Florent Lalys

Claire Haegelen

Alexandre Abadie

Pierre Jannin

Post-operative assessment in Deep Brain Stimulation based on Multimodal images: Registration Workflow and Validation

Keywords: Deep brain stimulation, Post-operative control, neurosurgery, registration, targeting accuracy

Object

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). This paper describes successive steps for constructing a digital Atlas gathering patient's location of electrodes and contacts for post operative assessment.

Materials and Method

12 patients who had undergone bilateral STN DBS have participated to the study. Contacts on post-operative CT scans were automatically localized, based on black artefacts. For each patient, post operative CT images were rigidly registered to pre operative MR images. Then, pre operative MR images were registered to a MR template (super-resolution Collin27 average MRI template). This last registration was the combination of global affine, local affine and local non linear registrations, respectively. Four different studies were performed in order to validate the MR patient to template registration process, based on anatomical landmarks and clinical scores (i.e., Unified Parkinson's disease rating Scale). Visualisation software was developed for displaying into the template images the stimulated contacts represented as cylinders with a colour code related to the improvement of the UPDRS.

Results

The automatic contact localization algorithm was successful for all the patients. Validation studies for the registration process gave a placement error of 1.4 +/-0.2 mm and coherence with UPDRS scores.

Conclusion

The developed visualization tool allows post-operative assessment for previous interventions. Correlation with additional clinical scores will certainly permit to learn more about DBS and to better understand clinical side-effects.

-INTRODUCTION

The subthalamic nucleus (STN) became the mean target of high-frequency deep brain stimulation (DBS) in patients with Parkinson's disease (PD) and severe disabled symptoms [START_REF] Lang | Parkinson's Disease[END_REF][START_REF]Deep-Brain Stimulation of the Subthalamic Nucleus or the Pars Interna of the Globus Pallidus in Parkinson's Disease[END_REF][START_REF] Rodriguez-Oroz | The subthalamic nucleus in parkinson's disease: somatotopic organization and physiological characteristics[END_REF][START_REF] Krack | Five-Year Follow-up of Bilateral Stimulation of the Subthalamic Nucleus in Advanced Parkinson's Disease[END_REF][START_REF] Vayssière | Deep brain stimulation for dystonia confirms a somatotopic organization in the Globus Pallidus Internus[END_REF]. While symptoms related to PD can be treated without surgical intervention, it remains patients for which medical therapy is not effective. The targeting of the STN is based on anatomic, imaging and statistical data obtained on anatomic and prospective clinical studies. Instead clinical data aren't often used yet to localize optimal target, teams worked on successful implantations where post-operative effects are satisfactory and side effects minimum. They can with these results find the best localization related to tremor, bradykinesia or rigidity pathologies, and provide the surgical team with a complete comprehensive neurosurgical system. New MR imaging protocols enable visualization of brain structures. But for dedicated clinical applications such as DBS, a more accurate localization requires the use of Atlases, such as histological [START_REF] Yelnik | A three-dimensional, histological and deformable atlas of the human basal ganglia. I. Atlas construction based on immunohistochemical and MRI data[END_REF][START_REF] Chakravarty | The creation of a brain atlas for image guided neurosurgery using serial histological data[END_REF] or high-resolution [START_REF] Aubert-Broche | A new improved version of the realistic digital brain phantom[END_REF][START_REF] Collins | Design and construction of a realistic digital brain phantom[END_REF] ones. This paper describes the image processing steps for constructing a digital Atlas gathering patient's location of electrode contacts and validation studies of the registration aspect. UPDRS (Unified Parkinson's disease rating Scale [START_REF] Fahn | Unified Parkison's disease rating scale[END_REF]) scores will be integrated in the Atlas to correlate position of stimulated contacts with clinical data.

-MATERIALS AND METHODS

Patients

Twelve patients (8 male, 4 female, mean age 55 +/-8 years) with idiopathic Parkinson's diseases had STN DBS according to selected inclusion criteria [START_REF] Lang | Parkinson's Disease[END_REF][START_REF]Deep-Brain Stimulation of the Subthalamic Nucleus or the Pars Interna of the Globus Pallidus in Parkinson's Disease[END_REF].

Images

MRI, even with the progress in imaging, is the source of non-predicable distortion, making difficult the possibility of visualizing deep brain structures during the procedure of targeting. Matching pre-operative CT with MRI allows overcoming such issue. Therefore, the geometry accuracy of the CT is preserved, and the structures can be identified with the MRI. Such technique is used here. Patients had pre-operative 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). Thirty-five slices of preoperative T2-weighted images involving basal ganglia were also acquired for helping the STN targeting. Images Pre-Processing: Pre and post-operative CT, T1-and T2-weighted MR 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]. 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 and T2 MR images.

Clinical procedure

Pre-operative planning was performed with the Stealthstation planning software (Medtronic, Minneapolis, Minnesota, USA), loading images, registering them together and proposing a 3D visualisation interface to define the target localisation in the Anterior and Posterior Commisures (AC-PC). T1, T2 and CT images were first co-register, and secondly experts localized manually AC-PC coordinates, the midsagittal and entry points on the MR images. The Talairach [START_REF] Talairach | Co-Planar Stereotaxic Atlas of the Human Brain[END_REF] Atlas was then displayed, where experts finally localized the optimal target position based on the anatomic information of the patient. Coordinates of the target were automatically transformed into CA-CP coordinate system, in order to reach the optimal position of contact with the quadripolar electrode (DBS 3389, Medtronic) during the surgical procedure. Surgical procedure: Stereotactic electrode implantation (Leksell, USA) is performed under local anaesthesia in a 1 day procedure. Both preoperative T1/T2-weighted MRI and CT are obtained early in the morning, following by the target localization explained above. The point calculated before the implantation is used as an initial position that has to be refined intra-operatively. A few causes of discrepancy between chosen target and the final implant might appear, such as the brain shift [START_REF] Elias | Cortical and subcortical brain shift during stereotactic procedures[END_REF][START_REF] Miyagi | Brain shift: an error factor during implantation of deep brain stimulation electrodes[END_REF] and the stereotactic surgical placement errors. The first one is due to the opening of the brain, but it is assumed that there are no significant errors which can causes real perturbation in our results. The second one is due to the mechanic placement errors. In spite of a submillimetric precision in graduation the frame causes a loss of accuracy that is no negligible. To take into account these different errors an X-ray control is done during the surgical procedure, helping the neurosurgeons to place correctly the electrode. In order to reach the optimal placement, a phase of intra-operative electrophysiological exploration is also performed. Two neurologists test the clinical effects with different settings for each contact, when the patient is still under local anaesthesia. Changing frequency, voltage, contact stimulated and electrodes trajectory they finally keep the best settings, knowing that these one might be change post-operatively as Parkinson's pathologies are often evolving and need readjustments. Of course this choice is also guide by the side effects which should be as minimum as possible. At every permutation of settings, a small time is necessary to allow the clinical effects of patient's pathology to come back. When all the test are finished, the surgeon anchor the electrode to the skull, and if the surgical procedure is a bilateral DBS implantation the second electrode is then subjected to the same steps. Typically a monolateral implantation is performed when patient's tremor disorders are located to only one side (in that case electrode is implanted in the other side of the brain). Instead of this step of intra-operative programming, clinical effects may take several weeks to appear, which complicate the task of the neurologists in finding the optimal settings.

Automatic contact localization

The spatial coordinates of the contacts for each electrode were computed post-operatively from CT images. Their positions were determined based on the black artefacts created on the CT. Recent works [START_REF] Pollo | Magnetic resonance artefact induced by the electrode activa 3389: an in vitro and in vivo study[END_REF] on electro-magnetic effects showed that artefacts appearing on images corresponded to the center of the real contact. This segmentation task was automatically realized, with at first an intensity threshold, followed by a search of artefacts on the image and constraints on neighbourhood. Usually just two or three contacts can be identified directly on the image because of the resolution of the slices, which caused loss of information. To find the last contact, it was necessary to extrapolate the points already found with the original electrode settings, such as the distance of a contact (1.5 mm) or the distance between each (0.5 mm or 1.5 mm). On every new post-operative data this automatic procedure was performed and gave all contacts localizations.

Contact representation

With the method mentioned previously, active contacts are represented by a point corresponding to the center of the contact. Some previous works estimated the height of the contact [START_REF] Pollo | Localization of electrodes in the subthalamic nucleus on magnetic resonance imaging[END_REF][START_REF] Videen | Validation of a fiducial-based atlas localization method for deep brain stimulation contacts in the area of the subthalamic nucleus[END_REF], while others [START_REF] Hemm | Postoperative control in deep brain stimulation of the subthalamic region, the contact membership concept[END_REF] considered all the structures involved in the stimulation, which means considering the contacts lying within the different structures. For the representation in the atlas, we decided to take into account all the geometry of a contact, modelled by a cylinder (length: 1.5mm, diameter: 1mm) (Fig 1). On the other hand, for the database we kept the representation as a point, in computing the centroid of the projected artefacts.

Registration

We used the state of the art of linear/non-linear registration algorithm. We decided to use the technique already described by Sanchez [START_REF] Sanchez | A Cross Validation Study of Deep Brain Stimulation Targeting : From Experts to Atlas-Based, Segmentation-Based and Automatic Registration[END_REF], which showed that the best patient images to Atlas registration in the context of DBS was a global linear image to Atlas registration with a mask on deep structures, following by a non-linear local registration with either Demons or BSplines algorithm. We added CT to MRI registration step. Here is the registration procedure proposed for each subject (Fig 2). The post-operative CT was first linearly registered to the pre-operative MRI, creating a 3D transformation matrix. The affine MR-to-atlas transformation was then computed. After the global warping, a local affine registration was computed on a region of interest including the deep brain structures. All the linear transformations were executed with the Newuoa optimization [START_REF] Wiest-Daesslé | Evaluation of a new optimisation algorithm for rigid registration of MRI data[END_REF]. The final step included a non-linear local algorithm called Demons [www.itk.org], which estimated a 3D deformation field between a source volume and a target volume. Non-linear was essential to take into account the difference of anatomy between each patient. We finally obtained a global matrix including the four linear transformations, and a deformation field corresponding to the non-linear one. With this procedure the contacts positions could be warp in the common Colin27 template and it allows visualization of contacts in deep brain structures of the Template. On the contrary, it also allows register the possible optimal electrode contacts from the Atlas to the pre-operative acquired data by an inverse of the original transformation, since linear and non-linear algorithms are both bijective transformations.

Registration Validation

Four different validation studies of the registration workflow were performed with increased clinical meaning, considering that rigid intra-patient CT to MR registration was almost perfect. The first validation study used statistic tools to evaluate the similarity of two coregistered images, in order to compare several input parameters of our method: "global" vs. "local" registration, the choice of non-linear algorithm and the choice of specific template. The performance criterion used was the intensity based correlation, as non-linear algorithms in our procedure are based on mutual information. Mathematical approach permits to characterize the intrinsic performance of a method to have first results on best settings to keep. The second validation got closer to the clinical context and was based on 6 anatomical landmarks defined by an expert and identified on each patient registered MRI and on the MR template. Euclidean distance for each landmark defined in both images was computed on the 12 patients, in order to get the global misplacement error. The third validation study was based on Talairach results [START_REF] Talairach | Co-Planar Stereotaxic Atlas of the Human Brain[END_REF], which mentioned that deep brain structures have more or less the same coordinates in images if those ones are taking into a reference space called Talairach (based on AC-PC). Thus contacts coordinates were computed at every step of our procedure in defining AC-PC on each reference, from rigid to non-linear registration. Then the Euclidean distance of the contact coordinates between each reference was computed. The reference in that case was based on clinical a priori. With that method we ensured that no significant errors existed and that our final results were valuable. The final validation permitted to assess our method as regards to patient outcome. An expert segmented the STN to ensure that stimulated contacts belonged to the structure and then simple correlations were made between the improved motor score of the Unified Parkinson's Disease Rating Scale (UPDRS) part III (which has been evaluated 3 pre-and 3 months postoperatively) and the contact's position to assess the patient outcome efficacy [START_REF] Pollo | Localization of electrodes in the subthalamic nucleus on magnetic resonance imaging[END_REF][START_REF] Voges | Bilateral high-frequency stimulation in the subthalamic nucleus for the treatment of Parkinson disease: correlation of therapeutic effect with anatomical position[END_REF].

Cluster

We assigned to each patient a colour code, related to the improved score of the UPDRS III. We considered the percentage of improvement between both, from 0% to 100%. Then we separated five clusters from these scores and we displayed the contacts on the template with a corresponding colour.

-RESULTS

Registration Validation

Our registration workflow studies gave us results on best methods and algorithms to keep. According to Tab 1, the local method widely gives best images warping, with a significant difference for mutual information. This study shows that local registration is fundamental to place correctly the deep structures.

Mutual Information

Correlation 1st method 2nd method 1st method 2nd method average on 10 patients 81,11% 68,01% 82,19% 80,46%

Tab 1 : Mutual information and correlation between the final images registered and the Template, using with the first method a local registration, and with the second a global registration.

We consider for granted, according to [START_REF] Sanchez | A Cross Validation Study of Deep Brain Stimulation Targeting : From Experts to Atlas-Based, Segmentation-Based and Automatic Registration[END_REF], that the Demons method is the most effectiveness in DBS non-linear registration. Table 2 shows that firstly the super-resolution Colin27 is better than the original, and secondly that the SymetricForces algorithm is more accurate than the Diffeomorphic one. These conclusions can be drag out from both correlation and mutual information calculation. Tab 2 : Mutual information and correlation between the final images registered and the Template, using either the original Colin27 or the super-resolution Colin27, and using the Diffeomorphic algorithm and the SymetricForces one respectively. We obtained, with the same ten patient's study, a placement error of 1.44 mm compare to 1.66mm with a single linear method. Even if the two averages are close, Anova shows that the majority of values for the non-linear registration are under 1.5mm. The best warping came from AC and PC so central deep structures seem to be well-warped.

Mutual Information Correlation

The contacts coordinates in AC-PC from image to image were coherent (3.0mm +/-1.0 mm) and motors score correlated with anatomical coordinates have shown that every stimulated contact belong the STN.

Cluster

The mean pre-operative UPDRS III without medication was 29.3 +/-6.1. The post-operative one without medication with stimulation was 13.1 +/-4.1. Recent publications have permitted to find the most effective stimulation point in Parkinson's diseases. The best stimulation point would be the dorsal area of the STN.

Database

Contacts localizations, following by the registration procedure permits a global display of previous surgical intervention in a common space. The database contains now all coordinates from previous operation, with corresponding patient images and clinical scores. Neurosurgeons have a first computer-aided-placement tool.

-DISCUSSION

Atlas

Use of digitalized atlases is important in DBS, for being able to help anatomical targeting. A digitalized Atlas can give information at the histological level which is impossible with actual imaging techniques. With this help, subcortical anatomy can be visible and can be match with every patient anatomy. Paper-based atlases were originally used for such purposes. Those of Schaltenbrand and Wahren [START_REF] Schaltenbrand | Atlas for Stereotaxy of the Human Brain[END_REF], or Talairach and Tournoux [START_REF] Talairach | Co-Planar Stereotaxic Atlas of the Human Brain[END_REF] have been used with success in various computer aided decision systems. More recently atlases were built from digital images. Digital atlases can be classified according to the number of subjects used for the computation. Multiple subject atlases are mainly built from single acquisition of different control subjects reflecting the population targeting by the clinical study [START_REF] Seghers | Construction of a Brain Template from MR Images Using State-of-the-Art Registration and Segmentation Techniques[END_REF][START_REF] Evans | 3D statistical neuroanatomical models from 305 MRI volumes[END_REF]. Such multi-subjects templates mainly aim at studying human anatomical or functional variability. Being able to merge anatomical or functional differences into a single image may improve the correct alignment before comparison. Single subject atlases aim at reaching the best spatial resolution. Different strategies were followed for defining such templates. The first strategy was the use of co-registered mono or multimodal acquisitions of a single particular subject [START_REF] Aubert-Broche | A new improved version of the realistic digital brain phantom[END_REF][START_REF] Collins | Design and construction of a realistic digital brain phantom[END_REF] mainly based on MR acquisitions. The second was the combination of images and histological atlases [START_REF] Yelnik | A three-dimensional, histological and deformable atlas of the human basal ganglia. I. Atlas construction based on immunohistochemical and MRI data[END_REF][START_REF] Chakravarty | The creation of a brain atlas for image guided neurosurgery using serial histological data[END_REF]. The interest of the first strategy is that the whole clinical acquisition set up is taken into account on healthy and alive control subjects. In opposition to pure histological Templates, MR templates are representing correctly in vivo anatomy of the brain. Moreover, they turn out to be easily feasible, whereas histological ones are complicated or time-cost to produce. These Atlases are constrained by both the resolution and the quality of available imaging technologies.

In the case of DBS, new family of Atlases appear, called probabilistic functional Atlases [START_REF] D'haese | Computer-aided placement of deep brain stimulators: From planning to intraoperative[END_REF][START_REF] Guo | Surgical targeting accuracy analysis of six methods for subthalamic nucleus deep brain stimulation[END_REF][START_REF] Lemaire | Brain mapping in stereotactic surgery: A brief overview from the probabilistic targeting to the patient-based anatomic mapping[END_REF]. A large panel of parameters can be integrated in this type of Atlases, such as position of electrodes, stimulation recordings or even electrophysiological recordings. For instance, studies proposed an Atlas integrating intra-operative recordings, which can be match with patient pathologies [START_REF] Dawant | The VU-DBS project : integrated and computer-assisted planning, intra-operative placement, and post-operative programming of deep-brain stimulators[END_REF][START_REF] Guo | Development and Application of Functional Databases for Planning Deep-Brain Neurosurgical Procedures[END_REF]. This technique allows understanding functional organization within deep brain structures. Such fusions of images should be taken with precaution, because differences of anatomy between each patient make difficult the representation of target/contact in a common space. Here we used the super-resolution Colin27 template, which gave us best results compare to a standard Atlas. The impact of this template was significant and it has improved not only the registration quality but also the retrospective visualization. The addition of clinical data has allowed understanding functional organization within deep brain structures. It's certainly a part of our procedure that can be more and more improved, with the help of new imaging technologies (3T machines) and post-processing. The more the Template will be accurate; the better will be the contacts visualization.

Accurate localization

Using conclusions of published works on electro-magnetic contacts effects, we have modelled the signal by a point corresponding to the center of the artefact. For further works, 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. The extrapolation created with the artefacts is based on electrode geometry and is therefore robust.

Registration validation

With all studies performed for the assessment, we have completely validated our registration workflow as we have found appropriate methods and algorithms [START_REF] Holden | A review of Geometric Transformation for Nonrigid Body Registration[END_REF]. Rigid registration algorithms provide mostly effectiveness results, whereas non-rigid algorithms have several limits. Various non-rigid algorithms for the DBS studies have been published but it's almost impossible to assess all the kind of approach, due to the difficulty to have access to a ground truth.

In DBS major sources of errors are due to the identification of basal ganglia from the patient specific images. Therefore, during the procedure we have added a local registration involving targeted structure (STN) which has to improve the basal ganglia registration. We are still working on development and improvement of the registration strategy, even though the results from validation studies were correct.

-CONCLUSION

In this paper we have reported on our current progress toward developing a procedure for computer-assisted postoperative assessment of DBS. We principally aimed to have robust and assessed results, using several kind of assessment in registration. Moreover, testing various methods and algorithms, we finally kept the most effective procedure of registration and use it for our study. The extrapolation created with the artefacts is based on electrode geometry and is therefore robust; furthermore if we add constraint on neighbourhood the risk of misplacement is considerably reduced. The integration in the same system of digitized brain Atlas, segmented structures, previous target coordinates of successful implantations and UPDRS score not only permits to provide to the neurosurgeons an help for targeting, but also permits to understand previous interventions which didn't give satisfactory results. This work yields many flourishing studies in the domain, including further clinical data such as neuro-psychological, life-quality, cognitive or motor criteria. Correlation with these additional clinical scores will certainly permit to learn more about DBS and to better understand clinical side-effects.

Fig 1 :

 1 Fig 1: Segmentation of two electrodes, their contacts and the skull of a patient with STN DBS for Parkinson's disease.

Fig 2 :

 2 Fig 2: Registration Workflow between post-operative CT and the MR template

Fig 3 :

 3 Fig 3 : Anova1 (MATLAB) performed on the previous study, for placement error coming from linear registration, and from linear + non-linear registration.

  Fig 4 shows four electrodes (from two patients) and their contacts, represented by cylinder in the Colin27 space.

Fig 4 :

 4 Fig 4: Representation of four electrodes (implanted in the STN) from two patients in the Colin27 space after registration.

Table 3

 3 shows the global registration errors on the Template, using first linear registration, and second adding the nonlinear one. Statistics are also display in Fig3. Tab 3 : Euclidean distance between landmarks on the linear registered MRI compare to the Template, and on the non-linear registered MRI compare to the Template.

	Point	CA	CP	Iter of Sylvius Chiasma opticum Mamillary bodies Left Tractus optici	Average
	Linear	1,26	1,29	1,51	2,21	1,6	2,1	1,66
	Linear + Non-linear	1,17	0,71	1,03	1,96	1,89	1,9	1,44


Motoaki Bamba

Cristiano Ciuti

Counter-polarized single-photon generation from the auxiliary cavity of a weakly nonlinear photonic molecule

We propose a scheme for the resonant generation of counter-polarized single photons in double asymmetric cavities with a small Kerr optical nonlinearity (as that created by a semiconductor quantum well) compared to the mode broadening. Due to the interplay between spatial intercavity tunneling and polarization coupling, by weakly exciting with circularly polarized light one of the cavities, we predict strong antibunching of counterpolarized light emission from the non-pumped auxiliary cavity. This scheme due to quantum interference is robust against surface scattering of pumping light, which can be suppressed both by spatial and polarization filters.

Single photons play an essential role in quantum information technologies and their generation is a fascinating subject in the fields of quantum optics and condensed matter physics. As deterministic (on-demand) sources of single photons, single semiconductor quantum dots embedded in optical microcavities have been investigated with impressive results in the case of nonresonant excitation. [1][2][3][4][5][6] However, if one wishes to build an array of single-photon emitters with intentional pattern on the same wafer, the completely random position of self-organized quantum dots is by definition a kind of limitation. In the case of non-resonant generation, the repetition rate of the single-photon source is limited by the relatively slow relaxation time of the injected carriers in the semiconductor device. For higher repetition rates and freedom in array design, the resonant photon blockade in photonic pillars including a Kerr medium has been proposed, where the nonlinear medium is a simple semiconductor quantum well, 7 which can be patterned with great flexibility. Unfortunately, the non-trivial difficulty of such approach is that the strength of the Kerr nonlinearity must be much larger than the mode broadening, thus requiring in practice the use of ultrasmall photonic resonators with very high quality factors.

In a recent letter, 8 it has been proved that by using two coupled pillars (a double cavity system or photonic 'molecule') it is possible to get very pure single-photon emission with a nonlinearity surprisingly small with respect to the losses. As analytically shown in Ref. 9, the antibunching originates from the destructive quantum interference between excitation and tunneling paths of photons. However, a practical hurdle still remains: in the proposed scheme, 8,9 single photons are emitted from the excited cavity with the same polarization of the pump. Hence, spurious effects as pump surface scattering could mask such an effect. In the present paper, we propose another scheme based on the generalization of a) E-mail: motoaki.bamba@univ-paris-diderot.fr b) E-mail: cristiano.ciuti@univ-paris-diderot.fr jξjξ (τ = 0)} are plotted as functions of nonlinearity U normalized to broadening γ. The tunneling strength is J = 5γ, the polarization splitting is ∆ = 2.5γ, and the pump frequency is tuned as δE = E -ωp = 0.2772γ. In addition to the antibunching of the pumped mode A+, nearly perfect antibunching is obtained in mode Bwith the relatively small nonlinearity U = 0.0438γ.

the photonic molecule approach by taking advantage of the polarization degree of freedom in asymmetric cavities having a frequency splitting between modes with orthogonal linear polarizations. We show how to get counterpolarized single-photons from the non-pumped auxiliary cavity, thus providing a way to get rid of the pump spurious scattering by both spatial and polarization filtering. As a realistic system, we consider two spatially separated semiconductor micropillars with asymmetric shape, 10 coupled with a photonic tunneling strength J. Each pillar has two different linearly polarized photonic modes (x and y directions), energetically split by 2∆ due to the shape anisotropy. Fig. 1(a) shows a sketch of con-sidered system. The Hamiltonian is represented as

Ĥ = j={A,B} (E + ∆)â † jx âjx + (E -∆)â † jy âjy + ξ={x,y} J(â † Aξ âBξ + H.c.) + (F e -iωpt â † A+ + H.c.) + j={A,B},ξ={+,-} U â † jξ â † jξ âjξ âjξ . (1)
Here, âjξ is the annihilation operator of a photon with polarization ξ in pillar j. The relation between circularly and linearly polarized modes is given by the standard operator expression âj± = (â jx ±iâ jy )/ √ 2. We consider the configuration where pillar A is pumped with σ + -circular polarization, being ω p and F the pump frequency and amplitude respectively. The pumping strength is moderate to guarantee the average number of photons in the system not exceeding unity. If the average number is increased, antibunching is worsened, because the quantum interference in the present scheme is valid if three-photon subspace can be neglected, as in the previously considered scenario. 8,9 The nonlinearity is represented by the last term in Eq. ( 1) conserving the total spin of two photons. The effective nonlinearity can be mediated by the presence of a quantum well excitonic resonance, 11 but this effective Kerr term is quite general for systems with a third-order nonlinearity. The cross-polarized term such as U cross â † j+ â † j-âj-âj+ is not considered in the present paper, because U cross is usually much smaller than U , 12 but it could be added without qualitative changes (not shown). By using the theoretical method detailed in Ref. 7, we have numerically calculated second-order correlation functions g

(2)

jξj ′ ξ ′ (τ ) = â † jξ â † j ′ ξ ′ (τ )â j ′ ξ ′ (τ )â jξ / â † jξ âjξ â † j ′ ξ ′ âj ′ ξ ′ at
the steady state under continuous pumping and a dissipation of photons with a rate γ/ in each mode.

In Fig. 1(b), we plot equal-time correlations {g

jξjξ (τ = 0)} as a function of nonlinearity U normalized to γ. We consider the tunneling strength J = 5γ, polarization splitting ∆ = 2.5γ, and pump detuning δE = E -ω p = 0.2772γ. In addition to antibunching at the pumped mode A+ due to the previously proposed scheme 8,9 strong antibunching is achieved for mode Bwith the (small) optimal nonlinearity U = 0.0438γ. In the weak pumping limit, g

B-B-(τ = 0) is reduced to zero. The underlying destructive quantum interference is different from the previous one in Refs. 8 and 9. By deriving the equations of motions for the amplitudes of the possible Fock states for the zero-, one-and two-photon states (generalizing the method in Ref. 9) we have derived the optimal conditions of the counter-polarized antibunching and found the interference paths leading to the antibunching in mode B-. In Fig. 2(a), the zero-, one-, and two-photon state manifolds are depicted and labeled as |0 , |jξ , and |jξ, j ′ ξ ′ , respectively. The paths responsible to antibunching in mode |B-, B-are the Jassisted (spatial tunneling) path from |A-, B-and the If there is already a "-" photon in pillar B, another "-" photon cannot exists in the same pillar because of the interference between the J-assisted (spatial tunneling) path from "-" photon in pillar A and the ∆-assisted (polarization coupling) path from "+" photon in pillar B. This quantum interference occurs for an optimal value of the nonlinearity and laser detuning.

∆-assisted (polarization coupling) one from |B+, B-: destructive interference occurs for an optimal value of the nonlinearity U , which is much smaller than the inverse of the cavity lifetime. Fig. 2(b) shows a pictorial interpretation. In presence of "-"-photon in cavity B, another photon cannot enter the same pillar due to the quantum interference. The presence of a cross-polarized nonlinear term U cross would not change this picture (not shown) and it does not create a new path to |B-, B-. Furthermore, while identical pillars are supposed in the reported calculation, we have numerically checked that nearly perfect antibunching in mode B-can be obtained even under a deviation of the order of γ on eigen frequencies E and splitting ∆ between the two pillars, and also tunneling strength J between two polarizations, while the pumping frequency ω p should be properly tuned.

From the equations of motions of up to the two-photon Fock states, we have calculated the optimal nonlinearity U opt for the perfect antibunching under the weak pumping limit. Fig. 3(a) shows U opt as a function of ∆/γ, and Fig. 3(b) represents the ratio between the average photon number n B-= â † B-âB-in mode B-and the total number n total = j,ξ â † jξ âjξ for the corresponding U opt . The minimum nonlinearity that is required for the antibunching is decreased by the increase of J, and the required nonlinearity is decreased together with the splitting ∆ (or the opposite behavior when J < ∆). However, together with the decrease of U opt , the occupation probability of mode B-is significantly decreased as seen in Fig. 3(b). For U opt < 0.1γ, the curve in Fig. 3(b) is almost saturated at J = 5γ, and we can obtain a probability n B-/n total ∼ 10 -2 , which corresponds to a gener- Under the optimal conditions, the ratios between the average number nBof photons in mode Band the number n total in the total system are plotted for corresponding Uopt/γ. (c) The obtainable g

B-B-(τ = 0) are plotted versus the dephasing rate Γ normalized to γ. The tunneling strength is J = 5γ, energy splitting ∆ and pumping frequency are chosen to give the nearly perfect antibunching for each nonlinearity U in the absence of pure dephasing.

ation rate of the order of 100 MHz for a cavity lifetime in the picosecond rage. This rate is higher than that of the quantum dots [1][2][3][4][5][6] by one order of magnitude.

Finally, we have examined the robustness of the present scheme against dephasing of photons. Since quantum interferences are responsible in the present and previous schemes, 8,9 pure dephasing can decrease the quality of the antibunching. By using the standard pure dephasing model due to quadratic coupling with a reservoir, 13 we consider dephasing with a rate Γ/ affecting linearly polarized modes of each pillar (the results shown below are not significantly modified even if the dephasing is supposed to affect the circularly polarized modes). Fig. 3(c) shows g

B-B-(τ = 0) as a function of Γ/γ. The tunneling strength is J = 5γ, and the splitting ∆ is chosen to give perfect antibunching for each nonlinearity U in the absence of the dephasing. As clearly shown, the antibunching can be significantly worsened in presence of pure dephasing for a given value of the nonlinearity. However, even if the nonlinearity quite small, for example U = 0.05γ, antibunching is still observable if Γ = 10 -2 γ and becomes very strong if Γ = 10 -3 γ. The curves in Fig. 3(c) does not strongly depend on the tunneling strength J if the nonlinearity U is large enough compared to the corresponding minimum shown in Fig. 3(a). Since the optimal nonlinearity can be weak in the present scheme, one can consider cavities with relatively small photon lifetime (small quality factor) in a regime where the pure dephasing time can be thus neglected, a very promising outlook.

In conclusion, we have proposed a scheme of singlephoton generation due to a destructive quantum interference effect in a weakly nonlinear double cavity system, where each cavity have two linearly polarized, frequencysplit modes. Due to the spatial tunneling between the two cavities and the coupling between opposite circular polarizations, we have found that strong antibunching of counter-polarized emission can be obtained at the nonpumped auxiliary pillar. This new effect is of practical implications, because it provides a direct way to suppress the pump scattering via spatial and polarization filters. This scheme can also exported to arrays of nonlinear photonic molecules.

We would like to thank A. Amo, A. Bramati, J. Bloch, I. Carusotto, E. Giacobino, and A. Imamoglu for stimulating discussions. We acknowledge support from ANR grants SENOQI and QPOL. C. Ciuti is member of Institut Universitaire de France (IUF).

FIG. 1 .

 1 FIG.1. (a) Sketch of the system consisting of two coupled micropillars: due to the shape anisotropy, the photon eigenmodes have orthogonal linear polarizations. The mode with ξ polarization in pillar j is denoted as jξ, and the energy levels for the single photon states in each pillar are depicted. By illuminating circularly polarized light on pillar A, counterpolarized single photons are emitted from pillar B even with a small nonlinearity. (b) The equal-time second-order correlation functions {g

FIG. 2 .

 2 FIG. 2. (a) Sketch of all the transition paths between zerophoton |0 , one-photon |jξ , and two-photon states |jξ, j ′ ξ ′ . The antibunching of mode Bis due to the destructive quantum interference between the two paths from |A-, Band |B+, Bto |B-, B-. (b) Pictorial representation.If there is already a "-" photon in pillar B, another "-" photon cannot exists in the same pillar because of the interference between the J-assisted (spatial tunneling) path from "-" photon in pillar A and the ∆-assisted (polarization coupling) path from "+" photon in pillar B. This quantum interference occurs for an optimal value of the nonlinearity and laser detuning.

FIG. 3 .

 3 FIG. 3. (a) Optimal nonlinearities Uopt are plotted as a function of ∆/γ for tunneling strengths J/γ = 2, 3, and 5. (b)Under the optimal conditions, the ratios between the average number nBof photons in mode Band the number n total in the total system are plotted for corresponding Uopt/γ. (c) The obtainable g


Isabelle Chaudieu
email: isabelle.chaudieu@inserm.fr

PhD Joanna Norton

PhD Karen Ritchie

PhD Philippe Birmes

PhD Guillaume Vaiva

PhD Marie-Laure Ancelin

LATE-LIFE HEALTH CONSEQUENCES OF EXPOSURE TO TRAUMA IN A GENERAL ELDERLY POPULATION: THE MEDIATING ROLE OF RE-EXPERIENCING POST-TRAUMATIC SYMPTOMS

Objectives: A history of trauma is associated with both poor mental and physical health but the specific impact of post-traumatic stress disorder (PTSD) symptoms on physical health using objective indicators of health status has rarely been evaluated in elderly civilians. This study investigates the long-term consequences of a lifetime exposure to trauma on health in a French elderly general population.

Methods: Psychiatric health, medical history and clinical examination (ICD-10 criteria) were assessed in 1662 subjects (mean (SD) age = 72.5 (5.2) years). Lifetime traumatic exposure, PTSD and psychiatric diagnoses were obtained using the Watson's PTSD Inventory and the Mini International Neuropsychiatric Interview.

Results:

We observed an increase in the number and severity of health-related outcomes between groups, non-traumatized subjects having the lowest risk, and those with trauma leading to recurrent re-experiencing of events (non-resilient subjects) having the highest risk.

Traumatized persons who did not report re-experiencing symptoms (resilient subjects) showed better current mental health than traumatized subjects who did and non-traumatized subjects. Both groups of traumatized subjects showed a higher rate of cardio-ischemic diseases notably current angina pectoris (multi-adjusted OR=2.27, 95%CI [1.31; 3.91] and 2.34, 95%CI [1.22; 4.49] for resilient and non-resilient groups, respectively). Traumatized persons, specifically those non-resilient, showed a higher waist/hip ratio, higher triglyceride levels and a greater frequency of hypertension.

Conclusion:

Our findings suggest that trauma could be associated with cardio-ischemic diseases independently of PTSD symptoms expression. However the presence of these symptoms appears associated with additional metabolic risk factors.

Presented at the international congress of the World Psychiatric Association "Treatments in Psychiatry: a new update", which was held April 1-4, 2009, in Florence, Italy.

INTRODUCTION

Several psychiatric studies have shown that exposure to a traumatic event induces a high level of psychological distress in a large majority of people. A history of trauma has been associated not only with higher levels of depression and post-traumatic stress disorder (PTSD) but also with poor physical health. Little is currently known about the precise mechanism underlying the relationship between trauma and physical health, particularly the possible intermediary role of PTSD. A number of studies have explored PTSD in relation to selfreported health status, e.g. in veterans and bus drivers who have experienced work-related accidents, sexual assault survivors and primary care patients. [START_REF] Eadie | Posttraumatic stress symptoms as a mediator between sexual assault and adverse health outcomes in undergraduate women[END_REF][START_REF] Boscarino | Diseases among men 20 years after exposure to severe stress: implications for clinical research and medical care[END_REF][START_REF] Weisberg | Nonpsychiatric illness among primary care patients with trauma histories and posttraumatic stress disorder[END_REF][START_REF] Vedantham | Posttraumatic stress disorder, trauma exposure, and the current health of Canadian bus drivers[END_REF] Such studies are open to a number of bias including secondary gain and the confounding effects of depression. Very few studies to date have used objective indicators of health status. The most important concerned male veterans where PTSD symptoms were associated with risk of onset for several medical problems; arterial, gastrointestinal, musculoskeletal disorders and dermatological problems. [START_REF] Schnurr | Physician-diagnosed medical disorders in relation to PTSD symptoms in older male military veterans[END_REF] However the specific impact of PTSD on physical health has only been examined in a small number of studies of civilians exposed to a much broader array of traumatic events, with inconsistent results. [START_REF] Sledjeski | Does number of lifetime traumas explain the relationship between PTSD and chronic medical conditions? Answers from the National Comorbidity Survey-Replication (NCS-R)[END_REF][START_REF] Dirkzwager | Disaster-related posttraumatic stress disorder and physical health[END_REF] There has been no study to date on the impact of trauma in the elderly, a particularly vulnerable group given their increased vulnerability to disease and disability, and a lifetime accumulation of stressful events. This study addresses two important clinical questions: does the experience of trauma have long-term health effects persisting into old age and are elderly persons who have experienced traumatic events with subsequent PTSD symptoms at particularly high risk of certain physical disorders. In terms of treatment this would require addressing the pathophysiological manifestations associated with trauma and PTSD symptoms.

The present study examines physical and psychiatric health correlates of traumatic exposure in elderly general population taking into account the development of recurrent re-experiencing symptoms, as a central indicator of PTSD while controlling for multiple confounding factors.

METHOD

Study population

The data were derived from a longitudinal study of neuropsychiatric disorders in 1873 community-dwelling French elderly, the ESPRIT study. [START_REF] Ritchie | Prevalence of DSM-IV psychiatric disorder in the French elderly population[END_REF] Participants aged 65 years and over and non-institutionalized were recruited by random selection from electoral rolls of Montpellier between 1999 and 2001. Refusals (27.3%) were slightly older and more likely to be living alone than those who agreed to participate. Ethics approval for the study was given by the National Ethics Committee and all participants gave written consent. This paper reports results obtained at baseline. Participants underwent a standardized ICD-10 9 criteria-based examination carried out by a neurologist. The present study was conducted on the 1662 dementia-free subjects for whom data on trauma status was available and with no missing data for the main covariates. The subjects included in the analyses did not differ from the whole Esprit cohort with regard to the principal socio-demographic variables.

Medical history and clinical examination

A detailed standardized health interview covered socio-demographic characteristics, height, weight, waist to hip ratio (WHR), smoking and alcohol consumption, medical history, and medication use (participants were asked to bring prescription or drugs used regularly during the preceding month to the centre). Blood samples were collected on the day of the examination after a 12h fast. The health interview covered the self-report history of vascular disease including age of onset with additional medical information obtained from the patient general practitioner. This concerned cardio-ischemic disease (angina pectoris, myocardial infarction and coronary heart disease), stroke and posterior limb arteritis, and non-ischemic pathologies (arrhythmia and congestive heart failure). . Other chronic illnesses were also recorded, including asthma, diabetes, hypercholesterolemia, elevated triglycerides, hypertension and hyper-or hypo-thyroidism. The metabolic syndrome was defined according to the National Cholesterol Education Program Adult Treatment Panel III criteria. [START_REF]Expert Panel on Detection E, Treatment of High Blood Cholesterol in A. Executive Summary of The Third Report of The National Cholesterol Education Program (NCEP) Expert Panel on Detection, Evaluation, And Treatment of High Blood Cholesterol In Adults (Adult Treatment Panel III)[END_REF][START_REF] Grundy | Definition of metabolic syndrome: Report of the National Heart, Lung, and Blood Institute/American Heart Association conference on scientific issues related to definition[END_REF][START_REF] Grundy | Diagnosis and management of the metabolic syndrome: an American Heart Association/National Heart, Lung, and Blood Institute Scientific Statement[END_REF] Cognitive function was assessed using the Mini-Mental State Examination (MMSE). [START_REF] Folstein | Mini-mental state". A practical method for grading the cognitive state of patients for the clinician[END_REF]

Psychiatric interview

The Watson PTSD Inventory (PTSD-I, DSM-IIIR [START_REF]American Psychiatric Association. Diagnostic and Statistical Manual Third Edition Revised (DSM-III-R)[END_REF] , internal consistency, alpha=0.92 and test-retest reliability total score=0.95) [START_REF] Watson | The PTSD interview: rationale, description, reliability, and concurrent validity of a DSM-III-based technique[END_REF] was used to obtain lifetime and current (last month) PTSD diagnoses, using the validated French self-report version. [START_REF] Brunet | Evaluation de la version française auto-administrée du PTSD-I. IV Conférence Européenne sur le Stress Traumatique[END_REF][START_REF] Jehel | Construction et étude de validité d'un autoquestionnaire de l'état de stress post-traumatique issu du PTSD-Interview: leQSPT[END_REF] The first question identifies past traumatic events spontaneously evoked by the participants. The second question, concerning the subject most frightening lifetime personal experience, is only to be completed if no traumatic event is spontaneously reported. The most severe traumatic event or frightening experience is then explored in the next 17 items which correspond to specific symptoms. Only reported traumatic events or reported frightening personal experiences which are defined according to A1 DSM-IV 18 criterion were considered as "traumatic". The main advantages of PTSD-I are its capacity to provide continuous measures of the severity of the disorder for every symptom and to allow the measurement of subsyndromic PTSD.

Lifetime DSM-IV diagnoses of other Axis I disorders was made using a standardized psychiatric examination, the Mini International Neuropsychiatric Interview (MINI, French version 5.00) validated in the general population (Kappa coefficients for inter-rater and testretest reliabilities, 0.88-1.0 and 0.76-0.93, respectively) [START_REF] Lecrubier | The MINI International Neuropsychiatric Interview (MINI). A short diagnostic structured interview: reliability and validity according to the CIDI[END_REF] Positive cases were reviewed by a panel of psychiatrists. We explored major depressive disorder, dysthimia, mania-hypomania, phobia, generalized anxiety disorder, obsessive-compulsive disorder, panic disorder, and suicide (current ideation and lifetime attempt). Severity of depressive symptoms was examined using the Center for Epidemiologic Studies-Depression scale (CES-D; a score ≥16 being considered as severe). [START_REF] Radloff | The CES-D scale: a self-report depression scale for research in the general population[END_REF]

Statistical analysis

Unadjusted analyses were carried out using  2 tests. Simple and multinomial logistic regression models were used to study the association between trauma [categorized as "no trauma" (comparison group), "trauma without re-experiencing symptoms", "trauma with reexperiencing symptoms"] and socio-demographic variables, and between trauma and current mental health, physical health and life-style habits, adjusted for age, gender and educational level. Three multivariate analyses were performed to study the association between trauma and angina pectoris (model 1), hypertension (model 2), and depressive symptomatology (model 3). Multivariate logistic regression included covariates that were commonly reported in the literature and found to be associated with each outcome in our sample (p<0.15). SAS version 9.1 was used for the statistical analyses with a significance level of p<0.05 (SAS Institute, Inc., North Carolina).

RESULTS

PTSD prevalence

The mean (SD) age of the subjects was 72.5 (5.2) years and 59% were women. More than half of the men (59.3%) and women (53.7%) reported a traumatic event. The most frequent traumatic events were linked to war (experiencing bombing, witnessing serious injury or unnatural death of another person due to torture or war combat, death threats; 52.9%), learning of the sudden, unexpected death of a family member or a close friend (20.3%) and serious/near fatal accident of the person or a loved one (8.0%). The interview took place at a median period of 54.6 years (IQR=20.2) after the exposure to the traumatic event.

The lifetime and current prevalence of PTSD in the sample was 2.4% and 1.2%, respectively. These rates were significantly higher in women than in men (3.8% vs. 0.4%, p=0.001 and 2.0% vs. 0.2%, p=0.02, respectively). Due to the low number of PTSD cases in our sample, we focused on the category of subjects having expressed re-experiencing symptoms, the most common PTSD symptoms associated with trauma (16.8%) and one of the most clinically relevant.

Demographic characteristics according to trauma status

Subjects aged 75 years and over reported more traumatic events with or without reexperiencing symptoms than younger participants (Table 1). Among the subjects who were exposed to a traumatic event, women were significantly more likely to have re-experiencing symptoms than men. Persons with a high school education level more frequently reported trauma without re-experiencing symptoms whereas no significant association was observed between education and the presence of re-experiencing symptoms.

Mental health as a function of traumatic event and re-experiencing symptoms

Subjects expressing re-experiencing symptoms were significantly more likely to have depressive symptoms, to be diagnosed with past or current major depression, current anxious disorder and psychiatric co-morbidity than subjects without trauma (Table 2). They also declared more lifetime suicide attempts. In contrast subjects exposed to a traumatic event but who did not report re-experiencing symptoms differ from comparison subjects in having significantly less current suicidal ideation or psychiatric co-morbidity and marginally less global cognitive dysfunction. They were also less cognitively impaired than traumatized subjects with re-experiencing symptoms (OR=0.57, 95%CI [0.37-0.88], p=0.01). By contrast no significant difference in cognitive functioning was observed between subjects with reexperiencing symptoms and comparison subjects.

Physical health as a function of traumatic event and re-experiencing symptoms

Table 3 describes the current physical health of persons having been exposed to a lifetime traumatic event, focusing on vascular diseases and metabolic risk factors. Regardless of the presence of re-experiencing symptoms, exposure to trauma was associated with current cardio-ischemic disease particularly angina pectoris. Re-experiencing symptoms was specifically associated with higher WHR, elevated triglycerides, hypertension and thyroid dysfunction. The subjects who reported a traumatic event without re-experiencing symptoms were more likely to be past or current smokers than the subjects unexposed to trauma. A similar tendency although not significant was observed in the group who reported traumatic events in presence of re-experiencing symptoms.

Association of trauma status with angina pectoris, hypertension and current depressive symptoms

In multivariate model, the association between trauma and angina pectoris persisted for the two traumatized groups (OR=2.27, 95%CI [1.31-3.91] without re-experiencing symptoms and OR=2.34, 95%CI [1.22-4.49] with re-experiencing symptoms), suggesting that trauma is associated with angina pectoris independently of re-experiencing post-traumatic symptoms (Table 4). For all subjects except one, age of the onset of angina pectoris was greater than age at the traumatic event. Likewise, multivariate analyses confirmed the independent and significant association between the exposure to re-experiencing symptoms in traumatized subjects and hypertension and the same marginal association with current depressive symptoms.

DISCUSSION

Exposure to traumatic experiences and PTSD prevalence

This general population survey of community dwelling French elderly reveals that 55.9% of the sample had experienced at least one lifetime traumatic event. This rate is comparable to that recently reported in non-institutionalized elderly general populations in Europe (55.5%-76.5% [START_REF] Frans | Trauma exposure and post-traumatic stress disorder in the general population[END_REF][START_REF] Spitzer | Trauma and Posttraumatic Stress Disorder in the Elderly: Findings From a German Community Study[END_REF][START_REF] Darves-Bornoz | Main traumatic events in Europe: PTSD in the European study of the epidemiology of mental disorders survey[END_REF][START_REF] Glaesmer | Traumatic experiences and post-traumatic stress disorder among elderly Germans: results of a representative population-based survey[END_REF] ) and Australia (52.5% [START_REF] Creamer | Trauma exposure and posttraumatic stress disorder in the elderly: a community prevalence study[END_REF] ). Exposure to lifetime traumatic events was associated with a wide range of psychiatric symptoms even long after the traumatic event (median=54.6 years). The rates of lifetime (2.4%) and current (1.2%) PTSD are also in agreement with other studies in elderly people (3.1-3.9% [START_REF] Frans | Trauma exposure and post-traumatic stress disorder in the general population[END_REF][START_REF] Spitzer | Trauma and Posttraumatic Stress Disorder in the Elderly: Findings From a German Community Study[END_REF] and 0.7-3.4% [START_REF] Spitzer | Trauma and Posttraumatic Stress Disorder in the Elderly: Findings From a German Community Study[END_REF][START_REF] Glaesmer | Traumatic experiences and post-traumatic stress disorder among elderly Germans: results of a representative population-based survey[END_REF][START_REF] Van Zelst | Prevalence and risk factors of posttraumatic stress disorder in older adults[END_REF][START_REF] Vaiva | Prevalence of trauma-related disorders in the French WHO study: Sante mentale en population generale (SMPG)[END_REF] for lifetime and current prevalence, respectively). In our study women were at 10-fold higher risk of current and lifetime PTSD, although less frequently exposed to traumatic events. This gender difference has been described in adult general populations [START_REF] Frans | Trauma exposure and post-traumatic stress disorder in the general population[END_REF][START_REF] Darves-Bornoz | Main traumatic events in Europe: PTSD in the European study of the epidemiology of mental disorders survey[END_REF][START_REF] Breslau | The epidemiology of posttraumatic stress disorder: what is the extent of the problem?[END_REF][START_REF] Kessler | Posttraumatic stress disorder in the National Comorbidity Survey[END_REF] but the data on elderly populations [START_REF] Spitzer | Trauma and Posttraumatic Stress Disorder in the Elderly: Findings From a German Community Study[END_REF][START_REF] Creamer | Trauma exposure and posttraumatic stress disorder in the elderly: a community prevalence study[END_REF][START_REF] Van Zelst | Prevalence and risk factors of posttraumatic stress disorder in older adults[END_REF][START_REF] Zlotnick | Epidemiology of trauma, post-traumatic stress disorder (PTSD) and co-morbid disorders in Chile[END_REF] are less consistent.

Mental health as a function of exposure to trauma and recurrent re-experiencing symptoms

Although the association of trauma with major depressive disorder and anxiety disorders has already been reported [START_REF] Kessler | Posttraumatic stress disorder in the National Comorbidity Survey[END_REF] , the association with suicidal behavior has not been previously examined. We observed a higher rate of lifetime suicide attempts only for subjects exposed to trauma with re-experiencing symptoms. Although the study design did not allow the inclusion of fatal suicides, this finding is consistent with recent data on lifetime suicide attempts in a community sample of American young adults. [START_REF] Wilcox | Posttraumatic stress disorder and suicide attempts in a community sample of urban american young adults[END_REF] Interestingly, our results further showed that elderly subjects who have not developed re-experiencing symptoms following trauma had generally a lower rate of current psychiatric comorbidity as well as less suicidal ideation and global cognitive dysfunction (even after adjustment for current depressive symptoms, data not shown) than the comparison group, suggesting compensatory strategies and resilience capacities. Such compensatory strategies have already been described in neglected children without physical abuse who demonstrate a greater capacity for problem solving, abstraction and planning [START_REF] Nolin | Using neuropsychological profiles to classify neglected children with or without physical abuse[END_REF] as well as in foster children whose capacity for everyday functioning has been observed to be positively associated with the number of maltreatment types. [START_REF] Pears | Developmental, cognitive, and neuropsychological functioning in preschool-aged foster children: associations with prior maltreatment and placement history[END_REF] In the elderly, we have also reported within the same population that some childhood traumatic experiences could be associated with a lower risk of cognitive impairment. [START_REF] Ritchie | Adverse childhood environment and late-life cognitive functioning[END_REF] In none of these studies however, has the link with PTSD symptoms been examined.

Physical health as a function of traumatic exposure and re-experiencing symptoms

We were able to distinguish physical disorders such as angina pectoris, associated with exposure to a lifetime traumatic event independently of PTSD symptoms, from disorders such as hypertension and thyroid dysfunction, more specifically associated with the expression of re-experiencing symptoms subsequent to trauma. Some studies have shown an association between full or partial PTSD and cardiovascular disease in male war veterans. [START_REF] Boscarino | Diseases among men 20 years after exposure to severe stress: implications for clinical research and medical care[END_REF][START_REF] Schnurr | Physician-diagnosed medical disorders in relation to PTSD symptoms in older male military veterans[END_REF][START_REF] Kang | Risk of selected cardiovascular diseases and posttraumatic stress disorder among former World War II prisoners of war[END_REF][START_REF] Kubzansky | Prospective study of posttraumatic stress disorder symptoms and coronary heart disease in the Normative Aging Study[END_REF] Of the four studies in civilian men and women or disaster survivors [START_REF] Sledjeski | Does number of lifetime traumas explain the relationship between PTSD and chronic medical conditions? Answers from the National Comorbidity Survey-Replication (NCS-R)[END_REF][START_REF] Dirkzwager | Disaster-related posttraumatic stress disorder and physical health[END_REF][START_REF] Kubzansky | A prospective study of posttraumatic stress disorder symptoms and coronary heart disease in women[END_REF][START_REF] Norman | Associations between psychological trauma and physical illness in primary care[END_REF] only two reported a mediating role of PTSD. [START_REF] Dirkzwager | Disaster-related posttraumatic stress disorder and physical health[END_REF][START_REF] Kubzansky | A prospective study of posttraumatic stress disorder symptoms and coronary heart disease in women[END_REF] Sledjeski et al [START_REF] Sledjeski | Does number of lifetime traumas explain the relationship between PTSD and chronic medical conditions? Answers from the National Comorbidity Survey-Replication (NCS-R)[END_REF] suggested that the relationship between PTSD symptomatology and chronic medical conditions (including cardiovascular disorders) could be explained by the number rather than by the severity of lifetime traumas, as is often considered. Thus the mediating effect of PTSD in the relationship between trauma and physical health, though supported by a dose-response relationship between PTSD symptoms and cardiovascular diseases in some studies [START_REF] Kubzansky | Prospective study of posttraumatic stress disorder symptoms and coronary heart disease in the Normative Aging Study[END_REF][START_REF] Kubzansky | A prospective study of posttraumatic stress disorder symptoms and coronary heart disease in women[END_REF][START_REF] Boscarino | A prospective study of PTSD and early-age heart disease mortality among Vietnam veterans: implications for surveillance and prevention[END_REF] remains to be clarified. Our findings suggest that a distinct pattern may coexist according to the type of chronic disorder developed after trauma, which may or may not be mediated by PTSD symptoms; cardio-ischemic disease in elderly persons appearing independently of PTSD symptoms in contrast with other chronic conditions (thyroid dysfunction) or other vascular factors such higher triglyceride levels, WHR, and hypertension. Overall our findings on anthropomorphic, metabolic and hemodynamic risk factors indicate an increase in cardiovascular risk associated with the expression of post-traumatic symptoms and thus severity.

Mental resilience as protective factor against somatic disorders

To our knowledge very few studies have examined both biological and clinical characteristics of individuals who do not develop post-traumatic symptoms following the exposure to a traumatic event. Our data show that not only do these exposed but non-traumatized persons have better overall mental health than those who re-experience the event but also suggest they may have acquired some form of positive protective effect compared to those who never experienced a traumatic event. Concerning physical health, this "mentally resilient" group had lower rates of hypertension (OR=0.68, 95%CI [0.50-0.93]) compared to other exposed persons. It was not possible to examine the biological mechanisms leading to psychological and physiological protection or dysfunction. It is however interesting to note a dose effect with an increase in the number and severity of health-related outcomes between groups, with non-traumatized subjects having the lowest risk, traumatized subjects without re-experiencing symptoms having an intermediary pattern of risk (lifetime smoking and a tendency for higher WHR) and those with trauma leading to re-experiencing symptoms having the highest risk level (lifetime smoking tendency, higher WHR, hypertension, higher triglyceride levels). In a subsample of 201 elderly subjects from the ESPRIT study, we also observed lower basal cortisol levels specifically in the group of traumatized subjects with re-experiencing symptoms but not in non-traumatized subjects or in traumatized subjects without reexperiencing symptoms. [START_REF] Chaudieu | Abnormal reactions to environmental stress in elderly persons with anxiety disorders: evidence from a population study of diurnal cortisol changes[END_REF] Together these observations suggest that the observed pathophysiological "gradient" as a function of re-experiencing symptom expression and severity, could reflect an increasing allostatic load which could be considered as a marker of PTSD. [START_REF] Mcewen | Protective and damaging effects of mediators of stress. Elaborating and testing the concepts of allostasis and allostatic load[END_REF] Finally, genetic vulnerability associated to certain stress-related genes, notably the glucocorticoid receptor, might also contribute to this resilience profile. Indeed, certain polymorphisms have been associated with a healthier metabolic profile and better cognitive function whereas other functional polymorphisms in the same gene were associated with worse vascular profile and modified cortisol response to a psychosocial stressor. [START_REF] De Kloet | Stress and the brain: from adaptation to disease[END_REF] The pleiotropic effects of glucocorticoids on lipid and glucose metabolism, their immunosuppressive and anti-inflammatory actions and their brain function, also support the hypothesis for their involvement in the balance between physical and mental health and in resilience profile which may be modulated by distinct genetic vulnerability.

Limitations and strength

Retrospective reports of traumatic events are subject to recall bias especially when considering that some traumatic events lie in the distant past from the perspective of our elderly sample. There is also a potential bias due to exclusion of demented persons or those with missing data as well as a survival bias, so that some associations might be underestimated. PTSD diagnosis was performed using a DSM-IIIR based questionnaire in which the definition of a traumatic event is linked to a normative objective standard, whereas DSM-IV focuses on a subjective standard, the emotional response of the individual exposed to the event. If this subjective definition, where trauma is defined as any event an individual found intensely distressing, offers an advantage in terms of sensitivity of clinical diagnosis, the objective definition is better adapted to the study of resilience. We did not collect information on the number of lifetime traumatic events and could not study the impact of cumulated burden of lifetime trauma on the long-term development of cardio-ischemic diseases. In addition the data on health symptoms were collected at baseline and we cannot firmly conclude that a traumatic event is a risk factor for current physical disorders, although, in most cases the trauma occurred more than 50 years before the clinical evaluation. The same results were however obtained including only subjects for whom we could confirm that the traumatic event preceded the onset of cardio-ischemic disease. Finally, multiple analyses have been performed which may have induced some chance associations, and although results are overall consistent with previous studies, our findings require replication within a larger sample.

This research was based on a large, random, community-dwelling elderly sample, for which a large number of biological, clinical and life-style risk factors of vascular and metabolic diseases were collected. The information on physical health used predominantly objective indicators obtained from different sources; standardized clinical examinations, medications validated by prescriptions, blood analysis. Finally we have distinguished the effects of trauma exposure from those of PTSD symptom expression.

Our results suggest that lifetime traumatic exposure may induce long-term vascular consequences which appear to be modulated by mental resilience. In clinical terms our results suggest that elderly persons with a history of exposure to traumatic events should be carefully monitored for vascular pathology, notably where this has led to re-experiencing symptoms.

Further large longitudinal studies (ideally birth cohorts) are needed to better understand the biophysiological mechanisms associated with trauma accumulation and mental resilience.

Clinical studies are also required to assess the potential protective effect of pharmaceutical and cognitive-behavioral intervention to terminate re-experiencing of traumatic events in exposed subjects in order to reduce their risk of future cardiovascular disorders.

Table 1 :

 1 Demographic characteristics according to trauma status (N=1662)Adjusted for other variables in the table b p value for two-by-two inter-group comparisons.

		No Trauma	Trauma without	Trauma with
			reexperiencing	reexperiencing
		n=792	n=612	n=258
		(0)	(1)	(2)
					p-value a
	Variable	%	%	%	(global test)	(1 vs. 0) a,b	(2 vs. 0) a,b	(2 vs. 1) a,b
	Age range (years)
	65-69	40.28	32.68	35.66	0.002	-	-	-
	70-74	35.23	33.66	32.56		0.226	0.715	0.606
	75+	24.49	33.66	31.78		<.0001	0.032	0.398
	Gender
	Female	61.94	49.36	72.66	<.0001	<.0001	0.001	<.0001
	School education
	≤ 5 years	26.39	18.49	23.60	0.007	-	-	-
	6-9 years	30.77	27.01	29.21		0.081	0.964	0.217
	> 9 years	42.84	54.50	47.19		0.0003	0.262	0.109

a

Table 2 :

 2 Current mental health according to trauma status (N=1662)

		No Trauma	Trauma without	Trauma with
			reexperiencing	reexperiencing
		(0)	(1)	(2)
					p-value a	OR [95% CI] a		OR [95% CI] a
	Variable	%	%	%	(global test)	(1 vs.0)	p-value	(2 vs. 0)	p-value
	Major Depressive Disorder
	never	77.13	78.61	56.97	<.0001
	past	21.54	19.65	36.48		1.01 [0.77; 1.34]	0.924	2.18 [1.57 ; 3.02]	<.0001
	current	1.33	1.74	6.56		1.44 [0.59; 3.53]	0.427	6.00 [2.64 ; 13.62]	<.0001
	At least 1 current anxious disorder	14.34	9.67	20.66	0.005	0.75 (0.53; 1.07]	0.111	1.52 [1.04 ; 2.22]	0.032
	Number of current psychiatric
	disorders
	0	78.63	82.33	67.22	0.0002
	1-2	15.75	14.87	20.43		1.01 [0.74; 1.38]	0.964	1.46 [1.00 ; 2.15]	0.053
	3+	5.62	2.69	11.91		0.52 [0.28; 0.96]	0.035	2.28 [1.35 ; 3.83]	0.002
	Current depressive symptoms	26.81	23.43	38.82	0.001	0.88 [0.69; 1.14]	0.338	1.59 [1.17 ; 2.15]	0.003
	Current suicidal ideation	9.31	6.09	13.93	0.011	0.66 [0.43; 1.01]	0.054	1.42 [0.91; 2.21]	0.122
	Lifetime suicide attempt	2.96	2.46	7.47	0.013	0.94 [0.47; 1.87]	0.851	2.36 [1.23; 4.51]	0.009
	Cognitive impairment :
	MMSE (<26)	14.97	9.85	18.43	0.033	0.72 [0.51; 1.01]	0.060	1.25 [0.85; 1.85]	0.254

a Adjusted for age, gender and education

Table 3 :

 3 Current physical health according to trauma status (N=1662)

		No Trauma	Trauma without	Trauma with
			reexperiencing	reexperiencing
		(0)	(1)	(2)
					p-value a	OR [95% CI] a		OR [95% CI] a
	Variable	%	%	%	(global test)	(1 v.0)	p-value	(2 v. 0)	p-value
	Ischemic diseases
	Cardio-ischemic diseases	6.90	11.65	13.55	0.002	1.55 [1.05; 2.27 ]	0.026	2.28 [1.43; 3.64]	0.001
	Angina pectoris	4.29	8.14	10.59	0.002	1.78 [1.12; 2.83]	0.015	2.56 [1.50; 4.38]	0.001
	Myocardial infarction	2.78	4.77	4.30	0.195	1.36 [0.76; 2.43]	0.298	1.72 [0.81; 3.65]	0.157
	Coronary heart disease	2.28	4.20	3.45	0.296	1.49 [0.79; 2.81]	0.215	1.87 [0.81; 4.32]	0.144
	Stroke	2.28	2.92	2.28	0.986	0.99 [0.50; 1.98]	0.985	1.07 [0.410; 2.77]	0.895
	Lower limb arteritis	3.76	2.42	3.08	0.677	0.53 [0.28 ; 1.01]	0.054	0.82 [0.36 ; 1.84]	0.625
	Non-ischemic diseases
	Arrhythmia	10.53	12.75	13.15	0.571	1.16 [0.83 ; 1.62]	0.390	1.22 [0.79 ; 1.88]	0.377
	Congestive heart failure	1.82	2.33	4.17	0.155	1.23 [0.58 ; 2.64]	0.592	2.25 [0.98 ; 5.17]	0.057
	Metabolic risk factors b
	Hypercholesterolemia	46.51	44.55	41.80	0.177	1.23 [0.99 ; 1.53]	0.067	1.14 [0.85 ; 1.53]	0.368
	Elevated triglycerides	15.88	18.51	20.31	0.144	1.14 [0.86; 1.52]	0.367	1.44 [1.00 ; 2.07]	0.050
	WHR (medium or high)	63.14	73.37	63.71	0.071	1.29 [0.96; 1.73]	0.088	1.43 [1.01; 2.03]	0.043
	Metabolic syndrome	13.71	13.76	17.23	0.298	1.03 [0.74; 1.42]	0.878	1.36 [0.91; 2.04]	0.132
	Glycaemia				0.211
	elevated	3.30	2.47	5.08		0.76 [0.39 ; 1.45]	0.399	0.98[0.56 ; 1.73]	0.173
	diabetes	7.50	9.88	6.64		1.28 [0.87; 1.88]	0.208	1.61 [0.81; 3.21]	0.954
	Other chronic conditions c
	Hypertension	44.83	44.97	52.05	0.054	0.92 [0.74; 1.16]	0.486	1.35 [1.00; 1.81]	0.049
	Thyroid dysfunction	6.20	5.94	10.94	0.113	1.14 [0.72; 1.80]	0.565	1.69 [1.03; 2.78]	0.038
	Life habits d
	Lifetime cigarette smoking	37.67	49.10	38.13	0.038	1.33 [1.05; 1.70]	0.020	1.34 [0.97; 1.86]	0.075
	Current heavy alcohol drinking	18.28	21.26	17.21	0.410	1.19 [0.90 ; 1.57]	0.214	0.99 [0.67 ; 1.45]	0.948

a Adjusted for age, gender and education

Table 4 :

 4 Multiple logistic regression analyses of trauma status predicting the presence of angina pectoris, hypertension and current depressive symptoms Model 1: adjusted for age, gender, education, alcohol intake; WHR; hypertension, elevated triglycerides, glycemia; physical activity and living alone. The variables "current CESD ≥16", "lifetime MDD" or lifetime smoking were not associated with the outcome in our sample (p=0.569, 0.563 and p=250, respectively) b Model 2: adjusted for age, gender, education, lifetime smoking, alcohol intake; BMI >25 kg/m 2 and physical activity. c Model 3: adjusted for age, gender, education, lifetime smoking, physical activity; living alone, cognitive impairment; at least one somatic disease, current antidepressant and anxiolytic use RS= Re-experiencing symptoms

	Outcome	Trauma status	Cases (n)	OR [95% CI]	p-value
	Angina Pectoris (n= 1281) a	No trauma	23	1	0.006
		Trauma without RS	41	2.27 [1.31; 3.91]
		Trauma with RS	20	2.34 [1.22;4.49]
	Hypertension (n=1424) b	No trauma	296	1	0.047
		Trauma without RS	220	0.86 [0.68; 1.10]
		Trauma with RS	109	1.32 [0.96; 1.82]
	CESD ≥16 (n=1421) c	No trauma	183	1	0.061
		Trauma without RS	126	0.91 [0.69; 1.20]
		Trauma with RS	83	1.39 [0.99; 1.95]

a

Acknowledgements

We gratefully acknowledge the participants of the Esprit Study.

The ESPRIT project has been financed by the regional government of Languedoc-Roussillon (France), the Agence Nationale de la Recherche (ANR) (Project 07 LVIE 004; France) and an unconditional grant from Novartis (France).