Tjeerd W Boonstra

Stéphane Perrey
email: stephane.perrey@umontpellier.fr

Grégoire Vergotte

Muthuraman Muthuraman

Stefan Janaqi

Kjerstin Torre

Concurrent Changes of Brain Functional Connectivity and Motor Variability When Adapting to Task Constraints

Keywords: adaptability, fNIRS, modularity, fractal properties, tapping

In behavioral neuroscience, the adaptability of humans facing different constraints has been addressed on one side at the brain level, where a variety of functional networks dynamically support the same performance, and on the other side at the behavioral level, where fractal properties in sensorimotor variables have been considered as a hallmark of adaptability. To bridge the gap between the two levels of observation, we have jointly investigated the changes of network connectivity in the sensorimotor cortex assessed by modularity analysis and the properties of motor variability assessed by multifractal analysis during a prolonged tapping task. Four groups of participants had to produce the same tapping performance while being deprived from 0, 1, 2, or 3 sensory feedbacks simultaneously (auditory and/or visual and/or tactile). Whereas tapping performance was not statistically different across groups, the number of brain networks involved and the degree of multifractality of the inter-tap interval series were significantly correlated, increasing as a function of feedback deprivation. Our findings provide first evidence that concomitant changes in brain modularity and multifractal properties characterize adaptations underlying unchanged performance. We discuss implications of our findings with respect to the degeneracy properties of complex systems, and the entanglement of adaptability and effective adaptation.

INTRODUCTION

The huge ability of the brain to exploit its inherent plasticity to adapt to intrinsic or extrinsic constraints over different time scales is stunning and vital (Bassett et al., 2011;[START_REF] De | Graph analysis of functional brain networks: practical issues in translational neuroscience[END_REF]. Depending on circumstances, adaptability may take the form of robustness against changing conditions as well as the form of innovation and evolvability [START_REF] Whitacre | Degeneracy: a link between evolvability, robustness and complexity in biological systems[END_REF][START_REF] Whitacre | Degeneracy: a design principle for achieving robustness and evolvability[END_REF]. In a complementary way the brain allows for preserving a given cognitive-motor performance in the face of tumor growth and resection [START_REF] Duffau | The huge plastic potential of adult brain and the role of connectomics: new insights provided by serial mappings in glioma surgery[END_REF] as well as diversifying the repertoire of our cognitive-motor behaviors with learning, for example (Bassett et al., 2011;[START_REF] Dayan | Neuroplasticity subserving motor skill learning[END_REF]. While some studies has focused on the precise neuro-physiological mechanisms sustaining the brain's capacity to adapt, others have provided insight into more generic organization principles inherent in complex systems, notably through the assessment of brain network connectivity (e.g., [START_REF] Tononi | A measure for brain complexity: relating functional segregation and integration in the nervous system[END_REF][START_REF] Mcintosh | Interactions of prefrontal cortex in relation to awareness in sensory learning[END_REF][START_REF] Sporns | From simple graphs to the connectome: networks in neuroimaging[END_REF][START_REF] Tognoli | The metastable brain[END_REF].

From this latter perspective, the brain's functional organization has been conceived as a dynamic balance between functional segregation and integration of subparts of the entire network [START_REF] Friston | Functional and effective connectivity in neuroimaging: a synthesis[END_REF][START_REF] Tononi | A measure for brain complexity: relating functional segregation and integration in the nervous system[END_REF][START_REF] Sporns | Network attributes for segregation and integration in the human brain[END_REF]. At a given observation scale, the brain network can thus be assessed as a modular organization, modules being defined as clusters that are densely connected within but weakly connected between them [START_REF] Bullmore | Generic aspects of complexity in brain imaging data and other biological systems[END_REF][START_REF] Bassett | Understanding complexity in the human brain[END_REF][START_REF] Sporns | Modular brain networks[END_REF]. Moreover, complexity is increased by the dynamic properties of the functional connections within and between modules, which may compose and recompose depending on circumstances. In particular, such connectivity scheme is closely related to degeneracy, a key property characterizing the structure-function relationship in the brain [START_REF] Tononi | Measures of degeneracy and redundancy in biological networks[END_REF][START_REF] Noppeney | Degenerate neural systems sustaining cognitive functions[END_REF]. Degeneracy refers to a manyto-one structure-function relationship, with a partial functional overlapping between modules of the network: different parts may perform the same function or specialized functions under circumstances [START_REF] Edelman | Degeneracy and complexity in biological systems[END_REF][START_REF] Price | Degeneracy and cognitive anatomy[END_REF][START_REF] Whitacre | Degeneracy: a design principle for achieving robustness and evolvability[END_REF]. Together, the modular and degenerate properties of network connectivity constitute an essential basis for adaptability, supporting robustness and adaptive changes facing various conditions [START_REF] Jirsa | Towards the virtual brain: network modeling of the intact and the damaged brain[END_REF][START_REF] Whitacre | Degeneracy: a link between evolvability, robustness and complexity in biological systems[END_REF][START_REF] Bassett | Understanding complexity in the human brain[END_REF][START_REF] Grefkes | Cortical reorganization after stroke: how much and how functional?[END_REF]. The variety of the dynamical states or network configurations involved to maintain a given function or performance, whether at rest [START_REF] Deco | Emerging concepts for the dynamical organization of resting-state activity in the brain[END_REF] or during a task may thus basically reflect adaptation to changing conditions.

Developing in parallel in a bio-behavioral literature, a significant amount of research focusing on the temporal dynamics of diverse macroscale variables (e.g., heartbeat intervals, [START_REF] Ivanov | From 1/f noise to multifractal cascades in heartbeat dynamics[END_REF]; force production, [START_REF] Athreya | Feedback about isometric force production yields more random variations[END_REF]gait and coordination dynamics, Hausdorff et al., 1996;inter-tapping intervals, Torre and Delignières, 2008) has considered that fractal fluctuations are the hallmark of underlying dynamic complexity and system's adaptability [START_REF] Ivanov | Stochastic feedback and the regulation of biological rhythms[END_REF][START_REF] Gilden | Cognitive emissions of 1/f noise[END_REF][START_REF] Ashkenazy | A stochastic model of human gait dynamics[END_REF][START_REF] Kello | Scaling laws in cognitive sciences[END_REF][START_REF] Manor | Physiological complexity and system adaptability: evidence from postural control dynamics of older adults[END_REF][START_REF] Torre | Disentangling stability, variability and adaptability in human performance: focus on the interplay between local variance and serial correlation[END_REF][START_REF] Delignières | Degeneracy and long-range correlations[END_REF]. Notably, a breakdown of the fractal properties in pathological and/or elderly compared to young and healthy subjects has been evidenced repeatedly, supporting the idea that loss of fractal properties can be considered a marker of the general loss of adaptability coming along with aging and disease [START_REF] Goldberger | Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside[END_REF][START_REF] Hausdorff | Fractal dynamics of human gait: stability of longrange correlations in stride interval fluctuations[END_REF][START_REF] Peng | Fractal mechanisms in neuronal control: human heartbeat and gait dynamics in health and disease[END_REF]Blaszczyk and Klonowski, 2001;[START_REF] Lipsitz | Dynamics of stability: the physiologic basis of functional health and frailty[END_REF]. In particular, in the context of neurological disorders such as Parkinson, Huntington or Alzheimer diseases, research programs have been assessing the diagnostic and/or prognostic [START_REF] Mäkikallio | Prediction of sudden cardiac death by fractal analysis of heart rate variability in elderly subjects[END_REF][START_REF] Goldberger | Fractal dynamics in physiology: alterations with disease and aging[END_REF][START_REF] Hu | Reduction of scale invariance of activity fluctuations with aging and Alzheimer's disease: involvement of the circadian pacemaker[END_REF] power of fractal properties in sensorimotor variables. Thereby studies have made implicit but strong assumptions on a close relationship between network alterations at the brain level and fractal properties at the effector level. In a complementary vein, the fractal properties of motor variables have been shown sensitive to experimental restriction/augmentation of the sensorial feedbacks available to subject's performance on given tasks [START_REF] Slifkin | Noise, information transmission, and force variability[END_REF][START_REF] Manor | Physiological complexity and system adaptability: evidence from postural control dynamics of older adults[END_REF][START_REF] Athreya | Feedback about isometric force production yields more random variations[END_REF][START_REF] Warlop | Dynamics of revolution time variability in cycling pattern: voluntary intent can alter the long-range autocorrelations[END_REF]. Finally, the literature has evidenced that fractal properties may be variable within a same time series (multifractal series). Different fractal scaling regimes may apply in an intermittent way to different windows of observation within the series, thus reflecting variations in the system's underlying dynamic organization and exploration of new solutions (e.g., [START_REF] Ivanov | From 1/f noise to multifractal cascades in heartbeat dynamics[END_REF][START_REF] Ivanov | Multiscale aspects of cardiac control[END_REF][START_REF] Nunes Amaral | Behavioral-independent features of complex heartbeat dynamics[END_REF][START_REF] Hu | Non-random fluctuations and multi-scale dynamics regulation of human activity[END_REF][START_REF] Stephen | Fractal fluctuations in gaze speed visual search[END_REF][START_REF] Dixon | Multifractal dynamics in the emergence of cognitive structure[END_REF][START_REF] Dutta | Multifractal detrended fluctuation analysis of human gait diseases[END_REF]. In fact, where comparison of the Gaussian properties of any variable of interest may indicate unchanged output across groups or experimental conditions, alterations of its fractal properties often reflect underlying reorganizations in the performing system. To our knowledge, however, the question of whether/to what extent the multiple connectivity patterns forming and reforming in the brain directly spill over into the behavioral outcome remains largely unanswered so far: When the brain adapts facing changing conditions to sustain steady motor-behavioral performance, are the ad hoc reorganizations in network connectivity reflected in some distinctive fractal properties of behavioral variability?

In view of the above literature, the degeneracy or intermittency of functional brain networks may be reflected in the multifractal properties at the behavioral level. Imposing constraints by manipulating the feedbacks available to perform a motor task is likely to alter the expression of degeneracy in the motor output. Therefore, the purpose of the study was to bridge levels of observation to establish a direct relationship between degenerate connectivity patterns enabling adaptation at the brain level, and fractal properties as their dynamic signature in the sensorimotor outcome. Herein we consider adaptability as the capacity to maintain a given function or performance despite changing constraints. Thus, a heuristic experimental paradigm should allow us to manipulate the experimental constraints imposed to subjects in a given task without these manipulations affecting their performance, by virtue of the system's capacity to adapt. In this way, we should be able to assess jointly the variety of patterns of brain connectivity that are involved intermittently during task performance, and the dynamic fractal properties of the task variable. Therefore, we used the well-known finger-tapping paradigm [START_REF] Wing | Response delays and the timing of discrete motor responses[END_REF], where previous literature has showed that experimental deprivations of visual, auditory, or tactile feedbacks are not such as to alter tapping performance (Aschersleben andPrinz, 1995, 1997;[START_REF] Stenneken | The effect of sensory feedback on the timing of movements: evidence from deafferented patients[END_REF][START_REF] Repp | Sensorimotor synchronization: a review of recent research (2006-2012)[END_REF]. Following from the above, we hypothesized that the variety and intermittency of brain networks (degeneracy) involved in the task and the dynamical fractal properties of tapping series would evolve jointly as a function of different conditions of feedback deprivation, while tapping performance should stay invariant.

MATERIALS AND METHODS

Participants

Thirty-two healthy volunteers took part in the study (9 women, 23 men, 26.9 ± 6.3 years of age). All participants signed a written informed consent before participating in the study. All participants were right-handed according to the Edinburgh Handedness Inventory [START_REF] Oldfield | The assessment and analysis of handedness: the Edinburgh inventory[END_REF] and reported normal hearing and normal or corrected vision. None showed any sign of neurological disease, nor reported extensive practice in music. All procedures were approved by the local ethics committee (IRB-EM: 1610C, Montpellier). All participants gave written informed consent in accordance with the Declaration of Helsinki for human experimentation.

Experimental Design and Procedure

The experimental design was an independent-group design, with the experimental factor being the numbers of sensorial feedbacks the participants were deprived from. Participants were randomized to one of the four following conditions: (i) no feedback deprivation (Control), (ii) deprivation of one feedback, either visual, or auditory, or tactile (-1 FB); (iii) simultaneous deprivation of two feedbacks, either visual and auditory, or visual and tactile, or auditory and tactile (-2 FB); (iv) simultaneous deprivation of three feedbacks, visual, auditory and tactile (-3 FB). Participants were deprived of visual and auditory feedbacks using a sleeping mask and ear defenders, respectively. The tactile feedback was prevented by the means of a removable striking surface at the place where the index finger tapped ("air tapping, " e.g., [START_REF] Aschersleben | Delayed auditory feedback in synchronization[END_REF]. Each participant performed three tapping trials in the assigned conditions. As mentioned above, none of the visual, auditory or tactile deprivations should alter tapping performance (Aschersleben andPrinz, 1995, 1997;[START_REF] Repp | Sensorimotor synchronization: a review of recent research (2006-2012)[END_REF], and no study to our knowledge conveys strong assumptions about any differential effect of these conditions on the temporal structure of tapping. Nevertheless, rather than arbitrarily removing one of the three feedbacks for each participant or for a whole group, participants of the -1 FB group performed one trial in each of the visual, auditory and tactile feedback deprivation conditions in a random order. Likewise, participants of the -2 FB group performed one trial in each of the visual-auditory, visual-tactile, and auditorytactile deprivation conditions in a random order. Participants of the Control and -3 FB groups performed three times the same.

The Tapping Task

The experiment was conducted in a quiet room. Participants were sitting comfortably on an adjustable chair, with their dominant side forearm and palm of the hand resting on a customized plinth (570 × 160 × 50 mm) on a table in front of them. Subjects realized a tapping task according to a conventional synchronization-continuation paradigm [START_REF] Wing | Response delays and the timing of discrete motor responses[END_REF][START_REF] Vergotte | Dynamics of the human brain network revealed by timefrequency effective connectivity in fNIRS[END_REF]: during the initial synchronization phase, the tempo was prescribed by a PCdriven auditory metronome delivering 20 signals at a frequency of 1.5 Hz (0.666 s inter-tap intervals), known as a comfortable tapping frequency [START_REF] Fraisse | L'anticipation de stimulus rythmiques. vitesse d'établissement et précision de la synchronisation[END_REF][START_REF] Torre | Unraveling the finding of 1/f β noise in selfpaced and synchronized tapping: a unifying mechanistic model[END_REF]. Once the metronome stopped, participants had to continue tapping by maintaining the prescribed tempo as accurately and regularly as possible for the whole trial duration. The duration of each trial was set to 6 min 40 s so as to ensure a sufficient number of inter-tap intervals to be submitted to subsequent fractal analysis [START_REF] Delignieres | Fractal analyses for 'short'time series: a re-assessment of classical methods[END_REF][START_REF] Eke | Pitfalls in fractal time series analysis: fMRI BOLD as an exemplary case[END_REF]. Between each of the three trials, participants had a 2-min rest.

Data Collection

Tapping Performance

Movements of the index finger were captured using a single-axis accelerometer (15 × 15 mm) fixed on the nail so as to minimize possible device-induced sensorial feedbacks. Acceleration data were collected using a Labjack U12 device and stored via its software (LJStream v1.07). The sampling rate was 300 Hz.

Functional Near-Infrared Spectroscopy Measurements

Hemodynamic changes in the cortex during the tapping tasks were measured by two synchronized continuous waves (CW) multi-channel functional near infrared spectroscopy (fNIRS) devices (Oxymon MkIII and Octamon, Artinis Medical Systems, The Netherlands) with a sampling rate of 10 Hz. fNIRS is an optical method using near-infrared light to measure relative changes of oxyhemoglobin (O 2 Hb) and deoxyhemoglobin (HHb) in the cortex [START_REF] Scholkmann | A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology[END_REF]. In the present study, a customized cap was used to place beside the vertex (Cz) a 16-channels array on three regions of interest [premotor cortex (PMC), primary motor cortex (M1) and supplementary motor cortex (SMA)] on both hemispheres. Another 8-channel array was placed on the prefrontal cortex [PFC, Nazion (Nz) was the reference point]. Due to different sensibility of light penetration among brain regions using fNIRS [START_REF] Brigadoi | How short is short? Optimum sourcedetector distance for short-separation channels in functional near-infrared spectroscopy[END_REF], the inter-probe distance was fixed at 30 mm for M1, PMC and SMA, and 35 mm for PFC. After positioning all we used a 3D-digitizer (Fastrack, Polhemus, United States) to collect the location of each probe for each subject. NFRI function [START_REF] Singh | Spatial registration of multichannel multi-subject fNIRS data to MNI space without MRI[END_REF] included in the NIRS-SPM toolbox [START_REF] Ye | NIRS-SPM: statistical parametric mapping for near-infrared spectroscopy[END_REF] was used to extract the Montreal Neurological Institute coordinates (MNI). The positioning of the 24 channels (MNI coordinates and Brodmann area correspondences) can be seen in Figure 1.

Data Analysis

Motor Variability Analysis Preprocessing of tapping data

Raw acceleration data were first low-pass filtered using a Butterworth zero-phase digital filter (Frequency = 15 Hz). Then, a MATLAB in-house script (MATLAB 2014b, The MathWorks) for peak detection was used to extract the onsets of the subsequent finger taps. Series of inter-tap intervals (ITI) were then computed as the differences between subsequent tap times. For each trial, the first twenty ITI (corresponding to the synchronization phase) were discarded, and series of 512 ITI in the continuation phase were retained for further analyses. For each ITI series, we computed the typical performance variables used in tapping studies [START_REF] Billon | The role of sensory information in the production of periodic finger-tapping sequences[END_REF][START_REF] Repp | Sensorimotor synchronization: a review of recent research (2006-2012)[END_REF], namely the mean, the coefficient of variation (CV) and the linear drift over the trial duration.

Characterizing fractal properties of inter-tap interval series

Fractal time series are basically characterized by fluctuations with scale invariant structure [i.e., obeying a power law distribution X(ct) = c H X(t), where X is the signal, c is a constant, H is the fractal exponent] and temporal long-range correlations (meaning the autocorrelation function of the time series decays as a powerlaw without falling to zero). To analyze the fractal properties of ITI series, we used the Multifractal Detrended Fluctuation Analysis [START_REF] Ivanov | Multifractality in human heartbeat dynamics[END_REF][START_REF] Kantelhardt | Multifractal detrended fluctuation analysis of nonstationary time series[END_REF]MFDFA, Ihlen, 2012). MFDFA is derived from the original Detrended Fluctuation Analysis (DFA), which estimates the monofractal properties of a time series [START_REF] Peng | Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series[END_REF]. In short, DFA exploits the diffusion properties of the time series, analyzing the relationship between the average amplitude of fluctuations and the size of the observation window within which these fluctuations are measured. For fractal series, a power-relationship characterized by the monofractal exponent α ε [0, 2] is expected: in particular, for α = 0.5 the series is white noise, for α = 1, the series is so-called 1/f noise, and for 0.5 < α < 1 the series is considered stationary and containing persistent longrange correlations. By yielding a single fractal exponent (α) characterizing the average fractal properties of a time series, the DFA assumes that the fractal properties are homogeneous over all scales of the entire time series.

However, instead of being characterized by a single homogeneous fractal exponent, time series of bio-behavioral variables are often characterized by an inhomogeneous distribution of variability (intermittent fluctuations). The fractal exponent may vary over time scales: the series is actually characterized by multiple fractal exponents [START_REF] Ihlen | Interaction-dominant dynamics in human cognition: beyond 1/f α fluctuation[END_REF] and with this viewpoint the MFDFA was developed [START_REF] Kantelhardt | Multifractal detrended fluctuation analysis of nonstationary time series[END_REF][START_REF] Ihlen | Introduction to multifractal detrended fluctuation analysis in Matlab[END_REF]. Since we hypothesized that the system's adaptations to imposed task constraints would be expressed through the variety of fractal properties in ITI series, we opted for MFDFA analysis. MFDFA basically uses the same steps as DFA, but the average amplitude of the fluctuations is calculated using q th order fluctuation function, with q varying from-10 to +10 in steps of 0.5, whereas DFA computes the amplitude of fluctuations only for q = 2. In brief, the time series x(i) is first integrated into X(k), and divided into N n adjacent segments of length n. Within each segment (s = 1, . . . , N n ) the local trend is then subtracted from X(k). So, the amplitude of fluctuations is computed for each detrended segment according to:

F 2 (n, s) = 1 n sn k = (s-1)n+1 [X(k) -X n,s (k)] 2 (1)
The variance is then averaged over all segments to obtain the q th order fluctuation function:

F q (n) = 1 N n N n s = 1 [F 2 (n, s)] q/2 1/q
(2)

If the series x(i) presents fractal properties, the generalized Hurst exponent h(q) is given by:

F q (n) ∝ n h(q) (3)
According to [START_REF] Kantelhardt | Multifractal detrended fluctuation analysis of nonstationary time series[END_REF], the result of MFDFA can then be converted into the classical multifractal formulation using simple transformations, to be finally summarized by the multifractal spectrum representing F(α) as a function of α(q), where F(α) is the fractal dimension (or dimension of the subset of the series that is characterized by α), and α is the Hölder (or singularity) exponent (see Figure 2). Our variable of interest is the width of the multifractal spectrum (MF-Width), meaning the range between the minimum and maximum exponents α(q) characterizing the time series, which represents the degree of multifractality. Figure 2 illustrates the distinction between mono and multifractal properties of two experimental time series as assessed by DFA and MFDFA.

Brain Connectivity Analysis fNIRS preprocessing

A common approach as described in [START_REF] Huppert | HomER: a review of time-series analysis methods for near-infrared spectroscopy of the brain[END_REF] was used to obtain O 2 Hb and HHb concentration changes. We extracted 6 min of raw (light intensity) data after the end of the metronome using the ARTINIS software (Oxysoft v3.0.95). Data were then uploaded in MATLAB. We first converted intensity data to optical density (OD). Then we applied the moving standard deviation and spline interpolation methods (SDThresh = 20, AMPThresh = 0.5, tMotion = 0.5 s, tMask = 2 s and p = 0.99; [START_REF] Scholkmann | How to detect and reduce movement artifacts in near-infrared imaging using moving standard deviation and spline interpolation[END_REF], combined with wavelet artifact correction (iqr = 0.1; [START_REF] Molavi | Wavelet-based motion artifact removal for functional near-infrared spectroscopy[END_REF] as recommended in [START_REF] Cooper | A systematic comparison of motion artifact correction techniques for functional near-infrared spectroscopy[END_REF] to remove possible head motion artifacts. To retrieve the relative concentration changes (expressed in µM) of O 2 Hb and HHb, we applied the modified Beer-Lambert law [START_REF] Kocsis | The modified Beer-Lambert law revisited[END_REF] on OD data, by including an age-dependent constant differential path length factor (4.99 + 0.067 × Age 0.814 ). The presence of a strong cardiac oscillation (frequency peak around 1 Hz) in the power spectrum of O 2 Hb signal indicates a good contact between the optical probe and the scalp [START_REF] Themelis | Near-infrared spectroscopy measurement of the pulsatile component of cerebral blood flow and volume from arterial oscillations[END_REF]. 6.25% of all channels analyzed did not satisfy this condition and were discarded. For subsequent analysis, a band pass zero-phase digital filter (4th order Butterworth, cut-off frequency [0.009 0.08]) was used to remove physiological noise like cardiac, respiratory, Mayer waves and very low frequencies [START_REF] Scholkmann | A review on continuous wave functional near-infrared spectroscopy and imaging instrumentation and methodology[END_REF]. A linear detrending was then used to remove possible slow drifts.

Functional connectivity analysis

In the line of assessing functional network connectivity free from the constraint of neuroanatomical a-priori assumptions, the most commonly used method is based on the bivariate Pearson's correlation analysis [START_REF] Biswal | Functional connectivity in the motor cortex of resting human brain using echo-planar MRI[END_REF]: it consists in computing the statistical dependency between two or more time series to explore the influence that one region of interest exerts on others (seed based correlation analysis), or in computing all possible connections at the level of the entire brain (whole brain correlation analysis), at rest or during a task [START_REF] Medvedev | Does the resting state connectivity have hemispheric asymmetry? A near-infrared spectroscopy study[END_REF].

Then an N × N adjacency matrix was constructed, reflecting the strength of the correlation between each time series. However, different studies applying such analyses have implicitly considered that patterns of connectivity were stationary and computed an average matrix over the whole scanning period. Instead, to assess the dynamic functional connectivity (dFC) between the present 24 fNIRS channels, we used a sliding window correlation analysis as proposed in the literature [START_REF] Hutchison | Dynamic functional connectivity: promise, issues, and interpretations[END_REF]. For each subject, this method yielded a number n of matrices depending on the window size and a shift (in samples), summarizing the evolution of all connections between channels over time. As there is no consensus in the literature we used three widespread window sizes (30, 75, and 120 s; [START_REF] Hutchison | Dynamic functional connectivity: promise, issues, and interpretations[END_REF] and a shift of 1 sample (100 ms). Figure 3 illustrates the pipeline for these analyses.

Modularity analysis

Once obtained the time evolution for all connections, one of the main challenges in dFC analysis is to classify the multiple networks obtained with reliable metrics [START_REF] De | Graph analysis of functional brain networks: practical issues in translational neuroscience[END_REF]. A network is a collection of nodes (vertices) and links (edges). All networks are represented mathematically through their connectivity (adjacency) matrices. Rows and columns correspond to nodes and entries denote links that are weighted. Based on the graph theory analysis, one of the relevant methods to extract the number of different communities involved during the task is the modularity analysis [START_REF] Newman | Modularity and community structure in networks[END_REF][START_REF] Rubinov | Complex network measures of brain connectivity: uses and interpretations[END_REF]. Modularity quantifies the degree to which the network may be subdivided into delineated and no overlapping groups. In other words, modularity reflects strong links within each community and weaker links between communities. The Modularity (Q) for a partition in communities m = [m1, . . . , mn] of a weighted undirected graph is defined [START_REF] Watts | The "new" science of networks[END_REF][START_REF] Newman | Modularity and community structure in networks[END_REF][START_REF] Rubinov | Complex network measures of brain connectivity: uses and interpretations[END_REF] as:

Q w (m1, ...,mn) = 1 l w i,j ∈ N w ij - k w i k w j l w δ mi,mj (4)
where w ij is the weight of the edge between node i and node j. The set of weights fits into a matrix w that represents the graph G. Here w ij is the correlation between the row i and row j of functional O 2 Hb matrix. Rows and columns of the square matrix G are indexed by the nodes of G (that is the time index of O 2 Hb matrix). When connections are non-oriented (as in the present study) this matrix G is symmetric: weight w ij = w ji and k i is the weight of vertex i that is the sum of w ij for all vertices j. The number l w is the total sum of weights. Modularity and the left-hand side accounts for the influence of low amplitude fluctuations (q negative). The width of the multifractal spectrum is then calculated by the difference α(q) maxα(q) min . Comparison of plots (B,C) shows that while both time series present globally the same monofractal exponent, the blue series is close to monofractal whereas the red one is clearly multifractal. optimization was done based on the assumption that a graph partitioning is the difference between the number of edges within the partitions found and the number of expected edges at random between vertices of an equivalent degree distribution [START_REF] Newman | Modularity and community structure in networks[END_REF]. In this formalism, the ratio k w i k w j /l w gives the null model, that is the probability that a random edge with a random weight w ij joins the nodes i and j [START_REF] Newman | Modularity and community structure in networks[END_REF]. Nodes of G are partitioned between the sets m1,. . . ,mn. So, m i is the set of the actual partition that contains vertex i. The δ (mi,mj) (delta of Dirac) function for given vertices i and j takes the value 1 if i and j are in the same subset of the partition (that is m i = m j ), and 0 otherwise. Importantly, in our study we used the modularity analysis across all time steps and not for each graph. We then considered that distinct community detected should reflect different network organization without extracting the exact topological organization. We determined the communities in each of these graphs by the algorithm that maximizes the modularity (see Equation 4) from the Brain Connectivity Toolbox [START_REF] Rubinov | Complex network measures of brain connectivity: uses and interpretations[END_REF].

Statistical Analysis

After normality testing (Lilliefors test), between-group differences were tested using one-way ANOVA on the three tapping performance variables (mean, CV and drift of ITI series), and on MF-Width with respect to our main hypothesis. Secondarily we also checked for any between-group difference in the monofractal exponent (α). We used Kruskal Wallis analysis, as the data were not normally distributed for the three sliding window sizes of community detection analysis. We used Spearman's correlation between the number of networks detected for each sliding window size (30, 75, and 120 s) and MF-Width of the tapping series.

RESULTS

Tapping Performance

All samples of the tapping performance variables (mean, CV, and drift) were normally distributed. Our experimental design was thought to impose different levels of constraints to the subjects without inducing differences in tapping performance. The ANOVA applied to the performance showed no significant difference between groups for all variables [mean: F (3, 28) = 1.519; p = 0.230; η 2 = 0.136, CV: F (3, 28) = 2.316; p = 0.523; η 2 = 0.045, drift: F (3, 28) = 0.634; p = 0.594; η 2 = 0.022, Figure 4].

Multi-Fractal Properties of Tapping Series

MF-Width samples were normally distributed after log-normal correction. The one-way ANOVA revealed a significant group effect [F (3, 28) = 2.822; p = 0.044; η 2 = 0.253]. LSD Fisher posthoc showed differences between the control group and the -1 FB and -2 FB groups (p = 0.012 and p = 0.021, respectively). Figure 5 summarizes the results obtained for the multifractal properties of tapping time series. Monofractal exponents (α) were normally distributed, and the one-way ANOVA did not show any significant difference between groups [F (3,28) = 0.845; p = 0.473; η 2 = 0.071].

Modularity Analysis

For all considered sliding window sizes, Kruskal Wallis test showed significant differences between Control and -1 FB, -2 FB and -3 FB groups [for 30 s: H (3) = 18.7, p = 0.003; η 2 = 0.561; for 75 s: H (3) = 18.5, p = 0.001; η 2 = 0.554; for 120 s: H (3) = 18.9; p = 0.003; η 2 = 0.568]. All corrected p-values for multiple comparisons are reported in Table 1. Results for each window size are shown in Figure 6.

Relationship Between Modularity in the Brain and Fractal Properties in Behavior

With regard to our main hypothesis, results showed a significant correlation (Figure 7) between MF-Width in tapping series and the number of brain networks detected for window sizes 30 s (rho = 0.277; p = 0.028) and 75 s (rho = 0.275; p = 0.038). However no significant correlation was found for window size 120 s (rho = 0.086; p = 0.526).

DISCUSSION

The present study aimed to establish a relationship between connectivity patterns underlying adaptation at the brain level and fractal properties as their dynamic signature in the behavior. We hypothesized that the number of brain networks involved in the task and the multifractal properties of the tapping series would evolve jointly, as a function of different conditions of feedback deprivation. We found that (i) the degree of multifractality (MF-Width) increased significantly in groups where feedbacks were suppressed as compared to the control group; (ii) the number of networks involved during the task was higher for groups with feedback deprivation than for the control group; and (iii) MF-Width and the number of networks involved in the task were correlated for sliding windows of 30 and 75 s. After discussing the suitability of the experimental design, we consider some notable implications of our results at the behavioral and brain levels, respectively, before focusing more specifically on the brain-behavior relationship.

Suitability of the Experimental Design

We considered the general definition of adaptability as the capacity to maintain a given function or performance despite changing constraints [START_REF] De Wolf | Emergence versus self-organisation: different concepts but promising when combined[END_REF], also referred to as robustness [START_REF] Whitacre | Degeneracy: a link between evolvability, robustness and complexity in biological systems[END_REF]. In this line, the experimental paradigm was required in order to impose different experimental constraints while leaving the global level of task performance substantially close: the system was thus deemed to handle adaptations-notably reorganization in brain-allowing for sustained performance. To meet these requirements, we used a finger-tapping task. A major advantage of such task was to allow for a simple manipulation of the amount of sensory feedbacks available (-1 FB,-2 FB,-3 FB), while overall tapping performance has previously been shown insensitive to feedback manipulations (Aschersleben andPrinz, 1995, 1997;[START_REF] Repp | Sensorimotor synchronization: a review of recent research (2006-2012)[END_REF]. That is, in the present study feedback manipulation has merely constituted a means to constrain the system and induce putative internal adaptation/reorganization, without any specific hypothesis as regards the sensory modalities. In this respect, our results are congruent with the literature [START_REF] Aschersleben | Delayed auditory feedback in synchronization[END_REF], as we observed no significant differences between conditions of feedback deprivation in any of the three variables commonly characterizing tapping performance (mean ITI, CV and drift; Figure 4). Moreover, such tapping task has previously been shown to entail fractal properties in the ITI series produced [START_REF] Lemoine | Testing for the presence of 1/f noise in continuation tapping data[END_REF][START_REF] Torre | Unraveling the finding of 1/f β noise in selfpaced and synchronized tapping: a unifying mechanistic model[END_REF]. Our present results on the monofractal exponent α are also in agreement with

-1 FB/-2 FB 1 1 1 -1 FB/-3 FB 1 1 1 -2 FB/-3 FB 1 1 1 Significant differences are in bold.
the literature in this respect (α = 0.75 ± 0.13 all groups taken together, without significant differences between groups). As regards the experimental design, we opted for an independent group design rather than repeated measures. Although this methodological choice obviously entailed limitations of sample sizes for each group, we deemed it preferable given the lengthy duration of tapping trials required for reliable fractal analysis [START_REF] Delignieres | Fractal analyses for 'short'time series: a re-assessment of classical methods[END_REF][START_REF] Vaz | Effects of visual and auditory guidance on bimanual coordination complexity[END_REF]. Indeed, we aimed to observe the effect of adaptations due to feedback deprivation, which implied avoiding as much as possible any putative effects of weariness and attentional fluctuations that may also alter the fractal properties of tapping series [START_REF] Damouras | An empirical examination of detrended fluctuation analysis for gait data[END_REF]. Finally, in contrast to previous studies we here investigated a motor task with adaptations being experimentally induced by different levels of task constraints. In return, this approach implied some a priori uncertainty as regards the precise effect of experimental constraints especially on brain connectivity, rather than a priori controlled variations as possible in simulation studies for example. All in all, the consistency of our results with previous literature leads us to consider the experimental design suitable, and following results with reasonable confidence.

Multifractal Properties Reflect Adaptations Underlying Unchanged Performance

Further gain of precision in appraising the functional significance of fractal properties in behavioral variables is a still-open challenge. A significant body of literature has converged to the general idea that mono and multifractal properties are a hallmark of the adaptability of biological systems [START_REF] Goldberger | Fractal dynamics in physiology: alterations with disease and aging[END_REF][START_REF] Lipsitz | Dynamics of stability: the physiologic basis of functional health and frailty[END_REF]. However, such conclusions mostly originate from indirect crosssectional observations revealing loss of fractal properties with aging, pathology, or different conditions of functional impairment that are generally associated with loss of adaptability [START_REF] Manor | Physiological complexity and system adaptability: evidence from postural control dynamics of older adults[END_REF][START_REF] Manor | Physiologic complexity and aging: implications for physical function and rehabilitation[END_REF]. Though adaptability (or loss of adaptability) may indeed constitute a common denominator, several potentially confounding effects, including effective adaptations to achieve task performance despite functional impairment, might actually be the cause of altered fractal properties [START_REF] Dingwell | Re-interpreting detrended fluctuation analyses of stride-to-stride variability in human walking[END_REF].

Our present results show significant variations of multifractal properties as a function of feedback deprivation imposed to the system (Figure 5) without significant functional decrement (Figure 4), which does not appear directly relevant to the issue of adaptability. At a first glance, this result may appear congruent with previous studies showing an alteration of monofractal properties as a function of the involvement of sensorial feedbacks in task performance (Slifkin andEder, 2012, 2014): it has indeed been proposed that weaker monofractal properties may be due to tighter sensorimotor control mechanism exerted on taskrelevant variables [START_REF] Dingwell | Re-interpreting detrended fluctuation analyses of stride-to-stride variability in human walking[END_REF][START_REF] Warlop | Dynamics of revolution time variability in cycling pattern: voluntary intent can alter the long-range autocorrelations[END_REF]. However, we observed that the degree of multifractality in tapping series increased in feedback deprivation conditions compared to the control group. Mono and multifractal properties do not capture the same features of time series: whereas monofractal properties summarize a homogeneous scaling behavior over the whole time series, multifractal analyses assess the possibly inhomogeneous scaling regimes present in the series, and capture the amount of intermittent changes in the systems/subjects functioning modes [START_REF] Ihlen | Interaction-dominant dynamics in human cognition: beyond 1/f α fluctuation[END_REF]. Thus, this result suggests an increasing involvement of different modes of regulation to achieve unchanged performance despite the imposed experimental constraints. Accordingly, we support the idea that rather than globally reflecting the adaptability of complex biological systems, changes in multifractal properties reflect effective adaptations underlying invariance of functional outcome.

In this line, characterizing multifractal properties in macroscale variables may constitute a fine-grained analysis to uncover masked adaptations underlying goal achievement. From a broader perspective, disentangling adaptability and effective adaptation actually constitutes a major challenge, as both come necessarily together to a certain extent [START_REF] Ulanowicz | The balance between adaptability and adaptation[END_REF]. Combining analysis at the task-relevant observation level (e.g., the level of motor performance) and an assessment of the correlates occurring at underlying observation levels (e.g., the level of brain dynamics) may contribute to this end.

Changes in Brain Modularity Reflect Functional Adaptation to Constraints

In this study, we hypothesized that the variety and intermittency of functional connectivity patterns would be influenced by different conditions of privation of sensorial feedbacks. Our results show that dynamical reorganizations of the brain network yielded multiple networks that were intermittently involved during task performance (Figures 3,6), and that the number of different networks involved depends on the experimental group, i.e., on the feedbacks subjects were deprived or not. The literature studying brain networks involved in a task has generally considered that for a given function or performance the functional organization of the brain is stable over time. Accordingly, the purpose of investigations has often been to extract the typical network engaged in a given task, using a number of computational methods [START_REF] Biswal | Functional connectivity in the motor cortex of resting human brain using echo-planar MRI[END_REF][START_REF] Witt | Functional neuroimaging correlates of finger-tapping task variations: an ALE meta-analysis[END_REF]. Nevertheless, another part of the literature studying the dynamic properties of functional networks in resting state has showed that the modular organization of the brain evolves within the scanning period [START_REF] Chang | Time-frequency dynamics of restingstate brain connectivity measured with fMRI[END_REF][START_REF] Hutchison | Dynamic functional connectivity: promise, issues, and interpretations[END_REF][START_REF] De | Graph analysis of functional brain networks: practical issues in translational neuroscience[END_REF] and that such natural fluctuations are likely to support the ability of quick adaptive responses [START_REF] Deco | Emerging concepts for the dynamical organization of resting-state activity in the brain[END_REF]. Previous studies using resting paradigm do not enable to reveal the actual implementation of such adaptability during a sensorimotor task. These results complement previous literature insofar as they show that the variety of brain networks that are involved in a single task depends on the experimental constraints imposed to the subjects. More precisely, the counter-intuitive character of these results (i.e., increased number of networks with decreasing feedbacks, Figure 6) could be explained by the fact that, under constraints, the brain navigates between numerous networks to find out the solution enabling achievement of its level of performance [START_REF] Kelso | Outline of a general theory of behavior and brain coordination[END_REF][START_REF] Tognoli | The metastable brain[END_REF]. Such explanation seems consistent with previous studies showing novel recruitment of cortical areas under conditions of chronic sensorial deprivation (blindness, deafness, [START_REF] Merabet | Neural reorganization following sensory loss: the opportunity of change[END_REF], although adaptation to transient experimental manipulations is not directly comparable with lifelong alterations.

From a broader perspective, considering that the brain possesses degenerate properties (i.e., multiple networks could perform the same function with some of them being possibly latent, [START_REF] Edelman | Degeneracy and complexity in biological systems[END_REF], the networks involved in a given function or performance can hardly be grasped in a comprehensive way without imposing internal and/or external constraints so as to induce variation in connectivity patterns [START_REF] Price | Degeneracy and cognitive anatomy[END_REF]. This idea was initially developed in theoretical papers, and few experimental tasks actually allow imposing constraints without changing the motor performance. Electroencephalography, functional magnetic resonance imagery and fNIRS studies [START_REF] Nedelko | Age-independent activation in areas of the mirror neuron system during action observation and action imagery. a fMRI study[END_REF][START_REF] Leff | Assessment of the cerebral cortex during motor task behaviours in adults: a systematic review of functional near infrared spectroscopy (fNIRS) studies[END_REF][START_REF] Muthuraman | Cortical representation of different motor rhythms during bimanual movements[END_REF] showed that the sensorimotor network (e.g., M1, PMC, and PFC) is engaged in a simple short fingertapping task and is supposed to reflect sensory integration, motor initiation and production. Conversely, our results suggest the existence of multiple networks that allow for the carrying out of a tapping task over time. Moreover, there is no single network dedicated specifically to tapping independently of the different conditions under which tapping is to be performed. However, these findings need to be examined with caution due to some methodological consideration. In this study, we used modularity analysis [START_REF] Newman | Modularity and community structure in networks[END_REF][START_REF] Sporns | From simple graphs to the connectome: networks in neuroimaging[END_REF]or community detection, Sporns and Betzel, 2016) at the macro scale level (between networks) and not on each network. One can hypothesize that the latter analysis would make it possible to highlight similar clusters of sub-networks linked in different ways. In particular, it has recently been shown that dynamic connectivity between different brain regions is not only dependent on the regions involved, but also on the interconnections between multiple EEG frequency bands [START_REF] Liu | Plasticity of brain wave network interactions and evolution across physiologic states[END_REF]. Future investigations using EEG combined with fNIRS would allow to better understand the dynamic functional organization of the brain, and the role of multifrequency connections in network coupling. It has been proposed that the modular organization of the brain is subtended by a relatively rigid network composed of nodes distributed in each sub-module [START_REF] Sporns | Network attributes for segregation and integration in the human brain[END_REF]. Nevertheless, although the origin of temporal fluctuations in dFC estimates remains largely unknown, sliding window analysis was shown as a promising method to highlight dynamic connectivity in multiple neuroimaging methods. As the optimal window size to compute correlation coefficient is still under debate [START_REF] Hutchison | Dynamic functional connectivity: promise, issues, and interpretations[END_REF], we used three-window sizes (30, 75, and 120 s, see Figure 7) to be confident in the results obtained. We found a strong statistical difference between the control group and other groups independently of the window size. This confirms our hypothesis and this allows us to confirm that our results are not dependent on the window size chosen (e.g., [START_REF] Hutchison | Dynamic functional connectivity: promise, issues, and interpretations[END_REF][START_REF] Hindriks | Can sliding-window correlations reveal dynamic functional connectivity in resting-state fMRI?[END_REF]. An additional step of our promising results would be to extract the characteristics of the different networks implemented with more fine-grained tools like those proposed in fMRI [START_REF] Bassett | Small-world brain networks[END_REF][START_REF] Bassett | Understanding complexity in the human brain[END_REF][START_REF] Papo | Complex network theory and the brain[END_REF].

Bridging the Gap Between Brain and Behavior

The literature has mostly been studying the dynamics of cerebral networks on one hand, and the temporal structure of behavioral variability on the other hand, though both communities share key concepts coming with the complex system approach [START_REF] Bullmore | Generic aspects of complexity in brain imaging data and other biological systems[END_REF][START_REF] Werner | Fractals in the nervous system: conceptual implications for theoretical neuroscience[END_REF][START_REF] Whitacre | Degeneracy: a design principle for achieving robustness and evolvability[END_REF][START_REF] Sleimen-Malkoun | Aging induced loss of complexity and dedifferentiation: consequences for coordination dynamics within and between brain, muscular and behavioral levels[END_REF]. Thus, attempts to link these two approaches seem valuable [START_REF] Price | Degeneracy and cognitive anatomy[END_REF][START_REF] Friston | Modules and brain mapping[END_REF]. In the present study, we provide novel evidence that the number of networks involved during a motor task in four experimental conditions significantly correlates with the degree of multifractality found in the sensorimotor outcome. This correlation was obtained for two of the three window sizes used (30 and 75 s). Previous literature has highlighted that the dynamics of functional connectivity increase with diminution of the window size, due to the non stationarity of Blood Oxygenation Level Dependent or fNIRS signals for short windows with an increase of transient nodes that were unobserved for large window size [START_REF] Hutchison | Dynamic functional connectivity: promise, issues, and interpretations[END_REF]. Therefore it is not surprising that fewer networks were detected for our largest window (120 s). As a consequence the correlation between the number of networks and the multifractal properties of tapping series was low and not significant for the 120 s window as compared to the smaller windows.

Previous theoretical and simulation approaches had shown that degeneracy plays a central role in the link between complexity, adaptability, and robustness [START_REF] Whitacre | Degeneracy: a link between evolvability, robustness and complexity in biological systems[END_REF] and that degeneracy may underlie fractal properties in the outcome variables [START_REF] Delignières | Degeneracy and long-range correlations[END_REF]. Our result provides experimental support highlighting the link between theoretically related properties across two different scales of observation, namely between degeneracy at the level of brain connectivity and measures of complexity at the level of behavior, both being considered tightly related with systems adaptability. As such this result may be of particular relevance for translational research, since a significant part of literature has proposed to assess the diagnostic and/or prognostic power of fractal properties in sensorimotor variables in neurodegenerative pathologies (e.g., Parkinson or Alzheimer diseases) conveying the strong but so far experimentally unproven assumption that alterations of the brain network would come out in the fractal properties of behavior. Consequently, we consider that (i) fractal properties in macroscale variables are (at least partly) dependent on the degenerate organization properties of the brain, and (ii) concomitant changes in network connectivity and multifractal properties in behavioral variability reflect (at least partly) effective adaptations underlying invariance of functional outcome.

Finally, the system's ability to adapt and effective adaptation go hand in hand [START_REF] Ulanowicz | The balance between adaptability and adaptation[END_REF], the first being a necessary condition for the latter, the latter in turn affecting the first. To be able to disentangle the brain and behavioral correlates of adaptability and adaptation is of importance seeing that evolution toward pathological states or advancing age often come along with a decreased ability to adapt, up to functional loss [START_REF] Lipsitz | Dynamics of stability: the physiologic basis of functional health and frailty[END_REF][START_REF] Manor | Physiological complexity and system adaptability: evidence from postural control dynamics of older adults[END_REF][START_REF] Stergiou | Human movement variability and aging[END_REF]. The joint analysis of motor variability and brain dynamics, as well as the use of an experimental paradigm that allows to gradually constraining the system so as to induce adaptations (maintenance of performance) up to the loss of further capacity to adapt (decrement of performance), may contribute to this end. Extending the present tapping paradigm may be appropriate in this view since, in contrast to visual, auditory or tactile feedbacks, further deprivation of proprioception has been shown to decrease tapping performance [START_REF] Stenneken | The effect of sensory feedback on the timing of movements: evidence from deafferented patients[END_REF]. Our present experimental design was not conceived such as to allow for investigation of putative differential effects among sensory modalities (e.g., auditory and visual cortex), and we limited ourselves to the assessment of sensorimotor and prefrontal regions. Future studies using a larger number of channels (whole brain) may examine in how far the networks dynamics underlying finger tapping are affected depending on the sensory modality suppressed.

CONCLUSION

To what extent the multiple networks in the brain restructure with some distinctive properties of motor variability has remained unanswered so far. Both conceptual considerations and simulation approaches have provided strong indications for such relationship but experimental evidence has been lacking. Our present work evidences a significant correlation between the number of brain networks and the degree of multifractality in tapping. We believe that this finding constitutes a step further toward bridging the gap between the degenerate connectivity patterns at the brain level and the properties of variability at the behavioral level. We anticipate that future work, possibly combining simulation and experimental methods like multimodal neuroimaging, will provide means for larger and/or more fine-grained ranges of variation in the number of brain networks involved and the fractal properties of motor performance, so as to further consolidate our present findings.

FIGURE 1 |

 1 FIGURE 1 | Localization of fNIRS probes, channels, MNI coordinates and Brodmann correspondences. (A) Yellow: transmitters, blue: detectors and red: channels. (B) MNI coordinates for each channel (n = 24) with x, y, and z coordinates. On the right, Brodmann area correspondence (number, name and %) extracted from the NIRS-SPM toolbox (NFRI function).

FIGURE 2 |

 2 FIGURE 2 | Distinction between DFA and MFDFA analysis for mono and multifractal time series. (A) Two experimental time series of 512 pts: in blue, the time series is closely mono-fractal; in red, the time series is multi-fractal. The Y-axis displays an arbitrary unit centered to zero. (B) Results yielded by DFA for the two time series.The plot shows the size of fluctuations F(n) as a function of the size n of observation windows in bi-logarithmic coordinates. The monofractal exponent α is given by the slope of log(F(n)) vs. log(n). According to the plot, both time series present long-range correlations and are characterized by the same monofractal exponent (α = 0.74). (C) Multifractal spectra for the two time series. The right-hand side of the spectrum accounts for the influence of large-amplitude fluctuations (q positive), and the left-hand side accounts for the influence of low amplitude fluctuations (q negative). The width of the multifractal spectrum is then calculated by the difference α(q) maxα(q) min . Comparison of plots (B,C) shows that while both time series present globally the same monofractal exponent, the blue series is close to monofractal whereas the red one is clearly multifractal.

FIGURE 3 |

 3 FIGURE 3 | Illustration of the functional connectivity analysis for one representative subject. (A) Extraction of O 2 Hb fNIRS time series for all channels after preprocessing and band pass filtering (cut off frequency [0.08 0.009]). (B) Sliding window Pearson's correlation analysis for window sizes of 30, 75, and 120 s. (C) Grand average correlation analysis between each matrix. The upper plot shows communities detected for 360 s (3 communities in this example). (D) Grand average matrix after putting in the order of community. Red squares delimit each community.

FIGURE 4 |

 4 FIGURE 4 | Dotplot of tapping performance for the four groups. Left, mean inter-tap intervals (ITI) produced. Middle, Coefficient of variation (CV) of ITI series. Right, drift of ITI series during the task. Error bars represent standard error.

FIGURE 5 |

 5 FIGURE 5 | Degree of multifractality of ITI series (MF-Width) for the four experimental groups. (A) Average multifractal spectrum for each group. (B) Dotplot MF-Width for the four experimental groups; gray horizontal line represent the mean. Star reflects the significant difference at p < 0.05.

FIGURE 6 |

 6 FIGURE 6 | Box plots with median, quartiles, and individual dots for the number of communities detected during the task for the four groups (Control,-1FB,-2 FB, and-3 FB), for (A) sliding window of 30 s, (B) sliding window of 75 s, and (C) sliding window of 120 s. Stars highlight significant difference at p < 0.05.

TABLE 1 |

 1 Corrected p-values of Kruskal Wallis analysis for each sliding window size.

			Window size
		30 s	75 s	120 s
	Control/-1 FB	<0.009	<0.04	<0.03
	Control/-2 FB	<0.003	<0.0002	<0.02
	Control/-3 FB	<0.006	<0.02	<0.01

Frontiers in Physiology | www.frontiersin.org

July 2018 | Volume 9 | Article 909

ACKNOWLEDGMENTS

The PHC PROCOPE 2017 (DAAD and Campus France, Project n • 37815RK) supported this work. Doctoral School (ED 463) in Human Movement Science also made this collaborative project possible. We thank Aïcha Louzir Vergotte for her helpful proofreading, Maxime Logez for his technical support, and Gérard Derosière and Didier Delignières for valuable discussions and comments on the manuscript.

AUTHOR CONTRIBUTIONS

All authors contributed to this study. GV, KT, and SP conceived and designed the study. KT, MM, and SP provided funding. GV performed the experiments. GV, MM, and SJ analyzed the data. GV, KT, and SP wrote the paper and SJ and MM edited the manuscript.

Conflict of Interest Statement:

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Pierre Besson

Makii Muthalib

Gerard Dray

John Rothwell

PhD Stephane Perrey
email: stephane.perrey@umontpellier.fr

Concurrent anodal transcranial direct-current stimulation and motor task to influence sensorimotor cortex activation

Keywords: online, neurovascular coupling, neuromodulation, functional neuroimaging, highdefinition montage, plasticity

 Functional near infrared spectroscopy probed the sensorimotor cortex activity when using online, offline and sham high definition anodal tDCS.

 Online and offline high definition anodal tDCS induced greater cortical activation 30 min after stimulation.

 Concurrent application of high definition anodal tDCS during a motor task induced more pronounced changes in sensorimotor cortex activation

Introduction 1

Transcranial direct current stimulation (tDCS) is a non invasive brain technique used to deliver weak electrical currents through electrodes to modulate cortical excitability in different brain regions (Nitsche and Paulus, 2000;[START_REF] Stagg | Physiological basis of transcranial direct current stimulation[END_REF]. Anodal tDCS (atDCS) is able to increase cortical excitability as reflected by an increase in amplitude of motor evoked potentials evoked at rest after tDCS [START_REF] Jacobson | tDCS polarity effects in motor and cognitive domains: a meta-analytical review[END_REF]. However, recent reports have suggested that around half of healthy subjects do not show the expected excitatory effect following atDCS [START_REF] Chew | Inter-and intra-individual variability in response to anodal tDCS at varying current densities[END_REF][START_REF] Li | The contribution of interindividual factors to variability of response in transcranial direct current stimulation studies[END_REF][START_REF] López-Alonso | Interindividual Variability in Response to Non-invasive Brain Stimulation Paradigms[END_REF][START_REF] Strube | Efficacy and interindividual variability in motor-cortex plasticity following anodal tDCS and paired-associative stimulation[END_REF][START_REF] Vallence | Inter-and intra-subject variability of motor cortex plasticity following continuous theta-burst stimulation[END_REF][START_REF] Wiethoff | Variability in Response to Transcranial Direct Current Stimulation of the Motor Cortex[END_REF]. In addition, there is a relative paucity of knowledge regarding the effects of task-concurrent atDCS on cortical activity in target brain regions.

The use of functional neuroimaging methods based on neurovascular coupling mechanisms allows indirect simultaneous measures to be made of brain activity during (online) and following (offline) tDCS [START_REF] Siebner | Consensus paper: combining transcranial stimulation with neuroimaging[END_REF]. Some early functional magnetic resonance spectroscopy (fMRI) studies investigating offline (after 20 min at 1 mA) and online (during periods of stimulation from 20 s to 2 min at 1 mA) atDCS protocols including motor tasks have reported contrasting findings in brain activation patterns [START_REF] Antal | Transcranial direct current stimulation over the primary motor cortex during fMRI[END_REF]Jang et al., 2009;[START_REF] Kwon | The enhanced cortical activation induced by transcranial direct current stimulation during hand movements[END_REF]. Offline atDCS (20 min, 1 mA)-hand movements increased activation in the targeted sensorimotor cortex (SMC) compared to sham [START_REF] Jang | The effect of transcranial direct current stimulation on the cortical activation by motor task in the human brain: An fMRI study[END_REF].

But online atDCS (8x 20 s, 1mA)-finger movements decreased activation of the supplementary motor area without notable changes over the targeted SMC (Antal et al., Abbreviations. fNIRS, functional near infrared spectroscopy; SFO, simple finger opposition; SMC, sensorimotor cortex; T1, time 1; T2, time 2; tDCS, transcranial direct current stimulation. 2011). In the latter study, the inability to measure alterations of activation in the targeted SMC during online atDCS might have been due to the low intensity (1 mA) and the short duration (20 s) of the stimulation protocol. Conversely, it was observed that online atDCS (2 min, 1 mA)-hand movements induced more SMC activation than sham [START_REF] Kwon | The enhanced cortical activation induced by transcranial direct current stimulation during hand movements[END_REF]. These contradictory findings using short duration and lower intensity atDCS protocols stem from the technological limitation of combined atDCS-fMRI techniques that cause possible distortions in fMRI signals by the tDCS electrical/magnetic fields, as well as subject safety due to heating of tDCS electrodes by the fMRI magnetic field. These limitations have therefore encouraged the search for alternative functional neuroimaging methods to determine the effect of task-concurrent atDCS on SMC activation.

In contrast to fMRI, motor-task related changes in the concentration of oxygenated (O 2 Hb) and deoxygenated (HHb) hemoglobin in the SMC measured by functional nearinfrared spectroscopy (fNIRS), reflect with good sensitivity the hemodynamic response to neuronal activity [START_REF] Leff | Assessment of the cerebral cortex during motor task behaviours in adults: A systematic review of functional near infrared spectroscopy (fNIRS) studies[END_REF] without interference from the tDCS environment. The combined use of atDCS with fNIRS as a relatively simple and safe method offers the possibility to investigate continuously the online and offline effects of atDCS on resting-state [START_REF] Muthalib | Focal Hemodynamic Responses in the Stimulated Hemisphere During High-Definition Transcranial Direct Current Stimulation[END_REF] and task-related SMC hemodynamic response [START_REF] Choe | Transcranial Direct Current Stimulation Modulates Neuronal Activity and Learning in Pilot Training[END_REF][START_REF] Gözenman | Working memory capacity differentially influences responses to tDCS and HD-tDCS in a retro-cue task[END_REF]. atDCS using a high-definition (HD-atDCS) electrode montage (4x1) has been shown to increase the focality and intensity of stimulation at the primary motor cortex target [START_REF] Datta | Gyri-precise head model of transcranial direct current stimulation: improved spatial focality using a ring electrode versus conventional rectangular pad[END_REF]. Our preliminary fNIRS study [START_REF] Muthalib | Effects of Anodal High-Definition Transcranial Direct Current Stimulation on Bilateral Sensorimotor Cortex Activation During Sequential Finger Movements: An fNIRS Study[END_REF] using HD-atDCS (2 mA, 20 min) during a sequential finger opposition (SFO) task found a decrease in task-related activation in the targeted left SMC compared to prestimulation. However, since the after effects of HD-atDCS show peak changes in cortical excitability after a delay of 30 minutes from the cessation of the stimulation [START_REF] Kuo | Comparing Cortical Plasticity Induced by Conventional and High-Definition 4 × 1 Ring tDCS: A Neurophysiological Study[END_REF], it is not known whether task-related SMC activation would also show greater neuromodulatory effects up to 30 min. Moreover, the relative effectiveness of online and offline HD-atDCS protocols to modulate motor task-related SMC activation needs to be clarified in order to develop the most optimal protocol. Therefore, the aim of the present study was to compare the time course of SFO motor task-related modulation of SMC activation between online and offline HD-atDCS protocols in a within-subjects sham-controlled and randomized design. It was hypothesized that online HD-atDCS would impact SFO motor task-related activation in the targeted SMC to a greater extent than both sham and offline HD-tDCS.

Results

Subjective sensation and anxiety when using tDCS

As indicated in Table 1, no difference (F(2,16)=0.633, p=0.544) was observed among the sessions for the resting state cutaneous sensation over the scalp during HD-atDCS, indicating that the participants were unable to differentiate real HD-atDCS from sham sessions. There was no significant difference (F(2,16)=0.440, p=0.652) in STAI values between the sessions.

Movement rate

As indicated in Table 2, there were no significant differences in the SFO movement rate over time (F(2,16)=1.377, p=0.692), between the experimental sessions (F(2,16)=1.167, p=0.337), and between the right and left hands (F(2,16)=1.651, p=0.235).

Functional near-infrared spectroscopy

Figure 1 shows the normalized (only for illustrative purposes) changes in HHb and Hb diff for the online, offline, and sham sessions over time. For HHb (Fig. 1A), there was no effect of Session (F(2,16)=0.098, p=0.907), but there was a Session x Time interaction effect (F (4,32)=3.228, p=0.025, Ƞ²p=0.288) and an effect of Time (F(2,16)=9.616, p=0.002, Ƞ²p=0.546). Post hoc analysis revealed significantly lower HHb (i.e., increased SMC activation) from Pre to T2 for both the online (p<0.0006) and offline (p<0.02) sessions, while there was no significant change for sham. At T2, HHb for the online session was significantly (p<0.01, g=1.08) lower than the sham session, but there was no significant difference in HHb between online and offline (g=0.54) or between offline and sham (g=0.38). At T1, although HHb was significantly (p<0.02, g=-0.63) higher (i.e., decreased SMC activation) for the online than offline session, these changes in HHb were not significantly different to sham (g=-0.48 vs. online, g=0.25 vs. offline).

For Hb diff (Fig. 1B), there was no effect of Session (F(2,16)=1.640, p=0.225), but there was a Session x Time interaction (F(4,32)=2.868, p=0.039, Ƞ²p=0.263) and a main effect of Time (F (2,16)=5.823, p=0.012, Ƞ²p=0.421). Post hoc analysis revealed significantly lower Hb diff (i.e., decreased SMC activation) from Pre to T1 (p<0.03) and higher Hb diff (i.e., increased SMC activation) from Pre to T2 for the online (p<0.02) session, while there was no significant change from Pre for the offline and sham session. At T2, Hb diff was significantly higher (i.e., increased SMC activation) for the online (p<0.0004, g=1.01) session compared to sham, and there was a trend for Hb diff in the online session to be higher than offline (p=0.061, g=0.53), as well as for offline to be higher than sham (p=0.053, g=0.52).

For O 2 Hb, there was no effect for the Session x Time interaction (F(4,32)=1.713, p=0.171) or the main effect of Session (F(2,16)=2.000, p=0.168), but there was a trend for a main effect of Time (F(2,16)=3.570, p=0.052, Ƞ²p=0.309).

Discussion

This study aimed to determine whether motor task-related SMC activation as measured simultaneously by the use of fNIRS would be modulated to a greater extent while performing a simple finger opposition motor task during (online) rather than after (offline) HD-atDCS (2 mA, 20 min). Our main novel finding showed that online and offline HD-atDCS sessions induced a delayed (30 min after stimulation) increase in SMC activation after performing the same SFO task, but only the online session was found to be significantly different from the sham condition.

For the SFO task used in this study, we sought a constant motor performance without any influence of learning. Our results confirm that the SFO task was performed at a similar movement rate within and between the three experimental sessions (see Table 1). During the SFO task, specific sensorimotor cortical networks (Anwar et al., 2016) are engaged, with the SMC showing the most consistent changes [START_REF] Witt | Functional neuroimaging correlates of fingertapping task variations: An ALE meta-analysis[END_REF]. Such a setup allowed us to investigate how HD-atDCS effects can be enhanced when the stimulated SMC region is concurrently activated by a motor task.

In the present study, we employed fNIRS as a relatively simple and safe method to reveal the online and offline effects of HD-atDCS on SFO motor task-related hemodynamic responses, which is a proxy of SMC activation. Based on the neurovascular coupling mechanism, the hemodynamic response measured by fNIRS is usually characterized with an increase in O 2 Hb and a concomitant smaller reduction in HHb in the cortical microcirculation.

Patterns of O 2 Hb and HHb changes are well correlated with the fMRI BOLD signal [START_REF] Leff | Assessment of the cerebral cortex during motor task behaviours in adults: A systematic review of functional near infrared spectroscopy (fNIRS) studies[END_REF] and can be used to identify the level of cortical activation [START_REF] Leff | Assessment of the cerebral cortex during motor task behaviours in adults: A systematic review of functional near infrared spectroscopy (fNIRS) studies[END_REF]. Due to the greater influence of superficial blood vessels on O 2 Hb signals [START_REF] Kirilina | The physiological origin of task-evoked systemic artefacts in functional near infrared spectroscopy[END_REF], HHb changes [START_REF] Muthalib | Effects of Anodal High-Definition Transcranial Direct Current Stimulation on Bilateral Sensorimotor Cortex Activation During Sequential Finger Movements: An fNIRS Study[END_REF] and an integrated measure combining O 2 Hb and HHb (i.e., Hb diff = O 2 Hb -HHb) [START_REF] Lu | Maintaining Gait Performance by Cortical Activation during Dual-Task Interference: A Functional Near-Infrared Spectroscopy Study[END_REF] is the most suitable metric for accurately detecting task-related changes in SMC activation. Indeed we found much larger variability in the O 2 Hb integral values between subjects, which could account for the non-significant ANOVA effects. However, normalizing O 2 Hb to HHb (i.e., Hb diff that is driven by increases in O 2 Hb with a smaller contribution from decreases in HHb) reduced this variability, which allowed Hb diff to better detect task-related changes in SMC activation during tDCS sessions. Hence a greater SMC activation is reflected in an elevated Hb diff and reduced HHb. Based on this relationship, we observed that when a SFO motor task was performed concurrently with HD-atDCS it produced a significant delayed increase (large effect size for HHb and Hb diff ) in SMC activation (see T2 in Fig. 1) when compared to sham. Looking at Fig. 1, offline HD-tDCS also led to a delayed increase in SMC at T2 but without reaching significance (medium effect size for Hb diff ) compared to sham. Finally, there was a non-significant trend but with a medium effect size, for Hb diff with a higher SMC activation in the online HD-atDCS session.

Overall, our findings reinforce the fact that HD-atDCS elicited more pronounced effects in the stimulated region of the SMC (Lang et al., 2005) that was evident after a 30 min delay.

Determining how long these effects exactly lasted requires further measurements over 30 min after HD-atDCS and in a larger sample size of subjects.

The slightly higher increase of SMC activation in the online than offline HD-atDCS session after 30 min could be explained by the greater efficacy of HD-atDCS at inducing neuroplasticity when networks are already involved in the task, since active networks are preferentially sensitive to neuromodulation [START_REF] Bikson | Origins of specificity during tDCS: anatomical, activity-selective, and input-bias mechanisms[END_REF][START_REF] Reato | Low-Intensity Electrical Stimulation Affects Network Dynamics by Modulating Population Rate and Spike Timing[END_REF]. atDCS alone increases the driving force of synaptic activity due to the synergistic effects of dendritic hyperpolarization and somatic depolarization [START_REF] Lafon | Direct Current Stimulation Alters Neuronal Input/Output Function[END_REF]. But synaptic modifications are more pronounced when the task and tDCS are concurrent (Karok & Witney, 2013).

Alternatively, rather than inducing synaptic plasticity, atDCS paired with a motor task may have a modulatory role (Kronberg et al., 2017). In addition, the fact that we combined both motor task and electrical stimulation with sufficient current (2 mA for 20 min) may have induced a "gating mechanism" that increased the calcium levels above a threshold to induce enhanced synaptic plasticity [START_REF] Moriyoshi | Molecular cloning and characterization of the rat NMDA receptor[END_REF]. In an fMRI study, [START_REF] Kwon | The enhanced cortical activation induced by transcranial direct current stimulation during hand movements[END_REF] observed a higher SMC activity when the motor task was applied during short tDCS application when compared to sham and the motor task alone. It may be hypothesized that when there is motor activity during prolonged HD-atDCS involving the same brain areas, the amount of current that enters the sensorimotor cortex triggers further changes in brain activity patterns for at least 30 min.

However, based on the theory of homeostatic plasticity [START_REF] Turrigiano | Homeostatic plasticity in the developing nervous system[END_REF], we might speculate that the increase of SMC activation after 30 min could be a consequence of the modification of excitation/inhibition balance at T1 requiring adjusting of their synaptic strengths [START_REF] Pozo | Unraveling Mechanisms of Homeostatic Synaptic Plasticity[END_REF]. Note that at T1, hemodynamic changes for online HD-atDCS (i.e. reduced consumption of oxygenated blood) were quite consistent with the neural efficiency hypothesis associated with lower brain activation for completion of the same task.

But later, the increase in SMC activity to perform the same motor task 30 min after HD-atDCS could represent a reduced neural efficiency, which is counterintuitive to the known enhancements of motor learning after tDCS and motor task application [START_REF] Reis | Modulation of motor performance and motor learning by transcranial direct current stimulation[END_REF]. We would rather consider that the delayed increase in SMC activation after HD-atDCS could represent a type of motor memory consolidation process [START_REF] Galea | Brain Polarization Enhances the Formation and Retention of Motor Memories[END_REF].

Previous work [START_REF] Reis | Noninvasive cortical stimulation enhances motor skill acquisition over multiple days through an effect on consolidation[END_REF][START_REF] Saucedo Marquez | Taskspecific effect of transcranial direct current stimulation on motor learning[END_REF] highlighted the beneficial effect of online tDCS and motor task training on consolidation of the motor task after a delay period from stimulation. This consolidation results in part from memory stabilization and as such requires energy with subsequent increases in cerebral blood flow [START_REF] Lisman | The molecular basis of CaMKII function in synaptic and behavioural memory[END_REF].

A limitation of the current study is that although we measured the cortical activity of the stimulated region, anodal stimulation can increase connectivity patterns near the stimulation electrode as well as to more distant sites intra-and interhemispherically [START_REF] Antal | Transcranial direct current stimulation over the primary motor cortex during fMRI[END_REF]. Another limitation of this work is the final number of subjects retained for the analysis (9 subjects) and the presence of only male participants. Further studies could utilize more subjects to examine the reproducibility of these first findings and examine the interactions with the rest of the motor network through cortico-cortical connections both intrahemispherically and across the corpus callosum.

In conclusion, this study highlights the importance of the relative timing of HD-atDCS and motor task in modulating brain activation of the targeted SMC. The novel finding suggests that functional targeting of motor task-concurrent atDCS is likely more effective at producing changes in SMC activation that lasted at least 30 min after stimulation. The increase in activation of the functionally targeted SMC could be the result of several neuroplastic mechanisms that modify excitation/inhibition balance. Future research with combined neurophysiological and neuroimaging techniques is needed to fully understand this phenomenon at a larger scale.

Experimental procedure

Design

In a single blind randomized within-subjects design, subjects participated in three HD-atDCS sessions (online, offline and sham; see Fig. 2). The order of the sessions was randomized and counterbalanced using an online algorithm (http://www.randomization.com/). Sessions were separated by at least 1-week and were performed at the same time (± 1 hour) of the day in a quiet and dimly lit room in order to prevent fNIRS channels contamination by ambient light.

Participants

Fifteen healthy males (mean age ± SD, 33.4 ± 12.2 yrs.) voluntarily participated in this study.

Subjects were right handed (laterality index 82.8 ± 14.0, range from 58 to 100) as determined by the Edinburgh handedness inventory [START_REF] Oldfield | The assessment and analysis of handedness: The Edinburgh inventory[END_REF]. All subjects had no history of neurology or physical disorders or any upper extremity muscle or joint injuries. The study was approved by the local Research Ethics Committee (IRB EuroMov, n°1701B) and was in accordance with the Declaration of Helsinki. All participants gave written informed consent after a description of the study procedures and associated risks.

Protocol

The subjects were seated comfortably at a desk on a height-adjustable chair in front of a LCD monitor. Both forearms were placed in supination position upon the surface of the table .   Subjects were then familiarized to perform a self-paced SFO task (i.e., sequential tapping of the index, middle, ring and fourth finger against the thumb) with their left and right hands at a rate of 2-3 Hz. Following the familiarization and a 3 min rest period the subjects were required to perform the SFO task before the stimulation with their right and left hands in an alternative block design (30-s rest and 30-s task, repeated five times for each hand). The start hand was randomized and counterbalanced across the subjects. The start and the stop of the SFO task was displayed on a LCD monitor for each block to better control the duration of the task, alertness of the participants and task-related hemodynamic response [START_REF] Colier | Human motor-cortex oxygenation changes induced by cyclic coupled movements of hand and foot[END_REF].

The experimenter counted the number of SFO taps during each of the experimental task blocks.

Three minutes after the pre-stimulation SFO task, subjects received one of 3 HD-atDCS sessions. Each session consisted of four phases (see Fig. 2): (i) Pre: SFO task before tDCS (ii) tDCS: 20 min tDCS or sham, iii) Time 1 (T1): SFO task with Online, Offline, or Sham tDCS, and (iv) Time 2 (T2): SFO task at 30 min after tDCS. For sham tDCS, 50% underwent Online and 50% underwent Offline. The current was always ramped up or down over the first and last 30 s of stimulation. All of the subjects were instructed that they would feel senseless or a mild tingling sensation under the electrodes that fades over seconds depending on the variability of individuals, who were blinded to tDCS protocols. The current was turned off after 30 s in the two sham protocols or continued for a total of 20 min during HD-atDCS sessions (with online-or offline-motor task). Even if HD-tDCS is well tolerated [START_REF] Turski | Feasibility and Dose Tolerability of High Definition Transcranial Direct Current Stimulation in healthy adults[END_REF], a questionnaire containing rating scales of 11 unpleasant sensations compared to resting state was filled out after the stimulation sequence. This questionnaire was based on the tDCS safety guidelines proposed by Poreisz et al. (2007). As variability in physiological measures can be due to psychological states [START_REF] Wehrwein | The Mind Matters: Psychology as an Overlooked Variable Within Physiology Studies[END_REF], the State-Trait Anxiety Inventory (STAI, [START_REF] Spielberger | Manual for the State-Trait Anxiety Inventory[END_REF] for assessing trait and state anxiety was completed at the beginning of each session.

Transcranial direct current stimulation

Direct current was generated by a current stimulator (Startim®, Neuroelectrics NE, Spain) and delivered to the left SMC of the subject through a 4x1 anodal HD-tDCS montage (active anode electrode on C3 surrounded by four return electrodes on FC1, FC5, CP5 and CP1; each at a distance of ~4 cm from the active electrode [START_REF] Muthalib | Effects of Anodal High-Definition Transcranial Direct Current Stimulation on Bilateral Sensorimotor Cortex Activation During Sequential Finger Movements: An fNIRS Study[END_REF]. The five electrodes (3.14 cm² AgCl electrodes) were secured on the scalp according to the 10-10 EEG electrode system positions using conductive paste (Ten20®, Weaver and Company, USA) and held in place using a specially designed plastic headgear to arrange the HD-tDCS electrodes and fNIRS probes on the head (see Fig. 3 for layout).

Functional near-infrared spectroscopy

Hemodynamic responses during rest and SFO task periods were recorded continuously using a continuous wave multi-channel fNIRS system (Oxymon MkIII Artinis, Medical Systems, The Netherlands) utilizing two wavelengths (765 and 856 nm) at a sampling of 10 Hz. NIR light was delivered via fiber optic cables to a customized plastic headgear. Two receivers (avalanche photodiode) and two transmitters (pulsed laser) probes were placed, creating a 4 channel array (each channel represented by a receiver-transmitter combination separated by ~3 cm). Based on 10-20 EEG electrode system [START_REF] Klem | The ten-twenty electrode system of the International Federation. The International Federation of Clinical Neurophysiology[END_REF], the headgear was aligned with the vertex (Cz) and channels covered the stimulated SMC regions (see Fig. 3).

The fNIRS system calculates the changes in O 2 Hb and HHb concentration values (expressed in μM) according to a modified Beer-Lambert Law and including an agedependent constant differential pathlength factor [START_REF] Duncan | Measurement of cranial optical path length as a function of age using phase resolved near infrared spectroscopy[END_REF]. During the recordings, the time course of changes in O 2 Hb and HHb concentration values were displayed in real time, and the signal intensity was verified for each channel before data collection.

Location of fNIRS probes and HD-atDCS electrodes

A 3-dimensional digitizer (Fastrack, Polhemus, USA) was used to measure the location of each fNIRS optode probe and tDCS electrode with a stylus marker in relation to the veridical landmarks of the participant's head (nasion, Cz, the pre auricular points anterior to the left and right ears). Subsequently, these coordinates were registered over a reference MRI atlas in the Montreal Neurological Institute (MNI) coordinates system [START_REF] Singh | Spatial registration of multichannel multi-subject fNIRS data to MNI space without MRI[END_REF], and the points on the scalp were projected over a three-dimensional reconstruction of the brain cortex (see Fig. 3) using the NIRS-SPM toolbox [START_REF] Ye | NIRS-SPM: Statistical parametric mapping for near-infrared spectroscopy[END_REF]. The Brodmann areas corresponding to the region were further determined using the Anatomy 1.8 toolbox for SPM [START_REF] Eickhoff | A new SPM toolbox for combining probabilistic cytoarchitectonic maps and functional imaging data[END_REF]. No difference in the location of fNIRS probes and HD-tDCS electrodes was found for the locations between sessions for each subject. Since the presence of cardiac pulsations in fNIRS O 2 Hb signals is indicative of a good contact between the optical probes and the scalp [START_REF] Themelis | Near-infrared spectroscopy measurement of the pulsatile component of cerebral blood flow and volume from arterial oscillations[END_REF], the quality of each of the four channels was checked using two pre-processing methods. First, we analyzed the power spectrum of each time series, where the detection of a peak value around 1 Hz reflects the presence of the cardiac pulsations in the fNIRS signal at rest. Then we used the continuous wavelet transform [START_REF] Grinsted | Application of the cross wavelet transform and wavelet coherence to geophysical time series[END_REF] which is a time-frequency analysis of the signal, where the presence of a strong power-band around 1 Hz reveals a good signal over time. After these preliminary pre-processing steps, 3 participants out of 12 were removed from further analysis due to many bad channels along sessions. Then the four channels (Fig. 3) were pooled because they covered the stimulated SMC region.

Data processing

The data processing was performed for each subject using some of the Homer2 processing package functions (http://homer-fnirs.org/) based in MatLab (version 2014a, Mathworks, USA) (see Appendix A. Supporting document). The fNIRS values retained for statistical analysis were changes in the averaged O 2 Hb and HHb computed over the 10 task blocks using the integral between 5 to 25 seconds out of the 30 seconds of the task. This integral analytic approach allows quantifying the concentration changes over time while being sensitive to task-related changes on O 2 Hb and HHb regardless of the shape of the hemodynamic response profile [START_REF] Näsi | Correlation of visual-evoked hemodynamic responses and potentials in human brain[END_REF][START_REF] Safi | Functional near-infrared spectroscopy for the assessment of overt reading[END_REF]. An index of hemoglobin differential (Hb diff = O 2 Hb -HHb) was also used to evaluate the level of cortical activation [START_REF] Lu | Maintaining Gait Performance by Cortical Activation during Dual-Task Interference: A Functional Near-Infrared Spectroscopy Study[END_REF]. Since the SMC activation (O 2 Hb, HHb and Hb diff ) and movement rate for the two sham sessions (sham online and sham offline conditions) were not significantly different, we pooled the data to represent one sham session.

Statistical Analysis

We used the Kolmogorov-Smirnov test to check for normal distribution. A repeated measures ANOVA (ANOVA RM ) was used to compare STAI values and sensation when using tDCS, the SMC activation (O 2 Hb, HHb and Hb diff ) with one within-subject factor (Session: online, offline and sham) and movement rate with three within-subject factors (Hand: left, right; Time: Pre, T1, T2 and Session: online, offline and sham). In case of a significant main or interaction effect, follow-up ANOVAs with post-hoc LSD Fisher tests for multiple comparisons were conducted. All statistical analyses were performed using Statistica version 7.1 (StatSoft France, 2006). In all statistical tests a significance level of 0.05 was used. The effect sizes were reported in the results section as follows: the partial-eta squared values (Ƞ²p) [START_REF] Lakens | Calculating and reporting effect sizes to facilitate cumulative science: a practical primer for t-tests and ANOVAs[END_REF] for the main and interaction effects of ANOVA RM and the magnitude of Hedges' g for the simple comparisons (post hoc) among sessions for a given time (T1 or T2).

Hedges' g is a variation of Cohen's d that corrects for biases due to small sample sizes (Hedges & Olkin, 1985) and the magnitude of Hedges' g may be interpreted using Cohen's convention as small (0.2), medium (0.5) and large (0.8).

  1. SFO Movement rateSFO Movement rate at each time point for each subject was calculated as the average of the number of SFO taps completed by the left and right hands divided by 300 s. Three participants out of 15 with an intra-individual coefficient of variation (CV) up to 5% for the movement rate were excluded from further analysis because they did not follow correctly the instructions of the experimental design.

Figure legends Figure 1 .

 legends1 Figure legends

Figure 2 .

 2 Figure 2. Experimental timeline. All subjects underwent three HD-atDCS (2 mA, 20 min)

Figure 3 .

 3 Figure 3. Locations of the functional near-infrared spectroscopy (fNIRS) transmitter (T, in

Table 1 .

 1 Mean (SD) simple finger opposition (SFO) movement rate (Hz) for the online, offline and sham HD-atDCS sessions before (Pre), immediately (T1) and 30 min (T2) after stimulation.

			Right hand			Left hand
	Session	Pre	T1	T2	Pre	T1	T2
	Online	2.4 (0.2)	2.4 (0.2)	2.4 (0.2)	2.4 (0.2)	2.4 (0.2)	2.4 (0.2)
	Offline	2.3 (0.2)	2.4 (0.3)	2.4 (0.2)	2.3 (0.2)	2.4 (0.2)	2.4 (0.2)
	Sham	2.5 (0.2)	2.4 (0.2)	2.4 (0.2)	2.4 (0.2)	2.4 (0.2)	2.4 (0.2)

Table 2 .

 2 Mean (SD) values for sensation and the state-trait anxiety inventory (STAI) completed after and at the beginning of online, offline and sham HD-atDCS sessions, respectively.

		Online	Offline	Sham
	STAI	26.1 (7.44) 25.9 (6.57) 27.0 (6.18)
	sensation 1.32 (0.24) 1.26 (0.27) 1.27 (0.24)

Acknowledgments

The authors thank Mr. Gregoire Vergotte for his help with the data collection and analysis.

Funding

This work was supported by LabEx NUMEV (ANR-10-LABX-20).

Author Contributions

PB, MM, and JR designed the study. PB conducted the study, data collection and data analysis under the supervision of MM, GD and SP. PB and SP prepared the manuscript draft with important intellectual input from JR, GD and MM. All authors approved the final manuscript.

Highlights

 Functional near infrared spectroscopy probed the sensorimotor cortex activity when using online, offline and sham high definition anodal tDCS.

 Online and offline high definition anodal tDCS induced greater cortical activation 30 min after stimulation.

 Concurrent application of high definition anodal tDCS during a motor task induced more pronounced changes in sensorimotor cortex activation