Harald Zophoniasson
email: harald.zophoniasson@cea.fr

Dependence of time reversal of acoustic waves in plates on mean frequency and plate's characteristics

Harald Zophoniasson 1 • Charles Hudin 1 • Christian Bolzmacher 1 • Moustapha Hafez 1 poor tactile feedback [START_REF] Mortimer | Vibrotactile transduction and transducers[END_REF]. Linear electromagnetic actuators [START_REF] Kildal | Kooboh: variable tangible properties in a handheld haptic-illusion box[END_REF] and other technologies such as piezoelectric ceramics [START_REF] Chen | Design and evaluation of identifiable key-click signals for mobile devices[END_REF][START_REF] Poupyrev | Ambient touch: designing tactile interfaces for handheld devices[END_REF] are able to provide richer interactions due to their larger frequency range. However, as vibrations are conveyed to the whole surface (not localized), multi feedback (i.e. presenting different haptic feedback to different touch locations simultaneously) is not possible with such approaches.

Time reversal of flexural waves has been previously implemented on thin plates in [START_REF] Hudin | Localized tactile stimulation by time-reversal of flexural waves: case study with a thin sheet of glass[END_REF], to address the multi-feedback challenge. The process relies on the focusing of flexural waves in a solid material. It generates a constructive interference of flexural waves produced by actuators located on the perimeter of the surface. This allows the production of multiple localized vibrations simultaneously. The choice of a transparent material makes time reversal compatible with any kind of visual display.

The spatial resolution of such a system is a crucial parameter in the design of a tactile feedback interface. According to [START_REF] Hudin | Focalisation par retournement temporel dans les plaques minces: application à la stimulation tactile[END_REF]) the spatial resolution is bounded by the smallest wavelength, λ-= c/f+, where c is the medium's wave propagation celerity, and f+ the highest frequency used in the re-focusing process. Time reversal has already been implemented on several materials, such as BoPET (Biaxially-oriented polyethylene terephthalate) [START_REF] Hudin | Focalisation par retournement temporel dans les plaques minces: application à la stimulation tactile[END_REF]) and glass [START_REF] Hudin | Localized tactile stimulation by time-reversal of flexural waves: case study with a thin sheet of glass[END_REF], which were in fact very thin membranes. However in order to implement it on touchscreens for tablet and even larger interactive screens, time reversal approach needs to be validated on thicker and larger surfaces. This paper addresses this issue.

After a brief explanation of the time reversal principles, we present an analytical model based on Kirchhoff's equation for wave propagation to compute the spatial resolution Abstract Time reversal is an approach that can be used to focus acoustic waves in a particular location on a surface, allowing a multitouch tactile feedback interaction. The spatial resolution in this case depends on several parameters, such as geometrical parameters, injected frequency and material properties. This can be efficiently described with the Kirchhoff model of wave propagation. This paper highlights the impact of frequency, in particular the mean frequency of the injected signal band, geometrical parameters such as plate thickness and transducer's surface on the focused spot dimension and displacement amplitude. Results show that the dimension of piezoelectric transducers has little influence on the spatial resolution. The resonant behavior of the plate and its implication on focus point dimension, in particular its shape and amplitude are investigated. On reduced bandwidths the predominant effect of the resonant frequencies on the amplitude and shape of the focus spot is shown.

Introduction

Touch interaction has become the main interaction modality with most mobile devices as it allows the user to interact naturally with simple and intuitive gestures. Touchscreens however lack realism and efficiency compared to physical keyboards or buttons [START_REF] Hoggan | Investigating the effectiveness of tactile feedback for mobile touchscreens[END_REF]. Adding haptic feedback addresses this problem. Simple solutions relying on small motors with a rotating eccentric mass provide of time reversal of flexural waves applied to plates. Measurements on a physical system are then confronted to the model prediction. A method to evaluate the material characteristics of the plate is introduced to adjust the model to the physical system. The system's resonant behavior is finally analyzed to propose an explanation for shape and height variations of the focalization point.

Principles of operation

An impact at a specific location on a plate generates a wave field in the plate. The Fresnel-Kirchhoff theorem states that this wave field can be entirely retrieved from the value of the solution and from that of its first derivative on a surface enclosing it. To simplify, an approximation of this wave field can be recorded at a finite set of locations on the boundary of the plate [START_REF] Fink | Time reversal of ultrasonic fields. I. Basic principles[END_REF][START_REF] Wu | Time reversal of ultrasonic fields. II. Experimental results[END_REF]. Time reversal consists in recording the wave propagation speed after an impact at one or more locations on the perimeter of the plate. Playing the time reversed signal at the recording locations, i.e. generating the displacements will result in the back propagation of the waves until the original point of impact, recreating an approximation of the displacement at the impact's point. For in-depth description of the phenomenon see [START_REF] Fink | Acoustic time-reversal mirrors[END_REF] The generation of the driving signals of the actuators follows the method presented in [START_REF] Hudin | Localized tactile stimulation by time-reversal of flexural waves: case study with a thin sheet of glass[END_REF], to avoid the complex tasks of creating calibrated and repeatable impacts at specific locations on a plate. Based on the reciprocity principle and the fact that the wave propagation equation is linear, one can generate impulses at the transducer locations and record the vibration at the focalization point. Instead of a mechanical impulse, a voltage impulse on the transducer is theoretically sufficient. A voltage impulse is however brief and injects too little energy in the plate which leads to noisy measurements and can be replaced by white noise as described in Eq. (1), with h i,j (t), the impulse response at the focus point j due to the impulse on actuator i, FT -1 the inverse Fourier transform, Û j(ω) the recorded displacement at point j and V i the white noise signal driving actuator i.

Analytical model

The displacement around the point of focalization u, located in r = 0, is described as superposition of plane waves (modeled by a Bessel function J 0 ) of amplitude A, angular velocity ω and wavenumber k coming from every (1)

h i,j (t) = FT -1 Ûj(ω) Vi(ω)
space direction and interfering additively in O (Cassereau and Fink 1992; Hudin 2014). T is the time of the focalization.

Spatial resolution R s is given by the width at half- height of the focus point at the time of focalization,

u R s 2 , t = T = 1 2 u(0, t = T ).
For a constant bandwidth between pulsation ω 1 andω 2 , A(ω) = 1, ∀ω ∈ [ω 1 , ω 2 ] 12(1-ν 2 ) the bending rigidity and ρ s = ρ × 2h the density per square meter. By injecting ω m = D ρ s k 2 , k = 2π m into Eq. ( 6), the spatial resolution can be expressed as a function of the mean wavelength m : With Eq. ( 6) the model links the spatial resolution to material properties contained in the terms D and ρ s and to the mean wavelength of the actuation bandwidth used. The mechanical properties for standard glass are: E = 69 GPa, ν = 0.25 and ρ = 2500. Equation ( 7) explicitly points out the relation between the spatial resolution and the mean wavelength induced by the excitation bandwidth.

Without the knowledge of the precise material properties a well-known method was used to estimate them [START_REF] Aki | Space and time spectra of stationary stochastic waves, with special reference to microtremors[END_REF][START_REF] Boschi | On measuring surface wave phase velocity from station-station cross-correlation of ambient signal[END_REF]. It relies on the measure of surface wave velocity through the correlation of the recording in different location of the plate of the same signal. The

2) u(r, t) = ω A(ω)J 0 (kr)e jω(t-T ) dω (3) ω 2 ω=ω 1 J 0 (kR s /2)dω = 1 2 ω 2 ω=ω 1 J 0 (0)dω = 1 2 (ω 2 -ω 1 ) (4) ω 2 -ω 1 - 1 16 ρ s D R 2 s ω 2 2 2 - ω 2 1 2 = 1 2 (ω 2 -ω 1 ) (5) R 2 s = 16 D ρ s ω 2 -ω 1 ω 2 2 -ω 2 1 = 8 D ρ s 2 ω 2 + ω 1 (6) R s = 4 D ρ s 8 ω m = 4 D ρ s 8 2πf m (7) R s = m √ 8 2π ≈ m 2.2
correlation C pq , in the spectral domain between two signals recorded in p and q is given by: where S * q (ω) is the complex conjugate of S q (ω). From Aki (1957) and [START_REF] Boschi | On measuring surface wave phase velocity from station-station cross-correlation of ambient signal[END_REF], we have:

With E the expected value, ℜ the real part and V ϕ (ω) the phase speed of the waves at angular velocity ω. This phase speed in thin plates is given by: For a group of angular velocity ω and pairs {p, q}, the coefficient α is the one which minimizes the quantity

ℜ C pq (ω) -J 0 α √ ωr pq 2 ,
To estimate the material properties, a signal was emitted and recorded at different locations. Those recordings were used to compute the correlation term. Inserted into Eq. ( 11), an estimate of α can be found, which is, accord- ing to Eq. ( 10) an estimate of 4 ρ s D . This value represents an aggregate of the material properties for each plate thickness shown in Table 1. Injected into Eq. ( 6) an adjustment to the proposed model was computed.

(8) C pq (ω) = S p (ω) • S * q (ω) S p (ω) S q (ω) (9) E ℜ C pq (ω) = J 0 ωr pq V ϕ (ω) = J 0 α √ ωr pq (10) V ϕ (ω) = 4 D ρ s √ ω = 1 α √ ω (11) α = arg ξ min   ω p q =q ℜ C pq (ω) -J 0 α √ ωr pq 2  
4 Device glass plates of dimensions 330 × 254 mm 2 with thicknesses of 2 mm and 3 mm are used in the set-up. The plates are laid on 4 simple supports and free on each border. The first resonant mode was measured at 41.5 and 54 Hz for the 2 and 3 mm plates, respectively. The transducers used are piezoelectric diaphragms, (Murata 7BB-12-9 and 7BB-35-3), of diameter 12 and 35 mm and with thickness of 0.12 and 0.23 mm respectively. 16 transducers (8 on each side, in pairs facing each other) are glued with epoxy resin on the glass plates at a distance of 10 mm from the edges. An uneven distribution as shown in Fig. 1 aims at avoiding any symmetrical arrangements that would give correlated waveforms. The 16 transducers are driven in pairs in order to maximize the plate's deformation.

A total of four plates are prepared, two 2 mm thick and two 3 mm thick plates. One of the 2 mm thick plates is equipped with 12 mm transducers, the other one, with 35 mm transducers. The same is done for the 3 mm thick plates.

The acquisition and control software is developed in LabVIEW. Command signals (sample frequency 50 kHz, giving a bandwidth of 25 kHz) are amplified to 30Vcc through a custom board employing OPA552 (gain set to 5) operational amplifier chips. The plate's displacements are measured with a laser vibrometer (Polytec OFV 534). The Fig. 2 Gain of the amplification stage for the 0-25 kHz bandwidth performance of the specifically built amplification stage is tested. Due to stability problems when driving the highly capacitive charge of PZT (lead zirconate titanate ceramic material) transducers (12 mm: 8 nF, 35 mm: 30 nF at 1 kHz), a hardware low pass filter was added on the amplification stage. Gain and phase were measured across the entire bandwidth (0-25 kHz). Figure 2 shows the transfer function with an almost constant gain of 5 between 0 and 8 kHz. At about 8-9 kHz the gain slowly decreases to reach 3.6 at 25 kHz, a decrease of 28 %.

Experiments

A first study aims at determining the effect of plate's thickness and PZT transducers surface on the dimension of the focus point while using the whole bandwidth (0-25 kHz) of the system. For each one of the four plates, the drive signals are computed for the coordinates (150 mm; 90 mm) on the plate as shown in Fig. 1. To obtain a complete recording of the wave's propagation around the focus point in time, measurements of the vibrations are taken along a grid 60 × 60 mm with a 2 mm step size, centered on the focus point as shown in Fig. 3. This allows to reconstruct the propagation of the wave in the glass plate. The duration of focalization is set to 2 ms. The corresponding timeframe is used to measure the width of the focus point. The width of the focus point is defined as its width at half-height as shown in Fig. 3. The measurement is done along the cross section AB.

Across the four experiments the width of the focus point is relatively constant, at about 23 mm, as shown in Table 2. The measurements for the 35 mm PZT transducer exhibit a really stable width, whilst those for the 12 mm PZT transducer show a slight variation. The height of the focus point decreases with the increase of the plate's thickness from 2 to 3 mm (-26 % for the 35 mm PZT and -16 % for the 12 mm PZT), as shown in Table 2. This is easily explained by the fact that energy input remains the same while the stiffness of the plate increases with its thickness.

To better understand the relation of the focus point's width with the other parameters, we measured it for different frequency bands, plate thicknesses and actuator size. For plate thicknesses of 2 and 3 mm and for 12 and 35 mm wide piezoelectric diaphragms, the time reversal process on 1 kHz signal bands beginning from 0-1 kHz up to 24-25 kHz is used.

Focus point's width

Figure 4 present the results for each frequency band compared to the spatial resolution computed with the analytical Fig. 4 Model and measurements of focus point's width on a 3 mm glass plate model from Sect. 2 for the 3 mm thick plate. On Fig. 4, the focus point's width generated with PZT of both dimensions (12 and 35 mm) on the 3 mm thick glass plate is plotted and compared to the computed analytical model of R s . Both the model based on Eq. ( 6) and its adjusted counterpart, with the measured physical properties estimated with Eq. ( 10), are plotted. Overall the experimental data matches the adjusted analytical model. The different frequency intervals produced a spot varying from 60 mm (0-1 kHz) to 13 mm (24-25 kHz) corroborating the Kirchhoff based model calculations. Both experimental data curves exhibit similar variations.

On Fig. 5, the focus point's width generated with PZT of both dimensions (12 and 35 mm) on the 2 mm thick glass plate is plotted. 12 and 35 mm piezoelectric diaphragms exhibit relatively close values to each other and to the adjusted model. The different frequency intervals produced a spot varying from 77 mm (0-1 kHz) to 15 mm (24-25 kHz), which is in good agreement to the Kirchhoff model. For both piezoelectric diaphragms' sizes the variation is similar.

In both cases the adjusted model with the measured physical properties shows a significant improvement in its prediction over the model without the adjustments.

Focus point's height

Figures 6 and 7 present the measurements for the focus point height, for each one of the four plates. The amplitude of the focalization varies strongly in the first half of the frequency domain for both plates with 35 mm wide PZT transducers. In the second half of the frequency domain a slow decrease is noted. For both plate thicknesses with 12 mm wide PZT transducers very similar variations were measured, albeit at a smaller scale.

Figure 8 presents scans of a selection of focus points from the 2 mm thick glass plate equipped with 35 mm PZT transducers. Depending on the bandwidth, the focusing does not always produce a perfect circular deformation. For example the focalization process in the 1-2 kHz band produces a circular shape, whereas in the 3-4 kHz it produces an ellipsoidal shape and in the 9-10 kHz band it produces a triangular shape.

To better understand the behavior of the plate and the amplitude of the focus point, the frequency response at the focus point was measured for a 0-12.5 kHz frequency sweep for the 2 mm thick plate equipped with 35 mm transducers and compared to the focus point height measurements in Fig. 9. A certain correlation between the density of high amplitude resonances and the focus point height can be observed, especially in the 3-4 kHz and the 8-9 kHz bandwidth.

Scans of the focus point region in the 3-4 kHz were made to detect the resonant frequencies and the modal shape. Two major resonant frequencies (3.06 and 3.51 kHz) were observed, the corresponding modal shapes are shown in Fig. 10.

Scans of the focus point region in the 9-10 kHz were also made. Two resonant frequencies (9.28 and 9.77 kHz) were observed, the corresponding modal shapes are shown in Fig. 11. It was noted that for certain frequency bands, the focus point was not perfectly circular, unlike in the case of a wide bandwidth excitation signal. The time reversal process adds every contribution from every frequency across the whole frequency bandwidth. However the modal shapes inside narrow bandwidth excitation signals could dominate in the time reversal process and explain the distortion observed in some cases.

According to the model, and confirmed by the measurements, spatial resolution increases the same way as the mean frequency of the excitation signal band is increased for given plate characteristics (material and geometry). Targeting a spatial resolution of 10 mm requires a mean frequency of the excitation signal around 50 kHz on the 2 mm thick plate. But the higher the frequency, the more difficult it is to drive the transducers in order to produce such high frequency waves in the plate as the energy consumption increases.

As seen with measurements, amplitude decreases when excitation frequencies increase. In order to get sufficient amplitude, lower frequencies should be used. For the 2 mm plate, the contribution of the 0-10 kHz is predominant. Nevertheless, the hearing range of humans is from 20 to 20 kHz. When generating sufficiently big deformations of the plate in this frequency range being able to recognize while exploring the surface with the finger, noise is emitted that alters user acceptance.

Another important matter is contrast ratio between the peak amplitude of the focus point and the mean amplitude of the waves in the plates. The higher the ratio, the easier it is to distinguish the stimulus. Two parameters are fundamental for the contrast ratio: the signal's bandwidth and the number of transducers [START_REF] Hudin | Focalisation par retournement temporel dans les plaques minces: application à la stimulation tactile[END_REF]). However, the wider the bandwidth, the harder it is to build an electronic with a flat response across the whole band. The number of transducers is easier to increase within a certain limit.

For a given application, the only geometrical parameter which can be modified is the plate's thickness. The plate's surface matches of course the surface of the screen. The model shows that with the decrease in thickness, the spatial resolution gets higher. But more importantly, the amplitude of the focus point is improved by a thinner plate.

Conclusion

This paper investigated the factors influencing the dimensions of a focus point obtained through time reversal of acoustic waves. The mean frequency of the bandwidth influences the width of the focus point and the plate's thickness influences primarily the displacement amplitude of the spot. Different sizes of piezoelectric diaphragms (12 and Fig. 11 Map of resonant frequencies in the 9-10 kHz bandwidth for the 2 mm thick plate with 35 mm transducers 35 mm) did not yield significant differences on the focus point dimensions (8 % in average). The resonant behavior of the plate and its implication on focus point dimension, in particular its shape and amplitude are investigated. On reduced bandwidths (1 kHz wide) the predominant effect of the resonant frequencies on the amplitude and shape of the focus spot is shown.

  , so: Taking the limited development of the second order Bessel function around O, J 0 (x) = 1 -x 2 2 and the dispersion relation in a thin plate ω = D ρ s k 2 from the propagation model of waves in plates by Kirchhoff, gives: which is, with ω m = ω 2 +ω 1 2 the mean angular velocity, D = E(2h) 2

(

Fig. 3

 3 Fig. 3 Displacement magnitude (µm) at the focus point for a 25 kHz wide bandwidth and A-B cross section detail

Fig. 5

 5 Fig. 5 Model and measurements of focus point's width on a 2 mm glass plate

Fig. 6

 6 Fig. 6 Height of focus point (µm) for the 35 mm transducers

Fig. 7 Fig. 10

 710 Fig. 7 Height of focus point (µm) for the 12 mm transducers

Table 1

 1 Computed value for α for each plate thickness Position of the piezoelectric transducers on the glass plate

	Plate thickness	2 mm	3 mm
	α	0.5434	0.4606

Table 2

 2

	Width (mm) and height (µm) of focus point	Width (mm)	PZT Ø35 mm	PZT Ø12 mm	Height (µm)	PZT Ø35 mm	PZT Ø12 mm
		Glass 2 mm	23.7	22.2	Glass 2 mm	3.59	0.61
		Glass 3 mm	23.1	25.7	Glass 3 mm	2.78	0.51


Frédéric Clarençon

Éric Bardinet

Jacques Martinerie

Vincent Pelbarg

Nicolas Menjot De Champfleur

Rajiv Gupta

Eléonore Tollard

Gustavo Soto-Ares

Danielle Ibarrola

Emmanuelle Schmitt

Fre ´de ´ric Clarençon

´ric Bardinet

Ele ´onore Tollard

Thomas Tourdias

Vincent Degos

Je ´rome Yelnik

Didier Dormont

Louis Puybasset

Damien Galanaud

Lesions in deep gray nuclei after severe traumatic brain injury predict neurologic outcome

Introduction

Deep gray matter (DGM) consists of the bilateral thalami and several gray matter nuclei regrouped under the name basal ganglia (BG). The BG include the neostriatum (consisting of the caudate nucleus [CN], putamen, and nucleus accumbens [NA]), globus pallidus (GP) (composed of GP externa and GP interna), substantia nigra (SN) (composed of pars compacta and pars reticulata), zona incerta (ZI), red nucleus (RN) and sub-thalamic nucleus (STN).

Severe traumatic brain injuries (TBI) are usually observed secondary to high velocity head trauma [START_REF] Young | When physics meets biology: low and high-velocity penetration, blunt impact, and blast injuries to the brain[END_REF]. Several demographic and clinical data, like age, sex (male), Glasgow coma scale (GCS) at admission or pupillary response [START_REF] Junior | Prognostic model for patients with traumatic brain injuries and abnormal computed tomography scans[END_REF][START_REF] Nelson | Extended analysis of early computed tomography scans of traumatic brain injured patients and relations to outcome[END_REF] may influence the neurological outcome in severe TBI. Most of the intracranial intraparenchymal traumatic lesions are located in the frontobasal area and at anterior aspect of the temporal lobes [START_REF] Gentry | MR imaging of head trauma: review of the distribution and radiopathologic features of traumatic lesions[END_REF]. Lesions' topography depicted on CT-scan [START_REF] Nelson | Extended analysis of early computed tomography scans of traumatic brain injured patients and relations to outcome[END_REF], morphologic MRI [START_REF] Moen | Traumatic axonal injury: the prognostic value of lesion load in corpus callosum, brain stem, and thalamus in different magnetic resonance imaging sequences[END_REF] and multimodality MRI [START_REF] Shakir | Prognostic Value of Quantitative Diffusion-Weighted MRI in Patients with Traumatic Brain Injury[END_REF][START_REF] Laouchedi | Deafferentation in thalamic and pontine areas in severe traumatic brain injury[END_REF][START_REF] Galanaud | Assessment of white matter injury and outcome in severe brain trauma: a prospective multicenter cohort[END_REF] has also a strong influence on the long-term clinical outcome. For instance, it has been demonstrated that thalamic, corpus callosum and brainstem traumatic lesions are associated with a poor neurological outcome [START_REF] Moen | Traumatic axonal injury: the prognostic value of lesion load in corpus callosum, brain stem, and thalamus in different magnetic resonance imaging sequences[END_REF][START_REF] Xu | The Role of Magnetic Resonance Imaging in the Prediction of Minimally Conscious State After Traumatic Brain Injury[END_REF]. Traumatic lesions of the DGM are frequent in severe TBI and are found in up to 46% of cases [START_REF] Kampfl | The persistent vegetative state after closed head injury: clinical and magnetic resonance imaging findings in 42 patients[END_REF]. Multiple case reports and series document lesions in DGM in comatose patients [START_REF] Comoglu | Methanol intoxication with bilateral basal ganglia infarct[END_REF][START_REF] Hopkins | Basal ganglia lesions following carbon monoxide poisoning[END_REF][START_REF] Parvizi | Neuroanatomical correlates of brainstem coma[END_REF]. However, only scant data are available on the influence of DGM lesions (DGML) on the clinical outcome in patients with severe TBI.

The purpose of this work was to evaluate the correlation between the DGML' burden depicted on T2 Fast Spin Echo (T2 FSE) images and long-term neurological prognosis in patients with severe TBI.

Materials and methods

Patients

The institutional review boards of the Pitie ´-Salpêtrière Hospital and all participating institutions approved the study. Written informed consent was obtained for all study participants (patient's next of kin during the acute stage, and patients themselves after recovery of consciousness). The protocol was registered on December 2007 (NCT00577954).

One hundred and five consecutive patients were prospectively enrolled from May 2001 to March 2009 in 6 different University Hospital Centers. Retrospective analysis of these prospectively collected data was conducted for this study.

All patients had severe traumatic brain injury (TBI) defined as an inability to follow simple commands that could not be explained by sedation one week after severe head trauma. The inclusion criteria were: [START_REF] Young | When physics meets biology: low and high-velocity penetration, blunt impact, and blast injuries to the brain[END_REF] adult patient between 15 and 75 year of age with severe TBI independently from the mechanism, except penetrating injury; and (2) comatose state with inability to follow simple commands that could not be explained by sedation at least 7 days, and not more than 45 days, after TBI. Exclusion criteria were: (1) moribund patients (expected survival< 24h); (2) physiological instability (e.g., due to hemodynamic instability, increased intracranial pressure, and/or rapidly deteriorating respiratory function) that would preclude MRI scanning; (3) contraindication to the MRI; (4) penetrating head injury; (5) major intraparenchymal, subdural or epidural hematoma requiring emergent surgical evacuation or decompressive craniectomy; and (6) a central nervous system condition such as stroke, brain tumor, or a neurodegenerative disease preceding TBI.

Patients' demographics are summarized in Table 1 . 80 males and 15 females from 15 to 77 years of age (m = 36.7±16) were included in the study. All the patients were hospitalized in the neurosurgical intensive care unit and presented a persistent coma, unexplained by chemical sedation. Neurological prognosis was evaluated on the Glasgow Outcome Scale (GOS) [START_REF] Jennett | Assessment of outcome after severe brain damage[END_REF] ( Table 2 ) at 6 months follow-up. A GOS between 1 and 3 was considered an unfavorable outcome while a GOS of 4 or 5 was considered a favorable outcome. 64 out of the 95 patients (67%) had a satisfactory registration of the DGM atlas. In the overall population, 2 patients were lost to the follow-up; one with a satisfactory DGM atlas registration; one with a poor registration. Thus, a total of 63 patients (66%) had both a satisfactory atlas registration and follow-up available (see the recruitment flow chart, Fig 1 ).

Imaging protocol

MRI acquisitions were performed with an average delay of 21±9 days (range: 7-45) from the traumatic insult. The T2 FSE sequence was acquired as part of a multimodal imaging protocol described in a previous paper [START_REF] Galanaud | Assessment of white matter injury and outcome in severe brain trauma: a prospective multicenter cohort[END_REF]. T2 FSE sequence parameters in the different institutions where the MRIs were acquired are detailed in S1 File.

Lesion scoring

The scoring of the deep gray matter lesions was based on a semi-quantitative scale as follows: 0 = absence of any lesion; 1 = a punctate lesion; 2 = lesion occupying less than 1/3 rd of the volume of the nucleus; 3 = lesion occupying between 1/3 rd And 2/3 rd of the volume; 4 = lesion occupying more than 2/3 rd but not the entire nucleus; 5 = involvement of the entire nucleus (Fig 3 ). If more than one lesion involved one nucleus, the extend of the different lesions involving the same nucleus were added in order to obtain the global traumatic lesions' burden for a given nucleus.

The volume of CP traumatic lesions was used as a surrogate marker of lesions involving the CP smaller nuclei. The above-mentioned score was used to evaluate the CP lesions' burden.

The average number of DGML per patient was also evaluated. All images were independently reviewed by 2 neuroradiologists (FC and DG) with respective experience of 6 and 14 years of experience in neuroradiology.

Use of a 3D deformable basal ganglia atlas

In order to improve the accuracy of the evaluation of the DGML' burden, a DGM nuclei atlas was employed in this research [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]. Briefly, this atlas consists of a canonical DGM nuclei template that was derived by correlating histology slices with MRI. For any given patient, this canonical template is mapped on patient specific images by applying an inter-patient, MRI to MRI registration using a non-rigid mapping to account for individual variability in the size and shape of the DGM nuclei. For details on the 3D-deformable DGM nuclei atlas, see S2 File .

Assessment of registration quality

The quality of the registration of the DGM nuclei atlas on to the T2 FSE images was evaluated qualitatively and quantitatively. For qualitative assessment, the concordance of the following boundaries was checked: medial boundaries of CN heads and thalami (Fig For quantitative assessment, a scale was elaborated to classify the fidelity of registration. For CN heads and thalami, we assigned a score of 0 if less than 10% of the volume of the registered nucleus was bulging into the adjacent ventricle (lateral ventricle for caudate heads, third ventricle for thalami). Scores of 1 and 2 were assigned for an overlap of 10-25% and 25% and more, respectively. For CP and OT, the following scale was used: 0 = no error; 1 = mild error; and, 2 = marked error. Only the patients presenting a correct registration for both the CN heads/thalami (grade 0) and for CP/OT (grade 0) were used for the final analysis of the DGML.

Statistical analysis

Sensitivity, specificity, positive predictive value (PPV), negative predictive value (NPV), odds ratios (OR), Chi 2 and Fisher's exact tests, as well as the Cohen kappa-weighted test for the Multivariate analysis was performed using a Support Vector Machine (SVM) with linear nucleus [START_REF] Vapnik | Statistical Learning Theory[END_REF]. Details about SVM are described in S3 File . The multivariate analysis (SVM) was performed on 63 out of 95 enrolled patients (31 patients were excluded due to atlas misregistration; 2 patients were lost on the follow-up; one patient both had misregistration and was lost on the follow-up). The aim of this statistical analysis was to evaluate the weight of lesions of each nucleus of the DGM on the patients' neurological outcome. Thus, 20 variables (right + left DGM lesions) were used for the multivariate analysis. We also performed the same multivariate analysis using the age as an additional variable (21 variables in total) in order to see if this variable would increase the ability of the classifier to predict good or poor clinical outcome.

The same analysis was performed using the DGML scoring system without the aid of the deformable atlas.

Finally, we compared the performances of our grading scale for DGML' evaluation with a semi-quantitative grading scale combining the evaluation of brain stem and corpus callosum post-traumatic lesion burden (Fig 5). Comparison between the areas under the curve (AUC) from the receiver operating characteristic (ROC) curves of the two grading scales was performed using the DeLong's approach [START_REF] Delong | Comparing the areas under two or more correlated receiver operating characteristic curves: a nonparametric approach[END_REF]. The DeLong's approach is a nonparametric method for computing the AUC that does not need the normality assumption. With this method, the value of AUC is obtained by summing the area of the trapezoids that are formed below the connected points making up the ROC curve.

Results

Registration fidelity

Satisfactory registration of DGM nuclei atlas on T2 FSE images ( Fig 6 ) was obtained in 67% of the cases (64/95). Hydrocephalus was present in 9 (56%) of these 16 cases of major misregistration and was statistically associated with a higher rate of major misregistration (Fisher's exact test: P = 0.000001, OR = 57.2; CI 95% [10.3; 317.8]). Midline shift due to mass effect was also statistically associated with major misregistration (Fisher's exact test: P = 0.006, OR = 7.8; CI 95% [1.95; 31.4]). Poor registration of the boundaries of the caudate heads was seen in all the cases of misregistrations (31/31); thalami and OT/CP were misregistered in 65% (20/31) and 58% (18/31) of cases, respectively.

Patients' outcome

Two patients were lost to the follow-up. In the overall population, 47 (51%) had an unfavorable outcome whereas 46 (49%) had a favorable outcome. Interestingly, patients with favorable outcome were younger than those with poor outcome (32±13.2 vs 42±17.3 years, P = 0.025). On the contrary, sex did not have any influence on the neurological outcome (P = 0.54).

At 6 months, among the 63 patients who had both a satisfactory registration and an available clinical follow-up, 36 (57%) had a favorable (GOS 4-5) outcome whereas 27/63 patients (43%) had an unfavorable (GOS 1-3) outcome.

Inter-rater agreement for lesions scoring

Interobserver kappa test performed to evaluate the agreement between the 2 observers for the DGML scoring was good with a kappa index of 0.71. Only 4% of the studied nuclei presented a Grading scale combining the evaluation of the lesions' burden of the brain stem (A, B and C) and of the corpus callosum (D). For the brain stem, the mesencephalon was divided into 4 regions (A), the pons into 4 regions as well (B) and the medulla oblongata corresponded to one region (C). For each lesion involving one region, one point was added (maximum total points = 9). D. Drawing of the brain with the corpus callosum colored in red (lateral view). The corpus callosum was divided into 3 areas: the genu, the body and the splenium. No lesion was graded 0, lesion involving < 50% of the genu: 1 point and 50%: 2 points; lesion involving less than 1/3 of the body: 1 point, 1/3 and< 2/3: 2 points, and 2/3: 3 points; lesion involving less than 50% of the splenium: 1 point and 50%: 2 points. The maximum total points for the corpus callosum was 7 (D). By combining the 2 scores, the brain-stem/corpus callosum (BS-CC) score was obtained (maximum points = 16).

scoring gap superior to 1. These were almost always seen in the smallest structures (ZI, SN, STN). These differences were settled by consensus.

Number and location of DGM lesions

Out of the 64 patients with a good registration of the 3D atlas, 47 (73%) presented at least a lesion in one nucleus. Among these, 139 DGML were counted, with 2.2 DGM lesions on average per patient. DGM regions most frequently affected were: putamen (26%), globus pallidum (16.5%) and thalamus (15%) ( Table 3 ). Interestingly, neither age nor sex had any influence on the DGML burden (corresponding to the addition of lesion scoring of each nucleus) (P = 0.91 and 0.27, respectively).

Correlation between DGML and neurological outcome

Patients without DGML had a favorable neurological outcome in 89% of cases (16/18) (P = 0.0016, Fisher's exact test). OR for favorable outcome in patients without DGML was 10 (CI 95% [2.1; 48.7]. Sensitivity, specificity, PPV, NPV for favorable outcome in patients without DGML were 89%, 44.5%, 39% and 91%, respectively. Bilateral lesions were seen in 20 patients. In 16/20 (80%) cases, patients with one or more bilateral DGML had an unfavorable outcome at 6 months (Fisher's exact test, P = 0.00008, OR = 11.6, CI 95%[3.2; 42.4]). Sensitivity, specificity, PPV and NVP for unfavorable outcome in patients with bilateral lesions were 59%, 89%, 80% and 74.4%, respectively.

The SVM analysis was performed to separate the group "favorable outcome" from the group "unfavorable outcome". Twenty variables were available, corresponding to the lesion scores of left and right caudate nucleus, putamen, thalami, globus pallidum, accumbens nuclei, subthalamic nuclei, red nuclei, zona incerta, subtansia nigra and cerebral peduncles. The learning set of the multivariate analysis showed that 96.9% of patients with unfavorable outcome and 96.8% of patients with favorable clinical outcome were correctly classified by the discriminant function, respectively. The Jacknife cross-validation method found 90.5% of correct classification in the "unfavorable outcome" group and 81% in the "favorable outcome" group ( Table 4 ). When the multivariate analysis was performed with "age" as an additional variable, the classification accuracy was not significantly increased (91.3% for unfavorable neurological outcome). Comparison of the AUC from ROC curves of the DGML scoring with and without the aid of the DGM nuclei atlas showed that the results obtained with the atlas were more accurate to predict poor neurological outcome (0.868, 95% CI [0.763-0.974] with the atlas vs 0.774, 95% CI [0.63-0.918] without the atlas). However, the difference was not statistically significant (Z = 1.6065, P = 0.1082).

Comparison of the AUC from ROC curve of our DGML grading scale versus the ones of brain stem and corpus callosum grading scale showed that the DGML grading scale was more accurate in predicting a poor neurological outcome (Z = 2.695, P = 0.007). Interestingly, the combination of DGML, brain stem and corpus callosum grading scales did not improve the accuracy in predicting a poor neurological outcome (Fig 7).

Discussion

Some predictive factors for unfavorable neurological outcome in severe TBI have already been described, in particular the 2 weeks' GCS [START_REF] Kouloulas | Prognostic value of time-related Glasgow coma scale components in severe traumatic brain injury: a prospective evaluation with respect to 1-year survival and functional outcome[END_REF], the shear-related white matter lesions on MRI [START_REF] Moen | A longitudinal MRI study of traumatic axonal injury in patients with moderate and severe traumatic brain injury[END_REF] or the white matter lesions depicted on multimodal imaging (DTI, MR spectroscopy) [START_REF] Galanaud | Assessment of white matter injury and outcome in severe brain trauma: a prospective multicenter cohort[END_REF][START_REF] Moen | Traumatic axonal injury: Relationships between lesions in the early phase and diffusion tensor imaging parameters in the chronic phase of traumatic brain injury[END_REF]. However, they still cannot correctly predict the individual neurological outcome for a large number of patients. In the present study, we chose to investigate the DGML because we hypothesized, according to our clinical experience, that few strategic small lesions affecting the DGM may be associated with a worse outcome than one voluminous brain lesion.

DGML count

After atlas registration, 71% of the patients had DGML. This rate is higher than previously reported in the literature, in which it ranges from 19 to 46% [START_REF] Masuzawa | Shearing injuries of parasagittal white matter, corpus callosum and basal ganglia: possible radiological evidences of hemiplegia in diffuse axonal injury[END_REF][START_REF] Kampfl | Prediction of recovery from post-traumatic vegetative state with cerebral magnetic-resonance imaging[END_REF][START_REF] Patrick | MRI patterns in prolonged low response states following traumatic brain injury in children and adolescents[END_REF][START_REF] Wedekind | Trauma to the pontomesencephalic brainstema major clue to the prognosis of severe traumatic brain injury[END_REF].

In the literature, only few studies analyzed individually DGML in TBI. Kampfl et al. [START_REF] Kampfl | Prediction of recovery from post-traumatic vegetative state with cerebral magnetic-resonance imaging[END_REF], in a prospective study on 80 patients with severe TBI, found that traumatic lesions involved the thalamus in 46% of cases; lenticular nuclei in 38% and caudate nuclei in 10%. Other series focused on the rate of thalamic traumatic lesions; especially neuropathological studies [START_REF] Graham | Neuropathology of the vegetative state after head injury[END_REF][START_REF] Graham | Novel aspects of the neuropathology of the vegetative state after blunt head injury[END_REF], in which this rate varies from 60 to 80% in patients who died or remained in vegetative state. Receiver operating characteristic (ROC) curves and area under the curve (AUCs) for the different grading scales used in this studies, alone or in combination, with or without the factor "age" taken into account. Note that the AUC of the ROC curve of the DGM nuclei grading scale was higher than the one of the other scores, alone or combined, with or without the age.

Neurological outcome and DGML

Our work underlines the correlation between unfavorable neurological outcome and DGML. The absence of DGM lesion on T2 FSE after atlas fusion was strongly predictive of favorable neurological outcome (89%, OR = 10). On the contrary, bilateral lesions of DGM nuclei were associated with an 80% rate of unfavorable outcome (OR = 11.6). Additionally, on the basis of the scoring of the DGM nuclei lesions using the atlas, the discriminative function allowed an accurate classification of patients with unfavorable outcome at 6 months with a rate of 90.5%.

According to the data in the literature, DGML are the third most common intracranial parenchymal lesions in severe TBI, after corpus callosum and brain stem [START_REF] Kampfl | Prediction of recovery from post-traumatic vegetative state with cerebral magnetic-resonance imaging[END_REF], which are often integrated in the large group of diffuse axonal injuries (DAI) [START_REF] Su | Diffuse Axonal Injury[END_REF].

Few series have studied the relationship between DGML and neurological outcome in severe TBI [START_REF] Kampfl | Prediction of recovery from post-traumatic vegetative state with cerebral magnetic-resonance imaging[END_REF]. One retrospective MRI study [START_REF] Patrick | MRI patterns in prolonged low response states following traumatic brain injury in children and adolescents[END_REF] on 15 patients (children with severe TBI) showed a rate of pejorative neurological outcome of 95% for patients with DGM lesions associated with brain stem involvement. Others series have demonstrated the strong implication of thalamic lesions in unfavorable neurological outcome [START_REF] Graham | Novel aspects of the neuropathology of the vegetative state after blunt head injury[END_REF][START_REF] Adams | The neuropathology of the vegetative state after an acute brain insult[END_REF][START_REF] De La Cueva | Usefulness of FDG-PET in the diagnosis of patients with chronic severe brain injury[END_REF][START_REF] Uzan | Thalamic proton magnetic resonance spectroscopy in vegetative state induced by traumatic brain injury[END_REF]. However, in our study, the multivariate analysis did not show that lesion of any given nucleus was by itself predictive of a poor outcome.

Additionally, in our study, the evaluation of DGML helped to predict more accurately a poor neurological outcome than other grading schemes involving brain regions known to be frequently involved in severe TBI like the corpus callosum and the brain stem [START_REF] Kampfl | Prediction of recovery from post-traumatic vegetative state with cerebral magnetic-resonance imaging[END_REF][START_REF] Yuan | Use of multisequence 3.0-T MRI to detect severe traumatic brain injury and predict the outcome[END_REF].

Interest of using a 3D deformable atlas

The originality of this work was to present a precise anatomic analysis of DGM lesions in severe TBI, using a 3D deformable atlas. The use of the 3D atlas was motivated by the fact that DGM is difficult to see on clinical MRI. While T2 FSE is one of the most adapted sequences for exploration of severe TBI lesions [START_REF] Weiss | Clinical review: Prognostic value of magnetic resonance imaging in acute brain injury and coma[END_REF][START_REF] Shibata | Differentiation of mechanism and prognosis of traumatic brain stem lesions detected by magnetic resonance imaging in the acute stage[END_REF], it cannot precisely determine the involvement of the DGM, due to the small size of some structures and their poor contrast with the rest of the parenchyma. Due to deformations of brain parenchyma secondary to TBI and the interindividual variation in normal anatomy, a deformable atlas was necessary to precisely localize the lesions. Yet, commonly used DGM nuclei atlases, like the Schaltenbrand and Wahren atlas [START_REF] Schaltenbrand | Atlas for stereotaxy of the human brain[END_REF], do not present elastic deformable characteristic and may give erroneous localization of small deep gray structures. In our study, there was a tendency for better performance in predicting poor neurological outcome using the atlas than without; however, this difference was not statistically significant (p = 0.1082). This may be explained by a lack of statistical power due to a too small population sample size (63 patients).

Limitations

Our study presents some limitations. The volume of the population of our series remains small with respect to the number of variables taken into account in the multivariate analysis. Some of the DGM nuclei were rarely involved (like ZI, which presented lesions in only 4% of the cases). This fact does not allow precise evaluation of their implication in unfavorable outcome.

In our study, the DGM nuclei atlas was, most of the time (67%), successfully registered on the T2 FSE. Fusion was totally non-interpretable, due to poor registration, in only 16/95 cases (17%). Moreover, the criteria used to consider a registration as accurate were very restrictive, leading to exclude 31 patients (33%) from the analysis. Most of the misregistrations were due to an overhanging of the CN in the lateral ventricles and were observed in cases of hydrocephalus and/or midline shift. Methodological developments on the atlas used are underway to minimize these errors, especially in case of ventricular dilatation.

Registration of the DGM nuclei atlas on susceptibility-weighted imaging (SWI) or 3D Fluid attenuation inversion recovery (FLAIR) volumes may have improved the evaluation of DGML' burden. However, these sequences were not available for clinical use in all centres participating in the study during the inclusion period. Additionally, even if T2 GE or SWI are highly sensitive sequences for the depiction of post-traumatic lesions, they only display haemorrhagic ones. It should also be mentioned that the hypo-intense signals related to the hemoglobin degradation products seen on these sequences are artefacts. They thus cannot be measured to evaluate the extend of the lesion burden.

Finally, some old ischemic lesions of the deep grey matter may have been wrongly interpreted on T2 FSE as post-traumatic lesions, leading to an overestimation of the lesions' burden. However, our population was young (mean age = 36.7 y), and the probability of such ischemic lesions in young patients is low.

Conclusion

DGML were frequently observed in our study population with severe TBI. Multivariate analysis performed on the basis of DGML scores may predict poor neurological outcome at 6 months' follow-up in severe TBI, with a 90.5% positive predictive value. These results need further studies in order to determine if an algorithm combining DGM lesions evaluation with other clinical/imaging/functional data may increase the accuracy of the prediction of outcome in severe TBI.

Center

Description of the atlas used in the study

The 3D-deformable basal ganglia atlas was generated from autopsy material of a donor with no neurological or psychiatric disease. A detailed MR scan was performed on this brain using a protocol that included the following two specific sequences: Fusion between images obtained from the histological atlas and MR images of the post-mortem brain enabled reconstruction of surface models of BG.

A deformation strategy was developed to morph the histological 3D atlas on to T1 and T2-weighted MR images. This was done in two steps. First, the histological atlas was mapped on the MR images using a global registration via a rigid transformation.

This global registration accomplished coarse matching between the histologic and MR data sets. This was followed by fine registration using a non-rigid mapping based on homology between regions of interest including BG on MR images of a given patient and MR images of the atlas.

  Impact of deep gray matter lesions on neurological outcome in severe TBI Deep grey matter structures Our study focused on the following deep grey nuclei: CN, thalamus, putamen, GP, NA, SN, STN, RN and ZI ( Fig 2 ). The degree of involvement of the smaller nuclei within the cerebral peduncles (CP), like the pediculopontine nucleus, the pontis oralis nucleus or the parabrachial nucleus, which are not yet registered by the DGM nuclei atlas, was indirectly estimated by evaluation of lesions' volume in CP by means of the semi-quantitative scale described bellow.

Fig 1 .

 1 Fig 1. Flow chart summarizing the study design. FU: follow-up.

  4A); boundaries of CP and optic tracts (OT) (Fig4B). Accurate registration of the boundaries of CN heads and thalami indicated correct registration of the deep gray matter of the cerebral hemispheres while satisfactory registration of CP and OT indicated accurate registration of the brain stem nuclei.

Fig 2 .

 2 Fig 2. A. Registration of the DGM nuclei atlas on axial T2 FSE slice passing through the foramen of Monro. 1. Putamen; 2. Globus pallidum; 3. Caudate nucleus head; 4. Thalamus. B. Registration of the DGM on axial T2 FSE slice passing through the mesencephalon. 5. Nucleus accumbens; 6. Sub-thalamic nucleus; 7. Zona incerta; 8. Red nucleus.

Fig 3 .

 3 Fig 3. DGML semi-quantitative scale. A. No lesion; B. Punctuate lesion; C. Lesion involving less than 1/3 rd of the nucleus. D. Lesion involving between 1/ 3 rd and 2/3 rd of the nucleus. E. Lesion of more than 2/3 rd of the nucleus. F. Total involvement of the nucleus.

Fig 4 .

 4 Fig 4. Example of satisfactory registration of the boundaries of the caudate nuclei heads (A, white arrows), of the optic tracts (B, white arrows) and of the cerebral peduncles (B, black arrows).

Fig 5 .

 5 Fig 5. Grading scale combining the evaluation of the lesions' burden of the brain stem (A, B and C) and of the corpus callosum (D). For the brain stem, the mesencephalon was divided into 4 regions (A), the pons into 4 regions as well (B) and the medulla oblongata corresponded to one region (C). For each lesion involving one region, one point was added (maximum total points = 9). D. Drawing of the brain with the corpus callosum colored in red (lateral view). The corpus callosum was divided into 3 areas: the genu, the body and the splenium. No lesion was graded 0, lesion involving < 50% of the genu: 1 point and 50%: 2 points; lesion involving less than 1/3 of the body: 1 point, 1/3 and< 2/3: 2 points, and 2/3: 3 points; lesion involving less than 50% of the splenium: 1 point and 50%: 2 points. The maximum total points for the corpus callosum was 7 (D). By combining the 2 scores, the brain-stem/corpus callosum (BS-CC) score was obtained (maximum points = 16).

Fig 6 .

 6 Fig 6. Example of a satisfactory registration of the DGM on a T2 FSE axial slice passing through the thalami (delineated in green) and striatum (delineated in blue). Note the punctuate lesion involving the left thalamus (arrow).

Fig 7 .

 7 Fig 7. Receiver operating characteristic (ROC) curves and area under the curve (AUCs) for the different grading scales used in this studies, alone or in combination, with or without the factor "age" taken into account. Note that the AUC of the ROC curve of the DGM nuclei grading scale was higher than the one of the other scores, alone or combined, with or without the age.

  (a) T1-WI (3DIR-FSPGR, TR = 11 ms, TE = 2 ms, TI = 600 ms, flip angle = 10°, NEX = 1, slice thickness = 1.3 mm, interslice gap = 0) and (b) T2 spin echo (TR = 2000 ms, TE = 90 ms, NEX = 1, slice thickness = 2 mm, interslice gap = 1 mm). Afterextraction of the brain from the skull, its hemispheres were separated and put into formol solution. "En bloc" coronal sections were performed, followed by a cryosection with a microtome (thickness = 70 μm) of the left hemisphere fixed in formol, and then frozen. After histological and immunohistochemical colorations, a delineation of the BG and thalamus, and their functional territories was performed.

Table 1 .

 1 Demographic characteristics of patients involved in our study.

	Characteristics	Overall population	Poor neurological outcome	Good neurological outcome	P value
	Patients (n, %)	95 (100)	47 (51)*	46 (49)*	-
	Gender (n, %)				0.54
	Male	80 (84)	40 (87)	36 (80)
	Female	15 (16)	6 (13)	9 (20)
	Age (years; average± SD)	36.7±16	42±17.3	32±13.2	0.025
	Patients with poor atlas registration (n, %)	31 (33)$	19 (61)	11 (39)	0.06
	Number of patients studied with the	63 (66)#	27 (43)	36 (57)	-
	multivariate analysis (n, %)
	* overall, 2 patients were lost to the follow-up
	$ 1 patient with poor atlas registration was lost to the follow-up
	# 1 patient with satisfactory atlas registration was lost to the follow-up
	n: number, SD: standard deviation

Table 3 .

 3 Characteristics of the deep grey matter lesions in our population.

	Characteristics	N (%)
	Total Nb of DGML	139
	Patients with bilateral lesions	19 (30)
	Patients without DGML	18 (28)
	Repartition of DGML
	Putamen	36 (26)
	Globus pallidus	23 (16.5)
	Thalamus	21 (15)
	Caudate nucleus	20 (14)
	SN	18 (13)
	STN	6 (4)
	ZI	5 (3.5)
	Accumbens nucleus	5 (3.5)
	RN	5 (3.5)
	Percentages are given in brackets
	nb: number, DGML: deep grey matter lesions, ZI: zona incerta, SG: substancia nigra, STN: subthalamic
	nucleus, RN: red nucleus

Table 4 .

 4 Cross validation (Jacknife test). In each validation test, we used data from all but one subject (S -1 of the S subjects) to train the classifier.

	Predicted/Initial	Good	Poor
	Good	34 (94.4%)	8 (29.6%)	Good predictive value: 81%
	Poor	2 (5.6%)	19 (70.4%)	Poor predictive value: 90.5%

  Details of the T2 FSE acquisitions in each center involved in the study.Nb: number, FOV: field of view, ET: echo time, RT: repetition time

	Supplemental material # 1
		Supplemental material # 2:
		MRI field	MRI	Matrix	ET	RT
	Nb	strength
	1	1.5T	GE Signa Excite	256x256	104.8	3340	3	0
		3T	GE Signa Hdx	512x256	92.2	3420	3	0
	2	1.5T	Siemens Sonata	256X192	129	5680	3	0
	3	1.5T	Symphony Tim	256x256	103	5580	3	0
	4	1.5T	GE Signa Hdx	256x256	92	4900	3	0
	5	1.5T	Philips Intera	256x203	92	4860	3	0
	6	1.5T	GE Signa Hdx	256x256	91	7000	3	0

rd and 2/3 rd of the nucleus. E. Lesion of more than 2/3 rd of the nucleus. F. Total involvement of the nucleus.

Acknowledgments

This work has been funded by the Projet Hospitalier de Recherche Clinique (PHRC) #P051061.

Supporting information

S1 File. Details of the T2 FSE acquisitions in each center involved in the study.

Nb: number, FOV: field of view, ET: echo time, RT: repetition time. Writing -original draft: Fre ´de ´ric Clarenc¸on.

Writing -review & editing: E ´ric Bardinet, Rajiv Gupta, Didier Dormont, Louis Puybasset, Damien Galanaud.

Supplemental material # 3

Details about support vector machine

Currently, support vector machine (SVM) is considered as the standard of classification methods in pattern recognition learning machine. SVM performs classification by constructing an N-dimensional hyperplane that optimally separates the data into two categories without hypothesis on variable distributions. The nonlinear mapping into a high dimensional space is affected by a kernel which could be a polynomial function, Gaussian, radial basic function, or a multi-layer perceptron. The aim of the multivariate analysis was to find a discriminative function to separate the group "favorable neurological outcome" (GOS = 4 or 5) from the group "unfavorable neurological outcome" (GOS from 0 to 3). We evaluated the performance of the classifier using the leave-one-subject-out cross validation test, also known as the Jacknife test. In this test, we used data from all but one subject to train the classifier.

Subsequently, the class assignment of the remaining subject, which was so far not seen by the algorithm, was calculated. If there are S data points, this procedure was repeated S times, each time leaving out a different subject. A nonparametric approach, such as permutation tests, can estimate empirically the distribution of the statistic under a null hypothesis. Nonparametric tests have been previously applied to fMRI data analysis [START_REF] Xu | The Role of Magnetic Resonance Imaging in the Prediction of Minimally Conscious State After Traumatic Brain Injury[END_REF]. By permuting the class labels 100 times randomly and training the SVM with this permutation of labels, we estimated a probability distribution for each variable v i under the null hypothesis of no relationship between the class labels and the global structure of the data. Based on this probability distribution and its mean (m) and its standard deviation (s), it is possible to evaluate the normalized weight of each variable v i by testing (v i -m)/s.