Julien Lombard

Thierry Biben

Samy

Samy Merabia

Electron-phonon effects on the photoacoustic response of gold core-silica shell nanoparticles : from the linear regime to nanocavitation

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Electron-phonon effects on the photoacoustic response of gold core-silica shell nanoparticles : from the linear regime to nanocavitation

I. INTRODUCTION

Gold nanoparticles are widely employed in photoacoustic imaging because of their strong ability to absorb light and the possibility to convert efficiently light in sound through expansion and heat transfer to the environment [START_REF] Mantri | Engineering plasmonic nanoparticles for enhanced photoacoustic imaging[END_REF]. As compared with light scattering and ultrasound scattering, photoacoustic imaging combines the advantage of the sensivity of gold nanostructures light absorption with the weak scattering of sound waves in biological media enabling signal propagation over centimeter length scales [START_REF] Xu | Photoacoustic imaging in biomedecine[END_REF]3]. At the core of this technique is the ability of metallic nanoparticles to convert light in heat, realizing controlled nanoscale sources of heat [START_REF] Govorov | Generating heat with metal nanoparticles[END_REF][START_REF] Baffou | Femtosecond-pulsed optical heating of gold nanoparticles[END_REF][START_REF] Baffou | Thermo-plasmonics: using metallic nanostructures as nano-sources of heat[END_REF]. The nanoparticle resonance wavelength may be shifted to the near infrared region where tissue presents very low absorption [START_REF] Qin | Thermophysical and biological responses of gold nanoparticle laser heating[END_REF].

Although bare gold nanostructures offer clear benefits for photoacoustic applications, they suffer from limitations which restrict their wide use in biological media. In particular, gold surfaces are not chemically stable in the presence of biomolecules [START_REF] Moreira | Gold-core silica shell nanoparticles application in imaging and therapy : a review[END_REF]. Also, the interaction between a laser and gold nanoparticles may yield nanoparticle melting and reshaping [START_REF] Plech | Laser-induced heating and melting of gold nanoparticles studied by time-resolved x-ray scattering[END_REF][START_REF] Hu | Investigation of the properties of gold nanoparticles in aqueous solution at extremely high lattice temperatures[END_REF].

To overcome these limitations it has been long considered to coat gold nanostructures with a dielectric shell [START_REF] Liz-Marzan | Synthesis of nanosized gold-silica core-shell particles[END_REF][START_REF] Chaudhuri | Core/shell nanoparticles : classes, properties, synthesis mechanisms, characterization, and applications[END_REF]. Among the different materials, silica turns out to be a popular choice, because of its chemical inertia, biocompatibility and the wide range of possibilities to functionalize silica surfaces [START_REF] Moreira | Gold-core silica shell nanoparticles application in imaging and therapy : a review[END_REF]. In addition, silica shell may enhance the nanoparticle stability and delay melting [START_REF] Luke | Silica-coated gold nanoplates as stable photoacoustic contrast agents for sentinel lymph node imaging[END_REF][START_REF] Chen | Enhanced thermal stability of silica-coated gold nanorods for photoacoustic imaging and image-guided therapy[END_REF][START_REF] Shen | Enhanced photoacoustic stability of gold nanorods by silica matrix confinement[END_REF].

The photoacoustic response of silica coated nanoparticles has been investigated in the past decade by several groups [START_REF] Chen | Silica-coated gold nanorods as photoacoustic signal nanoamplifiers[END_REF][START_REF] Jokerst | Photoacoustic imaging of mesenchymal stem cells in living mice via silica-coated gold nanorods[END_REF][START_REF] Chen | Environment-dependent generation of photoacoustic waves from plasmonic nanoparticles[END_REF][START_REF] Kumar | Simulation studies of photoacoustic response from gold-silica core-shell nanoparticles[END_REF][START_REF] Shahbazi | Photoacoustics of core-shell nanospheres using comprehensive modeling and analytical solution approach[END_REF][START_REF] Pang | Theoretical and study of photoacoustic excitation of silica-coated gold nanospheres in water[END_REF][START_REF] Pang | Quenching of nonlinear photoacoustic signal generation in gold nanoparticles through coating[END_REF]. Both experimental and modeling studies reported contradictory results concerning the enhancement of the photoacoustic signal of core-shell nanoparticles as compared with bare gold nanoparticles in water. In particular, Chen et al. reported a threefold increase of the photoacoustic response of silica-coated gold nanorods as compared with the uncoated nanorods [START_REF] Chen | Silica-coated gold nanorods as photoacoustic signal nanoamplifiers[END_REF]. This enhancement is thought not to originate from the change of the plasmonic absorption cross-section, but rather to facilitated heat transfer introduced by the silica shell. This interpretation is, at least qualitatively, consistent with time-resolved spectroscopy experiments demonstrating faster heat transfer for gold nanoparticles coated with thin silica shells and immersed in water as compared with bare gold nanoparticles [START_REF] Hu | Heat dissipation in gold-silica core-shell nanoparticles[END_REF]. Faster heat transfer is also found in two-temperature model simulations of heat transfer across gold nanoparticles embedded in very thin silica shell [START_REF] Alkurdi | Enhanced heat transfer with metaldielectric core-shell nanoparticles[END_REF]. Facilitated heat transfer is, in this case, ascribed to electron-phonon processes taking place at the interface between gold and the silica shell. The change of Kapitza resistance due to the presence of the silica shell plays also an important role in photoacoustic enhancement [START_REF] Chen | Silica-coated gold nanorods as photoacoustic signal nanoamplifiers[END_REF][START_REF] Shahbazi | Photoacoustics of core-shell nanospheres using comprehensive modeling and analytical solution approach[END_REF].

Recent experimental and numerical works concluded, however, at a deterioration of the photoacoustic signal for coated gold nanostructures [START_REF] Pang | Theoretical and study of photoacoustic excitation of silica-coated gold nanospheres in water[END_REF][START_REF] Pang | Quenching of nonlinear photoacoustic signal generation in gold nanoparticles through coating[END_REF]. These observations are consistent with earlier heat transfer dynamics studies from gold nanorods [START_REF] Nguyen | Study of heat transfer dynamics from gold nanorods to the environment via timeresolved infrared spectroscopy[END_REF] showing heat transfer slowing down by silica shell. Further, numerical simulations by Pang et al. concluded that the Kapitza resistance has only a mild effect on the photoacoustic response [START_REF] Pang | Theoretical and study of photoacoustic excitation of silica-coated gold nanospheres in water[END_REF].

The relative enhancement or deterioration of photoacoustic signal should be highly dependent on the shell thickness and also on the pulse duration pulse. Indeed, very thin silica shells and short pulse durations yield faster heat transfer to the environment [START_REF] Kumar | Simulation studies of photoacoustic response from gold-silica core-shell nanoparticles[END_REF][START_REF] Alkurdi | Enhanced heat transfer with metaldielectric core-shell nanoparticles[END_REF]. By the way contrast, it is clear that thick shells should slow down heat transfer because of the low thermal conductivity of silica, resulting in photoacoustic decrease [START_REF] Pang | Theoretical and study of photoacoustic excitation of silica-coated gold nanospheres in water[END_REF][START_REF] Nguyen | Study of heat transfer dynamics from gold nanorods to the environment via timeresolved infrared spectroscopy[END_REF]. It is the purpose of this article to study numerically the transition between thin silica shells and thick ones for picosecond and nanosecond laser pulses.

Recent computational studies [START_REF] Kumar | Simulation studies of photoacoustic response from gold-silica core-shell nanoparticles[END_REF][START_REF] Shahbazi | Photoacoustics of core-shell nanospheres using comprehensive modeling and analytical solution approach[END_REF][START_REF] Pang | Theoretical and study of photoacoustic excitation of silica-coated gold nanospheres in water[END_REF] predicted the photoacoustic response of silica coated nanoparticles by considering a single temperature field to describe heat transfer in these composite systems. This one temperature description is a fair approximation for nanosecond pulses, but at sub picosecond time scales, electron-phonon processes neglected in the one temperature description become important. Indeed, we recently showed the role played by electron-phonon processes on the heating kinetics of colloidal gold-core silica shell nanoparticles [START_REF] Alkurdi | Enhanced heat transfer with metaldielectric core-shell nanoparticles[END_REF]. In the context of nanoscale thermal transport, several experimental studies investigated heat transport at metal/dielectric interfaces, at picosecond time scales. Recent transient thermoreflectance experiments probing heat transfer from a gold film to silicon or silica substrates [START_REF] Hopkins | Effects of electron scattering at metal-nonmetal interfaces on electron-phonon equilibration in gold films[END_REF][START_REF] Guo | Heat transfer across metal-dielectric interfaces during ultrafast-laser heating[END_REF][28] concluded on the existence of a direct electron-substrate energy transfer, resulting in an enhanced thermal boundary conductance [START_REF] Lombard | Influence of the electron-phonon interfacial conductance on the thermal transport at metal/dielectric interfaces[END_REF]. This direct electronphonon coupling energy channel has been predicted theoretically twenty years ago [START_REF] Huberman | Electronic Kapitza conductance at a diamond-Pb interface[END_REF][START_REF] Sergeev | Electronic Kapitza conductance due to inelastic electron-boundary scattering[END_REF][START_REF] Mahan | Kapitza thermal resistance between a metal and a nonmetal[END_REF][33],

although the exact nature of this coupling is still an open issue. One important consequence is that thermal transport at metal-non metal interfaces is enhanced when such electronphonon conductance is present [START_REF] Lombard | Influence of the electron-phonon interfacial conductance on the thermal transport at metal/dielectric interfaces[END_REF].

In this work, we compute theoretically the photoacoustic response of silica coated nanoparticles illuminated by short duration laser pulses by taking into account electron-phonon processes inside the nanoparticles. To this end, we employ numerical simulations based on the combination of the two temperature model [START_REF] Kaganov | Relaxation between the electrons and the crystalline lattice[END_REF][START_REF] Anisimov | Electron emission from metal surfaces exposed to ultrashort laser pulses[END_REF] and phase field hydrodynamics simulations [START_REF] Lombard | Threshold for vapor nanobubble generation around plasmonic nanoparticles[END_REF]. Two temperature model can capture the coupled evolution of the electronic and phonon temperatures in metallic systems following laser excitation. In addition, they have been shown to describe accurately the heat transfer kinetics down to nanoscale sizes and for subpicosecond time scales for moderate to strong excitation.

Another regime that we touch upon is the nanocavitation generation which occurs for strong laser pulses. It is known, indeed, that nanocavitation around illuminated gold nanoparticles yields enhanced photoacoustic response [START_REF] Gao | Opto-acoustic effect of au nanoparticles in water under irradiation of pulse laser[END_REF][START_REF] Dixon | Oscaillatory dynamics and in vivi photoacoustic imaging performance of plasmonic nanoparticle-coated microbubbles[END_REF][START_REF] Cavigli | Impact of Kapitza resistance on the stability and efficiency of photoacoustic conversion from gold nanorods[END_REF][START_REF] Lombard | Strong and fast rising pressure waves emitted by plasmonic vapor nanobubbles[END_REF]. However, few studies have considered the effect of silica coating on nanocavitation and on the subsequent photoacoustic response [START_REF] Dagallier | Multiscale modeling of plasmonic enhanced energy transfer and cavitation around laser-excited nanoparticles[END_REF]. Let us mention, however, recent time resolved spectroscopy experiments which concluded that coating delays the onset of cavitation [START_REF] Nguyen | Study of heat transfer dynamics from gold nanorods to the environment via timeresolved infrared spectroscopy[END_REF], but these effects are not understood from a theoretical point of view. The remainder of this article is organized as follows. Section. II introduces the model. Numerical results are presented and discussed in Sec. III. A summary and perspectives are given in Sec. IV.

II. MODEL

Our model is a combination of the two-temperature model [START_REF] Kaganov | Relaxation between the electrons and the crystalline lattice[END_REF][START_REF] Anisimov | Electron emission from metal surfaces exposed to ultrashort laser pulses[END_REF] for the nanoparticle dynamics with a phase field description of the water dynamics. We first present the equations governing the thermal relaxation of the core-shell nanoparticle before introducing the equations supposed to ruling the thermal dynamics of water.

A. Nanoparticle

The system we investigate is a core-shell nanoparticle immersed in water and irradiated by a laser pulse, as represented in (Fig. 1.a). In all the following, we concentrate on a gold core-silica shell nanoparticle and gold nanoparticles for the sake of comparison. After pulsed illumination, thermal relaxation around the nanoparticle involves different channels, as summarized in Figure 1.b. The metal free electrons absorb instantaneously the laser energy, causing a rapid increase of the electronic temperature. This excess energy is then transferred to the silica shell by two different channels. The first channel is a direct coupling between gold electrons and silica phonons and occurs at the core/shell interface through the electron-phonon thermal conductance σ es . The second channel is an indirect coupling which involves electron-phonon energy exchange inside the gold core, quantified by the coupling factor G, and then phonon-phonon thermal coupling at the core/shell interface, quantified by the conductance σ ps . With the heat diffusing in the shell, a thermal flux proportional to the phonon-water conductance σ sw is induced across the shell/water interface, allowing the energy to diffuse in the infinite water reservoir. In the case of a bare gold nanoparticle, Fig. 1.c depicts the different energy channels. They involve, in particular, a thermal flux across the metal/water interface through the interfacial phonon-phonon conductance σ pw .

For the core-shell nanoparticles, the evolution of the different temperatures is supposed to be governed by the following set of equations :

V c c e ∂T e (t) ∂t = -V c G (T e -T p ) -S c σ es (T e -T s (R c , t)) + P(t), (1)
V c c p ∂T p (t) ∂t = V c G (T e -T p ) -S c σ ps (T p -T s (R c , t)) (2)
c s ∂T s (r, t) ∂t = k s ∇ 2 T s , (3)
Here, T e , c e denote the gold electronic temperature and heat capacity respectively; T p and c p denote the gold phonon temperature and heat capacity, T s , c s and k s the silica temperature, heat capacity and thermal conductivity and T w , c w and k w the water temperature, heat capacity and thermal conductivity. While r is the radial distance, R c , S c and V c are the radius, surface and volume of the nanoparticle core. R = R c + d, S and V are the same quantities for the entire nanoparticle, including the shell of thickness d, whose volume is

V s = V -V c .
It is important to realize that, in the previous set of equations eq. 1 and eq. 2, we have assumed uniform temperatures for both the electronic and metal phonon degrees of freedom, as we have already shown that heat diffusion inside the metal core has little effect on the nanoparticle thermal relaxation following the laser excitation [START_REF] Alkurdi | Enhanced heat transfer with metaldielectric core-shell nanoparticles[END_REF].

In the following, we consider for simplicity a square pulse characterized by the power : P(t) = P Θ(t pul -t), with P the average laser power, Θ the Heaviside function and t pul the pulse duration. The average power P is simply related to the laser fluence F and nanoparticle absorption cross-section σ abs (λ), through : P = σ abs (λ)F/t pul , where σ abs is described here by Mie-theory [START_REF] Baffou | Femtosecond-pulsed optical heating of gold nanoparticles[END_REF][START_REF] Bohren | Absorption and scattering of light by small particles[END_REF] for the spherical nanoparticles of interest here.

FIG. 1. Heat transfer from a core-shell nanoparticle and gold nanoparticle heated by a laser pulse.

G is the coupling constant between electrons and phonons in the metal. σ es , σ ps , σ sw and σ pw are the interfacial conductances at the electron/silica, phonon/silica, silica/water and phonon/water interfaces respectively.

In addition to Eqs. ( 1)-(3) describing the temporal evolution of temperatures, the continuity of the heat flux across an interface implies the following boundary conditions at the core/shell interface r = R c and at the the shell/water interface r = R c + d:

-k s ∇T s (R c , t) =σ es (T e -T s (R c , t)) + σ ps (T p -T s (R c , t)) , (4)
-k s ∇T s (R, t) =σ sw (T s (R, t) -T w (R, t)) = -k w ∇T w (R, t). (5)
Finally, as regards initial conditions, all the temperatures are assumed to be at room temperature T 0 .

The equations for the bare gold nanoparticle can be written in a similar manner and are given here for the sake of completeness :

V c c e ∂T e (t) ∂t = -V c G (T e -T p ) + P(t), (6)
V c c p ∂T p (t) ∂t = V c G (T e -T p ) -S c σ pw (T p -T w (R c , t)) (7) = -k w ∇T w (R c , t). ( 8
)
quantity electron phonon silica

k (W m -1 K -1 ) 320.0 3.0 1.37 c (MJ m -3 K -1 )
T 0 = 300 K. quantity value Reference G (MW m -3 K -1 ) 2.5 × 10 10 [43] σ ps (MW m -2 K -1 )
141 [START_REF] Lombard | Influence of the electron-phonon interfacial conductance on the thermal transport at metal/dielectric interfaces[END_REF] σ sw (MW m -2 K -1 ) 150 [START_REF] Hu | Water nanoconfinement induced thermal enhancement at hydrophilic quartz interfaces[END_REF] σ pw (MW m -2 K -1 ) 139 [START_REF] Ge | Thermal conductance of hydrophilic and hydrophobic interfaces[END_REF][START_REF] Shenogina | How wetting and adhesion affect thermal conductance of a range of hydrophobic to hydrophilic aqueous interfaces[END_REF] TABLE II. Electron-phonon coupling constant G and thermal boundary conductances.

We have listed in Tabs. I and II the parameters relevant for the gold-silica core-shell nanoparticles. If not otherwise mentioned, all properties are taken at a temperature T 0 = 300 K.

There are three quantities, however, for which it is essential that the temperature dependence is taken into account, namely the electronic heat capacity c e , the interfacial electronphonon conductance at the core/shell interface σ ep and the coupling factor G. The interfacial electron-phonon conductance at the core/shell interface can be written as :

σ es = A es + B es T e (9)
with the constant A es = 96.1 MW m -2 K -1 and B es = 0.18 MW m -2 K -2 [START_REF] Hopkins | Effects of electron scattering at metal-nonmetal interfaces on electron-phonon equilibration in gold films[END_REF]. For the temperature dependence of the electronic heat capacity and coupling factor, we use results of ab-initio calculations [START_REF] Lin | Electron-phonon coupling and electron heat capacity of metals under conditions of strong electron-phonon nonequilibrium[END_REF]. The resulting quantities are expressed using polynomial fits of the ab-initio calculations in the form described in the Appendix V.

B. Water dynamics

The dynamics of the fluid is described by a hydrodynamic phase field model based on the generic mass, momentum and energy conservation equations:

∂ρ ∂t + ∇ • (ρv) = 0, ( 10
)
mρ(r) ∂v ∂t + v • ∇v = -∇ • (P -D) , (11)
mρ(r)c v (r) ∂T w ∂t + v • ∇T w = -l(r)∇ • v (12) +∇ • (k w (r)∇T w ) + D : ∇v,
In these equations, ρ(r) stands for the molecular density at a given position r outside the nanoparticle, T w (r) and v(r) are respectively the temperature and the velocity field inside the fluid. Due to the thermal gradient generated by the nanoparticles, properties like the thermal conductivity of the fluid k w (r), the specific heat c v (r) and the Clapeyron coefficient l(r) have a spatial dependence that we emphasize in equation [START_REF] Chaudhuri | Core/shell nanoparticles : classes, properties, synthesis mechanisms, characterization, and applications[END_REF]. m is the molecular mass and the two tensors P and D stand respectively for the pressure tensor and the dissipative stress tensor. The dissipative stress tensor takes the usual newtonian form:

D αβ = η (∂ α v β + ∂ β v α ) + µ - 2η 3 ∇.v δ αβ ,
with η and µ the shear and bulk viscosities respectively, and δ αβ is the Kronecker symbol.

We shall assume here µ ≃ 5η/3 [START_REF] Schweizer | Activated hopping, barrier fluctuations, and heterogeneity in glassy suspensions and liquids[END_REF], as it is the case for hard-sphere fluids. Since the viscosities may differ in the liquid and the vapor phases, we use a linear prescription for their local expression:

η(r) = η vap + ρ(r) -ρ vap ρ liq -ρ vap (η liq -η vap ) ,
where the subscripts "vap" and "liq" refer to the bulk values at 297 K referenced in Table III.

The same linear relationship with the density will be used for the thermophysical coefficients including the thermal conductivity λ and the specific heat c v .

Due to the inhomogeneity of the system, and the possible formation of interfaces, the pressure tensor is not necessarily isotropic. A generic prescription for P is given by the Korteweg expression, that accounts for interfacial effects: where P bulk is the bulk pressure, that controls the phase behavior of the fluid, and serves to calculate the Clapeyron coefficient :

P αβ = P bulk -wρ∆ρ - w 2 (∇ρ) 2 δ αβ + w∂ α ρ∂ β ρ,
l = T w ∂P bulk ∂T ρ
w is a parameter related to the liquid-vapor interface thickness and controls the value of the surface tension. We set w = 1.16 10 -20 J m 5 /mol 2 to reproduce water surface tension at

room temperature σ LV = 72 10 -3 J m -2 .
The equations [START_REF] Hu | Investigation of the properties of gold nanoparticles in aqueous solution at extremely high lattice temperatures[END_REF][START_REF] Liz-Marzan | Synthesis of nanosized gold-silica core-shell particles[END_REF][START_REF] Chaudhuri | Core/shell nanoparticles : classes, properties, synthesis mechanisms, characterization, and applications[END_REF] are quite generic and combined with the fluid equation of state, they form the basis of conventional diffuse interface approaches [START_REF] Anderson | Diffuse-interface methods in fluid mechanics[END_REF], that have been applied succesfully to describe boiling at the nanoscale [START_REF] Onuki | Dynamic van der waals theory of two-phase fluids in heat flow[END_REF][START_REF] Onuki | Dynamic van der waals theory[END_REF].

The specificity of the present approach is to describe the properties of water in a more quantitative way. To extend previous studies using the van der Waals thermodynamic model for the fluid [START_REF] Lombard | Threshold for vapor nanobubble generation around plasmonic nanoparticles[END_REF][START_REF] Lombard | Strong and fast rising pressure waves emitted by plasmonic vapor nanobubbles[END_REF][START_REF] Onuki | Dynamic van der waals theory of two-phase fluids in heat flow[END_REF][START_REF] Onuki | Dynamic van der waals theory[END_REF][START_REF] Lombard | Kinetics of nanobubble generation around overheated nanoparticles[END_REF][START_REF] Lombard | Nanobubbles around plasmonic nanoparticles: Thermodynamic analysis[END_REF], we shall make use of a better thermodynamic model specially designed for water: this model of Jeffery and Austin [START_REF] Jeffery | A new analytic equation of state for liquid water[END_REF]. Although based on a van der Waals description, the model includes temperature dependences of the coefficients that have been adjusted to reproduce more accurately the thermodynamic properties of water, both on the liquid and the vapor side. Furthermore, the model contains low temperature corrections that permit to account for many specificities of water, like its maximal density around 3 C.

These properties are due to the existence of hydrogen bonds that are absent in the generic van der Waals description. Thanks to this model we aim at a better quantitative description of the acoustic response of water following thermal exictation of the nanoparticle.

The model is constructed as follows: the bulk pressure is splitted in two contributions, a van der Waals like contribution P EOS and the hydrogen bonds contribution P HB [START_REF] Jeffery | A new analytic equation of state for liquid water[END_REF]:

P bulk = P EOS + P HB , P EOS ρRT w = 1 -b * + a vW RT w ρ + αρ 1 -λb(T w )ρ .
The function b(T w ) takes the form:

b(T w ) =v B 0.2 exp -21.4 (T w /T B + 0.0445) 3 -b 1 exp (1.016 T w /T B ) + b 2 } .
Here, v B and T B are respectively the Boyle volume and temperature, and the constants appearing in these expressions are given by:

v B = 0.069405 nm 3 b 1 = 0.25081 T B = 1408.4 K b 2 = 0.99859 b * = 0.075117 nm 3 λ = 0.3241 α = 0.148874 nm 3 a vW = 27R 2 T 2 c 64Pc = 1.
5292 MPa nm 6 Note that b 1 , b 2 and λ are dimensionless constants. Following [START_REF] Jeffery | A new analytic equation of state for liquid water[END_REF], the hydrogen bond contribution is given by:

P HB = -ρ 2 RT w ∂f ∂ρ log Ω 0 + Ω HB exp(-ǫ HB /RT w ) Ω 0 + Ω HB with: f = 1 + C 1 exp ρ-ρ HB σ 2 + C 1 exp -0.18 T w T f 8 ,
the fraction of hydrogen bonds in a dense state. The various constants entering in these expressions are given by [START_REF] Jeffery | A new analytic equation of state for liquid water[END_REF]:

Ω 0 = exp(-S 0 /R) Ω HB = exp(-S HB /R) S 0 = -61.468 J/mol/K S HB = -5.128 J/mol/K ǫ HB = -11.490 kJ/mol C 1 = 0.7140 σ = 0.1687ρ HB ρ HB = 28.2nm -3 T f = 273.15 K
As previously mentionned, the temperature evolution of the fluid is coupled to that of the nanoparticle through the conductive flux at its surface [START_REF] Baffou | Femtosecond-pulsed optical heating of gold nanoparticles[END_REF]. Note that our model neglects the nanoparticle expansion due to its heating. Indeed, we have observed that this expansion plays a minor role in the amplitude of the emitted pressure wave in the cavitation regime [START_REF] Lombard | Strong and fast rising pressure waves emitted by plasmonic vapor nanobubbles[END_REF]. Far away from the nanoparticle, perfectly match layers are implemented to avoid any reflection of the pressure waves generated by the sudden vapor generation, as detailed in [START_REF] Lombard | Nanobubbles around plasmonic nanoparticles: Thermodynamic analysis[END_REF]. We consider a spherically symmetric system that allows us to focus only on the radial component of the fields. The nanoparticles have a total radius ranging from 50 to 70 nm. The simulation cell, which is centered on the nanoparticle, has a size L=6 µ m.

We use a space step of 0.2 nm and a maximum time step of dt max = 0.4 fs. Note that the initial thermal relaxation of the nanoparticle is much faster than the subsequent processes, in particular in the case of the 1 ps duration heating. To obtain a valid description of this relaxation, the time step is automatically reduced so that the maximum temperature variation in the particle during a time step is less than or equal to 0.1 K. A faster convergence of the code is obtained using a second order Runge-Kutta implementation of the conservation equations 1-3 and 10-12. The velocity field is calculated on a staggered grid, shifted from the main grid by half a lattice constant [START_REF] Lombard | Nanobubbles around plasmonic nanoparticles: Thermodynamic analysis[END_REF].

The radius of the metallic core of the particles is maintained at 50 nm and we focus our study on the effect of the thickness d of the silica shell. The effective absorption section of the particles therefore remains constant and is equal to σ = 7.906 10 -15 m 2 at the plasmon resonance wavelength λ = 530 nm.

III. RESULTS

In this section, we present the results for the photoacoustic response of core-shell nanoparticles immersed in water and compare to the case of bare gold nanoparticles. The nanoparticles are supposed to be irradiated by a laser pulse having a wavelength close to the plasmon resonance, λ = 530 nm, and we consider two pulse durations, t p = 1 ps and t p = 1 ns.

In all the following, the gold core radius R c is fixed at the value R c = 50 nm, so that the comparison between homogeneous gold nanoparticle and core-shell is made at a constant value of the absorption cross-section σ abs (λ). We will separate the case where the fluence is below the threhsold for nanocavitation to the case where the fluence is above the threshold.

A. Below the nanocavitation threshold

We first consider the case of relatively low fluences F . In this regime, water in the vicinity of the nanoparticle is heated up at a maximal temperature below water spinodal temperature T s ≃ 550 K, and no bubble formation occurs.

Figure 2 illustrates the pressure propagation in water for a short duration-picosecond-pulse.

The waves are emitted at the nanoparticle surface and propagate over microns in water, the propagation being accompanied by dispersion. From the analysis of the position of the maximum wave position, one can infer an apparent sound velocity, whose value c w = 1524 m/s is found to be close to the value of sound velocity in water under normal conditions.

The wave amplitude decays spatially as r α , with α = 1.57, a value typical of laser-induced stress wave propagation [START_REF] Doukas | Physical characteristics and biological effects of laser-induced stress waves[END_REF][START_REF] Shahbazi | Photoacoutsics of core-shell nanospheres using comprehensive modeling and analytical solution approach[END_REF]. The temporal evolution of the pressure in water at a distance R = 500 nm from the nanoparticle center is shown in Fig. 3. We choosed a distance R = 500 nm as it is a typical distance in a biological cell environment. Two different behaviours may be highlighted depending on the laser pulse duration. For a short pulse duration, core shell nanoparticles with a thin silica shell display the largest photoacoustic response. Core-shell nanoparticles having a silica thickness larger than 10 nm display, however, a photoacoustic response lower than the corresponding bare nanoparticle. Also importantly, when the electron-phonon channel is switched off, the maximal pressure signal generated by core-shell nanoparticles, whatever the silica thickness, is lower than the signal corresponding to the homogeneous nanoparticle.

100
This tends to conclude that electron-phonon processes taking place at the interface between gold and silica play a leading role in the enhancement of the photoacoustic response of coreshell nanoparticles.

For longer pulse durations, a slighty different scenario holds. First, the pressure signal has a longer duration, being of compressive nature before the end of the pulse and tensile after the pulse is switched off, as seen in in Fig. 4. In this figure, we generalize the qualitative behaviour discussed before. First, for picosecond laser pulses, the maximal values of the pressure correspond to the core-shell nanoparticle having the thinnest silica shell, d = 5 nm. Core-shell nanoparticles having shell thickness larger than 10 nm display a photoacoustic response lower than the homogeneous gold nanoparticle. When the electron-phonon coupling at interface is switched off, however, the maximal pressure is always smaller for the core-shell nanoparticles in comparison with the homogeneous nanoparticle. Secondly, for the nanosecond pulse case, the bare gold nanoparticle displays the highest photoacoustic response. The maximal amplitude generated by core-shell nanoparticles is relatively lower and decreases for thick silica coating. In the nanosecond case also, the electron-phonon conductance σ es contributes to enhance the photoacoustic response of core-shell nanoparticles, though its role is less critical as compared to the short pulse duration case. To interpret the relatively high response of core-shell nanoparticles, we examined in Fig. 6 the temporal evolution of the different temperatures across the system. Apart from the electronic temperature T e and the gold phonon temperature T core , we considered also the silica and water temperatures at the position of the nanoparticle/water interface. Let us first concentrate on the case where the electron-phonon coupling at gold-silica interface is on. In this case, it is clear that electrons cool down faster in the core-shell nanoparticle as compared with the gold particle. This fast cooling is a direct consequence of the coupling between the metal electrons and the silica shell. Consequently, the silica shell is heated up on a 10 picosecond time scale and contributes to heat up water on the same short time scale.

This fast heating is responsible for the peak pressure observed in water at short times, giving rise to the photoacoustic propagation in water. By the way of contrast, in the case of the homogeneous nanoparticle, liquid water is heated up on a much longer time scale. This is a result of the slow cooling kinetics of the electrons and the subsequent heating of the core phonons. Figure 5 shows that the relative low temperature level reached in water around the bare gold nanoparticle explains the fact that the photoacoustic response is of moderate amplitude. The situation is different when the electron-phonon coupling is turned off as demonstrated in Fig. 6. In this latter case, the gold electrons cooling kinetics is the same for the bare nanoparticle and the core-shell nanoparticle. As a consequence, silica is heated up on longer time scales as compared to the case σ es = 0. The direct coupling between the gold particle and water enables a relatively fast heating of the environment and the subsequent photoacoustic response. In the case of the core-shell nanoparticle, water is heated up on a longer time scale, due to the presence of the silica coating. The resulting maximal surface pressure is therefore lower, in qualitative agreement with the lower photoacoustic response. The effect of the silica shell thickness on water heating may be seen in fig. 6 for the two laser pulse durations. For the picosecond pulse case, the electronic temperature T e is maximal after 1 ps. The electron cooling occurs faster in the core-shell nanoparticles with electron-phonon interfacial coupling. Note that even in the absence of electron-phonon coupling, the electrons in the core-shell nanoparticles cool down faster than in the homogeneous particle, when the silica shell thickness is larger than 5 nm. The effect of σ es may be clearly seen in the heating of the silica shells, as shown in the middle figure. Silica may be significantly heated up on a short ∼ 10 ps time scale if the shell thickness is thin enough (5 nm). For thicker shells, silica is less heated up and the maximal temperature is reached on a longer time scale. This observation is related to the relatively low thermal conductivity of silica. The effect of the electron-phonon coupling is here again striking and plays a pivotal role in the silica heating kinetics. As a result, water in the vicinity of the nanoparticle may see its temperature raising on a 10 picosecond time scale, especially for 5 nm thick silica shells, noticeably faster than the water kinetics surrounding the gold nanoparticle. This effect disappears for thick silica shell or when the electron-phonon interfacial channel is turned off. In the nanosecond pulse case, the analysis of the different temperatures may shed some light in the behavior outlined before. Here again, despite the fact that the laser duration is longer, the electrons cool down faster in the core-shell nanoparticles even in the absence of electron-phonon coupling. Note that the maximal electronic temperature is attained at the end of the pulse, t = 1 ns. At this time, the silica temperature starts to decrease. Note that the electron-phonon conductance σ es has less influence on the silica cooling kinetics on these time scales. This observation may be explained by the fact that, in the nanosecond time scale, the electrons maximal overheating 300 K is one order of magnitude lower than the corresponding overheating reached in the picosecond time scale 3000 K. As a consequence, core-shell nanoparticles heat up water less than homogeneous gold particles.

B. Nanocavitation regime

Here, we discuss the photoacoustic response displayed by the core-shell nanoparticles in the high fluence regime, where cavitation around the nanoparticles occurs. As shown in [START_REF] Lombard | Threshold for vapor nanobubble generation around plasmonic nanoparticles[END_REF][START_REF] Metwally | Fluence Threshold for Photothermal Bubble Generation Using Plasmonic Nanoparticles[END_REF], cavitation occurs when water temperature at a distance 1 nm from the nanoparticle surface reaches water spinodal temperature, around 550 K. Under these conditions, transient nanobubbles are generated and we already studied their dynamics elsewhere [START_REF] Lombard | Strong and fast rising pressure waves emitted by plasmonic vapor nanobubbles[END_REF][START_REF] Lombard | Nanobubbles around plasmonic nanoparticles: Thermodynamic analysis[END_REF].

Here, we concentrate on the effect of the silica shell thickness on the acoustic emission fol- lowing the generation of a nanobubble.

Figure 7 shows the evolution of the cavitation fluence threshold with the silica shell thickness.

Is is seen that the cavitation threshold is higher for core-shell nanoparticles as compared with bare gold particles. The threshold increases with the shell thickness and is relatively higher for nanosecond pulses. Again, we can see the role of the interface electron-phonon processes, which tend to lower the cavitation threshold : in the absence of this channel, the threshold fluence is slightly enhanced, both for picosecond and nanosecond pulse durations.

Next, we examine the photoacoustic response of the core-shell nanoparticles beyond cavitation, see Fig. 8. In the case of a picosecond pulse, we clearly see that still beyond cavitation threshold, the core shell nanoparticles with a thin silica shell display higher photoacoustic response as compared to the bare gold nanoparticle. Even core-shell nanoparticles with a thicker silica coating 10 nm may perform better than the bare gold nanoparticle at high fluences. This being said, we note that the interface electron-phonon conductance plays a leading role in the high values of the maximal pressure amplitude.

In the absence of this energy channel, the pressure wave amplitude emitted by core-shell nanoparticles decreases significantly. In the case of a nanosecond pulse, the situation is slightly different. As seen in Fig. 8, the cavitation fluence threshold is marked by a jump of the pressure amplitude. Note that we already observed this behaviour in the case of the pressure emission around bare gold nanoparticles irradiated by nanosecond pulse [START_REF] Lombard | Strong and fast rising pressure waves emitted by plasmonic vapor nanobubbles[END_REF]. Here, we can remark that the jump occurs for increasing fluence levels when the shell thickess increases. Noteworthy also is the fact that beyond the cavitation threshold, the pressure amplitude seems to be weakly dependent on the shell thickness. Contrary to the low fluence regime, core shell nanoparticle may display relatively high photoacoustic response, especially for thin silica shells. The electron-phonon coupling at the interface plays a role here, though it has a least effect as compared to the picosecond pulse case. We highlighted the major role played by the electron-phonon coupling between gold electrons and silica inside the core-shell nanoparticle. The existence of this energy channel has been recently evidenced experimentally by means of time resolved thermoreflectance. The effect of this channel is particularly important when electrons and phonons are highly out of equilibrium, a situation occuring when the nanoparticle is irradiated by a short duration laser pulse. To preserve the benefit of the gold electron-silica phonon coupling one needs, however, to minimize the silica shell thickness in which large temperature gradients may set in as a result of the low thermal conductivity of silica. Following these qualitative conclusions, our numerical simulations show that core-shell nanoparticles having a shell thickness smaller than 10 nm and irradiated by picosecond laser pulse display a larger photoacoustic response as compared with bare gold nanoparticles having the same absorption cross-section.

On the contrary, core shell nanoparticles with a thicker shell or core shell nanoparticles irradiated by a nanosecond laser pulse generally have a relatively low photoacoustic response as compared with homogeneous gold nanoparticles.

These results are, at least qualitatively, consistent with earlier investigation of heat transfer across core-shell nanoparticles [START_REF] Hu | Heat dissipation in gold-silica core-shell nanoparticles[END_REF] which demonstrated better efficiency to transfer heat to their water environment as compared with gold nanoparticles. Our conclusions are also in line with other computational studies which concluded on the deterioration of the photoacoustic signal induced by the silica coating [START_REF] Shahbazi | Photoacoustics of core-shell nanospheres using comprehensive modeling and analytical solution approach[END_REF][START_REF] Pang | Theoretical and study of photoacoustic excitation of silica-coated gold nanospheres in water[END_REF][START_REF] Pang | Quenching of nonlinear photoacoustic signal generation in gold nanoparticles through coating[END_REF]. In particular, for nanosecond pulses we concluded that silica coating tends to diminish the photoacoustic signal unless nanocavitation occurs which is beneficial for thin silica shells.

This work may be extended in different directions. First, we considered here gold-silica core shell nanoparticles, but electron-phonon processes should take place in a wide array of metal/dielectric interfaces. Considering different core materials and coatings may help optimize the photothermal response of core shell nanoparticles. Modelling these effects calls for the determination of the electron-phonon conductance of different metal/dielectric interfaces using either time resolved thermoreflectance or first principles calculations. Secondly, we concentrated in this article on gold silica nanospheres, but interfacial electron-phonon processes should obviously play a role for other geometries. Apart from silica coated nanorods, concentrated core-shell multilayers offer the promise to tune the photoacoustic conversion efficiency of heterogeneous nanoparticles [START_REF] Bardhan | Nanospherein-a-nanoshell: A simple nanomatryushka[END_REF][START_REF] Meng | Plasmonic nano-oven by concatenation of multishell photothermal enhancement[END_REF].

In this appendix, we give the expressions of the temperature dependent electron-phonon coupling constant and the electronic heat capacity.

G =           
where T inf = 2700 K and T sup = 20000 K are two reference temperatures used for the polynomial fits. The parameters in equations 13-14 are given in Table IV.

FIG. 2 .

 2 FIG. 2. Propagation of thermally-induced pressure waves away from the nanoparticle. Pressure profile at different times. The dashed lines indicate the pressure amplitude as it propagates in liquid water. Inset : Evolution of the maximum wave position as a function of time. The nanoparticle considered here is a gold core silica shell particle with a core radius R c = 50 nm, a shell thickness d = 5 nm, the pulse duration t p = 1 ps and the fluence F = 77 J/m 2 .

FIG. 3 .

 3 FIG.3. Temporal evolution of the pressure at a distance 500 nm from the nanoparticle surface, for a 1 ps pulse (left) and 1 ns pulse (right). For the two pulse durations, the laser fluence is F = 77 J/m 2 . Black lines correspond to a gold nanoparticle, while red, green and blue lines correspond to core-shell nanoparticles having respectively a shell thickness 5, 10 and 20 nm. Solid lines refer to the case with electron-phonon coupling at interfaces, while dashed lines correspond to the absence of electron-phonon coupling σ es = 0. The gold core considered here has a radius R c = 50 nm.

Fig 3 .FIG. 4 .

 34 FIG. 4. Maximum of the pressure wave measured at a distance R = 500 nm from the nanoparticle center, for core-shell nanoparticles having different silica thicknesses, 5 nm (down triangles), 10 nm (diamonds) and 20 nm (up triangles) compared with bare gold nanoparticles (black circles). For core-shell nanoparticles, open symbols correspond to the case with electron-silica conductance σ es , while filled symbols correspond to the case without electron-silica conductance σ es = 0. Left : picosecond pulse duration. Right : nanosecond pulse duration. The gold core considered here has a radius R c = 50 nm.

FIG. 5 .

 5 FIG.5. Temporal evolution of the electronic temperature (red curves), gold phonon temperature (black), silica temperature (purple) and surface water temperature (blue) for a gold-core silica shell nanoparticle having a silica thickness of 5 nm (solid curves) and a homogeneous gold nanoparticle (dashed curves). Left : case with electron -phonon coupling at interface. Right : without electron-phonon coupling σ es . The green curves display the temporal evolution of the pressure at the nanoparticle surface. The pulse duration is t p = 1 ps and the fluence is F = 77 J/m 2 . The gold core considered here has a radius R c = 50nm.

FIG. 6 .

 6 FIG.[START_REF] Baffou | Thermo-plasmonics: using metallic nanostructures as nano-sources of heat[END_REF]. Temporal evolution of the electronic temperature T e (left figures), the silica temperatures (middle) and the water temperature at the nanoparticle surface (right figures) for the gold nanoparticle (black lines) and the core-shell nanoparticles having shell thickness : 5 nm (red), 10 nm (green) and 20 nm (blue). Solid lines refer to the case with electron-phonon coupling at interfaces, while dashed lines correspond to the absence of electron-phonon coupling σ es = 0. for the electronic temperatures T e , we have zoomed the long time behaviour in the insets of the corresponding figures. The fluence is F=77 J/m 2 and the gold core considered here have all a radius R c = 50nm.

FIG. 7 .

 7 FIG. 7. Fluence threshold for nanocavitation as a function of the silica shell thickness. Vanishing shell thickness corresponds to the bare gold nanoparticle. Left : case with electron-silica conductance σ es . Right : without electron-silica conductance σ es = 0. Solid lines are guides to the eye.The gold core considered here has a radius R c = 50 nm.

FIG. 8 .FIG. 9 .

 89 FIG. 8. Same as Fig. 4 in the high fluence regime, where cavitation occurs. Left : picosecond pulse duration. Right : nanosecond pulse duration.

Figure 9

 9 Figure 9 summarizes our findings : for picosecond pulses, thin silica shells display the highest photoacoustic response, both in the low fluence and high fluence regimes. By contrast, in the case of nanosecond pulses, the presence of a silica shell tends to diminish the photoacoustic signal in the low fluence regime, below nanocavitation. Beyond cavitation, however, the photoacoustic signal is amplified and the generation of nanobubbles may help core-shell nanoparticles to emit relatively strong pressure waves.

- 2 1 - 4 . 2 - 6 .64 10 8 3 1.01 10 6 4 - 1 .35 10 2 6 - 1 .23 10 - 7

 2142683641261107 Jm -3 K -3 d 3 -1.46 10 -5 Jm -3 K -4 d 4 2.61 10 -9 Jm -3 K -5 g 0 3.03 10 16 Wm -3 K -1 g 98 10 12 Wm -3 K -2 g Wm -3 K -3 g Wm -3 K -4g Wm -3 K -5 g 5 6.84 10 -3 Wm -3 K -6g Wm -3 K -7

  Coefficient Value at ρ liq Value at ρ vap

				Unit
	λ	0.606	0.019	W m -1 K -1
	η	8.98 10 -4	9.9 10 -6	Pa s
	c v	4.13	1.44	kJ kg -1 K -1

TABLE III .

 III Thermophysical parameters for water at its saturation densities.

6

  j=0 g j T j inf , if T e ≤ T inf 6 j=0 g j T j e , if T e ∈ [T inf , T sup ] 6 j=0 g j T j sup , if T e ≥ T sup

			,	(13)
	
	  	4 j=0 d j T j e , if T e ≤ T inf
	
	
	c e =	4 j=0 c j T j e ,	if T
	
	
	
	
	

e ∈ [T inf , T sup ] 4 j=0 c j T j sup , if T e ≥ T sup ,

TABLE IV .

 IV Coefficient appearing in the eqs. 13 and eq. 14.

ACKNOWLEDGMENTS

JL thanks funding from DGAPA UNAM. SM acknowledges financial support from the FET Open project EFINED under the grant agreement 766853.


Keywords: titanium, total hip prosthesis, corrosion, osteolysis, femoral stem inserm-00342857

This study prospectively assessed the outcome of 134 cemented titanium stems and serum ion levels. The stems were smooth and collarless with circular cross-sections.

At endpoint, only one stem revision was performed for aseptic loosening, and two were planned due to subsidence superior to 5 millimetres. Non-progressive radiolucencies in zones 1 and 7 were observed in 16 hips at the cement-interface, without osteolysis. Median serum titanium concentrations were below the detection limit (30 nmol/l) except in patients with failed stems.

The overall stem survival rate was 97.7% at a mean follow-up of 9 years, which is comparable to other series of cemented stems. The protective layer of titanium oxide coating the stem and a thick cement mantle may help resist aseptic loosening.

Introduction

Titanium and its alloys are commonly used for orthopaedic implants such as screws, plates, and spinal implants. This success is explained by the mechanical and biological properties of these materials such as resistance to fatigue, low elasticity modulus to reduce stress shielding, and bio inertness in a physiological environment [START_REF] Head | Titanium as the material of choice for cementless femoral components in total hip arthroplasty[END_REF][START_REF] Krupa | Corrosion resistance and bioactivity of titanium after surface treatment by three different methods: ion implantation, alkaline treatment and anodic oxidation[END_REF]. Despite these properties, the use of polished cemented titanium stems is still debated [START_REF] Barrack | Early failure of modern cemented stems[END_REF][START_REF] Emerson | A comparison of cemented and cementless titanium femoral components used for primary total hip arthroplasty: a radiographic and survivorship study[END_REF][START_REF] Thomas | Corrosion of cemented titanium femoral stems[END_REF]. Titanium stems are thought to be highly sensitive to corrosion and micromotion leading to early aseptic loosening [START_REF] Emerson | A comparison of cemented and cementless titanium femoral components used for primary total hip arthroplasty: a radiographic and survivorship study[END_REF][START_REF] Thomas | Corrosion of cemented titanium femoral stems[END_REF][START_REF] Jergesen | Clinical outcome in total hip arthroplasty using a cemented titanium femoral prosthesis[END_REF].

Like other metallic orthopaedic implants, titanium stems can release metal debris and ions from their coated surface that may also contribute to titanium stem failure [START_REF] Coleman | Concentration of wear products in hair, blood, and urine after total hip replacement[END_REF][START_REF] Brodner | Serum cobalt levels after metal-on-metal total hip arthroplasty[END_REF][START_REF] Macdonald | Metal-on-metal versus polyethylene in hip arthroplasty: a randomized clinical trial[END_REF][START_REF] Savarino | Ion release in patients with metal-on-metal hip bearings in total joint inserm-00342857, version 1 -28 Nov 2008 replacement: a comparison with metal-on-polyethylene bearings[END_REF][START_REF] Gleizes | Value and limits of determining serum cobalt levels in patients with metal on metal articulating prostheses[END_REF]. Several previous studies investigated ion and particle release into the biological fluid from joint replacement, but to the best of our knowledge no series concerning cemented titanium stems are available [START_REF] Jacobs | Metal release in patients who have had a primary total hip arthroplasty. A prospective, controlled, longitudinal study[END_REF][START_REF] Buly | Titanium wear debris in failed cemented total hip arthroplasty. An analysis of 71 cases[END_REF][START_REF] Jacobs | Release and excretion of metal in patients who have a total hip-replacement component made of titanium-base alloy[END_REF][START_REF] Dorr | Histologic, biochemical, and ion analysis of tissue and fluids retrieved during total hip arthroplasty[END_REF].

In this prospective study, we hypothesized that satisfactory results could be reached with cemented smooth titanium stems that are oval in section. In addition, the titanium ions released into the serum from the stems was measured up to the last time-point, in both unilateral and bilateral hip replacements, to monitor the behaviour of the stems. inserm-00342857, version 1 -28 Nov 2008

Materials and methods

Demographic data:

From January 1997 to December 2000, we prospectively followed a consecutive series of 109 patients who underwent primary total hip replacements performed at our institution (134 joint replacements/ 25 bilateral). All patients provided informed consent for the long duration of this prospective clinical and biological study. They received complete information, including the goals and procedures for blood sampling.

The inclusion criteria were strict; patients with orthopaedic titanium implants other than their hip stem, professional or dental exposure to titanium, previous hip conservative surgical procedures, or renal disease were excluded. Additionally, all patients enrolled were under 60 years of age at the time of surgery. In our practice, this represented less than 20% of all primary total hip arthroplasty performed during the study period.

The average follow up was 9 years, with follow up ranging from 7 to 11 years. The age at the time of arthroplasty ranged from 30 to 60 years (mean age: 54 years). Fifty-three females and 56 males were included. Sixty eight right hips were treated, and 66 left hips. Etiologies were essentially symptomatic stage of osteonecrosis or primary arthritis. Patients were evaluated preoperatively and followed-up with clinical and radiological examinations at regular intervals. Hip function results were rated according to the Harris Hip Score grading system in the preoperative period and latest follow up [START_REF] Harris | Traumatic arthritis of the hip after dislocation and acetabular fractures: treatment by mold arthroplasty. An end-result study using a new method of result evaluation[END_REF].

Prostheses:

The cemented femoral stem was collarless, oval in cross section, and straight (Alizé ® Fournitures Hospitalières, Quimper, France). The implant was made of titanium alloy (TiA16V4) with a polished surface coated with titanium oxide (TiO2) obtained by anodization [START_REF] Lappalainen | Potential of coatings in total hip replacement[END_REF][START_REF] Mouel | 10-year actuarial analysis of a cohort of 156 total hip prostheses of a cemented polished aluminum/polyethylene alloy[END_REF]. The thickness of the titanium oxide layer was 1/10000 micron. Six different sized stems were available.

inserm-00342857, version 1 -28 Nov 2008

This modular stem was combined with a 28 millimeter (mm) Metasul® femoral head (Centerpulse-Zimmer, Warsaw, Indiana, U.S.) using a 12 -14, 5°43 taper.

Tapers were inspected individually before micro threading, using an electro pneumatic system (HIGH PRESSURE ELECTRONIC PNEUMO TRANSDUCER 150015, Solex Metrologie, La Boisse, France) for the taper angle (precision, 1 minute), the diameter at the base, and the diameter at the summit (precision, 1 micron). This inspection was counter-checked by a unit control on a tridimensional machine with 1-micron precision. The micro threading was inspected using a projected side view with a 20x enlargement for the pace, profile, and dimension of the threading (Pexit 14 VS Profile Profector, Pixit Dorsey Gage, Cambridge, UK). Compatibility between cones and heads were controlled and guaranteed by the manufacturers. All of the sockets were "sandwich" cemented Metasul® cups (Weber cups, Centerpulse-Zimmer, Warsaw, Indiana, U.S.). Palacos Genta® cement (Scherring Plough, Brussels, Belgium) was used to cement both components in all cases.

Surgical technique: All procedures were performed following the standard procedure at our institution via an antero-lateral approach on a Judet orthopaedic table [START_REF] Siguier | Mini-incision anterior approach does not increase dislocation rate: a study of 1037 total hip replacements[END_REF]. In order to obtain a complete and thick cement mantle, the canal was over-reamed by 2 mm. Then the femoral canal was washed, brushed, and distally occluded by a resorbable femoral plug (Synplug®, Zimmer, Warsaw, Indiana, U.S). The cement was inserted retrogradedly using a gun.

Radiological evaluation and clinical assessment:

Anteroposterior (AP) and lateral radiographs of each hip were available before and immediately after surgery, 6 weeks after discharge from the hospital, and at 3 months, 6 months, 1 year, and then yearly thereafter.

We defined radiographic loosening of the cup as the presence of radiolucent lines measuring at least two millimeters according to DeLee-Charnley zones, axial cup migration of > 5 mm, or > 5° of change in cup inclination on the AP radiographs of the pelvis [START_REF] Delee | Radiological demarcation of cemented sockets in total hip replacement[END_REF].

inserm-00342857, version 1 -28 Nov 2008

Parameters investigated on the femoral side included presence and progression of radiolucent lines according to Gruen et al, calcar resorption or atrophy, subsidence, periprosthetic osteolysis, and cortical hypertrophy [START_REF] Gruen | Modes of failure" of cemented stem-type femoral components: a radiographic analysis of loosening[END_REF]. Loosening of the stem was defined as a migration exceeding 3 mm or a continuous radiolucent line greater than 2 mm. Heterotopic ossifications, if present, were graded according to Brooker et al. [START_REF] Brooker | Ectopic ossification following total hip replacement. Incidence and a method of classification[END_REF].

Titanium serum level determination:

In order to determine titanium release from the femoral stem, dosages were determined in two patient groups: those with unilateral replacements and those with bilateral replacements. Blood samples were taken just before implantation and at 3 months, 6 months, 1 year, and then yearly thereafter until the last end point was reached.

To avoid metallic contamination, blood samples were drawn using a sampling kit specifically After centrifugation, aliquots of plasma were placed in metal-free plastic tubes (2 tubes/sample) and frozen at -20°C. All metal measurements were performed on two samples in order to control for any contamination.

Titanium was measured in blood plasma diluted by Inductively Coupled Optical Emission

Spectrometry (ICP-OES) on a JY24 spectrometer® (Jobin Yvon, Longjumeau, France). The detection limit (DL) was 30 nmol/L of plasma. Concentrations under the DL were set at half the DL value (15 nmol/L) to allow for statistical calculation by convention.

Meanwhile, chromium and cobalt were also determined in the serum from the same samples.

Cobalt and chromium were determined by Electrothermal Atomic Absorption Spectrometry on a simultaneous SIMAA 5100 spectrometer® UNTIL 2004, and then 6100 (Perkin Elmer,

inserm-00342857, version 1 -28 Nov 2008

Courtaboeuf, France). The detection limits were 3 nmol/L for cobalt and 1 nmol/L for cromium. Seronorm Levels I and II (Sero, distributed by Ingen, Rungis, France) were analyzed in each analytical run as internal quality controls. The serum titanium level was expressed in nmol/L (1 nmol/L = 47.9 ng/L=0.0479 µg/L =0.0479 ppb).

inserm-00342857, version 1 -28 Nov 2008

Statistical analysis

Survival analyses were calculated according to the Kaplan-Meier method. Loosened stems (revised or not) were considered as end points. For each time-point, the median as well as the twenty-fifth and seventy-fifth percentiles of serum titanium concentrations were calculated in the unilateral and the bilateral replacement groups. Continuous data were tested for normal distribution using the Kolmogorov-Smirnov test. Normally distributed data were analysed with t-tests.

In order to test for any difference between small stems and larger ones regarding subsidences or radiolucencies, we selected two subgroups of stems within the unilateral hip replacement group. The first subgroup was composed of stems with a size of 1 to 3. In the second subgroup, the sizes of the stems ranged from 4 to 6. A non-parametric Wilcoxon test was performed to detect any difference in these 2 subgroups. Statistical significance was set at p <0.05.

All statistical analyses were carried out with PRISM 3 (GraphPad Software, Inc,San Diego,

U.S.). inserm-00342857, version 1 -28 Nov 2008

Results

Survival rate (Fig 1 ): Overall stem survival (loosened, revised or not) was 97.7% at a mean follow-up of 9 years (95% CI, 95.4%-99.5%).

Complications: Two recurrent dislocations required revisions due to impingement between the titanium femoral neck and the edge of the chromium-cobalt insert of the cup, 1 month and 6 months, respectively, after the implantation. At the time of revision, the components were not loosened; black staining of the joint space was observed due to titanium release from femoral neck notches. In both cases, the patient's serum titanium levels were high due to the release of titanium from the femoral neck lesions. All of the components were revised with the same polished cemented stem and a cemented polyethylene cup.

Eight revisions were performed for loosened Metasul® cemented cups with radiolucencies superior to 2 millimeters and osteolysis.

In the first 3 cases, hips were revised using new metal-on-metal or polyethylene cups with respect to the femur.

Considering the high cobalt-chromium serum levels and the local conditions in 2 revision cases, the bearing surfaces were converted to alumina-on-alumina using a new cementless stem. In last three cases, the hips were revised using alumina-on-alumina with sleeved femoral heads (Ceramtec, Plochingen, Germany) as the taper and the stem fixation was intact.

One case of progressive subsidence due to poor cement technique required a unipolar femoral revision using a cementless stem, 5 years after implantation.

One prosthesis was revised due to persistent and unexplained pain. At the time of the revision, we found no abnormalities apart from a massive and macroscopic metallosis of the joint. The cobalt serum level was increased more than 20-fold compared with the detection inserm-00342857, version 1 -28 Nov 2008 limit. The implants were changed, and new metal-on-metal bearing surfaces were again implanted, but did not resolve the symptoms.

Clinical results:

The mean Harris Hip Score improved significantly (p<0.05) from 39

(range 15-68) preoperatively to 91 (range 83-97) at the ultimate follow-up.

Radiological results:

We observed 4 cases with osteolysis and 16 cases with evolutive radiolucencies at the cement-bone interface on the acetabular side.

Three stem subsidences due to poor cement technique were identified on the early postoperative radiographs. Two were inferior to 10 mm and slowly evolutive with time requiring potential revision in the future (Fig 2). The third was of more concern (subsidence superior to 10 mm) and was revised, as mentioned previously. It was associated with osteolysis in zone 6 of Delee and Charnley [START_REF] Delee | Radiological demarcation of cemented sockets in total hip replacement[END_REF].

Non-progressive femoral radiolucent lines were present in zone 1 at the cement-prosthesis interface in 10 hips, and had spread into zone 7 in six more hips. We did not observe femoral hypertrophic reaction around the distal stem or calcar resorption.

No statistically significant difference (p > 0.05) was observed between small and large titanium stems regarding subsidences (p=0.74) and radiolucency frequencies (p=0.96).

Periarticular ossification, according to the method of Broocker et al. [START_REF] Brooker | Ectopic ossification following total hip replacement. Incidence and a method of classification[END_REF], was observed in 30% of the hips. Eight percent were type III and IV.

Serum titanium concentration:

In both the unilateral and bilateral replacement groups, the median titanium concentration was constant and within range, and always below the detection limit of 15 nmol/l (Tables 1 and2).

inserm-00342857, version 1 -28 Nov 2008

Failed stems, as shown in Table 3, caused the highest titanium serum levels at their end-point in the series, and titanium levels were much higher than the detection limit ranging from 196 to 1274 nmol/l. Titanium serum levels remained below the detection limit in cases with loosened cups.

inserm-00342857, version 1 -28 Nov 2008

Discussion

Use of cemented titanium alloy stems remains extremely controversial and has caused some surgeons to renounce them [START_REF] Barrack | Early failure of modern cemented stems[END_REF][START_REF] Emerson | A comparison of cemented and cementless titanium femoral components used for primary total hip arthroplasty: a radiographic and survivorship study[END_REF][START_REF] Thomas | Corrosion of cemented titanium femoral stems[END_REF]. Some series showed a large rate of early aseptic loosening, usually when the stem was rough and cemented [START_REF] Emerson | A comparison of cemented and cementless titanium femoral components used for primary total hip arthroplasty: a radiographic and survivorship study[END_REF][START_REF] Thomas | Corrosion of cemented titanium femoral stems[END_REF][START_REF] Jergesen | Clinical outcome in total hip arthroplasty using a cemented titanium femoral prosthesis[END_REF][START_REF] Mcgrath | A retrieval study of capital hip prostheses with titanium alloy femoral stems[END_REF][START_REF] Tompkins | A prospective study of a titanium femoral component for cemented total hip arthroplasty[END_REF][START_REF] Ebramzadeh | Long-term radiographic changes in cemented total hip arthroplasty with six designs of femoral components[END_REF]. Jergesen reported an 11.5% aseptic loosening rate in a series of 118 total hip replacements at a mean follow-up of 66 months [START_REF] Jergesen | Clinical outcome in total hip arthroplasty using a cemented titanium femoral prosthesis[END_REF]. In the Scholl E series, the revision rate was 88% at a mean of 6.6 years due to loosened stems, and 30% of cases showed a significant osteolysis of the proximal femur [START_REF] Scholl | Osteolysis in cemented titanium alloy hip prosthesis[END_REF].

Two factors are suggested that explain the early stem failure for the cemented titanium solutions. Firstly, the high elasticity of titanium and the excessive stresses in the mantle of the cement could lead to micromotion and debonding of the stem [START_REF] Emerson | A comparison of cemented and cementless titanium femoral components used for primary total hip arthroplasty: a radiographic and survivorship study[END_REF]. Micro-movements at the cement-stem interface may be responsible for cement mantle breakage and titanium-debris generation inducing necrosis and osteolysis [START_REF] Mcgrath | A retrieval study of capital hip prostheses with titanium alloy femoral stems[END_REF]. The failure risk could be higher for smaller stems due to their greater elasticity, and in males who are physically active [START_REF] Scholl | Osteolysis in cemented titanium alloy hip prosthesis[END_REF], while larger diameter titanium stems may be more successful [START_REF] Jergesen | Clinical outcome in total hip arthroplasty using a cemented titanium femoral prosthesis[END_REF]. In our series, we did not observe this relationship.

The second factor in early stem failure for the cemented titanium implants could be corrosion affecting the cemented, titanium alloy, stem surface. The implant could be deeply damaged by micromotion at the cement-stem interface leading to a progressive abrasion, which later induces a surface corrosion. Retrieval studies on loosened titanium alloy cemented stems report severe corrosion with associated typical crevices [START_REF] Thomas | Corrosion of cemented titanium femoral stems[END_REF][START_REF] Willert | Crevice corrosion of cemented titanium alloy stems in total hip replacements[END_REF]. Scholl found such abrasions in corroded areas in all stem revisions with radiographic osteolysis at the same location [START_REF] Scholl | Osteolysis in cemented titanium alloy hip prosthesis[END_REF].

Tissues were stained black with granuloma, including titanium wear particles. These findings suggest that corrosion could initiate an inflammatory foreign-body reaction that is responsible for the osteolysis of the adjacent bone, and aseptic loosening as seen with polyethylene wear particles.

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The results of this prospective series are not in accordance with these observations.

The overall survival rate of the stems was 97.7% at a mean of 9 years, which makes the failure rate consistent with the survival rate at 10 years of other cemented stems as reported in the Swedish Hip registry |28]. In the past, satisfactory results have been reported in the literature with cemented titanium stems. Known as the "French paradox", the stems were rectangular in cross section, filling the medullary canal of the femur as much as possible with the largest implant associated with a thin cement mantle [START_REF] Langlais | The 'French paradox[END_REF]. Survivorship at ten years ranged from 97% to 99% in these series [START_REF] Nizard | Ten-year survivorship of cemented ceramic-ceramic total hip prosthesis[END_REF][START_REF] Mouel | 10-year actuarial analysis of a cohort of 156 total hip prostheses of a cemented polished aluminum/polyethylene alloy[END_REF].

The present study demonstrated that good results could be achieved with a different design and a different concept. In this cohort, the alloyed femoral stems were smooth, anodized, collarless, oval in section proximally, and circular for the distal 2/3 to reduce stress contact areas around the implants. Collarless implants have been associated with an increase in the frequency and width of radiolucent areas in zones 2 and 7 [START_REF] Kelley | A prospective randomized study of a collar versus a collarless femoral prosthesis[END_REF]. Nevertheless, we did not find such radiographic results and the rate of radiolucent lines was low in our study (14/119) at a mean follow-up of 9 years. Moreover, Meding et al. performed a prospective randomized study of collared versus collarless femoral prosthesis and reported that there was no difference in stem subsidence or functional scores [START_REF] Meding | A comparison of collared and collarless femoral components in primary cemented total hip arthroplasty: a randomized clinical trial[END_REF]. Irrespective of their design or surface coating, all stems have been shown to move inside of their cement mantle in the first years after implantation [START_REF] Alfaro-Adrian | Mid-term migration of a cemented total hip replacement assessed by radiostereometric analysis[END_REF]. Obviously, a polished surface limits the abrasion due to micromotion and ipso facto reduces production of active biological debris. On the contrary, it is established that the roughness of the stem directly influences the amount of debris produced and the rate of femoral loosening [START_REF] Mcgrath | A retrieval study of capital hip prostheses with titanium alloy femoral stems[END_REF][START_REF] Anthony | Localised endosteal bone lysis in relation to the femoral components of cemented total hip arthroplasties[END_REF][START_REF] Mohler | Early loosening of the femoral component at the cement-prosthesis interface after total hip replacement[END_REF]. Better results have been obtained after implantation of titanium alloy stems with a polished surface compared with a rough surface with regard to the aseptic loosening rate [START_REF] Hinrichs | A comparative clinical outcome evaluation of smooth (10-13 year results) versus rough surface finish (5-8 year results) in an otherwise identically designed cemented titanium alloy stem[END_REF]. Resistance to abrasion and corrosion of titanium implants depends on a thin and highly protective surface of oxide film [START_REF] Fini | In vitro and in vivo behaviour of Ca-and P-enriched anodized titanium[END_REF]. The inserm-00342857, version 1 -28 Nov 2008 protective, passive, titanium oxide film (TiO2) is obtained by anodization during the manufacturing process. This titanium oxide surface protects against exposure to air or other oxidizing elements. If scratches occur, this passive layer is supposed to heal and restore itself.

In our series, we experienced 3 femoral subsidences that could be clearly explained by a poor cementing technique. The cementing technique did not follow the "French paradox" guidelines; our cement mantle had to be complete and superior to 2 millimiters thickness using a pressurized cementing technique. Studies focused on stress at the interfaces demonstrated minimal micromotion of the stem when the cement mantle was 3 to 4 millimeter thick around either a titanium or a more rigid, cobalt-chromium implant [START_REF] Ramaniraka | The fixation of the cemented femoral component. Effects of stem stiffness, cement thickness and roughness of the cement-bone surface[END_REF][START_REF] Kawate | Importance of a thin cement mantle. Autopsy studies of eight hips[END_REF].

Moreover, in these studies, high micromovement occurred when the cement was thinner than 2 mm and there was no difference in micromotion or debonding between a titanium and a cobalt-chromium stem [START_REF] Ramaniraka | The fixation of the cemented femoral component. Effects of stem stiffness, cement thickness and roughness of the cement-bone surface[END_REF][START_REF] Kawate | Importance of a thin cement mantle. Autopsy studies of eight hips[END_REF]. A finite-element analysis study identified factors influencing cement strains of the femoral component [START_REF] Estok | Factors affecting cement strains near the tip of a cemented femoral component[END_REF]. The authors of this study found that mantle thickness had the greatest effect on cement strains and suggested that a cement mantle thickness of 2.5 to 5.0 mm was optimal.

In addition to the clinical assessment, we measured the serum titanium levels at each patient follow-up. The only source of titanium particles and ions in this study was the femoral stem. The aim was to monitor the behaviour of the implant as previously performed with chromium or cobalt [START_REF] Brodner | Serum cobalt levels after metal-on-metal total hip arthroplasty[END_REF][START_REF] Jacobs | Can metal levels be used to monitor metal-on-metal hip arthroplasties?[END_REF]. Regarding titanium, several previous reports have shown significantly increased levels in case of failure in arthroplasty [START_REF] Buly | Titanium wear debris in failed cemented total hip arthroplasty. An analysis of 71 cases[END_REF][START_REF] Dunstan | Metal ion levels after metal-on-metal proximal femoral replacements: a 30-year follow-up[END_REF][START_REF] Leopold | Serum titanium level for diagnosis of a failed, metal-backed patellar component[END_REF]. Buly reported a series of failed cemented all-titanium alloy femoral stems with high titanium levels in either dry tissues or synovial fluid [START_REF] Buly | Titanium wear debris in failed cemented total hip arthroplasty. An analysis of 71 cases[END_REF]. Leopold and von Schroeder reported a failed patellar component in total knee arthroplasty, with elevated serum titanium at least 20 times higher than normal values [START_REF] Leopold | Serum titanium level for diagnosis of a failed, metal-backed patellar component[END_REF][START_REF] Kasai | Metal concentrations in the serum and hair of patients with titanium alloy spinal implants[END_REF].

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Although a few studies have analysed titanium release from femoral stems previously, it is difficult to compare their results with ours because of differences in the type of stems (design, coating, etc), mean follow-up, and units [START_REF] Jacobs | Metal release in patients who have had a primary total hip arthroplasty. A prospective, controlled, longitudinal study[END_REF][START_REF] Buly | Titanium wear debris in failed cemented total hip arthroplasty. An analysis of 71 cases[END_REF][START_REF] Jacobs | Release and excretion of metal in patients who have a total hip-replacement component made of titanium-base alloy[END_REF][START_REF] Dorr | Histologic, biochemical, and ion analysis of tissue and fluids retrieved during total hip arthroplasty[END_REF]. In the present study, medians were constant in range up to a mean follow-up of 9 years in both unilateral and bilateral hip replacement groups, and were always under the detection limit. The low serum concentrations observed are reassuring with regard to some concerns about potential titanium toxicity [START_REF] Kasai | Metal concentrations in the serum and hair of patients with titanium alloy spinal implants[END_REF]. Although titanium is considered safe except for its potential osteolytic activity, it circulates throughout the body and particles have been found in hair, lungs, brain, urine, and serum [START_REF] Kasai | Metal concentrations in the serum and hair of patients with titanium alloy spinal implants[END_REF][START_REF] Haynes | The differences in toxicity and release of bone-resorbing mediators induced by titanium and cobalt-chromium-alloy wear particles[END_REF].

The highest titanium serum concentrations were found in cases of mechanical complications such as stem fixation (subsidences) or neck impingement. These findings are in accordance with previous studies that monitored metal release. They could also emphasize the ability of polished and titanium oxide coated surfaces to resist against corrosion and micromotion.

Another potential source of titanium particle release could be the junction between the cobalt-chromium femoral head and the softer femoral taper due to fretting and corrosion. In all of our revision cases, we carefully studied the femoral taper. In the 2 revisions with an exchange of the femoral stem, both the head and taper were under the specifications and we did not observe significant lesions in the contact areas. Our interpretation of higher serum titanium levels in a few patients is the unusual fretting and corrosion of the stem against the cement mantle. In the revision cases without femoral stem exchange, an inspection of the taper did not show significant alteration of the implant, allowing us to use sleeved revision femoral heads according to the recommendations.

In conclusion, this series shows that satisfactory results can be achieved using cemented, smooth, and oval in section titanium alloy stems. In addition, these results are consistent with series using other cemented implants [START_REF] Malchau | The Swedish Total Hip Replacement Register[END_REF]. A thick cement mantle combined inserm-00342857, version 1 -28 Nov 2008 with a polished, anodized surface may play a major role in minimizing the debris source and the stress at the interfaces.

The high rate of acetabular loosening in this series of cemented cups questions the potential role of titanium debris. We could not find an argument for this hypothesis. We did not observe relationships between acetabular loosening and high titanium serum levels; headneck modularity did not seem responsible. Moreover, all the tapers were intact at the time of the revision. In addition, titanium serum levels found in this study showed satisfactory monitoring of the stems.

  dedicated to trace element determination: a needle for S-Monovette ® (ref. 85.1162.400) and 7.5 mL S-Monovette ® Lithium Heparin for Trace Metal analysis (ref. 01.1604.400) from Sarstedt (Marnay, France). Two Monovettes were sampled and numbered in sampling order.

FiguresFig 1 :Fig 2 :

 12 Figures

Table 1 :

 1 Serum titanium levels in the unilateral hip replacement group

Table 2 :

 2 Serum titanium levels in the bilateral hip replacement group

Table 3 :

 3 Serum titanium levels in the group with failed stems inserm-00342857, version 1 -28 Nov 2008