Lubin Kerhuel

Stéphane Viollet

Nicolas Franceschini

The VODKA sensor: a bio-inspired hyperacute optical position sensing device

Keywords: Astronomy, hyperacuity, metrology, Micro Aerial Vehicle (MAV), optical sensor, photodiode, photoreceptor, Position Sensing Device (PSD), robotics, Unmanned Aerial Vehicle (UAV), vibration, vision

We have designed and built a simple optical sensor called Vibrating Optical Device for the Kontrol of Autonomous robots (VODKA), that was inspired by the "tremor" eye movements observed in many vertebrate and invertebrate animals.

In the initial version presented here, the sensor relies on the repetitive micro-translation of a pair of photoreceptors set behind a small lens, and on the processing designed to locate a target from the two photoreceptor signals. The VODKA sensor, in which retinal micro-scanning movements are performed via a small piezo-bender actuator driven at a frequency of 40Hz, was found to be able to locate a contrasting edge with an outstandingly high resolution 900-fold greater than its static resolution (which is constrained by the interreceptor angle), regardless of the scanning law imposed on the retina. Hyperacuity is thus obtained at a very low cost, thus opening new vistas for the accurate visuo-motor control of robotic platforms. As an example, the sensor was mounted onto a miniature aerial robot that became able to track a moving target accurately by exploiting the robot's uncontrolled random vibrations as the source of its ocular microscanning movement. The simplicity, small size, low mass and low power consumption of this optical sensor make it highly suitable for many applications in the fields of metrology, astronomy, robotics, automotive, and aerospace engineering. The basic operating principle may also shed new light on the whys and wherefores of the tremor eye movements occurring in both animals and humans.

I. INTRODUCTION

T HE human visual system is able to detect an object subtending an angle of only a few secs of arc between two objects, which is an angle much smaller than the interreceptor angle. This property has been called hyperacuity [START_REF] Westheimer | Visual hyperacuity[END_REF]. Another type of hyperacuity is the ability of a natural or artificial optical sensor to locate a contrasting object with a higher resolution than the theoretical (static) resolution. Although the mechanisms involved in the various kinds of hyperacuity have not yet been completely elucidated, retinal micro-movements seem to play an important role [START_REF] Martinez-Conde | The role of fixational eye movements in visual perception[END_REF], [START_REF] Ko | Microsaccades precisely relocate gaze in a high visual acuity task[END_REF]. Hennig et al. have shown, for example, that the tiny eye movements called tremor can improve the spatial resolution and induce hyperacuity in the case of vernier L.Kerhuel was with the Institute of Movement Sciences, Biorobotics team, National Center for Scientific Research, University of the Mediterranean, F-13288 Marseille cedex 09, France. He is now with MOVEA S.A., F-38000 Grenoble, France (email: lubin@kerhuel.eu).

S.Viollet and N.Franceschini are with the Institute of Movement Sciences, Biorobotics team, National Center for Scientific Research, University of the Mediterranean, F-13288 Marseille cedex 09, France (email: stephane.viollet@univmed.fr, nicolas.franceschini@univmed.fr). OSCAR 2 robot equipped with the hyperacute VODKA sensor. The 100-gram aerial robot, which is usually suspended from the ceiling with a long 100µm nylon wire [START_REF] Kerhuel | A sighted aerial robot with fast gaze and heading stabilization[END_REF]- [START_REF] Kerhuel | Steering by gazing: An efficient biomimetic control strategy for visually guided micro aerial vehicles[END_REF] controls its yaw on the basis of what it sees. Here it was mounted on the axis of a frictionless resolver that allowed its heading to be accurately monitored. The twin-engine robot orients itself by driving its two propellers differentially. The inset shows the robot's retina (after the lens has been removed), which can be subjected to repetitive microtranslations at a frequency of 40Hz by means of a piezo-bender (see Fig. 2). VODKA's retina is composed of an Ic-Haus LS2C package comprising 6 vertically elongated photoreceptors with integrated amplifiers. The VODKA vibrating sensor actually uses only the two central photoreceptors (2 pixels, as sketched in Fig. 2).

stimuli [START_REF] Hennig | Eye micro-movements improve stimulus detection beyond the nyquist limit in the peripheral retina[END_REF]. Chen et al. have noted that visual scanning may also provide a useful means of enhancing the visual acuity of subjects wearing visual prostheses [START_REF] Chen | Psychophysics of prosthetic vision: I. visual scanning and visual acuity[END_REF]. In a more general framework, Altes reported that jitter sensitivity in echolocation, differential pitch sensitivity in audition, and vernier acuity in vision seem to be based on similar principles [START_REF] Altes | Ubiquity of hyperacuity[END_REF].

However, hyperacuity can also exist without requiring any visual scanning movements. Krotkov studied hyperacuity by combining classical information theory with image processing algorithms [START_REF] Krotkov | Visual hyperacuity: Representation and computation of high precision position information[END_REF]. Riley et al. recently implemented a hyperacute visual sensing machine, using a complex optical arrangement and high-sensitivity optical sensors [START_REF] Riley | Musca domestica inspired machine vision sensor with hyperacuity[END_REF]. Brückner et al. assessed the hyperacuity of an artificial compound eye in terms of its ability to locate a point source or an edge [START_REF] Brückner | Artificial compound eye applying hyperacuity[END_REF]. The robustness of this visual sensors' performance with respect to contrast and the distance from the object targeted has not been addressed so far, however. In many cases, the hyperacuity of artificial visual sensors results from rather complex processing steps. In the field of image processing, for example,there has been a considerable amount of work on edge detection and edge localization over the past decades. Several authors have used discrete subpixel image displacement methods (called « dithering ») to enhance the resolution of large image sensors, but this is at the cost of large memory resources [START_REF] Morokawa | Image pickup system[END_REF]- [START_REF] Koekemoer | Hubble Space Telescope dither handbook[END_REF].

In the optical sensor presented here, hyperacuity in edge localization results from an active visual process whereby specific continuous micro-movements are applied to an artificial retina. This approach was inspired by the retinal micro-movements observed in the eyes of many invertebrates (Arachnids [START_REF] Land | Movements of the retinae of jumping spiders (salticidae: dendryphantinae) in response to visual stimuli[END_REF], [START_REF] Kaps | Mechanism and possible behavioural relevance of retinal movements in the ctenid spider cupiennius salei[END_REF], Molluscs [START_REF] Land | Scanning eye movements in a heteropod mollusc[END_REF], and Insects [START_REF] Franceschini | Repetitive scanning in the fly compound eye[END_REF]). The retinal micro-scanning which occurs in the housefly's eye [START_REF] Franceschini | Repetitive scanning in the fly compound eye[END_REF] has already served as a biological model for miniature visual sensors [START_REF] Mura | Obstacle avoidance in a terrestrial mobile robot provided with a scanning retina[END_REF]- [START_REF] Viollet | A hyperacute optical position sensor based on biomimetic retinal micro-scanning[END_REF], the efficiency of which has been assessed onboard various mobile robots [START_REF] Kerhuel | Steering by gazing: An efficient biomimetic control strategy for visually guided micro aerial vehicles[END_REF], [START_REF] Mura | Obstacle avoidance in a terrestrial mobile robot provided with a scanning retina[END_REF], [START_REF] Mura | Visual guidance of a small mobile robot using active, biologically-inspired, eye movements[END_REF]- [START_REF] Viollet | A high speed gaze control system based on the vestibulo-ocular reflex[END_REF]. Retinal scanning in jumping spiders [START_REF] Land | Movements of the retinae of jumping spiders (salticidae: dendryphantinae) in response to visual stimuli[END_REF] has also served as a biological model for a visual sensor [START_REF] Landolt | Visual sensor with resolution enhancement by mechanical vibrations[END_REF]. Prokopowicz and Cooper designed an active imaging system based on human eye tremor, which led them to the concept of dynamic retina [START_REF] Prokopowicz | The dynamic retina: Contrast and motion detection for active vision[END_REF] whereas Hongler et al. used vibration noise to improve dramatically edge detection in an image [START_REF] Hongler | The resonant retina: exploiting vibration noise to optimally detect edges in an image[END_REF].

Here we focus on a novel optical position sensing device called VODKA, which is endowed with hyperacuity. Contrary to previous studies [START_REF] Kerhuel | Steering by gazing: An efficient biomimetic control strategy for visually guided micro aerial vehicles[END_REF], [START_REF] Viollet | Biologically-inspired visual scanning sensor for stabilization and tracking[END_REF], [START_REF] Viollet | Visual servo system based on a biologically inspired scanning sensor[END_REF], [START_REF] Viollet | A high speed gaze control system based on the vestibulo-ocular reflex[END_REF], [START_REF] Viollet | Characteristics of three miniature bio-inspired optic flow sensors in natural environments[END_REF], in which hyperacute target location performance required a specific micro-scanning law imposed on the sensor's retina, VODKA can deal with any scanning law and even exploit random movements caused by uncontrolled vibrations of the platform supporting the eye.

Section II describes the model for the VODKA optical system presented in section III and explains how the VODKA sensor works. In section IV, we describe how changes in several parameters can affect the sensor's static characterictics. In section V,the noteworthy features of the sensor are discussed. In section VI, two experiments are described which show the high accuracy of VODKA in terms of its target localization performance. VODKA's responses were found to depend quasi-linearly on the target's bearings, showing a relatively high robustness to distance and contrast. Lastly, it was established that VODKA shows an outstanding degree of hyperacuity, with the ability to locate a target about 900 times more accurately than might be expected, given the interreceptor angle.

II. MODELING THE MICRO-SCANNING SENSOR VODKA

A. Optics

The sensor optics include two photodiodes (Ic-Haus LS2C shown in Fig. 1) placed behind a lens (diameter D = 5mm, focal length f = 8.5mm) and driven in small translation by a piezo bender actuator (Physik Instrumente PL128), as shown in Fig. 2. A bell-shaped directivity function simulating the angular sensitivity function of the fly's photoreceptors [START_REF] Götz | Optomotorische Untersuchengen des visuellen Systems einiger Augnmuntanten der Fruchfliege Drosophila[END_REF]- [START_REF] Stavenga | Angular and spectral sensitivity of fly photoreceptors. ii. dependence on facet lens f-number and rhabdomere type in drosophila[END_REF] was obtained here by slightly defocusing the lens (actually reducing the distance between the lens and the retina). The Gaussian-like directivity of each of the two VODKA's photoreceptors can be defined by the parameter denoted ∆ρ, which was defined as the Full Width at Half Maximum (FWHM) (see the directivity functions on the left part of Fig. 3). The directivity function s(Ψ) of a photoreceptor is therefore given by:

s(Ψ) = 2 √ π ln(2) π∆ρ e -4 ln(2) Ψ 2 ∆ρ 2 (1)
where Ψ is the angle between the photoreceptor optical axis and that of a point light source.

B. Temporal Output Signal of a Photoreceptor

The output signal of a photoreceptor placed in front of a contrasting feature (an edge or a bar) is the convolution of the projected light intensity with the directivity function s(Ψ).

When a vertical edge is placed at an angular position Ψ c within the Field of View (FOV) of a photoreceptor, its output signal resulting from the convolution of the edge image with the directivity function s(Ψ) is defined as follows:

P h(Ψ c ) = k 1 2 + Ψc -∞ s(Ψ) dΨ = k 2 1 + erf 2 ln(2) * Ψ c ∆ρ (2)
where the factor k depends on both the contrast and the lighting conditions and erf is the so-called error function defined by:

erf (Ψ) = 2 √ π Ψ 0 e -x 2 dx (3)
When a vertical bar of finite width L is encountered, the photoreceptor's output signal resulting from the convolution ). An optional peak filter removes all frequencies not associated with the vibration. A demodulator extracts the envelope of the signal. The relative difference between the two signals is computed as (P h 1 -P h 2 )/(P h 1 + P h 2 ) to yield the VODKA sensor output.

of the bar image with the directivity function s(Ψ) is defined as follows:

P h(Ψ c ) = k 2 erf 2 √ ln(2)(Ψc+ L 2 ) ∆ρ -erf 2 √ ln(2)(Ψc-L 2 ) ∆ρ (4)

III. PRINCIPLE OF THE VODKA SENSOR

The VODKA sensor is designed to estimate the azimuthal position of a vertically oriented contrasting target. Here we take the case of a sensor measuring the angular position of a vertical edge or bar.

The optical assembly comprising the two photoreceptors separates their optical axes by a constant angle denoted ∆ϕ (see Fig. 2 & Fig. 3), which is called the interreceptor angle. The VODKA sensor's main axis is defined as the bisector of these two axes. Each of the two photoreceptors' output signals, which are denoted P h 1 and P h 2 , depends on the angle between its optical axis and the target (the edge or the center of the bar). Let us take Ψ c to denote the angular position of the visual target relative to the main VODKA axes. The combined vibration of the two optical axes adds a high frequency modulation denoted Ψ mod . The two photoreceptors' output signals can therefore be written as follows:

P h 1 (Ψ(t)) = P h Ψ c (t) + Ψ mod (t) - ∆ϕ 2 P h 2 (Ψ(t)) = P h Ψ c (t) + Ψ mod (t) + ∆ϕ 2 (5)
where Ψ(t) = Ψ c (t) + Ψ mod (t) and where

• the expression (2) for P h is used in the case of an edge;

• the expression (4) for P h in the case of a bar.

To summarize, the VODKA principle mainly involves:

• a Gaussian-like angular sensitivity function for each photoreceptor, mimicking the angular sensitivity function of flies' photoreceptors [START_REF] Götz | Optomotorische Untersuchengen des visuellen Systems einiger Augnmuntanten der Fruchfliege Drosophila[END_REF]; • a joint micro-scanning movement of the two photoreceptors, mimicking the retinal micro-movements observed in single ommatidia of the fly compound eye [START_REF] Franceschini | Repetitive scanning in the fly compound eye[END_REF]; • a temporal derivative of the photoreceptor output signals, similar to the high pass filtering function occurring in the first order neuron of the fly's compound eye [START_REF] Zettler | Neural principles in vision[END_REF], [START_REF] Juusola | Visual acuity for moving objects in firstand second-order neurons of the fly compound eye[END_REF].

The VODKA output signal results from the two photoreceptor signals being suitably processed to obtain the ratio between the difference and the sum of the differentiated photoreceptor signals.

S V ODKA = P h 1 Ψ(t) -P h 2 Ψ(t) P h 1 Ψ(t) + P h 2 Ψ(t) (6)
where Ψ(t) is the sum of the angular position Ψ c of the contrasting feature and the small vibration Ψ mod (t).

The derivative filter used here was a classical analog band-pass filter (H band-pass in Fig. 3), in which the high-pass filter section acts as the differentiator proper and the low-pass filter section reduces the high frequency noise and prevents the subsequent analog-to-digital conversion from undergoing any aliasing effects.

When the sensor is placed in front of an edge, developing the expression S V ODKA (6) yields a remarkably simplified expression, under the assumption that:

1) the amplitude of Ψ mod is very small (thus, Ψ mod ≈ 0 but Ψ mod = 0); [START_REF] Kerhuel | Capteurs optiques minimalistes et réflexes oculomoteurs biomimétiques ; application à la robotique aérienne[END_REF]. When a bar is encountered, there exists no obvious means of simplifying the expression of eq.( 6) (here ∆ϕ = 2.87 • and ∆ρ = 2 • ).

2) the temporal variations of Ψ c are much slower than those of Ψ mod (thus,

Ψ c ≈ 0 but Ψ c = 0).
Under these conditions, the derivatives of the two photoreceptors can be expressed as follows, using eq.( 1) and eq.( 2):

P h 1 Ψ(t) = k * π ln(2)Ψ (t) π∆ρ * e -4 ln(2) (Ψ(t)- ∆ϕ 2 ) 2 ∆ρ 2 P h 2 Ψ(t) = k * π ln(2)Ψ (t) π∆ρ * e -4 ln(2) (Ψ(t)+ ∆ϕ 2 ) 2 ∆ρ 2 (7)
Substituting ( 7) into (6) gives, after some rewriting:

S V ODKA = tanh Ψ c * 4 ln(2)∆ϕ ∆ρ 2 (8)
This remarkably simple expression gives the theoretical value of the VODKA sensor output as a function of the angular position Ψ c of an edge present in its FOV. The characteristic curve plotted in Fig. 4a is this hyperbolic tangent function, which is an even, monotonic function of the angular position Ψ c . The central part of the characteristic curve varies quasi linearly with the angular position Ψ c , which makes the sensor capable of locating the angular position of a contrasting edge with great accuracy.

When the sensor is placed in front of a contrasting bar, developing the expression S V ODKA [( 6) with the temporal derivative of (4)] does not simplify easily. However, the expression obtained is still an even function, as shown in Fig. 4b. It can be seen from this Figure that apart from the two "glitches " located at (±∆ϕ/2), the characteristic curve obtained in the case of a bar is fairly similar to that obtained in the case of an edge ( Fig. 4 a andb).

The two parameters ∆ρ and ∆ϕ as well as the angular amplitude A of the vibration and the width L of the bar all affect the sensor's responses. The effects of these parameters are studied in Section IV.

IV. PARAMETERS AFFECTING THE SENSOR'S OUTPUT

The two theoretical characteristic curves presented in Fig. 5 and in Fig. 6 were plotted from the equation ( 8) and [( 6) with ( 2 Fig. 5a presents the theoretical characteristic curve [obtained from [START_REF] Kerhuel | Capteurs optiques minimalistes et réflexes oculomoteurs biomimétiques ; application à la robotique aérienne[END_REF]] of the VODKA sensor in the case of a contrasting edge when ∆ρ varies from 1.43 • to 6 • . These values of ∆ρ correspond to a ratio ∆ρ/∆ϕ ranging from 0.5 to 2.09. This ratio is often used to characterize the optical properties of a compound eye [START_REF] Götz | Optomotorische Untersuchengen des visuellen Systems einiger Augnmuntanten der Fruchfliege Drosophila[END_REF]. Curves in Fig. 5a show that the lower the ratio ∆ρ/∆ϕ , the more accurate the sensor becomes, at the expense of the sensor's angular range. Fig. 5b presents the theoretical characteristic curve obtained from (6) of the VODKA sensor in the case of a bar when the same parameter ∆ρ varies in the same range as in Fig. 5a. Curves in Fig. 5b show that the sensor is capable of locating a bar only when the ratio ∆ρ/∆ϕ is smaller than 1. When ∆ρ/∆ϕ is greater than 1, the slope of the characteristic curve becomes negative in its central part. It is noteworthy that the characteristic curve for a bar is similar to that obtained for an edge when ∆ρ/∆ϕ = 0.5, showing that the sensor can locate a bar as well as an edge, provided the optical parameters are chosen appropriately. Fig. 6a shows the effects of changes in the amplitude A of the vibration on the theoretical characteristic curve (8) presented in Fig. 4a. The theoretical result of equation ( 8) does not depend on the amplitude A. However, the effect of A was determined by considering the averaging effect of the lowpass filter placed after the absolute value function (see Fig. 3). Therefore, in the case of a triangular (linear) periodic scanning law applied to the retina, the average over one temporal period (noted T Ψ ) is: 10), plotted in Fig. 6a, shows the influence of the scanning amplitude A on the characteristic curve of the VODKA sensor. It is worth noting that when the scanning amplitude A tends to be small or null, equation [START_REF] Krotkov | Visual hyperacuity: Representation and computation of high precision position information[END_REF] tends to be equal to equation [START_REF] Kerhuel | Capteurs optiques minimalistes et réflexes oculomoteurs biomimétiques ; application à la robotique aérienne[END_REF]. Fig. 6a shows that in the case of a very small amplitude A (A = 0.3 • , which is about 10 times smaller than the interreceptor angle ∆ϕ) the theoretical characteristic curve nearly matches the theoretical tanh (8) curve.

P h 1 -P h 2 P h 1 + P h 2 = TΨ 0 1 T Ψ tanh Ψ(t) * 4 ln(2)∆ϕ ∆ρ 2 dt = 1 2A A -A tanh (Ψ c (t) + x) * 4
Fig. 6b shows the effect of a change in the angle L subtended by the bar on the predicted characteristic curve obtained from equations ( 6) and (4). Interestingly, the change in L has similar effects on the linearity of the characteristic curve to those observed in Fig. 5b, where only the ratio ∆ρ/∆ϕ varied.

To summarize, several parameters liable to affect the characteristics of the sensor output were modeled and characterized for a contrasting edge (see Fig. 5a and6a) and for a bar (see Fig. 5b and6b). Therefore, to obtain a suitable characteristic curve, both the ratio ∆ρ/∆ϕ and the scanning amplitude A can be selected and set accurately. The effect of a few other parameters was studied in [START_REF] Kerhuel | Capteurs optiques minimalistes et réflexes oculomoteurs biomimétiques ; application à la robotique aérienne[END_REF].

V. NOTEWORTHY FEATURES OF THE VODKA SENSOR A. Robustness to Lighting Conditions

The temporal derivation, which is part of the frontend bandpass filter (see Fig. 3) amplifies high frequencies and removes the DC component from each photoreceptor output signal. Very large AC signal gain amplification can be obtained since the DC value is filtered out. These filtering and amplification steps in the signal processing make the VODKA sensor relatively robust to the lighting conditions (affecting the DC value) at this early stage in the signal processing.

B. Robustness to Contrast Value and Contrast Polarity

It is the absolute value of signals P h 1 and P h 2 that is used in equation ( 6). The sensor is therefore robust to the polarity of the contrasting feature encountered (an edge or a bar), that is, it will respond equally to a white-to-dark or a dark-to-white target.

By calculating the relative difference [with expression [START_REF] Altes | Ubiquity of hyperacuity[END_REF]], the influence of contrast [modeled by the factor k in equations ( 2) and ( 4)] can be removed. However, this is a theoretical result, and the experimental data obtained with the sensor we implemented show a minimum detectable contrast (11) of about 5%.

C. Robustness to Vibration Types

Joint vibration of the two optical axes affects the signals delivered by both photoreceptors. From the amplitude of these signals, the angular position Ψ c of a contrasting target lying in VODKA's visual field is obtained. From equation ( 8), it can be seen that the vibration frequency has no influence on the ability of the sensor to locate the target. Consequently, not only periodic signals such as sine waves but also random patterns of vibration can be used. For example, the "natural" undesirable vibration produced by the sensor's mechanical support (e.g., a robotic platform) can be exploited to drive the VODKA sensor's visual processing system, as described in part VI-B.

According to the VODKA principle described in section III, a vibration pattern of some kind is a prerequisite to obtain hyperacuity, even though the type of vibration has no effect on the predicted sensor output. Taking the case of the low pass filter in the digital demodulation scheme (see Fig. 3), for example, the best results will be obtained with relatively high frequency and low amplitude vibrations [because the derivative of the high frequency in (7) counteracts the low vibration amplitude].

VI. EXPERIMENTAL RESULTS

In the first experiment (Fig. 8), the sensor with its vibrating retina was kept stationary in front of a contrasting edge that was set into slow translation (see Fig. 7). In the second experiment (Fig. 9), the VODKA sensor was mounted onboard the 100g OSCAR 2 aerial robot [START_REF] Kerhuel | Steering by gazing: An efficient biomimetic control strategy for visually guided micro aerial vehicles[END_REF], which is able to rotate freely in yaw. Here, the natural vibrations produced by the robot itself (vibrations generated by the two propellers) were exploited by the VODKA sensor and used to control the robot's yaw orientation. Illuminance was varied (from 118 Lux to 5 Lux) to test the robustness of the sensor to dimly lit environments.

In these two experiments, the digital filters H peak and H low-pass (Fig. 3) were suitably tuned to meet the requirements of the experimental situation: the VODKA principle can be adapted to work in various situations and to achieve various objectives. Fig. 7. CAD of the experimental setup. The aerial robot (OSCAR 2, see Fig. 1) is placed 1.1m ahead of a vertical edge that is set in horizontal motion in micro-steps of 62µm. In the first experiment (section VI-A), the robot's propellers were switched off (i.e., the robot was stationary) and the VODKA sensor's retina was vibrated at a high frequency (fa = 40Hz) by means of the piezo-bender (see Fig. 2 and3). The output of the VODKA sensor was monitored via a BlueTooth connection, while the contrasting edge was slowly translated (hence modifying the angle Ψc). In the second experiment (section VI-B), the robot's propellers were switched on and the piezo driver was switched off. The VODKA sensor used the robot's natural vibrations. Mounted on the axis of a frictionless resolver, the robot was free to rotate about its yaw axis and tracked the contrasting edge accurately on the basis of what it saw. (adapted from [START_REF] Kerhuel | Steering by gazing: An efficient biomimetic control strategy for visually guided micro aerial vehicles[END_REF]. Fig. 7 shows the test bench used in the two experiments. The contrasting edge used here had a high contrast: m = 0.85, based on the Michelson contrast definition:

m = I 1 -I 2 I 1 + I 2 ( 11
)
where the light intensities I 1 and I 2 are the higher and lower luminances measured on the two surfaces, respectivly (I 1 and I 2 measured with a similar photoreceptor to the VODKA photoreceptors).

The digital fixed point processing of the VODKA sensor was implemented in a 16-bit microcontroller (dsPIC30f4013) running at 20 MIPS. It requires only a very small part (3.3%) of the available calculation resources. Program code was generated with a simulink Real time Workshop embedded target and the custom made dsPIC blockset [START_REF] Kerhuel | dspic blockset for simulink[END_REF].

A. VODKA: a Hyperacute Visual Sensor Fig. 8 shows the sensor's output when a contrasting edge (contrast m = 0.85) placed 1.1 meter ahead was slowly moved along the bench.

In this experiment, the robot was stationary and the two optical axes were vibrated in concert via the piezo-bender set in the eye tube, as depicted in Fig. 2. The input signal to the piezo-bender was a sine wave with a frequency of 40Hz and an amplitude A = 0.2 • (creating thus the angular vibration noted Ψ mod ). Each translational micro-step displacement of the target was equivalent to a rotational microstep of 0.0032 • in the angular position Ψ c of the edge. As predicted in section III [( 6) and Fig. 4a, Fig. 5a, Fig. 6a], the experimental characteristic curve in Fig. 8 was a hyperbolic tangent function of the angular position Ψ c . The inset in Fig. 8 illustrates the remarkable property of hypercuity with which the VODKA sensor is endowed, since each micro step displacement (0.0032 • ) led to a noticeable change in the response of the sensor as detailed below. Since the static resolution of the sensor is determined by the interreceptor angle (∆ϕ = 2.87 • ), the retinal micro-scanning process can be said to enhance the resolution in the task of locating an edge by an outstandingly high factor of 2.87/0.0032 = 897.

Let us compute a few statistics on the 21 consecutive sensor output values (corresponding to the 21 dots traced at each target position on Fig. 8, and in the inset of Fig. 8). The target displacement from the angular position -1 • to +1 • is done through 615 micro-step offsets. Within theses 615 positions, the mean of the intra-step standard deviation is σ Svodka = 0.922 * 10 -3 and the mean of the interquartile range is IQR Svodka = 0.817 * 10 -3 . The sensor's output S vodka increases quasi linearly from -0.8 at -1 • to 0.8 at 1 • . Consequently, the mean inter-step distance is ∆ Svodka = 2.6 * 10 -3 that is about three times the standard deviation of intra-step measurement. Thus, each of theses 615 angular positions can be resolved from the VODKA sensor output.

To achieve such a highly accurate target angular detection performance, the various filters involved in the visual processing system (see Fig. 3) were tuned with the following parameters:

The transfer function H band-pass of the analog band-pass filter (detailed in [START_REF] Kerhuel | Capteurs optiques minimalistes et réflexes oculomoteurs biomimétiques ; application à la robotique aérienne[END_REF]) is given by:

H band-pass = 30 * 50 * 2π s + 50 * 2π * s s + 50 * 2π (12)
The transfer function H P eak of the digital peak filter (peak frequency f a = 40Hz, sampling frequency 500Hz) is given by: Lastly, the transfer function of the digital second order low-pass filter H low-pass (cut-off frequency 5Hz, sampling frequency 500Hz) is given by:

H P eak = 0.036 * z 2 -1 z 2 -1.68z + 0.93 (13)
H low-pass = 9.447 * 10 -4 (z + 1) 2 z 2 -1.911z + 0.915 (14)

B. Pursuit of a Moving Target Using the Robot's Own Vibrations

The results presented in Fig. 9 show the tracking performance of which the VODKA sensor is capable, using only the vibrations naturally generated by its own two propellers. The frequencies of these vibrations are visible on the rate gyro spectrogram (curve d), and on the spectrogram obtained with one photoreceptor derivative (curve c). The piezo-bender shown in Fig. 2 was not activated here and the retina therefore remained stationary behind its lens. This experiment first confirms the accuracy of the sensor and its robustness to a relatively wide range of lighting conditions (curve a), from DC lighting (switched to various illuminances) to fluorescent lighting [which causes strong 100-Hz interferences in each photoreceptor signal (as attested by curve b, from 97s to 120s)]. The robot's yaw angular orientation was monitored accurately by the miniature resolver endowed with neglegible friction (Fig. 1). The robot's yaw control depended only on the output signal yielded by the embedded VODKA sensor. The rotational speed of each propeller was driven differentially by a feedback control loop based on the VODKA sensor's output signal (f:red curve) and involving some state-space controler detailed in [START_REF] Kerhuel | Steering by gazing: An efficient biomimetic control strategy for visually guided micro aerial vehicles[END_REF].

The edge was moved sinusoidally in front of the robot [the black curve in (e) shows the azimuthal orientation of the target]. The robot can be seen to have followed the target faithfully (e). The standard deviation of the robot's orientation error signal (f:black curve) turned out to be only σ = 0.15 • . This value [approximately 20-fold smaller than the static resolution of the robot's eye (2.87 • )] is very small, especially if one takes into account the additional error introduced by the control process of the aerial robot itself (the 100g robot attained its steady yaw rate with a time constant of 306ms in response to a differential open loop step command over its two propellers). The result of this experiment therefore confirms that the VODKA principle can be implemented to meet various requirements in terms of accuracy and dynamics as a means of controlling an aerial robot effectively and safely.

The filters present in the visual processing scheme described in Fig. 3 were adapted to be able to meet the dynamic and precision requirements using random vibrations.

The transfer function H band-pass was not changed and is therefore given by equation [START_REF] Brückner | Artificial compound eye applying hyperacuity[END_REF].

The transfer function H P eak in equation ( 13) is not appropriate because the visual signal is not modulated periodically at 40Hz. The H P eak filter was therefore replaced by a comb filter of order 10 with a quality factor Q = 10 running at 500Hz that removes both the DC part of the signal and the 50Hz with all its harmonics created by the neon lighting. The H Comb transfer function replaces the H P eak transfer function:

H Comb = 0.7729 * z 10 -1 z 10 -0.5459 (15)
The remaining signals are then mostly due to the vibration of the optical axes.

The cut-off frequency of the transfer function H low-pass was increased to 10Hz so as to increase the dynamic response of the sensor. The new transfer function (sampling frequency of 500Hz) is:

H low-pass = 3.622 * 10 -3 * (z + 1) 2 z 2 -1.823z + 0.8372 (16)

VII. CONCLUSION

The VODKA sensor is a highly accurate optical Position Sensing Device (PSD). VODKA is able to determine the angular position of a naturally lit target by extracting and processing the low amplitude and high frequency signals transmitted by two jointly vibrating photoreceptors. Even in its elementary form described here (only two pixels), the VODKA sensor was found to be capable of locating the angular position of an edge with a far better (900-fold better) resolution than that anticipated from the static resolution (as determined on the basis of the interreceptor angle ∆ϕ) regardless of the scanning law and scanning frequenc. The tremendous hyperacuity factor achieved by this two-pixelretina results from (i) the micro-vibration of the retina behind the lens and (ii) the specific signal processing of the visual signals. The evenness of the characteristic curve obtained (Fig. 8) shows that the sensor is a good candidate for being integrated into visuomotor control loops -in the context of micro aerial vehicle stabilization and tracking, for example. In another biomimetic approach, Lichtsteiner et al. built a CMOS vision sensor [START_REF] Lichtsteiner | A 128 x 128 120db 30mw asynchronous vision sensor that responds to relative intensity change[END_REF] encoding the pixel intensity changes. This asynchronous CMOS imager was incorporated into an original demonstrator, in terms of a fast visual feedback control loop that was able to balance a pencil [START_REF] Conradt | A pencil balancing robot using a pair of AER dynamic vision sensors[END_REF] with a latency smaller than 2ms. Despite this small latency, the accuracy of the visual servo-loop was strongly dependent on the imager resolution (128x128 pixels). In future developments of the VODKA sensor, an increase in the scanning frequency should likely overcome the trade-off existing between accuracy and refresh rate. In any case, the hyperacuity achieved by the VODKA sensor in locating an edge does not rely on using an array or a matrix of photoreceptors, and it is obtained already when using just two photodiodes.

All in all, the VODKA sensor is an Position Sensing Device (PSD) featuring the following remarkable properties:

1) It is able to locate a contrasting edge with an outstanding precision (ca 900-fold hyperacuity factor). 2) It responds to naturally lit objects.

3) It is insensitive to contrast polarity (ON edges or OFF edges). 4) It is largely insensitive to contrast intensity (down to about 5% [START_REF] Kerhuel | Capteurs optiques minimalistes et réflexes oculomoteurs biomimétiques ; application à la robotique aérienne[END_REF]). 5) It responds in the presence of interferences (e.g. 100Hz or 120Hz caused by artificial lighting: Fig. 9). 6) It responds within a relatively large range of illuminance (factor 20: Fig. 9) despite its nonadaptive photoreceptors. 7) It features a low response latency (35ms at the vibration frequency tested, f a = 40Hz [START_REF] Kerhuel | Capteurs optiques minimalistes et réflexes oculomoteurs biomimétiques ; application à la robotique aérienne[END_REF]). 8) It is low weight, powerlean and simple to implement. 9) It can be organized in arrays of similar sensors to build an imager with outstanding positioning accuracy within a large FOV [START_REF] Kerhuel | Method and device for measuring the angular position of a rectilinear contrasting edge of an object, and system for fixing and tracking a target comprising at least one such contrasting edge[END_REF]. 10) The parallel architecture of such a sensor array is appropriate for analog VLSI implementation, all the more since the elementary processing requires only nextneighbor interactions.

The basic principles described here are still applicable in the case of random vibrations of the eye, such as vibrations produced by the propellers of an aircraft. We have shown an example of the highly accurate heading and tracking ability of a miniature aerial robot equiped with a VODKA sensor exploiting the uncontrolled, random vibrations generated by the propellers. This unique property makes the sensor much simpler to construct since it can do without any embedded microscanners. Although the VODKA principle can cope with natural vibrations, it remains that imposing specific vibrations upon the retina by means of a dedicated micro-actuator (piezobender, electromagnetic actuators, etc. . . ) yields better performance because the signal processing steps can be finely tuned to the (known) scan frequency, allowing the modulated visual output signals to be extracted with a better signal-to-noise ratio. Since the VODKA sensor shares the same processing front end (the band-pass filter) as our optic flow sensors [START_REF] Blanès | Appareil visuel élémentaire pour la navigation à vue d'un robot mobile autonome[END_REF]- [START_REF] Viollet | Performances of three miniature bio-inspired optic flow sensors under natural conditions[END_REF], it is possible to obtain dual optical position and optic flow sensors sharing the same FOV, and the same (optical and electronical) frontend hardware. [START_REF] Kerhuel | Capteurs optiques minimalistes et réflexes oculomoteurs biomimétiques ; application à la robotique aérienne[END_REF], [START_REF] Kerhuel | Method and device for measuring the angular position of a rectilinear contrasting edge of an object, and system for fixing and tracking a target comprising at least one such contrasting edge[END_REF], [START_REF] Kerhuel | Method and device for measuring the angular velocity of a luminance transition zone and steering aid system for fixation and tracking a target comprising at least one such luminance transition zone[END_REF].

On the one hand, the simplicity, parallel architecture and small size of the VODKA hyperacute position sensing device make it appropriate for applications in the fields of metrology, robotics, astronomy, automotive and aerospace engineering. All the more so than one may extend the VODKA principle to a large imager, whose resolution will be enhanced across its whole FOV without the cost of large memory resources [START_REF] Kerhuel | Method and device for measuring the angular position of a rectilinear contrasting edge of an object, and system for fixing and tracking a target comprising at least one such contrasting edge[END_REF]. On the other hand, the hyperacuity achieved in the VODKA sensor may shed new light on the principles underlying miniature eye movements (tremor) that have been described in both vertebrates' camera eyes and arthropods' compound eyes.

Fig. 1 .

 1 Fig. 1.OSCAR 2 robot equipped with the hyperacute VODKA sensor. The 100-gram aerial robot, which is usually suspended from the ceiling with a long 100µm nylon wire[START_REF] Kerhuel | A sighted aerial robot with fast gaze and heading stabilization[END_REF]-[START_REF] Kerhuel | Steering by gazing: An efficient biomimetic control strategy for visually guided micro aerial vehicles[END_REF] controls its yaw on the basis of what it sees. Here it was mounted on the axis of a frictionless resolver that allowed its heading to be accurately monitored. The twin-engine robot orients itself by driving its two propellers differentially. The inset shows the robot's retina (after the lens has been removed), which can be subjected to repetitive microtranslations at a frequency of 40Hz by means of a piezo-bender (see Fig.2). VODKA's retina is composed of an Ic-Haus LS2C package comprising 6 vertically elongated photoreceptors with integrated amplifiers. The VODKA vibrating sensor actually uses only the two central photoreceptors (2 pixels, as sketched in Fig.2).

Fig. 2 .

 2 Fig. 2. CAD and sketch diagram of the VODKA sensor. The two photoreceptors are moved back and forth by a piezo-bender located inside the vertical eye tube, making their optical axes jointly scan a fraction of a degree of the environment. The VODKA sensor's output is simply the relative difference between the two filtered photoreceptor signals P h 1 and P h 2 .

Fig. 3 .

 3 Fig. 3. Sketch diagram of the VODKA sensor. The left part shows the Gaussian angular sensitivity of each of the two photoreceptors placed in front of a contrasting edge. Mechanical vibration is applied to the two photoreceptors, causing their optical axes to rotate jointly. A band-pass filter acting as a pseudo derivative filter extracts the signals generated in each photoreceptor by the relatively high frequency vibration (fa = 40Hz). An optional peak filter removes all frequencies not associated with the vibration. A demodulator extracts the envelope of the signal. The relative difference between the two signals is computed as (P h 1 -P h 2 )/(P h 1 + P h 2 ) to yield the VODKA sensor output.

( a )Fig. 4 .

 a4 Fig. 4. Theoretical characteristic curve of the VODKA sensor. When an edge is encountered (a), a tanh function is obtained[START_REF] Kerhuel | Capteurs optiques minimalistes et réflexes oculomoteurs biomimétiques ; application à la robotique aérienne[END_REF]. When a bar is encountered, there exists no obvious means of simplifying the expression of eq.(6) (here ∆ϕ = 2.87 • and ∆ρ = 2 • ).

  Fig. 5. Effects of the optical parameters ∆ρ on the ability to locate an edge (a) and a bar (b)

  )] by taking the interreceptor angle ∆ϕ = 2.87 • , and the angle subtended by the bar to be L = 0.25 • . These two Figures show the effects of a change in the ration ∆ϕ/∆ρ, (a) Effects of the vibration amplitude A on the theoretical characteristic curve in the case of an edge. (b) Effects of the bar's angular width on the characteristic curve.

Fig. 6 .

 6 Fig. 6. Effects of various parameters on the theoretical characteristic curve.

  ln(2)∆ϕ ∆ρ 2 dx (9) After developing and simplifying these expressions, (9) becomes: ∆ρ 2 2A * 4 ln(2)∆ϕ *   ln cosh 4 ln(2)∆ϕ ∆ρ 2 * (Ψ c (t) + A) cosh 4 ln(2)∆ϕ ∆ρ 2 * (Ψ c (t) -A)

Fig. 8 .

 8 Fig. 8. Experimentally determined characteristic curve of the implemented VODKA sensor. Relative sensor output as a function of the angular position Ψc of an edge (contrast m = 0.85) placed 1.1m ahead, at an illuminance of approximatly 120 lux. The edge was displaced slowly via a stepper motor in micro steps of 62µm, corresponding to an angular shift of only 0.0032 • (Fig. 7). In this Figure, 21 consecutive sensor outputs were measured and plotted for each step position. The experimental curves fit the theoretical hyperbolic tangent function of the contrast position Ψc [(8), Fig.4a]. The thinness of the resulting curve shows the high resolution obtained. The lower right inset gives a highly magnified picture of the central part of the characteristic curve within an angular range of only ±0.02 • . The parameters used here were ∆ϕ = 2.87 • , ∆ρ = 3 • , scan shape: sine wave, scan frequency: fa = 40Hz, scan amplitude: A = 0.2 • .

Fig. 9 .

 9 Fig.9. Smooth pursuit of a contrasting edge (contrast m = 0.85) set in sinusoidal motion in front of the tethered OSCAR 2 robot (Fig.1 & 7) equipped with the VODKA sensor (see Fig.2 & 3). Here, the piezo-bender (on Fig.2) is inactive and the VODKA sensor makes use of the natural random vibrations caused by the two robot propellers. Curve (a) shows that the DC light intensity was decreased about twenty-fold (from 118 Lux to 6 Lux) and finally switched to Neon room lighting (after 97s). Curve (b) shows the two photoreceptors' derivatives P h 1 and P h 2 , and curve (c) shows the spectrogram of P h 1 . Curve (d) shows the spectrogram of an embedded rate gyro measuring the yaw rate. It can be seen from the spectrograms in (c) and (d) that the robot's vibrations affect the photoreceptor signal at the typical frequencies (16Hz, 125Hz, 150Hz and 210Hz) observable in the robot's own yaw spectrogram (d). The curves in (e) show the angular position of the translating edge (in red), and the angular orientation of the OSCAR robot (in black), respectively. At all times, the robot realigns itself towards the edge accurately, based on the VODKA sensor output. These two curves are remarkably well superimposed despite the illuminance changes. Curves (f) show (in a magnified form) the angular tracking error (in black), which is the difference between the two curves in (e), and the VODKA visual sensor's output (in red), which controls the robot's yaw orientation. This experiment confirms the ability of theVODKA sensor to make use of natural vibrations and shows that it is relatively robust to the lighting conditions. The VODKA output signal itself (f, red curve) is hardly affected at all by the dimming of the DC light or by the presence of artificial light, although the latter causes major interferences in the photoreceptors' derivatives [curve (b), from 97s to 120s].

ACKNOWLEDGMENT

The authors acknowledge the assistance of M. Boyron in designing and producing the miniature electronic boards used here, including the piezo driver. They also thank Y. Luparini for his help with the mechanical construction of the robot. We thank J. Blanc for revising the English manuscript. This work was supported by the CNRS, the University of the Mediterranean, the French National Research Agency (ANR with the RETINAE and EVA projects) and the European Union (Future and Emerging Technologies, Seventh Framework Programme for Research of the European Commission, FET-Open grant number: 237940 (CURVACE project).

His research interests cover neural information processing, vision, eye movements and retinal micromovements, micro-optics, neuromorphic circuits, sensory-motor control systems, and their potential applications to micro-air-and space-vehicles. He received several national and international awards in both Neuroscience and Engineering, and is a member of the Academia Europaea.


L N Van Steenbergen

L V Van De Poll-Franse

Mwjm W J M Wouters

Mlea Jansen-Landheer

Jww W W Coebergh

H Struikmans

Vcg C G Tjan-Heijnen

Cjh J H Van De Velde

Variation in management of early breast cancer in the Netherlands, 2003-2006

Keywords: early breast cancer, breast conserving surgery, axillary lymph node dissection, sentinel lymph node procedure, adjuvant systemic therapy

published or not. The documents may come

Introduction

Breast cancer is the most frequent cancer in females in the Netherlands, with a lifetime risk of 12-13% 1 . Early detection, mainly due to population-based screening, and adjuvant treatment resulted in an improved survival of patients with breast cancer and lower mortality since the mid 1990s. Breast cancer staging and treatment is evolving and, therefore, clinical practice guidelines were developed since 1999, coming into practice in 2002 2 .

Oncological care for breast cancer is rapidly changing through surgical, pharmacological and technological innovations, thereby also becoming increasingly subspecialized. Quality increasingly becomes measurable, being considered as vital for both patients and doctors and, last but not least for health insurance companies. Important aspects are thought to be volume [START_REF] Van Lanschot | Hospital volume and hospital mortality for esophagectomy[END_REF][START_REF] Wouters | High-volume versus low-volume for esophageal resections for cancer: the essential role of case-mix adjustments based on clinical data[END_REF][START_REF] Begg | Impact of hospital volume on operative mortality for major cancer surgery[END_REF][START_REF] Finlayson | Hospital volume and operative mortality in cancer surgery: a national study[END_REF][START_REF] Roohan | Hospital volume differences and five-year survival from breast cancer[END_REF][START_REF] Bilimoria | Directing surgical quality improvement initiatives: comparison of perioperative mortality and long-term survival for cancer surgery[END_REF] and type of hospital [START_REF] Cheung | Impact of teaching facility status and high-volume centers on outcomes for lung cancer resection: an examination of 13,469 surgical patients[END_REF][START_REF] Chaudhry | Breast cancer survival by teaching status of the initial treating hospital[END_REF] , depending on the type of cancer, population density, and prosperity of region or country.

According to the Dutch clinical practice guidelines of 2002, patients with early stage (T1T2M0) breast cancer are generally eligible for breast conserving surgery (BCS), unless they are of young age or prefer otherwise. Patients who undergo BCS should receive adjuvant radiotherapy at any age 2 . The sentinel lymph node procedure (SNP) is advised in patients with a clinically node-negative breast tumour, while a primary axillary lymph node dissection (ALND) is advised in all other patients. 2 Adjuvant chemotherapy, HER2-targeted therapy and hormone therapy have proven to be effective in preventing or delaying relapses and increasing survival in patients with early stage or locally advanced breast cancer. [START_REF]Effects of chemotherapy and hormonal therapy for early breast cancer on recurrence and 15year survival: an overview of the randomised trials[END_REF][START_REF] Giordano | Use and outcomes of adjuvant chemotherapy in older women with breast cancer[END_REF] Therefore, patients with a node-positive tumour or a node-negative tumour with unfavourable characteristics should receive adjuvant systemic treatment. 2

Methods

Data collection

We used the population-based database from the Netherlands Cancer Registry (NCR), which started in 1989 and is maintained and hosted by the Comprehensive Cancer Centres (CCCs). 1 The NCR is based on notification of all newly diagnosed malignancies in the Netherlands by the national automated pathological archive (PALGA) that covers 70 laboratories. Additional sources are the national registry of hospital discharge data, which accounts for up to 8% of new cases, [START_REF] Visser | Incidence of cancer in the Netherlands 1999/2000[END_REF] and regional radiotherapy institutes. Information on patient characteristics like date of birth, and tumour characteristics such as date of diagnosis, histology, stage (Tumour Lymph Node Metastasis (TNM) classification), [START_REF]UICC. TNM Classification of Malignant Tumours[END_REF] grade, and primary treatment as well as staging procedures, are obtained routinely by data registration clerks from the cancer registry from the medical records about nine months after diagnosis. [START_REF] Visser | Incidence of cancer in the Netherlands 1999/2000[END_REF] The quality of the data is high due to thorough training of the data managers and a variety of computerized consistency checks at regional and national level. Completeness is generally estimated to be at least 95% for all tumours but higher for breast cancer due to its high level of histological verification. [START_REF] Schouten | Completeness of cancer registration in Limburg, The Netherlands[END_REF] For the current analysis, hospital characteristics including type and volume were retrieved from Prismant, an organisation which collects objective data about hospitals for e.g. quality of care assessment. 16 Presence of the 21 institutes of radiotherapy was known through the Comprehensive Cancer Centres.

Patients

For the present study, all female cases with primary invasive primary breast cancer (ICD-0:

Statistical analyses

Patient, tumour, and hospital of staging and treatment characteristics as well as region were described in relation to received treatment. Surgical and radiotherapy treatment were analysed according to stage. Multivariable logistic regression analysis was performed stratified by age (<40 years, 40-69 years, and ≥70 years) to examine the influence of hospital type and volume on the possibility to receive BCS with adjustments for the presence of radiotherapy in a hospital, region, and year of diagnosis. Since there was significant interaction between type and volume of a hospital, these variables were merged into one variable of both type and volume of a hospital. Similarly, multivariable logistic regression analysis was performed to examine determinants of ALND, which was also done for the application of adjuvant systemic treatment. In this analysis the independent effect of hospital type and volume were analysed separately, since no interaction was found between these factors in relation to adjuvant systemic therapy and then stratified by age (<55 and ≥55 years). Variation in utilization of ALND and adjuvant systemic treatment was displayed as scatter plots with the average number of breast cancer patients per hospital on the X-axis and of ALNDs or adjuvant systemic treatment on the Y-axis. Hospital type was classified through symbols in the scatter plot. All analyses were done in SAS (version 9.1, SAS Institute, Cary, NC). 95% Confidence intervals were estimated and a p-value of 0.05 was considered statistically significant.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

14.06.2010 6

Results

In 2003, 12 460 women were diagnosed with primary invasive breast cancer in the Netherlands, which gradually increased to 13 280 in 2006, an increase of 7% in four years.

Over 40% of patients were treated in a large teaching hospital, 33% in a small general hospital, and only 8% in an academic hospital (Table 1). No change in stage distribution was seen over time in the period 2003-2006 (data not shown).

Surgery

Most patients underwent BCS with radiotherapy, although this depended on the stage of disease, being 63% of patients with stage I disease, 41% in stage II, and 19% in stage III.

Almost all patients who underwent BCS received radiotherapy. Mastectomy was the treatment of choice in 51% of patients with stage II disease and in 69% with stage III (Figure 1). Application of BCS in patients with T1T2 N0 disease varied from 30% to 82% among hospitals (data not shown). Patients aged <40 years were more likely to receive BCS in a general (nonteaching) hospital, whereas patients of ≥70 years less often received BCS in a small general or teaching hospital. Patients aged 40-69 years less often received BCS in a small hospital (Table 2a). After adjustments similar results were found, although patients aged 40-69 years were less likely to receive BCS in academic centres. The presence of radiotherapy in an -often largerhospital positively affected the chance for BCS in patients 40-69 years. Over time, more patients underwent BCS compared to mastectomy, especially in older women, but with substantial variation between geographic regions in the Netherlands (Table 2b). When considering type of hospital alone, patients <40 years were more likely to receive BCS (OR 1.3 (95% CI 1.1-1.5)), contrasting patients ≥70 years (OR 0.9 (95% CI 0.8-0.9)) when treated in a general hospital compared with a teaching hospital. Academic hospitals were not different from teaching hospitals with regard to choice of BCS for patients aged <40 years or ≥70 years.

However, patients of 40-69 years treated in academic hospitals were less likely to receive BCS (OR 0.9 (95% CI 0.8-1.0)) compared with teaching hospitals.

Axillary lymph node dissection

After a start at larger scale in 1998, the sentinel lymph node procedure (SNP) was applied in 2003 in 59% of T1T2 N0 breast cancer patients, which became 78% in 2006. Consequently, primary ALND decreased over time from 22% in 2003 to 11% in 2006. Patients with T1T2 N0 disease more often received primary ALND in a general hospital, followed by the teaching and the academic hospitals. Older age (≥70 years) and clinical T2 stage were positively associated with application of ALND, clearly decreasing over time. There still was large but declining variation in ALND among regions (Table 3). T1T2 N0 patients treated in a general hospital were more likely to receive ALND (OR 1.4 (95% CI 1.3-1.5)), but less in an academic hospital (OR 0.9 (95% CI 0.8-1.0)), compared to a teaching hospital. ALND in N0 patients varied from 5% to 70% between hospitals, the proportions being higher in a general or low volume hospital than in a teaching or academic hospital (Figure 2).

Adjuvant systemic treatment

Multivariable logistic regression analyses showed that hospital factors including type and volume as well as the presence of radiotherapy in a hospital did not affect the odds of receiving adjuvant systemic therapy in T1T2 N0 patients. This decreased sharply with the rise of age, but was higher for patients with a T2 tumour or a poor differentiation grade, and also over time (Table 4). Application of adjuvant systemic treatment in T1T2 N0 breast cancer patients ranged from 20% to 45% between hospitals, being larger in low volume hospitals (Figure 3).

Discussion

In this nationwide study we have shown that breast cancer, as a very common tumour with generally accepted treatment guidelines since 2002, still exhibited considerable variation in staging and treatment across the Netherlands in the various hospitals, regardless of hospital size. Significantly more patients <40 years underwent BCS in general hospitals compared to teaching and academic hospitals, whereas women aged 40-69 years less often received BCS in an academic hospital versus teaching hospitals. Moreover, too many patients with clinically node-negative T1T2 disease diagnosed in general hospitals still received primary ALND, in the absence of a SNP compared to teaching and academic hospitals. However, almost all patients undergoing BCS received radiotherapy. The prescription of adjuvant systemic therapy did not depend on hospital type, but there was no specification according to regimen. Differences in surgical breast treatment and lymph node staging were still seen between geographic regions, but decreased over time.

Surgical breast treatment

According to the first national, Dutch clinical practice guidelines of 2002 patients with early stage breast cancer are generally eligible for BCS. There are exceptions besides the size of the tumour in relation to the size of the breast, because higher local recurrence rates have been reported in patients aged <40 years compared to those >60 years. [START_REF] Arriagada | Late local recurrences in a randomised trial comparing conservative treatment with total mastectomy in early breast cancer patients[END_REF][START_REF] Voogd | Differences in risk factors for local and distant recurrence after breast-conserving therapy or mastectomy for stage I and II breast cancer: pooled results of two large European randomized trials[END_REF] But the preference of the treating surgeon and the wish of the patient are of major importance. We found that hospital type and volume as well as region were important determinants of BCS in each age group, as also found in a French randomized trial. [START_REF] Collins | Can women with early-stage breast cancer make an informed decision for mastectomy?[END_REF] In the US, the mastectomy rate has been rising again since 2003, especially in younger patients. [START_REF] Katipamula | Trends in mastectomy rates at the Mayo Clinic Rochester: effect of surgical year and preoperative magnetic resonance imaging[END_REF][START_REF] Mcguire | Are mastectomies on the rise? A 13-year trend analysis of the selection of mastectomy versus breast conservation therapy in 5865 patients[END_REF] This trend is not yet observed in the Netherlands, although patients of 40-69 years received less often BCS in academic centres than in general and teaching hospitals. This might indicate the start of a change towards an increasing mastectomy rate, also in younger women.

Lymph node analysis

Lymph node analysis is of critical importance for adequate staging of patients with early breast cancer. Since the introduction of ALND has been the standard of care for axillary lymph node staging, until long-term complications of this procedure appeared to be relatively common [START_REF] Ververs | Risk, severity and predictors of physical and psychological morbidity after axillary lymph node dissection for breast cancer[END_REF][START_REF] Voogd | Lymphoedema and reduced shoulder function as indicators of quality of life after axillary lymph node dissection for invasive breast cancer[END_REF] without conferring a gain in life-expectancy. In 1996, the SNP was introduced in a few hospitals in the Netherlands with supposedly similar staging capacities [START_REF] Roumen | Lymphoscintigraphy and feasibility of sentinel node biopsy in 83 patients with primary breast cancer[END_REF][START_REF] Ho | Implementation of sentinel node biopsy in breast cancer patients in the Netherlands[END_REF][START_REF] Veronesi | Sentinel-node biopsy to avoid axillary dissection in breast cancer with clinically negative lymph-nodes[END_REF][START_REF] Cox | Lymphatic mapping and sentinel lymph node biopsy in patients with breast cancer[END_REF] but with markedly lower morbidity. [START_REF] Schijven | Comparison of morbidity between axillary lymph node dissection and sentinel node biopsy[END_REF]

Adjuvant systemic treatment

Adjuvant chemotherapy, hormonal therapy and trastuzumab have increasingly been proven to be effective in preventing or delaying relapses and increasing survival in patients with early stage breast cancer, also at older age. [START_REF]Effects of chemotherapy and hormonal therapy for early breast cancer on recurrence and 15year survival: an overview of the randomised trials[END_REF][START_REF] Giordano | Use and outcomes of adjuvant chemotherapy in older women with breast cancer[END_REF] Therefore, these therapies have become part of the treatment plan for many of these patients. Guidelines for adjuvant systemic treatment have evolved over time and strategies have become more tumour and patient-specific than ever before. 2, [START_REF] Aebi | Treatment of premenopausal women with early breast cancer: old challenges and new opportunities[END_REF] The rising trend in the use of adjuvant systemic treatment of breast cancer patients was described earlier in southern Netherlands and the US. [START_REF] Harlan | Community-based use of chemotherapy and hormonal therapy for early-stage breast cancer: 1987-2000[END_REF][START_REF] Sukel | Substantial increase in the use of adjuvant systemic treatment for early stage breast cancer reflects changes in guidelines in the period 1990-2006 in the southeastern Netherlands[END_REF] Our finding that patients with a large or poorly differentiated tumour more often received adjuvant systemic treatment is in line with the literature and guidelines. [START_REF] Sukel | Substantial increase in the use of adjuvant systemic treatment for early stage breast cancer reflects changes in guidelines in the period 1990-2006 in the southeastern Netherlands[END_REF][START_REF] Du | Patterns of use of chemotherapy for breast cancer in older women: findings from Medicare claims data[END_REF] Hospital variation in utilization of adjuvant systemic treatment in early stage node negative breast cancer patients was also found in the southern Netherlands during 2003-2006, when the proportion of adjuvant systemic treatment ranged between 26-42%. [START_REF] Sukel | Substantial increase in the use of adjuvant systemic treatment for early stage breast cancer reflects changes in guidelines in the period 1990-2006 in the southeastern Netherlands[END_REF]

Quality of care

The large, but decreasing variation in breast cancer care for patients with early breast cancer between the various hospitals in both application of ALND and adjuvant systemic treatment cannot only be explained by patient or tumour characteristics, but is likely to result from differential fast and slow adaptors. But to what extent was the delayed introduction of the SNP or adjuvant systemic treatment in hospitals acceptable, since the SNP and adjuvant systemic treatment have proven their effectiveness in international literature since about 2005. [START_REF]Effects of chemotherapy and hormonal therapy for early breast cancer on recurrence and 15year survival: an overview of the randomised trials[END_REF][START_REF] Giordano | Use and outcomes of adjuvant chemotherapy in older women with breast cancer[END_REF][START_REF] Veronesi | Sentinel-node biopsy to avoid axillary dissection in breast cancer with clinically negative lymph-nodes[END_REF][START_REF] Cox | Lymphatic mapping and sentinel lymph node biopsy in patients with breast cancer[END_REF] In medical oncology, the usual consultancy of experts in oncology meetings in the Netherlands should lead to small differences in application of adjuvant systemic treatment between academic, teaching and general hospitals. But, the consultancy structure is less common in surgical-oncological treatment, because surgical experience is generally supposed to be larger in general and teaching hospitals. Therefore, a specific consultancy structure for surgical staging and treatment of breast cancer patients should be considered. The differences in care between the regions probably reflect differences in previous academic or large teaching hospital practices transmitted by training.

The results of the analyses on intermediate outcome in this study must be interpreted carefully, not only because hospital characteristics such as type and volume, may be rough proxies for hospital characteristics like anaesthesia equipment and nurse-patient ratio. Patient factors like comorbidity and socioeconomic status could also partly explain the observed associations with outcome. [START_REF] Laine | Does practice really make perfect?[END_REF][START_REF] Louwman | Less extensive treatment and inferior prognosis for breast cancer patient with comorbidity: a population-based study[END_REF] In conclusion, there was considerable variation in quality of care for patients with early breast cancer in the Netherlands after, albeit limited, adjustment for case mix (only age, tumour size and grade) in the period 2003-2006, just after the first national guideline became official. The differences, especially concerning breast surgery and axillary lymph node staging could be partly explained by hospital characteristics such as presence of specialist training and volume of care, but there also seemed to be differential loco-regional practices. Variation in application of adjuvant systemic treatment seemed to be mainly caused by patient and tumour characteristics. Research of the determinants of the differences should not only focus on case-mix and hospital characteristics, but should also address often selective, referral patterns and thus provide combined regional analysis. There are certainly gains to be attained. The situation in 2010 is likely to be much better, already.

  In the Netherlands a biannual mammography mass screening program for breast cancer in women from 50 to 70 years was gradually introduced since 1990, being fully implemented since 1997 and extended to women of 75 years since 1999. The purpose of this nationwide study was to describe variation in staging and treatment of patients with early breast cancer by hospital characteristics including type and volume and by region. The results of this study on all patients newly diagnosed in the Netherlands in 2003-2006 will support the ongoing efforts to improve quality of care for breast cancer patients in the Netherlands and abroad.

C50. 0

 0 ) newly diagnosed in the period 2003-2006 in the Netherlands were included (n=51 354). Exclusion criteria were diagnosis by autopsy, living and treatment abroad, incomplete registration status in the NCR, clinical diagnosis only, histology of sarcoma, lymphoma, Paget's disease, neuro-endocrine tumour or carcinoid. Reported stage is postoperative, and clinical when postoperative stage was unknown. Patients who received BCS followed by mastectomy without signs of relapse were coded as having had mastectomy. Hospitals The categorization of hospitals was based on data from Prismant for the period 2003-2005. Hospitals with several locations, but organized as one hospital in 2003 were considered as one hospital. Patients were considered to be treated in the hospital where the tumour was diagnosed. A non-teaching hospital was categorized as a general hospital. A teaching hospital provides in-house training to surgical and/or internal medicine residents. An academic hospital was a teaching hospital uniquely affiliated with a university. The one specialized oncology centre in the Netherlands was classified as an academic hospital. Hospital volume was based on the mean number of breast cancer diagnoses per year in the and was categorized into <150 and ≥150 diagnoses per year. Hospital type was categorized based on teaching hospital for surgery and hospital volume, resulting in six categories. The regions were based on the areas served by one of the nine CCCs. Each CCC serves the population in an area of five to twenty hospitals. Each of the hospitals was affiliated to one CCC only. Data were analysed by researchers of the nine CCCs in the Netherlands, supervised by experienced clinicians. The CCCs intend to improve and monitor the quality of cancer care by provision of consultancy services, implementation of national guidelines, improving organisation of cancer care, coordinating palliative care, and organising the cancer registry.

  Therefore, Dutch guidelines developed between 2000 and 2002, stated that most early stage breast cancer patients should receive SNP, for which often investments in nuclear detection equipment and training were needed. Although rapidly decreasing over time the general hospitals still performed too many ALNDs in the study period. Moreover, during the study period the indication for SNP changed with an M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 14.06.2010 9 increase in the cut-off value of tumour size from 3 to 5 cm, but SNP seems contra-indicated due to e.g. multifocality of the tumour or disturbed lymph drainage.

14 CaptionsFigure 1 :Figure 3 :

 1413 Figure 1: Treatment of breast cancer by stage, the Netherlands 2003-2006 BCS: breast conserving surgery; RT: Radiotherapy

Table 1 :

 1 Number of new cases of breast cancer in theNetherlands, 2003-2006

	N	%

Table 2b :

 2b The odds of receiving breast conserving surgery in patients with T1T2 breast cancer, the

		ACCEPTED MANUSCRIPT
	7	1.49*	1.13-1.97	1.27*	1.15-1.39	1.85*	1.59-2.15
	8	0.86	0.59-1.28	0.88*	0.78-1.00	0.98	0.81-1.18
	9	0.78	0.57-1.08	0.65*	0.59-0.72	1.18	0.99-1.41
	Incidence year
	2003	1.0		1.0		1.0
	2004	0.89	0.73-1.09	0.96	0.90-1.03	1.01	0.90-1.13
	2005	1.32*	1.07-1.63	1.14*	1.06-1.22	1.14*	1.02-1.27
	M 0.92-1.41 1.14* A N U S C R I P T 1.07-1.22 1.28* 1.14-1.43 a Adjusted for radiotherapy in hospital, region, and incidence year 2006 1.14 * p< 0.05
	Netherlands, 2003-2006 Hospital type small (<150), general large (≥150), general small (<150), teaching large (≥150), teaching small (<150) academic large (≥150), academic Radiotherapy in hospital yes no A C C E P T E D <40 yrs (n=2,958) OR a 95% CI 1.29* 1.44* 1.14 1.0 0.92 0.90 1.05-1.59 1.07-1.92 0.84-1.53 0.65-1.29 0.55-1.49 1.19 1.0 0.91-1.56	40-69 yrs (n=29,658) OR a 95% CI 1.03 1.02 0.86 1.0 0.74* 0.79* 0.96-1.10 0.93-1.13 0.78-0.95 0.65-0.84 0.68-0.93 1.20* 1.0 1.10-1.32	≥70 yrs (n=10,645) OR a 95% CI 1.00 0.94 0.83* 1.0 0.80 1.04 0.90-1.12 0.81-1.10 0.71-0.97 0.63-1.01 0.78-1.39 1.57 1.0 1.35-1.82
	Region
	1	0.88	0.66-1.16	0.90*	0.82-0.99	0.97	0.84-1.12
	2	0.76	0.56-1.04	0.84*	0.76-0.93	1.20*	1.02-1.41
	3	1.39*	1.01-1.91	1.45*	1.30-1.63	1.24*	1.04-1.47
	4	1.0		1.0		1.0
	5	0.70*	0.52-0.95	1.00	0.90-1.11	0.75*	0.64-0.88
	6	0.96	0.73-1.26	0.73*	0.67-0.79	0.65*	0.56-0.75

Table 3 :

 3 The odds of undergoing lymph node dissection by patients with pT1T2 N0 breast cancer, Adjusted for radiotherapy in hospital, age, clinical T stage, region, and incidence year

	the Netherlands 2003-2006
		Unadjusted		Adjusted a
		OR	95% CI	OR	95% CI
	Hospital type
	small (<150), general	1.44*	1.34-1.55	1.52*	1.39-1.67
	large (≥150), general	1.17*	1.04-1.31	1.69*	1.48-1.93
	small (<150), teaching	1.06	0.95-1.19	1.15	1.00-1.31
	large (≥150), teaching	1.0		1.0
	small (<150) academic	1.28*	1.10-1.50	1.20	1.00-1.43
	large (≥150), academic	0.44*	0.35-0.56	0.68*	0.51-0.89
	Radiotherapy in hospital
	yes			1.35	1.19-1.52
	no			1.0
	Age (yrs)
	<40			1.02	0.89-1.18
	40-69			1.0
	≥70			1.78*	1.65-1.91
	Clinical T stage
	1			1.0
	2			2.46*	1.65-1.91
	Region
	1			2.67*	2.36-3.02
	2			1.05	0.90-1.22
	3			1.18	1.00-1.38
	4			1.0
	5			1.48*	1.29-1.70
	6			1.72*	1.51-1.94
	7			1.33*	1.17-1.52
	8			0.58*	0.47-0.71
	9			3.09*	2.68-3.55
	Incidence year
	2003			1.0
	2004			0.63*	0.57-0.69
	2005			0.45*	0.41-0.49
	2006			0.34*	0.31-0.38

a

Table 4 :

 4 The odds of receiving adjuvant systemic therapy by T1T2 N0 breast cancer patients in the Netherlands, 2003-2006 Adjusted for radiotherapy in hospital, hospital size, region, incidence year, age, T stage, and grade b Pathological stage, when unknown clinical stage was used

	OR a	95% CI

a

Acknowledgements

The authors would like to thank the working group Output of the NCR for providing data from the cancer registry and all the members of the Quality of Cancer Care working party of the Dutch Cancer Society for financing.

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