Dual-Band Beams Generation with Metasurface based on the EFIE

Dual-Band Beams Generation with Metasurface based on the EFIE Modeste Bodehou 1 , David González-Ovejero 2 , Christophe Craeye 1 and Isabelle Huynen 1

1 Université catholique de Louvain: ICTEAM Institute, Place du Levant, 3, 1348, Louvain-la-Neuve, Belgium 2 Univ Rennes, CNRS, IETR (Institut d' Électronique et de Télécommunications de Rennes), UMR 6164, 35000 Rennes, France 1 modeste.bodehou, christophe.craeye, isabelle.huynen @uclouvain.be, 2 david.gonzalez-ovejero@univ-rennes1.fr Abstract-This paper investigates the generation of dual-band beams by modulated metasurface antennas. The developed technique combines a semi-separable model dependence of the sheet impedance (with respect to frequency and patch parameters) with the resolution of the electric field integral equation (EFIE). This allows us to express the impedance modulation at one frequency as a function of the modulation at the second frequency. Then, we can formulate the EFIE at both frequencies while referring to the surface impedance at a single frequency, still fully taking into account the frequency dispersion of the substrate. The method is illustrated through the synthesis of a circularly polarized conical beam and a broadside pencil beam at two different frequencies. Numerical validation with two different Method of Moments (MoM) codes is provided.

I. INTRODUCTION

Surface waves (SW) to leaky waves (LW) transformation using metasurfaces (MTS) has been the subject of intense research over the past decade [START_REF] Fong | Scalar and tensor holographic artificial impedance surfaces[END_REF]- [START_REF] Minatti | Modulated metasurface antennas for space: synthesis, analysis and realizations[END_REF]. This interest is due to the multiple advantages offered by this type of antennas (low profile, low cost, limited power losses, etc). A lot of progress has been made in the synthesis of modulated MTS antennas, which include the generation of high-gain polarized beams [START_REF] Minatti | Modulated metasurface antennas for space: synthesis, analysis and realizations[END_REF], shaped beam synthesis [START_REF] Minatti | Synthesis of modulated-metasurface antennas with amplitude, phase, and polarization control[END_REF]- [START_REF] Bodehou | Electric field integral equationbased synthesis of elliptical-domain metasurface Antennas[END_REF], multibeam with multiple feeds [START_REF] González-Ovejero | Multibeam by metasurface antennas[END_REF], [START_REF] Bodehou | Multibeam and beam scanning with modulated metasurfaces[END_REF] etc.

However, MTS antennas are relatively narrowband given the highly frequency dispersion of the SW. This means that a change in the frequency of operation strongly impacts the SW mode supported by the MTS. The interaction between the modulation parameters, and the new SW mode is no longer consistent with the desired radiation effect. In many contexts, multiple-band operation is required since it allows one to multiplex several channels at different frequencies, while sharing the same MTS aperture. In [START_REF] Li | Multi-wavelength multiplexing hologram designed using impedance metasurfaces[END_REF], the authors use holographic theory to design a dual-band antenna based on a scalar (isotropic) MTS. In particular, the method consists of superimposing several holograms corresponding to different beams and different feed positions. However, scalar MTSs are limited in terms of beam polarization control as proven in [START_REF] Minatti | Modulated metasurface antennas for space: synthesis, analysis and realizations[END_REF].

Reference [START_REF] Faenzi | Dual-band self-diplexed modulated metasurface antennas[END_REF] superimposes tensorial (anisotropic) impedances associated with broadside pencil beams and different feed positions. However, the case of beams with different shapes is not treated

The method proposed here is based on a direct solution of the electric field integral equation (EFIE) at the frequencies of interest and can be used for one or multiple feeds. This leads to an over-constrainted system of equations. The design of a MTS radiating a conical beam and a broadside pencil beam at different frequencies is presented. A general discussion and possible improvements on the method is also provided.

The paper is structured as follows. Section II briefly recalls the EFIE based MTS synthesis at one frequency. Section III extends the EFIE synthesis method to multiple frequencies. Section IV presents some numerical results and section V concludes the paper.

II. SINGLE BAND OPERATION

Let us consider a circular MTS antenna modeled as a sheet transition impedance boundary condition laying on a grounded substrate. The usual polar system of coordinates is used to identify each point on the MTS. The current distribution J and the aperture electric field is linked to the sheet impedance Z S on the MTS plane through the following EFIE [START_REF] González-Ovejero | Gaussian ring basis functions for the analysis of modulated metasurface antennas[END_REF], [START_REF] Bodehou | Method of Moments simulation of modulated metasurface antennas with a set of orthogonal entire-domain basis functions[END_REF]:

n × S G EJ (ρ, ρ ) J(ρ ) dS -Z S (ρ) J(ρ) = -n × E i (1)
where G EJ is the dyadic Green's function of the grounded substrate, E i is the MTS excitation and n is the normal to the surface. The polar unit vector is used for the current distribution and surface impedance modulation expansion [START_REF] Bodehou | Method of Moments simulation of modulated metasurface antennas with a set of orthogonal entire-domain basis functions[END_REF]. Fourier-Bessel basis functions (FBBFs) are a class of scalar functions defined on the whole circular domain [START_REF] Bodehou | Method of Moments simulation of modulated metasurface antennas with a set of orthogonal entire-domain basis functions[END_REF]. Each component of the current distribution and the surface impedance modulation are now discretized into FBBFs as detailed in equations ( 21)-(23) in [START_REF] Bodehou | A Quasi-direct method for the surface impedance design of modulated metasurface antennas[END_REF]. The synthesis problem consists in, first, computing the objective surface current distribution based on the desired radiation pattern. Next, one must solve the EFIE to derive the corresponding surface impedance, while constraining the surface impedance to be anti-Hermitian so as to avoid losses on the sheet. This leads to a system of equations written in compact form as:

Z S X S = U (2)
A c c e p t e d m a n u s c r i p t

where the vector X S is the unknown sheet impedance discretized into FBBFs. The matrix Z S and the vector U depend on the radiation pattern, the excitation, and on the average impedance. The reader is referred to [START_REF] Bodehou | A Quasi-direct method for the surface impedance design of modulated metasurface antennas[END_REF] for the formulation details.

III. DUAL BAND OPERATION

To extend this formulation to dual-band operation, one needs to model the frequency variation of the sheet impedance with respect to the used patches. Let us denote by p a vector characterizing the patch parameters used to implement the surface impedance. In turn, Z S (p, ω) denotes each component of the sheet impedance corresponding to a given patch p at a given radian frequency ω. For an elliptical patch for example, p represents the semi-major axis, the semi-minor axis and the orientation of the ellipse. The frequency variation of each component of the sheet impedance tensor is now characterized by the following model [START_REF] Bodehou | Multi-frequency band synthesis of modulated metasurface antennas[END_REF]:

Z S (p, ω) = a(ω)Z S (p) + b(ω) (3)
where a(ω) and b(ω) are arbitrary non linear functions. This model is very accurate provided that we stay in the homogenizable region [START_REF] Bodehou | Multi-frequency band synthesis of modulated metasurface antennas[END_REF], i.e, considering the unit cell very small with respect to the wavelength of operation. Equation (3) allows us to express the modulation parameters at a given frequency ω 2 with respect to the modulation at a reference frequency ω 1 . One can therefore proceed to the synthesis by stacking the system of equations corresponding to each frequency. In these stacked systems, we obtain the modulations at other frequencies with respect to the one at a given reference frequency using (3). The matrix corresponding to the obtained system of equations can then be written as [START_REF] Bodehou | Multi-frequency band synthesis of modulated metasurface antennas[END_REF]:

Z S = Z S (ω 1 , V 1 , F 1 ); Z S (ω 2 , V 2 , F 2 ) (4)
and U takes the form:

U = U(ω 1 , V 1 , F 1 ); U(ω 2 , V 2 , F 2 ) (5)
where F i and V i are respectively the radiation pattern and the excitation used at the radian frequency ω i . The obtained system of equations is then solved in a least-squares sense.

Note that, if one is interested in stronger requirements for a given radiation pattern in comparison with the others, one can perform a weighted least-squares.

IV. NUMERICAL RESULTS

In this section, we present a MTS design capable of radiating two different beams at two different frequencies. The first one is a right-handed circularly polarized (RHCP) conical beam (pointing at θ = 20 o from broadside), and should be generated at f 1 = 24 GHz. The second beam is a RHCP pencil beam generated at f 2 = 20 GHz. The MTS is printed on a substrate with relative permittivity r = 3.66 and thickness 1.524 mm. The antenna radius is 10 λ 1 , where λ 1 is the free-space wavelength at 24 GHz. At both frequencies, the antenna is excited from the center with an infinitesimal vertical dipole placed in the middle of the substrate [START_REF] Bodehou | Method of Moments simulation of modulated metasurface antennas with a set of orthogonal entire-domain basis functions[END_REF], [START_REF] González-Ovejero | Gaussian ring basis functions for the analysis of modulated metasurface antennas[END_REF].

This excitation model is sufficient to provide an excellent idea about the radiation pattern obtained with practical feeds, as already demonstrated in several papers [START_REF] Minatti | Modulated metasurface antennas for space: synthesis, analysis and realizations[END_REF], [START_REF] Bodehou | Fourier-Bessel basis functions for the analysis of elliptical domain metasurface antennas[END_REF]. The reactance is modulated around an average value X 0 = -1301 Ω at 24 GHz and we used a ρρ (w

2 ) = 1.2, a ρφ (w 2 ) = 1.1, b ρρ (w 2 ) = b ρφ (w 2 ) = 0.
Fig. 1 shows the designed reactance modulation at 24 GHz. Fig. 2 illustrates the simulated radiation pattern obtained with two independent MoM codes at f 1 = 24 GHz. The first code is based on Gaussian ring basis functions (GRBF) [START_REF] González-Ovejero | Gaussian ring basis functions for the analysis of modulated metasurface antennas[END_REF] and the second one uses Fourier-Bessel basis functions (FBBF) [START_REF] Bodehou | Method of Moments simulation of modulated metasurface antennas with a set of orthogonal entire-domain basis functions[END_REF]. The latter functions consist in Gaussian-type rings and linear azimuthal phase. Their spectrum can be written in analytical form. Hence, they enable a closed-form evaluation of the MoM impedance matrix's entries and lead to an efficient solution of the MoM system of equations. One can observe a good agreement between the two simulation results except the side lobes level. The difference is due to the evolution of the currents at a distance very close to the feed. Indeed GRBFs allow a more accurate current evaluation close to the feed because of the possible zero admissible current (see [START_REF] Bodehou | Method of Moments simulation of modulated metasurface antennas with a set of orthogonal entire-domain basis functions[END_REF] for a detailed discussion regarding this aspect). The obtained aperture efficiency is about 79%. This efficiency is computed in comparison with the power density radiated by an ideal conical beam antenna of the same radius. Fig. 3 shows the radiation pattern at 20 GHz. The directivity obtained with GRBF code is 2 dB higher than that of FBBF code due to the better treatment of GRBFs for the currents near the center, as previously mentioned.

A. Improvement of the method

One of the main advantages of the proposed EFIE approach is the fact that the method is systematic and starts directly from the radiation pattern, not from the aperture electric field. That means, we specified at input the desired radiation pattern in amplitude, phase and polarization at the frequencies of interest. Despite this flexibility is useful for near-field applications (see some near-field designs in [START_REF] Bodehou | Near-field shaping by leakywave metasurfaces: OAM and Bessel beams synthesis[END_REF]), the phase distribution is usually less or even not important for antenna (far-field) applications. Here, we specified for the conical beam, a linear phase evolution along the azimuthal direction. The simulated pattern phase evolution of the designed MTS is represented in Fig. 4. One can see an excellent agreement with respect to the prescribed phase. It is worth mentioning that the designed pattern amplitude and polarization depends on the prescribed phase. When one is interested in realizing complex radiation patterns at multiple frequencies, with strong requirements, the prescribed phase evolution should be optimized to get better results. The phase optimization problem is a complex issue that deserves further research.

Fig. 1 :

 1 Fig. 1: Reactance modulation at 24 GHz.

  Directivity cut in the plane φ = 0. The inset disk represents the absolute value of the current distribution on the MTS in logarithm scale.

Fig. 2 :

 2 Fig. 2: Radiation pattern at 24 GHz.

Fig. 3 :

 3 Fig. 3: Radiation pattern at 20 GHz. The inset disk represents the absolute value of the current distribution on the MTS in logarithm scale.

Fig. 4 :

 4 Fig. 4: Conical beam radiation pattern phase evolution at 24 GHz and θ = 20 o

  A c c e p t e d m a n u s c r i p t


Judith Luckman

Sylvie Chokron
email: sylvie.chokron@gmail.com

Shalom Michowiz

Eugenia Belenky
email: drbelenky@gmail.com

Helen Toledano
email: helen.toledano@gmail.com

Alon Zahavi

MD Nitza Goldenberg-Cohen

The need to look for deficit after stroke in children

Keywords: arterial stroke, children, ophthalmological complication, eye exam

PURPOSE:

To evaluate the role of the ophthalmologist at presentation and during follow-up of children with arterial stroke.

METHODS:

This retrospective case series comprised 26 children with arterial stroke who were followed for at least 12 months in our tertiary pediatric medical center in [2005][2006][2007][2008][2009][2010][2011][2012][2013][2014][2015]. Demographic data and findings on radiological neuroimaging, ophthalmological and neurological examination were retrieved from the patient medical files.

RESULTS:

Of the 26 children identified with stroke, 5 (20%) had a metabolic syndrome, 3 (11%) cardiac anomaly, 3 (11%) recent major surgery for repair of cardiac anomaly, 3 (11%) vascular anomaly, 3 (11%), head trauma with traumatic dissection, 1 (4%) had hypercoagulability and in 8 patients (31%), no apparent cause was found (idiopathic).

Only 9 (35%) had an eye exam during the follow-up. Eleven patients had a nonophthalmological neurological deficit as a result of the stroke. Positive ophthalmological manifestations included hemianopic visual field defect in 2 patients (8%), complete blindness and visual acuity deficit in one patient each (4%). At the last visit, no change in visual function was detected in those with ophthalmological deficit and 5 (20%) of the patients with other neurologic manifestations still had residual neurological deficit.

CONCLUSION:

Arterial stroke in children is a rare event and only a few are referred for an eye examination. In view of the significant ophthalmological manifestations revealed in the current study, children with arterial stroke should be referred for early ophthalmological evaluation.

Introduction

Stroke is relatively rare in children, but it can lead to significant morbidity and mortality [START_REF] Tsze | Pediatric stroke: a review[END_REF][START_REF] Mirabelli-Badenier | Pathophysiological role of inflammatory molecules in paediatric ischaemic brain injury[END_REF]. International incidence rates for childhood arterial stroke (from age 30 days to 18 years) range from 1.3 per 100,000 to 13 per 100,000 [START_REF] Lynch | Cerebrovascular disorders in children[END_REF]. In children, arterial brain stroke differs from venous stroke in terms of clinical presentation, signs and symptoms, outcome, and consequences. Risk factors are numerous and vary by age; many are unique to children [START_REF] Deveber | Stroke in children: recognition, treatment, and future directions[END_REF][START_REF] Roach | Etiology of stroke in children[END_REF][START_REF] Roach | Stroke in children[END_REF]. The main risk factors for pediatric arterial stroke are congenital heart disease, hematologic disorders, and traumatic arterial dissection.

Congenital as well as acquired heart diseases are the most common causes of repeated stroke in children [START_REF] Brankovic-Sreckovic | The recurrence risk of ischemic stroke in childhood[END_REF].

The reported failure to identify risk factors in about one-third of children with stroke implies that many cases may go undiagnosed or misdiagnosed [START_REF] Tsze | Pediatric stroke: a review[END_REF]. The diagnosis is confirmed by neuroimaging, either computed tomography or magnetic resonance imaging with venographic sequencing. Treatment requires a combination of medical and surgical approaches in a multidisciplinary pediatric hospital setting. Prognosis depends on the extent of vessel and brain parenchymal involvement and the timeliness of diagnosis and therapy.

Ophthalmological symptoms and signs may be present in the course of arterial stroke but the rate of referral for ophthalmological evaluation is not clear. The aim of this study was to explore the role of the ophthalmologist at presentation and during follow-up of pediatric arterial stroke based on the 10-year experience of a major pediatric ophthalmology service.

Materials and methods

The study was designed as a retrospective case series. The study protocol was approved by the local Institutional Review Board Committee. Data was collected by reviewing the computerized hospital admission databases as well as the database from the radiology and ophthalmology services of a tertiary, university-affiliated, pediatric medical center.

Inclusion criteria were diagnosis of arterial brain stroke on imaging, children aged 2 to18 years and a follow-up for at least 2 months after the acute event. The files of all patients with arterial stroke between January 2005 and February 2016 were reviewed (n=53, incidence of 4.81 per year). Children with venous stroke (n=3) or with perinatal stroke and its sequelae (n=22) were excluded from the study. Also were excluded 2 patients with stroke and pernicious anemia due to incomplete information and lack of timely imaging. Data on demographics and findings on ophthalmological and neurological examination and neuroimaging were collected from the medical files.

Ophthalmological and neurological symptoms and signs were summarized at presentation and at last follow-up.

Results

Twenty-six children met the inclusion criteria. Their clinical data are summarized in Table 1. Median age was 9.13 years (IQR 6.13-13), 18 were males (69%) and 8 were females (31%).

Clinical data of the arterial-stroke group (Table 1, Figures 1-4)

Twenty one (81%) children with arterial stroke had a disturbance in the anterior circulation territory while 5 (19%) had stroke in the posterior circulation territory. Of the 26 children with stroke, 5 (19%) had congenital metabolic syndrome, 3 (12%) cardiac anomaly, 3 (12%) recent major surgery for repair of cardiac anomaly, 3 (12%) vascular anomaly, 2 (8%) suffered stroke immediately following intracranial tumor resection, 2 (8%) head trauma with traumatic dissection, 1 (4%) had hypercoagulability, and in 7 patients (27%), no apparent cause was found (idiopathic). Nine (35%) of the patients who presented with arterial stroke underwent ophthalmological evaluation at presentation, of whom one patient (4%) suffered complete blindness, 4 (15%) had visual field defect (hemianopia); 3 of them had reduced visual acuity and 2 (8%) had gaze paralysis. The child with bilateral occipital stroke had multiple uneventful cardiac catheterizations, but was rendered completely blind following Fontan repair of cardiac anomalies. Twenty

Discussion

This study describes the findings of ophthalmological evaluation in children with arterial brain stroke. Only 35% were referred for ophthalmological evaluation, which revealed significant findings in 56% of patients examined (5 out of 9).

The visual defects (visual loss or visual field defect) persisted in these patients during the follow-up period and improved in one. This is not surprising, since 40% of the brain involves the visual pathway. Visual impairment due to stroke usually occur secondary to damage to the posterior circulation. Occipital stroke is a rare event, especially if is bilateral. Only one child had complete blindness in this study, as a complication of cardiac surgery and bilateral occipital stroke. In line with our results [START_REF] Ganesan | Outcome after ischaemic stroke in childhoodDevelopmental[END_REF], the location of the ischemic strokes in children involved mainly the territory of the anterior cerebral circulation (73%), and only 14% the posterior circulation.

The recent consensus and evidence-based guidelines for the treatment of stroke in children [START_REF] Monagle | Antithrombotic therapy in neonates and children: American College of Chest Physicians Evidence-Based Clinical Practice Guidelines (8th edition)[END_REF][START_REF] Roach | Council on Cardiovascular Disease in the Young. Management of stroke in infants and children: a scientific statement from a Special Writing Group of the American Heart Association Stroke Council and the Council on Cardiovascular Disease in the Young[END_REF][START_REF] Dowling | International Paediatric Stroke Study: stroke associated with cardiac disorders[END_REF] found that children with cardiac sources of stroke need different management. Dowling et al. [START_REF] Dowling | International Paediatric Stroke Study: stroke associated with cardiac disorders[END_REF] noted that one-quarter of the children with stroke and cardiac disorders (31% of the total children with stroke) had procedure-related strokes.

Children without cardiac disorders were older, but showed similar complications (focal deficits, seizures, or recent infection). None of the children in their cohort underwent ophthalmology exam. These guidelines regarding treatment of children with stroke did not mention visual complications, although the posterior circulation was commonly involved. Bilateral strokes and hemorrhagic conversion were more prevalent in children with cardiac disorders [START_REF] Dowling | International Paediatric Stroke Study: stroke associated with cardiac disorders[END_REF].

The International Pediatric Stroke Study Group reported that among the presenting signs of ischemic stroke summarizing 557 children, papilledema was detected in only 13 children (2%). [START_REF] Mackay | on behalf of the International Pediatric Stroke Study Group. Arterial Ischemic Stroke Risk Factors: The International Pediatric Stroke Study[END_REF] Visual field defects are more common in post-chiasmal ischemic damage. When only unilateral involvement of the visual pathway occurs in children, a hemi-field defect may be "asymptomatic", unnoticed or not reported [START_REF] Harbert | Unrecognized visual field deficit in children with primary central nervous system brain tumors[END_REF]. Children rarely complain that they cannot see things to their right or left. In some cases, it may be detected only during targeted exam when it is specifically sought, for example head turning -to determine the whole field of vision, since the variable etiology and presentation may mask specific ophthalmological signs.

The presenting clinical features and outcome of pediatric stroke differ from adult stroke due to the greater brain plasticity observed in younger patients. Similar to previous reports [START_REF] Tsze | Pediatric stroke: a review[END_REF][START_REF] Deveber | Stroke in children: recognition, treatment, and future directions[END_REF][START_REF] Roach | Etiology of stroke in children[END_REF][START_REF] Roach | Stroke in children[END_REF][START_REF] Ganesan | Outcome after ischaemic stroke in childhoodDevelopmental[END_REF][START_REF] Monagle | Antithrombotic therapy in neonates and children: American College of Chest Physicians Evidence-Based Clinical Practice Guidelines (8th edition)[END_REF][START_REF] Roach | Council on Cardiovascular Disease in the Young. Management of stroke in infants and children: a scientific statement from a Special Writing Group of the American Heart Association Stroke Council and the Council on Cardiovascular Disease in the Young[END_REF][START_REF] Dowling | International Paediatric Stroke Study: stroke associated with cardiac disorders[END_REF][START_REF] Mackay | on behalf of the International Pediatric Stroke Study Group. Arterial Ischemic Stroke Risk Factors: The International Pediatric Stroke Study[END_REF][START_REF] Harbert | Unrecognized visual field deficit in children with primary central nervous system brain tumors[END_REF][START_REF] Ganesan | Investigation of risk factors in children with arterial ischemic stroke[END_REF][START_REF] Kirkham | Risk factors for arterial ischemic stroke in childhood[END_REF][START_REF] Dai | Paediatric cerebral venous thrombosis[END_REF], the most common etiologies in children were metabolic and cardiac congenital anomalies. Etiological data available for 667 children with arterial ischemic stroke, aged 29 days to 19 years [START_REF] Dowling | International Paediatric Stroke Study: stroke associated with cardiac disorders[END_REF], showed cardiac disorders in 31%. Of those, congenital defects in 59%, acquired 20%, and isolated patent foramen ovale in 15%. These data are in line with our small cohort of 24 children with arterial stroke, but in contrast to another report by Tsze & Valente [START_REF] Tsze | Pediatric stroke: a review[END_REF] that included patients with sickle cell anemia, infection, or vasculitis. This is probably because of the variance in population between the studies and the different nature of reporting. Nintey children were included in another study with ischemic etiology of stroke, mainly arterial stroke [START_REF] Ganesan | Outcome after ischaemic stroke in childhoodDevelopmental[END_REF].

Risk factors for stroke in adults include hypertension, diabetes, and smoking, whereas in children, they are mainly congenital syndromes and hypercoagulability. Similar to previous reports [START_REF] Tsze | Pediatric stroke: a review[END_REF][START_REF] Deveber | Stroke in children: recognition, treatment, and future directions[END_REF][START_REF] Roach | Etiology of stroke in children[END_REF][START_REF] Roach | Stroke in children[END_REF][START_REF] Monagle | Antithrombotic therapy in neonates and children: American College of Chest Physicians Evidence-Based Clinical Practice Guidelines (8th edition)[END_REF][START_REF] Roach | Council on Cardiovascular Disease in the Young. Management of stroke in infants and children: a scientific statement from a Special Writing Group of the American Heart Association Stroke Council and the Council on Cardiovascular Disease in the Young[END_REF][START_REF] Dowling | International Paediatric Stroke Study: stroke associated with cardiac disorders[END_REF][START_REF] Mackay | on behalf of the International Pediatric Stroke Study Group. Arterial Ischemic Stroke Risk Factors: The International Pediatric Stroke Study[END_REF][START_REF] Harbert | Unrecognized visual field deficit in children with primary central nervous system brain tumors[END_REF][START_REF] Ganesan | Investigation of risk factors in children with arterial ischemic stroke[END_REF][START_REF] Kirkham | Risk factors for arterial ischemic stroke in childhood[END_REF][START_REF] Dai | Paediatric cerebral venous thrombosis[END_REF], in the present study, the children had cardiac anomalies, prothrombotic states, vascular anomalies, and trauma/surgery for brain tumor or cardiac anomaly as well as metabolic disorders. In about one-third of the patients, the etiology was not identified (idiopathic stroke). Kieslich et al. [START_REF] Kieslich | Minor head injury as cause and co-factor in the aetiology of stroke in childhood: a report of eight cases[END_REF] suggested that a detailed medical history of the days before stroke manifestation may identify more traumatic events, especially in idiopathic stroke.

In our study, 2 children had a history of trauma prior to the development of an arterial stroke. One of them presented to the emergency room with anisocoria and was diagnosed with Horner syndrome due to carotid dissection. On follow-up, traumatic optic neuropathy associated with monocular visual loss was diagnosed. The other patient had minor trauma and was also diagnosed with carotid dissection, but without visual complications.

Our extensive search of the literature did not reveal data on the diagnosis, followup, or treatment of children with stroke in terms of ophthalmological pathologies. This might be due to a failure of physicians to refer children with arterial stroke for ophthalmological examination at presentation, or because no change in visual deficits occurs during follow-up. In our series, an eye examination was conducted in only 9 children (35%), mainly during follow-up and rehabilitation efforts, while few were referred because of a suspected relationship between the stroke and a background syndrome. We are convinced that an eye exam is vital to the rehabilitation process.

In the United States, the mortality rate of stroke in children has decreased dramatically over the last 20 years [START_REF] Fullerton | Deaths from stroke in US children, 1979 to 1998[END_REF][START_REF] Fullerton | Pediatric stroke belt: geographic variation in stroke mortality in US children[END_REF]. Most stroke-related deaths involve the middle cerebral artery and not the occipital area. In our study, none of the children diagnosed with arterial stroke died during the study period. Only 3 had obstruction in the posterior circulation, while one suffered hemorrhagic thalamic stroke following resection of a suprasellar tumor.

The outcome in children aged 3 months to 15 years at the time of stroke (median age 5 years) with median follow up duration of 3 year showed that only 13 (14%) of 90 had no residual impairments [START_REF] Ganesan | Outcome after ischaemic stroke in childhoodDevelopmental[END_REF]. Poor outcome with impairment in daily life activity was reported in 53 (60%) children, but surprisingly no attention was paid to the visual outcome. Parents and therapist were not asked regarding vision impairment.

Even when visual acuity is normal, children can experience impaired visual cognition. The central visual functions of visual acuity, contrast sensitivity, and color vision, as well as the peripheral visual fields can be afflicted by lesions from the chiasm towards the primary visual cortices [START_REF] Chokron | Evaluation of visuo-spatial abilities (EVA): a simple and rapid battery to screen for CVI in young children[END_REF][START_REF] Chokron | Behavioral consequences and cortical reorganization in homonymous hemianopia[END_REF]. Cerebral visual impairment (CVI) arises as a consequence of damage or disorder of the brain. CVI may cause very low visual acuity in both eyes, or alternatively, significant visual difficulties may be evident in the context of normal visual acuities. Homonymous visual field impairment may present. A definitive diagnosis is made from the overall clinical picture supported by imaging and electrophysiological investigations.

Vision has a cardinal role in a child's visual development and CVI can compromise learning, behavioral development, and interaction with the outside world.

CVI is invisible and often goes unnoticed by the child and the physicians. Therefore, there is an urgent need for greater understanding of these impairments in events of arterial brain stroke, to enable better and earlier diagnosis and treatment, and optimal differentiation visual impairment from stroke-induced neurological impairments [START_REF] Chokron | Evaluation of visuo-spatial abilities (EVA): a simple and rapid battery to screen for CVI in young children[END_REF][START_REF] Chokron | Behavioral consequences and cortical reorganization in homonymous hemianopia[END_REF].

10/

The main limitation of the present study is its retrospective nature which results in potential bias. Although we searched all data of children with arterial stroke during a long period, only 53 were identified in our large referral center, and 26 included to the study.

We assume these numbers reflect the real incidence, as only one child was excluded due to missing data and none were lost to follow-up.

The study is important because it provides essential insights into the incidence of arterial stroke, etiologies, visual involvement and the need for a multidisciplinary approach in the diagnosis and management of stroke in children, with emphasis on the role of the ophthalmologist. Not much data have been collected since the report of Ganesan et al in 2000 [START_REF] Ganesan | Outcome after ischaemic stroke in childhoodDevelopmental[END_REF]. The personal and economic sequelae of childhood stroke in adult life yet remained unexplored. Exam of the visual function of these children may help professionals involved in the rehabilitation of children having stroke.

Conclusion

For children with arterial stroke, the variable etiology and presentation may mask specific ophthalmological signs. Therefore, visual function, if examined at all, is usually examined only on follow-up, after diagnosis and disease stabilization. We believe that eye exam including visualization of the retinal arteries, evaluation of the visual fields and visual acuity is important for rehabilitation and should be an essential part of the initial exam and follow-up of all children with an arterial ischemic event to the brain.

Legends to Figures

Acute right basal ganglia infarctmagnetic resonance (MR) findings (patient 7, Table 1

  children (77%) had a non-visual/non-ophthalmological neurological deficit, manifesting as hemiparesis/plegia with or without central VII nerve palsy. During the follow-up, one patient with Marfan syndrome had recurrent episodes of transient ischemic attacks, and 2 patients with hypoplastic left heart, including 2 with Moya-Moya syndrome (part of Schimke syndrome and alagille syndrome), one had recurrent stroke and one underwent arterial bypass with no recurrent stroke over 15 years of follow-up. The visual acuity and gaze paralysis in one child (stroke after resection of suprasellar tumor) improved while no change in the ophthalmological symptoms was noted during the follow-up period in the others.

Figure 3 .

 3 Figure 3. Bilateral Lt>Rt occipital stroke in a patient after recent Fontan procedure due to a thromboembolic event (patient 24, Table 1) A. FLAIR B. T2 C. STIR D. DWI axial studies, showing old bilateral occipital infarct (PCA distribution), No restriction on DWI.

Figure 4 .

 4 Figure 4. Subacute stroke, left MCA territory (patient 17, Table 1) A. T2 B. FLAIR C. DWI -axial studies, subacute fronto-parietal stroke with restriction on DWI. A left sylvian MCA acute infarct is visualized with restricted diffusion. The finding is visualized on a T2, FLAIR and DWI images. D (right eye) and E (Left eye) demonstrate by ocular coherent tomography-angiography (OCT-A). Showing Segmentation of different vascular layers using OCTA: left to right: superficial plexus, deep plexus of the inner retina, outer retina (shows absence of vasculature) and choriocapillaris layer . Severe attenuation of the retinal arteries in the superficial layer is demonstrated in both eyes, Lower line: superficial retina and OCT bscan image of the retina, showing normal retinal layers.

Author Contributions

Design of the study (NG-C, EB and JL); collection of data (NG-C, EB and DR); analysis and interpretation (NG-C, HL, EB, JL and SM); preparation of the manuscript (NG-C, EB, DR and SM); review and approval of the manuscript (all authors)

Conflict of interest:

The authors declare no conflict of interest.

Financial Disclosures: This study was supported in part by the Zanvyl and Isabelle Krieger Fund, Baltimore, MD (NGC). The funding organization had no role in the design or conduct of this research.