Modesto Mateos
email: mmateos@mondragon.edu

Laurent Gornet

Patrick Rozycki

Laurentzi Aretxabaleta

Laurentzi Aretxabaleta Hysteretic

Hysteretic shear behaviour of fibre-reinforced composite laminates

Keywords: Hysteresis, fibre reinforced composites, damage mechanics, strain rate

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

Introduction

Composite materials are essential in applications in which significant stiffness combined with lightweight are needed. Knowledge of their behaviour until rupture is necessary in order to optimise the structures made of these materials. Carbon fibre reinforced composite materials have been studied for many years. Their linear orthotropic elastic behaviour is well known and important work has been done on the understanding and modelling of damage by analysis at the mesoscale of the elementary ply [START_REF] Ladevèze | Damage modelling of the elementary ply for laminated composites[END_REF][START_REF] Marguet | A rate dependent constitutive model for carbonfiber reinforced plastic woven fabrics[END_REF][START_REF] Johnson | Computational methods for predicting impact damage in composites structures[END_REF][START_REF] Mateos | Comportement hystérétique en cisaillement des composites renforcés des fibres[END_REF]. This work focuses on the hysteretic shear behaviour of these materials together with its coupling with damage mechanics. In this work the hysteretic shear behaviour will be dealt with by the use a non-modified fractional model, based on the experience on previous works [START_REF] Mateos | Comportement hystérétique en cisaillement des composites renforcés des fibres[END_REF][START_REF] Rabius | A modified fractional calculus approach to model hysteresis[END_REF]. The main advantage of fractional models is the need of a very few number of parameters for the material characterisation and their ability to deal with phenomena which are history-dependent, such as hysteretic phenomena.

Hysteresis modelisation enables, for instance, to improve composite thermomechanical behaviour modelling in fatigue, where, in general, hysteresis is not included within the damage models [START_REF] Hochard | A generalized damage model for woven ply laminates under static and fatigue loading conditions[END_REF][START_REF] Gornet | High cycle fatigue damage model for delamination crack growth in cf/epoxy composite laminates[END_REF]. Another area of interest could be heating modelling during fatigue tests [START_REF] Westphal | Thermomechanical analysis of fatigue degradations in carbon epoxy laminates[END_REF], where thermomechanical behaviour could be improved by hysteresis-loops modelling with fractional operators.

The aim of this analysis is to develop a model which includes both damage phenomena and irreversible strain, together with hysteretic behaviour under shear. The main advantage of fractional models is the need of a very few number of parameters for the material characterisation and their ability to deal with phenomena which are history-dependent, such as hysteretic phenomena.

Experimental

In order to define the shear behaviour, mainly the damage and irreversible strain evolution laws and model parameters, loading-unloading shear tests have been performed.

Materials and samples

The carbon fibre reinforced composite plates are composed of Toray GV 170U carbon fibre and SiComin SR8100 resin, manufactured at Mondragon Unibertsitatea. The samples have been obtained by water jet cutting.

Shear tests

The tests have been fulfilled in an Instron universal test machine (figure 1) on samples with ±45 • fibre orientation at 50 mm/min (v50).

Material model

The model is written at the mesoscale of the layer which establishes a good compromise between the scales of the constitutive materials and the structure. A plane-stress state is assumed and only small strains are taken into account. In what follows, subscripts 1 and 2 stand for the fibre direction and the transverse direction, respectively. where G 0 12 and d 12 stand for the undamaged elastic shear modulus and damage variable associated with stiffness loss in shear due to matrix microcracking, respectively. In the general damage mechanics formulation, the thermodynamic force Y 12 , associated to damage in shear, monitors damage development and is defined by:

Y 12 = 2G 0 12 e 12 2 (4)
In order to model the hysteretic behaviour observed in experimental tests (fig. 2), a fractional model is chosen [START_REF] Mateos | Comportement hystérétique en cisaillement des composites renforcés des fibres[END_REF]. To take into account the existence of clockwise hysteresis loops observed during the tests, a fractional fractional derivative constitutive law is used [START_REF] Mateos | Comportement hystérétique en cisaillement des composites renforcés des fibres[END_REF][START_REF] Rabius | A modified fractional calculus approach to model hysteresis[END_REF]. In the presence of interfacial debondings and slipping is taken into account with the internal damage variable

d v k
12 [START_REF] Hild | Matrix cracking and debonding of ceramic-matrix composites[END_REF]. The modified fractional model yields:

σ 12 (t) = 2G 0 12 (1 -d 12 ) e 12 (t) + N k=1 2G k 1 -d v k 12 D α k e 12 (t) (5)
where G k are material parameters and D α k is the fractional derivative of order α k , 0 ≤ α k ≤ 1 and k ∈ [1, . . . , N]. Finally, α k is assumed to be function of damage d 12 . Furthermore, within the loops, the elastic strain is defined in the following way:

e 12 = σ 12 2G 0 12 (1 -d 12 ) (6)
Fractional calculus allows defining the derivative and integral of generalised order. The fractional derivative of a function f (t) can be defined as [START_REF] Oldham | The fractional calculus[END_REF][START_REF] Cortés | Applications of fractional calculus for the impact of elastic spheres[END_REF]:

D α f (t) = d α f (t) dt α = 1 Γ(1 -α) d dt t 0 (t -y) -α f (y) dy ( 7
)
where Γ is the gamma function [START_REF] Cortés | Applications of fractional calculus for the impact of elastic spheres[END_REF].

Depending on the definition used and on the order of fractional operators, fractional derivatives and integrals at any time t n can be calculated numerically by using several numerical algorithms [START_REF] Oldham | The fractional calculus[END_REF][START_REF] Mateos | Characterisation of impact indentation behaviour of polymeric materials by fractional models[END_REF]. Using the L1-algorithm, the expression obtained is:

D α f (t n ) = (∆t) -α Γ(2 -α)         1 -α n α f 0 + n-1 j=0 ( j + 1) 1-α -j 1-α f n-j -f n-j-1         (8)

Evolution laws

The damage parameter d 12 is defined by the damage evolution function f 12 . After experimental results on unidirectional fibre reinforced composites [START_REF] Ladevèze | Damage modelling of the elementary ply for laminated composites[END_REF], assuming that damage during unloading remains constant until further positive loading is applied and causes further damage accumulation, the parameter Ȳ12 , based on the maximum value reached by the thermodynamic damage force along the previous loading history, is defined to describe the damage development. Thus:

Ȳ12 = max τ≤ t Y 12 (τ) (9)
The model's ability to reproduce the clockwise hysteresis loops is shown (fig. 3, 4 and 5). Furthermore, the values for the damage parameters are consistent with the ones obtained experimentally. Concerning the fractional parameter, its values are very small and suggest a quasi-linear behaviour with respect to the elastic strain. This may be due to the definition of the elastic strain within the loops. If one considers the order of the derivatives to be zero, the sum of the values obtained for G 0 12 and G 1 turns out to be the same as the one obtained from the parameters identification process (3487 MPa).

Loop G 0 12 [MPa] G 1 [MPa.s -α 1 ]

Conclusion

A fractional model has been developed for a carbon fibre reinforced composite, which includes both intra-ply damage and hysteresis under shear loadings with only a very few number of parameters. The construction of the model is based on the thermodynamics framework of irreversible processes, continuum damage mechanics and the use of fractional calculus in order to reproduce the hysteretic behaviour. The model's ability to reproduce the clockwise hysteresis loops has been shown. The values obtained for the fractional derivative are very low, which suggest a quasi-linear behaviour with respect to the elastic strain.

It has been shown that the model is able to reproduce the damage and hysteretic behaviour of the material for low strain rates without modifying the fractional model construction developed for quasi-static conditions. Further work is in progress concerning the explicit implementation of the strain rate effect in fractional models and its implementation in finite element codes.

Figure 1 .

 1 Figure 1. Universal test machine.

Figure 3 .Figure 5 .

 35 Figure 3. Stress-strain relation for the first loop v50 Figure 4. Stress-strain relation for the second loop v50

Table 1 .

 1 Parameters of the fractional model for v50

	α 1

Acknoledgements

The author gratefully acknowledges the help provided by Haritz Zabala, from Mondragon Unibertsitatea, for this research.

Constitutive law

The model is applied to a fibre reinforced composite ply, which is modelled as a homogeneous orthotropic elastic or viscoelastic damaging material whose properties are degraded after loading mainly by matrix microcracking. Continuum damage mechanics theory is used to describe ply degradation by the use of internal damage parameters [START_REF] Ladevèze | Damage modelling of the elementary ply for laminated composites[END_REF]. In fiber-reinforced materials, matrix cracking is usually accompanied by interfacial debonding followed by sliding, giving rise to irreversible strains and hysteresis loops. To model hysteresis loops, different models have been proposed [START_REF] Mateos | Comportement hystérétique en cisaillement des composites renforcés des fibres[END_REF][START_REF] Hild | Matrix cracking and debonding of ceramic-matrix composites[END_REF][START_REF] Maire | Etude théorique et expérimentale du comportement de matériaux composites en contraintes planes[END_REF].

In order to study the behaviour of the material, shear tests with discharge were performed on woven carbon fibre epoxy-matrix laminates with a [±45] 2s stack sequence following the same procedure as in [START_REF] Mateos | Comportement hystérétique en cisaillement des composites renforcés des fibres[END_REF]. The irreversible strains and loading-unloading hysteretic behaviour may be observed in fig. 2. The following split of shear strain is assumed to deal with the reversible and irreversible effects:

where e 12 stands for the elastic shear strain, i 12 stands for the irreversible shear strain and v 12 stands for the viscous shear strain. Nevertheless, viscous shear strains have been neglected after considering the experimental results, which have revealed small values for them. Thus, the strain split yields:

Taking into account Helmholtz's free energy [START_REF] Marguet | A rate dependent constitutive model for carbonfiber reinforced plastic woven fabrics[END_REF], and only considering shear loading conditions, the following constitutive law for in-plane stress is considered:

A logarithmic form was found to be a good approach for shear behaviour, thus the damage evolution law is defined as:

where + is the Macaulay bracket, a 12 is a coeficient, Y 0 12 is the damage initiation thermodynamic force and Y c 12 is the critical thermodynamic force.

Parameters identification

The identification procedure consists in determining by experimental data the values of the parameters appearing in the constitutive relations of the model [START_REF] Ladevèze | Damage modelling of the elementary ply for laminated composites[END_REF][START_REF] Marguet | A rate dependent constitutive model for carbonfiber reinforced plastic woven fabrics[END_REF][START_REF] Mateos | Comportement hystérétique en cisaillement des composites renforcés des fibres[END_REF][START_REF] Hochard | A generalized damage model for woven ply laminates under static and fatigue loading conditions[END_REF].

Evolution master curves

After determining G 0 12 , damage parameters d M 12 and i M 12 in loop M have been obtained. Then, once the damage parameters have been identified, the shear damage and irreversible strain evolution master curves can be determined. From experimental data, a quadratic evolution form has been obtained making it possible to estimate the irreversible strain threshold Y i 12 .

Fractional model parameters

In order to obtain the values for the parameters of the fractional model, an optimisation problem has been formulated aimed at minimising the error function e, which has been calculated adding all the individual data point errors in the interval considered. During the optimisation process and based on equation 5, the following model has been used:

The error function e , which is calculated from the error e m at time t m , has been defined as:

where σm 12 and σ m 12 are the shear stress value obtained from experimental tests and from the mathematical model, respectively, both evaluated at time t m . The unknown parameters of the model, namely G 0 12 , G k v , α k and d v k 12 can be then be obtained by minimising the error.

Results

After having obtained the values for the initial (undamaged) shear modulus from the shear stress-strain curve, damage initiation and irreversible strain threshold thermodynamic forces have been determined from the evolution master curves. In order to perform the optimisation problem, only one derivative order has been retained, that is, N = 1. Therefore, after the minimisation procedure only G 0 12 , G 1 and α 1 have been taken into account. Nevertheless, in order to analyse their evolution, their respective values for the M-th loop, G 0 M 12 ,G M 1 and α M 1 have been calculated. The results can be seen in table 1.


Mohamed Naoufal Mahfoudi

Thierry Parmentelat

Thierry Turletti

Walid Dabbous

Raymond Knopp
email: raymond.knopp@eurecom.fr

Raymond Knopp Deploy

Mohamed Naoufal

Mahfoudi Ierry Parmentelat Ierry Turle

Deploy a 5G network in less than 5 minutes: Demo Abstract

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

INTRODUCTION

Open Air Interface (OAI) [START_REF]Openairinterface: A exible platform for 5g research[END_REF] is an open-source so ware-based LTE ecosystem for prototyping 5th Generation Mobile Networks and devices. OAI currently provides a standard-compliant implementation of a subset of Release 10 LTE for UE (User Equipment), eNB (LTE Base station), MME (Mobility Management Entity ), HSS (Home Subscriber Server), SGW (Serving Gateway) and PGW (Packet Data Network Gateway) on standard Linux-based computing equipment (Intel x86 PC architectures). It is therefore possible to run advanced experiment scenarios such as Cloud Radio Access Network (C-RAN) with di erent functional splits, Beamforming or Coordinated Multipoint.

However, several challenges need to be tackled to ease the deployment of such scenarios:

• Cost and hardware availability: to build such an experimentation scenario, it is required to dedicate a handful of PCs with the right OS and proper low-latency avored kernel. A typical deployment will require one box to host an eNB (e-NodeB, or base station), another box to host the HSS (Home Subscriber Service), and a last box to run the MME (Mobility Management Entity) and SGW and PGW (Serving and Packet gateways, respectively). As far as the base station is concerned, the right kind of ETTUS Universal So ware Radio Peripheral (USRP) device is required as well such as a B210 or a X210 board. Furthermore, when using a USRP B210 board, a duplexer band 7 needs to be a ached, as the distance between the RX and TX antenna SMA connectors on the USRP B210 board is such that the TX antenna generates too much interferences to the RX channel.

Finally, whether the UE (User Equipment) is implemented on a commercial phone, or as a so ware component, each option comes with its own set of challenges. e former option requires a dummy SIM card while the la er requires proper con guration and another B210 board with a duplexer band 7 a ached di erently than for the one for the base station.

• Licensed frequency spectrum: the 2.6GHz band 7 is dedicated to LTE and LTE Advanced operators. So, running an LTE experimentation without authorization license is problematic. On the one hand, production LTE networks will add noise to the experimentation scenario and on the other hand, the experimentation may prevent legitimate LTE users from reaching their network. • High complexity to set up the OAI demo: even if the hardware is available and a license is obtained, there is a long list of operations to perform in order to deploy OAI scenarios 1 .

DEPLOYMENT IN R2LAB

In this demonstration2 , we use the FIT R2lab [1] wireless testbed to overcome the above mentioned challenges and provide an experimentation environment with a much lower barrier to entry. e R2lab testbed is an anechoic chamber located at Inria Sophia Antipolis, o ering 37 remotely accessible PCs and equipped with di erent wireless technologies, for instance Wi-Fi a/b/g/n cards, 5 USRP B210 with duplexer band 7 a ached, plus a dozen of USRP2/-N210/USRP1 that could be used for spectrum analysis or noise generator. In addition, R2lab also exposes a commercial Nexus 5 Phone, with OAI SIMcard, and programmable with Android Debug Bridge. In addition, the testbed provides hardware and so ware support for OAI. erefore R2lab would allow to control the entire chain in a complex 5G scenario from the C-RAN to the RF frontends. is addresses the rst challenge mentioned above.

R2lab provides a controlled environment, shielded from the outside interferences, and thus allows to test wireless experimental setups that uses licensed bands without the need for any special authorization. is solves the second challenge mentioned above. In addition, easy reservation of the whole testbed is also supported through the R2lab website. is allows avoiding interference from other experiments possibly running in parallel.

We also developed e cient scripts that automate the whole OAI demo set-up in few minutes using nepi-ng 3 . Network Experiment Programming Interface -new generation is a tool for orchestrating network experiments in an automated and e cient way. It is mainly used for alleviating problems related to provisioning the environment and running all the di erent steps of the wireless scenarios. is allows for a limited human intervention and thus less manipulation errors. We used nepi-ng to write and automate the whole experimentation scenario, including collection of all log les. As mentioned earlier, the base station and the core network are implemented on Intel x86 machines using OAI; a commercially available unmodi ed Nexus 5 with an OAI SIMcard is used as a user equipment (UE), see Figure 1. We chose to use a B210 ETTUS USRP with a duplexer band 7 as a radio front-end for the eNB hosted on t-23 node. We allocate node t-35 for the (HSS), this node is dedicated to authenticating. On node t-34, we run other pieces of the LTE infrastructure, namely the MME, as well as the SGW and PGW gateways, that primarily implement external connectivity to UE terminals. All these elements are depicted in Figure 2. Additionally, during the experiment we also dedicate two other USRPs for analyzing the spectrum, called watchers; it is very easy to use such nodes to generate controlled interferences, using respectively gnuradio's uhd fft and siggen.

As mentioned before, we reserve the whole testbed in our experiments to avoid interference from other users, and we only setup resources dedicated to the experiment to avoid problems of unintended RF activities from idle nodes. We also make sure to provision the infrastructure in the right order: rst the HSS; then the MME, the SGW and the PGW; then only the eNodeB; and nally the phone connects to the network. is allows to avoid problems related to synchronization. During this phase, the UE remains in airplane mode until the provisioning is nished.

In order to measure the upload and download speed of the UE through the deployed 5G network, we use the speedtest.net application. Figure 3 is demonstration shows that advanced realistic 5G scenarios can be easily and rapidly deployed with OAI so ware support in the R2lab anechoic chamber. Several scenarios can be run in this environment, thus exploiting the full control of end-to-end scenarios.

Debugging OpenAirInterface can be tricky, even for experts. e anechoic R2lab testbed o ers a controlled environment that is key in reproducing experiments and debugging. Indeed, using the R2lab utilities, it is straightforward to run the same experimentation scenario with two versions of OAI and compare the performance obtained or analyze logs, e.g., pcap traces to nd out and solve possible issues.

Figure 1 :

 1 Figure 1: OAI-based 5G network deployed in R2lab

Figure 2 :

 2 Figure 2: R2lab scenario

  provides a screen shot with the speedtest App interface on the right and the output of two tra c analyzers on the le side, showing the activity one for the downlink and the other for the uplink.

Figure 3 :

 3 Figure 3: Download performance and tra c analyzer

See the full list of these operations at h ps://gitlab.eurecom.fr/oai/openairinterface5g/ wikis/HowToConnectCOTSUEwithOAIeNBNew

See h ps://www.youtube.com/watch?v=N1nl PqWlKw

See h ps://nepi-ng.inria.fr/

ACKNOWLEDGMENTS Research and development leading to these results have received funding from the French Government (National Research Agency, ANR) through the Investments for the Future Program reference ANR-11-LABX-0031-01.

Technical requirements for the demo:

• Equipment to be used for the demo: None • Space needed: regular • Setup time required : 5 minutes • Additional facilities needed: power and Internet access are needed.


MSc Ashesh Shah

Jerome Coste

MD, PhD Jean-Jacques Lemaire

PhD Erik Schkommodau

MD Ethan Taub

MD Raphael Guzman

MD Philippe Derost

PhD Simone Hemm
email: simone.hemm@fhnw.ch.

PhD Jérôme Coste

A novel assistive method for rigidity evaluation during deep brain stimulation surgery using acceleration sensors

Keywords: deep brain stimulation, Parkinson's disease, rigidity, acceleration sensor, quantification, intraoperative, subthalamic nucleus, fields of Forel, functional neurosurgery

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

ABSTRACT

OBJECTIVE Despite the widespread use of deep brain stimulation (DBS) for movement disorders such as Parkinson's disease (PD), the exact anatomical target responsible for the therapeutic effect is still a subject of research. Intraoperative stimulation tests by experts consist of performing passive movements of the patient's arm or wrist while the amplitude of the stimulation current is increased. At each position, the amplitude that best alleviates rigidity is identified. Intrarater and interrater variations due to the subjective and semiquantitative nature of such evaluations have been reported. The aim of the present study was to evaluate the use of an acceleration sensor attached to the evaluator's wrist to assess the change in rigidity, hypothesizing that such a change will alter the speed of the passive movements. Furthermore, the combined analysis of such quantitative results with anatomy would generate a more reproducible description of the most effective stimulation sites. METHODS To test the reliability of the method, it was applied during postoperative follow-up examinations of 3 patients. To study the feasibility of intraoperative use, it was used during 9 bilateral DBS operations in patients suffering from PD. Changes in rigidity were calculated by extracting relevant outcome measures from the accelerometer data. These values were used to identify rigidity-suppressing stimulation current amplitudes, which were statistically compared with the amplitudes identified by the neurologist. Positions for the chronic DBS lead implantation that would have been chosen based on the acceleration data were compared with clinical choices. The data were also analyzed with respect to the anatomical location of the stimulating electrode.

RESULTS

Outcome measures extracted from the accelerometer data were reproducible for the same evaluator, thus providing a reliable assessment of rigidity changes during intraoperative stimulation tests. Of the 188 stimulation sites analyzed, the number of sites where rigiditysuppressing amplitudes were found increased from 144 to 170 when the accelerometer evaluations were considered. In general, rigidity release could be observed at significantly lower amplitudes with accelerometer evaluation (mean 0.9 ± 0.6 mA) than with subjective evaluation (mean 1.4 ± 0.6 mA) (p < 0.001). Of 14 choices for the implant location of the DBS lead, only 2 were the same for acceleration-based and subjective evaluations. The comparison across anatomical locations showed that stimulation in the fields of Forel ameliorates rigidity at similar amplitudes as stimulation in the subthalamic nucleus, but with fewer side effects.

INTRODUCTION

Deep brain stimulation (DBS) is a neurosurgical technique in which electrodes are implanted in deep-seated brain structures (e.g., the subthalamic nucleus [STN], globus pallidus, or thalamus) so that these structures can be stimulated with electrical pulses generated in an attached, extracranially implanted neurostimulator device. DBS is a highly effective symptomatic treatment for Parkinson's disease (PD) and other movement disorders. [START_REF] Wichmann | Deep-brain stimulation for basal ganglia disorders[END_REF] More than 100,000 patients have been treated with DBS in the past 3 decades. [START_REF] Strauss | Where are we with surgical therapies for Parkinson's disease?[END_REF] The current incomplete understanding of the mechanisms of action of DBS and interindividual variation of brain anatomy necessitate patient-specific planning. Most centers also perform intraoperative stimulation tests under local anesthesia at multiple anatomical locations in the vicinity of a preoperatively chosen target (1) to evaluate the therapeutic effects and side effects of stimulation before the DBS lead (permanent electrode) is definitively fixed in place. For some patients with PD, the therapeutic effects of stimulation tests are estimated by assessing the changes in rigidity as the stimulation current is increased. Expert evaluators (generally a neurologist) perform passive movements of the patient's arm continuously to assess the changes in rigidity. When either a reduction in rigidity or a side effect is observed, the amplitude and the effect of stimulation are noted. After completion of all stimulation tests, the results are compared to identify the best implant position, that is, the one that yields the best improvement with the fewest side effects.

Different evaluators assess rigidity during surgery in different ways, [START_REF] Fung | Objective quantification of resting and activated parkinsonian rigidity: a comparison of angular impulse and work scores[END_REF] but with the same basic concept: the baseline rigidity is rated before any stimulation, and the changes in rigidity are assessed in comparison with this baseline value. Intraoperatively used rating scales for PD are based on those commonly used outside the operating room (OR), mainly the Unified Parkinson's Disease Rating Scale [START_REF] Goetz | Movement Disorder Society-sponsored revision of the Unified Parkinson's Disease Rating Scale (MDS-UPDRS): scale presentation and clinimetric testing results[END_REF] and the Hoehn and Yahr staging scale. [START_REF] Hoehn | Parkinsonism: onset, progression and mortality[END_REF] Previous studies have shown that such rating scales have low interrater [START_REF] Palmer | Unified Parkinson's Disease Rating Scale-Motor Exam: interrater reliability of advanced practice nurse and neurologist assessments[END_REF][START_REF] Post | Unified Parkinson's disease rating scale motor examination: are ratings of nurses, residents in neurology, and movement disorders specialists interchangeable?[END_REF] and intrarater [START_REF] Post | Unified Parkinson's disease rating scale motor examination: are ratings of nurses, residents in neurology, and movement disorders specialists interchangeable?[END_REF] reliability, because they are subjective and depend highly on the experience of the evaluating neurologist. (8) Additionally, these scales have only discrete levels and were not designed for continuous rigidity evaluation.

(2) To increase the sensitivity for intraoperative use, some neurologists add intermediate levels to the existing rating scales. [START_REF] Kwon | Quantitative evaluation of parkinsonian rigidity during intraoperative deep brain stimulation[END_REF] An alternative way to increase sensitivity is to measure movement parameters during passive movement with sensors and thereby quantify the change in rigidity.

Various methods have been proposed for quantifying the absolute level of rigidity in patients with PD by measuring responses to passive movement. [START_REF] Kirollos | Objective measurement of activation of rigidity: diagnostic, pathogenetic and therapeutic implications in parkinsonism[END_REF][START_REF] Park | Analysis of viscoelastic properties of wrist joint for quantification of parkinsonian rigidity[END_REF][START_REF] Prochazka | Measurement of rigidity in Parkinson's disease[END_REF]) Some researchers have used surface electromyography (S-EMG) to measure muscle activity and have shown that the signals differ between healthy subjects and patients with PD. [START_REF] Levin | Objective measurement of muscle rigidity in Parkinsonian patients treated with subthalamic stimulation[END_REF][START_REF] Wright | Research and development of a portable device to quantify muscle tone in patients with Parkinsons disease[END_REF] Other techniques have also been proposed, which use a torque-motor setup to perform precise movements of a patient's arm or wrist while measuring joint angle and resistance. [START_REF] Askari | An EMG-based system for continuous monitoring of clinical efficacy of Parkinson's disease treatments[END_REF][START_REF] Fung | Objective quantification of resting and activated parkinsonian rigidity: a comparison of angular impulse and work scores[END_REF][START_REF] Sepehri | Quantification of rigidity in Parkinson's disease[END_REF] These studies showed that the features extracted from such precise movements are more strongly correlated with rating scales than those extracted from S-EMG signals. (4) However, the intraoperative use of such techniques to quantify rigidity would be excessively cumbersome or impossible. Usable signals from S-EMG electrodes can only be obtained when they are in close contact with the skin; the prolonged use of such electrodes might cause discomfort. In addition, the mechanical torque-motor setup limits the evaluation of rigidity to a single joint, and the apparatus is typically too large for use in the OR.

Rigidity is defined as the resistance to passive movement; thus, it can be presumed that during stimulation tests, the speed of the movement would increase with a reduction in rigidity. To the best of our knowledge, no such method has been proposed, in which the change in rigidity is assessed by measuring the change in speed (acceleration) of the passive movement. One reason for the lack of such a method could be the variations associated with the passive movements. In general, each expert evaluator has a preferred joint (arm/wrist) to perform passive movements to evaluate rigidity. Each expert can also choose the pattern of passive movement (extension, flexion, or circular) to be performed during a test. An expert may also stop and restart passive movements to prevent the patient's active participation in the movements. Therefore, any method for assessing rigidity that is based on the speed of movement should have robust outcome measures that are not influenced by the intrarater and interrater variability associated with passive movement.

We previously published a method [START_REF] Shah | A method to quantitatively evaluate changes in tremor during deep brain stimulation surgery[END_REF] for evaluating tremor during DBS surgery by using acceleration sensors. In the current study, we present various modifications of this method, with the aim of helping the neurologist assess the effect of stimulation on rigidity during intraoperative stimulation tests. Our hypothesis is that the relative change in rigidity can be assessed by measuring the acceleration of the evaluator's wrist during passive movement. To validate our approach, we studied the intra-and interrater variability of accelerometer measurements of passive movement in postoperative follow-up examinations of patients with PD treated with DBS. We evaluated the feasibility of intraoperative use of the system in a total of 9 DBS operations. The impact that this method would have had on the DBS surgery was studied by analyzing differences in the choice of position for the chronic DBS lead implantation (clinical choice vs choice based on accelerometry), a decision that is based on results of intraoperative stimulation tests. In addition, the accelerometry-based change in rigidity was correlated with the anatomical location of the stimulating electrode to identify the most effective stimulation sites.

METHODS

Recording Equipment

A commercially available accelerometer sensor evaluation board (STEVAL-MKI022VI, ST Microelectronics) was used to measure the acceleration of the passive movements. It was housed inside a printed plastic case (Full-Cure 830 Vero White, Stratasys) that could be attached to the wrist with a Velcro strap (Fig. 1). The sensor board was connected through a Universal Serial Bus (USB) cable to the laptop running custom-made in-house software (LemurDBS). A wireless sensor system was not used to avoid any possible interference with the microelectrode recording (MER) of the signal. Acceleration data were recorded and visualized with LemurDBS.

Filtering and Outcome Measures

The acceleration data were processed with MATLAB version R2015b (MathWorks, Inc.). They were filtered with a smoothness priors [START_REF] Tarvainen | An advanced detrending method with application to HRV analysis[END_REF] filter to remove the influence of gravity. To identify the changes in rigidity during intraoperative stimulation tests, the data were analyzed in a windowed manner. Various time lengths, ranging from 1 to 4 seconds with 0%-50% overlap, were tested. On the basis of the duration of a single passive movement (approximately 1 second), the duration of a single stimulation current amplitude, and the sampling frequency of the accelerometer, the 4-second window with 50% overlap was found to be optimal. To simplify the comparisons between various data sets, outcome measures were extracted from all windowed data. The measures previously found to be correlated with changes in tremor ( 22) (standard deviation, signal energy, and spectral amplitude of the dominant frequency) were used, along with others (entropy and primary frequency). For simplicity, these outcome measures will be referred to numerically as follows: 1) standard deviation, 2) signal energy, 3) spectral amplitude of the dominant frequency, 4) dominant frequency, and 5) entropy.

Data Acquisition

Reliability Tests

To study the intra-and interrater variability of the outcome measures, it was necessary to collect data in a controlled environment. Such data collection during intraoperative stimulation tests would have prolonged the operations and put the patients under additional stress. Moreover, because of restrictions imposed by the OR environment, only 1 sensor could be used at a time to measure acceleration. Theoretically, acceleration of passive movements could be measured by attaching the sensor either to the patient or to the evaluator. We hypothesized that attaching the sensor to the evaluator would record higher-quality data than placing the sensor on the patient during passive movements of the wrist joint. To study this matter further and investigate the intra-and interrater variability of accelerometer data measured during passive movement, we performed special tests during the postoperative follow-up of patients with PD treated with DBS.

A specific protocol was set up to be followed by each evaluator when obtaining data from a patient. The evaluators were required to perform a set of 4 passive movements (left elbow, left wrist, right elbow, and right wrist) twice, with a short pause in between. Data from 2 acceleration sensors (1 attached to the patient and 1 attached to the evaluator) were recorded simultaneously and in a synchronized manner to test the quality of acceleration data obtained from the 2 fixation positions during different evaluations.

Feasibility of Intraoperative Use

To study the intraoperative feasibility of the system, it was used during DBS operations at the University Hospital in Clermont-Ferrand, France. Surgical Procedure.

The clinical team uses direct targeting on patient-specific imaging data as part of the surgical procedure. ( 14) During the planning session, with the aid of a brain atlas developed in-house [START_REF] Lemaire | Contribution of 4.7 Tesla MRI in the analysis of the MRI anatomy of the human subthalamic area[END_REF] and multiple image sets of the patient (CT scans and MR images), including a specific white matter-attenuated inversion recovery sequence, the neurosurgeon identified and outlined the different deep brain structures in the subthalamic region with the iPlan Stereotaxy 3.0 planning software (Brain-lab). Two trajectories per hemisphere were planned, from an entry point in the skull to the target structure, avoiding sensitive structures (blood vessels, cerebral ventricles). For stimulation tests, multiple positions were identified along these trajectories in the region of interest, in 1-mm steps.

The surgery was performed on awake patients. Two exploration electrodes (Alpha Omega) were inserted and electrophysiological mapping (MER) was performed at the preplanned positions in both trajectories simultaneously. After MER, stimulation tests were performed at the same positions: first in one trajectory, then in the other, moving progressively deeper into the brain tissue in steps of 1 mm. At each position, the stimulation current was increased from 0 to 3 mA in steps of 0.2 mA. To evaluate rigidity, the neurologist first passively moved the patient's arm/wrist to assess baseline rigidity, before any stimulation was delivered. Then, during stimulation, changes in rigidity compared with baseline were rated on a scale from 0 (no change) to 4 (complete suppression of rigidity). Rigidity could be rated multiple times in a single evaluation, but only the maximum reduction in rigidity was noted and used for comparison with the results at other stimulation positions. The evaluator continuously interacted with the patient to observe any side effects and to make sure that he or she was not actively moving the limb.

At each position, 2 stimulation amplitudes were identified: 1) the amplitude at which the highest reduction in rigidity was observed (subjectively assessed amplitude [AmpS]), and 2) the amplitude at which the first side effect occurred (side-effect threshold). When stimulation tests were completed, the surgical team determined the best implant position, according to the following criteria: 1) low AmpS value, 2) large difference ("therapeutic window") between AmpS and the side-effect threshold, 3) neighboring positions having a comparatively large therapeutic window, and 4) anatomical position. Depending on the number of preoperatively chosen positions, stimulation tests in 1 cerebral hemisphere can take 15-30 minutes.

Intraoperative Protocol for Data Recording.

To avoid prolonging the surgical procedure while maximizing the data recorded during all of the stimulation tests, a systematic data-recording procedure was followed. The acceleration sensor was mounted on the evaluator's wrist during the stimulation tests. The strap was tightened snugly, but not uncomfortably, to prevent slippage. Data recording was started during the baseline evaluation and continued until the stimulation test for 1 position was completed. A new recording was started in a similar manner for each position, and the data were saved in separate files for offline analysis.

The stimulation current amplitude was varied in quick succession. To identify the exact amplitude responsible for the therapeutic effects, recording of acceleration data was synchronized with the electrophysiological system. For this purpose, the electrophysiology system (Microguide Pro, Alpha Omega) was connected to a laptop running LemurDBS with a USB-Bayonet Neill-Concelman (USB-BNC) cable (Fig. 1).

Clinical Application

The clinical use of the afore-described data-recording system for the purpose of intraoperative and postoperative symptom evaluation in the framework of this study was approved by the institutional review boards of the University Hospital in Clermont-Ferrand (France) and the University Hospital of Basel (Switzerland).

For the tests of intra-and interrater reliability in postoperative follow-up, 3 different evaluators were asked to perform passive movements to assess rigidity in 3 patients with PD, according to a predefined protocol. To simulate OR conditions, the tests were done with the patients supine. Each evaluator completed 8 passive movements for each patient, yielding a total of 72 evaluations (3 patients × 3 evaluators × 2 sides × 2 joints × 2 evaluations).

To investigate the feasibility of using the system during intraoperative stimulation tests, the recording system was used during the DBS operations of 9 patients with PD, who had rigidity as their primary symptom. The patients gave their written informed consent to participate in the study (for details, see Table 1). Four different neurologists performed routine passive movements to evaluate rigidity while wearing the acceleration sensor on their wrist (each patient was evaluated intraoperatively by only 1 neurologist).

Reliability Tests

To validate the outcome measures, they were extracted from the acceleration sensors in both positions (attached to the patient and to the evaluator, respectively) with the MATLAB scripts after verification of synchronization. Because these measures were extracted in a windowed fashion, multiple sets of measures were available per evaluation. The outcome measures extracted from the sensors on the patient and on the evaluator would be expected to be strongly correlated with each other (pairwise) because of the simultaneous synchronized recording of data. An absence of correlation would indicate insufficient quality of acceleration data. For each evaluation, the multiple sets of outcome measures were averaged to create a pairwise data set. To confirm our presumption that the sensor on the patient would not be sensitive enough to detect wrist movements, the pairwise correlation of the outcome measures from the patient's and the evaluator's sensors was tested for wrist and elbow evaluations separately with the Spearman correlation test.

For reliable assessment of changes in rigidity, the outcome measures of the evaluator's sensor were checked for intrarater variability by comparing data from evaluations 1 and 2 of each evaluation type. From the data set of averaged outcome measures, only those for the evaluator's sensor were separated into data from evaluations 1 and 2 for pairwise comparison. The Wilcoxon signed-rank test was used to verify similarity between the outcome measures of these 2 groups.

To study interrater variability, the multiple outcome measures per evaluation were compared independently for the different evaluators and patients. The data were grouped for the 4 different joints (left elbow, left wrist, right elbow, and right wrist). The Kruskal-Wallis ANOVA test was used for each patient to check for interrater variations.

The different groupings and statistical tests described above are summarized in Table 2.

TABLE 2. Categorization, comparison, and statistical tests used for analysis of data collected during reliability tests

Feasibility of Intraoperative Use

The intraoperatively recorded acceleration data were synchronized with the stimulation current amplitude according to the time-stamped synchronization signal (Fig. 2,upper). The repetitive nature of passive movements facilitated the identification and removal of data corresponding to other movements of the evaluator's arm. The data corresponding to 1 stimulation test were divided into 2 parts as follows: 1) the data recorded during passive movements without any stimulation were called baseline data, and 2) the remaining data were called stimulation data. These data were then filtered and outcome measures were extracted with the MATLAB scripts as described above. Further, to perform comparative analysis in a manner similar to the neurologists' evaluations, the extracted outcome measures from the stimulation data were normalized to the highest outcome measures at baseline (Fig. 2, lower).

FIGURE 2. Graphical representation of the recorded acceleration data synchronized with the stimulation current amplitude (upper) for 1 stimulation test, and outcome measures extracted in a windowed manner from the recorded signal along with the stimulation current amplitude (lower).

To investigate the pairwise correlation between normalized outcome measures and clinical ratings, Spearman's correlation test was used. Because a neurologist's assessment of change in rigidity was only noted once for each stimulation position (change at AmpS), the subjective ratings were compared with the normalized outcome measures at AmpS. Furthermore, the mean of the normalized outcome measures that were well correlated was called the quantitatively assessed change (QC) in rigidity.

Identification of Rigidity Release Threshold

During subjective evaluations, the AmpS (that is, the stimulation current amplitude for the highest change in rigidity) was determined by the evaluator for each stimulation position. In addition, the amplitude inducing a QC similar to the subjectively assessed reduction at AmpS was identified and designated as quantitatively identified rigidity-suppressing amplitude (AmpQ). The Wilcoxon 2-sided signed-rank test was used to compare AmpS and AmpQ for stimulation tests where both the AmpQ and the AmpS were identified.

Impact on Surgical Decision Making

During the routine procedure, the surgical team would determine the best implant position of the DBS lead on the basis of the AmpS, the side-effect threshold, and the anatomy, as described above. To study the effect of accelerometry-based rigidity change assessment on the final implant position chosen, the clinical staff was asked which final implant position they would have chosen if they had considered the AmpQ rather than the AmpS values. These choices were compared with the actual best implant positions chosen after intraoperative stimulation testing for each patient.

Anatomical Analysis

The intraoperative accelerometric assessment of change in rigidity was used to study the efficacy of stimulation in different anatomical structures as targets for the reduction of rigidity. On the basis of the planning data, the surgical team postoperatively identified the anatomical structure present at the center of the stimulating contact for every stimulation position and verified it with the MER data. To compare the efficacy of the different anatomical locations on the basis of the accelerometric measurements, at each stimulation test position the lowest stimulation current amplitude at which the QC value increased to more than 75% was identified, if it existed (Amp75). The threshold value of 75% was chosen to identify only the structures responsible for high reduction of rigidity. We also compared the side-effect thresholds and the number of stimulation tests where side effects were observed as a percentage of the total number of stimulation tests in a particular structure. These data sets, composed of Amp75, occurrence of side effects, and side-effect thresholds, were used to compare the efficacies of different anatomical structures.

RESULTS

The accelerometric method could be successfully applied in the postoperative validation tests and in 9 DBS operations without prolonging the procedures. All evaluators and patients were comfortable with wearing the acceleration sensor while performing the rigidity evaluations. Routine evaluations and routine surgical procedures took place as usual, without any interruptions. During implantation in the left hemisphere of Patient 1, the sensor was mounted on the patient's wrist and not on the evaluator's. Data recorded during these stimulation tests were not included in the analysis. No electrophysiological data were available for implantation in the left hemisphere of Patient 3. For Patient 7, due to the absence of rigidity, akinesia was evaluated during stimulation tests in the left hemisphere.

Reliability Tests Figure 3 shows an example of a comparison between data sets acquired with acceleration sensors mounted on the patient and on the evaluator for elbow and wrist movements. For the elbow tests, of the 5 outcome measures, 3 showed a strong correlation (outcome measure 1: R = 0.766, p < 0.001; outcome measure 2: R = 0.756, p < 0.001; and outcome measure 3: R = 0.697, p < 0.001) between the 2 sensors, whereas the remaining outcome measures (4 and 5) showed a weak or no correlation. In contrast, none of the features exhibited a correlation between patient-derived and evaluator-derived measurements of passive movement of the wrist.

FIGURE 3. Filtered acceleration data from the sensors mounted on the evaluator (solid gray line) and on the patient (solid black line). The graphs show data from the passive movements of the elbow (upper) and wrist joint (lower).

In the analysis of intrarater variability, the results of the paired-sample Wilcoxon signed-rank tests showed that 3 outcome measures did not change (outcome measures 1, 2, and 3; p < 0.001) between repeated evaluations of the same joint. Therefore, only these 3 outcome measures were retained in the further analysis.

The interrater variability analysis (Kruskal-Wallis ANOVA test) for the different joints and for each patient showed that outcome measures 1, 2, and 3 were significantly different (p < 0.05) among the 3 evaluators. Box plots in Fig. 4 represent the interrater variations in outcome measure 1. They show that for some evaluations (left elbow, right elbow, and right wrist of Patient 3), the interrater variability was very low, but for others (left and right elbow of Patient 1, and right wrist of Patient 3) there were significant interrater differences. Outcome measures 2 and 3 have similar distributions.

FIGURE 4. Box plots showing the interrater variations (E1, E2, E3) for outcome measure 1 for passive movements of the left elbow (A), left wrist (B), right elbow (C), and right wrist (D).

The statistical results of the above tests are summarized in Table 2.

Feasibility of Intraoperative Use

The comparison between the normalized outcome measures and the subjectively rated change in rigidity during intraoperative stimulation tests indicates a strong correlation for outcome measures 1 (R = 0.308, p < 0.001), 2 (R = 0.313, p < 0.001), and 3 (R = 0.237, p < 0.05).

Therefore, QC (the quantitatively assessed change in rigidity) was calculated as the mean of the normalized values of these outcome measures.

Identification of Rigidity Release Threshold

Of 188 stimulation tests during which acceleration data were recorded, AmpS and AmpQ were available and could be compared for 140 stimulation tests. The other 48 were composed of 14 evaluations where neither method identified any reduction in rigidity, 30 evaluations where the subjective evaluation did not find any threshold, and 4 evaluations where the accelerometric evaluation did not identify a threshold. The mean value of AmpQ (0.9 ± 0.6 mA) was lower than AmpS (1.4 ± 0.6 mA), and the results of the Wilcoxon 2-sided signed-rank test confirmed inequality between AmpQ and AmpS values (Fig. 5, p < 0.001). For stimulation tests where the value for AmpQ was lower than for AmpS, it was observed that the value of QC during stimulation was uniform between these 2 amplitudes.

FIGURE 5. Box plot comparing the rigidity-suppressing stimulation current amplitudes (n = 140

) identified with subjective evaluation (AmpS) and from the quantitative data (AmpQ). Upper whiskers are at the 95th percentile and lower whiskers are at the 5th percentile. Asterisks represent outliers.

Impact on Surgical Decision Making

The comparison of choices of the final implant position is shown in Table 3. Because of error in the synchronization setup, only 2 stimulation tests were analyzed for the left implantation in Patient 5, for which data were insufficient to identify the best implant position for this hemisphere. Of the remaining 14 implantations, for only 2 positions (rows in boldface type in Table 3), the choice was the same when made with AmpS or AmpQ. In 4 cases, a position on another trajectory was chosen on the basis of the AmpQ compared with the AmpS values.

TABLE 3. Choice of best implant position for the DBS lead

NA = not available (that is, for stimulation tests in the left hemisphere of Patients 1, 3, and 5, acceleration data were insufficient to make a choice). The choice of the best implant position was the same for the rows in boldface type.

Anatomical Analysis

For this analysis, 125 stimulation tests were used for which QC values were higher than 75%. Furthermore, the number of stimulation tests in the substantia nigra (1 test) and thalamus (4 tests) were not large enough to provide statistically significant results. Of the remaining 120 stimulation tests, 64 were in the STN, 35 were in the zona incerta (ZI), and 21 were found in the fields of Forel (FF). The results depicted on the left in Fig. 6 show that the STN requires lower stimulation current amplitudes than the ZI and FF to reduce rigidity by at least 75%. The average values of side-effect thresholds were similar for all 3 structures (STN 2.68 ± 0.36 mA, ZI 2.72 ± 0.17 mA, and FF 2.5 ± 0.22 mA), but the STN had a significantly higher occurrence of side effects (Fig. 6, right).

DISCUSSION

This article describes a novel method of recording and analyzing rigidity evaluation during DBS surgery by means of an acceleration sensor strapped on the evaluator's wrist. The aim was to test the hypothesis that changes in the patient's rigidity can be assessed by measuring acceleration during passive movement. Validation tests were performed to confirm the optimal mounting position of the acceleration sensor, to check for low intrarater variability of the outcome measures, and to assess interrater variability, before using the system intraoperatively.

Reliability Tests

The comparison between the data of the sensor on the patient's wrist and the sensor on the evaluator's wrist (Fig. 3) and the Spearman's correlation test confirmed our hypothesis that a fixation on the evaluator's wrist is more robust for measuring passive movements of both joints. Therefore, for an intraoperative use without altering the existing surgical procedure, the sensor should be mounted on the wrist of the evaluator, as done in the current study.

The low intrarater variability in 3 of the 5 outcome measures shows that these outcome measures are sufficiently robust for use in the intraoperative environment. During our intraoperative stimulation tests, intrarater variability would not have been relevant because the evaluator performs no other activity than passive movement, pausing only between stimulation test positions. In any case, even if the evaluator has to stop and then resume passive movements, the current method will be able to reliably assess the change in rigidity.

As mentioned previously, the performed passive movements vary between evaluators, (27) so interrater variations are expected in the accelerometer data. These variations also influence the outcome measures, as depicted in the box plots in Fig. 4 and as statistically confirmed. It must be borne in mind that the results of the Kruskal-Wallis ANOVA test are based on a small sample size, thus reducing their power. Because of the high inherent interrater variability of passive movements, the determination of the absolute level of rigidity in patients by measuring the acceleration is not possible. Thus, the aim of the current study was to develop a method for the determination of relative changes compared with baseline evaluations.

Feasibility of Intraoperative Use

The method proposed in this article is designed to assist the neurologist in estimating the changes in rigidity during intraoperative stimulation tests of DBS surgery. Considering that in most centers only 1 evaluator is present to perform the passive movements, the current method will produce reliable results because of the high intrarater reliability. Additionally, the technique of normalization of the outcome measures used in the current method not only mimics the subjective evaluation method (that is, assess changes compared with baseline values), but also minimizes the effect of any residual intrarater variability between different stimulation test positions. The evidence is provided by the results of the Spearman's correlation tests between the 3 normalized outcome measures and the clinically rated changes in rigidity.

Moreover, such an evaluation is superior to absolute evaluation, because the rigidity of the patient may also change due to other factors such as microlesional effects, patient stress, and so on. However, it was also noted during the data analysis that a minimum recording of 5 seconds of baseline evaluation is needed to obtain evaluable results. When such data were unavailable, the baseline data from the previous stimulation test position (a maximum of 3 minutes before) were used. The results of the application of this method in 9 DBS operations support its future use in the OR.

Quantitative rigidity evaluations have rarely been performed during DBS surgery. To our knowledge, only Kwon et al. [START_REF] Kwon | Quantitative evaluation of parkinsonian rigidity during intraoperative deep brain stimulation[END_REF] have used a mechanical setup to measure parameters of rigidity in the wrist joint while the patient underwent surgery. An expert evaluator passively moved the patient's wrist around the joint through a handle while the input force of the evaluator and the inertia of the movement were measured. Mechanical parameters such as work, impulse impedance, and so on were extracted. In contrast to our method, their setup enables the measurement of multiple variables simultaneously, but is restricted to evaluation of the wrist joint. Moreover, for proper functioning, instructions were given to the evaluator to perform a specific movement, which resulted in longer evaluations. In addition, the evaluator had to change his or her routine evaluation protocol. In order not to prolong the surgical procedure, fewer evaluations were performed when their setup was used. (12) Our system was specifically designed for use in routine evaluation; no instructions were given to the patient or the evaluator.

Because the evaluator could follow his or her usual evaluation protocol, the duration of the routine surgery was unaltered.

Identification of Rigidity Release Threshold

One of the advantages of using our method rather than subjective evaluation is in the identification of rigidity release thresholds. Twenty-six more thresholds were found with our data analysis technique. Also, the results of the Wilcoxon 2-sided signed-rank test and the box plot show that values tend to be lower for AmpQ than for AmpS. We believe that the human evaluator, on observing the change in rigidity, may need a few seconds to verify and assess the amount of reduction. During this time, the amplitude may have already been increased, resulting in higher AmpS values. This result suggests that the current setup enhances the sensitivity of the subjective rigidity evaluation. On the other hand, there were 4 positions where AmpS values, but no AmpQ values, were found. On inspection of these 4 positions, it was observed that the baseline data were insufficient to extract outcome measures for normalization. Because they were the first positions tested, baseline evaluations of previous positions were unavailable to use the workaround. This underscores the need for sufficient baseline recording for data analysis.

Impact on Surgical Decision Making

The differences in the rigidity release amplitudes identified by the 2 methods significantly influenced the choice of the best implant position. Only 2 of the 12 choices would have been at the same position. This clearly shows the potential of using an assistive method during intraoperative symptom evaluation for DBS surgery. From the current data, it is not possible to judge which of the 2 choices was better. One possible way would be to compare the choice of best implant position with the choice of postoperative contact; the relative closeness of one or the other choice may help to judge whether the assistive evaluation system can identify better implant positions. However, such an analysis would need a very large data set to result in statistically significant conclusions.

Anatomical Analysis

The anatomical analysis gives interesting insight into the target selection procedure of DBS. It shows that stimulation in the STN requires the lowest current amplitude to achieve a 75% reduction in rigidity. However, in view of the fact that side effects were observed in nearly 50% of stimulations in the STN, it may not be the optimum target structure. The FF require an additional 0.3 mA, on average, to achieve a comparable reduction in rigidity, but have significantly fewer side-effect occurrences. Hence, to achieve a better outcome of DBS for patients with rigidity, the DBS lead might be placed closer to the FF or the ZI and not inside the STN, to avoid side effects. This would be in accordance with reported findings [START_REF] Aström | Patientspecific model-based investigation of speech intelligibility and movement during deep brain stimulation[END_REF][START_REF] Godinho | Subthalamic nucleus stimulation in Parkinson's disease: anatomical and electrophysiological localization of active contacts[END_REF][START_REF] Hamel | Deep brain stimulation of the subthalamic nucleus in Parkinson's disease: evaluation of active electrode contacts[END_REF][START_REF] Saint-Cyr | Localization of clinically effective stimulating electrodes in the human subthalamic nucleus on magnetic resonance imaging[END_REF][START_REF] Zheng | Subthalamic deep brain stimulation for Parkinson's disease: correlation of active contacts and electrophysiologically mapped subthalamic nucleus[END_REF] implying that the FF and the ZI may also be responsible for the therapeutic effects of DBS. However, this analysis has a limitation. It only considers the center of the electrode when associating a structure with a stimulation test position. Because the effect of stimulation spreads beyond the center, electric-field simulations would be a helpful tool to deepen the analysis of the available intraoperative data.

Future Work

In its current state, the method proposed in this study has various advantages over the existing subjective ratings used in the OR. It provides a reproducible assessment of the change in rigidity, which can be reviewed at any time during surgery without any discomfort to the patient or evaluator, and without prolonging the operation. Nevertheless, because the changes in rigidity are assessed indirectly, the results produced are only semiquantitative. In the future, to make the method a comprehensive evaluation system for use in DBS surgery, the current setup will be modified to enable data recording and analysis from 2 smaller acceleration sensors simultaneously. By mounting one sensor on the evaluator and the other on the patient, [START_REF] Strauss | Where are we with surgical therapies for Parkinson's disease?[END_REF] it will be possible to evaluate rigidity and tremor at the same time. We intend to use the system in more operations (optimally, in additional clinical centers as well) so that we can continue to adapt it to physicians' needs. The long-term aim is to integrate this method in commercially available and currently used intraoperative stimulation systems to facilitate visualization of the symptom improvement in real time, along with other stimulation parameters and anatomical data. Such a system would enable the surgical team to interpret the results of intraoperative stimulation tests more easily and thus facilitate surgical decision making.

CONCLUSIONS

We have described a new way to assess changes in rigidity by measuring the acceleration of the examiner's wrist during passive movement while the patient is undergoing intraoperative stimulation testing in DBS surgery. Outcome measures are reproducible over time but are influenced by variations in the passive movements of different evaluators. The intraoperatively assessed change in rigidity is reliable and is correlated with the subjective ratings. The quantitatively identified effective stimulation amplitudes show the potential of the method to optimize surgical decision making. Moreover, our findings concerning the thresholds for effective stimulation at different anatomical sites suggest that the optimal DBS target may, in fact, lie closer to the FF, just dorsal to the STN. The proposed method may be a clinically and scientifically useful aid to optimal targeting in DBS.

FIGURE 1 .

 1 FIGURE 1. Data recording setup used to assist rigidity evaluations performed during DBS surgery.

TABLE 1 .

 1 Details about patients participating in the clinical study and their surgical procedures UPDRS = Unified Parkinson's Disease Rating Scale. Acceleration data were unavailable for the stimulation tests in boldface type.Data Analysis MethodThe data were analyzed with MATLAB. Statistics were performed with SOFA Statistics version 1.4.5 (Paton-Simpson & Associates Ltd.) and OriginPro (Origin-Lab Corporation).

FIGURE 6 .

 6 FIGURE 6.Left: Column charts comparing the average stimulation current amplitude required to observe at least a 75% reductionin the mean of the 3 outcome measures (standard deviation, signal energy, and spectral amplitude of the primary frequency). Right: Stacked 100% column charts present the number of stimulation tests where side effects were observed (black) as a percentage of the total number of stimulation tests in the corresponding structure. The numbers inside the black part of the bars indicate the actual count of the side-effect occurrences; the numbers below the bars indicate the total number of stimulation tests.

ACKNOWLEDGEMENTS

This research was funded by the Swiss National Science Foundation as a part of the project 205321_135285 and partly by the Germaine de Stael program of the Swiss Academy of Engineering Sciences. We acknowledge and thank Prof. F. Durif, Dr. M. Ulla, and Dr. A. Marques of the Department of Neurology at the CHU Clermont-Ferrand, France, and Ms. Bianca Raffaelli and Prof. Dr. Peter Fuhr of the Department of Neurology at the University Hospital of Basel, Switzerland, for performing the routine passive movements for rigidity evaluations.

Disclosures

The authors report no conflict of interest concerning the materials or methods used in this study or the findings specified in this paper.

Author Contributions