Gizem Temiz

Marie Des

Neiges Santin

Claire Olivier

Antoine Collomb-Clerc

Sara Fernandez-Vidal

Elodie Hainque

Eric Bardinet

Brian Lau

Chantal François

Carine Karachi

Marie-Laure Welter
email: marielaure.welter@icm-institute.org

Parkinsonism

Freezing of gait depends on cortico-subthalamic network recruitment following STN-DBS in PD patients

Keywords:

Introduction

Deep brain stimulation of the subthalamic nucleus (STN-DBS) has been widely demonstrated to improve Parkinsonian motor disability with dramatic alleviation of rigidity, akinesia and tremor, along with improvement of dopa-related motor complications [START_REF] Limousin | Electrical stimulation of the subthalamic nucleus in advanced Parkinson's disease[END_REF]. A link between dopa-responsiveness and the effects of STN-DBS on akinesia, rigidity and tremor has been well established [START_REF] Welter | Clinical predictive factors of subthalamic stimulation in Parkinson's disease[END_REF], this feature being the most predictive factor of a good STN-DBS outcome. The effects of STN-DBS on PD gait and balance disorders, and freezing of gait (FOG) are more variable among patients [START_REF] Fasano | Axial disability and deep brain stimulation in patients with Parkinson disease[END_REF][START_REF] Karachi | Clinical and anatomical predictors for freezing of gait and falls after subthalamic deep brain stimulation in Parkinson's disease patients[END_REF][START_REF] Ferraye | Effects of subthalamic nucleus stimulation and levodopa on freezing of gait in Parkinson disease[END_REF][START_REF] Vercruysse | Effects of deep brain stimulation of the subthalamic nucleus on freezing of gait in Parkinson's disease: a prospective controlled study[END_REF], and found to be less correlated with their preoperative dopasensitivity. Indeed, FOG improves in about a third of patients, whereas in another third it is rapidly worsened in the year following surgery [START_REF] Karachi | Clinical and anatomical predictors for freezing of gait and falls after subthalamic deep brain stimulation in Parkinson's disease patients[END_REF][START_REF] Ferraye | Effects of subthalamic nucleus stimulation and levodopa on freezing of gait in Parkinson disease[END_REF]. The factors that contribute to the negative outcome for FOG have not yet been fully identified. Some authors point out the potential role of demographic factors and disease features, in particular old age [START_REF] Welter | Clinical predictive factors of subthalamic stimulation in Parkinson's disease[END_REF][START_REF] Fasano | Axial disability and deep brain stimulation in patients with Parkinson disease[END_REF], the severity of gait disorders before surgery [START_REF] Karachi | Clinical and anatomical predictors for freezing of gait and falls after subthalamic deep brain stimulation in Parkinson's disease patients[END_REF][START_REF] Ferraye | Effects of subthalamic nucleus stimulation and levodopa on freezing of gait in Parkinson disease[END_REF][START_REF] Vercruysse | Effects of deep brain stimulation of the subthalamic nucleus on freezing of gait in Parkinson's disease: a prospective controlled study[END_REF], cognitive deficit [START_REF] Fasano | Axial disability and deep brain stimulation in patients with Parkinson disease[END_REF], and the stimulating contact location or parameter settings [START_REF] Moreau | STN-DBS frequency effects on freezing of gait in advanced Parkinson disease[END_REF][START_REF] Varriale | Decreasing subthalamic deep brain stimulation frequency reverses cognitive interference during gait initiation in Parkinson's disease[END_REF].

More recently, some authors have searched for "sweetspots" for improving the cardinal motor and non-motor signs of PD with STN-DBS, by using MRI approaches and correlation analysis. For the improvement of akinesia and rigidity, a link between the positive effects of STN-DBS was found for a volume of activated tissue (VAT) with a centre of mass (sweetspot) located in the most posterior part of the STN [START_REF] Horn | Connectivity Predicts deep brain stimulation outcome in Parkinson disease[END_REF][START_REF] Akram | Subthalamic deep brain stimulation sweet spots and hyperdirect cortical connectivity in Parkinson's disease[END_REF], and a functional connectivity profile with negative correlations with sensorimotor cortices and positive correlations with specific frontal regions and motor cerebellum [START_REF] Sobesky | Subthalamic and pallidal deep brain stimulation: are we modulating the same network?[END_REF]. A correlation was also found for non-motor signs, including apathy or depression, and linked to an increase in the left prefrontal connectivity with VAT induced by STN-DBS [START_REF] Boon | Structural and functional correlates of subthalamic deep brain stimulation-induced apathy in Parkinson's disease[END_REF][START_REF] Irmen | Left prefrontal connectivity links subthalamic stimulation with depressive symptoms[END_REF]. In a large retrospective cohort study, we found that the sweet spot for improving FOG was located more anteriorly within the STN, roughly corresponding to its centre, just beyond the posterior sensorimotor part of the nucleus [START_REF] Karachi | Clinical and anatomical predictors for freezing of gait and falls after subthalamic deep brain stimulation in Parkinson's disease patients[END_REF]. In a recent retrospective study performed on a cohort of 47 PD patients with STN-DBS, a significant correlation between FOG improvement and the recruitment of premotor, motor and prefrontal dorsolateral corticosubthalamic fibres was also reported [START_REF] Strelow | Structural connectivity of subthalamic nucleus stimulation for improving freezing of gait[END_REF], suggesting a possible influence of cortico-subthalamic fibres recruitment in post-operative FOG improvement. Taken together, these data suggest that the effects of STN-DBS can be explained by both the modulation of the target site inside the STN and the fibres recruited within the VAT, especially the fibres belonging to the hyperdirect cortico-subthalamic pathway [START_REF] Ashkan | Insights into the mechanisms of deep brain stimulation[END_REF]. Nevertheless, the optimal stimulation site for improving gait remains to be prospectively assessed, also using objective assessment, and the potential link between FOG and cortico-subthalamic fibres recruited within the VAT induced by STN-DBS is not fully identified.

Here, we aimed to identify the clinical and diffusion weighted imaging (DWI) factors that could correlate with post-operative FOG severity. For this purpose, we prospectively studied a cohort of 19 PD patients to examine the link between the hyperdirect corticosubthalamic tracts included in each individual VAT and the effects of STN-DBS on gait and balance disorders including FOG.

Patients and methods

This study includes 4 steps:1) we prospectively assessed gait and balance disorders in 19 PD patients before and 6 months after STN-DBS, using validated clinical scales and instrumented gait recordings; 2) we built a PD normative whole brain tractogram using DWI obtained before surgery in another cohort of 33 PD patients not oper-ated but with similar demographic and clinical characteristics; 3) we modelled individual VATs for each hemisphere using the individual DBS parameters for each of the 19 patients; and 4) we normalised all the VATs into a common brain space and searched for potential relationships between the severity of postoperative FOG and the specific cortico-subthalamic streamlines included in each individual VAT.

Patients

Two separate cohorts of PD patients were included at the Pitié-Salpêtrière Hospital, Paris. A first cohort of 20 PD patients (15 M/5F) candidate for STN-DBS were included for complete pre and postoperative clinical and gait assessments (Table 1). One patient was not operated due to eye infection and therefore excluded. A second cohort of 33 patients with Parkinson's disease (24 M/10F) were included pre-operatively for a 3 T MRI acquisition (Table 1).

Inclusion criteria for both patient groups for STN-DBS in our centre were as follows: (1) age below 70 years; (2) severe form of PD; (3) >50% reduction in motor symptoms On-dopa; and (4) disabling dopa-induced motor complications despite optimal medical treatment. Exclusion criteria were dementia, ongoing psychiatric disturbances, surgical contraindications, and relevant brain lesions detected on MRI [START_REF] Karachi | Clinical and anatomical predictors for freezing of gait and falls after subthalamic deep brain stimulation in Parkinson's disease patients[END_REF].

All patients provided their informed written consent in accordance with the declaration of Helsinki, and the local ethics committee approved the study (CPP Ile-de-France Paris VI; INSERM promotion RBM 2012-A00225-38 and 2016-A00231-50; ClinicalTrials.gov: NCT01682668 and NCT02800460).

Clinical evaluation and gait initiation recordings

In the first cohort of PD patients, clinical assessments and gait recordings were performed: (1) before surgery with no dopaminergic treatment for at least 12 h (Off-dopa) and after a supra-threshold of dopaminergic treatment (On-dopa; usual morning dose + 50 mg), and (2) 6 months after surgery with STN-DBS using chronic individual settings without dopaminergic treatment. We assessed parkinsonian disability with the Unified Parkinson's Disease Rating Scale (UP-DRS parts I to IV), gait and balance disabilities with the Gait and Balance Scale (GABS), and FOG severity with the Freezing of Gait Questionnaire (FOG-Q) [START_REF] Giladi | Construction of freezing of gait questionnaire for patients with Parkinsonism[END_REF]. Cognitive status was assessed using the Mattis Dementia Rating Scale (MDRS) performed before and after surgery (Table 1). We measured gait initiation parameters using a force platform (0.9 × 1.8 m, AMTI, Advanced Mechanical Technology Inc. Watertown, MA, USA). In order to obtain a better reproducibility of gait recordings, the patient initiated gait barefoot on the platform following an auditory Go signal, walked for 5-6 m, and returned for 15 to 30 trials (Fig. S1) [START_REF] Chastan | Gait and balance disorders in Parkinson's disease: impaired active braking of the fall of centre of gravity[END_REF]. Gait initiation events for the first two steps were manually identified and the following temporal and spatial parameters calculated: (1) the duration of the anticipatory postural adjustments (APA) and double-stance phases, and (2) the maximum posterior and (3) lateral CoP displacements during the APA, (4) length, [START_REF] Vercruysse | Effects of deep brain stimulation of the subthalamic nucleus on freezing of gait in Parkinson's disease: a prospective controlled study[END_REF] width and (7) velocity of the first step [START_REF] Chastan | Gait and balance disorders in Parkinson's disease: impaired active braking of the fall of centre of gravity[END_REF].

In the second cohort of 33 PD patients, clinical assessment was also performed Off-dopa and On-dopa, and also included the UPDRS parts I to IV, and the MDRS (Table 1).

Neurosurgical procedure, parameter setting and modelling of the individual volume of activated tissue

The STN was directly targeted using 3D T2 Flair weighted images on the inclusion MRI and indirect targeting using our in-house YeB atlas [START_REF] Karachi | Clinical and anatomical predictors for freezing of gait and falls after subthalamic deep brain stimulation in Parkinson's disease patients[END_REF]. The day of the surgery, a pre-operative stereotactic 1.5 T MRI acquisition with T1 weighted images and gadolinium was performed (GE Healthcare, Optima MR 450W, USA) for surgical planning to calculate the target coordinates in the Leksell space and to define trajectories avoiding blood vessels, ventricles and the caudate nucleus. Quadripolar electrodes (Medtronic, 3389-28) were implanted using microelectrode recordings and clinical testing in awake patients, and connected to a pulse generator (Medtronic, Kinetra, Minneapolis). After surgery, the electrode and contact locations were determined using postoperative helical tomography and merged with the preoperative stereotactic MRI. Parameter settings were chosen according to the patient's clinical exam after surgery and adjusted during outpatient visits.

The precise therapeutic contact location was calculated with reference to the posterior commissure [START_REF] Karachi | Clinical and anatomical predictors for freezing of gait and falls after subthalamic deep brain stimulation in Parkinson's disease patients[END_REF] and the VATs modelled on the individual MRI using chronic parameter settings for each hemisphere by considering the contact dimensions (1.5 mm height, 1.27 mm diameter) and a homogenous isotropic tissue medium with conductivity of 0.3 S/m, as using PyDBS tool as explained previously [START_REF] Dergachyova | Automatic preoperative planning of DBS electrode placement using anatomo-clinical atlases and volume of tissue activated[END_REF] by using finite element methods to calculate electrical potentials to determine the neural activation volumes as a function of stimulus parameters and the magnitude of capacitive component of electrode-tissue interface. All the VATs of the 19 patients were then computed and normalised hemisphere by hemisphere within a common space using linear transformation (block-matching algorithm) with 6°of freedom.

Diffusion weighted imaging data and processing for normative whole brain probabilistic tractography

The 3 T MRI images were acquired using magnetisation-prepared 2 rapid acquisition gradient echo (MP2RAGE) sequences (TR/ TE = 5000/3.12, voxel size = 0.9 × 0.9 × 0.9 mm³) with an acquisition time of 8 min together with a multi shell DWI using a singleshot 2D spin-echo multiband Echo Planar Imaging (EPI) sequence. Each DWI dataset contained 3 shells that were acquired with reverse phase encoding directions (anterior-posterior and posterior-anterior, with b-values of 300, 1000, 2000 s/mm 2 and with respectively 8, 32, and 64 directions per shell with the following parameters: TR/ TE = 3500/75, voxel size = 1.76 × 1.76 × 1.76 mm³). The total acquisition time for the DWI dataset was 12 min. All DWI data were preprocessed in order to remove Rician noise, Gibbs ringing, head motion and susceptibility-based artefacts and eddy current distortion. An additional correction for intensity inhomogeneities was applied (see supplementary methods).

Individual response functions were estimated using multi-shell multi-tissue constrained spherical deconvolution framework and averaged in order to use group-based response functions for different tissues (white matter, grey matter and cerebro-spinal fluid). Fibre orientation distributions (FOD) were calculated for each subject using their individual DWI data and population averaged response functions. Individual FODs were used in order to create PD patient-group specific FOD templates by applying affine and diffeomorphic alignment with MRtrix.

For the segmentation of regions of interest, an anatomical template was also constructed by applying the same transformations to the subjects' T1w images (reconstructed in individual DWI space, and preprocessed with histogram matching). We segmented all 39 cortical Brodmann areas (BA) included in the Brodmann atlas MRIcro (https://www.mccauslandcenter.sc.edu/crnl/mricro) by first linear registration (FLIRT from FSL) followed by a non-linear registration (FNIRT from FSL), and finally adjusting each segmentation to the cortical ribbon computed with Freesurfer. The FOD template was used to reconstruct the whole brain tractography using a probabilistic approach (for details see Ref. [START_REF] Temiz | The anatomofunctional organization of the hyperdirect cortical pathway to the subthalamic area using in vivo structural connectivity imaging in humans[END_REF]). Spherical informed filtering techniques (SIFT2) were applied to the whole brain tractography, in order to compute the weighting factor of each streamline.

Analysis of cortical connectivity for individual VAT

Each individual VAT of the first cohort was aligned to the normative space and the cortical connectivity of each VAT extracted from the whole brain tractography. Tracks of interest were extracted between each VAT and each cortical region by using whole brain tractography and the corresponding weighting factor. The sum of the weights of each streamline involved in tracks of interest was then calculated. These metrics represent the fibre bundle capacity (FBC) of each tract of interest and provide quantitative information to estimate connectivity.

Tractography-based STN anatomical-functional subdivisions based on cortical connectivity

The cortico-subthalamic pathway was isolated using normative whole brain tractography, and the cerebellar peduncles, striatum and pallidum were excluded to ensure specificity for the hyperdirect cortico-subthalamic pathway. STN subdivisions were created by measuring similarity between cortical connectivity of STN voxels as previously reported [START_REF] Temiz | The anatomofunctional organization of the hyperdirect cortical pathway to the subthalamic area using in vivo structural connectivity imaging in humans[END_REF]. For this purpose, we first evaluated the optimal number of clusters using the Davies and Bouldin criterion by generating 2 to 6 clusters for the cortical connectivity profile of each voxel located in the STN. Using these criterion, we then determined the number of clusters with the highest similarity score within each cluster and lowest similarity score between clusters (Matlab version 2020b).

Statistical analysis

For the first cohort of patients, we assessed the changes in parkinsonian disability and gait and balance disorders after STN-DBS relative to baseline (Off-dopa) using Wilcoxon-rank sum tests. We compared the demographic and clinical scores at baseline in patients with a score for FOG-Q greater than or equal to 10 vs patients with a score less than 10. Finally, we also compared the demographic and clinical scores between the first and the second cohort of patients using nonparametric Kuskall Wallis tests.

For VAT analysis, we first assessed the correlations between connectivity of each VAT with the 39 BAs using Pearson correlation and clustered the cortical VAT connectivities regarding their intercorrelations (connectivity tendency similarity: co-increase or co-decrease of connectivity) by Ward's minimum variance method into two clusters. We then summed the connectivity of each VAT within these clusters.

Finally, we examined the correlations between the severity of gait and balance disorders after STN-DBS, and the cortical fibres contained in each VAT using univariate correlations between UPDRS-III, FOG-Q, GABS and MDRS scores. We further examined the correlations using multiple linear regression to include UPDRS-III, FOG-Q, GABS, and MDRS scores as simultaneous explanatory variables. A separate model was fitted for each hemisphere (left and right) and connectivity network (sensorimotor and prefrontal), and we corrected for multiple comparisons to control the false discovery rate. We also assessed the correlation between the clinical scores and the intersected VAT volumes with STN subdivisions in order to analyse spatial information with respect to STN organization. We ran separate multivariate regression models to assess the linear relationship of gait initiation parameters (APA and double-stance durations, step length) after STN-DBS, first with VAT connectivity and then with the intersected VAT volumes with STN subdivisions. A p-value < 0.05 was considered significant.

Results

Effects of levodopa treatment and STN-DBS on parkinsonian disability and gait assessment

Before surgery, 15 out of 19 patients of the first cohort had mild FOG (Fig. 1), and 15/19 recurrent falls (mean [SD] item 13-UPDRS II: 2.3 [1.4]). In these patients, the UPDRS III improved by 75%, the axial score by 71%, and the GABS score by 72% On-versus Off-Dopa (Table 1). Gait kinetics were also significantly improved On-versus Off-dopa, with increases of the step length and velocity, posterior and lateral APA CoP displacements, and decreases of the APAs and double-stance phases (Fig. S2). In the second cohort of 33 PD patients, the UPDRS III improved by 66% and the axial score by 67% On-versus Off-Dopa (Table 1). We found no significant differences in the demographic and clinical features between the first and second cohorts of PD patients (Table 1).

In the first cohort of PD patients, we compared clinical scores with STN-DBS alone to Off-Dopa before surgery, and found that the UP-DRS-III score decreased by a mean of 56%, the GABS score by a mean of 49%, and the axial score (including dysarthria) by a mean of 18% (Table 1). Relative to before surgery, the FOG-Q also decreased by a mean of 36% (with usual dopaminergic treatment). Lastly, the LEED decreased by a mean of 43% (Table 1). For gait recordings, we found that the posterior APA CoP displacement, step length and velocity significantly increased (Fig. 1, Fig. S2). The lateral APA CoP displacement, APA and double-stance phase durations were not significantly different (Fig. S2), indicating little or no improvement in postural control.

We observed different effects of STN-DBS on gait and postural control at the individual level, with changes ranging from a 100% improvement to a 166% worsening in the GABS score and a worsening of FOG severity for 5/19 patients (Fig. 1), and, for gait parameters, an absence of increase in the step length in 8/19 patients (Fig. 1). We found no significant differences in the baseline demographic and clinical features between patients with a FOG-Q greater than or equal 10 compared to those with a FOG-Q less than 10 after surgery (Table S1).

Relationship between therapeutic contact location, VAT cortical connectivity and PD disability

The mean (SD) coordinates of the stimulating contacts were not significantly different between right and left sides (Fig. S3). We found no significant correlation between the therapeutic contact location and the UPDRS-III, FOG-Q, and GABS scores, or gait parameters after surgery (not shown).

The correlation analysis of the connectivity between each VAT showed that the VAT connectivity of the BA 8-11,25,32,35,36 and 45-48 were positively correlated between themselves, and negatively with the BA 1-4,6,7,19-23,34, and 37-41 (Fig. 2A), for both hemispheres. Similarly, the VAT connectivity of the BA 1-4,6,7,19-23,34 and 37-41 were positively correlated between themselves (Fig. 2A). We therefore, separated VAT connectivity into two large clusters: one including predominantly BA 8, 9, 10, 11, 32 named "prefrontal" and one including predominantly BA 1-2-3, 4, 6 named "sensorimotor" (Fig. 2A).

Using univariate correlations between different measures of parkinsonian disability (UPDRS-III, FOG-Q, GABS, MDRS scores), and VAT connectivity profiles, we found significant correlations for prefrontal and sensorimotor VAT connectivity of the right hemisphere (p = 0.001, R 2 = 0.62; and p = 0.046, R 2 = 0.33; for right prefrontal and right sensorimotor connectivity, respectively, Fig. 2B). Multiple linear regression analysis confirmed the univariate correlation with a significant positive association between FOG severity and right prefrontal VAT connectivity (FOG-Q; semi-partial correlation = 0.58, adjusted p = 0.0027), and a significant negative corre- lation between FOG severity and right sensorimotor VAT connectivity (semi-partial correlation = -0.55, adjusted p = 0.023).

Relationship between intersected VAT and STN subdivision in relation to PD disability

Based on cortico-subthalamic connectivity, we found that the STN could be divided into two subdivisions: one posterior that mainly connected the sensorimotor areas (BA 4,[START_REF] Vercruysse | Effects of deep brain stimulation of the subthalamic nucleus on freezing of gait in Parkinson's disease: a prospective controlled study[END_REF], and one anterior that mainly connected the prefrontal areas (BA 8, 9, 10 and 32) for both hemispheres with a smooth gradient of change of connectivity between them (Fig. 3A). However, we found size differences for the sensorimotor and the prefrontal subdivisions occupying respectively 55% and 45% for the right STN, and 77% and 23% for left STN (Fig. S5).

We found that the overlap between the VAT and the right sensorimotor STN subdivision was significantly correlated (p = 0.009; R 2 = 0.47), and negatively with post-operative FOG severity (FOG-Q score, ß = -1.69, p = 0.0017, Fig. 3B).

For gait parameters, we found a significant negative correlation between the overlap between the VAT and the left sensorimotor STN subdivision (p = 0.02, R 2 = 0.35) and the post-operative double stance duration (ß = -230.8, p = 0.037), and a significant positive correlation with the post-operative APA duration (β = 151.8, p = 0.018) (Fig. S6).

Discussion

In this study, we found a significant link between corticosubthalamic fibres recruitment and post-operative FOG severity in PD patients with STN-DBS. Using PD DWI data, we found that lower postoperative FOG severity correlated with a higher connectivity of the individual VAT induced by STN DBS with the right sensorimotor cortical areas and with a VAT located more posterior within the right STN. Conversely, more severe post-operative FOG correlated with a higher VAT connectivity with the right prefrontal cortical areas. We also found that better post-operative executive functions correlated with a higher VAT connectivity with the right sensorimotor cortical areas.

In these PD patients that have mild axial motor symptoms that respond to dopaminergic treatment before surgery, we observed differential effects of STN-DBS on gait and balance at the individual level, with, for some patients a dramatic alleviation of gait after STN-DBS whereas an aggravation was observed in about 1/3 of patients [START_REF] Karachi | Clinical and anatomical predictors for freezing of gait and falls after subthalamic deep brain stimulation in Parkinson's disease patients[END_REF][START_REF] Ferraye | Effects of subthalamic nucleus stimulation and levodopa on freezing of gait in Parkinson disease[END_REF][START_REF] Vercruysse | Effects of deep brain stimulation of the subthalamic nucleus on freezing of gait in Parkinson's disease: a prospective controlled study[END_REF], with no difference at baseline between "freezers" and "non-freezers" patients. This confirms that a good response to dopaminergic treatment before surgery does not guarantee a good outcome of axial motor symptoms after STN-DBS [START_REF] Fasano | Axial disability and deep brain stimulation in patients with Parkinson disease[END_REF][START_REF] Moro | The impact on Parkinson's disease of electrical parameter settings in STN stimulation[END_REF]. Interestingly, gait recordings showed that STN-DBS improved forward gait parameters (such as walking velocity) but not the postural and preparatory phases of gait (such as double stance and APA durations). This result suggests that STN-DBS has a positive impact on the akinetic gait components but may modify the functional network involved in more complex motor programs, including gait initiation and postural control [START_REF] Collomb-Clerc | Effects of deep brain stimulation on balance and gait in patients with Parkinson's disease: a systematic neurophysiological review[END_REF]. Such differential effects of STN-DBS on gait and posture have been previously reported in PD patients, with an alteration of dual-task walking with STN-DBS [START_REF] Varriale | Decreasing subthalamic deep brain stimulation frequency reverses cognitive interference during gait initiation in Parkinson's disease[END_REF], also identified as a driver for the occurrence or FOG aggravation [START_REF] Delval | Auditory cueing of gait initiation in Parkinson's disease patients with freezing of gait[END_REF][START_REF] Bloem | The "posture second" strategy: a review of wrong priorities in Parkinson's disease[END_REF][START_REF] Heremans | Freezing of gait in Parkinson's disease: where are we now?[END_REF]. This suggests that STN-DBS, especially when recruiting prefrontal-subthalamic fibres, could negatively influence executive functions [START_REF] Parsons | Cognitive sequelae of subthalamic nucleus deep brain stimulation in Parkinson's disease: a meta-analysis[END_REF], and, in consequence, FOG. In line with this hypothesis, we found that the severity of FOG after surgery was linked to a higher VAT connectivity with the prefrontal corticosubthalamic pathway. However, this relationship was observed independently of cognitive status (quantified by MDRS score) suggesting that the modulation of these cortico-subthalamic tracts participate in post-operative FOG. This prefrontal network includes the frontal eye field (area 8), the dorsolateral prefrontal (area 9), anterior prefrontal (area 10), the dorsal anterior cingulum (area 32), and weakly the frontal orbital (area 47) cortices. These brain areas are involved in cognitive information processing, such as complex movement planning, action control and working memory [START_REF] Rosenbloom | The functional neuroanatomy of decision-making[END_REF][START_REF] Fuster | The prefrontal cortex in the neurology clinic[END_REF]. Recent imaging studies performed in PD patients with FOG showed a decrease of cortical thickness in the orbital, prefrontal dorsolateral and anterior cingulum cortices [START_REF] Bharti | Neuroimaging advances in Parkinson's disease with freezing of gait: a systematic review[END_REF]. These data suggest that STN-DBS modifies the functioning of non-motor cortico-STN pathways which could result in an impairment of some complex aspects of gait control.

Conversely, lower FOG severity was related to a higher connectivity of the VAT with sensorimotor cortices (mainly BA 1, 2, 3, 4, 6 and 8), which have been widely demonstrated to be activated in the preparation and execution phases of movement, including gait [START_REF] Karachi | Functional parcellation of the lateral mesencephalus[END_REF]. This result is in accordance with the recent report of a significant link between FOG improvement after STN-DBS and a higher connectivity with motor and premotor cortico-subthalamic fibres [START_REF] Strelow | Structural connectivity of subthalamic nucleus stimulation for improving freezing of gait[END_REF], as also reported for other parkinsonian motor signs, such as rigidity or akinesia [START_REF] Akram | Subthalamic deep brain stimulation sweet spots and hyperdirect cortical connectivity in Parkinson's disease[END_REF]. In PD patients with STN-DBS, PET imaging also suggested that FOG severity improvement was associated with metabolic activity changes in sensory associative cortices [START_REF] Lyoo | Different cerebral cortical areas influence the effect of subthalamic nucleus stimulation on parkinsonian motor deficits and freezing of gait[END_REF]. Interestingly in our patients, the intersected VAT connectivity within the STN for lower FOG severity was not only located in the dorsolateral part of the nucleus, as reported by others for akinesia [START_REF] Horn | Connectivity Predicts deep brain stimulation outcome in Parkinson disease[END_REF][START_REF] Akram | Subthalamic deep brain stimulation sweet spots and hyperdirect cortical connectivity in Parkinson's disease[END_REF], but towards its centre which roughly corresponds to the sweet spot for FOG that we previously obtained in our large retrospective cohort [START_REF] Karachi | Clinical and anatomical predictors for freezing of gait and falls after subthalamic deep brain stimulation in Parkinson's disease patients[END_REF]. This spot is located within the STN at the junction between the motor and associative subparts of the GPe-STN projections (defined previously in monkeys) and also at the junction between the sensorimotor and prefrontal cortico-subthalamic tracts in the right hemisphere, suggesting that FOG improvement may be linked to the combined modulation of mainly sensorimotor cortico-STN tracts and associative GPe-STN connections. However, our DWI technique does not allow to study the influence of other basal ganglia-mesencephalic locomotor networks with high reliability mainly because of the large number of fibres crossing towards the STN and the GPe, pedunculopontine (PPN) and cuneiform nuclei. It is also possible that STN-DBS altered or alleviated the functioning of other pathways involved in gait control such as PPN-STN fibres, known to be altered in PD with dopa-resistant FOG [START_REF] Nonnekes | Freezing of gait: a practical approach to management[END_REF], or lenticular fasciculus fibres as recently suggested in a retrospective study [START_REF] Strelow | Structural connectivity of subthalamic nucleus stimulation for improving freezing of gait[END_REF]. Lastly, the effects of STN-DBS could also be related to the abnormal STN neuronal activity patterns observed in PD patients with increased beta band activity previously found in freezers PD patients at rest or during arrests of stepping movements [START_REF] Georgiades | Hitting the brakes: pathological subthalamic nucleus activity in Parkinson's disease gait freezing[END_REF].

We observed differences for correlation for the right and left VAT connectivity, with significant results only for the right hemisphere. This could be explained by the different volumes of the sensorimotor and the prefrontal subdivisions of the right and left STN, with a larger left sensorimotor STN subdivision and therefore a smaller intersected VAT with the small left prefrontal STN subdivision. Another possibility would be that right and left STN have distinct influences on locomotion, as reflected by their distinct cortico-subthalamic connectivity, with a pre-eminence of the right STN for gait control as observed using functional MRI in healthy controls [START_REF] Marchal | Deep brain activation patterns involved in virtual gait without and with a doorway: an fMRI study[END_REF], and the observation of asymmetric PPN connectivity in PD patients with FOG [START_REF] Fling | Asymmetric pedunculopontine network connectivity in parkinsonian patients with freezing of gait[END_REF]. Some recent studies have examined the impact of asymmetric STN-DBS for improving FOG in PD patients [START_REF] Fasano | Modulation of gait coordination by subthalamic stimulation improves freezing of gait[END_REF]. The published data are however contradictory up to now. In a recent randomized cross-over study, reducing left STN-DBS amplitude by 50% was found to decrease axial motor signs and FOG-Q, but no significant change was found when reducing the right STN-DBS amplitude [START_REF] Lizárraga | Lateralized subthalamic stimulation for axial dysfunction in Parkinson's disease: a randomized trial[END_REF]. In another randomized study, reducing stimulation amplitude by 30% contralateral to the least affected side had no positive effect with conversely an aggravation of symptoms, leading to a premature drop-out for 8/12 patients [START_REF] Meoni | Asymmetric STN DBS for FOG in Parkinson's disease: a pilot trial[END_REF]. Lastly, comparing unilateral right and left side STN-DBS effects ◀ in 22 patients, Castrioto et al. [START_REF] Castrioto | The dominant-STN phenomenon in bilateral STN DBS for Parkinson's disease[END_REF] observed no significant difference in the reduction of gait and axial scores when comparing the right and left STNs (25% with the right STN and 30% with the left STN for axial scores). In that study, it was however suggested that it was not the side of the hemisphere per se that impacts the most the effects of STN-DBS. Indeed, 8 patients had better effects on gait with unilateral left STN-DBS whereas only 3 patients had better effects on gait with unilateral right STN-DBS, thus not favoring the right STN as the best STN for gait disorders.

C O R R E C T E D P R O O F

Limitations

Our study has some limitations. First, the number of patients included in this analysis is low even though we precisely analysed gait and balance prospectively and used validated clinical scales and gait recordings. In our study, we can also not fully rule out the role of a higher post-operative LEDD or other medication in the FOG severity after surgery, nor the role of lead implantation trajectories as previously reported for post-operative cognitive deficit [START_REF] Witt | Relation of lead trajectory and electrode position to neuropsychological outcomes of subthalamic neurostimulation in Parkinson's disease: results from a randomized trial[END_REF]. However, we observed no significant post-operative cognitive deficit in any of the patients with post-operative FOG, and no obvious difference in other medication (see Table S2). The higher LEDD in these patients could mainly be the consequence of the less efficacy of STN-DBS on their gait problems (and not the cause) as we found no significant difference in the UPDRS III score with STN-DBS between freezers and nonfreezers patients (see Table S1). Since these patients had no individual diffusion data, we used a normative tractogram of another cohort of PD patients, all candidates for STN DBS, with individual DWI to assess VAT connectivity. Our normative tractogram was obtained in a cohort of PD patients with similar clinical features suggesting that DWI results should be similar to PD patients already operated. Moreover, the use of normative tractograms could improve the signal to noise ratio for the connectivity assessment, but conversely it could smooth small individual differences. We also did not examine other fiber tracts that could be involved in gait control such as the GPe-STN, STN-GPi or STN-PPN [START_REF] Strelow | Structural connectivity of subthalamic nucleus stimulation for improving freezing of gait[END_REF], or functional connectivity profile [START_REF] Sobesky | Subthalamic and pallidal deep brain stimulation: are we modulating the same network?[END_REF]. Even though we used multi-shell diffusion data to improve diffusion signal modelling, these networks are difficult to isolate with high reliability due to the high numbers of crossing fibres. An improvement in tractogram reconstruction accuracy for quantitative analysis is still needed [START_REF] Smith | Mapping connectomes with diffusion MRI: deterministic or probabilistic tractography?[END_REF] together with methodological developments to explore small brain pathways using DWI in vivo.

Conclusion

Our study showed that the severity of FOG after surgery is related on the recruitment of the right cortico-subthalamic fibres, with lower FOG severity when VAT includes more sensorimotor and less prefrontal cortico-subthalamic fibres. This result could be important regarding the possibility for postoperative current shaping with the aim of improving FOG using directional DBS electrodes that could take into account individual modulations of these different corticosubthalamic networks. Our study paves the way for the possibility in the near future to use DWI to provide additional individual information to refine surgical targeting, taking into account the precise topography of the cortical projections. However, higher resolution imaging approaches are now needed to propose individual anatomofunctional maps.

Fig. 1 .Fig. 2 .

 12 Fig. 1. Effects of STN-DBS on freezing of gait, parkinsonian disability, and step length The graphs show the changes in the freezing of gait questionnaire (FOG-Q, On-dopa, left panel), UPDRS-III score (Off-dopa, middle panel) and step length (Offdopa, right panel) before and after subthalamic deep brain stimulation (STN-DBS). The box plots show upper and lower quartiles and median of these observations. Each colour point represents an individual patient. .(For interpretation of the references to colour in this figure legend, the reader is referred to the Web version of this article.)

Fig. 3 .

 3 Fig. 3. Cortico-subthalamic clusters and relationship between intersected VAT with STN subdivisions and FOG severity. A. Left panel: Subthalamic (STN) clusters obtained with hierarchical clustering from an anterior (top) and posterior (bottom) axial views. Right panel: histograms showing the connectivity profiles of the STN subdivisions with Brodmann areas (BA) which are outlined regarding their functions (sensorimotor in blue, associative in red and limbic in pink) on the y-axis and tract density values on the y-axis for respectively cluster 1 in blue and cluster 2 in red for RH and LH.B. Upper panel: cortico-STN streamlines arising from prefrontal cortical areas (red streamlines, BA 8,9,10,32), sensorimotor (BA 1-2-3, 4, 6) and parietal (BA 7) cortical areas (blue streamlines) and bipartition of the STN based on sensorimotor (blue) and prefrontal (red) STN connectivity. Bottom panel: Graphs showing bivariate relationship between the FOG-Q score and the volume of the intersected zone of the VATs with the Prefrontal (Pf) and sen-

Table 1

 1 Demographic and clinical characteristics of PD patients with STN-DBS and PD patients with DWI analysis.

	STN-DBS cohort

Before surgery After surgery with STN-DBS Off-dopa On-dopa Off-dopa On-dopa Off-dopa On-dopa

	Parkinsonian disability UPDRS part I UPDRS part II UPDRS part III Axial score UPDRS part IV Gait and balance scale FOG-Q ABC-scale MDRS LEDD (mg/d)	20.4 ± 7.2 37.8 ± 11.7 6.1 ± 3.5 17.3 ± 10.4	1.1 ± 1.5 5.5 ± 4.0 10.3 ± 7.6 1.8 ± 1.7 8.6 ± 3.9 4.5 ± 4.4 17.5 ± 12.2 64.8 ± 21.9 139.6 ± 4.3 1082 ± 351	9.2 ± 4.2* 16.8 ± 9.3* 4.6 ± 2.8 8.8 ± 6.3*	0.6 ± 1.3 6.6 ± 3.7 10.6 ± 7.3 2.9 ± 2.4 1.8 ± 1.8* 9.8 ± 4.1 10.6 ± 8.3 71.0 ± 18.7 137.6 ± 5.0 598 ± 386*	20.2 ± 8.8 38.8 ± 12.0 6.2 ± 3.8	1.6 ± 1.1 8.6 ± 6.4 13.4 ± 8.3 2.8 ± 1.7 9.8 ± 4.1 _ _ _ 139.0 ± 3.7 1072 ± 426
	*P < 0.05 between before and after surgery with STN-DBS for the same dopa conditions. ABC: activities balance confidence; FOG-Q: freezing of gait questionnaire; MDRS: Mattis dementia rating scale; LEDD: levodopa equivalent daily dosage; STN-

DBS: subthalamic nucleus deep brain stimulation; UPDRS: Unified Parkinson's Disease Rating Scale.

Acknowledgments

We are grateful to Anais Hervé and Clementine Trosch for their excellent patient care during the research trials, Angèle Van Hamme and Pasquale Varialle for helping in acquisition and analysis of gait data, and Hayat Belaid for neurosurgery assistance.

Financial support

This study was supported by the Institut National de la Santé et de la Recherche Médicale (INSERM, RBM C11-40), the program 'Investissements d'avenir' (ANR-10-IAIHU-06). Funding was provided by grants from the 'Institut du Cerveau et de la Moelle Epinière' (ICM) Foundation, the 'Régie Autonome des Transports Parisiens' (RATP), and the Agence Nationale de la Recherche (ANR-16-CE37-0007-02). Gizem Temiz and Marie des Neiges Santin received research funding support from Boston Scientific.

Declaration of competing interest

The Authors declare to have no conflict of interest relative to this research.

Appendix A. Supplementary data

Supplementary data to this article can be found online at https:// doi.org/10.1016/j.parkreldis.2022.10.002.


Cécile Charles
email: cecile.charles@gustaveroussy.fr

Antonio Di Meglio

Monica Arnedos

Johanna Arvis

Giulia Baciarello

Pierre Blanchard

Nardjes Djehal

Agnès Dumas

Antoine Hollbecque

Elise Martin

Margarida Matias

Gwenn Menvielle

Anna Zingarello

Sarah Dauchy

Ines Vaz-Luis

QualFatigue Study: Which Factors Influence the Use of Specific Interventions for Breast Cancer Survivors with Fatigue? A Cross-Sectional Exploratory Study

Keywords: breast cancer, survivors, cancer-related fatigue, specific interventions, barriers

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

Introduction

Breast cancer is the second most prevalent cancer worldwide and accounts for almost 12% of new cases of cancer annually [START_REF] Bray | Global cancer statistics 2018: GLOBOCAN estimates of incidence and mortality worldwide for 36 cancers in 185 countries[END_REF]. In most developed countries, up to 85% of patients with breast cancer can expect a longterm disease-free survival [START_REF] Allemani | Global surveillance of trends in cancer survival 2000-14 (CONCORD-3): analysis of individual records for 37 513 025 patients diagnosed with one of 18 cancers from 322 population-based registries in 71 countries[END_REF][START_REF] Siegel | Cancer statistics[END_REF]. However, a substantial proportion of survivors experience short-term to longterm health effects of cancer and its treatments (e.g., chronic pain, axillary web syndrome, lymphedema, concerns about body image, cognitive impairment…) and, therefore, have impaired quality of life [START_REF] Michelotti | Tackling the diversity of breast cancer related lymphedema: Perspectives on diagnosis, risk assessment, and clinical management[END_REF][START_REF] Miller | Cancer treatment and survivorship statistics[END_REF][START_REF] Lovelace | Long-Term Effects of Breast Cancer Surgery, Treatment, and Survivor Care[END_REF].

Cancer-related fatigue (CRF) is one of the most common and disturbing symptoms affecting up to 90% of cancer patients both during and after treatment [START_REF] Susanne | Predictors of fatigue in cancer patients: a longitudinal study[END_REF]. Although most patients experience a reduction in their fatigue over time, about 30% endure persistent fatigue for several years after the completion of primary treatment [START_REF] Susanne | Predictors of fatigue in cancer patients: a longitudinal study[END_REF][START_REF] Jones | Cancer-related fatigue and associated disability in post-treatment cancer survivors[END_REF].

CRF is defined as "a distressing, persistent, subjective sense of physical, emotional, and/or cognitive tiredness or exhaustion related to cancer and/or cancer treatment that is not proportional to recent activity and interferes with usual functioning" [START_REF]Cancer-Related Fatigue[END_REF]. Compared with the fatigue reported by non-cancer individuals, CRF is more severe and less responsive to rest [START_REF]Cancer-Related Fatigue[END_REF]. It can have a detrimental impact on many levels of the individual's functioning, capabilities to cope with daily life activities, and fulfilling one's family, social, and professional roles [START_REF] Susanne | Predictors of fatigue in cancer patients: a longitudinal study[END_REF]. CRF demonstrates inter-individual variability, as it is a multifactorial and complex phenomenon [START_REF] Susanne | Predictors of fatigue in cancer patients: a longitudinal study[END_REF][START_REF] Jones | Cancer-related fatigue and associated disability in post-treatment cancer survivors[END_REF], and its underlying mechanisms have not been clearly elucidated [START_REF] Yang | A Narrative Review of Cancer-Related Fatigue (CRF) and Its Possible Pathogenesis[END_REF][START_REF] Thong | 21:17. related fatigue: Ready for implementation to practice?[END_REF].

Although data that support the use of any pharmacological agent for treating CRF are limited, international clinical practice guidelines recommend specific interventions, such as physical activity (PA), education, and psychosocial (e.g., cognitive-behavioral therapies [CBT]) approaches as the most efficacious strategies to reduce CRF [START_REF]Cancer-Related Fatigue[END_REF]12,[START_REF] Bower | Screening, Assessment, and Management of Fatigue in Adult Survivors of Cancer: An American Society of Clinical Oncology Clinical Practice Guideline Adaptation[END_REF]. Particularly, in breast cancer survivors, systematic reviews have reported consistent improvement in CRF after PA interventions, and a significant support from psychological interventions, including CBT; cognitive therapies help patients to better identify unhelpful cognitions and maladaptive behavioral patterns that may be contributing to the CRF [START_REF] Lahart | Physical activity for women with breast cancer after adjuvant therapy[END_REF][START_REF] Corbett | The effectiveness of psychological interventions for fatigue in cancer survivors: systematic review of randomised controlled trials[END_REF][START_REF] Abrahams | The efficacy of Internet-based cognitive behavioral therapy for severely fatigued survivors of breast cancer compared with care as usual: A randomized controlled trial[END_REF]. Yoga and mindfulness-based interventions have also been proved effective in the short term [START_REF] Cramer | Yoga for improving health-related quality of life, mental health and cancer-related symptoms in women diagnosed with breast cancer[END_REF][START_REF] Haller | Mindfulness-based interventions for women with breast cancer: an updated systematic review and meta-analysis[END_REF]. However, previous evidence suggests that the implementation of the guidelines and recommendations is still not optimal [START_REF] Thong | 21:17. related fatigue: Ready for implementation to practice?[END_REF]. Consequently, CRF remains globally undertreated [START_REF] Ripamonti | Fatigue, a major still underestimated issue[END_REF]. Several barriers, affecting its management, have been identified at the patient, clinician, and health system levels (e.g., personal factors such as misconceptions, lack of motivation or time, environmental factors such as availability of settings and opportunities) [START_REF] Ripamonti | Fatigue, a major still underestimated issue[END_REF][START_REF] Martin | A qualitative evaluation of the use of interventions to treat fatigue among cancer survivors: A healthcare provider's view[END_REF].

In Europe, nearly half of the general population do not practice any leisure PA [START_REF]Special Eurobarometer 472. Sport and physical activity[END_REF]; in France, a third of adults do not meet the public health recommendations for PA, despite the fact that the majority of French people are aware of the beneficial effects of PA on health [START_REF] Praznoczy | État des lieux de l'activité physique et de la sédentarité en France[END_REF]. In the cancer population, several studies have observed a significant decrease in the level of PA after cancer diagnosis [START_REF] Fassier | Variations of physical activity and sedentary behavior between before and after cancer diagnosis: Results from the prospective population-based NutriNet-Santé cohort[END_REF][START_REF] Eng | Patterns, perceptions, and perceived barriers to physical activity in adult cancer survivors[END_REF] and the estimated rates of patients who are or remain not regularly active during and after treatment completion range up to 30% [START_REF] Turner | Interventions for promoting habitual exercise in people living with and beyond cancer[END_REF]. Among current or later cancer-related adverse events, CRF is, with pain, one of the main physical obstacles to practicing PA, and can justify, in case of significant physical deconditioning, referral to rehabilitation specialists [START_REF]Cancer-Related Fatigue[END_REF][START_REF]Bénéfices de l'activité physique pendant et après cancer. Des connaissances scientifiques aux repères pratiques[END_REF]. Regarding CBT, interventions targeting CRF are very little developed in France, in particular because of a lack of trained professionals and reimbursement related problems [START_REF] Dolbeault | The effectiveness of a psycho-educational group after earlystage breast cancer treatment: results of a randomized French study[END_REF].

To the best of our knowledge, most of the qualitative studies that have explored CRF focused on patients' perception of fatigue (experience and impact) and their coping strategies [START_REF] Rosman | Fatigue experienced by patients suffering from cancer[END_REF][START_REF] Gledhill | A qualitative study of the characteristics and representation of fatigue in a French speaking population of cancer patients and healthy subjects[END_REF][START_REF] Levkovich | The Experience of Fatigue in Breast Cancer Patients 1-12 Month Post-Chemotherapy: A Qualitative Study[END_REF]. Thus far, there is limited understanding on how and why breast cancer survivors use or not use specific interventions to relieve CRF.

Our study aimed to address this gap and to explore possible ways to optimize the uptake of the recommended specific interventions to relieve CRF. The purpose of the study was to investigate the barriers and facilitators that may influence the use of specific interventions to relieve CRF, among French breast cancer survivors, with moderate to severe CRF, after the completion of their primary treatment.

Methods

Design

QualFatigue ("A qualitative exploration of the use of interventions to relieve fatigue among breast cancer survivors") was a monocentric, cross-sectional, and explorative study based on semi-structured interviews. The protocol was approved by the French regulatory and ethics authorities. All participants received oral and written information about the purpose and procedures of the study, and signed a consent form.

Population

Participants were included if they met the following inclusion criteria: 1) stage I-III breast cancer [START_REF] Kalli | American Joint Committee on Cancer's Staging System for Breast Cancer, Eighth Edition: What the Radiologist Needs to Know[END_REF], 2) age ≥18 years at the time of study entry, 3) within 6-24 months after the end of primary treatment (defined as the endpoint of primary surgery, chemotherapy, or radiotherapy, whichever came last. Anti-human epidermal growth factor receptor therapy and hormonal therapy, if indicated, could be ongoing), and 4) level of CRF ≥4 on a 10-point numerical scale (this score was retained because it was considered as an optimal cut-off for identifying clinically moderate CRF [score: [START_REF] Michelotti | Tackling the diversity of breast cancer related lymphedema: Perspectives on diagnosis, risk assessment, and clinical management[END_REF][START_REF] Miller | Cancer treatment and survivorship statistics[END_REF][START_REF] Lovelace | Long-Term Effects of Breast Cancer Surgery, Treatment, and Survivor Care[END_REF] and severe CRF [score: 7-10]) [12]. The following were the main exclusion criteria: 1) evidence of relapse, 2) history of other cancers at the time of inclusion, and 3) obvious treatable medical conditions that can explain CRF.

Procedures and measures

From March to July 2019, participants pre-screened, according to the eligibility criteria for the QualFatigue study, from the list of outpatients, with breast cancer, of a French cancer center were approached with the help of their medical oncologists. If interested, patients met one of the investigators who provided them with further information about the study. After signing the consent form, patients were asked to rate their level of fatigue over the past seven days on a 10-point numerical scale from zero ("no fatigue") to ten ("worst fatigue you can imagine"). Only women with a score ≥ 4/10 were included. A trained psychologist (with a PhD degree) conducted individual semi-structured interviews by phone. All interviews lasted for approximately 30 to 45 min, and followed a pre-defined interview guide that was developed with diverse inputs from stakeholders, including clinicians, researchers, and breast cancer survivors. The interview guide included open-ended questions to encourage participants to discuss issues and covered the following areas: 1) description of the onset and the stabilization of CRF during treatment; 2) solutions to relieve CRF, including already tried solutions, and those intended; 3) expectations about the management of CRF; and 4) representations of the recommended interventions to manage CRF.

Demographics and medical features of the participants were collected from their medical records, including age, stage at diagnosis, time since the end of primary cancer treatment, treatments received, current hormonal therapy, marital status, family status, level of education, and professional status. All interviews were audio recorded in full, and transcribed verbatim by a medical secretary for analyses, with all personal identifiers removed. After 10 interviews, a preliminary analysis was conducted to check whether information collected was adequate, and to establish the extent at which it would be sufficiently rich; then the interviews were continued until the research team felt that no more information could be obtained. Five more patients were included. Finally, data saturation was achieved with 15 interviews, additional interviews were not deemed necessary to increase thematic content [START_REF] Saunders | Saturation in qualitative research: exploring its conceptualization and operationalization[END_REF]. A descriptive inductive coding strategy was first applied by a researcher to the transcripts in order to identify and group meaningful phrases according to the primary objectives of the study [START_REF] Castleberry | Thematic analysis of qualitative research data: Is it as easy as it sounds?[END_REF], aided by the QDA Miner software. Following this, thematic matrices were constructed to examine the relationship between response patterns in the codes. The emerging themes were discussed within the research team to achieve valuable inter-coder reliability. Although the thematic analysis was performed by one of the researchers, the results were discussed within the research team. Additionally, the research team presented their interpretation via a seminar, to an independent team involved in clinical research; the interpretation was critically scrutinized.

Results

Sample characteristics

After prescreening, 46 women were considered eligible for inclusion in this qualitative study. Of them, only 15 were included. The flowchart demonstrating the selection process is shown in Fig 1 . Demographic and medical characteristics of the participants are summarized in Table 1. Nearly two-thirds of the participants reported severe CRF (≥7) (Table 2).

Use of specific interventions to relieve CRF

The majority of participants reported as moderately to highly physically active (Table 2). The most frequent activities were walking, dancing, swimming, and gardening. None of the participants had undertaken any educational or psychosocial interventions. Some participants mentioned using mind-body interventions, such as sophrology and yoga, as alternatives to manage sleep disorders associated with CRF, and several others considered relaxation, meditation, and acupuncture as interesting approaches in the context of CRF, even if they had not tried it.

Barriers and facilitators influencing the use of specific interventions to relieve CRF

Four main themes emerged from the participants' discourse as potential sources of influence in their use of specific interventions. They are presented below without any significance-based prioritization.

Expectations for the management of CRF Half of the participants considered that they did not require help in CRF management, either because they thought that they had to face difficulties or because they "knew what to do." In addition, almost all patients mentioned rest as the main strategy for coping with CRF, and for some, rest was even considered the only solution to reduce CRF: "The only thing I can do when I am like this is lie down and wait for it to pass." For most participants, rest meant to lie down, which could last from a few minutes to several hours.

Half of the participants spontaneously mentioned that they raised the problem of CRF with a health care provider. Among those, only two participants had been informed about the benefits of exercise, and in one case, the participant was already physically active. In the other cases, participants described a frequent lack of attention or banalization from health care providers regarding CRF: "According to my doctor, this is just normal fatigue. It is normal, it takes time," "I have talked to him before, but he does not pay too much attention. When I tell him, I am tired he tells me to take rest." In addition, the majority of the participants found impossible to discuss CRF with a health care provider because of the short duration of medical consultations and/or they do did not know how to approach the topic: "Well, talking to the doctor… We see her for about ten minutes you know it's not easy. There's really no time to discuss…," "I've never been told about my fatigue anyway, and then I do not really talk about it." However, several participants expressed the need for listening and recognition of CRF. In addition, global health assessment was expected by some patients, for example, one participant was "waiting for in-depth medical exams to better understand and treat her fatigue." Another said that a physical examination helped to reassure her about the objective existence of CRF: "When I go to my doctor, I'm happy when she measures my blood pressure and she tells me "you have ten," because sometimes you wonder if it's not in your head."

Among participants who declared need for more information and support, the preference was clearly given to non-pharmacological interventions, with only a few participants preferring the idea of a medication, defined as a "stimulant." Several participants indicated that they were looking for an energizing effect, which is why some of them had taken dietary supplements (vitamins, probiotics, ginseng, and magnesium) for their "boost" effect, or they voluntarily changed their eating habits.

Representations of the benefits provided by the interventions

Almost three-quarters of the participants, including some of them who were not physically active, expressed positive representations about PA. The benefits associated with PA could be general ("It feels good") or specific, including : 1) relief of symptoms, such as CRF, pain, sleep disorders, 2) relief of stress ("It clears one's mind," "It allows me to think about something other than the illness"), 3) maintenance and strengthening of physical capacities ("It helps me to lose weight," "It keeps me in good physical shape"), or 4) promotes support ("Seeing other people"). None of the participants reported negative representations of PA. All non-physically active participants acknowledged that they "should move more." However, only one had a defined project to start in order to be physically active, which included starting an individual coaching. In contrast, a large majority of the participants did not have a picture of what educational or psychosocial interventions targeting CRF could be like.

Individual physical and psychological conditions

Several participants mentioned having experienced symptoms known to be associated with CRF, in particular pain -muscular and/or joint and/or neuropathic pain, sleep disorders, and some referred to preexisting chronic diseases, such as obesity or diabetes. Also CRF ("I am weary quickly"), pain ("When I walk sometimes my legs hurt"), and overweight ("I'm over 100 kilos, that also makes me tired quickly") were cited as obstacles to the use of recommended interventions, particularly PA, as well as psychological factors such as lack of motivation ("This weekend I didn't have the courage to get up on Sunday to go out"), or fear ("Fear of not being able to keep pace with the group and of being misjudged by others").

Social and environmental situations

Some participants pointed out the influence of their relatives on their attitudes toward CRF. They talked about the "pressure" from their immediate environment to take a rest: "They tell me to rest, you must be patient, you must not be too stressed," "I have a friend who always says to me: 'You do too much, you don't care of yourself.'" On the contrary, one participant reported a lack of understanding by her family and colleagues regarding the intensity of CRF and the need to have regular rest periods: "And the comments that you heard coming back all the day: 'But go out, go walk, it will do you good' […] Actually the trick is that people do not understand this fatigue, and me, I do not necessarily want them to see it." More globally, family responsibilities and workload appeared to be major obstacles to finding the time and energy to devote to specific interventions targeting CRF ("I don't take the time to do that, I really need to be reminded of that"). Especially, if these were is combined with environmental/logistics aspects, such as long distance to places of practice, bad transportation, and poor weather conditions ("There are soft gymnastics lessons and it's a long way from home and I have no way to get there," "It's true that in winter, it rains, it's cold, I don't really feel like going out").

Social support was considered a major lever for engaging in any of the recommended interventions, particularly PA, however, only one participant mentioned that her family encouraged her to practice PA. In addition, being accompanied by a friend, joining a group of people in a similar life situation or in the same age range, but also personalized coaching were mentioned as motivational factors.

Discussion

Interviews were performed on breast cancer survivors with CRF, to explore the barriers and facilitators that may influence the use of specific interventions, by them, to relieve CRF. Several interesting findings emerged.

Regarding the interventions that participants used, PA was cited as a frequent resource to manage CRF, but some participants stated that they did not exercise at all, or mentioned barriers to regular exercise. In addition, participants were mostly unaware of the other recommended treatment options for CRF. This finding was particularly striking regarding the educational and psychosocial interventions, of which they seemed to be totally unaware. The limited use of mind-body interventions was an unexpected result, particularly given the exponential development of this kind of approach and the positive image promoted by the media.

Four main sources of influence in the use of specific interventions were highlighted: 1) expectations regarding the management of CRF, 2) representations of the benefits that interventions could provide, 3) individual physical and psychological conditions, and 4) social and environmental situations.

Needs in terms of information, evaluation, personalization, and support from health care providers were reported by several participants. As previously mentioned in the literature [START_REF] Spichiger | Prevalence and contributors to fatigue in individuals hospitalized with advanced cancer: a prospective, observational study[END_REF], lack of time and attention during medical consultations, but also on the part of participants, the willingness to get by on their own, or the fear of having a drug prescription as the only answer, emerged as factors interfering with patient-provider communication. Unmet needs in this field may have contributed to some participants turning towards products and physical techniques, which have no consistent evidence of efficacy on CRF [START_REF] Greenlee | Clinical practice guidelines on the use of integrative therapies as supportive care in patients treated for breast cancer[END_REF]. The risk is that the complementary and alternative strategies that can have associated adverse events may replace the recommended and proven effective interventions [START_REF] Saghatchian | Exploring frontiers: use of complementary and alternative medicine among patients with early-stage breast cancer[END_REF].

The influence of representations in the use of specific interventions was most evident in the expected and/or perceived benefits of PA. Although almost all participants considered resting as a core strategy to relieve CRF, PA was unanimously positively represented and associated with numerous benefits, with all participants feeling that "they had to move." On the other hand, participants had no representation of what benefits psychosocial interventions, such as CBT would provide. In Europe, CBT is particularly seen through the prism of mental disorders and consulting mental health professionals remains difficult for a section of the population due to fears (e.g., stigmatization) and false beliefs (e.g., one must resolve its own problems) [START_REF] Leichsenring | Is Cognitive Behavioral Therapy the Gold Standard for Psychotherapy? The Need for Plurality in Treatment and Research[END_REF][START_REF] Tirintica | Factors that influence access to mental health services in South-Eastern Europe[END_REF]. The difference in representations between PA and psychosocial interventions could also be linked to the representations that participants had about CRF. Thus, bodily sensations and physical factors are particularly present in patients' common descriptions of CRF, unlike the cognitive dimension, which is less represented [START_REF] Spichiger | Prevalence and contributors to fatigue in individuals hospitalized with advanced cancer: a prospective, observational study[END_REF][START_REF] Picariello | It feels sometimes like my house has burnt down, but I can see the sky': A qualitative study exploring patients' views of cognitive behavioural therapy for chronic fatigue syndrome[END_REF]. This could explain the foremost use of interventions that work on physical aspects.

Consistent with previous studies, the barriers to the use of specific interventions included somatic symptoms such as CRF itself and pain, but also psychological factors, social, environmental, and logistic constraints [START_REF] Eng | Patterns, perceptions, and perceived barriers to physical activity in adult cancer survivors[END_REF][START_REF]Bénéfices de l'activité physique pendant et après cancer. Des connaissances scientifiques aux repères pratiques[END_REF]. Well described for PA, these barriers were also clearly apparent in our study for other interventions such as mind-body approaches. Benefits are largely related to the regularity with which participants practice mind-body techniques [START_REF] Greenlee | Clinical practice guidelines on the use of integrative therapies as supportive care in patients treated for breast cancer[END_REF]. It is possible that having difficulty in focused attention that is prevalent among patients with CRF can be an obstacle for this subset of patients. Moreover, the use of mind-body techniques often implies an initial in-person instruction phase, which allows feedback [START_REF] Carlson | Mind-Body Therapies in Cancer: What Is the Latest Evidence?[END_REF]. For instance, it has been shown that yoga was best undertaken when guided by a qualified instructor [START_REF] Greenlee | Clinical practice guidelines on the use of integrative therapies as supportive care in patients treated for breast cancer[END_REF]. This is why issues of access to professional resources and of distances to be traveled may be a central obstacle for some patients.

Several limitations of this exploratory study should be acknowledged with respect to the generalizability of the results. First, even if thematic saturation was rich, the sample size was small. Second, CRF is a complex symptom, and has a strong association with emotional distress, including depression and anxiety. This is particularly notable in the period after the end primary treatment for breast cancer. Although we have identified the role of some psychological factors, which act as barriers in the treatment of fatigue, we did not explore the contribution of anxiety and depression in the utilization of these interventions. Third, despite a diversified sample (e.g., different age groups, levels of education, and professional status), this monocentric and crosssectional study design cannot reflect the diversity of the geographical situations and the possible evolution of practices during and after the primary treatment. Worthy of note is the fact that all patients were enrolled in a single French cancer center, which has a psycho-oncology unit, and has been offering a structured set of nonpharmacological interventions complementary to care (e.g. PA, mindfulness-based interventions), for free of charge, since last seven years. We acknowledge that this organization may not be shared by the other centers in France.

As the main clinical implication of this study, six key levers came out in the interviews to overcome identified barriers and optimize the use of specific interventions in patients with CRF: 1) listening and recognition for individual difficulties and needs; 2) individual and global health assessment; 3) information and advice on how to manage CRF; 4) discussion groups focused on the management of CRF; 5) group activities (e.g., walking, soft gymnastics, relaxation); and 6) professional and personalized guidance.

  At the end of the interview, participants were given the "Fatigue et Cancer" guide distributed by the French National Institute of Cancer [32]. Analyses Descriptive statistics were performed to characterize samples according to demographic and medical variables, and the use of specific interventions or other resources, using the Statistical Package for the Social Sciences (SPSS), version 21.0, IBM Software.

This research was supported by a Career Catalyst Research grant from Susan G. Komen (CCR17483507) to Ines Vaz-Luis, a grant from the ARC Foundation (CANTO-WORK labelled program) to Ines Vaz-Luis, the Gustave Roussy Foundation to Ines Vaz Luis, and the Philanthropic Odyssea Gustave Roussy Program. We would like to thank Editage (www.editage.

Availability of data and material: Available on request.

Code availability: N.A.

Conflict of Interest statement: A. Di Meglio reports personal fees from Thermo Fisher and grants from the European Society for Medical Oncology (ESMO; clinical research fellowship), outside the submitted work. I.

Vaz-Luis reports personal fees from AstraZeneca, Kephren, Amgen, and Novartis, outside the submitted work.

No other authors reported any disclosures.

Ethics approval:

The study protocol was approved by the French regulatory and ethics authorities' (N° ID IRB

2017-A01944-49).

Consent to participate: All participants received oral and written information about the purpose and the procedures of the study, before signing a consent form.

Consent for publication:

We confirm that the manuscript has been read and approved for submission by all authors; all persons listed as authors have contributed to the preparation of this manuscript and no persons other than the listed authors have contributed significantly to its preparation.


Emile Hohnadel
email: emile.hohnadel@inria.fr

Tomohiko G Sano
email: sano@mech.keio.ac.jp

Toshiyuki Kawata

Thibaut Métivet

Thibaut Metivet

Florence Bertails- Descoubes

Investigating the compaction of open ring stacks through real and numerical experiments

Keywords: Thin elastic rods, frictional contact, simulation, mechanical metamaterials, snap-fits

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

We investigate the mechanical response of a stack of bidimensional flexible open rings subject to compression cycles, by the means of experiments and simulations. To perform reliable and scalable simulations, we build a numerical model based on an unclamped version of the 2D super-helix [START_REF] Bertails | Super-Helices for Predicting the Dynamics of Natural Hair[END_REF] for open thin elastic rods, coupled to frictional contact constraints [START_REF] Daviet | A hybrid iterative solver for robustly capturing Coulomb friction in hair dynamics[END_REF]. We carefully validate this numerical model, first against theoretical predictions given by the analysis of a single ring snap fit [START_REF] Yoshida | Mechanics of a Snap Fit[END_REF], second by comparing numerical and experimental results for an assembly of rings of moderate size (30 rings). Our excellent predition results allow us to rely on the simulator for investigating the mechanical behaviour of a large collection of (300) randomly stacked rings, depending on their opening angle and their friction coefficient. In particular, we find that such a system, which acts as a disordered mechanical metamaterial, can absorb and store mechanical energy upon compression in a controlled fashion, exploiting large displacement and rearrangment of rings, snap-fits, and friction.

Fig. 1 :

 1 Fig. 1: Left: Our experimental set-up with 30 open rings. Center: Simulation of our set-up scaled up to 300 open rings. Right: Stress-strain plot from our simulation, for 5 consecutive compression cycles.