Sylvain Durand
email: sylvain.durand@inrialpes.fr

Julien Minet

Jose Fermi

Guerrero Castellanos

Nicolas Marchand

ASYNCAR, a Radio-Controlled Vehicle for Asynchronous Experiments Implementation of an Event-Based Cruise Control

Keywords: Experimental platform, asynchronous cruise control, event-based control

The main contribution of this paper is to develop an experimental platform in order to test some event-based control strategies. Contrary to the time-triggered fashion which calculates the control signal at each sampling time, an eventdriven controller updates the control signal only when required. This theoretically allows to reduce the computational cost. In this paper, we propose to firstly test an asynchronous cruise control mechanism. Some first results clearly show a noticeable reduction of the mean control computation cost, which is really encouraging for developing such a platform.

INTRODUCTION

The classical so-called discrete time framework of controlled systems consists in sampling the system uniformly in time with a constant sampling period h nom and in computing and updating the control law every time instants t k = k • h nom . This field, denoted the time-triggered case (or the synchronous case in sense that all the signal measurements are synchronous), has been widely investigated in [START_REF] Åström | Computer Controlled Systems[END_REF], even in the case of sampling jitter or measure loss that can be seen as some asynchronicity. However, some works addressed more recently event-based sampling (also called asynchronous) where the control law is event-driven [START_REF] Åström | Comparison of Riemann and Lebesque sampling for first order stochastic systems[END_REF], [START_REF] Sandee | Event-driven control as an opportunity in the multidisciplinary development of embedded controllers[END_REF], [START_REF] Lunze | A state-feedback approach to event-based control[END_REF], [START_REF] Anta | To sample or not to sample: Self-triggered control for nonlinear systems[END_REF], for instance when the output crosses a certain level q j = j•q nom . Thus in this scheme, the term sampling period denotes a time interval between two consecutive level crossings of the measure, that is two successive sampling instants, and the sampling intervals are hence not equidistant in time anymore.

Many reasons are motivating the event-triggered systems and in particular because more and more asynchronous systems or systems with asynchronous needs are encountered. Actually, the demand of low-power electronic components in all embedded and miniaturized applications encourages companies to develop asynchronous versions of the existing time-triggered components, where a significant power consumption reduction can be achieved by decreasing the samplings and consequently the CPU utilization: about four times less power than its synchronous counterpart for the 80C51 microcontroller of Philips Semiconductors in [START_REF] Van Gageldonk | An asynchronous low-power 80C51 microcontroller[END_REF] for example. An original and simple event-based PID control architecture was proposed in [START_REF] Årzén | A simple event-based PID controller[END_REF]. The suggested scheme updates the control signal only when required. Whereas an event was enforced with a mix of level crossings and a maximal sampling period (for stability reason) in the initial approach, this maximal period was then removed in [START_REF] Durand | Further results on event-based PID controller[END_REF] because, in fact, the Nyquist-Shannon sampling condition is no more consistent thanks to the level detection. Different event-based PID algorithms without safety limit condition were also developed. They clearly showed in simulation that the CPU cost can be considerably reduced without performance loss. Nevertheless, a safety limit is uselessly applied since then in the literature [START_REF] Sánchez | Comparative study of event-based control strategies: An experimental approach on a simple tank[END_REF], [START_REF] Sánchez | On the application of different event-based sampling strategies to the control of a simple industrial process[END_REF], [START_REF] Heemels | Analysis of eventdriven controllers for linear systems[END_REF], [START_REF] Mounier | Event driven intelligent PID controllers with applications to motion control[END_REF] and, therefore, we propose to clearly highlight the efficiency of an approach without safety limit condition by implementing such a controller in a real-time testbed. The ASYNCAR experimental platform was thus especially developed to test some asynchronous techniques. It is a radio-controlled vehicle which embeds an event-based cruise control mechanism. The paper is structured as follows. Firstly, the platform is presented in section I. The event-based cruise control principle is then depicted in section II and some experimental results are provided in section III.

I. THE ASYNCAR PLATFORM

The ASYNCAR platform is depicted in Fig. 1. It is based on a 1 / 18 -scale Mini Rock Crawler radio-controlled car from LOSI [13], where some extra components were added to make possible the cruise control of the vehicle.

A. The microcontroller

The main added component is a STM3210C-EVAL electronic card from STMICROELECTRONICS [14]. This evaluation board is represented in Fig. 2. The development kit embeds a ARM microcontroller and several generic tools which will allow the implementation of a cruise control mechanism. It aims at providing a speed control signal to the car from some given setpoint and some measurements. Thus, different connection ports exist, such as RS232 or Ethernet ports. A LCD screen is also present and could be useful for debugging whereas a microSD card is available and will allow to store some log information.

B. The shaft encoder

A speed sensor is also required in the cruise control scheme. Therefore, a shaft encoder was directly connected to the drive-shaft of the car's motor in order to dynamically measure its current velocity.

C. The extra electronics

Another PCB was designed to make compatible the STM32 card with the car and the shaft encoder, adapting the voltage levels of the different components.

D. The testbed

A testbed was developed to fix the ASYNCAR on a hard platform in order to make easier the different experiments. This testbed is shown in Fig. 3. It allows to make indoor experiments (when only small place is available in a room) and some perturbations can be added on the wheel of the car. Nevertheless, the ASYNCAR can also run without this testbed, using a remote control for instance.

E. The data acquisition

The data acquisition is performed in a real-time framework and all data are stored in the microSD card. A network connection then allows to get these information in order to next analyze them off line.

II. EVENT-BASED CRUISE CONTROL

In fact, the motion of a vehicle can be controlled with a proportional-integral-derivative (PID) strategy. The cruise control principle is firstly introduced in subsection II-A. Then, whereas the classical time-triggered control scheme is called back in subsection II-B, some event-based approaches are introduced in subsections II-C and II-D.

A. Cruise control principle

As explained in introduction, event-based control is a computational cost-aware solution especially for all systems which do not need to be constantly controlled. For this reason, we decided to highlight such a scheme with the cruise control mechanism depicted in [START_REF] Åström | Feedback Systems: An Introduction for Scientists and Engineers[END_REF]. Indeed, the desired speed of the car is constant most of time and, in fact, a new control signal is only required when the setpoint changes or when the load (i.e. the slope of the road) varies. The equation of motion of the car is

m ν = F -F d ( 1
)
where ν is the velocity and m the mass of the vehicle. The driving force F is generated by the engine, whose torque is proportional to a control signal 0 ≤ u ≤ 1 that controls the throttle position and depends on engine velocity too.

F = α n uT m 1 -β α n ν ω m -1 2 (2)
where the maximal torque T m is obtained for a given engine speed ω m and β. A physical interpretation of α n , which depends on the gear ratio n, is the inverse of the effective wheel radius. On the other hand, the disturbance force F d has three major components due to the gravity F g , the rolling friction F r and the aerodynamic drag F a , which yields

F d = F g + F r + F a (3)
with

F g = mgsin(θ) F r = mgC r sgn(ν) F a = 1 2 ρC d Aν 2
where g is the gravitational constant, C r and C d are the rolling friction and the shape-dependent aerodynamic drag coefficients respectively, ρ is the density of air, A is the frontal area of the vehicle and θ is the slope of the road, that is the disturbance. Such a system can then be approximated by a first-order system and so is quite simple a PID control.

B. Time-based control

The textbook PID controller in frequency domain is [START_REF] Åström | PID controllers: theory, design, and tuning[END_REF]

U (s) = K E(s) + 1 T i s E(s) + T d sE(s) (4)
where U (•) is the control signal and E(•) the error between the measured output of the controlled system and a given setpoint. K, T i and T d are some tunable parameters. A discrete time controller is finally obtained, that is

u p (t k ) = Ke(t k ) u i (t k ) = u i (t k-1 ) + K i h nom e(t k ) u d (t k ) = T d T d + N h nom u d (t k-1 ) + KT d N T d + N h nom e(t k ) -e(t k-1 ) (5)
where K i = 1 / Ti . The proportional part u p (•) was straightforward while the backward difference approximation was used for integral and derivative parts u i (•) and u d (•) respectively. A low-pass filter was also added in the derivative term to avoid problems with high frequency measurement noise, where N denotes the low-pass filter gain. Finally, t k and t k-1 are the current and last sampling time respectively.

C. Årzén's event-based control

As explained in introduction, Karl-Erik Årzén initially proposed an original event-based PID controller in [START_REF] Årzén | A simple event-based PID controller[END_REF] in 1999. The basic setup consists in two parts: i) a timetriggered event detector used for the level-crossing detection and ii) an event-triggered controller which calculates the control signal. The first part runs with the constant sampling period h nom -that is the same as for the corresponding conventional time-triggered controller -whereas the second part is driven by some requests sent by the event detector. These requests are provided when a new control signal has to be calculated and, therefore, the length of the varying sampling intervals h(•) for the control part is the time between two successive requests. Let τ a denote the beginning time of the current control sample, that is the last time a request was sent by the event detector because the input signal crossed a level. Respectively, let τ a+1 denote the next time where a control signal will be calculated and so on. Note that the event-based sampling instant τ a occurs at a discrete instant time t k by construction. Furthermore, let h(τ a ) denote the sampling interval used to calculate the current control signal, i.e. h(τ a ) = τ a -τ a-1 . The initial Årzén's setup updates the control signal either i) when the absolute error crosses a certain level, that is when the current error crosses a certain limit, i.e. abs e(τ a ) > q nom , or ii) if the maximal sampling period is achieved, i.e. h(τ a ) ≥ h max . This second condition was added to guarantee the stability by fulfilling the Nyquist-Shannon sampling condition.

Actually, the relative measurement was used instead of the absolute one in the initial proposal. Also, a small discretization improvement was also proposed (one could refer to [START_REF] Durand | Further results on event-based PID controller[END_REF] for further details).

D. Event-based control without safety limit condition

We proposed in [START_REF] Durand | Further results on event-based PID controller[END_REF] to remove the safety limit condition h(τ a ) ≥ h max -in order to improve and simplify the eventbased setup (and because the Nyquist-Shannon sampling condition is no more consistent in asynchronous systems thanks to the level detection) -which results in only computing the control signal when required from a performance point of view. However, this modification requires to change the integral part in the control law, i.e. u i (τ a ) = u i (τ a-1 ) + K i he(τ a ), where he(τ a ) = h(τ a )e(τ a ) afterwards denotes the integral gain. Indeed, the product h(•)e(•) can become huge in absence of event or when the setpoint varies, causing some important overshoots. Actually, a steady-state interval can be divided into i) a first part where the sampling interval increases a lot but the error remains small and ii) a second part where the error becomes very large but only during a few instant. Therefore, the product he(•) does not cause any problem anymore since h(•) and e(•) compensate themselves each other. Finally, a bound of the integral gain is

he(τ a ) ≤ h(τ a ) -h nom q nom + h nom e(τ a ) (6)
This observation is taken into account in the proposed algorithms in [START_REF] Durand | Further results on event-based PID controller[END_REF], whose best ones are summarized before testing them on the experimental platform in section III.

Saturation of the integral gain

This algorithm consists in bounding the product he(•) after a long steady-state interval in order to reduce the overshoots. Thus, the product is saturated such that he(τ a ) = h(τ a ) -h nom q nom + h nom e(τ a )

Exponential forgetting factor of the sampling interval Another method consists in adding a forgetting factor of the sampling period so that, after a long steadystate interval, the value of h(•) is reduced enough to not impact the control signal too much. An exponential function is chosen to decrease its impact as the elapsed steady-state time increases, that is

h exp (τ a ) = h(τ a ) -h nom exp h nom -h(τ a ) (8)
The new sampling interval h exp (•) is thus used in the integral part, such that he(τ a ) = h exp (τ a )e(τ a )

At the end, this function leads to have a nominal sampling period during the transients, i.e. when h(τ a ) = h nom , and an exponential decreasing sampling period during the steady-state intervals.

Hybrid algorithm

This algorithm is a mix between the two previous ones. Thus, we propose to use the exponential forgetting factor into the algorithm with saturation, which leads he(τ a ) = h exp (τ a ) -h nom q nom + h nom e(τ a ) (10)

III. EXPERIMENTAL RESULTS

In this section, we propose to test the different event-based PID strategies on the ASYNCAR platform.

A. System model and controller's parameters

The model of the velocity of a vehicle was introduced in subsection II-A but, in fact, an open-loop identification easily gives a first-order transfer-function between the measured speed and the control signal. The system response is represented in Fig. 4, which leads to

H(s) = G 1 + T s (11)
where G = 0.45 is the steady-state gain. In fact, the system velocity varies from 0 to about 3000 tr.min -1 (measured by the encoding shaft when the input is 100 %) but, afterwards, we prefer to work with a percentage of the maximum speed. Note that a negative value is also possible to inverse the direction of the vehicle. A conversion is finally applied to achieve a pulse width modulation (PWM) signal whose duty cycle is 1.5 ms ± 0.5 ms with a period equal to 5 ms.

On the other hand, T = 180 ms is the time constant of the car. Note that a short time delay induced by the car's technology is neglected. Furthermore, the measured signal is quite noisy (due to the mechanics) and, for this reason, we next propose to add a digital filter using a weighted average of the measured velocity ν. This yields

ν(t k ) = (1 -κ)ν(t k-1 ) + κν(t k ) ( 12
)
where ν is the estimated velocity (then used in the control algorithms) and κ = 0.1 is the weighted value. Also, in order to be as reactive as possible, we suggest to not apply this filtering during the transients or when a perturbation occurs. A solution consists in avoiding the estimation when the variation of the measured velocity becomes important. That is when ν(t k ) -ν(t k-1 ) > ∆ν, where ∆ν = 6 % is a parameter fixed by the designer. Finally, the parameter's values of the different controllers are obtained by pole placement of the closed-loop system with the time-triggered controller. They yield K = 1, T i = 250, T d = 1.1 and N = 20. The nominal sampling interval is h nom = 10 ms. The event-based controllers are then designed with these same values and they will finally try to be as closed as possible of the time-triggered closed-loop shaping. Also, the maximum sampling interval needed in the Årzén's controller is h max = 100 ms and the detection level used in all event-driven strategies is q nom = 4 %. Additionally, an anti-windup mechanism is added since the control signal can only vary from 0 % to +100 % of the maximum speed in order to prevent windup when the actuator is saturated. At the end, the extra term is

u w (τ a ) = K a h(τ a ) u(τ a-1 ) -u sat (τ a-1 ) (13)
where u sat (•) is the saturated value of the control signal and K a = 0.2 is another tunable parameter. The control law finally becomes

u(τ a ) = u p (τ a ) + u i (τ a ) + u d (τ a ) + u w (τ a ) (14)
where proportional, integral and derivative terms were defined in [START_REF] Anta | To sample or not to sample: Self-triggered control for nonlinear systems[END_REF].

B. Comparison of the algorithms

The first experiment runs the conventional approach. The results are represented in Fig. 5(a), where the top plot shows the setpoint and the measured velocity. The bottom plot shows the sampling intervals which are, of course, all equal to h nom in this time-triggered case. The number of samples needed to perform the testbench is also indicated in the righttop corner of the figure. The system is then tested with the Årzén's controller. The experimental results are shown in Fig. 5(b), where the bottom plot now refers to the sampling instants: an event is drawn each time the control signal is updated. This representation will be preferred in the next figures. The control law is now event-driven when the measured signal crosses a given level, that is why a lot of samples occur during the transients. Moreover, a maximal sampling interval was also introduced enforcing an event even if the measurement remains unchanged. The resulting behavior can be seen during the steady-state intervals where some samples hit every 0.1 s. This principle allows to considerably reduce the number of samples anyway (about 88 % less than in the conventional case) with similar final performance.

Our proposal finally consists in removing the safety limit condition in order to decrease again the number of samples. In this paper we only test both algorithms i) with an exponential forgetting factor of the sampling interval

AsynCar cruise control --Perturbations on the vehicle's wheel (hybrid algorithm)

Fig. 6. Analysis of the hybrid algorithm when applying some perturbations on the wheel of the ASYNCAR. and ii) with hybrid strategy. The experimental results are provided in Fig. 5(c) and (d) respectively. These algorithms without safety limit condition allow to considerably reduce the number of samples (about 97 % and 80 % of samples less than in the conventional and Årzén's cases respectively). The vehicle still tracks the given setpoint with a system response as fast as previously, but one could remark a steady-state error due to the level detection. Actually, its value is important because of the noise (even after numerical filtering). Consequently, the event-based proposed approaches have to make a tradeoff between performance and computational cost. At the end, these results for a simple first-order system are very encouraging and advantages of the asynchronous scheme are clearly demonstrated.

C. Perturbations and robustness

The ASYNCAR is then submitted to some perturbationsslowing down the wheels -in order to see if the proposed scheme still works when the system does not perform as well as expected. The experimental results for the hybrid algorithm are depicted in Fig. 6. The system reacts as soon as a perturbation occurs at about 3, 9 and 20 s (because the measurement crosses the detection level). The asynchronous PID control without safety limit condition hence allows the velocity to track the reference even in case of perturbations. The robustness is hence demonstrated in practice.

CONCLUSIONS AND FUTURE WORKS

An experimental platform was introduced, called the ASYNCAR platform, which aims at testing some eventbased control schemes. In this paper, an asynchronous cruise control mechanism was presented in order to drive the radio-controlled vehicle with a given speed setpoint. The practical implementation clearly gives good performance with a minimum of samples: more than 97 % of samples less than with the classical PID controller. The advantage of an asynchronous scheme is hence highly highlighted and the encouraging results strongly motivate to continue developing event-based control strategies. Next step is to develop a full asynchronous scheme where the communication with the remote control will be based on an event-based scheme too.

Fig. 1 .

 1 Fig. 1. The ASYNCAR platform.

Fig. 2 .

 2 Fig. 2. The electronic card placed on top of the ASYNCAR platform.

Fig. 3 .

 3 Fig. 3. The tesbed used to fix the ASYNCAR platform.

Fig. 4 .

 4 Fig.[START_REF] Lunze | A state-feedback approach to event-based control[END_REF]. Identification of the system response when applying a step in input of the ASYNCAR's motor.

  AsynCar cruise control --Event-based PID control without safety limit condition (exponential algorithm) 80 samples (c) Event-based PID control without safety limit condition: algorithm with an exponential forgetting factor of the sampling interval.

Fig. 5 .

 5 Fig. 5. Control of the velocity of the ASYNCAR: comparison of the existing techniques and the event-based proposals without safety limit condition.

ACKNOWLEDGMENT

This project is part of a collective project in the ENSE3 engineer school curriculum (from Grenoble university), where a eight-students team works on a project with some technical and team management constraints [17].


M.Sc Mathieu Maurin
email: mmaurin@spectro.ujf-grenoble.fr

Ph.D Olivier Stéphan
email: ostephan@spectro.ujf-grenoble.fr

Ph.D Jean-Claude Vial
email: jcvial@spectro.ujf-grenoble.fr

Ph.D Seth R Marder
email: seth.marder@chemistry.gatech.edu

Ph.D Boudewijn Van Der Sanden
email: boudewijn.vandersanden@ujf-grenoble.fr

Deep in vivo Two-Photon Imaging of Blood Vessels with a new Dye encapsulated in Pluronic Nanomicelles

Keywords: Intravital two-photon microscopy, cerebral and tumor microvasculature, Pluronic nanomicelles

The purpose of this work was to validate the use of Pluronic fluorescent nanomicelles for in vivo two-photon imaging of both the normal and the tumor vasculature. The nanomicelles were obtained after encapsulating a hydrophobic two-photon dye: di-stryl benzene derivative, in Pluronic block copolymers. Their performance with respect to imaging depth, blood plasma staining, and diffusion across the tumor vascular endothelium was compared to a classic blood pool dye Rhodamin B dextran (70 kDa) using two-photon microscopy. Pluronic nanomicelles showed, like Rhodamin B dextran, a homogeneous blood plasma staining for at least 1 hour after intravenous injection. Their two-photon imaging depth was similar in normal mouse brain using 10 times less injected mass. In contrast with Rhodamin B dextran, no extravasation is observed in leaky tumor vessels due to their large size: 20-100 nm. In conclusion, Pluronic nanomicelles can be used as a blood pool dye, even in leaky tumor vessels. The use of Pluronic block co-polymers is a valuable approach for encapsulating twophoton fluorescent dyes that are hydrophobic and not suitable for intravenous injection.

Introduction

Two-photon laser scanning microscopy (TPLSM) allows deep imaging (< 1 mm) of biological tissues in living animals with a micrometric spatial resolution [START_REF] Denk | Two-photon laser scanning fluorescence microscopy[END_REF] . The observation depth depends among others on: tissue parameters, laser characteristics, optics and finally the physical-chemical properties of the fluorescent dye. Relevant fluorescent dyes for optical imaging are often hydrophobic and can therefore not be injected in animals. In the present study, a new approach of encapsulating hydrophobic two-photon dyes in Pluronic block copolymers was validated for two-photon imaging of the normal and the tumor vasculature in mice. In both cases, especially in the leaky vasculature of tumors, the nanomicelles should not diffuse across the vascular endothelium for proper detection of the local functional blood volume [START_REF] Murphy | Serial changes in CT cerebral blood volume and flow after 4 hours of middle cerebral occlusion in an animal model of embolic cerebral ischemia[END_REF][START_REF] Sawka | Blood volume: importance and adaptations to exercise training, environmental stresses, and trauma/sickness[END_REF] . In other words, an enhanced permeability and retention (EPR) effect is not desired during the measurements. This will overestimate the local blood volume and blur the twophoton images. This latter parameter is of crucial interest in biomedical applications such as tumor diagnosis and therapy follow-up [START_REF] Tozer | Intravital imaging of tumour vascular networks using multi-photon fluorescence microscopy[END_REF] . Tumors have most often an abnormal vascular blood volume in comparison to normal adjacent tissue, which determines drug delivery and consequently their therapy response.

The new two-photon dyes should allow imaging at low laser power (< 30 mW) at nontoxic concentrations without modifying the blood viscosity. For TPLSM, main fluorescent dye specifications are: a high two-photon absorption cross section (σ TPA ) and a fluorescence quantum yield Φ with an emission and a two-photon absorption wavelength located in the spectral region of interest for bio-imaging (680-1040 nm). Actually, regular intravascular dyes consist of branched polysaccharides, e.g.: dextrans, grafted with organic dyes such as fluorescein or rhodamin [START_REF] Verant | A direct method for measuring mouse capillary cortical blood volume using multiphoton laser scanning microscopy[END_REF][START_REF] Andrieux | Characterization of fluorescein isothiocyanate-dextrans used in vesicle permeability studies[END_REF] . Numerous other strategies use quantum dots [START_REF] Larson | Water-soluble quantum dots for multiphoton fluorescence imaging in vivo[END_REF] , water-soluble dendrimers [START_REF] Krishna | Water-soluble dendrimeric two-photon tracers for in vivo imaging[END_REF] or fluorescent dye doped silica mesoporous nanoparticles [START_REF] Lebret | Synthesis and characterization of fluorescently doped mesoporous nanoparticles for two-photon excitation[END_REF] . Most of these particles are of limited use due to their in vivo instability or biotoxicity. Another approach involves nanodispersion of hydrophobic organic preformed compounds in aqueous solutions using special formulation techniques such as micro-emulsions [START_REF] Horn | Organic nanoparticles in the aqueous phase -theory, experiment, and use[END_REF] .

In this field, we recently reported the elaboration of organic fluorescent nanomicelles based on a micro-emulsion process using a well known polyethylene-polypropylene glycol (Pluronic) surfactant [START_REF] Maurin | Fluorescent Pluronic nanodots for in vivo two-photon imaging[END_REF] . This process leads to hydrophilic micelles encapsulating hydrophobic fluorescent molecules with dimensions ranging from 20 to 100 nm. This method can be applied to numerous hydrophobic dyes [START_REF] Maurin | Pluronic Organic Fluorescent Probes for Two-photon Vascularisation Imaging[END_REF] . Here, a di-stryl benzene-modified derivative [START_REF] Pond | One-and two-photon spectroscopy of donoracceptor-donor distyrylbenzene derivatives: effect of cyano substitution and distortion from planarity[END_REF] has been used, exhibiting a 2500 GM (1 GM = 10 -50 cm 4 s photon -1 molecules -1 ) two-photon absorption cross section at 800 nm. Its structure is shown in figure 1. To illustrate the potential for vasculature imaging of such probes, imaging of the cerebral vasculature has been performed in the cortex of normal mice. The maximum imaging depth and blood plasma staining have been compared to the regular blood pool dye Rhodamin B Dextran (70 kDa).

Quantitative blood volume measurement has been performed for both dyes and compared to values in the literature. Finally, the diffusion properties of the Pluronic nanomicelles has been analyzed, and compared to those of Rhodamin B dextran, in the leaky tumor neo-vasculature of human lung carcinoma growing in dorsal skin fold chambers.

Materials and Methods

Dyes preparation

Pluronic F68 was purchased from Sigma-Aldrich (France). Synthesis of the di-stryl benzene derivative (figure 1) has already been reported [START_REF] Pond | One-and two-photon spectroscopy of donoracceptor-donor distyrylbenzene derivatives: effect of cyano substitution and distortion from planarity[END_REF] . For the Pluronic nanomicelles (figure 2), 2 mg of di-stryl benzene-modified derivative was dissolved in 100 µl chloroform and added to 5 ml of Pluronic F68 (2 wt. %) aqueous solution containing 0,9% NaCl. After 15 min stirring for pre-emulsification, the micro-emulsion was prepared by ultrasonicating for 15 minutes (bath, 150 W). After sonication, the mixture was stirred in a regulated bath at 50° C for 30 min to evaporate the chloroform. The colloidal particle size (20-100nm) was fixed by mechanical filtration (Nylon-Cameo, Fisher, France) of the solution. Typically dye concentrations, ranging from 0.1 to 0.15 g.L -1 (0.15 mmol.L -1 to 0.23 mmol.L -1 ), can be obtained in a 10 g.L -1 Pluronic aqueous solution [START_REF] Maurin | Fluorescent Pluronic nanodots for in vivo two-photon imaging[END_REF] . As a reference, a 100 g.L -1 Rhodamin B dextran 70-kDa solution (Sigma-Aldrich, France) in 0.9% NaCl was prepared. Depending on the degree of Rhodamin B labeling of the dextran, the Rhodamin B dye concentrations varied between 4 mmol.L -1 and 11 mmol.L -1 .

Animal models

Healthy Swiss white mice (n = 6, 6 -8 weeks old) and tumor bearing Swiss nude mice (n = 3, 6 months old, Charles River Laboratories, Lyon, France) were used. All experiments were performed in accordance with the French Government guidelines (license A3851610008).

During surgery and imaging, mice were anesthetized by a continuous inhalation of 2% isoflurane in a gas mixture of 30% O 2 and 70% N 2 O, and placed on a modified stereotaxic frame or on a homemade frame for proper fixation of mice with dorsal skin fold chambers.

Core temperature was maintained at approximately 37°C using a warm water blanket. For the cerebral micro-vessel imaging experiments, a craniotomy (ø = 3 mm) was carried out above the left parietal cortex. A rubber ring was placed on the top of the skull to trap saline for continuous objective immersion.

For tumor vasculature imaging, 3 Swiss nude mice were implanted with small dorsal skin fold chambers (small dorsal kit SM100, APJ Trading Co., Ventura, CA, USA) as described in a previous protocol [START_REF] Tozer | Intravital imaging of tumour vascular networks using multi-photon fluorescence microscopy[END_REF] . Briefly, two symmetrical titanium frames with central holes (ø = 1 cm) flanked the dorsal skin-fold of animals sandwich the extended double layer of skin and create the dorsal skin-fold chamber, which consisted of one layer of striated muscle, s.c. tissue, and epidermis. An observation window, covered with a glass coverslip, allowed for intravital microscopic observations. One day after surgery, mice were checked on the presence of infection. At the absence of infection, 2.10 6 human lung carcinoma cells (NCI-H460, ATCC # HTB-177) in 200 µL vehicule (50 % RPMI medium, 50 % matrigel (BD Matrigel TM Matrix #354234, Bedford, MA)) were injected in the dorsal skin fold chamber. Two-photon imaging of the tumor vasculature was performed at 14 days after tumor cell injections.

For each experiment, 100 µl of Pluronic microemulsion or Rhodamin B dextran solution in saline was injected in the tail vein of the mice approximately 1 min before imaging.

Microscopy set up

In vivo two-photon laser scanning microscopy was performed with a confocal microscope consisting of a Biorad (MRC 1024) scanhead and an Olympus BX50WI microscope. A 800 nm excitation beam originating from a femtosecond Ti:sapphire laser (5 W pump; Spectra-Physics, Millenia V) was focused into the cortex using a 20× water-immersion objective (0.95 numerical aperture, Xlum Plan FI Olympus). The laser beam was then scanned in the x-y plane to acquire a 512×512 image (0.9 s/image) with laser powers varying between 10 and 30 mW. The z scan (variation of the observation depth) was realized by translation of the motorized objective. For these experiments, the confocal configuration was not used and the non-descanned fluorescence was directly collected with an external photomultiplier (PMT) protected by a BG39 filter (Schott Glass-Jena, Germany). Planar scans of the fluorescent intensity were acquired at successive depths in the animal with a 5 µm z step between scans.

Image reconstruction and analysis were performed using free Image J software (http://rsbweb.nih.gov/ij/).

Relative blood volume measurement

Relative blood volume measurements (= total blood volume / total sample volume) have been performed using a method described by Verant et al. [START_REF] Verant | A direct method for measuring mouse capillary cortical blood volume using multiphoton laser scanning microscopy[END_REF] . For each stack, the background (rolling ball algorithm with a radius varying between 30-60 µm) and the saturated pixels due to artifacts are removed using Image J software. Per slice in a z-stack, fluorescence intensities are normalized between 0 and 255 gray values using plunging vessels with maximum intensity (gray value 255). This is necessary to correct for the variation of fluorescence generation and collection as a function of depth. To finish, an average z-projection of the stack is performed. In this z-projection, the corresponding blood volume is proportional to the sum of the pixel intensities.

Results and Discussion

Cerebral vasculature imaging

Imaging of the cerebral vasculature in the cortex of normal Swiss white mice (6-8 weeks old) has been performed with Pluronic nanomicelles and Rhodamin B dextran. As shown in figure 3, vessels as far as 600 µm below the dura were detected with both dyes. It is noticed that two-photon optimized Pluronic nanomicelles exhibit the same efficiency when compared to Rhodamin B Dextran in spite of a ten time less mass. Minor effects on the blood viscosity and hemodynamics are expected after injection of Pluronic nanomicelles (100µL containing 1 mg Pluronic) in comparison with Dextran dyes (100µL containing 10mg Dextrans) without modifying the observation depth.

Ideally, blood dye concentration must be constant during the intravital microscopic studies which take approximately 1 hour. Therefore, stacks were acquired every ten minutes during 1 hour after injection of both dyes in different mice and the fluorescence intensity of specific vessels was quantified using ImageJ software (figure 4). For both dyes, it was noticed that the fluorescence intensity is rather stable: 90% of the initial signal remained after 1 hour.

Thus no important dye accumulation or clearance occurred within 1 hour.

The stability of the Pluronic nanomicelles in blood was not investigated in details [START_REF] Chen | Fast release of lipophilic agents from circulating PEG-PDLLA micelles revealed by in vivo forster resonance energy transfer imaging[END_REF] . The stability of the Pluronic nanomicelles depends on many physico-chemical parameters that are unique for each encapsulated hydrophobic dye and Pluronic unimers. In the current study, our di-stryl benzene chromophore is known to aggregate in a hydrophobic environment. This favored π-π stacking and increased the two-photon absorption cross section [START_REF] Maurin | Pluronic Organic Fluorescent Probes for Two-photon Vascularisation Imaging[END_REF] . This stacking of di-stryl benzene inside the hydrophobic core of the Pluronic nanomicelles might further increase their stability: a larger surface for hydrophobic interactions with the hydrophobic poly (propylene oxide) blocks. Binding of the aggregated di-stryl benzenes to hydrophobic components of the blood could not be excluded [START_REF] Chen | Fast release of lipophilic agents from circulating PEG-PDLLA micelles revealed by in vivo forster resonance energy transfer imaging[END_REF] , but might be retarded several hours.

Relative cortical blood volume measurements

Relative cortical blood volume (rCBV) measurements have been performed with previous stacks after Pluronic nanomicelles or Rhodamin B dextran injection using for both dyes 3 mice. For the relative blood volume calculations, the slices were taken at 50 µm below the dura to suppress large superficial vessels of the subarachnoid space. An example of average Z-projection of a specific area is shown in figure 5.

Using Pluronic nanomicelles, a rCBV of 2,4 ± 0,5 (standard deviation) % was found, which was in good agreement with Rhodamin B dextran results: rCBV = 2,3 ± 0,3 %. Those results, close to the rCBV literature values [START_REF] Tsai | Correlations of neuronal and microvascular densities in murine cortex revealed by direct counting and colocalization of nuclei and vessels[END_REF] , demonstrate that our Pluronic nanomicelles are strictly plasmatic dyes.

Two photon imaging of the tumor vasculature.

In most high grade tumors, the endothelium of new neo-vessels is often leaky for small molecules [START_REF] Dvorak | Identification and characterization of the blood vessels of solid tumors that are leaky to circulating macromolecules[END_REF] , which leads to an higher interstitial fluid pressure [START_REF] Jain | Transport of molecules across tumor vasculature[END_REF][START_REF] Leunig | Angiogenesis, microvascular architecture, microhemodynamics, and interstitial fluid pressure during early growth of human adenocarcinoma LS174T in SCID mice[END_REF] . For proper local tumor blood volume measurements, the dye should stay in the vasculature and not diffuse across the leaky endothelium. In the present study, we tested if Pluronic nanomicelles could be used as blood pool dyes in tumors and compared their performance to the Rhodamin B dextran 70 kDa dye. In figure 6, both dyes were injected with a 30 minutes interval in a mouse bearing a dorsal skin fold chamber with human lung carcinoma. The largest Pluronic nanomicelles were injected first and during 30 minutes, no dye diffusion across the vascular endothelium into the extravascular space was observed: the background between the vessels remained black and showed a good contrast with the functional tumor vessels (figure 6A). In a previous study, Pluronic nanomicelles were found to stay inside the tumor vasculature until 4 hours after i.v.

injection (results not shown).

Thirty minutes after the second injection of Rhodamin B dextran 70 kDa, the contrast between the vessels and the background got lost due to the diffusion of the rhodamin B dextran dyes into the extravascular space (figure 6B). This difference can be related to the important size of Pluronic nanomicelles (20 to 100 nm) in comparison to 70 kDa Rhodamin B dextran with a hydrodynamic radius of 6 nm. Even, the largest dextrans (200 kDa) with a hydrodynamic radius of 27 nm are known to diffuse across the leaky tumor blood vessels [START_REF] Dvorak | Identification and characterization of the blood vessels of solid tumors that are leaky to circulating macromolecules[END_REF][START_REF] Jain | Transport of molecules across tumor vasculature[END_REF] .

Note that at this molecular size, the solubility of the dextran decreases (maximum concentration 10 mg/ml) in comparison to the 70 kDa dextran (maximum concentration 100 mg/ml), which results in approximately 10 times less dyes in the blood plasma.

The fast uptake of Pluronic nanomicelles could only be observed after treatment with a vascular disrupting agent that was known to drastically increase the vascular permeability (figure 6C-D)

Conclusions

In the present study, we have demonstrated that Pluronic nanomicelles can be used as blood pool dyes in intravital two-photon imaging of both the normal and the tumor vasculature. In the normal vasculature, the blood plasma staining is homogeneous and similar to the results obtained with the Rhodamin-B isothicyanate-Dextran at ten times less injected mass (1 mg Pluronic versus 10 mg 70 kDa grafted Dextran). In comparison to Dextran dyes, minor effects on the blood viscosity and hemodynamics are expected with Pluronic nanomicelles. In a human lung carcinoma, Pluronic nanomicelles stayed in the vasculature, whereas Rhodamin B dextran diffused across the leaky tumor vascular endothelium. Therefore, Pluronic nanomicelles can be used for local tumor blood volume measurements during tumor growth and follow up of anti-angiogenic therapies.

In general, the use of Pluronic block co-polymers is a valuable approach for encapsulating two-photon fluorescent dyes that are hydrophobic and not suitable for intravenous injection.

Legends to figures

Figure 1 :Figure 2 :

 12 Figure 1: Structure of the di-strylbenzene derivative

Figure 3 :

 3 Figure 3: Reconstructed 3D data sets of z-stacks (600*600*600 µm) acquired below the dura

Figure 4 :

 4 Figure 4: Images acquired at 150 µm bellow the dura at 20 (A), 40 (B) and 60 min (C) after 100 µL Pluronic nanomicelles (10 g.L -1 ) injection. Figure 4D, shows the decrease of the mean

Figure 5 :

 5 Figure 5: Z-projection of the average fluorescence intensity of 41 images acquired from 100

Figure 6 :

 6 Figure 6: Images (size: 848.53 µm 2 ) of the tumor vasculature in Swiss nude mice bearing

Acknowledgements

This work was supported by a grant from the Ministère de l'Education Nationale, de l'Enseignement Supérieur et de la Recherche. The authors thank Patrice Baldeck for helpful discussion, Cyril Zenga and Aurelie Juhem for biotechnical assistance in two-photon imaging of the tumor vasculature.


N Verscheure

C Finot

Pulse doubling and wavelength conversion through triangular nonlinear pulse reshaping

Introduction: All-optical wavelength conversion is a key function for the development of future transparent networks. Among the various photonic solutions that have been proposed so far, Kerr nonlinearity in highly nonlinear fibres seems particularly attractive. Several approaches using four-wave mixing or self-/ cross-phase modulation (SPM / XPM) followed by offset spectral filtering have been reported [START_REF] Parmigiani | An efficient wavelength converter exploiting a grating based saw-tooth pulse shaper[END_REF][START_REF] Parmigiani | Efficient all-optical wavelength conversion scheme based on a saw-tooth pulse shaper[END_REF]. SPM and XPM are highly affected by the temporal intensity profile of the pulse and, consequently, the wavelength conversion performance will depend on the initial pulse shape. In particular, temporal triangular or sawtooth (asymmetric triangular) profiles are very promising candidates for achieving clean and efficient conversion [START_REF] Parmigiani | An efficient wavelength converter exploiting a grating based saw-tooth pulse shaper[END_REF][START_REF] Parmigiani | Efficient all-optical wavelength conversion scheme based on a saw-tooth pulse shaper[END_REF].

The problem of generating such non-conventional pulse shapes has attracted a good deal of attention in recent years. Various solutions have been proposed, including linear shaping methods (superstructured fibre Bragg gratings [START_REF] Parmigiani | An efficient wavelength converter exploiting a grating based saw-tooth pulse shaper[END_REF][START_REF] Parmigiani | Efficient all-optical wavelength conversion scheme based on a saw-tooth pulse shaper[END_REF] or frequency-totime conversion [START_REF] Ye | Photonic generation of triangular-shaped pulses bases on frequency to time conversion[END_REF]) and nonlinear pulse shaping in photonic crystal fibre [START_REF] Bale | Effects of fourth-order fiber dispersion on ultrashort parabolic optical pulses in the normal dispersion regime[END_REF] or normally dispersive (ND) fibre [START_REF] Boscolo | Passive nonlinear pulse shaping in normally dispersive fiber systems[END_REF].

In [START_REF] Boscolo | Passive nonlinear pulse shaping in normally dispersive fiber systems[END_REF], Boscolo et al have numerically shown that an initial, sufficiently powerful pulse with anomalous linear chirp can evolve towards a triangular shape in a passive, ND fibre. In contrast with parabolic pulses that can be generated through the asymptotic pulse reshaping occurring upon nonlinear propagation in ND fibre amplifiers [START_REF] Finot | Optical parabolic pulse generation and applications[END_REF], triangular pulses represent transient states of the nonlinear pulse evolution in a passive ND fibre. Additional experimental studies have confirmed that a precise trade-off between the system parameters (initial chirp value, peak power, fibre length) is required for triangular pulse formation [START_REF] Wang | Generation of triangular-shaped optical pulses in normally dispersive fibre[END_REF].

In this Letter, we experimentally demonstrate spectral and temporal optical pulse doubling and frequency conversion using triangular pulses generated in ND fibre. We show that the frequency/time spacing between the two pulse replica can be easily tuned by control of the initial power.

Experimental set-up: The all-fibred experimental set-up relies exclusively on telecommunication-ready devices and is sketched in Fig. 1, which also includes the parameters of the fibre segments being used. A 2.4 ps soliton pulse train is delivered by a mode-locked fibre laser (MLFL) operating at a repetition rate of 10 GHz (see inset of Fig. 1). An intensity modulator (IM) is used to decrease the repetition rate down to 2.5 GHz. The reshaping of the initial sech pulses into triangular pulses is achieved through propagation in a set of two carefully chosen fibres [START_REF] Wang | Generation of triangular-shaped optical pulses in normally dispersive fibre[END_REF]. The choice of the fibres was guided by the design rules proposed in [START_REF] Boscolo | Passive nonlinear pulse shaping in normally dispersive fiber systems[END_REF], which were slightly modified to account for the non-Gaussian shape of the initial pulses. The first stage of propagation is to impose an anomalous chirp on the pulses and relies on linear propagation in a standard single mode fibre (SMF). The pre-chirped, broadened pulses are amplified by an erbium-doped fibre amplifier (EDFA) with an output average power of 20 dBm, and then propagated through a non-zero dispersion shifted fibre (NZ-DSF) with normal dispersion to realize the nonlinear triangular pulse reshaping. The output triangular pulses from the NZ-DSF are amplified by a highpower EDFA before entering a highly nonlinear fibre (HNLF). A fibre with normal dispersion was favoured to avoid the modulational instability effects that can occur in the anomalous dispersion regime. This stage of propagation is dominated by SPM and the nonlinear phase shift generated by an intensity profile with linear gradient [START_REF] Parmigiani | An efficient wavelength converter exploiting a grating based saw-tooth pulse shaper[END_REF] : the linear leading (trailing) edge of the triangular pulse induces a constant, red (blue) frequency shift. The output SPM-shaped spectrum from the HNLF is sent into either a linear SMF segment to realize temporal pulse doubling or a wavelength demultiplexer filter for wavelength conversion processing. The filter channels have a full-width at half-maximum (FWHM) of 100 GHz and are spaced by 200 GHz.

At each propagation stage, the temporal intensity profiles of the pulses are monitored by an optical sampling oscilloscope (OSO) with picosecond temporal resolution. The optical spectra are also recorded.

Temporal and spectral evolutions: The temporal and spectral pulse evolutions are summarized in Fig. 2. After propagation in the SMF, the initial transform-limited pulses are broadened up to 7.1 ps (Fig. 2a). The unchanged spectrum at the SMF output confirms the purely linear nature of the propagation in this fibre segment. At the output of the NZ-DSF, the pulses clearly exhibit the expected reshaping with a typical triangular intensity profile with a FWHM duration of 34 ps (Fig. 2b). Although deviations from a perfect triangular shape are noticeable on the pulse top, the highly linear wings of the profile qualitatively confirm the conclusions drawn from frequency resolved optical gating measurements in [START_REF] Wang | Generation of triangular-shaped optical pulses in normally dispersive fibre[END_REF].

Due to the triangular temporal profile along with SPM, upon propagation in the HNLF the pulse spectrum goes through a reshaping leading to a structure consisting of two equal peaks. Results are presented in Fig. 2c for an average power at the HNLF input of 24.4 dB. The two spectral peaks at the end of the HNLF contain most of the pulse energy and are separated by 600 GHz. It is also seen from Fig. 2c that the temporal triangular profile is maintained over propagation in the HNLF.

Spectral and temporal signal copying and wavelength conversion: Additional measurements were made to highlight the influence of the optical power launched into the HNLF on the spectral reshaping process. The evolution of the output spectrum from the HNLF as a function of the launched average power is presented in Fig. 3a. It can be clearly seen that for powers ranging from 18.5 dBm to 28.5 dBm, the spectrum exhibits the typical signature of SPM-induced reshaping of a triangular pulse, i.e. a double peak structure. Note that in Ref. [START_REF] Parmigiani | An efficient wavelength converter exploiting a grating based saw-tooth pulse shaper[END_REF] sawtooth pulses were voluntarily used to promote the transfer of energy to a single spectral peak. The spectral structure that we observe here is nearly symmetric with respect to the input pulse wavelength. The width and form of the two spectral peaks is almost preserved over the aforementioned range of initial powers and quite remarkably, the separation between the peaks can be tuned continuously between 300 GHz and 900 GHz [START_REF] Latkin | Doubling of optical signals using triangular pulses[END_REF].

The nearly linear variation of the frequency spacing with the initial power is illustrated in Fig. 3b. By use of linear propagation in the SMF segment following the HNLF, we were able to realize the function of temporal pulse copying as theoretically predicted in [START_REF] Latkin | Doubling of optical signals using triangular pulses[END_REF].

Under propagation of the modulated output pulse from the HNLF in the SMF, the produced spectral separation of the pulse components leads to their subsequent separation in time, thus allowing temporal replication of the pulse. The evolution of the temporal intensity profile recorded at the output of the SMF with the power launched into the HNLF is presented in Fig. 3c and shows that, as a result of the time-to-frequency mapping occurring in the SMF, the time separation between the two copies of the original pulse can be adjusted by control of the input power to the HNLF.

We have also investigated the quality of the pulse trains obtained from spectral filtering of the output pulses from the HNLF. Converted pulses trains obtained for the frequency spacings 400 GHz (1548.51 nm and 1545.32 nm, respective ITU channels 36 and 40 on a 100 GHz grid spacing) and 800 GHz (ITU channels 34 and 42) have been measured and no significant amplitude or timing jitters have been detected. The output FWHM pulse duration measured on the OSO was 9.7 ps. The electrical eyes corresponding to a 10 Gbps pulse train formed by a pseudo random bit sequence with 25% of 1 bits are presented in Fig. 3d for the ITU channels 34 and 42. Further bit error rate (BER) measurements have confirmed that error-free operation of the wavelength converter can be achieved.

Conclusion:

We have experimentally demonstrated an easy-to-implement all-fibre wavelength converter using triangular-shaped pulses. The nonlinear approach presented takes advantage of the SPM experienced by triangular pulses in a HNLF and enables efficient splitting of the optical spectrum into two symmetric, equal peaks whose spacing can be easily controlled through the input power. The quality of the obtained signals has been assessed by BER measurements. The principle of temporal pulse doubling has also been experimentally validated.

While the proof-of-principle experiments presented in this paper rely on optical fibres, we can anticipate that the rapid recent progress in highly nonlinear waveguide fabrication may enable integration of such high-speed wavelength conversion function based on Kerr nonlinearity on a photonic chip.

Acknowledgements: This research was supported by the Conseil Regional de Bourgogne (PARI PHOTCOM). We thank Sonia Boscolo and Julien Fatome for stimulating discussions as well as Philippe Morin for technical help in the BER measurements. We also acknowledge the support of the Ministère des affaires étrangères (Alliance Grant 22836ZJ).

Authors' affiliations:

Noémie VERSCHEURE