T Attia

H Di Benedetto

C Sauzéat

S Pouget

2T3C HCA, a new hollow cylinder device using Digital Image Correlation to measure properties of interfaces between asphalt layers

Keywords: Pavement layers, Asphalt concrete, Interface behavior, Hollow Cylinder Apparatus (HCA), Digital Image Correlation (DIC), Experimental results

To improve pavement resistance, asphalt concrete layers are bonded together with a tack coat. A new device has been developed to describe the mechanical behavior of interfaces between asphalt concrete layers. The 2T3C Hollow Cylinder Apparatus (2T3C HCA) can apply torsion and tension-compression to hollow cylinder samples composed of two asphalt concrete layers with a tack coat in between. Normal and shear stresses can be applied independently with any type of loading (monotonic or cyclic). In addition to global measurements, a local optical method, based on Digital Image Correlation (DIC), is used to observe the deformation of the interface. The first interface characterization results are presented in this paper.

Introduction

Pavement sustainability is a major issue both economically and environmentally. Building long-life pavements that require little maintenance saves money and energy. Pavement structure is constituted by multiple layers made in different materials such as cement concrete or asphalt concrete. Each layer has a different function in the structure. The top layer, the wearing course, guarantees the adherence with the tires. The layer under the wearing course, the base course, diffuses in the lower layers the loads caused by traffic and climate. In pavements subjected to high traffic, both of these layers are generally made in asphalt concretes. Numerical simulations [START_REF] Uzan | Investigation of adhesion properties between asphaltic-concrete layers[END_REF][START_REF] Diakhaté | Fatigue et comportement des couches d'accrochage dans les structures de chaussée[END_REF] showed that binding the layers between them reduces the maximal deformation in the pavement improving its lifetime. In order to achieve this bonding, a tack coat, often made of bitumen emulsion, is applied at the interface between the two layers. Assuming the tack coat has been correctly applied, the asphalt concrete layers are considered perfectly bonded in some of the current pavement design methods [START_REF] Lcpc | Conception et dimensionnement des structures de chaussée[END_REF][START_REF] Aashto | Guide for design of Pavement Structure[END_REF]. However, premature degradations linked with the debonding of the layers have been reported [START_REF] Meunier | Le décollement des couches de revêtement de chaussées[END_REF][START_REF] Blomberg | Tack Coat Specifications and Testing[END_REF]. In this case, the pavement is subjected to loads it is not designed to resist to, implying a shortened lifetime. It is also possible that even for tack coat applied carefully and with a good dosage the interface will fail in fatigue before the asphalt concretes [START_REF] Petit | Pavement design for curved road sections: fatigue performance of interfaces and longitudinal topdown cracking in multilayered pavements[END_REF]. Yet, interface fatigue behavior is not considered in the design methods. The study of the mechanical behavior of interfaces between asphalt concrete layers is then critical to help designing better roads.

The mechanical testing of interfaces began in the 1970's [START_REF] Uzan | Investigation of adhesion properties between asphaltic-concrete layers[END_REF][START_REF] Leutner | Untersuchung des Schichtenverbundes beim bituminosen Oberbau[END_REF] and has gained more and more importance with time. Traffic and climate loads create complex stress states in the pavement. Different types of tests were developed to evaluate the bond strength at the interface between two asphalt pavement layers: tensile tests [START_REF] Tschegg | Investigation of Bonding between Asphalt Layers on Road Construction[END_REF], shear tests [START_REF] Leutner | Untersuchung des Schichtenverbundes beim bituminosen Oberbau[END_REF][START_REF] Canestrari | Advanced Testing and Characterization of Interlayer Shear Resistance[END_REF][START_REF] Zofka | Advanced shear tester for evaluation of asphalt concrete under constant normal stiffness conditions[END_REF][START_REF] Zhao | Investigation of the interface bonding between concrete slab and asphalt overlay[END_REF], wedge splitting tests [START_REF] Tschegg | Investigation of Bonding between Asphalt Layers on Road Construction[END_REF][START_REF] Brühwiler | The wedge splitting test, a new method of performing stable fracture mechanics tests[END_REF], torque test [START_REF] Collop | Development of an automatic torque test to measure the shear bond strength between asphalt[END_REF] (for broader overviews, see [START_REF] Canestrari | Mechanical Testing of Interlayer Bonding in Asphalt Pavements[END_REF][START_REF] Raposeiras | Test methods and influential factors for analysis of bonding between bituminous pavement layers[END_REF]). The shear tests are the most common and some of them can also apply compressive or tensile stress. Most of these tests aimed at evaluating only the shear strength of interfaces, which is the highest possible shear stress the interface can endure before failing. The influence of factors such as temperature [START_REF] Graziani | Time-temperature superposition principle for interlayer shear strength of bituminous pavements[END_REF], normal stress application [START_REF] Canestrari | Advanced Testing and Characterization of Interlayer Shear Resistance[END_REF], nature and dosage of tack coat [START_REF] Mohammad | Influence of asphalt tack coat materials on interface shear strength[END_REF] have been investigated. Several shear tests are used to assess interface fatigue properties under cyclic shear loadings [START_REF] Diakhaté | Fatigue et comportement des couches d'accrochage dans les structures de chaussée[END_REF][START_REF] Tozzo | Fatigue Investigation of the Interface Shear Performance in Asphalt Pavement[END_REF][START_REF] D'andrea | Dynamic tests on bituminous layers interface[END_REF][START_REF] Isailović | Interface shear fatigue performance of asphalt pavement structures in function of normal stress and temperature[END_REF][START_REF] Raab | Static and cyclic evaluation of interlayer bonding[END_REF] in order to obtain the fatigue law of interfaces for different test conditions or different materials. All these shear tests are inhomogeneous: the shear stress is not uniform at the interface.

It appears that a powerful test on interfaces should, (i) be able to apply shear and compressive/tensile stress, in monotonic or cyclic modes, to reproduce the actual pavement conditions, and (ii) be homogeneous in order to be analyzed correctly.

This paper presents the development of a new device to test interfaces between pavement layers. It is called 2T3C Hollow Cylinder Apparatus (2T3C HCA) and can apply torsion and tension-compression to hollow cylinder samples composed of two asphalt concrete layers. This apparatus uses 3D Digital Image Correlation (3D DIC) to observe the behavior of the interface. Additionally, the first experimental characterization of the viscoelastic behavior of asphalt concretes and of the interface using 2T3C HCA is presented.

This work is part of the industrial chair Eiffage/ENTPE dedicated to pavement materials and structures.

2

Description of 2T3C Hollow Cylinder Apparatus (2T3C HCA)

Hollow cylinder sample

Applying a torque to a cylinder creates an inhomogeneous shear stress field. For example, if the material is elastic linear isotropic, the shear stress varies linearly with the radius, being nil at the center of the cylinder. In a hollow cylinder, the inner part of the cylinder is removed. If the thickness left is thin enough then one can consider that the shear stress is homogeneous with a good approximation [START_REF] Sayao | A critical assessment of stress nonuniformities in hollow cylinder test specimens[END_REF] which ensures simplified but accurate test analysis. This is why a hollow cylinder apparatus is relevant to study interfaces behavior. Hollow cylinder tests have been broadly used for the testing of soils and granular materials [START_REF] Hight | The development of a new hollow cylinder apparatus for investigating the effects of principal stress rotation in soils[END_REF][START_REF] Duttine | Anisotropic small strain elastic properties of sands and mixture of sand-clay measured by dynamic and static methods[END_REF] and they have also been used for the study of asphalt concrete [START_REF] Sousa | Dynamic properties of materials for pavement design[END_REF][START_REF] Brown | A torsional hollow cylinder research apparatus for studying the permanent deformation characteristics of asphalt[END_REF][START_REF] Rueda | A new approach for the advanced mechanical characterisation of asphalt mixtures using the hollow cylinder methodology[END_REF]. However, no example of application to the study of interfaces between asphalt layers was found in the literature.

A new hollow cylinder apparatus has been developed at the University of Lyon/ENTPE: it is called 2T3C (in French, Torsion-Traction-Compression sur Cylindre Creux) Hollow Cylinder Apparatus (2T3C HCA). It allows applying torsion and tension-compression to hollow cylinder samples. The sample dimensions are: height of 125 mm, internal diameter of 122 mm, external diameter of 172 mm and thickness of 25 mm. The sample section area is 115.5 cm 2 . The samples are composed of two asphalt concrete layers with a tack coat at the interface located in the middle of the sample (Figure 1). The external diameter and the height are chosen considering fabrication constraints. The selected thickness is a compromise between having a thickness large enough compared to the maximum aggregate size and small enough to obtain the maximum shear stress applicable and a good shear stress homogeneity. The ratio between internal radius and external radius is 0.71, this value is between 0.65 and 0.82, the range recommended for a reasonable assumption of homogeneity of shear stress for a hollow cylinder test [START_REF] Sayao | A critical assessment of stress nonuniformities in hollow cylinder test specimens[END_REF].

Sample preparation

In this section, the fabrication of laboratory samples is presented (Figure 2) but samples from real pavements cored in situ can also be tested with the 2T3C HCA. A slab with two layers and a tack coat at the interface is created using the French wheel compactor [START_REF]Mélange bitumineux -Méthodes d'essai pour mélange hydrocarboné à chaud -Partie 33 : confection d'éprouvettes au compacteur de plaque[END_REF] (Figure 3). This is done in three steps. First, half a slab (600x400x75 mm 3 ) of the material representing the base course, the lower layer, is compacted. Then, after a 24 h rest period, a tack coat made of asphalt emulsion is applied on the surface of the lower layer using a brush (Figure 3). Finally, after another 24 h rest, the upper layer is compacted using the compacting wheels again to get the complete slab (600x400x150 mm 3 ). First the inside of a hollow cylinder is cored and then the outside. The two ends of the sample are then sawed to guarantee their planarity. A speckle pattern consisting of sprayed black paint over a thin white paint coat is applied on the surface of the sample for Digital Image Correlation (DIC) analysis. Samples are glued to aluminum plates using epoxy resin. A specially designed gluing device ensures that the axis of the hollow cylinder is coincident with the axes of the plates and thus of the hydraulic press.

2T3C HCA measuring systems

Torsion and tension-compression are applied to the samples using a servohydraulic press. Load cells measure the axial force up to ± 100 kN (with an accuracy of 0.010 kN) and the torque up to ± 2 kNm (accuracy of 0.1 Nm). Axial loadings and rotation loadings can be applied independently with any type of loading history: monotonic or cyclic (up to 10 Hz), stress or displacement controlled, following any load path. The sample with the plates, fixed to the press, is located in a thermal chamber with a temperature range from -20 °C to + 60 °C (Figure 4). The temperature is measured on the surface of the sample with two PT100 sensors, one on the inside surface of the sample and one on the outside surface of the sample (Figure 5) in order to verify the homogeneity of the temperature field in the sample. Two pairs of non-contact sensors measure the global displacements (in rotation and axial direction) between the top and the bottom of the samples. They can measure displacements with an accuracy of about 0.1 µm on a 1000 µm range. Sensors are fixed to the top plate and their aluminum target is fixed to the bottom plate. On each side of the sample there is one pair of non-contact sensors with one sensor that measures vertical displacement and one sensor that measures the displacement related to the rotation (Figure 5). The value of global vertical displacement is taken as the average of the values of the two sensors measuring the vertical displacement (V1 and V2 in Figure 5). The global horizontal displacement related to the rotation is obtained in a similar way. Tests can be performed under displacement control using the non-contact sensors values. In addition to global measurements, a local optical measurement method, the 3D DIC is used in the 2T3C HCA. This method finds the displacement field in the three dimensions on the surface of the sample and is presented in the next section.

Analysis from Digital Image Correlation

Two pairs of CCD cameras take digital pictures of 4 Mpx of each side of the sample (Figure 4) with a maximum acquisition frequency of 10 Hz. In each pair, the optical axii of the two cameras form an angle of 30° in order to use 3D DIC. Cameras are located outside the thermal chamber, 600 mm from the surface of the sample. At this distance and considering the CCD sensor characteristics, one pixel of a picture represents 150 µm of material. The thermal chamber has windows on its sides, which makes it possible to take pictures of the sample during tests at controlled temperature.

DIC principle is schematized in Figure 6. During a test, grayscale pictures of the sample are taken at different levels of deformation. The first image, representing the reference state, is called the reference picture. The goal of DIC is to obtain the displacement of the points at the surface of the sample at each level of deformation, i.e. for each picture, relatively to the reference state. For each pixel of the reference picture located in the area of interest (area where displacements are researched), a subset of the picture is selected. It is a square, usually a dozen pixels long, centered around the pixel. A correlation algorithm finds the subset of the deformed pictured that looks the most like the subset in the reference picture and deduces the displacement of the pixel [START_REF] Sutton | Determination of displacements using an improved digital correlation method[END_REF].

There needs to be a very contrasted and random pattern at the surface of the studied material. Asphalt concretes samples are naturally not well-contrasted. A speckle pattern, as the one described in section 2.2, is usually applied on the samples surface [START_REF] Romeo | Two-dimensional digital image correlation for asphalt mixture characterisation: interest and limitations[END_REF]. DIC has been used for the study of asphalt concretes cracking behavior [START_REF] Buttlar | Digital image correlation techniques to investigate strain fields and cracking phenomena in asphalt materials[END_REF] and rarely for the study of interfaces [START_REF] Ktari | Pavement interface damage behavior in tension monotonic loading[END_REF]. It has proved to be a consistent tool in the study of deformations of many materials such as cement concrete [START_REF] Golewski | Estimation of the optimum content of fly ash in concrete composite based on the analysis of fracture toughness tests using various measuring systems[END_REF][START_REF] Golewski | Measurement of fracture mechanics parameters of concrete containing fly ash thanks to use of Digital Image Correlation (DIC) method[END_REF], glass [START_REF] Jin | Thermal buckling measurement of a laminated composite plate under a uniform temperature distribution using the digital image correlation method[END_REF] or metals [START_REF] Chemisky | Analysis of the deformation paths and thermomechanical parameter identification of a shape memory alloy using digital image correlation over heterogeneous tests[END_REF]. For 3D DIC, two pictures of the same surface taken from different angles are needed at each state of deformation. An algorithm between the two pictures associates a spatial position to any pixel of the images. Displacements in the three dimensions are found using the correlation algorithm between reference and deformed states on one image of each pair [START_REF] Sutton | Advances in twodimensional and three-dimensional computer vision[END_REF].

The Vic-3D ® software developed by Correlated Solutions is used for 3D DIC measurements in the 2T3C HCA. It computes displacements in the three dimensions on the hollow cylinder surface and expresses them in the cylindrical coordinate system related to the hollow cylinder (ur, uθ, uz, Z being the axis of the cylinder). The heterogeneity of the asphalt concretes induces high spatial variability of displacements due to the difference in mechanical behaviors of bitumen and aggregates. A specific analysis developed at the ENTPE computes the three strain tensor components (εθθ, εzz, εθz) of both asphalt concrete layers and the displacement gaps at the interface (Δuz, Δuθ) throughout a test, anytime a picture is taken. Strain is obtained with an accuracy of about 1 µm/m and displacement gaps with an accuracy of 0.1 µm.

For εzz computation, horizontal strips (100 mm long and 3 mm thick) are drawn on the pictures as illustrated in Figure 7. The number of strips in each layer depends on the sample dimensions (between 10 and 15). For each state of deformation, the displacement component uz is averaged on each strip and the average value is affected to the coordinate Z of the center of the strip. The slopes of the lines obtained with linear regressions in the diagram Z-uz, one in each layer, give the strain components εzz in both asphalt concretes. These two lines do not intersect at the interface and the gap between them at the level of the interface (located visually) defines the axial displacement gap Δuz. The strain tensor component εθz is obtained using the same method as above, but replacing the displacement component uz with uθ. The displacement gap Δuθ is then found. In the analysis method presented in this paper, the interface thickness is considered nil, corresponding to a structural point of view. However, it is also possible to use DIC to look at the interface from a closer range and to define the thickness of the interfacial transition zone [START_REF] Ktari | Pavement interface damage behavior in tension monotonic loading[END_REF]. The latter approach can be used to model interfaces at a smaller scale, taking precisely into account aggregate interlocking. Assuming that the hollow cylinder remains a hollow cylinder during a test, the strain tensor component εθθ is equal to the relative variation of external perimeter of the cylinder. The computation of εθθ is illustrated in Figure 8. In each layer, about 20 vertical strips (4 mm thick and 45 mm high) are drawn on the pictures so that the central points of the strips are situated along an arc. Its length in the reference picture can be calculated. For each level of deformation, i.e. for each picture, the three displacement components (ur, uθ, uz) of the points in each strip are averaged and affected to the center of the strip. The coordinates of the center after transformation are obtained using this averaged displacement. The centers of the strips after transformation are situated along a deformed arc, the length of which is also calculated. The strain tensor component εθθ, equal to the relative variation of arc length, is thus obtained at each state of deformation in both asphalt concretes.

In the 2T3C HCA, two pairs of cameras are used on opposite sides of the sample. The strain tensors components (εθθ, εzz, εθz) and the displacement gaps (vertical Δuz and rotation Δuθ) are calculated on each side. Then, for each quantity, the two obtained values are averaged. The average values are used for the mechanical analysis of the sample.

3

Interface mechanical properties

Asphalt complex moduli and complex interface stiffnesses definitions

The axial stress σzz and the shear stress τθz in the sample are obtained from load cells measurement considering equations ( 1) and ( 2). These equations are derived with the assumption that stress field is homogeneous in the sample:

= ( 1
)
where F is the axial force measured with press load cell and A the section area of the hollow cylinder, and:

= 3 2 * ( - ) (2)
where T is the torque measured with press load cell, Rext the external radius and Rint the internal radius.

For a small number of applied loading cycles and for small loadings amplitudes, conditions similar to those existing in a real pavement, asphalt concretes present a linear viscoelastic (LVE) behavior [START_REF] Gayte | Influence of transient effects for analysis of complex modulus tests on bituminous mixtures[END_REF]. For a sinusoidal loading in stress control mode, the LVE material strain response is also a sinusoidal signal with a phase lag.

For an axial stress sinusoidal signal σzz such as equation ( 3), the strain tensor component εzz is given in equation [START_REF] Aashto | Guide for design of Pavement Structure[END_REF].

( ) = _ ( ) (3)
( ) = _ ( -! ) ( 4
)
where σzz_0 is the vertical stress amplitude, εzz_0 the vertical strain amplitude and φE the phase angle. The Young's complex modulus Ezz* is defined in equation ( 5):

" * = _ _ # $ % = |" * |# $ % (5)
When shear stress is applied, for example τθz in direction "θz", the complex shear modulus Gθz* is given in equation ( 6):

' * = _ 2 _ # $ ( = |' * |# $ ( (6)
with τθz_0 the amplitude of shear stress and εθz_0 the shear strain amplitude. φG is the phase angle in shear mode. It is observed that when a sinusoidal stress signal is applied to the interface, displacement gaps are also sinusoidal (as in Figure 9). It is then possible to define a complex interface stiffness.

The normal complex interface stiffness Kzz* is defined in equation ( 7).

) * = _ *+ _ # $ ,--= |) * |# $ ,-- (7)
with Δuz_0 the amplitude of the vertical displacement gap at the interface. φKzz is the phase angle for interfaces in tension-compression mode.

If torsion is applied, the shear complex interface stiffness Kθz* is given in equation [START_REF] Leutner | Untersuchung des Schichtenverbundes beim bituminosen Oberbau[END_REF].

) * = _ *+ _ # $ ,.-= |) * |# $ ,.- (8)
with Δuθ_0 the amplitude of the horizontal (tangential) displacement gap at the interface. φKθz is the phase angle for interfaces in shear mode.

The complex Poisson's ratio νθz* in each layer can also be found using equation ( 9):

/ * = _ _ # $ 0.-= |/ * |# $ 0.- (9)
with εθθ_0 the amplitude of the relative variation of cylinder perimeter. φνθz is the phase angle for Poisson's ratio.

Procedure and tested material

One sample with two asphalt concrete layers and a tack coat at the interface has been tested. The upper layer was in BBSG3 0/10 [START_REF]1 Septembre 2007 Mélange bitumineux -Spécification des matériaux -Partie 1 : Enrobés bitumineux[END_REF], representing the wearing course of a pavement, and the lower layer was in GB5 ® 0/14, usually used as a base course. The two layers had the same thickness. The tack coat is a bituminous emulsion of pure bitumen with a residual dosage of 350 g/m 2 .

In order to characterize the viscoelastic properties of the interface and of the asphalt concretes, sinusoidal loading cycles at small strain amplitude were applied to the sample. The tests presented in this paper were performed at four different temperatures (about 10, 20, 30, and 40 °C). At each temperature, two types of tests were done successively: axial tests and rotation tests (Table 1). During axial tests, vertical displacement was controlled with the averaged value of the two vertical non-contact sensors while torque was maintained nil. During rotation tests, rotation displacement was controlled with the averaged value of the horizontal non-contact sensors and axial force was maintained at a very small compressive value (around 15 kPa). The amplitude values for non-contact sensors were calculated in order to get 200 µm/m in global vertical strain εzz (corresponding to the case where the sample would be constituted of one homogeneous material) for axial tests and 200 µm/m in global shear strain εθz for rotation tests. For each type of test, four frequencies were tested with five sinusoidal cycles applied for each frequency. 10) except for cycles at 0.3 Hz where 30 pictures were taken at each cycle. The subset size for DIC was 21 x 21 pixels, which corresponds to 3.1 x 3.1 mm 2 on the material. The capture time of a picture was 6 ms.

Results and discussion

All stress and strain signals were fitted with sinusoidal functions using the least square method before being analyzed. An indicator was used to quantify and check the signal quality. With 3D DIC, the measured vertical strain amplitudes εzz_0 for axial tests ranged from 200 to 250 µm/m in the upper layer and from 100 to 150 µm/m in the lower layer, the vertical displacement gap amplitude Δuz_0 being between 1 and 3.5 µm. εθθ amplitude was between 70 and 100 µm/m in the upper layer and between 25 and 50 µm/m in the lower layer. For rotation tests, the shear strain amplitudes εθz_0 were between 250 and 350 µm/m in the upper layer and between 75 and 100 µm/m in the lower layer, the rotation displacement gap amplitude Δuθ_0 was between 4 and 8 µm/m. The difference in strain values between the two layers is related to the difference in modulus between the two asphalt concretes, it depends on the temperature and the frequency.

For the asphalt concretes layers, isothermal curves of the Young's complex modulus norm |Ezz*| are shown in the Figure 11 and isothermal curves of the complex shear modulus norm |Gθz*| are represented in Figure 12. The BBSG 3 asphalt concrete is less rigid than the GB5 ® at the same temperature and frequency. This can be seen in axial tests (Figure 11) and in rotation tests (Figure 12) and is consistent with the specifications of these asphalt concretes.

Isotherms of normal complex interface stiffness norm |Kzz*| obtained from axial tests and shear complex interface stiffness norm |Kθz*| obtained from the rotation tests are presented in Figure 13. Interfaces are more rigid in tension-compression mode than in shear mode. and 0.4 which is a good order of magnitude for asphalt concretes at these temperatures and frequencies [START_REF] Perraton | 3Dim experimental investigation of linear viscoelastic properties of bituminous mixtures[END_REF]. No significant differences could be observed between the two layers.

Conclusions

The 2T3C Hollow Cylinder Apparatus (2T3C HCA) is an innovative prototype with unique characteristics to study the interfaces between pavement layers. It can apply torsion and/or tension-compression independently to hollow cylinder samples. The tests can be cyclic or monotonic with temperature control. The thickness of the wall is small regarding the external diameter so the stress distribution can be considered as homogeneous in the sample.

3D DIC measurements and the developed analysis method enable to obtain the strain tensor components (εθθ, εzz, εθz) of both asphalt concrete layers and the displacement gaps at the interface (vertical Δuz and rotation Δuθ). The Young's and shear complex moduli (Ezz*, Gθz*) and Poisson's ratio (νθz*) of the two asphalt mixes and the complex interface stiffnesses (Kzz*, Kθz*) are obtained.

In this paper, tests at four temperatures (from 10 °C to 40 °C) and four frequencies (from 0.01 Hz to 0.3 Hz) in shear mode and in tension-compression mode were performed on a sample with two asphalt layers and a tack coat at the interface. The following conclusions were drawn from these tests:

1) Presented results show the accuracy and efficiency of the 2T3C HCA prototype to study interfaces in the small strain domain.

2) Displacement gaps with amplitudes as low as 1 µm were observed. Magnitude of measured strain amplitude in asphalt layers was of some 10 -5 m/m.

3) The interfaces seem more rigid in tension-compression than in shear.

The developed 2T3C HCA device appears as a powerful experimental tool to investigate interface properties between bituminous layers.

Fig. 1 .

 1 Fig. 1. 2T3C HCA hollow cylinder samples: (a) schematic, (b) picture

Fig. 2 .Fig. 3 .

 23 Fig. 2. Process to obtain hollow cylinder sample from a two layered slab with a tack coat at the interface

Fig. 4 .

 4 Fig. 4. Picture and scheme of the 2T3C HCA with measuring systems

Fig. 5 .

 5 Fig. 5. 2T3C HCA sample instrumentation: (a) Side view, (b) Top view

Fig. 6 .

 6 Fig. 6. 3D Digital Image Correlation: determination of 3D displacements of each point M of the area of interest

Fig. 7 .

 7 Fig. 7. Vertical displacement uz measurements from DIC and illustration of computation of εzz in both asphalt layers and of the displacement gap Δuz at the interface (picture at 12.5 µm in extension)

Fig. 8 .

 8 Fig. 8. Computation of εθθ in one asphalt layer (picture at 12.5 µm in compression)

Fig. 9 .

 9 Fig. 9. Example of stress, strain and displacement gap measurements in one layer and at the interface for an axial test (with least square approximations in continuous lines)

Fig. 10 .

 10 Fig. 10. Global displacement from non-contact sensors and acquisition of pictures on one side of the sample during the tests (T is the loading period)

Fig. 11 .Fig. 12 .

 1112 Fig. 11. Isothermal curves of Young's complex modulus norm |Ezz*| for asphalt concretes in the upper layer (BBSG) and in the lower layer (GB)

Fig. 13 .

 13 Fig. 13. (a) Isothermal curves of normal complex interface stiffness norm |Kzz*| for axial tests and (b) isothermal curves of shear complex interface stiffness norm |Kθz*| for rotation tests The isotherms of complex Poisson's ratio norm |νθz*| in the upper (BBSG) layer and in the lower (GB) layer are presented in Figure 14 for axial tests. Poisson's ratios values are between 0.3 and 0.4 which is a good order of magnitude for asphalt concretes at these temperatures and frequencies[START_REF] Perraton | 3Dim experimental investigation of linear viscoelastic properties of bituminous mixtures[END_REF]. No significant differences could be observed between the two layers.

3

 3

Fig. 14 .

 14 Fig. 14. Isothermal curves of complex Poisson's ratio norm |νθz*| for asphalt concretes in the upper layer (BBSG) and in the lower layer (GB)

Table 1 .

 1 Mechanical loading for each temperature

	Type of test	Axial loading	Torsion loading	Frequencies (Hz)	Amplitude Non-contact sensors	Cycles per frequency
	Axial Rotation	Sinusoidal displacement Small compression 15 kPa	Zero torque Sinusoidal displacement	0.01; 0.03; 0.1; 0.3	ax = 25 µm rot = 90 µm	5 5
	Each camera took 50 pictures of the sample per cycle (Figure


Nolwenn Delaby
email: n.delaby@rennes.unicancer.fr

Sandrine Martin

Anaïs Barateau

Olivier Henry

Nicolas Perichon

Renaud De Crevoisier

Enrique Chajon

Joël Castelli

Caroline Lafond

Implementation of an optimization method for parotid gland sparing during inverse planning for head and neck cancer radiotherapy Implémentation d'une méthode optimisée pour l'épargne des glandes parotides lors de la planification d'arcthérapie volumétrique modulée (VMAT) des cancers ORL

Keywords: Planification dosimétrique, prédiction de la dose, VMAT, contrôle qualité Optimization method for parotid gland sparing -N. Delaby Treatment planning, prediction dose, VMAT, quality control

Optimization method for parotid

Introduction

Intensity modulated radiotherapy (IMRT) is the standard treatment for head-andneck (H&N) cancer, sparing the parotid glands (PGs) with sharp dose gradients, and thereby limiting xerostomia [START_REF] Kam | Prospective Randomized Study of Intensity-Modulated Radiotherapy on Salivary Gland Function in Early-Stage Nasopharyngeal Carcinoma Patients[END_REF][START_REF] Feng | Intensity-Modulated Chemoradiotherapy Aiming to Reduce Dysphagia in Patients With Oropharyngeal Cancer: Clinical and Functional Results[END_REF][START_REF] Pow | Xerostomia and quality of life after intensity-modulated radiotherapy vs. conventional radiotherapy for early-stage nasopharyngeal carcinoma: Initial report on a randomized controlled clinical trial[END_REF]. However, there is variability during the treatment planning optimization process depending on the clinical case complexity, treatment planning system (TPS), modulation degree, or operator experience. A dose planning only based on the standard dose recommendations does not provide the optimal treatment planning for every patient [START_REF] Bentzen | Quantitative Analyses of Normal Tissue Effects in the Clinic (QUANTEC): An Introduction to the Scientific Issues[END_REF]. Since 2006, several studies have proposed dose and/or geometric indexes/tools based on their own experience to limit treatment planning variability [START_REF] Moore | Experience-Based Quality Control of Clinical Intensity-Modulated Radiotherapy Planning[END_REF][START_REF] Hunt | Geometric factors influencing dosimetric sparing of the parotid glands using IMRT[END_REF][START_REF] Wu | Patient geometry-driven information retrieval for IMRT treatment plan quality control[END_REF][START_REF] Mattes | A predictive model to guide management of the overlap region between target volume and organs at risk in prostate cancer volumetric modulated arc therapy[END_REF][START_REF] Stanhope | Utilizing knowledge from prior plans in the evaluation of quality assurance[END_REF][START_REF] Lian | Modeling the dosimetry of organ-at-risk in head and neck IMRT planning: An intertechnique and interinstitutional study: IMRT intertechnique and interinstitutional modeling[END_REF][START_REF] Tol | Can knowledge-based DVH predictions be used for automated, individualized quality assurance of radiotherapy treatment plans[END_REF]. In 2011, Moore et al. proposed a method based on a mathematical model to guide operators during the dose planning process about the compromise between the delivered dose to the target volume and the organ at risk (OAR) dose constraints [START_REF] Moore | Experience-Based Quality Control of Clinical Intensity-Modulated Radiotherapy Planning[END_REF].

The mathematical model (based on a knowledge of prior patients) allows prediction of the lowest achievable mean dose (Dmean) to an OAR knowing the prescribed dose to the PTV and the overlap volume between the PTV and considered OAR. Moreover, they shown that this method better saves healthy tissues while decreasing inter-operator variability.

However, the proposed model was not specific for tumor localization, and was conceived as part of the specific practices from the authors' institution (Washington University School of Medicine, St Louis, MO). To our knowledge, this type of method has not been developed in another institution, with an optimized model for PG sparing during H&N cancer radiotherapy. In addition, the inter-operator variability with the implementation of such a method has not been evaluated.

In the context of volumetric modulated arc therapy (VMAT) for H&N cancer radiotherapy, the objectives of this study were:

-to optimize the published model of Moore et al. [START_REF] Moore | Experience-Based Quality Control of Clinical Intensity-Modulated Radiotherapy Planning[END_REF] for PG dose sparing, with our institution practices -to evaluate the optimized model's performance in a large cohort of patients -to quantify the PG dose sparing with the use of the optimized model (compared to the standard approach) -to evaluate inter-operator variability

Methods

Patient characteristics, image acquisition and delineation

A cohort of 160 consecutive patients with histologically confirmed locally advanced H&N squamous cell carcinoma treated from December 2015 to September 2017 was used for this study. All patients had bilateral cervical lymph node irradiation. Thirtyeight patients included in the first phase of the study (optimization and evaluation of the mode) had post-operative radiotherapy. Computed tomography (CT) contrast-enhanced images, indexed every 2-3 mm, were acquired, from the vertex to the carina (Brilliance, Big Bore, Philips, Netherlands). Target volume and OARs were delineated slice-by-slice on CT images. The gross tumor volume (GTV) was defined by clinical examination, CT, and FDG-PET scan. The GTV encompassed all visible and palpable primary and nodal disease. In post-operative cases, areas of involved margins or lymph node stations containing lymph nodes with extracapsular extension were considered to be at very high risk. High-risk clinical target volume (CTV) was defined as areas potentially containing microscopic disease limited by anatomic barriers or by the GTV plus a 10 mm margin, when an anatomic barrier was not clearly identified (e.g., base of the tongue), or when the lymph node levels containing involved lymph nodes and neighbouring node levels were considered at risk of subclinical involvement greater than 15-20%. Low-risk CTV encompassed the remaining lymph node areas at risk of potential microscopic spreading greater than 5%. The PTV, designed to account for setup uncertainties, was defined using an additional margin of 5 mm. OARs included spinal cord, brainstem, mandible, larynx, bilateral inner ears, oesophagus, pharyngeal constrictors, oral cavity, contralateral PG (CPG), ipsilateral PG (IPG), and submandibular glands (SMGs). These OARs were delineated by radiotherapists regarding international recommendations [START_REF] Brouwer | CT-based delineation of organs at risk in the head and neck region: DAHANCA, EORTC, GORTEC, HKNPCSG, NCIC CTG, NCRI, NRG Oncology and TROG consensus guidelines[END_REF]. The term ipsilateral or contralateral makes reference to the relationship between the OAR and the highest dose level PTV.

Dose planning

All patients received definitive or post-operative external beam radiotherapy using VMAT technique. Patients were immobilized in the supine position with custom aquaplast masks holding both the neck and shoulders (Posicast-Lite PR5, CIVCO, Iowa, US). Two or three dose levels in simultaneously integrated boost (SIB) were used, depending on the clinical situation (Table 1). Treatment planning was carried out on the Pinnacle v.9.10 (Philips) TPS using 6 MV photon beams from a Synergy or VERSA HD linear accelerator (Elekta, Stockholm, Sweden) equipped with an Agility (160 leafs) multileaf collimator. The collapsed cone convolution algorithm and a dose grid size of 3x3x3 mm 3 were used for dose calculation. Two 358° clockwise and counter-clockwise arcs (control point every 2°) were used. The highest priority was assigned to PTVs with the following constraints: more than 95% of any PTV should receive more than 95% of the prescribed dose, or more than 98% of any PTV should receive more than 90% of the prescribed dose; no more than 2% of any PTV could receive more than 110%. The following OAR dose constraints were used [START_REF] Brouwer | CT-based delineation of organs at risk in the head and neck region: DAHANCA, EORTC, GORTEC, HKNPCSG, NCIC CTG, NCRI, NRG Oncology and TROG consensus guidelines[END_REF][START_REF] Lee | Skin toxicity due to intensity-modulated radiotherapy for head-and-neck carcinoma[END_REF][START_REF] Maingon | Chapitre commun à la prise en charge et à la procédure de préparation des traitements des cancers de la tête et du cou[END_REF][START_REF] Toledano | Intensity-modulated radiotherapy in head and neck cancer: Results of the prospective study GORTEC 2004-03[END_REF]: brainstem and spinal cord maximum doses (D2%) were 50 Gy and 45 Gy, respectively; for the PG, the mean dose (Dmean) was <26 Gy or the maximum dose received by 50% of the volume was <30 Gy; for the SMG, Dmean was ≤39 Gy; for the oral cavity, Dmean was as low as possible; for the larynx, Dmean was ≤45 Gy; for the pharyngeal constrictors, Dmean was ≤40 Gy; for the oesophagus, Dmean was ≤35 Gy; for the internal and inner ears, D2% was ≤40 Gy; and for the mandible, D2% was ≤65 Gy.

All dose plans were performed by physicists or dosimetrists, and validated by a radiation oncologist.

Moore et al. optimization model

Moore et al. defined a mathematical model allowing for prediction of a radiation plan to achieve the lowest possible mean dose to an OAR [START_REF] Moore | Experience-Based Quality Control of Clinical Intensity-Modulated Radiotherapy Planning[END_REF]. This model depends on the prescribed dose to the PTV and the overlap volume between the PTV and considered OAR [START_REF] Moore | Experience-Based Quality Control of Clinical Intensity-Modulated Radiotherapy Planning[END_REF]. The equation of the model was the following:

_ = + - ! "# $% /! '( )* (,)
Voverlap is the intersection between PTV and PG.

This model was created from 17 H&N patients (overlap between PGs and PTV) When the optimized model was used, the mean dose objective of the entire PG was adjusted in the TPS according to the Dachievable_mean (obtained from Dprescribed, Voverlap and VPG).

Evaluation of the optimized model (difference between the achievable PG mean dose calculated by the model and the planned PG mean dose)

The robustness of the adapted Moore model was assessed for a cohort of 110 H&N patients. Treatment plans were optimized knowing lowest achievable PG mean dose from the optimized model, from the equation [START_REF] Kam | Prospective Randomized Study of Intensity-Modulated Radiotherapy on Salivary Gland Function in Early-Stage Nasopharyngeal Carcinoma Patients[END_REF]. When the PG Dpredicted was not reached, an analysis was performed to understand the model limits.

Comparison between the standard planning and the use of the optimized model for achievable PG mean dose prediction

A comparison between the standard planning and the planning with the use of achievable PG mean doses was performed in a cohort of 30 H&N patients treated with definitive radiotherapy. Patients with post-operative irradiation were not included in this phase of the study to avoid biases in the data analysis. Dose planning was first performed with standard planning dose constraints [START_REF] Brouwer | CT-based delineation of organs at risk in the head and neck region: DAHANCA, EORTC, GORTEC, HKNPCSG, NCIC CTG, NCRI, NRG Oncology and TROG consensus guidelines[END_REF][START_REF] Lee | Skin toxicity due to intensity-modulated radiotherapy for head-and-neck carcinoma[END_REF][START_REF] Maingon | Chapitre commun à la prise en charge et à la procédure de préparation des traitements des cancers de la tête et du cou[END_REF]. Then, three planners retrospectively replaned the 30 H&N cases using the lower achievable PG mean dose provided by the optimized model during the dose planning process.

Inter-operator variability with standard planning and the use of the optimized model for achievable PG mean dose prediction

The impact of the model application on inter-operator variability was evaluated in one H&N representative case of our clinical practices, with three dose levels (IPG overlap with PTV: 3.3 cm 3 ; CPG overlap with PTV: 1.7 cm 3 ). Twelve operators (medical physicists and dosimetrists) with different dosimetric experience (from 3 months to 10 years, median = 2.75 years) performed two plans of the same case: one with the standard planning and one using PG achievable mean dose provided by the optimized model.

Endpoints and statistical analysis

a. Dose endpoints Dose distributions were assessed with dose volume histograms (DVHs) and particular dosimetric points, including the volume of the PTV receiving at least 95% of the prescribed dose (V95%), the mean dose to PG, and the maximum dose (D2%) to the spinal cord.

In addition, the delta index (δ) was computed to evaluate the ability of the model to be respected [START_REF] Moore | Experience-Based Quality Control of Clinical Intensity-Modulated Radiotherapy Planning[END_REF]. It was defined as:

. = / %0 - 1 1 (2)
Ideal δ value is 0 (no difference between mean doses predicted and planned). δ index allows to define the deviation between the predicted dose value by the model (Dpredicted) and the final calculated dose (Dachieved).

NTCP values were calculated for PGs with the parameters defined by Dijkema et al. [START_REF] Dijkema | Parotid Gland Function After Radiotherapy: The Combined Michigan and Utrecht Experience[END_REF] and Houweling et al. [START_REF] Houweling | A Comparison of Dose-Response Models for the Parotid Gland in a Large Group of Head-and-Neck Cancer Patients[END_REF]: TD50 = 39.9 Gy; n = 1; m = 0.40.

b. Treatment plan quality

Plans were assessed by conformity [START_REF] Lomax | Quantifying the degree of conformity in radiosurgery treatment planning[END_REF], and homogeneity [START_REF] Icru | Prescribing, Recording, and Reporting Photon-Beam Intensity-Modulated Radiation Therapy (IMRT)[END_REF] indexes, and complexity metrics. These indexes are defined as follows:

3"04" / 15 0 6 (37

) = ! '8! 9:% ! '8! (<)
where VPTV95% is the volume of PTV receiving 95% of the prescribed dose. VPTV is the volume of the PTV. Ideal CI value is 1.

="/"> 0 15 0 6 = 2% -9?% :@% (A)

where D2%, D98% and D50% represent the doses to 2%, 98% and 50% of the PTV, respectively. Ideal HI value is 0.

Complexity of treatment plans was calculated with different metrics described by Du el al. [START_REF] Du | Quantification of beam complexity in intensity-modulated radiation therapy treatment plans[END_REF]:

-number of monitor units (MU) planned (1 UM = 1 cGy in reference conditions: Correlation test (Spearman) was performed between dose difference (optimized model minus standard method) and Voverlap/VPG.

Results

Moore et al. model optimization: determination of the minimum PG achievable mean dose

Figure 1 displays the PG mean dose normalized to the prescribed doses for PTV in function of the relative overlap between PG and PTV. The mathematical model defined by equation ( 4) showed better fitting PG sparing considering overlap with the PTV and the prescribed dose to the PTV (solid curve in Fig. 1 representing the inferior shape).

/ %0 = @. ,C + @. ? ,. @2 -! "# $% /! '( )* (:

)
where Dmean is the achievable PG mean dose, prescribed dose is the dose prescribed to the PTV, Voverlap is the overlap volume between PG and PTV, and VPG is the PG volume.

Then, the Dmean provided by this optimized model for each PG was used during the planning process. These values were implemented as optimization goals with a script.

Evaluation of the optimized model (difference between the achievable PG mean dose calculated by the model and the planned PG mean dose)

Figure 2 displays the normalized mean doses (Dmean/Dprescribed) to PGs plotted against the ratio between volume overlap between the PTV and the PG, within a cohort of 110 patients.

The mean (± SD) δ index value was 0.13 (± 0.11) for the IPG and 0.9 (± 0.12) for the CPG. The δ index value of 26 PGs was outside the range [mean δ ± 1 SD], including 15 IPGs and 12 CPGs (circles in Figure 2).

Evaluation of PG sparing with the optimized model compared to the standard method

Figure 3 and Figure 4 presents the mean PTV and PG DVHs for treatment plans performed with and without the optimized model, within a cohort of 30 patients. Table 2 presents the delivered doses to PTVs and OARs, δ index and NTCP. Plans performed with the use of optimized model showed an increase of mean PTV coverage and an increase of PTV maximum dose (+1.1 Gy on average). On average, the IPG mean dose decreased of - 4 shows the PTV CI and HI indexes. The PTV CI indexes were not significantly different between the standard planning and the use of the optimized model. However, treatment plans performed with the optimized model provided HI indexes significantly higher for high and middle dose PTVs and not significantly different for low dose PTV.

Evaluation of inter-operator variability with standard planning and the use of the optimized model for achievable PG mean dose prediction

Discussion

For H&N treatment planning, we showed the dosimetric benefit of using a simple, personalized and realistic model to predict achievable dose to the PGs. With this model, the PG mean doses decreased by 6.1 Gy on average compared to a standard planning, without compromising PTV coverage and without OAR overdose (Table 2). Moreover, the inter-operator variability was divided by 2 and by 3 for IPG and CPG mean doses, with the optimized model. In average, for standard method, IPG mean doses were above GORTEC recommendation (32.4 Gy for 26 Gy recommended) [START_REF] Brouwer | CT-based delineation of organs at risk in the head and neck region: DAHANCA, EORTC, GORTEC, HKNPCSG, NCIC CTG, NCRI, NRG Oncology and TROG consensus guidelines[END_REF]. Using optimized method, mean IPG dose was equal to GORTEC recommendation. For CPG, optimized method reduced in average PG mean dose below GORTEC recommendation (26.9 Gy to 21 Gy).

PG mean doses obtained using the optimized model were consistent with Moore et al. [START_REF] Moore | Experience-Based Quality Control of Clinical Intensity-Modulated Radiotherapy Planning[END_REF] results. In their study, the model was applied to rectal and H&N IMRT cases. For H&N, the δ index varied from 0.28 +/-0.24 without the model, to 0.13 +/-0.10 with the model. In our study, for H&N VMAT cases, δ index varied from 0.42 +/-0.28 to 0.09 +/-0.14 (Table 2). This method seems useful for all localizations with overlap between the PTV and OARs requiring a dose compromise. Powis et al. [START_REF] Powis | Clinical implementation of a knowledge based planning tool for prostate VMAT[END_REF] recently defined their own model based on Moore's method for rectum sparing in case of prostate VMAT.

Guidelines recommend to deliver a mean dose lower than 26 Gy to the CPG and as low as possible to the IPG [START_REF] Bentzen | Quantitative Analyses of Normal Tissue Effects in the Clinic (QUANTEC): An Introduction to the Scientific Issues[END_REF]. The way to achieve these constraints is strongly dependant on operator experience, especially for the CPG. In this study, regardless of operator experience, the inter-operator variability significantly decreased using the optimized model (Figure 7).

In this study, only 10% of 110 treatment plans realized with the optimized model were outside the arbitrary range [mean δ index ± 1 SD] (represented with points on Figure 2). Some cases could be explained both by the small overlap volume between PGs and PTV, and a PG location on the whole length close to the PTV. For such geometry, more sophisticated models might provide better dose prediction, as the overlap volume histogram (OVH) proposed by Wu et al. [START_REF] Wu | Patient geometry-driven information retrieval for IMRT treatment plan quality control[END_REF]. The OVH describes the fractional OAR volume that is within a specified distance to the PTV. This concept could be more suitable for non-overlapping cases but is more complex to implement in clinical routine. Another cause of deviation (between predicted and planned doses) can appear in case of PTV proximity to OAR requiring stringent dose constraints, such as brainstem or spinal cord.

We stress that implementation of such model must be institution-specific because TPS, treatment techniques, or OAR dose constraints can affect the performance of the model. Institution-specific trade-offs have also a major influence on the model. For now, we have only optimized the model for H&N VMAT treatment planning. Even in our institution, the model will need to be re-evaluated to be applied on another clinical localization or irradiation technique.

The optimized model used in this study increased the treatment plan complexity (Table 3). Improving PG sparing generated thinner and smaller segments and increased the number of MUs. Planners should be attentive to avoid too complex treatment plans, by using complexity index thresholds for example. Higher modulation complexity may result in lower dose accuracy. In that way, we performed quality controls to check the dose accuracy. Plans with the optimized model did not show significant difference (Table 3).

Our standard method did not provide any index to inform planner if the lowest OAR dose value is achieving, while covering PTV. Since several years, new automated planning tools were commercialized (AutoPlanning module for Pinnacle (Philips) TPS, RapidPlan for Varian TPS, etc.). Those tools can improve OAR sparing and/or PTV coverage, especially for new planners [START_REF] Speer | Automation of radiation treatment planning: Evaluation of head and neck cancer patient plans created by the Pinnacle3 scripting and Auto-Planning functions[END_REF]. Implementation of such tools, needs time to be configured (especially for knowledge-based methods) and evaluated to be confident with.

Several studies evaluated the impact of those commercial solutions on PG sparing [START_REF] Speer | Automation of radiation treatment planning: Evaluation of head and neck cancer patient plans created by the Pinnacle3 scripting and Auto-Planning functions[END_REF][START_REF] Fogliata | RapidPlan head and neck model: the objectives and possible clinical benefit[END_REF][START_REF] Gintz | Initial evaluation of automated treatment planning software[END_REF][START_REF] Ge | Knowledge-based planning for intensity-modulated radiation therapy: A review of data-driven approaches[END_REF].

Compared to manual planning, the use of RapidPlan in a H&N study including 20 patients, allowed a mean PG decrease of 2.2 Gy [START_REF] Fogliata | RapidPlan head and neck model: the objectives and possible clinical benefit[END_REF]. With AutoPlanning software, a H&N study on 10 patients reported on average a PG mean dose decrease of 3 Gy [START_REF] Gintz | Initial evaluation of automated treatment planning software[END_REF], and another study on 10 patients found a PG mean dose reduction of 1.5 Gy [START_REF] Speer | Automation of radiation treatment planning: Evaluation of head and neck cancer patient plans created by the Pinnacle3 scripting and Auto-Planning functions[END_REF]. Such tools appear attractive but are always a TPS add-on with additional cost. Our implementation of optimized model required only methodology and time. The two approaches, commercial tool and optimized model, are not rivals and can be implemented together [START_REF] Ge | Knowledge-based planning for intensity-modulated radiation therapy: A review of data-driven approaches[END_REF][START_REF] Moore | Automated Radiotherapy Treatment Planning[END_REF].

Mean dose PG sparing is a crucial objective for H&N IMRT/VMAT techniques.

Indeed, due to large anatomical variations during treatment course, the delivered dose may differ from the initial planned dose, especially a dose increase for the PGs [START_REF] Brouwer | Identifying patients who may benefit from adaptive radiotherapy: Does the literature on anatomic and dosimetric changes in head and neck organs at risk during radiotherapy provide information to help?[END_REF][START_REF] Castelli | Adaptive radiotherapy for head and neck cancer[END_REF][START_REF] Castelli | Impact of head and neck cancer adaptive radiotherapy to spare the parotid glands and decrease the risk of xerostomia[END_REF].

Adaptive radiotherapy (ART), using one or several replannings [START_REF] Graff | Radiothérapie adaptative ORL[END_REF][START_REF] Heukelom | Head and Neck Cancer Adaptive Radiation Therapy (ART): Conceptual Considerations for the Informed Clinician[END_REF], has been proposed to spare the PGs [START_REF] Schwartz | Adaptive radiotherapy for head and neck cancer-Dosimetric results from a prospective clinical trial[END_REF][START_REF] Dewan | Impact of Adaptive Radiotherapy on Locally Advanced Head and Neck Cancer -A Dosimetric and Volumetric Study[END_REF][START_REF] Capelle | Adaptive Radiotherapy Using Helical Tomotherapy for Head and Neck Cancer in Definitive and Postoperative Settings: Initial Results[END_REF][START_REF] Jensen | A Clinical Concept for Interfractional Adaptive Radiation Therapy in the Treatment of Head and Neck Cancer[END_REF][START_REF] Olteanu | Comparative dosimetry of three-phase adaptive and non-adaptive dose-painting IMRT for head-and-neck cancer[END_REF]. Weekly replannings can reduce the PG mean dose by 5 Gy, translating a reduction of 11% in the NTCP risk for xerostomia [START_REF] Castelli | Impact of head and neck cancer adaptive radiotherapy to spare the parotid glands and decrease the risk of xerostomia[END_REF]. Thus, ART workflow can provide PG dose sparing and clinical benefit for some patients (30 to 65% of patients [START_REF] Castelli | Adaptive radiotherapy for head and neck cancer[END_REF]). However, it was known as very time consuming and requiring resources strategy. In this context, the integration of an adapted Moore's method to local dosimetric protocols could reduce PG mean dose easier than an ART strategy.

This study has some limitations. In the model optimization and robustness phase of this work, 38 patients with post-operative bilateral neck irradiation were included to reflect our institutional daily practice. However, in the comparison phase (optimized model versus standard method) only patients with radical radiotherapy were included to avoid biases in the data analysis. Because the achievable lowest dose delivered to the PGs are driven by the prescribed dose to the PTV and the Voverlap between this PTV and the PG, we may assume that the results obtained for patients with radical radiotherapy would be similar to those with the post-operative radiotherapy. Indeed, our radical radiotherapy protocol include dose levels quite similar to our post-operative protocol for the high risk and elective target volumes. The optimized model was based on a cohort of 20 patients and would likely be more robust with a larger cohort, including more complex geometries to improve the dose prediction of non-standard cases. The inter-operator variability was assessed only on one case, and could be extended on more clinical cases. As using the optimized model increases treatment plan complexity, a constraint in term of minimum segment area or maximum MU could have been introduced. Moreover, this study could be supplemented by a multi-centric study to extent methodology to other practices.

Conclusions

A simple and optimized mathematical model was implemented in our department to spare the PGs during H&N treatment dose planning. Using the achievable PG mean dose provided by the optimized model, the PG mean dose decreased of 6.1 Gy on average.

Moreover, the optimized model allows to significantly reduce the inter-operator variability, whatever the planner's experience. The optimized model has been used in our daily clinical practices for the last two years. The benefits of PG dose sparing need to be evaluated in terms of clinical benefits (e.g., xerostomia, local control).

and 8

 8 prostate patients (overlap between rectum and prostate) static IMRT plans, with A = 0.2; B = 0.8; C = 1; D = 3.An adapted Moore's model was fitted based on 20 H&N standard treatment plannings from our institution. A script was developed in the TPS to extract volumes of PTV, PGs and overlaps between PTV and each PG. Delivered mean doses to the PGs were collected. Using these data, the ratio of the PG Dmean to the prescription dose to PTV (Dprescribed) was plotted against the ratio of the overlap volume between PTV and PG (Voverlap) to the PG volume (VPG), for each patient PG. Moore's equation coefficients (A, B, C and D) were modified by a dichotomy process, so that the curve of the model fits along the lower bound of our local data, representing the optimal average PG dose achievable in our selected cohort of patients (N = 20).

10 cm x 10

 10 cm square field, Skin Surface Distance = 95 cm, depth = 5 cm) -aperture area (computed as the total area of all MLC segments openings, in cm²) -aperture irregularity (calculated the non-circularity of the aperture, equal to 1 in case of circular aperture) -beam modulation (taking into account aperture area and MU number associated to each segment, equal to 0 with a treatment plan without modulation) Quality assurance of treatment plans was performed with EBT3 Gafchromic films (Ashland) in an Octavius 40043-CT homogeneous phantom (PTW). Films were scanned using the Epson 11000XL desktop flat-bed scanner in association with FilmQAPro software (Ashland). Comparison between delivered and calculated dose distributions was performed by local gamma analysis[START_REF] Low | A technique for the quantitative evaluation of dose distributions[END_REF] (Verisoft software v7.0.1, PTW) with 3%/3 mm and 30% low dose threshold criteria.c. Statistical analysisWilcoxon (non-parametric) tests were performed to compare standard planning with planning using the optimized model. A p-value ≤ 0.05 was considered as significant.

6. 4

 4 Gy, and the CPG mean dose of -5.8 Gy. Mean doses were similar with standard planning for oral cavity and SMG (p>0.05) and significantly different for larynx and spinal cord (D2%), but accepted by physician. Using the optimized model on the PGs, δ index values were significantly lower and NTCP values significantly lower (p-value < 0.01).

Figure 5

 5 Figure 5 displays box plots of the PG mean dose with the standard planning, the

Figure 7

 7 Figure 7 displays the minimum and maximum envelopes of the PG DVH for the H&N case

  Table3gathers also the conformity, homogeneity and complexity indexes and the results of agreement between TPS dose calculation and measurement. Plans performed with the optimized model were more heterogeneous for high-and middle-dose PTV than with standard planning. Plans performed with the optimized model were more complex than those performed with standard planning. In fact, significant smaller field sizes (mean of 50.1 cm² versus 56.8 cm²

with standard planning) and significant MU increase (745 MU versus 673 MU with standard planning) were obtained with the use of the optimized model. Agreement between the TPS dose calculation and measurement was not significantly different between the planning methods.

Table 1 . Patient's study characteristics: patient cohort size, dose prescription, PG volume and, overlap between PG and PTV

 1

		Cohort size (number of	Dose prescription (number of patients)		PG volume (mean ± SD, in cm 3 )	PG overlap (mean ± SD, in cm 3 )
		patients)	70-63-56 Gy	66-59.4-54.1 Gy	60-54 Gy	IPG	CPG	IPG	CPG
	Model optimization	20	10	4	6	28.9 ± 10.2	29.1 ± 9.3	4.8 ± 2.6	3.4 ± 2.1
	Robustness	110	82	20	8	29.6 ± 8.0	30.3 ± 9.1	5.0 ± 3.0	3.0 ± 2.1
	Standard vs optimized model	30	30	0	0	27.5 ± 10.7	26.1 ± 11.0	4.9 ± 3.0	3.0 ± 1.9
	Total	160	122	24	14	29.1 ± 8.1	29.4 ± 9.6	4.9 ± 2.9	3.1 ± 2.1

IPG: ipsilateral parotid gland CPG: contralateral parotid gland


Sébastien Thureau
email: sebastien.thureau@chb.unicancer.frimagerie

Pierre Decazes

David Gensanne

Romain Modzelewski

Sébastien Hapdey

Pierrick Gouel

Isabelle Gardin

Bernard Dubray

Pierre Vera

Intérêt de l'imagerie fonctionnelle pour la radiothérapie Value of functinal imaging for radiotherapy

La radiothérapie a connu depuis 20 ans des avancées majeures, essentiellement liées aux progrès de l'imagerie et aux progrès techniques. Ces avancées ont permis une meilleure définition des volumes cibles et une délivrance optimisée de la dose à l'origine du développement de la radiothérapie conformationnelle par modulation d'intensité (RCMI) et guidée par l'image (IGRT). L'impact principal a été une diminution de la dose délivrée aux organes à risque et, par conséquent, une diminution des toxicités (cancer prostatique, cancer ORL notamment). En parallèle, l'imagerie par Tomographie par Emissions de Positons (TEP) a pris un essor majeur en cancérologie, devenant indispensable dans le bilan de nombreux cancers, l'évaluation et le suivi thérapeutique.

Dans un premier temps, la TEP a été utilisée par les onco-radiothérapeutes pour optimiser la définition des volumes cibles. Sa forte sensibilité pour de nombreux cancers a permis de diminuer les zones irradiées ou les doses délivrées en l'absence de fixation (par exemple, arrêt de l'irradiation ganglionnaire prophylactique dans le cancer pulmonaire). A contrario, elle permet d'éviter l'omission de zones envahies, notamment ganglionnaires, par sa bonne spécificité dans les cancers ORL. Idéalement, cet examen doit être réalisé en position de traitement pour éviter les biais liés aux recalages et fusions des images [START_REF] Thureau | Definition of target volume: When et how can the radiation oncologist use PET?[END_REF].

Le caractère pronostique de nombreux paramètres de la TEP (SUVmax, MTV, TLG…) en fait un examen intéressant pour optimiser et personnaliser les traitements. Dans ce contexte, de nombreux essais ont proposé d'adapter la dose de radiothérapie aux données de la TEP soit pré-thérapeutiques, soit per-radiothérapie. La technicité de la radiothérapie permet aujourd'hui de délivrer une dose hétérogène au sein d'un même volume (dose painting), permettant d'envisager une escalade de la dose sur les volumes les plus hypermétaboliques, par exemple [START_REF] Differding | Radiation dose escalation based on FDG-PET driven dose painting by numbers in oropharyngeal squamous cell carcinoma: a dosimetric comparison between TomoTherapy-HA and RapidArc[END_REF].

Enfin, d'autres traceurs peuvent avoir un intérêt tant pour ce concept du dose painting que pour une personnalisation des traitements. C'est notamment le cas des traceurs de l'hypoxie qui mettent en évidence un pronostic défavorable et permettent d'envisager des traitements plus agressifs chez les patients ayant des tumeurs hypoxiques [START_REF] Vera | all investigators of RTEP5 study (list in annexe). Radiotherapy boost in patients with hypoxic lesions identified by 18F-FMISO PET/CT in non-small-cell lung carcinoma: can we expect a better survival outcome without toxicity? [RTEP5 long-term followup[END_REF] ou, au contrainte, une diminution de la dose chez les patients non hypoxiques ou voyant l'hypoxie de leur tumeur disparaitre au cours du traitement [START_REF] Lee | A phase I/II study of the hypoxic cell sensitizer misonidazole as an adjunct to high fractional dose radiotherapy in patients with unresectable squamous cell carcinoma of the head and neck: a RTOG randomized study (#79-04)[END_REF]. D'autres traceurs comme ceux de la prolifération pourraient avoir également un intérêt. L'association de la très haute technicité de la radiothérapie actuelle et de l'information de l'imagerie notamment fonctionnelle est une voie d'amélioration des traitements encore en cours.