Florent Lalys

Laurent Riffaud

Xavier Morandi

Pierre Jannin

Automatic phases recognition in pituitary surgeries by microscope images classification

Keywords: Surgical phase, digital microscope, neurosurgery, feature extraction

The segmentation of the surgical workflow might be helpful for providing context-sensitive user interfaces, or generating automatic report. Our approach focused on the automatic recognition of surgical phases by microscope image classification. Our workflow, including images features extraction, image database labelisation, Principal Component Analysis (PCA) transformation and 10-fold cross-validation studies was performed on a specific type of neurosurgical intervention, the pituitary surgery. Six phases were defined by an expert for this type of intervention. We thus assessed machine learning algorithms along with the data dimension reduction. We finally kept 40 features from the PCA and found a best correct classification rate of the surgical phases of 82% with the multiclass Support Vector Machine.

Introduction

With the increased number of technological tools incorporate in the OR, the need for new computer-assisted systems has emerged [START_REF] Cleary | The operating room of the future[END_REF]. Moreover, surgeons have to deal with adverse events during operations, coming from the patient itself but also from the operation management. The idea is to limit and be aware of these difficulties, and to better handle risks situations as well as to relieve surgeon's responsibilities. The purpose of recent works is not to substitute medical staff in the OR but to increase medical safety and support decision making. One solution is to assist surgeries through the understanding of operating room activities, which could be introduce in current surgical management systems. It could be useful for OR management optimization, providing context-sensitive user interfaces or generating automatic reports. Thus, surgical workflow recovery as well as surgical process modelling has gained much interest during the past decade.

Neumuth et al. [START_REF] Neumuth | Validation of Knowledge Acquisition for Surgical Process Models[END_REF] defined Surgical Process (SP) as a set of one or more linked procedures or activities that realize a surgical objective. Surgical Process Models (SPMs) are simply defined by models of surgical interventions. A detailed SPM may help in understanding the procedure by giving specific information of the intervention course. Applications of SPMs are the evaluation of surgeons (training and learning), system comparison, procedures documentations and surgical feedbacks. As Jannin et al. [START_REF] Jannin | Surgical models for computer-assisted neurosurgery[END_REF] mentioned, the modeling must address behavioral, anatomical, pathological aspects and surgical instruments. They also defined surgical workflow, which relates to the performance of a SP with support of a workflow management system.

Teams have understood the necessity of real-time information extraction for the creation of complex surgeries models. The difference in the level of granularity for the extraction process allows deriving complementary numeric models for workflow recovery. Thus, data extraction is performed either from a human sight or from sensor devices. In this context, different methods have been recently used for data acquisition: patient specific procedures description [START_REF] Neumuth | Validation of Knowledge Acquisition for Surgical Process Models[END_REF][START_REF] Jannin | Surgical models for computer-assisted neurosurgery[END_REF][START_REF] Jannin | Model of surgical procedures for multimodal image-guided neurosurgery[END_REF], interview of the surgeons [START_REF] Morineau | Decision making during preoperative surgical planning[END_REF], sensor-based methods [START_REF] Padoy | A boosted segmentation method for Surgical Workflow Analysis[END_REF][START_REF] Rosen | Task decomposition of laparoscopic surgery for objective evaluation of surgical residents' learning curve using hidden markov model[END_REF][START_REF] Lin | Towards automatic skill evaluation: Detection and segmentation of robot-assisted surgical motions[END_REF][START_REF] Voros | Towards "real-time" tool-tissue interaction detection in robotically asisted laparoscopy[END_REF][START_REF] Ahmadi | Motif discovery in OR sensor data with application to surgical workflow analysis and activity detection[END_REF][START_REF] Bhatia | Real-time identification of operating room state from video[END_REF][START_REF] Xiao | An algorithm for processing vital sign monitoring data to remotely identify operating room occupancy in realtime[END_REF][START_REF] James | Eye-gaze driven surgical workflow segmentation[END_REF][START_REF] Nara | Surgical workflow analysis based on staff's trajectory patterns[END_REF][START_REF] Speidel | Situation modelling and situation recognition for a context-aware augmented reality system[END_REF][START_REF] Sanchez-Gonzales | Segmentation and 3D reconstruction approaches for the design of laparoscopic augmented reality[END_REF], using fixed protocols created by expert surgeons [START_REF] Mackenzie | Hierarchical decomposition of laparoscopic surgery: a human factors approach to investigating the operating room environment[END_REF], or combination between them [START_REF] Neumuth | Computer assisted acquisition of surgical process models with a sensors-driven ontology[END_REF].

Within sensor-based approaches, Padoy et al. [START_REF] Padoy | A boosted segmentation method for Surgical Workflow Analysis[END_REF] segmented the surgical workflow into phases based on temporal synchronization of multidimensional state vectors, using Dynamic Time Warping (DTW) and Hidden Markov Models (HMMs). These algorithms permit to recognize patterns and extract knowledge. Signals recorded were binary vectors indicating the instrument presence.

At a lower level, the force/torque signals of the laparoscopic instruments recorded during a suturing task can be learned with HMMs [START_REF] Rosen | Task decomposition of laparoscopic surgery for objective evaluation of surgical residents' learning curve using hidden markov model[END_REF]. Close to this work, Lin et al. [START_REF] Lin | Towards automatic skill evaluation: Detection and segmentation of robot-assisted surgical motions[END_REF] also trained HMMs to automatically segment motion data during a suturing task perform with the Da Vinci robot. With the same robot, Voros and Hager [START_REF] Voros | Towards "real-time" tool-tissue interaction detection in robotically asisted laparoscopy[END_REF] used kinematic and visual features to classify tool/tissue interactions in real-time. Their work was a first step towards intelligent intraoperative surgical system. Recent work of Ahmadi et al. [START_REF] Ahmadi | Motif discovery in OR sensor data with application to surgical workflow analysis and activity detection[END_REF] used accelerometers placed on the operator along with motif discovery technique to identify alphabets of surgical activity. Models of gestures relied on tools only and motions may not be well segmented with rare movements.

Using others data extraction techniques, Bhatia et al. [START_REF] Bhatia | Real-time identification of operating room state from video[END_REF] analyzed OR global view videos for better management, whereas Xiao et al. [START_REF] Xiao | An algorithm for processing vital sign monitoring data to remotely identify operating room occupancy in realtime[END_REF] implemented a system that record patient vital signs in order to situate the intervention process. James et al. [START_REF] James | Eye-gaze driven surgical workflow segmentation[END_REF] installed an eye-gaze tracking system on the surgeon combined with visual features to detect one important phase. Nara et al. [START_REF] Nara | Surgical workflow analysis based on staff's trajectory patterns[END_REF] introduced an ultrasonic location aware system that continuously tracks 3-D positions of the surgical staff. Results on identifying key surgical events were presented. For the construction of a contextaware system, Speidel et al. [START_REF] Speidel | Situation modelling and situation recognition for a context-aware augmented reality system[END_REF] used laparoscopic videos to create a situation recognition process. In their work, they focused on risk situation for surgical assistance. Finally, Sanchez-Gonzales et al. [START_REF] Sanchez-Gonzales | Segmentation and 3D reconstruction approaches for the design of laparoscopic augmented reality[END_REF] extracted useful information from videos such as 3D map to help surgeons performing operating techniques.

Our project is based on the extraction of information from digital microscope videos. It permits not only to avoid the installation of supplementary materials in the OR, but also to have a source of information that has not to be controlled by human. Computer vision techniques bring processing algorithms to transform images and videos into a new representation that can be further used for machine learning techniques (supervised or non-supervised classification). We decided in a first phase to use image from videos (called frames) in a static way without taking into account the motion. The problem is thus reduced to an image classification problem. Even with this restriction, technical possibilities remain very large. We focused on the automatic recognition of surgical phases and validated our methodology with a specific type of neurosurgical interventions.

Materials and Methods

We evaluated our algorithm on pituitary adenoma surgeries [START_REF] Ezzat | The prevalence of pituitary adenomas: a systematic review[END_REF]. It's tumors that occur in the pituitary gland and which are representing around ten percent of all intracranial tumour removals. Neurosurgeons mostly use a direct transnasal approach, where an incision is made in the back wall of the nose. Rarely, a craniotomy is required. In this work all surgeries were performed according to the first approach.

Data

Our project is currently composed of 16 entire pituitary surgeries (mean time of surgeries: 50min), all performed in Rennes by three expert surgeons. Videos were recorded using the surgical microscope OPMI Pentero (Carl Zeiss). The initial video resolution was 768 x 576 pixels at 33 frames per second. Recordings were obtained from nasal incision until compress installation (corresponding to the microscope use). From these videos, we randomly extracted 400 images which were supposed to correctly represent the six phases of an usual pituitary surgery. These phases, which were validated by an expert surgeon, are: nasal incision, nose retractors installation, access to the tumor along with tumor removal, column of nose replacement, suturing and nose compress installation (Fig. 1). Each image of the database was manually labeled with its corresponding surgical phase.

Feature extraction

We defined for each image a feature vector that represented a signature. Images signatures are composed of three main information that usually describe an image: the color, the texture and the form.

The color has been extracted with two complementary spaces [START_REF] Smeulders | Content-based image retrieval at the end of the early years[END_REF]: RGB space (3 x 16 bins) along with Hue (30 bins) and Saturation (32 bins) from HSV space.

The texture has been extracted with the co-occurrence matrix along with Haralick descriptors [START_REF] Haralick | I: Textural features for image classification[END_REF]. The co-occurrence matrix is used to describe the patterns of neighboring pixels in an image I at a given distance. Mathematically, the matrix C is defined over an image n x m and an offset:

∑ ∑ = = Δ Δ ⎩ ⎨ ⎧ = Δ + Δ + = = n p m q y x otherwise j y q x p I and i q p I if j i C 1 1 , , 0 ) , ( ) , ( , 1 ) , ( (1)
Four such matrices are needed for different orientations (horizontal, vertical and two diagonal directions). A kind of invariance was achieved by taking into account the four matrices. Haralick descriptors were then used by computing the contrast, the correlation, the angular second moment, the variance of the sum of squares, the moment of the inverse difference, the sum average, the sum variance, the sum entropy, the difference of variance, the difference of entropy, and the maximum correlation coefficient of the co-occurrence matrix.

The form was represented with spatial moments [START_REF] Hu | Visual pattern recognition by moment invariants[END_REF], which describe the spatial distribution of values. For a grayscale image the moments j i, M are calculated by:

∑∑ n = p m = q j i j i, q) I(p, q p = M 1 1 (2)
The 10 first moments were included in the signatures. We then computed the Discrete Cosine Transform (DCT) [START_REF] Ahmed | Discrete Cosine Transform[END_REF] coefficients pq B that reflect the compact energy of different frequencies. DCT is calculated by: 2N

1 2n cos 2M 1 2m cos 1 0 1 0 )q + π( )p + π( A α α = B M = m N = n mn q p pq ∑∑ -- , 1 0 1 0 - ≤ ≤ - ≤ ≤ N q M p (3) with ⎪ ⎩ ⎪ ⎨ ⎧ = M M p 2 1 α , p=0 1≤ p≤ M -1 and ⎪ ⎩ ⎪ ⎨ ⎧ = N N q 2 1 α , p=0 1≤ p≤ M -1
The pq B coefficients of upper left corner represent visual information of lower intensities, whereas the higher frequency information is gathered at right lower corner of the block. Most of the energy is located in the low frequency area, that's why we took the 25 features of the upper left corner. Each signature was finally composed of 185 complementary features.

Data reduction

Original frames were first downsampled by a factor of 8 with a 5-by-5 Gaussian kernel (internal studies have shown that until this downsampling rate, it had no impact on the classification process). After features extraction, we performed a statistical normalization. On each feature value we subtracted the mean and divided by the variance. After normalization, data closely followed a normal distribution (mean=0 and standard deviation=1) and were more easily used for data variations comparisons.

In order to decrease the data dimension, and knowing that many features can decrease the correct classification rate, we also performed a Principal Component Analysis (PCA) [START_REF] Jolliffe | Principal component analysis[END_REF]. PCA is a statistical method used to decrease the data dimension while retaining as much as possible of the variation present in the data set to process the data faster and effective. Fig. 3 shows the extracted cumulative variance.

Cross-validation

With the image data-base we are now able to train models by using machine learning techniques. We performed a study to find the most appropriate algorithm. We tested multiclass Support Vector Machine (SVM), K-Nearest Neighbors (KNN), Neural Networks (NN), decision tree and Linear Discriminant Analysis (LDA).

The goal of SVM is to find the optimal hyperplane that separates the data into two categories. The multiclass SVMs [START_REF] Crammer | On the Algorithmic Implementation of Multi-class SVMs[END_REF] extends it into a K-class problem, by constructing K binary linear SVMs. The KNN algorithm (used with the Euclidean distance) is the simplest method for classification. Each point in the space is assigned to the class C if it is the most frequent class label among the k-nearest training samples. NN [26] are non-linear statistical methods based on biological neural networks. They are often used to model complex relationships between inputs and outputs. We used it in a supervised way with a back-propagation neural network. The decision tree is a quick classification algorithm where each internal node tests an attribute. It is specially used when data are noised and classes are discrete. Finally, the LDA is based on a Fisher analysis. It is a linear combination of features that best separate two or more classes.

Algorithms were evaluated with a random 10-fold cross-validation study [START_REF] Duda | Pattern Classification[END_REF]. The data-set was divided into 10 random subsets. Nine were used for training while the prediction is made on the 10 th subset. This procedure was repeated 10 times and correct classification rates were averaged. In addition, the cross-validation study allows computing the sensitivity and the specificity. The specificity is defined by: The cross-validation was computed for each algorithm but also for each number of principal components used in order to keep the best classification algorithm and to decide how many principal components we had to take. Fig. 2 shows the cross-validation study. Multiclass SVMs and LDA give best results. For both algorithms the correct classification rate increase until 40 principal components and then LDA decreases while SVMs stays at a higher recognition rate. From 30 principal components, correct classification rates of the NN and KNN are almost unchanging, but their best scores are significantly lower than for SVM and LDA. Finally, the decision tree gives the worst results compare to other classifiers. We decided to keep 40 principal components, which represent 91.5% of the energy of all the data set (Fig. 3). With these features we obtained accurate statistical results: We can see from Tab. 1 that specificity is always upper than sensitivity for all algorithms. Not surprisingly, multiclass SVMs obtained best sensitivity (78.7%) and specificity (98.1%) whereas the decision tree shows its limits (specificity: 52.3%).

The computation time of the classification process of one image (feature extraction + data transformation + classification) was less than 0.5s. We didn't take into account the computation time of the learning database, considering that it was done off-line.

Discussion

Our global workflow, including image database labelisation, features extraction, PCA, and cross-validation studies make possible the extraction of discriminant image features for each phase. After experiments, we finally kept 40 principal components for a best correct classification rate of the surgical phases of 82% with SVMs.

Images database

The performance is strongly linked to the diversity and the power of discrimination of the database. We can easily imagine that accuracy may sorely decrease if images are not efficiently representing all phases or all scene possibilities within phases.

There are other limitations to this type of study. The image database may not be adaptable to other neurosurgery departments, due to the difference of materials and equipment in each department. For instance, the color of surgical tissue in Rennes may be different elsewhere and the corresponding features would completely affect the training process. The solution would be to train specific image databases for each department which would be well adapted to the surgical environment. The idea would also be to have several databases for each type of procedure with specific phases. For other departments and/or surgeries, discriminant images features may differ, which would require adapting the feature extraction process by launching identical studies.

Other factors of variability within the data-set can affect the recognition. For instance, differences can be found in the way that surgeons are working or in patient specific surgery. Ideally, one database should be created for each department, associated with each type of surgery and each surgeon.

Explanation of classification errors

We decided to fuse the initial possible phases "access to the tumor" and "tumor removal" because for this type of surgical procedure it's currently hard to distinguish them only with image features. The transition between both is not clearly defined due to similar tools and same microscope zooms used while performing these tasks.

The correct classification rate includes the results of the cross-validation study for the six phases. From these results, we noticed frequent confusions mainly between phase n°3 and n°4, and also between n°1 and n°5. These errors are explained by the very close image features of these phases. Same microscope zooms, along with similar colors and same surgical instruments make the recognition task very difficult. One solution of this issue would be to integrate one other signal: the surgery time. This information would for instance permit to correctly recognize an image originally identified as part of phase n°5 or part of phase n°1. On the other hand it would still be hard to separate consecutive phases.

Classification algorithms

In this study (Fig. 2), multiclass SVMs and LDA gave the best correct classification rates. SVMs have been used in a linear way and are known to have good generalization properties that permit to outperform classical algorithms. LDA, used as a classifier, is like many others optimal when the features have a normal distribution (true in our case after normalization). On the opposite, the decision tree, NN and KNN gave worse results. Decision trees are often instable, especially with small changes in the training samples. Our data-set was probably too variable (in color, texture...) and not enough discriminant to train accurate models with decision trees. While KNN is generally outperformed by other classifiers, it may be well interesting because of its simplicity and flexibility. Nevertheless, our results showed that it was not suitable for our data-set. Concerning NNs, it was quite surprising regarding their capabilities to improve their performances when the amount of data increases. Nonlinear algorithms are generally more suitable for complex systems, which is not the case here. On the opposite, linear ones are more straightforward and easy to use, that's why it seems that they are more adaptable for our system.

The correct classification rates for SVMs, KNN and NN are almost constant until 185 features, whereas accuracy of the decision tree and especially LDA decrease. This is due to the high dimension of inputs which usually decreases results of classifiers. It's also the reason why we only kept 40 features for images signatures. If PCA would not have been performed, we would only have obtained an accuracy of 78% (with KNN), which demonstrated the usefulness of this step in our workflow.

According to Tab. 1, most of the difference between classifiers is made by sensitivities, which are lower than specificities. A high specificity is due to the absence of FP (image belonging to phase x not identified as part of phase x), whereas a low sensitivity is due to a high FN rate (image not belonging to phase x identified as part of phase x). Thus the challenge in the future would be to increase FN rates.

In presence of unexpected events, such as bleeding or brutal microscope move, the specificity sensibly decreases and thus affects global accuracy. Such situations, as being unpredictable, are a high limitation to the classification from static images only. One solution of this issue, not implemented yet, would be to detect such images (containing features that are very different from the others, and therefore easily detectable) and to take into account the recognized phase of the precedent image.

Applications

The idea is to assist surgeries through the understanding of operating room activities. This work could be integrated in an intelligent architecture that extracts microscope images and transform it in a decision making process. The purpose would be to bring a plus-value to the OR management (as in [START_REF] Ahmadi | Motif discovery in OR sensor data with application to surgical workflow analysis and activity detection[END_REF]) and to the surgery (as in [START_REF] Nara | Surgical workflow analysis based on staff's trajectory patterns[END_REF]). For now, even with a low on-line computation time (< 0.5s), the best obtained correct classification rate is certainly not accurate enough to be included in such systems. For intra-operative clinical applications, accuracy must definitively be higher than our results before establishing on-line surgical phases detection.

However, with the present methodology, the system could be introduced in the surgical routine as an help for post-operative indexation of videos. Surgical videos are very useful for learning and teaching purposes, but surgeons often don't use them because of the huge amount of surgical videos, the lack of data organization and storage. The created video data-base would contain relevant surgical phases of each procedure for easy browsing. Moreover, we could imagine the creation of postoperative reports, automatically pre-filled by recognized events that will have to be further completed by surgeons themselves. For such clinical applications, even with few errors, the automatic indexation would be relevant, as there is no need of perfect detection and it has no impact on the surgery itself.

We deliberately remain at a high level of granularity with the recognition of global phases. The recognition of lower level information, such as surgical gestures, is very difficult (almost impossible) only with images. Other computer vision techniques (such as tracking) or specific video processing methods (such as spatio-temporal features extraction) will have to be inserted and mixed for dynamic information extraction.

Conclusion

With this large labeled images database, we are now able to recognize surgical phases of every unknown image, by computing his signature and then simulating with machine learning techniques. We have validated our methodology with a specific type of neurosurgery, but it can easily be extended to other type of interventions. With this recognition process, it's a first step toward the construction of a context-aware surgical system. Currently this work could be used for post-operative video indexation as a help for surgeons. Image features will have to be mixed with other type of information to generate a more robust and accurate recognition system. Other methods usually used by the computer vision community (segmentation, tracking) could also be integrated in future works in order to bring complementary features.

Fig. 1 .

 1 Fig. 1. Example of typical digital microscope images for the six phases: 1) nasal incision, 2) nose retractors installation, 3) access to the tumor along with tumor removal, 4) column of nose replacement, 5) suturing, 6) nose compress installation.

  TP is True Positive, FN is false Negative and TN is True Negative.

Fig. 2 .

 2 Fig. 2. Correct classification rate of the surgical phases with five different algorithms, according to the number of principal components.

Fig. 3 .

 3 Fig. 3. Cumulative variance of the Principal Component Analysis.

Table 1 .

 1 Correct classification rate (accuracy), sensitivity and specificity of classification algorithms. Image signatures are composed of the 40 first principal components.

	Algorithms	Accuracy	Sensitivity	Specificity
	Multiclass SVMs	82.2%	78.7%	98.1%
	KNN	74.7%	66.0%	95.4%
	Neural Network	71.3%	65.1%	92.8%
	Decision tree	66.2%	52.3%	94.0%
	LDA	81.5%	77.0%	97.6%

Acknowledgments. The authors would like to acknowledge the financial support of Carl Zeiss Surgical GmbH.


Pierre Nataf

Cristiano Ciuti

Protected quantum computation with multiple resonators in ultrastrong coupling circuit QED

Keywords: numbers: 03.65.Yz, 85.25.Hv, 42.50.Pq, 03.67.Pp

We investigate theoretically the dynamical behavior of a qubit obtained with the two ground eigenstates of an ultrastrong coupling circuit-QED system consisting of a finite number of Josephson fluxonium atoms inductively coupled to a transmission line resonator. We show an universal set of quantum gates by using multiple transmission line resonators (each resonator represents a single qubit). We discuss the intrinsic 'anisotropic' nature of noise sources for fluxonium artificial atoms. Through a master equation treatment with colored noise and manylevel dynamics, we prove that, for a general class of anisotropic noise sources, the coherence time of the qubit and the fidelity of the quantum operations can be dramatically improved in an optimal regime of ultrastrong coupling, where the ground state is an entangled photonic 'cat' state.

The study of quantum decoherence is believed to be crucial in order to understand the transition from the microscopic quantum world to the macroscopic classical one. Moreover, a control and limitation of decoherence is essential towards the realization of a robust, scalable quantum computer. The study of cavity QED systems in atomic physics [1] has led to spectacular fundamental investigations of non-unitary evolution due to decoherence mechanisms. In particular, it has been possible to observe the fragility of states of the form |Ψ cat = 1 √ 2 {|α phot |g at + |αe iη phot |e at } (usually dubbed 'cat states' [1]), where |α phot is a coherent photon state with a large mean photon number |α| 2 ≫ 1, |αe iη phot is another coherent state with a phase difference η, while |g at (|e at ) is the ground (excited) state of a two-level atom [START_REF] Brune | [END_REF]3]. These states have been prepared in a cavity QED system well described by the Jaynes-Cummings model, where the ground state is |0 phot |g at , i.e., the vacuum of photons times the atomic ground state. Recently, a growing interest has been generated by the so-called ultrastrong coupling regime of cavity (circuit) QED , both theoretically [4,5,[7][8][9][10][11][12][13] and experimentally [14][15][16][17][18]. Such a regime is achieved when the vacuum Rabi frequency Ω 0 , which quantifies the coupling between one photon and one elementary matter excitation, is comparable or larger than the cavity (resonator) photon frequency ω cav . In such a regime, the Jaynes-Cummings model based on the rotating wave-approximation (valid for small ratio Ω 0 /ω cav ) breaks down. In particular, the ground state of the system is no longer the standard vacuum: recently, it was shown [9,10] that in the limit of very large coupling the ground state can become quasi-degenerate with the entangled structure:

|Ψ G ≃ 1 √ 2 |α ph Π N j=1 |+ j + (-1) N | -α ph Π N j=1 |-j (1)
where N is the number of atoms embedded in the cavity resonator, |α ph is a coherent state for the photonic field which satisfies |α| ∼ √ N Ω 0 /ω cav , and |± j are pseudospin polarized states for the j-th artificial atom, which are defined in the following. For each two-level system {|e j , |g j } one can introduce the Pauli operators σj x = |e j g| j + |g j e| j , σj y = i(|g j e| j -|e j g| j ) and σj z = (2|e j e| j -1). With a light-matter coupling Hamiltonian of the form H coupling = N j=1 λ j â σj

x + h.c, (λ j being the local coupling strength and â the photonic bosonic annihilation operator), |± j = 1 √ 2 (|e j ± |g j ) are the eigenstates of σj

x . Interestingly, the (orthogonal) first excited state has the similar form:

|Ψ E ≃ 1 √ 2 |α ph Π N j=1 |+ j -(-1) N | -α ph Π N j=1 |-j (2)
In this letter, we show how |Ψ G and |Ψ E surprisingly can form a robust qubit, whose decoherence can diminish while increasing the 'size' of the corresponding photonic 'cat' states (see Fig. 1). Moreover, we also provide a universal set of quantum computation gates and demonstrate via a thorough master equation treatment the fidelity enhancement in a regime of ultrastrong coupling.

The energy difference δ between the two considered states diminishes exponentially [9,10] with the vacuum Rabi coupling, namely δ ∼ ω eg exp(-2

Ω 2 0 ω 2 cav N )
, where ω eg is the frequency of the single atom two-level transition (set to be equal to the cavity mode frequency). Either in the ultrastrong (Ω 0 /ω eg → +∞) or 'thermodynamic' (N → +∞) limit, the two states become degenerate. In the ultrastrong coupling limit, the other excited states are much higher in energy, separated by a frequency gap ∆ ∼ ω eg >> δ. Importantly, these interesting features can not be obtained in every ultrastrong light-matter coupled system. In particular, using the Pauli matrix FIG. 1: Description of the considered system. The building block is a superconducting transmission line resonator embedding N Josephson atoms (N = 2 in the sketch here). By choosing judiciously the type of artificial atom (the depicted circuit represents fluxonium atoms inductively coupled to the resonator) , the first two ground levels of the resonator are entangled states (|α is a photon coherent state, |± is a Josephson junction state 'polarized' along the pseudospin xdirection). One resonator represents a single qubit: a register of M qubits is given by M resonators. language, the 'direction' of the bare atomic Hamiltonian must be orthogonal to the one of the light-matter interaction Hamiltonian [10]. This is the case in the following spin-boson Hamiltonian:

Ĥ/ = ω cav â † â + ω eg 2 N j=1 σj z + N j=1 i Ω 0 √ N (â -â † )σ j x . (3)
In the present letter, we limit our description to a single bososic mode and an uniform light-matter coupling , but all the following results may be generalized to several and spatially non uniform modes [9]. It has also been shown recently that in the ultrastrong coupling regime, the quasi-degeneracy of the states |Ψ G and |Ψ E is robust with respect to a local and static perturbation of the type H pert y,z = N j=1 h y,j σy,j + h z,j σz,j where h y,j and h z,j are random perturbation amplitudes [9]. The reason is that in the subspace {|Ψ G , |Ψ E } such perturbation couples (at the N th order) coherent states of opposite phase | -α and |α . The effect of the perturbation is proportional to the overlap -α|α = exp (-2|α| 2 ) ∼ exp(-2

Ω 2 0 ω 2 cav N ).
Indeed, the stronger is the coupling Ω 0 or the larger is the number of artificial atoms N , the larger is |α| 2 , the 'size' of the photonic 'cat' states |Ψ G and |Ψ E . Importantly, the protection is not complete [19], because these states are not robust with respect to noise terms like H pert x = N j=1 h x,j σx,j and

H pert â = h a â + h * a â † ,
namely the noise in the direction of the light-matter coupling and the noise associated to the resonator field. However, if in a superconducting system, perturbations like H pert y,z happen to be the dominant ones, the lifetime and the fidelity of the quantum operation involving the states |Ψ G and |Ψ E can be dramatically improved by increasing Ω 0 /ω eg and/or N .

In fact, among the different flux Josephson atoms [17,18,20,21], this noise anisotropy appears to be realistic at least for a fluxonium [20] . Under conditions detailled in [20], its Hamiltonian can be written as:

H F = 4E CJ N 2 J + E LJ ( φJ ) 2 2 -E J cos( φJ + Φ ext ) (4)
The ĤF,pert / ≃ ∆Φ ext sin(ϕ 01 )(E J / )σ x + ∆N 0 ϕ 01 ω eg σy ( 5)

+ ( ∂ω eg ∂E J E J ∆I 0 I 0 + ∂ω eg ∂E CJ E CJ ∆E CJ E CJ + ∂ω eg ∂E L E L ∆E L E L )σ z
The spectral density of the flux noise is typically S 1/2 ∆Φext ≈ 10 -6 / √ Hz [22,23]. The critical current noise ∆I 0 /I 0 = ∆E J /E J , which is also believed to follow a 1/f law [24,25], has been recently measured [26] in a fluxonium : S 1/2 ∆EJ /EJ ≈ 3.10 -5 / √ Hz. It proves that the dissipation due to the σz channel is much larger than the σx channel contribution. To study the behavior of the qubit {|Ψ G , |Ψ E } in the presence of dissipation, we used the master equation [START_REF] Breuer | The Theory of Open Quantum Systems[END_REF]:

dρ dt = 1 i [ Ĥ, ρ] + r=rv,r f Ûr ρ Ŝr + Ŝr ρ Û † r -Ŝr Ûr ρ -ρ Û † r Ŝr + N j=1 m=xj,yj ,zj Ûm ρ Ŝm + Ŝm ρ Û † m -Ŝm Ûm ρ -ρ Û † m Ŝm ( 6
)
where ρ is the density matrix, Ĥ refers to Hamiltonian (3) and where the 'jump' operators are Ŝrv = â + â † , Ŝr f = i(â -â † ), Ŝxj = σj x , Ŝyj = σj y , Ŝzj = σj z . Moreover [START_REF]The Hamiltonians Ĥ considered in the numerical simulations are either time-independent (for the calculation of the coherence times), either slowly-varying (for the calculation of the quantum gate dynamics) within a typical time scale much longer than the reservoir correlation time (∼ 1/ωc). In the latter case, Û (t) is time-dependent[END_REF],

Ûk = ∞ 0 ν k (τ )e -i Ĥτ
Ŝk e i Ĥτ dτ,(7)

ν k (τ ) = ∞ -∞ Γ k (ω){n k (ω)e iωτ + [n k (ω) + 1]e -iωτ }dω, for k = r v , r f or k = x j , y j , z j ∀j = 1..N .
Here we consider the zero temperature limit [29], where the spectral functions Γ k (ω) must vanish for ω < 0 because they are proportional to the density of states (of the baths) at energy ω. For sake of simplicity, we have set Γ k (ω) = Γ k for ω ∈ [0; ω c ] and Γ k (ω) = 0 elsewhere ∀k, with ω c an upper cut-off which is consistent with decreasing spectral noise. Finally, one must include many excited states in the master equation treatment. To investigate the robustness of the coherence between the 2 quasi-degenerate vacua |Ψ G and |Ψ E , we have studied the non-unitary dynamics of the initially prepared pure state |Ψ 0 = cos(θ)|Ψ E + sin(θ)e iφ |Ψ G in presence of anisotropic Josephson dissipation rates Γ y , Γ z ≫ Γ x and for several cavity loss rates Γ r /ω eg = Γ rv /ω eg = Γ r f /ω eg (see caption of Fig. 2). Our simulations plotted in Fig. 2 prove that the coherence time increases while increasing the normalized vacuum Rabi frequency Ω 0 /ω eg . Indeed, if the dominant dissipation channels are along the y and z directions, their effect decreases as exp (-2|α| 2 ) where α = √ N Ω 0 /ω cav . Hence, the coherence time is enhanced exponentially before reaching a saturation value given by Γ r , Γ x and eventually decreasing with the usual power law of cat states. The location of the coherence time peaks with respect to the photonic amplitude α = √ N Ω 0 /ω eg is almost independent of the number of atoms N (see top right panel of Fig. 2), indicating that α is the relevant dimensionless parameter for the protection. Depending on Γ r and Γ x (see bottom right panel of Fig. 2), the maximum coherent times have a different behavior versus N . For smaller values of Γ x , the protection increases monotonically with N ≥ 2 (we have been able to calculate up to N = 5). For larger values of Γ x instead the maximum of the coherence time is achieved for N = 1. Finally, since the number of photons n of |Ψ G and |Ψ E increases like 2), we conclude that there is a regime where the larger is the number of photons in |Ψ G and |Ψ E , the stronger is their robustness against decoherence contrary to the usual cavity QED 'cat' states [1], obtained when Ω 0 /ω eg << 1. Indeed, it is well known [1][START_REF] Brune | [END_REF][3][START_REF] Hofheinz | [END_REF] that the coherence time of those standard 'cat' states decreases monotonically while increasing their size. Now, we show how to obtain an universal set of gates for quantum computation [31] using the two states |Ψ G and |Ψ E as computational basis for the qubit and we will study the fidelity of such quantum opera- Even without optimizing the temporal shape of t → Ω 0 (t) , excellent fidelities can be reached. For instance, for the Z-Pauli gate (corresponding to θ z = π/2), with one atom and for a linear back and forth between Ω 0 /ω eg = 2 and Ω 0 /ω eg = 1.3, fidelity ≥ 99.9% is obtained for a typical time T ∼ 300/ω eg in presence of realistic dissipation. In practice, to modulate in situ Ω 0 (t), one can use an intermediate loop between the resonator and the artificial atom with a tunable magnetic flux through it [9,12]. x with Ĥ(t = 0) the initial spin-boson Hamiltonian (3) with N = 1 (black solid), N = 2 (blue dashed) and N = 3 (red solid) Josephson atoms in the resonator. Inset: time evolution of C(t). Right panel: fidelities of the 2-qubit gate e -iθx 12 Σx 1 ⊗ Σx 2 for θx 12 = π/2 with respect to Ω 0 ωeg the vacuum Rabi Frequency in each resonator in which there is 1 atom embedded. The 2-qubits coupling constant C 12 (t) follows the same time evolution as C(t) in the inset. Note that we have included noise in the mutual coupling, via the jump operator Ŝx12 = σ1

Ω 2 0 ω 2 cav N (see Fig.
x,1 σ1

x,2 and the loss rate Γx12 = ωeg10 -6 .

In order to get a complete set of quantum operations, one needs to perform a 2-qubit control gate. Here, we will describe how to obtain the conditional quantum gate e -iθx 12 Σx 1 ⊗ Σx 2 in the 4-dimensional basis

{{|Ψ G 1 , |Ψ E 1 } ⊗ {|Ψ G 2 , |Ψ E 2 }} = { 1 √ 2 (|+ | + α 1 ± |-| -α 1 ) ⊗ 1 √ 2 (|+ | + α 2 ± |-| -α 2 )}
= Ĥ1 + Ĥ2 + C 12 (t)σ 1 x,1 σ1
x,2 , where Ĥ1 ( Ĥ2 ) stands for the spin-boson Hamiltonian (3) for the resonator 1 (2), while σ1

x,1 (resp. σ1

x,2 ) stands for the x-Pauli matrix acting on the first two levels system of the resonator 1 (2). Applying such a perturbation will partially lift the 4 times degeneracy of the fundamental subspace so that the two states Other proposals for the practical coupling between the 2 resonators could be envisaged [33,34]. Concerning the read-out of our qubit, this can be done by a projective measurement on the states |+ | + α and |-| -α : the flux across the Josephson junctions is polarized and can be in principle measured via the surrounding quasi-static magnetic field.

In conclusion, we have shown that it possible to considerably enhance the coherence times of a qubit given by the first two eigenstates of a circuit QED system in the ultrastrong coupling regime: such states are entangled states of photons and polarized Josephson atomic states, which are robust with respect to a general class of 'anisotropic' environment. In our proposal, the resonator is used to protect quantum information [35,36] , contrary to the approach [37][38][39] where it acts as a bus joining several embedded Josephson qubits. The present work shows that the qualitative modification of the quantum ground state in ultrastrong coupling circuit QED can have a significant impact on the decoherence and manipulation of quantum states in multiple resonators. We would like to thank M.H.Devoret for a critical reading of the manuscript and useful discussions.

  Hamiltonian parameters are subject to noise fluctuations : Φ ext = π + ∆Φ ext with ∆Φ ext some flux noise (in units of Φ 0 = /2e), E J = E J + ∆E J with ∆E J = ∆I 0 /Φ 0 proportional to the critical current fluctuation, NJ = NJ + ∆N 0 , ∆N 0 being the charge offset fluctuation. One can also introduce some capacitive and inductive noise E CJ = E CJ + ∆E CJ and E LJ = E LJ + ∆E LJ . When the fluctuation sources are off, the first two eigenstates of the fluxonium are very well isolated from the higher states provided that E J ≫ E LJ and E J ≫ E CJ . Then, the Hamiltonian (4) reads ĤF ≃ (ω eg /2)σ z in the basis of the two first eigenstates which are symmetric and antisymmetric superpositions of clockwise and anticlockwise persistent current states. On the same basis φJ ≃ -ϕ 01 σx and NJ ≃ ωeg 8EC ϕ 01 σy (where ϕ 01 ≃ 3). The fluctuations produce (at the first order) the perturbation:

4 FIG. 2 :

 42 FIG. 2:Coherence time in units of 1/ωeg calculated via the master equation(6) for ωeg = ωcav and with the initial state |Ψ0 = cos(θ)|ΨE + sin(θ)e iφ |ΨG . Results are averaged over the possible initial values for θ and φ. Left panel: coherence time versus the normalized vacuum Rabi frequency Ω0/ωeg for one atom (N = 1) with Josephson loss rates {Γx, Γy, Γz} = ωeg{10 -6 , 10 -3 , 10 -3 }. The different cavity loss rates: Γr/ωeg = 10 -6 , 10 -7 , 0 correspond[1] to different quality factors Q = ωeg/(4πΓr) ≃ 10 5 , 10 6 , ∞. Inset : the number of photons n = |α| 2 = a † a is plotted versus Ω0/ωeg for N = 1. Top right panel: coherence time for N = 1, 2 and 3 atoms for Γr/ωeg = 10 -6 and with a lower anisotropy in the atomic loss rates: {Γx, Γy, Γz} = ωeg{10 -5 , 10 -3 , 10 -3 } as a function of the photonic amplitude α = √ N Ω0/ωeg. Bottom right panel: maximum coherence time as a function of the number of atoms N for different values of Γx, hence for different noise anisotropy.

2 FIG. 3 :

 23 FIG.3: Left panel: fidelity of the single qubit X rotation gate (for θx = π/2) versus Ω0/ωeg. Master equation (6) was used with a time-dependent Hamiltonian, Ĥ(t) = Ĥ(t = 0) + C(t)σ 1x with Ĥ(t = 0) the initial spin-boson Hamiltonian (3) with N = 1 (black solid), N = 2 (blue dashed) and N = 3 (red solid) Josephson atoms in the resonator. Inset: time evolution of C(t). Right panel: fidelities of the 2-qubit gate e -iθx 12 Σx 1 ⊗ Σx 2 for θx 12 = π/2 with respect to Ω 0 ωeg the vacuum Rabi Frequency in each resonator in which there is 1 atom embedded. The 2-qubits coupling constant C 12 (t) follows the same time evolution as C(t) in the inset. Note that we have included noise in the mutual coupling, via the jump operator Ŝx12 = σ1

(|+ |+α 1

 1 ⊗|+ |+α 2 and |-|-α 1 ⊗|-|-α 2 ) will have a different energy than the states (|+ | + α 1 ⊗ |-| -α 2 and |-|-α 1 ⊗|+ |+α 2 ). Fidelity of that operation for θ x12 = π/2 is given in the right panel of Fig. 3 in presence of dissipation, showing again the enhancement for increasing values of the normalized vacuum Rabi frequency.


Florent Lalys

Claire Haegelen

Alexandre Abadie

Muriel Baillieul

Pierre Jannin

ANATOMO-CLINICAL ATLASES IN SUBTHALAMIC DEEP BRAIN STIMULATION CORRELATING CLINICAL DATA AND ELECTRODE CONTACTS COORDINATES

Introduction

Movement disorders in Parkinson disease patients may require functional surgery, when medical therapy isn't effective. In Deep Brain Stimulation (DBS), electrodes are implanted within the brain to stimulate deep structures such as SubThalamic Nucleus (STN). The targeting of the STN is based on anatomic, imaging and statistical data obtained on anatomic and prospective clinical studies. An accurate localization requires the use of Atlases, such as histological or high-resolution ones. A new family, called probabilistic functional Atlases, integrate various parameters like the position of electrodes, stimulation recordings or electro-physiological recordings. In STN DBS, there remain interrogations about contacts location that provide the largest motor improvement while producing the least neuro-psychological side effects.

Methods

To approach this issue and understand phenomena better, we created atlases that associate anatomical position of active contacts with different clinical scores. The study population was composed of twelve patients with bilateral SNT DBS. Three motor scores (UPDRS, Schwab & England, Hoen & Yahr) and five neuro-psychological ones (STROOP, verbal fluency, MATTIS, TMT, WCST) were integrated in the study. Electrode contacts of patients were automatically extracted from post-operative images, and then warped (using a dedicated registration workflow with linear and non-linear transformations) in the same high-resolution MRI template. Correlations between contacts localization and clinical scores were carried out using non-supervised classification and have enabled the extraction of clusters and the definition of rules to find the optimum site for therapeutic STN DBS.

Results

The postero-superior region has been found to be very effective for stimulation, whereas the anteroinferior region has shown neuro-psychological deteriorations.

Conclusion

Comparisons with existing results have shown that such anatomo-clinical atlases are very promising for understanding phenomena better.

Keyword

Deep Brain Stimulation, Anatomo-clinical atlases, clinical data, MRI template


Florent Lalys

Laurent Riffaud

Xavier Morandi

Pierre Jannin

Surgical phases detection from microscope videos by combining SVM and HMM

Keywords: Surgical phase, digital microscope, neurosurgery, SVM, HMM

In order to better understand and describe surgical procedures by surgical process models, the field of workflow segmentation has recently emerged. It aims to recognize high-level surgical tasks in the Operating Room, with the help of sensors or human-based systems. Our approach focused on the automatic recognition of surgical phases by microscope images analysis. We used a hybrid method that combined Support Vector Machine and discrete Hidden Markov Model. We first performed features extraction and selection on surgical microscope frames to create an image database. SVMs were trained to extract surgical scene information, and then outputs were used as observations for training a discrete HMM. Our framework was tested on pituitary surgery, where six phases were identified by neurosurgeons. Cross-validation studies permitted to find a percentage of detected phases of 93% that will allow the use of the system in clinical applications such as post-operative videos indexation.

Introduction

In recent years, due to the progress of medicine and computers, there has been an increased use of technologies and in the Operating Room (OR). To develop computer assisted systems that better handle and integrate this new OR [START_REF] Cleary | The operating room of the future[END_REF], a more detailed comprehension of the surgical workflow is needed. From this area, the challenge of surgical workflow recovery has emerged. Clinical applications are the evaluation of surgeons, OR management optimization or the creation of context-sensitive user interfaces. As mentioned in [START_REF] Jannin | Surgical models for computer-assisted neurosurgery[END_REF], the modelling must address behavioural, anatomical, pathological aspects and instruments. The concepts of Surgical Process (SP) and SP models (SPM) have been introduced for such purposes [START_REF] Jannin | Surgical models for computer-assisted neurosurgery[END_REF][START_REF] Neumuth | Validation of Knowledge Acquisition for Surgical Process Models[END_REF].

Related data extraction techniques can be classified according to the addressed level of granularity where the surgery is studied. These approaches yield to various methods used for data acquisition: patient specific procedures description [START_REF] Jannin | Surgical models for computer-assisted neurosurgery[END_REF][START_REF] Neumuth | Validation of Knowledge Acquisition for Surgical Process Models[END_REF], interview of surgeons [START_REF] Morineau | Decision making during preoperative surgical planning[END_REF], sensor-based methods [START_REF] Darzi | Skills assessment of surgeons[END_REF][START_REF] Padoy | On-line recognition of surgical activity for monitoring in the operating room[END_REF][START_REF] Bouarfa | Discovery of high-level tasks in the operating room[END_REF][START_REF] Ahmadi | Motif discovery in OR sensor data with application to surgical workflow analysis and activity detection[END_REF][START_REF] James | Eye-gaze driven surgical workflow segmentation[END_REF][START_REF] Nara | Surgical workflow analysis based on staff's trajectory patterns[END_REF][START_REF] Speidel | Situation modeling and situation recognition for a context-aware augmented reality system[END_REF][START_REF] Sanchez-Gonzales | Segmentation and 3D reconstruction approaches for the design of laparoscopic augmented reality[END_REF][START_REF] Bhatia | Real-time identification of operating room state from video[END_REF][START_REF] Xiao | An algorithm for processing vital sign monitoring data to remotely identify operating room occupancy in realtime[END_REF], using fixed protocols created by expert surgeons [START_REF] Mackenzie | Hierarchical decomposition of laparoscopic surgery: a human factors approach to investigating the operating room environment[END_REF], or combination between them [START_REF] Neumuth | Computer assisted acquisition of surgical process models with a sensors-driven ontology[END_REF]. Within sensor-based methods, an approach for finer classification is to differentiate materials used: such as a robot-simulator in virtual environments [START_REF] Darzi | Skills assessment of surgeons[END_REF], using existing or additional materials.

Most of studies used sensors additionally installed. Padoy et al. [START_REF] Padoy | On-line recognition of surgical activity for monitoring in the operating room[END_REF] positioned sensors on instruments, and the workflow was segmented using Dynamic Time Warping (DTW) and Hidden Markov Model (HMM). Similarly, mechanisms for dataset pre-processing using Bayesian network before HMM training were presented in [START_REF] Bouarfa | Discovery of high-level tasks in the operating room[END_REF]. In both works, data acquisition was performed manually. Accelerometers placed on the operator were used in [START_REF] Ahmadi | Motif discovery in OR sensor data with application to surgical workflow analysis and activity detection[END_REF] to identify alphabets of activity. James et al. [START_REF] James | Eye-gaze driven surgical workflow segmentation[END_REF] installed an eye-gaze tracking system on surgeons combined with visual features to detect one important phase. Nara et al. [START_REF] Nara | Surgical workflow analysis based on staff's trajectory patterns[END_REF] introduced an ultrasonic location aware system that tracks 3-D positions of the staff for the identification of surgical events.

From existing sensors within the OR, videos are a rich source of information, as demonstrated on laparoscopy [START_REF] Speidel | Situation modeling and situation recognition for a context-aware augmented reality system[END_REF]. A situation recognition process was created based on augmented reality and computer vision techniques. Helpful information such as 3D map were also extracted from laparoscopic videos in [START_REF] Sanchez-Gonzales | Segmentation and 3D reconstruction approaches for the design of laparoscopic augmented reality[END_REF]. Bhatia et al. [START_REF] Bhatia | Real-time identification of operating room state from video[END_REF] analyzed global view videos for better OR management. Finally, Xiao et al. [START_REF] Xiao | An algorithm for processing vital sign monitoring data to remotely identify operating room occupancy in realtime[END_REF] implemented a system that record patient vital signs to situate the intervention process.

Our project focused on the extraction of information from microscope videos for high-level tasks recognition. Compare to other techniques, it permits not only to avoid the installation of materials, but also to have a source of information that has not to be controlled by human. Even if the approach and the application differ, we followed a methodology similar to the one described in [START_REF] Bhatia | Real-time identification of operating room state from video[END_REF] along with results of our previous work [START_REF] Lalys | Automatic phases recognition in pituitary surgeries by microscope images classification[END_REF], where we presented in detail the image feature extraction process and performed studies on machine learning algorithms. Here the goal was to add a temporal reasoning for better detection. That's why we first took advantage of the ability of SVMs as binary classifiers to extract scene information from frames. Then outputs of the classification were treated as observations to train a HMM. This combination permitted to take into account the sequential nature of high-level tasks for accurate recognition. We focused in this paper on the detection of surgical phases and validated our methodology with a specific type of neurosurgical interventions: the pituitary surgeries.

Materials and Methods

The process for automatic recognition is introduced here: frames were first extracted from microscope videos, and reduced with spatio-temporal downsampling to perform feature extraction. Image signatures were composed of 185 features, in which discriminant ones were chosen with a specific feature selection. SVMs were then used to classify relevant surgical scene information. These results alone were not enough informative to correctly classify surgical phases, so a HMM has then been trained, taking as observations the outputs of the SVMs and as hidden states the surgical phases. The Viterbi decoder finally permitted to find the optimal path for a given observation sequence. We assessed this process with cross-validation studies.

Data-set

We evaluated our algorithm on pituitary surgeries [START_REF] Ezzat | The prevalence of pituitary adenomas: a systematic review[END_REF], presented in [START_REF] Lalys | Automatic phases recognition in pituitary surgeries by microscope images classification[END_REF]. Pituitary adenomas are tumors that occur in the pituitary gland, where neurosurgeons use a trans-nasal approach with an incision in the back wall of the nose. The anonymous data set was composed of 16 pituitary surgeries (mean time: 40min), all performed in the neurosurgical department of Rennes University Hospital by three expert surgeons. Videos focused on the operative field of view and were recorded using the surgical microscope OPMI Pentero (Carl Zeiss) (Videos: 768 x 576 pixels at 33 frames per second). The labeling of surgical phases was manually performed by surgeons (Fig. 1.). Original frames were first spatially downsampled by a factor of 8 with a 5-by-5 Gaussian kernel (internal studies have shown that it had no impact on accuracy) and then downsampled to 1 frame every 2s (0.5Hz). We performed a statistical intensity normalization of images, where data closely followed a normal distribution.

Feature extraction and selection

From these videos, we randomly extracted 500 frames which were supposed to correctly represent the six phases of a common pituitary surgery. We defined for each frame a feature vector, representing a signature. Signatures are composed of three main information that usually describe an image: the color, the texture and the form.

The color has been extracted with two complementary spaces [START_REF] Smeulders | Content-based image retrieval at the end of the early years[END_REF]: RGB space (3 x 16 bins) along with Hue (32 bins) and Saturation (32 bins) from HSV space. The texture has been extracted with the co-occurrence matrix along with Haralick descriptors [START_REF] Haralick | Textural features for image classification[END_REF]. The form was represented with spatial moments [START_REF] Hu | Visual pattern recognition by moment invariants[END_REF], and we also computed the Discrete Cosine Transform (DCT) [START_REF] Ahmed | Discrete Cosine Transform[END_REF] coefficients. Each signature was finally composed of 185 complementary features.

The main goal of feature selection is to remove redundancy information and to keep essential ones. Feature selection methods can be divided into two groups [START_REF] Duda | Pattern classification and scene analysis[END_REF]: the filter and the wrapper approach. We fused them using the method described by Mak and Kung [START_REF] Mak | Fusion of feature selection methods for pairwise scoring SVM[END_REF], where they argued that both methods are complementary to each other. Algorithms were first independently applied to find two feature subsets. They were then merged by selecting one feature at a time from the two subsets, starting from the highest rank. The Recursive Feature Elimination (RFE) SVM [START_REF] Guyon | Gene selection for cancer classification using support vector machine[END_REF] was chosen for wrapper method. The principle is to generate the ranking using backward feature elimination. The mutual information (MI) [START_REF] Hamming | Coding and Information Theory[END_REF] was chosen for the filter method, where a feature is more important if the MI between the target and the feature distributions is larger. In order to a have a good compromise between computation time and accuracy, we kept the 40 first features.

Supervised classification

Based on our last work [START_REF] Lalys | Automatic phases recognition in pituitary surgeries by microscope images classification[END_REF], multiclass SVMs [START_REF] Crammer | On the Algorithm implementation of multiclass SVMs[END_REF]

i b) + w (x y i i    0, 1 . (2)
Four discriminant scene information were defined: global-zoom views, presenceabsence of nose retractors, of the column of nose and of compress. Combinations of these 4 binary outputs resulted in 16 possible observations for the HMM.

HMM

HMMs [START_REF] Rabiner | A tutorial on Hidden Markov Models and selected applications in speech recognition[END_REF] are statistical models used for modeling of non-stationary vector timesseries. An HMM is formally defined by a five-tuple  

B A, Π, O, S,

, where

    N s s = S ... 1 is a finite set of N states,     M o o = O ... 1 is a set of M symbols in a vocabulary,     i π = Π are the initial state probabilities,     ij a = A
the state transition probabilities and

    k) (o b = B i the output probabilities.
Here, outputs of SVMs were treated as observations for the HMM. States were represented by the surgical phases that generated a left-right HMM (Fig. 2.). The transition probabilities were low because of the sampling rate of frames (0.5Hz). We set two probabilities for the transition from one state to its consecutive state: 005 . 0  α for state n°3, 01 . 0  β for the others. The probability of remaining in the same state is then:

α  1 or β  1
. The outputs probabilities were obtained from SVMs results. They were computed as the probability of having an observation in a specific state. Videos were applied to SVMs and observation probabilities were manually computed. All these probability computations were part of the training process of our framework, and were therefore obtained only from the training sample of the cross-validation. Furthermore, the Baum-Welch algorithm has not been used for the training because of the limited size of the training sample.

Lastly, given observations and the HMM structure, the Viterbi algorithm [START_REF] Viterbi | Errors bounds for convolutional codes[END_REF] find the most likely sequence of states. This procedure was repeated 10 times and results were averaged. We computed the correct classification rate for SVMs evaluation and the percentage of phases misclassified, namely the Frequency Error Rate (FER), for HMM assessment. In addition, the confusion matrix was extracted, showing exactly where states were misclassified.

Results

Statistical results of the cross-validation study for the SVMs (Tab. 1.) showed that very good detections (~88%) along with low standard deviations (max=2.5%) were obtained, getting a maximum accuracy of 94.6% for the column of nose detection. The HMM study showed a mean FER of 7.1 +/-5.3%, with a min of 2.5% and a max of 15.2%. This error rate is low, but values are very scattered (resulting in a high standard deviation). A recognized sequence compare to the true one is shown on Fig.

3. On this particular example, each state is correctly classified with a maximum delay of 40s. Fig. 3. Phases recognition of one video made by the HMM compared to the ground truth From Tab. 2., we see that state n°3 contains the bigger number of frames, and all confusions are always between neighbouring states. The most significant error is for state n°5, where the detection is around 75%. The highest accuracy (excluding the first and the last state) is for state n°4, where the detection reaches 95%.

Discussion

In this paper, we proposed a framework that automatically recognizes surgical phases from microscope videos. The combination of SVMs and HMM showed a total accuracy of 93% of detected phases.

Microscope video data

As mentioned in [START_REF] Bhatia | Real-time identification of operating room state from video[END_REF], the information extracted from the OR must be discriminant, invariant to task distortion, compact in size and easy to monitor. Microscope video data meet all of these constraints. Image features are first very discriminant for scene information extraction, as the SVMs validation indicated. Secondly, within a same surgical environment, procedures are reproducible and image features are thus invariant to task distortion. This constraint addresses the issue of the adaptability of the system. Due to the different equipments in each department, the system could be not flexible. The solution would be to train dedicated image databases for each department which would be adapted to the corresponding surgical environment and microscope scene layout. The idea would also be to have several models for each type of procedure, adapting the scene information to be extracted and optimising the HMM. The third crucial parameter is the sample size which must be compact. Image signatures are composed of 40 features and are thus reduced. Finally, the real added value is the use of microscope videos. This device is not only already installed in the OR, but it has also not to be monitored by the staff.

Accuracy of the detection

We decided to use frames in a static way (without motion), and deliberately remained at a high level of granularity with the detection of phases. The recognition of lower level information, such as gestures, is difficult with microscope videos only. Spatiotemporal features will have to be inserted for the segmentation of such information.

The possible phases -access to the tumor‖ and -tumor removal‖ were fused because the transition between both was not clear due to similar tools and zooms. The confusion matrix showed that there was no main confusion and that the HMM was helpful for separating phases with same image features (like phase n°1 and n°5).

The high recognition rates of binary SVMs, associated with their small standard deviations, indicates that they are very robust for images classification. Then graphical probabilistic models allow an efficient representation of the problem by modelling time varying data. This association permitted to obtain good detection accuracy.

Clinical applications

Workflow recovery might be helpful for various applications. Purposes are generally to bring a plus-value to the surgery or to the OR management. This work could be integrated in an architecture that would extract microscope frames and transform it into information helping the decision making process. For now, even with a low computation time (feature extraction/selection + classification < 0.5s), accuracy must definitively be higher than our results before establishing on-line surgical phase detection.

However, the system could be introduced for video indexation. Surgical videos are very useful for learning and teaching purposes, but surgeons often don't use them because of the huge amount of surgical videos. The data-base would contain relevant surgical phases of each procedure for easy browsing. Moreover, we could imagine the creation of pre-filled reports that will have to be completed by surgeons. For such applications, even with few errors, the automatic indexation would be helpful, as there is no need of perfect detection and it has no impact on the surgery.

Conclusion

Using the proposed framework, we are now able to recognize the major surgical phases of every new procedure, by computing frames signatures, classifying scene information, and decoding SVMs outputs with the Viterbi algorithm. Thanks to this combination, we obtained high detection accuracy. We have validated this framework with pituitary surgeries. Six phases were defined by an expert, and we found a global accuracy of 93% of detected phases. This recognition process is a first step toward the construction of context-aware surgical systems. Currently, it could be used for postoperative video indexation or reports generation. In future works, spatial image features will have to be mixed with other information (such as spatio-temporal features) to generate a more robust system.

Fig. 1 .

 1 Fig. 1. Example of typical digital microscope images for the six phases: 1) nasal incision, 2) nose retractors installation, 3) access to the tumor along with tumor removal, 4) column of nose replacement, 5) suturing, 6) nose compress installation.

  have been found to be effective for microscope images classification. We decided to use binary SVMs for scene information extraction. SVMs are supervised learning algorithms used for classification data into two categories. The idea is to maximize the margin between the positive and negative examples. The parameter pair   b w; is finally the solution to the optimization problem:

Fig. 2 .

 2 Fig. 2. Left-right HMM, where each state corresponds to one surgical phase

Table 1 .

 1 Mean accuracy and standard deviation (Std) of the 4 scene information recognition

		Global-zoom	Presence-absence	Presence-absence	Presence-absence
		view	of nose retractors	of column of nose	of compress
	Accuracy (%)	87.6	88.0	94.6	87.4
	Std (%)	2.4	2.2	1.6	2.5

Table 2 .

 2 Confusion matrix for the surgical phases detection with the Viterbi decoder. Rows indicate the recognized surgical steps and columns the ground truth.

		1	2	3	4	5	6
	1	5.68	0.97	0	0	0	0
	2	0	4.68	4.09	0	0	0
	3	0	0	72.99	0.12	0	0
	4	0	0	0.45	3.12	0.07	0
	5	0	0	0	0.04	3.31	0
	6	0	0	0	0	0.99	3.49

Acknowledgments. The authors would like to acknowledge the financial support of Carl Zeiss Surgical GmbH.


Florent Lalys

Claire Haegelen

Alexandre Abadie

Pierre Jannin

Correlating clinical scores with anatomical electrodes locations for assessing deep brain stimulation

Keywords: Deep Brain Stimulation, digital atlases, subthalamic nucleus, Parkinson disease

Movement disorders in patients with Parkinson's disease may require functional surgery, when medical therapy isn't effective. In Deep Brain Stimulation (DBS), electrodes are implanted within the brain to stimulate deep structures such as SubThalamic Nucleus (STN). This paper describes successive steps for constructing digital atlases gathering patient's location of electrode contacts and clinical scores. Three motor and three neuropsychological scores were integrated in the study. Correlations between active contacts localization and clinical data were carried out using an adapted Hierarchical Ascendant Classification and have enabled the extraction of clusters aiming to suggest optimum sites for therapeutic STN DBS. The postero-superior region has been found to be effective for motor score improvement whereas the antero-inferior region revealed noticeable neuropsychological scores deterioration. Comparison with existing results has shown that such atlases are very promising for understanding phenomena better.

Introduction

Parkinson's disease (PD) is recognized as one of the most common neurological disorders, affecting 1% of people older than 60 years. The pathology is an age-related deterioration of certain nerve systems, which affects the patient's movement, balance, and muscle control. Major symptoms are indeed characterized by abnormalities of motor functions, several of which predominate, but all do not necessarily occur in all individuals. While these symptoms related to PD can be treated with medication therapy, few patients have side effects or treatments for which it is not effective. In such cases, Deep Brain Stimulation (DBS) [START_REF] Benabid | Deep brain stimulation of the subthalamic nucleus for Parkinson's disease: methodologic aspects and clinical criteria[END_REF] might be necessary, according to strict patient inclusion criteria. The target for DBS in Parkinson's disease has been moved from the ventro-lateral thalamic nucleus (Vlc) to the medial global pallidus (Gpm) and the Sub-Thalamic Nucleus (STN). Among these three deep brain structures, the STN became the mean target of high-frequency DBS in patients with PD and severe disabled symptoms [START_REF] Rodriguez-Oroz | The subthalamic nucleus in parkinson's disease: somatotopic organization and physiological[END_REF]. Even if STN DBS has proved its efficiency for motor symptoms improvement, several studies have reported adverse-events after DBS surgery affecting cognitive functions, emotion or behavior [START_REF] Parsons | Cognitive sequelae of subthalamic nucleus deep brain stimulation in Parkinson's disease: a meta-analysis[END_REF][START_REF] Biseul | Fear recognition is impaired by subthalamic nucleus stimulation in Parkinson's disease[END_REF][START_REF] Houeto | Behavioural disorders, Parkinson's disease and subthalamic stimulation[END_REF]. It remains interrogations about contacts location that provide the largest motor improvement while producing the least clinical side effects.

Preoperative definition of the target is based on the relief of symptoms and results of previous implantations only. Its precise localization from patient images is unfeasible mainly due to contrast and spatial resolutions limitations. Consequently, the surgeon needs additional information and knowledge for indirect identification of such small-targeted structures. Some are explicit such as anatomical atlases adapted to the patient images thanks to image registration. Some are implicit knowledge, such as the one acquired from learning, literature, and previous surgical cases. Different strategies have recently studied methods for making explicit this implicit information and knowledge. The concept of probabilistic functional atlases has been introduced [START_REF] St-Jean | Automated atlas integration and interactive three-dimensional visualization tools for planning and guidance in functional neurosurgery[END_REF]. After a step of normalisation within a common space, effective contacts are linked to a large panel of parameters acquired during the various stages of the procedure. The spatial normalisation allows performing retrospective studies, where statistical techniques are used to study anatomical or functional variability between patients. Response to stimulation, electro-physiological recordings, and clinical scores related to motor or cognitive evolution are all possible information that can be integrated in such atlases [START_REF] D'haese | Computer-aided placement of deep brain stimulators: From planning to intraoperative[END_REF][START_REF] D'haese | CranialVault and its CRAVE tools: A clinical computer assistance system for deep brain stimulation (DBS) therapy[END_REF][START_REF] Guo | Surgical targeting accuracy analysis of six methods for subthalamic nucleus deep brain stimulation[END_REF][START_REF] Pallavaram | Effect of brain shift on the creation of functional atlases for deep brain stimulation surgery[END_REF]. This fusion of information permits to understand functional organization within deep brain structures that helps for the identification of the optimal zone of therapy.

As far as we know, no functional atlases were proposed yet for representing the relationships between the anatomy and a large panel of clinical scores. While most of these atlases are using a single motor score for modelling the global outcome of the patient, we proposed in this paper to extend this research by adding motor and neuropsychological scores. We thus introduce the concept of anatomo-clinical atlases and describe the methods for their computation.

Materials and Methods

In this study, the objective was to correlate anatomical position of electrode contacts with clinical outcomes in STN DBS. After an automatic segmentation of electrode contacts for each patient, the crucial step was to perform an accurate patient-totemplate registration, allowing expressing contacts coordinates in a common reference space. Then the integration of clinical scores obtained pre and postoperatively permitted the extraction of representative anatomo-clinical clusters. We describe in this section every stage of our procedure, from the extraction of electrode's contacts to the creation of atlases.

Data

The study population consisted of 23 patients (10 women and 13 men, mean age 60 years old) with idiopathic PD who had bilateral STN DBS according to selected inclusion criteria at the University Hospital of Rennes (France). Patients had preoperative 3-T T1-weighted MR (1 mm x 1 mm x 1 mm, Philips Medical Systems), pre and post-operative CT scans (0.44 mm x 0.44 mm x 0.6 mm in post-operative acquisitions and 0.5 mm x 0.5 mm x 0.6 mm in pre-operative acquisitions, GE Healthcare VCT 64). All images were denoised with the Non-local means algorithm [START_REF] Coupe | An Optimized Blockwise Non Local Means Denoising Filter for 3D Magnetic Resonance Images[END_REF], and a bias correction algorithm [START_REF] Mangin | Entropy minimization for automatic correction of intensity non uniformity[END_REF] based on intensity values was also applied on T1 MR images.

Contact localization and registration workflow

Electrode contacts coordinates have to be first extracted from patient's post-operative images, and then warped into a common space to perform a retrospective study for population comparison. The spatial coordinates of each electrode contact were determined based on black artefacts from CT images, corresponding to the center of the actual contact [START_REF] Pollo | Magnetic resonance artefact induced by the electrode activa 3389: an in vitro and in vivo study[END_REF]. The segmentation process included an intensity threshold, a search for the artefacts, and constraints on neighborhood. An additional step of extrapolation was necessary when just two or three contacts were identified from the four (due to the resolution of the CT scan).

We then used, as a common space, a mono-subject high-resolution 3T MRI brain template, constructed and assessed in [START_REF] Lalys | Construction and assessment of a 3T MRI brain template[END_REF]. The registration workflow was described and validated within the validation part of the template in the context of DBS in [START_REF] Lalys | Post-operative assessment in Deep Brain Stimulation based on multimodal images : registration workow and validation[END_REF]: the post-operative CT was first linearly registered to the pre-operative MRI. An affine MR-to-template transformation was then computed, followed by a local affine registration computed on a region of interest within deep brain structures. With this procedure the contacts positions could be precisely warp into our template.

Clinical scores

From numerous clinical scores assessed in our population, we studied UPDRS III (Unified PD Rating Scale [START_REF] Fahn | Unified Parkinson's disease rating scale[END_REF], part III, taking into account akinesia, tremor, rigidity) widely used to assess bilateral motor improvement of patients, the Schwab & England [START_REF] Schwab | Projection techniques for evaluating surgery in Parkinson[END_REF] scale, and the Hoehn & Yahr [START_REF] Hoehn | Parkinsonism: onset, progression and mortality[END_REF] scale. We also studied 3 neuro-psychological scores that are often assessed through the STROOP score [START_REF] Stroop | Studies of interference in serial verbal reactions[END_REF] that tests the global cognitive efficiency, and the verbal fluency tests [START_REF] Troyer | Clustering and switching on verbal fluency tests in Alzheimer's and Parkinson's disease[END_REF] (both categorical and phonemic) that determine the ease with which patients can produce words. For each score, patients were tested without medication just before surgery (DBS OFF) and three months after it under stimulation (DBS ON). We took the difference between DBS ON and DBS OFF to compute a value that represents for all scores the degree of improvement or worsening of the patient.

Atlases

Atlases were computed as the 3D visualization of active contacts that are represented by a color code related to the patient clinical scores values. Due to errors or missing in report scoring, 15 patients were incorporated in the motor studies, and 22 in the neuro-psychological ones. Left and right contacts are shown on atlases. The x-axis represents the left-right direction, the y-axis represents the antero-posterior direction, and the z-axis represents the caudo-cranial direction.

Creation of clusters

After atlas construction, we performed a segmentation step with the help of nonsupervised techniques. The Hierarchical Ascendant Classification (HAC) was used on clinical scores and coordinates to search homogeneous groups of patients. Feature vectors are composed of 4 features: the value of the x-axis, y-axis, z-axis, and the score value:

Score) z, y, (x, = X

. The HAC operates by successively merging pairs of existing clusters, where the next pair of clusters to be merged is chosen as the pair with the smallest distance. This linkage between clusters a and b was performed with the Ward criterion along with the weighted Euclidean distance:

b a M = k bk ak k b a n + n ) x x ( w n n = b) (a, d

Results

For all following figures, we superimposed an ellipse to improve clinical representation and interpretation. This ellipse was extracted from the segmentation of the STN by an expert, and has sensibly the same dimension of a standard STN (10 x 6 x 3 mm). For each clinical score, analyses were made for both hemispheres, but all clusters found included same patients. This assumes a symmetry of the contact coordinates between the left and the right sides of patients.

Discussion

Contact localization

Using conclusions of published works on electro-magnetic contacts effects, we have modeled the signal by a point corresponding to the center of the artifact. For further developments, it will be crucial to integrate not only the real electric current that contacts emit but also the influence of stimulation on the biological tissues. Moreover, brain shift has a real impact on the final location of electrode's contacts. A full DBS modeling would integrate all of these information to be as precise as possible.

Registration workflow

Use of digitalized atlases is vital in DBS, for being able to help anatomical targeting. The impact of our high-resolution 3T MRI template on registration accuracy was significant and it has improved the registration quality around the basal ganglia area (about 0.8 mm. [START_REF] Pallavaram | Effect of brain shift on the creation of functional atlases for deep brain stimulation surgery[END_REF]). Such fusion of images should be taken with precaution, because differences of anatomy between each patient make difficult the representation of contacts in a common space. Moreover, the subject used for the mono-subject template was younger than all patients, introducing a potential bias considering the differences of anatomy between the reference subject and the patients. Nevertheless, in opposition to pure histological templates made from cadaver brain, MR templates are representing correctly in vivo anatomy of the brain.

Many active contacts are situated outside the STN within atlases. It can be partially explained by the error during the warping step, but this particularity has another explanation. First, the electrical stimulation zone is in fact larger than the simple contact position, recovering a region wide enough to accept a targeting inaccuracy. Secondly, deep brain tissues and nerves are deeply inter-connected and nerves at the periphery of structures had a role on the structure itself.

Clinical scores

Retrospective studies with clinical data allowed understanding functional organization within deep brain structures. Each clinical score has permit to extract specific meaningful clusters. Motor scores were first analysed to assess the global outcome and then neuro-psychological scores have permitted to determine sites that were the cause of side-effects.

The main issue of this procedure is the incapacity to distinguish the response to the DBS stimulation of the right and left sided. Every test has been performed with both activated contacts. Separate evaluations would involve many hours without medication and stimulation in order to lose previous therapeutic and stimulation effects. In the preoperative targeting procedure, surgeons first localized the optimal target position of one side, and the target position of the other side was automatically computed with the definition of the midsagittal plane. These targets were used as an initial position that has to be refined per-operatively, but for this study we considered them symmetric which may explain some errors on the electrode position.

Because of their low granularity, values of the S&E and H&Y scales turned out to be less representative than UPDRS III. Even if results of motor scores studies were almost identical, the visualization of the atlas containing the UPDRS III shows that the postero-superior region was the most effective region for motor improvement. This follows conclusions of previously published works [START_REF] Pallavaram | Effect of brain shift on the creation of functional atlases for deep brain stimulation surgery[END_REF][START_REF] Lanotte | Deep Brain Stimulation of the subthalamic nucleus: anatomical, neurophysiological, and outcome correlations with the effects of stimulation[END_REF], and can be explained by the fact that this part of the STN (usually named the dorso-lateral part) is implicated in sensory and motor functions [START_REF] Theodosopoulos | Locations of movementrelated cells in the human subthalamic nucleus in parkinson's disease[END_REF].

The STN is also subdivided into a ventromedial associative and a medial limbic territory. This subdivision explains that the antero-inferior (corresponding to the limbic territory) region has shown significant neuro-psychological side effects (deterioration of the Stroop score). This side effect is usually avoided by an implantation within the postero-superior region of the STN, but can easily appear if the contact is located not far from the antero-inferior region. Finally, the posterior region has shown a loss of categorical fluency. This last result was not surprising as the deterioration of the verbal fluency is one of the most observed side effects in STN DBS, with no real comprehension of the phenomena [START_REF] Saint-Cyr | Neuropsychological consequences of chronic stimulation of the subthalamic nucleus in Parkinson's disease[END_REF].

Clinical use

The proposed anatomo-clinical atlases have been created to provide the surgeons with an additional help for better comprehension of DBS related phenomena. It could find its application in pre-operative planning as well as for post-operative assessment. As the targeting is mainly based on surgeon's knowledge and experience, it could serve as an additional source of information obtained from retrospective studies for reducing time and improving patient outcome. The underlying challenge would be to reduce the intra-operative time required for electrode's contacts adjustment by microelectrode recordings. The actual local anaesthesia would be replaced by a general anaesthesia which would completely alter the surgical routine by reducing works of the surgical staff and improve patient's care. Alternatively, such atlases also permit to understand previous interventions which didn't give satisfactory results. In such cases, active contacts of the new patient can be warped in the common space and can be displayed.

Conclusion

In this paper, we focused on finding the optimum site for STN DBS by creating anatomo-clinical atlases. Such functional atlases associate anatomical position of active contacts with clinical scores for a population of cases, and are helpful for determining sites within the STN that could be the source of side effects. We showed how to extract clusters and knowledge gained from the population data based on the correlation between anatomical location of contacts and clinical data. It permits to provide the neurosurgeons with a help for targeting, but also permits to understand previous interventions which didn't give satisfactory results. This work is an example of news that can be performed in the domain, including further clinical data such as life-quality or cognitive criteria. Further studies will certainly allow learning more about DBS, better understanding of clinical side-effects and defining the optimum site for each patient according to its clinical preoperative scores.

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  of cluster a (resp. b), a n (resp. b n ) is the number of objects in cluster a (resp. b)The dendrogram was cut in order to obtain two or three clusters for each clinical score. Validation of the non-supervised classification was performed with an ANOVA test. Different clusters were computed in order to correlate clinical scores and anatomical location of electrode contacts. Compare to clustering on clinical scores only, adding the coordinates permits better definition of clusters and better appreciation of the efficiency of DBS according to contacts locations.

Fig. 1 .

 1 Fig. 1. UPDRS III analysis, with the dendrogram (left hemisphere), the cluster display and the ANOVA validation. Coordinates are defined in mm in the template reference space. Euclidean distances are between centroïds of clusters.

Fig. 1 .From Fig. 2 .

 12 Fig. 1. shows an improvement of UPDRS III in the postero-superior region (cluster 3 in red including 2 patients), whereas the worst scores are situating mainly outside the STN and in the antero-inferior region (

Fig. 2 .

 2 Fig. 2. Categorical fluency analysis, with the dendrogram (left side), the cluster display and the ANOVA validation. Coordinates are defined in mm in the template reference space. Euclidean distances are between centroïds of clusters.

Acknowledgments.

The authors would like to acknowledge Pr. M. Vérin, Dr. S. Drapier, both neurologists from the University Hospital Of Rennes for allowing access to the clinical scores.