance of the FPN group, given the low sample sizes. Future studies with larger samples and more statistical power should test the covariance relations within each clinical group.

DISCUSSION

The goals of this study were to describe imitation deficits in independently defined clinical groups of patients with neurogenerative diseases. A secondary goal was to study the nature of cognitive disruption that can give rise to visuo-imitative apraxia in patients with neurodegenerative diseases In our findings, visuo-imitative apraxia was rare in patients with semantic dementia (SD), whereas it was both frequent and pronounced in patients from the "Frontal-Parietal Network" (FPN) group. These findings are in line with previous lesion studies on stroke patients that have demonstrated that fronto-parietal lesions are associated with deficits in imitating meaningless actions [START_REF] Binkofski | Two action systems in the human brain[END_REF][START_REF] Buchmann | Selection and application of familiar and novel tools in patients with left and right hemispheric stroke : Psychometrics and normative data[END_REF][START_REF] Buxbaum | Learning, remembering, and predicting how to use tools : Distributed neurocognitive mechanisms: Comment on Osiurak and Badets (2016)[END_REF][START_REF] Dressing | Distinct Contributions of Dorsal and Ventral Streams to Imitation of Tool-Use and Communicative Gestures[END_REF][START_REF] Goldenberg | The neural basis of tool use[END_REF][START_REF] Goldenberg | Facets of Pantomime[END_REF][START_REF] Mengotti | Selective imitation impairments differentially interact with language processing[END_REF]. Patients with Alzheimer's disease (AD) showed a more nuanced picture, probably reflecting clinical heterogeneity but also patient selection: Contrary to previous studies, we have included "typical" amnestic AD and patients with posterior cortical atrophy (PCA) in separate groups based on the ventral-dorsal model of imitation. That said, the performance varied as a function of conditions. This confirms that meaningless gestures are not monolithic: Slight changes in the model performing the action may lead to substantial differences in performance across patients, both within and across clinical groups. This may explain why the meaningless imitation skills of AD patients have been subject to large variations in previous studies (from 10% to 100% of the maximum score; see [START_REF] Lesourd | Apraxia and Alzheimer's Disease : Review and Perspectives[END_REF]. The next sections will, therefore, focus on the effects of imitation conditions.

THE BODY PART EFFECT

While individual "Finger > Hand" dissociations were rare and inconsistent across conditions, "Finger < Hand" dissociations were observed in 13 cases (i.e., 21% of the clinical sample). They were more frequent in the FPN group than in the SD group, suggesting that this dissociation was relatively specific to patients with lesions of fronto-parietal areas. These dissociations were also observed in the AD group, mainly with bimanual postures, which is consistent with previous studies [START_REF] Johnen | Dementia Apraxia Test (DATE) : A Brief Tool to Differentiate Behavioral Variant Frontotemporal Dementia from Alzheimer's Dementia Based on Apraxia Profiles[END_REF]. Of note, [START_REF] Sanin | Bimanual Gesture Imitation in Alzheimer's Disease[END_REF] found similar levels of finger and hand impairments in Alzheimer's disease, but they compared static finger postures and alternate hand movements; by using static postures only, and by controlling the asymmetry of the model, we found that bimanual finger postures are more difficult than bimanual hand postures for some AD or FPN patients.

Two hypotheses predicted a body part effect. The body representation hypothesis predicted a "Finger > Hand" dissociation, whereas the visuoconstructive hypothesis predicted the reverse "Finger < Hand" dissociation. We observed more "Finger < Hand" dissociations, which is more in line with the visuoconstructive hypothesis than with the body representation hypothesis. The higher frequency of these dissociations in the FPN group (Table 5), as well as the possible link to visuoconstructive impairments (Table 3), is also consistent with this hypothesis. These findings are consistent with a causal effect of visuoconstructive abilities on imitation performance. Previous studies have documented abnormal finger imitation in patients with dementia with Lewy bodies, which cognitive profile is roughly characterized by visuoconstructive and executive dysfunction [START_REF] Kemp | Cognitive profile in prodromal dementia with Lewy bodies[END_REF]. [START_REF] Nagahama | Impaired imitation of gestures in mild dementia : Comparison of dementia with Lewy bodies, Alzheimer's disease and vascular dementia[END_REF] have found that AD patients scored higher than patients with dementia with Lewy bodies on unimanual finger postures (96% and 83% of the maximum score, respectively), a pattern similar to the AD/FPN differences we observed. They interpreted this finding as a consequence of frontal-parietal cortical lesions associated with attentional, executive and visuospatial impairments. [START_REF] Souza | The interlocking finger test in patients with Parkinson's disease and healthy subjects[END_REF] have also found a correlation between finger imitation and cognitive (visuospatial and executive) scores in patients with Parkinson's disease. So, patients from the FPN group probably had more difficulties with finger postures than with hand postures because they had more important visuoconstructive deficits than other patients. This may be explained by visual-spatial deficits following right parietal lesions and preventing patients from extracting the visual model (especially in the light of positive correlations between the visuoconstructive score and all imitation conditions). Another explanation could be that visuoconstructive deficits following left parietal lesions prevented patients from selecting and organizing the different subcomponents of finger postures. It should be noted that the dissociations of interest, including "Finger < Hand" dissociations, were documented in each of the three clinical groups, meaning that no dissociation can be considered pathognomonic. This may reflect the complexity and multi-determined nature of imitation. Of note, many FPN cases failed to imitate not only finger, but also hand postures, resulting in the absence of Finger/Hand dissociation. Perhaps these patients had both visual-spatial and visuoconstructive deficits (altering finger postures), and body representation deficits (altering hand postures) due to widespread, bilateral lesions of the parietal lobes. Studies with larger numbers of participants, and hence higher statistical power, will be able to decisively separate the relative contributions of visuoconstructive and body representations in supporting imitation performance. Future studies may also investigate the lesion patterns that are associated with different directions of dissociations.

Our findings allow us to discuss other hypotheses sometimes invoked to explain visuoimitative apraxia. While the visuoconstructive hypothesis has endeavored to break down the direct route for imitation [START_REF] Goldenberg | The meaning of meaningless gestures : A study of visuo-imitative apraxia[END_REF][START_REF] Rothi | A Cognitive Neuropsychological Model of Limb Praxis[END_REF], the recently revived sensori-motor conversion hypothesis [START_REF] Achilles | Using multi-level Bayesian lesion-symptom mapping to probe the body-part-specificity of gesture imitation skills[END_REF]; see also [START_REF] Geschwind | The apraxias. Neural mechanisms of disorders of learned movement[END_REF] assumes that hand postures are more sensitive to brain damage that also affects finger postures, which boils down to a difficulty effect. Our findings of frequent "Finger < Hand" dissociations are at odds with this hypothesis. They rather suggest that finger and hand postures call for different cognitive processes, as previously proposed on the basis of research with individuals who have had stroke [START_REF] Goldenberg | The meaning of meaningless gestures : A study of visuo-imitative apraxia[END_REF][START_REF] Goldenberg | Hemisphere asymmetries for imitation of novel gestures[END_REF][START_REF] Goldenberg | Matching and imitation of hand and finger postures in patients with damage in the left or right hemispheres[END_REF]. It should be acknowledged however that Achilles et al. have focused on functions of the left hemisphere only whereas we studied patients with typically bilateral lesions, resulting in a likely influence of right hemisphere lesions. Finally, according to the limited resource theory (Rumiati & Tessari, 2002;Tessari & Rumiati, 2002), finger imitation may require more motor resources than proximal movements, and hence poor finger imitation may arise from a deficit of motor programming. This hypothesis is based on the widespread motor representation of finger movements in the parietal [START_REF] Hoeren | Neural bases of imitation and pantomime in acute stroke patients : Distinct streams for praxis[END_REF][START_REF] Tanaka | Neural substrates involved in imitating finger configurations : An fMRI study[END_REF], left frontal [START_REF] Goldenberg | The Neural Basis of Imitation is Body Part Specific[END_REF][START_REF] Haaland | Neural representations of skilled movement[END_REF][START_REF] Tanaka | Cortical involvement for action imitation of hand/arm postures versus ¢nger con¢gurations : An fMRI study[END_REF], and motor cortex (Rumiati & Tessari, 2002;Tessari & Rumiati, 2002). This could be an important aspect of an account of why individuals with corticobasal syndrome, who typically have frontal-parietal lesions and limb-kinetic apraxia, may show dissociations between finger and hand configurations [START_REF] Leiguarda | Limb-kinetic apraxia in corticobasal degeneration : Clinical and kinematic features: Limb-Kinetic Apraxia[END_REF]; see also [START_REF] Holl | Impaired Ideomotor Limb Apraxia in Cortical and Subcortical Dementia : A Comparison of Alzheimer's and Huntington's Disease[END_REF]. However, it does not apply well to caseswith posterior cortical atrophy, who do not have motor symptoms. Future studies may help disentangle the motor and spatial components of imitation. [START_REF] Lesourd | Apraxia and Alzheimer's Disease : Review and Perspectives[END_REF] have stressed a possible unimanual/bimanual dissociation in Alzheimer's disease. [START_REF] Yamaguchi | Yamaguchi Fox-Pigeon Imitation Test : A Rapid Test for Dementia[END_REF] have demonstrated that bimanual finger imitation was more affected than unimanual finger imitation in this disease. Interestingly, [START_REF] Nagahama | Impaired imitation of gestures in mild dementia : Comparison of dementia with Lewy bodies, Alzheimer's disease and vascular dementia[END_REF] have found that unimanual finger imitation was more disrupted in patients with dementia with Lewy bodies than in those with Alzheimer's disease, while bimanual imitation was affected to the same extent in both groups . Similarly, the FPN group had imitation impairments with both unimanual and bimanual finger postures, whereas Alzheimer patients showed a selective impairment of bimanual postures. This has two implications. First, impairment of unimanual imitation is likely to reflect atrophy of fronto-parietal areas, as already demonstrated in stroke patients [START_REF] Dressing | Distinct Contributions of Dorsal and Ventral Streams to Imitation of Tool-Use and Communicative Gestures[END_REF][START_REF] Goldenberg | Apraxia and the parietal lobes[END_REF][START_REF] Goldenberg | Facets of Pantomime[END_REF][START_REF] Mengotti | Selective imitation impairments differentially interact with language processing[END_REF]; see also [START_REF] Tanaka | Neural substrates involved in imitating finger configurations : An fMRI study[END_REF][START_REF] Tanaka | Cortical involvement for action imitation of hand/arm postures versus ¢nger con¢gurations : An fMRI study[END_REF]. Second, bimanual imitation can be selectively impaired in (typical, amnestic) Alzheimer's disease.

THE BIMANUAL EFFECT

Nevertheless, some, but not all of the bimanual conditions were impaired in these patients.

We did not observe a higher prevalence of bimanual apraxia [START_REF] Sanin | Bimanual Gesture Imitation in Alzheimer's Disease[END_REF]. This may be due to having experimentally separated multiple dimensions of the actions to be imitated that modulate performance (asymmetry, midline crossing). Although bimanual apraxia has not been clearly defined yet, it is logical to diagnose it in presence of normal unimanual imitation but impaired bimanual imitation, otherwise patients should be diagnosed with apraxia but not "bimanual" apraxia. Previous studies that have documented bimanual imitation impairments in Alzheimer's disease [START_REF] Li | The Gesture Imitation in Alzheimer's Disease Dementia and Amnestic Mild Cognitive Impairment[END_REF][START_REF] Sanin | Bimanual Gesture Imitation in Alzheimer's Disease[END_REF] did not use unimanual imitation as a baseline, and studies that have directly compared uni-and bimanual imitation have used finger postures only [START_REF] Nagahama | Impaired imitation of gestures in mild dementia : Comparison of dementia with Lewy bodies, Alzheimer's disease and vascular dementia[END_REF][START_REF] Yamaguchi | Yamaguchi Fox-Pigeon Imitation Test : A Rapid Test for Dementia[END_REF]. This may have led to exaggerate conclusions regarding bimanual apraxia -especially since we found "Finger < Hand" dissociations. Two of our findings do not confirm the prevalence of bimanual (visuo-imitative) apraxia in AD: (1) the performance of most AD patients on bimanual hand subtests was actually normal after controlling for body part, asymmetry, and midline-crossing (condition G in Figure 1); ( 2) "Unimanual > Bimanual" dissociations were relatively rare in all groups, after controlling for intrinsic task difficulty (using t-scores instead of raw scores).

In fact, "Unimanual < Bimanual" dissociations were unexpectedly frequent, a finding that might reveal a facilitatory effect of the tactile feedback during bimanual imitation: Perhaps the tactile feedback given by the contact of the left and right hands in the bimanual condition may partially compensate for visuoconstruction/visuospatial deficits in the bimanual condition, in some cases. Viewing unimanual actions as bimanual asymmetrical actions (since there is an asymmetry of motor innervations during unimanual imitation) might also explain this dissociation. We compared the imitation of unimanual configurations to the imitation of bimanual, symmetrical configurations (Table 5). Therefore, this dissociation between unimanual and bimanual imitation might, in fact, hide an effect of asymmetry. It is also possible that the need to use one hand puts higher loads on right-left discrimination, which may be problematic for patients with posterior lesions. In any case, the need to use both hands to imitate the model was not at stake in the poor performance of Alzheimer patients and hence, it cannot be concluded that the latter have "bimanual" apraxia. In all likelihood, failure to imitate bimanual postures arises from other dimensions of imitation tests, like asymmetry. The higher prevalence of bimanual imitation deficits in [START_REF] Sanin | Bimanual Gesture Imitation in Alzheimer's Disease[END_REF] work (63% of maximum score, against 92% in the present study) might also indicate that movements, instead of static postures, add an additional layer of difficulty to imitation tests for patients with Alzheimer's disease (see also [START_REF] Buxbaum | Critical brain regions for tool-related and imitative actions : A componential analysis[END_REF] on posture versus kinematic components of imitation).

THE ASYMMETRY EFFECT

Asymmetrical postures were more difficult than their symmetrical equivalent for 11 cases (i.e., 17% of the clinical sample), including 8 AD cases (i.e., 25% of AD cases). The same dissociation has been documented in patients with Alzheimer's disease or amnestic mild cognitive impairment with finger postures [START_REF] Li | The Gesture Imitation in Alzheimer's Disease Dementia and Amnestic Mild Cognitive Impairment[END_REF], as well as in healthy older adults [START_REF] Baumard | Imitation of meaningless gestures in normal aging[END_REF]. Why is asymmetry difficult for patients?

Two hypotheses predicted this pattern. The visuoconstructive hypothesis is unlikely given that "Asymmetrical < Symmetrical" dissociations were found only in the SD and AD groups, who had normal visuoconstructive skills. The findings are consistent with the goal-directed theory of imitation [START_REF] Bekkering | Imitation of Gestures in Children is Goal-directed[END_REF][START_REF] Bekkering | Goal-directed imitation in patients with Ideomotor Apraxia[END_REF][START_REF] Gleissner | Children's coding of human action : Cognitive factors influencing imitaation in 3-year-old[END_REF] and may reflect a disorganization of hierarchical goal structure: The higher the number of subgoals (i.e., same configuration for both hands in symmetrical postures, but different configurations in asymmetrical ones), the higher the difficulty of the task for patients. That said, SD and AD patients did not commit more symmetry errors than healthy controls, which weakens this hypothesis. An alternate hypothesis could be that AD patients struggled with task complexity because of executive dysfunction. Indeed, the number and ambiguity of visually similar elements logically increase with asymmetrical postures, as compared to symmetrical ones. This presumably calls for high executive control in the form of strategic analysis, planning and working memory, a necessary condition for detecting minor left-right differences, sequencing and maintaining relevant subgoals temporarily (e.g., left hand, then right hand), and checking the quality of the production [START_REF] M293 Luria | Les fonctions corticales supérieures de l'homme[END_REF][START_REF] Luria | The programming of constructive activity in local brain injuries[END_REF]. Based on the bimanual control system theory [START_REF] Brinkman | CEREBRAL CONTROL OF CONTRALATERAL AND IPSILATERAL ARM, HAND AND FINGER MOVEMENTS IN THE SPLIT-BRAIN RHESUS MONKEY[END_REF][START_REF] Kelso | On the coordination of two-handed movements[END_REF][START_REF] Kinsbourne | The corpus callosum equilibrates the cerebral hemispheres[END_REF][START_REF] Huhn | Symmetries in action : On the interactive nature of planning constraints for bimanual object manipulation[END_REF], one could also argue that patients had difficulties in desynchronizing hand movements, which boils down to a deficit of inhibition of dominant patterns. Nevertheless, difficulties in inhibiting hand synchrony should also have resulted in more symmetry errors in patients than in healthy controls, which was not the case. This strengthens the hypothesis that planning and/or working memory deficits, but not inhibition deficits, are at the root of visuo-imitative apraxia in Alzheimer's disease, regarding finger postures at least. This "complexity account" of imitation may explain why the performance of patients (but also of healthy controls) decreased as a function of the number of effects combined into one and the same gesture (Table 4; e.g., bimanual+asymmetry yield the most marked impairments). Of note, the Frontal Assessment Battery probably failed to capture the abovementioned executive deficits properly as it does not assess working memory and planning, a limitation that future studies would need to address.

THE MIDLINE CROSSING INHIBITION EFFECT

The "Crossed < Uncrossed" dissociation, as well as midline crossing errors, were observed mainly in the group of patients with fronto-parietal brain lesions (FPN), in both cases with posterior cortical atrophy, and cases with corticobasal syndrome. Using one crossed finger configuration, [START_REF] Yamaguchi | Yamaguchi Fox-Pigeon Imitation Test : A Rapid Test for Dementia[END_REF] have found significant imitation impairment in Alzheimer patients. By dissociating Alzheimer and FPN cases, we found that midline crossing was actually more clearly an issue for the latter, with hand configurations at least. These findings may support an association of midline crossing inhibition with cortical atrophy of fronto-parietal areas, although a contribution from subcortical lesions is possible regarding cases with corticobasal syndrome.

Two hypotheses predicted a midline-crossing effect. The goal-directed theory assumed that midline crossing, a secondary subgoal, would be more sensitive to brain lesions than higher-order goals [START_REF] Bekkering | Goal-directed imitation in patients with Ideomotor Apraxia[END_REF][START_REF] Gleissner | Children's coding of human action : Cognitive factors influencing imitaation in 3-year-old[END_REF]. Goal-directed, contralateral movements have been associated with increased fMRI signals in dorsal premotor areas [START_REF] Koski | Modulation of Motor and Premotor Activity during Imitation of Target-directed Actions[END_REF], a brain region frequently affected in CBS cases. The findings are therefore consistent with this hypothesis, even more so as the FPN group committed more midline-crossing errors than healthy controls. That said, if the performance was only a function of the number of subgoals, then we should also have observed an "Asymmetrical < Symmetrical" dissociation in the FPN group (see section 5.3). So, the goal-directed theory only partially accounts for the results.

According to the body representation hypothesis, midline crossing inhibition may reflect left-right disorganization (a possible role of asomatognosia, i.e. imperceptions of some parts of the body, has been suggested; see [START_REF] Ajuriaguerra | A propos de quelques problèmes posés par l'apraxie dans les démences[END_REF][START_REF] Ajuriaguerra | Quelques aspects de la désintégration des praxies idéomotrices dans les démences de grand âge[END_REF]; see also [START_REF] Feinberg | Somatoparaphrenia : Evolving theories and concepts[END_REF]. Since the ability to seamlessly cross the body midline reflects the integrity of body schema [START_REF] Furlanetto | Effects of Arm Crossing on Spatial Perspective-Taking[END_REF][START_REF] Gooddy | SOME ASPECTS OF HUMAN ORIENTATION IN SPACE : (I) SENSATION AND MOVEMENT[END_REF][START_REF] Yamamoto | Reversal of subjective temporal order due to arm crossing[END_REF], midline-crossing inhibition may be interpreted as an impairment of the body schema in the FPN group. The role of the left parietal lobe in left-right orientation has long been demonstrated by cases of Gerstmann syndrome (for a review, see [START_REF] Rusconi | A disconnection account of Gerstmann syndrome : Functional neuroanatomy evidence[END_REF][START_REF] Vallar | Spatial Neglect, Balint-Homes' and Gerstmann's Syndrome, and Other Spatial Disorders[END_REF], a syndrome that has also been described in PCA cases [START_REF] Benson | Posterior cortical atrophy[END_REF]; see also [START_REF] Tang-Wai | Clinical, genetic, and neuropathologic characteristics of posterior cortical atrophy[END_REF]. Interestingly, patients with pure forms of this syndrome do not show problems in distinguishing left from right on their own body, but they do on the examiner's body. It turns out that establishing correspondence between left-right parameters of the self and of the examiner is critical when it comes to imitation. To sum up, lesions of frontoparietal areas may disrupt the body schema, resulting in midline-crossing inhibition (see also [START_REF] Wallon | Espace postural et espace environnant (le schéma corporel)[END_REF]. It should be acknowledged that the body representation hypothesis also predicted a "Hand < Finger" dissociation, while we found the reverse pattern in the FPN group. This may suggest that body image (i.e., knowledge about the visual image of the body, needed to imitate hand postures; [START_REF] Goldenberg | Matching and imitation of hand and finger postures in patients with damage in the left or right hemispheres[END_REF] is more resistant to fronto-parietal brain lesions than the body schema.

LIMITATIONS OF THE STUDY

This study was not without limitations. First, while we used classical coding systems to make our study comparable to previous ones, the use of different coding systems for finger and hand postures may have influenced the findings. Second, even though we included patients with distinct diagnoses and cognitive profiles, patients with neurodegenerative diseases may have multiple neuropsychological impairments (e.g., visual-spatial, visuoconstructive, body representation deficits), resulting in the absence of dissociation between imitation conditions in some cases. Third, future studies could explore imitation-cognition correlations using more specific neuropsychological tests than in the present work, as well as larger samples. Future studies may also incorporate measures of lesion extent. Fourth, we cannot rule out a possible effect of the subtest and item sequence on the performance. For example, the imitation of asymmetrical configurations always preceded the imitation of symmetrical ones, which might have contributed to the overall better performance with the latter than with the former.

CONCLUSION

Different neurodegenerative processes affect fronto-parietal versus temporal lobe structures, resulting in different performance levels on tests of imitation. Patients with semantic dementia had subnormal imitation skills, while patients with lesions to fronto-parietal areas (posterior cortical atrophy, corticobasal syndrome) showed frequent and marked imitation deficits.

Only in this group was unimanual imitation impaired. By making a distinction between the amnestic form of Alzheimer's disease, and posterior cortical atrophy, we found that visuo-imitative apraxia was less marked in AD.

This study also demonstrated significant effects of imitation conditions, confirming the need to further break down the direct route for imitation. "Finger < Hand" dissociations were more frequent in patients with lesions of fronto-parietal areas, probably because of visuoconstructive deficits. Furthermore, our findings did not confirm the prevalence of "bimanual apraxia" in dementia, defined as a selective impairment of bimanual imitation. Difficulty rather arises from the asymmetry of the model, which probably puts high demands on executive control and working memory. Finally, difficulties crossing the body midline were more frequent in the FPN group, presumably reflecting body schema disorganization.

To conclude, our findings have implications for future clinically oriented research. First, unimanual configurations may offer a basis to detect apraxic deficits in posterior cortical atrophy and corticobasal syndrome, but not Alzheimer's disease. Second, the finding of betweentask dissociations in 34/63 cases (54%) suggests that meaningless imitation is a complex task tapping multiple processes. Performance in meaningless imitation is modulated by a number of parameters of the imitated actions (midline crossing, asymmetry). The implication is that imitation tests which include only a limited set of postures cannot properly assess patients' imitation ability. The use of mixed lists of postures with variability in the body part, bimanual, asymmetry, and midline-crossing dimensions, is recommended to avoid misestimating the severity of apraxia in this clinical population. As the present study focused on meaningless imitation, future works may directly compare meaningful and meaningless postures and gestures. Finally, future studies may explore how the presentation of the postures (i.e., first person versus third person) may impact the performance [START_REF] Lesourd | Imitation and matching of meaningless gestures : Distinct involvement from motor and visual imagery[END_REF][START_REF] Sugaya | Imitation de gestes non significatifs dans la maladie d'Alzheimer : L'influence des cadres de référence spatiale égocentrique et allocentrique[END_REF].

TABLE 1. CORE HYPOTHESES AND PREDICTIONS

Hypothesis Predicted effects

Body representation hypothesis. Imitation of hand or crossed configurations calls for tridimensional or left-right representation of the body (respectively).

( 1) "Body part effect α": Unimanual hand < unimanual finger.

(2) "Midline crossing effect": Bimanual hand symmetrical crossed < bimanual hand symmetrical uncrossed. Midline crossing errors should be observed.

Visuoconstructive hypothesis. Imitation, especially of finger postures, calls for visual-spatial skills and executive functions. The more complex the model, the more difficult the task.

(1) "Body part effect β": Unimanual hand > unimanual finger.

(2) "Bimanual effect α": Bimanual finger (symmetrical) < unimanual finger + bimanual hand (symmetrical, uncrossed) < unimanual hand.

(3) "Asymmetry effect": bimanual asymmetrical finger < bimanual symmetrical finger + bimanual asymmetrical hand (crossed) < bimanual symmetrical hand (crossed). Positive correlation with visuoconstructive and/or executive scores.

Goal-directed theory. Imitation results from the combination of elementary action patterns (subgoals) into more general action patterns (goals). Impaired imitation of asymmetrical gestures (i.e., different goals for each hand) but not of symmetrical gestures (i.e., similar goals) may be interpreted as a disruption of the hierarchical goal structure. Midline crossing is represented as an additional subgoal and hence increases the difficulty of imitation.

(1) "Asymmetry effect": same as above (except regarding correlations).

(2) "Midline crossing effect": same as above.

Notes. Only the hypotheses that predicted opposite patterns of performance (referred to as "α" and "β") are shown; see the text for details on other existing hypotheses. None of the hypotheses predicted "Symmetrical < Asymmetrical" or "Uncrossed < Crossed" dissociations. t-scores and cut-off scores were determined using Crawford and Garthwaite's method (Crawford & Garthwaite, 2002, 2005).

Imitation in neurodegenerative diseases 57 Notes.

a Dissociations: unimanual finger < unimanual hand, or bimanual finger symmetrical < bimanual hand symmetrical uncrossed postures. For n = 1 case, the pattern was inconsistent between uni-and bimanual postures so it was decided to include him in the "Finger < Hand" subgroup to avoid over representing an atypical pattern.

b Dissociations: unimanual finger < bimanual finger symmetrical, or unimanual hand < bimanual hand symmetrical uncrossed postures.

c Dissociation: unimanual finger > bimanual finger symmetrical postures.

d Dissociations: bimanual finger asymmetrical < bimanual finger symmetrical, or bimanual hand asymmetrical crossed < bimanual hand symmetrical crossed postures.

e Dissociation: bimanual hand asymmetrical crossed > bimanual hand symmetrical uncrossed.

f Dissociation: bimanual hand symmetrical crossed < bimanual hand symmetrical uncrossed.

FIGURE 1 .

 1 FIGURE 1. MEANINGLESS POSTURES

TABLE 2 . DEMOGRAPHIC AND CLINICAL DATA

 2 Notes. Data between brackets are standard deviations. Bold values are significant differences between patients and healthy controls. Missing data due to comprehension impairments, depressive symptoms or scheduling issues: a n = 6;

		HC group	SD group	AD group	FPN group
		N = 32	N = 16	N = 32	N = 15
	Women/men	22/10	8/8	22/10	10/5
	Age (M, (SD))	75.4 (6.4)	67.3 (7.4)	77.1 (7.4)	69.5 (6.1)
	Years of education (M, (SD))	12.3 (4.7)	12.1 (2.8)	9.0 (4.3)	9.4 (5.1)
	MMSE	27.3 (1.8)	22.8 (4.9) a	20.1 (2.7)	18.8 (7.0) c
	FAB	-	12.8 (2.7) a	12.9 (2.4)	11.6 (3.7) b
	BEC 96 Total	87.6 (5.3)	62.1 (14.1) b	67.0 (8.8)	62.4 (20.6) c
	Working memory	11.7 (1.6)	10.8 (3.0)	11.5 (2.2)	10.0 (4.1)
	Orientation	11.5 (1.0)	9.3 (3.5)	5.5 (3.9)	8.3 (4.2)
	Verbal learning	10.7 (1.5)	6.8 (2.9)	6.6 (2.8)	6.9 (3.9)
	Visual recognition	10.8 (1.0)	8.3 (2.7)	5.2 (2.3)	7.3 (2.9)
	Verbal reasoning	9.1 (1.9)	6.7 (2.7)	8.7 (2.0)	6.3 (2.9)
	Verbal fluency	11.7 (1.1)	4.9 (2.7)	9.6 (2.7)	9.3 (3.7)
	Naming	11.4 (0.8)	4.6 (2.7)	10.2 (1.9)	9.1 (2.3)
	Visuoconstructive skills	10.9 (1.4)	10.8 (2.2)	9.8 (2.7)	4.5 (4.9)

b n = 4; c n = 3. HC: Healthy controls; SD: Semantic dementia; AD: Alzheimer's disease; FPN: Frontal-parietal network.

TABLE 3 . SEVERITY OF IMITATION DEFICIT AND RELATIONSHIP TO COGNITION

 3 Notes. Values between brackets are standard deviations.

			N cases			Cognitive scores
	N imitation conditions impaired	SD	AD	FPN	MMSE (0-30)	FAB (0-18)	BEC Visuoconstruc-tive score (0-12)
	0	11	17	2	21.0 (3.6)	13.6 (2.4)	10.4 (2.3)
	1-2	5	7	3	22.1 (2.9)	12.3 (2.5)	9.6 (3.2)
	3-4	0	8	0	18.9 (4.1)	12.1 (2.4)	9.0 (3.5)
	5-6	0	0	7	19.0 (6.9)	11.5 (2.5)	6.0 (4.6)
	7	0	0	3	15.0 (7.9)	10.3 (4.8)	0.0 (0.0)

TABLE 4 . GROUP PERFORMANCE ON IMITATION TASKS

 4 Notes. Mean score: bold values are significant comparisons (p < .05) with the HC group (two-way ANOVA with Group x Condition, and posthoc Tukey HSD tests with p-value adjustment). N patients with pathological score: bold values are significant comparisons (p < .05) with the SD group (Chi-square or Fisher tests with N NORMAL/N IMPAIRED and GROUP/GROUP factors). The SD group was used in this comparison because SD patients had normal to subnormal performance, and because it allowed to address the ventral-dorsal hypothesis of imitation.

		Unimanual			Bimanual
				Finger		Hand
				Asymmetric	Symmetric	Asymmetric	Symmetric	Symmetric
	Group	Finger (A)	Hand (B)	(C)	(D)	crossed (E)	crossed (F)	uncrossed (G)	Total score
	Mean score (Standard deviation)
	HC	98.4 (3.7)	97.3 (5.4)	58.4 (19.4)	82.2 (19.5)	80.6 (22.9)	92.8 (11.1)	93.1 (13.5)	88.8 (8.4)
	SD	99.4 (2.5)	97.8 (4.1)	48.8 (28.3)	81.3 (23.1)	77.5 (23.2)	98.8 (3.4)	93.3 (6.2)	88.5 (7.4)
	AD	96.4 (7.6)	96.4 (5.7)	24.8 (24.2)	64.4 (26.8)	58.0 (24.8)	86.8 (15.5)	92.0 (11.5)	79.1 (9.8)
	FPN	60.7 (31.5)	74.6 (25.5)	16.0 (25.0)	28.0 (31.0	30.0 (39.6)	53.3 (36.4)	67.3 (31.5)	50.6 (28.7)
	N (%) patients with pathological score
	Cut-off	<91	<87	<19	<42	<34	<70	<66	<72
	SD	1 (6)	0 (0)	3 (19)	2 (13)	1 (6)	0 (0)	0 (0)	0 (0)
	AD	7 (22)	3 (9)	11 (34)	7 (22)	4 (13)	2 (6)	1 (3)	6 (19)
	FPN	13 (87)	9 (64)	10 (67)	11 (73)	10 (67)	9 (60)	4 (27)	11 (73)
	Mean t-scores (Standard deviation)
	SD	0.2 (0.7)	0.1 (0.8)	-0.5 (1.4)	0.0 (1.2)	-0.1 (1.0)	0.5 (0.3)	0.2 (0.5)	0.0 (0.9)
	AD	-0.5 (1.8)	-0.2 (1.1)	-1.6 (1.2)	-0.9 (1.2)	-0.9 (1.1)	-0.5 (1.4)	-0.1 (0.8)	-1.1 (1.1)
	FPN	-10.0 (8.4)	-4.1 (4.6)	-2.2 (1.3)	-2.7 (1.6)	-2.2 (1.7)	-3.5 (3.2)	-1.9 (2.3)	-4.5 (3.4)

TABLE 5 . BETWEEN-TASK DISSOCIATIONS AND LINKS TO COGNITION

 5

				N cases			Cognitive scores
	Effect	Dissociation	SD (n = 16)	AD (n = 32)	FPN (n = 15)	MMSE (0-30)	FAB (0-18)	BEC -Visuoconstru ctive score (0-
								12)
	Body part	Finger < Hand a	1	5	7	17.5 (5.3)	11.1 (2.2)	4.9 (4.6)
		No dissociation	15	27	8	21.1 (4.0)	13.1 (2.7)	10.0 (2.9)
	Bimanual	Unimanual < Bimanual b	1	3	10	16.6 (5.3)	10.6 (3.2)	3.8 (3.7)
		Unimanual > Bimanual c	2	5	0	21.0 (2.3)	12.5 (2.6)	9.3 (3.7)
		No dissociation	13	24	5	21.2 (4.1)	13.3 (2.4)	10.3 (2.7)
	Symmetry	Asymmetrical < Symmetrical d	3	8	0	21.4 (4.2)	13.0 (2.3)	10.8 (1.6)
		Asymmetrical > Symmetrical e	0	1	2	19.0 (4.2)	10.0 (2.5)	3.7 (1.5)
		No dissociation	13	23	13	20.1 (4.6)	12.8 (3.4)	8.7 (3.6)
	Midline crossing	Crossed < Uncrossed f	0	4	7	19.4 (5.6)	11.8 (3.6)	7.4 (5.0)
		No dissociation	16	28	8	20.5 (4.3)	12.8 (2.5)	9.1 (3.7)

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 from the Région Pays de la Loire (Project Outils et Vie Quotidienne/Tool use and Daily Life Activities, 2012-09689 OVQ), and was performed within the framework of the LABEX CORTEX (ANR-11-LABX-0042) of Université de Lyon, within the program "Investissements d'Avenir" (ANR-11-IDEX-0007; F. Osiurak,) operated by the French National Research Agency (ANR).

DATA AVAILABILITY STATEMENT

The authors confirm that the data supporting the findings of this study are available within the article [and/or] its supplementary materials.

Notes. Multiple linear regression performed on the whole clinical sample (without healthy controls), testing how the MMSE, visuoconstructive, and executive (FAB) scores predicted the imitation scores. "df": degrees of freedom.