G Tommei
email: tommei@dm.unipi.it

A Milani
email: milani@dm.unipi.it

D Vokrouhlický

Light-time computations for the BepiColombo Radio Science Experiment

Keywords: Mercury, Interplanetary tracking, Light-time, Relativistic effects, Range, Range rate, Shapiro effect

The Radio Science Experiment is one of the on board experiments of the Mercury ESA mission BepiColombo that will be launched in 2014. The goals of the experiment are to determine the gravity field of Mercury and its rotation state, to determine the orbit of Mercury, to constrain the possible theories of gravitation (for example by determining the post-Newtonian parameters), to provide the spacecraft position for geodesy experiments and to contribute to planetary ephemerides improvement. This is possible thanks to a new technology which allows to reach great accuracies in the observables range and range rate; it is well known that a similar level of accuracy requires studying a suitable model taking into account numerous relativistic effects. In this paper we deal with the modelling of the spacetime coordinate transformations needed for the light-time computations and the numerical methods adopted to avoid rounding-off errors in such computations.

Introduction

BepiColombo is an European Space Agency mission to be launched in 2014, with the goal of an in-depth exploration of the planet Mercury; it has been identified as one of the most challenging long-term planetary projects. Only two NASA missions had Mercury as target in the past, the Mariner 10, which flew by three times in [1974][1975] and Messenger, which carried The BepiColombo mission is composed by two spacecraft to be put in orbit around Mercury. The Radio Science Experiment is one of the on board experiments, which would coordinate a gravimetry, a rotation and a relativity experiment, using a very accurate range and range rate tracking. These measurements will be performed by a full 5-way link to the Mercury orbiter; by exploiting the frequency dependence of the refraction index, the differences between the Doppler measurements (done in Ka and X band) and the delay give information on the plasma content along the radio wave path [START_REF] Iess | Advanced radio science instrumentation for the mission BepiColombo to Mercury[END_REF]. In this way most of the measurements errors introduced can be reduced by about two orders of magnitude with respect to the past technologies. The accuracies that can be achieved are 10 cm in range and 3 × 10 -4 cm/s in range rate.

How do we compute these observables? For example, a first approximation of the range could be given by the formula

r = |r| = |(x sat + x M ) -(x EM + x E + x ant )|, ( 1
)
which models a very simple geometrical situation (Fig. 1). The vector x sat is the mercurycentric position of the orbiter, the vector x M is the position of the center of mass of Mercury (M) in a reference system with origin at the Solar System Barycenter (SSB), the vector x EM is the position of the Earth-Moon center of mass in the same reference system, x E is the vector from the Earth-Moon Barycenter (EMB) to the center of mass of the Earth (E), the vector x ant is the position of the reference point of the ground antenna with respect to the center of mass of the Earth.

Using (1) means to model the space as a flat arena (r is an Euclidean distance) and the time as an absolute parameter. This is obviously not possible because it is clear that, beyond some threshold of accuracy, space and time have to be formulated within the framework of Einstein's theory of gravity (general relativity theory, GRT). Moreover we have to take into account the different times at which the events have to be computed: the transmission of the signal at the transmit time (t t ), the signal at the Mercury orbiter at the time of bounce (t b ) and the reception of the signal at the receive time (t r ).

Formula ( 1) is used as a starting point to construct a correct relativistic formulation; with the word "correct" we do not mean all the possible relativistic effects, but the effects that can be measured by the experiment. This paper deals with the corrections to apply to this formula to obtain a consistent relativistic model for the computations of the observables and the practical implementation of such computations.

In Sect. 2 we discuss the relativistic four-dimensional reference systems used and the transformations adopted to make the sums in (1) consistent; according to [START_REF] Soffel | The IAU 2000 resolutions for astrometry, celestial mechanics, and metrology in the relativistic framework: explanatory supplement[END_REF], with "reference system" we mean a purely mathematical construction, while a "reference frame" is a some physical realization of a reference system. The relativistic contribution to the time delay due to the Sun's gravitational field, the Shapiro effect, is described in Sect. 3. Section 4 deals with the theoretical procedure to compute the light-time (range) and the Doppler shift (range rate). In Sect. 5 we discuss the practical implementation of the algorithms showing how we solve the rounding-off problems.

The equations of motion for the planets Mercury and Earth, including all the relativistic effects (and potential violations of GRT) required to the accuracy of the BepiColombo Radio Science Experiment have already been discussed in Milani et al. (2010), thus this paper focuses on the computation of the observables.

Space-time reference frames and transformations

The five vectors involved in formula (1) have to be computed at their own time, the epoch of different events: e.g., x ant , x EM and x E are computed at both the antenna transmit time t t and receive time t r of the signal. x M and x sat are computed at the bounce time t b (when the signal has arrived to the orbiter and is sent back, with correction for the delay of the transponder). In order to be able to perform the vector sums and differences, these vectors have to be converted to a common space-time reference system, the only possible choice being some realization of the BCRS (Barycentric Celestial Reference System). We adopt for now a realization of the BCRS that we call SSB (Solar System Barycentric) reference frame and in which the time is a re-definition of the TDB (Barycentric Dynamic Time), according to the IAU 2006 Resolution B31 ; other possible choices, such as TCB (Barycentric Coordinate Time), only can differ by linear scaling. The TDB choice of the SSB time scale entails also the appropriate linear scaling of space-coordinates and planetary masses as described for instance in [START_REF] Klioner | Relativistic scaling of astronomical quantities and the system of astronomical units[END_REF] or [START_REF] Klioner | Units of relativistic time scales and associated quantities[END_REF].

The vectors x M , x E , and x EM are already in SSB as provided by numerical integration and external ephemerides; thus the vectors x ant and x sat have to be converted to SSB from the geocentric and mercurycentric systems, respectively. Of course the conversion of reference system implies also the conversion of the time coordinate. There are three different time coordinates to be considered. The currently published planetary ephemerides are provided in TDB. The observations are based on averages of clock and frequency measurements on the Earth surface: this defines another time coordinate called TT (Terrestrial Time). Thus for each observation the times of transmission t t and reception t r need to be converted from TT to TDB to find the corresponding positions of the planets, e.g., the Earth and the Moon, by combining information from the pre-computed ephemerides and the output of the numerical integration for Mercury and for the Earth-Moon barycenter. This time conversion step is necessary for the accurate processing of each set of interplanetary tracking data; the main term in the difference TT-TDB is periodic, with period 1 year and amplitude 1.6 × 10 -3 s, while there is essentially no linear trend, as a result of a suitable definition of the TDB.

The equation of motion of a mercurycentric orbiter can be approximated, to the required level of accuracy, by a Newtonian equation provided the independent variable is the proper time of Mercury. Thus, for the BepiColombo Radio Science Experiment, it is necessary to define a new time coordinate TDM (Mercury Dynamic Time), as described in Milani et al. (2010), containing terms of 1-PN order depending mostly upon the distance from the Sun and velocity of Mercury.

From now on, in accordance with [START_REF] Klioner | Units of relativistic time scales and associated quantities[END_REF], we shall call the quantities related to the SSB frame "TDB-compatible", the quantities related to the geocentric frame "TT-compatible", the quantities related to the mercurycentric frame "TDM-compatible" and label them TB, TT and TM, respectively.

The differential equation giving the local time T as a function of the SSB time t, which we are currently assuming to be TDB, is the following:

dT dt = 1 - 1 c 2 U + v 2 2 -L , ( 2
)
where U is the gravitational potential (the list of contributing bodies depends upon the accuracy required: in our implementation we use Sun, Mercury to Neptune, Moon) at the planet center and v is the SSB velocity of the same planet. The constant term L is used to perform the conventional rescaling motivated by removal of secular terms, e.g., for the Earth we use L C [START_REF] Soffel | The IAU 2000 resolutions for astrometry, celestial mechanics, and metrology in the relativistic framework: explanatory supplement[END_REF].

The space-time transformations to perform involve essentially the position of the antenna and the position of the orbiter. The geocentric coordinates of the antenna should be transformed into TDB-compatible coordinates; the transformation is expressed by the formula

x T B ant = x T T ant 1 - U c 2 -L C - 1 2 v T B E • x T T ant c 2 v T B E ,
where U is the gravitational potential at the geocenter (excluding the Earth mass), L C = 1.48082686741 × 10 -8 is a scaling factor given as definition, supposed to be a good approximation for removing secular terms from the transformation and v T B E is the barycentric velocity of the Earth. The next formula contains the effect on the velocities of the time coordinate change, which should be consistently used together with the coordinate change:

v T B ant = v T T ant 1 - U c 2 -L C - 1 2 v T B E • v T T ant c 2 v T B E dT dt .
Note that the previous formula contains the factor dT /dt (expressed by ( 2)) that deals with a time transformation: T is the local time for Earth, that is TT, and t is the corresponding TDB time.

The mercurycentric coordinates of the orbiter have to be transformed into TDB-compatible coordinates through the formula

x T B sat = x T M sat 1 - U c 2 -L C M - 1 2 v T B M • x T M sat c 2 v T B M ,
where U is the gravitational potential at the center of mass of Mercury (excluding the Mercury mass) and L C M could be used to remove the secular term in the time transformation (thus defining a TM scale, implying a rescaling of the mass of Mercury). We believe this is not necessary: the secular drift of TDM with respect to other time scales is significant, see Fig. 5 in Milani et al. (2010), but a simple iterative scheme is very efficient in providing the inverse time transformation. Thus we set L C M = 0, assuming the reference frame is TDM-compatible. As for the antenna we have a formula expressing the velocity transformation that contains the derivative of time T for Mercury, that is TDM, with respect to time t, that is TDB:

v T B sat = v T M sat 1 - U c 2 -L C M - 1 2 v T B M • v T M sat c 2 v T B M dT dt .
For these coordinate changes, in every formula we neglected the terms of the SSB acceleration of the planet center [START_REF] Damour | General-relativistic celestial mechanics. IV. Theory of satellite motion[END_REF], because they contain beside 1/c 2 the additional small parameter (distance from planet center)/(planet distance to the Sun), which is of the order of 10 -4 even for a Mercury orbiter.

To assess the relevance of the relativistic corrections of this section to the accuracy of the BepiColombo Radio Science Experiment, we computed the observables range and range rate with and without these corrections. As shown in Fig. 2, the differences are significant, time, days from arc beginning Range-rate, cm/s at a signal-to-noise ratio S/N 1 for range, much more for range rate, with an especially strong signature from the orbital velocity of the mercurycentric orbit (with S/N > 50).

Shapiro effect

The correct modelling of space-time transformations is not sufficient to have a precise computation of the signal delay: we have to take into account the general relativistic contribution to the time delay due to the space-time curvature under the effect of the Sun's gravitational field, the Shapiro effect [START_REF] Shapiro | Fourth test of general relativity[END_REF]. The Shapiro time delay t at the 1-PN level, according to [START_REF] Will | Theory and Experiment in Gravitational Physics[END_REF] and [START_REF] Moyer | Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation[END_REF], is

t = (1 + γ )μ 0 c 3 ln r t + r r + r r t + r r -r , S(γ ) = c t
where r t = |r t | and r r = |r r | are the heliocentric distances of the transmitter and the receiver at the corresponding time instants of photon transmission and reception, μ 0 is the gravitational mass of the Sun (μ 0 = G m 0 ) and r = |r rr t |. The planetary terms, similar to the solar one, can also be included but they are smaller than the accuracy needed for our measurements. Parameter γ is the only post-Newtonian parameter used for the light-time effect and, in fact, it could be best constrained during superior conjunction [START_REF] Milani | Testing general relativity with the BepiColombo Radio Science Experiment[END_REF]. The total amount of the Shapiro effect in range is shown in Fig. 3. The question arises whether the very high signal to noise in the range requires other terms in the solar gravity influence, due to either (i) motion of the source, or (ii) higher-order corrections when the radio waves are passing near the Sun, at just a few solar radii (and thus the denominator in the log-function of the Shapiro formula is small). The corrections (i) are of the post-Newtonian order 1.5 (containing a factor 1/c 3 ), but it has been shown in Milani et al. (2010) that they are too small to affect our accuracy. The corrections (ii) are of order 2, (containing a factor 1/c 4 ), but they can be actually larger for an experiment involving Mercury. The relevant correction is most easily obtained by adding 1/c 4 terms in the Shapiro formula, due to the bending of the light path:

S(γ ) = (1 + γ )μ 0 c 2 ln r t + r r + r + (1+γ )μ 0 c 2 r t + r r -r + (1+γ )μ 0 c 2 .
This formulation has been proposed by [START_REF] Moyer | Formulation for Observed and Computed Values of Deep Space Network Data Types for Navigation[END_REF] and it has been justified in the small impact parameter regime by much more theoretically rooted derivations by Klioner and Zschocke (2007), [START_REF] Teyssandier | General post-Minkowskian expansion of time transfer functions[END_REF] and [START_REF] Ashby | Accurate light-time correction due to a gravitating mass[END_REF]. Figure 4 shows that the order 2 correction is relevant for our experiment, especially when there is a superior conjunction with a small impact parameter of the radio wave path passing near the Sun. In practice there is a lower bound to the impact parameter because of the turbulence of the solar corona: below 10 solar radii the measurement accuracy is degraded, thus this effect is marginally significant, but is not entirely negligible. Note that the 1/c 4 correction (∼10 cm) in the Shapiro formula effectively corresponds to ∼ 3 × 10 -5 correction in the value of the post-Newtonian parameter γ . The Shapiro correction for the computation of the range rate will be shown in Sect. 4.

Light-time iterations

Since radar measurements are usually referred to the receive time t r the observables are seen as functions of this time, and the computation sequence works backward in time: starting from t r , the bounce time t b is computed iteratively, and, using this information the transmit time t t is computed.

The vectors x T B M and x T B EM are obtained integrating the post-Newtonian equations of motion. The vectors x T M sat are obtained by integrating the orbit in the mercurycentric TDM-compatible frame. The vector x T T ant is obtained from a standard IERS model of Earth rotation, given accurate station coordinates, and x T T E from lunar ephemerides [START_REF] Milani | Theory of Orbit Determination[END_REF]. In the following subsections we shall describe the procedure to compute the range (Sect. 4.1) and the range rate (Sect. 4.2).

Range

Once the five vectors are available at the appropriate times and in a consistent SSB system, there are two different light-times, the up-leg t up = t bt t for the signal from the antenna to the orbiter, and the down-leg t down = t rt b for the return signal. They are defined implicitly by the distances down-leg and up-leg

r do (t r ) = x sat (t b (t r )) + x M (t b (t r )) -x EM (t r ) -x E (t r ) -x ant (t r ), r do (t r ) = |r do (t r )|, c(t r -t b ) = r do (t r ) + S do (γ ),
(3)

r up (t r ) = x sat (t b (t r )) + x M (t b (t r )) -x EM (t t (t r )) -x E (t t (t r )) -x ant (t t (t r )), r up (t r ) = |r up (t r )|, c(t b -t t ) = r up (t r ) + S up (γ ), (4)
respectively, with somewhat different Shapiro effects:

S do (γ ) = (1 + γ ) μ 0 c 2 ln r t (t b ) + r r (t r ) + |r r (t r ) -r t (t b )| + (1+γ ) μ 0 c 2 r t (t b ) + r r (t r ) -|r r (t r ) -r t (t b )| + (1+γ ) μ 0 c 2 , S up (γ ) = (1 + γ ) μ 0 c 2 ln r t (t t ) + r r (t b ) + |r r (t b ) -r t (t t )| + (1+γ ) μ 0 c 2 r t (t t ) + r r (t b ) -|r r (t b ) -r t (t t )| + (1+γ ) μ 0 c 2 .
Note that, for the down-leg, the vector r t refers to the heliocentric position of the spacecraft and it is computed at the bounce time, while, for the up-leg, the same vector refers to the heliocentric position of the antenna and it is computed at the transmit time. This difference occurs also for the vector r r : in the down-leg it refers to the position of the antenna at the receive time, while in the up-leg to the position of the spacecraft at the bounce time. Then t rt b and t bt t are the two portions of the light-time, in the time attached to the SSB, that is TDB; this provides the computation of t t . Then these times are to be converted back in the time system applicable at the receiving station, where the time measurement is performed, which is TT (or some other form of local time, such as the standard UTC). The time t r is already available in the local time scale, from the original measurement, while t t needs to be converted back from TDB to TT. The difference between these two TT times is t tot , from which we can conventionally define r (t r ) = c t tot /2. Note that the difference t tot in TT is significantly different from t rt t in TDB, by an amount of the order of 10 -7 s, while the sensitivity of the BepiColombo Radio Science Experiment is of the order of 10 -9 s, thus these conversions change the computed observable in a significant way (Fig. 5).

Fig. 5

The difference in the observables range and range rate using a light-time in TT and a light time in TDB: the difference in range is very high, more than 13 meters in one day, while the difference in range rate is less than the accuracy of the experiment The practical method for solving t b (t r ) and t t (t r ) in ( 3) and ( 4) is as follows. Since the measurement is labeled with the receive time t r , the iterative procedure needs to start from (3) by computing the states x EM , x E and x ant at epoch t r , then selecting a rough guess t 0 b for the bounce time (e.g., t 0 b = t r ). Then the states x sat and x M are computed at t 0 b and a successive guess t 1 b is given by ( 3). This is repeated computing t 2 b , and so on until convergence, that is, until

t k b -t k-1 b
is smaller than the required accuracy. This fixed point iteration to solve the implicit equation for t b is convergent because the motion of the satellite and of Mercury, in the time t rt b , is a small fraction of the total difference vector. After accepting the last value of t b we start with the states x sat and x M at t b and with a rough guess t 0 t for the transmit time (e.g., t 0 t = t b ). Then x EM , x E and x ant are computed at epoch t 0 t and t 1 t is given by ( 4), and the same procedure is iterated to convergence, that is to achieve a small enough t k tt k-1 t . This double iterative procedure to compute range is consistent with what has been used for a long time in planetary radar, as described in [START_REF] Yeomans | Asteroid and comet orbits using radar data[END_REF]. We conventionally define r = (r do + S do + r up + S up )/2.

Range rate

After the two iterations providing at convergence t b and t t are complete, we can proceed to compute the range rate. We shall use the following notation: -d dt r stands for the total derivative with respect to the receive time t r ; -∂ ∂t b stands for the partial derivative with respect to the receive time t b ; -∂ ∂t t stands for the partial derivative with respect to the receive time t t . We rewrite the expression for the Euclidean range (down-leg and up-leg) as a scalar product:

r 2 do (t r ) = [x Ms (t b ) -x Ea (t r )] • [x Ms (t b ) -x Ea (t r )] , r 2 up (t r ) = [x Ms (t b ) -x Ea (t t )] • [x Ms (t b ) -x Ea (t t )]
, where x Ms = x M + x sat and x Ea = x EM + x E + x ant . The light-time equation contains also the Shapiro terms, thus the range rate observable contains also additive terms d S do /dt r and 123 d S up /dt r , with significant effects (a few cm/s during superior conjunctions). Since the equations giving t b and t t are still (3) and (4), in computing the time derivatives, we need to take into account that t b = t b (t r ) and t t = t t (t r ), with non-unit derivatives. By computing the derivative with respect to the receive time t r we obtain

d dt r [r do (t r ) + S do (t r )] = rdo • ∂x Ms (t b ) ∂t b dt b dt r - dx Ea (t r ) dt r + d S do dt r (5)
where

rdo = x Ms (t b ) -x Ea (t r ) r do (t r ) , dt b dt r = 1 - dr do (t r )/dt r + d S do /dt r c
and

d dt r [r up (t r ) + S up (t r )] = rup • ∂x Ms (t b ) ∂t b dt b dt r - ∂x Ea (t t ) ∂t t dt t dt r + d S up dt r (6)
where

rup = x Ms (t b ) -x Ea (t t ) r up (t r ) , dt t dt r = 1 - dr do (t r )/dt r + d S do /dt r c - dr up (t r )/dt r + d S up /dt r c .
The derivatives of the Shapiro effect are

d S do dt r = 2 (1 + γ )μ 0 c 2 r t (t b ) + r r (t r ) + (1 + γ )μ 0 c 2 2 -|r r (t r )-r t (t b )| 2 -1 × -|r r (t r ) -r t (t b )| ∂r t ∂t b dt b dt r + dr r dt r + r r (t r )-r t (t b ) |r r (t r )-r t (t b )| • dr r dt r - ∂r t ∂t b dt b dt r × r t (t b ) +r r (t r ) + (1 + γ )μ 0 c 2 , ( 7
) d S up dt r = 2 (1 + γ )μ 0 c 2 r t (t t ) + r r (t b ) + (1 + γ )μ 0 c 2 2 -|r r (t b )-r t (t t )| 2 -1 × -|r r (t b ) -r t (t t )| ∂r t ∂t t dt t dt r + ∂r r ∂t b dt b dt r + r r (t b )-r t (t t ) |r r (t t )-r t (t b )| • ∂r r ∂t b dt b dt r - ∂r t ∂t t dt t dt r r t (t t ) +r r (t b ) + (1 + γ )μ 0 c 2 . ( 8
)
Note that, because of different definitions of r t and r r in the down-leg and up-leg (Sect. 4.1), the term ∂r t /∂t b in the second row of ( 7) is exactly the same thing as ∂r r /∂t b in the second row of (8). However, the contribution of the time derivatives of the Shapiro effect to the dt b /dt r and dt t /dt r corrective factors is small, of the order of 10 -10 , which is marginally significant for the BepiColombo Radio Science Experiment. We conventionally define the range rate dr/dt r = c(1dt t /dt r )/2 = (dr do /dt r + d S do /dt r + dr up /dt r + d S up /dt r )/2. These equations are compatible with the equations in [START_REF] Yeomans | Asteroid and comet orbits using radar data[END_REF], taking into account that they use a single iteration. Equations ( 7) and ( 8) are almost never found in the literature and has not been much used in the processing of the past Radio Science Experiments [START_REF] Bertotti | A test of general relativity using radio links with the Cassini spacecraft[END_REF] because the observable range rate is typically computed as difference of ranges divided by time; however, for reasons explained in Sect. 5, these formulas are now necessary.

Since the time derivatives of the Shapiro effects contain dt b /dt r and dt t /dt r , the Eqs. ( 5) and ( 6) are implicit, thus we can again use a fixed point iteration. It is also possible to use a very good approximation which solves explicitly for dr do /dt r and then for dr up /dt r , neglecting the very small contribution of Shapiro terms:

dr do dt r = rdo • ∂x Ms (t b ) ∂t b 1 - d S do /dt r c - dx Ea (t r ) dt r 1 + 1 c ∂x Ms (t b ) ∂t b • rdo -1
, All the above computations are in SSB with TDB; however, the frequency measurements, at both t t and t r , are done on Earth, that is with a time which is TT. This introduces a change in the measured frequencies at both ends, and because this change is not the same (the Earth having moved by about 3 × 10 -4 of its orbit) there is a correction needed to be performed. The quantity we are measuring is essentially the derivative of t t with respect to t r , but in two different time systems (for readability, we use T for TT, t for TDB):

where
dT t dT r = dT t dt t dt t dt r dt r dT r ,
where the derivatives of the time coordinate changes are the same as the right hand side of the differential equation giving T as a function of t in the first factor and the inverse of the same for the last factor. However, the accuracy required is such that the main term with the gravitational mass of the Sun μ 0 and the position of the Sun x 0 is enough:

dT t dT r = 1 - μ 0 |x E (t t ) -x 0 (t t )| c 2 - 1 2 c 2 dx E (t t ) dt t 2 dt t dt r × 1 - μ 0 |x E (t r ) -x 0 (t r )| c 2 - 1 2 c 2 dx E (t r ) dt r 2 -1 . ( 9
)
Note that we do not need the L C constant term discussed in Sect. 2 because it cancels in the first and last term in the right hand side of (9). The correction of the above formula is required for consistency, but the correction has an order of magnitude of 10 -7 cm/s and is negligible for the sensitivity of the BepiColombo Radio Science Experiment (Fig. 5).

dr(t r )/dt r = (dr do (t r )/dt r + d S do /dt r + dr up (t r )/dt r + d S up /dt r )/2. In fact, the measurement is not instantaneous: an accurate measure of a Doppler effect requires to fit the difference of phase between carrier waves, the one generated at the station and the one returned from space, accumulated over some integration time , typically between 10 and 1000 s. Thus the observable is really a difference of ranges

r (t b + /2) -r (t b -/2) (10)
or, equivalently, an averaged value of range rate over the integration interval 1

t b + /2 t b -/2 dr(s) dt r ds. ( 11
)
In order to understand the computational difficulty we need to take also into account the orders of magnitude. As said in the introduction, for state of the art of tracking systems, such as those using a multi-frequency link in the X and Ka bands, the accuracy of the range measurements can be 10 cm and the one of range-rate 3 × 10 -4 cm/s (over an integration time of 1,000 s). Let us take an integration time = 30 s, which is adequate for measuring the gravity field of Mercury: in fact, if the orbital period of the spacecraft around Mercury is 8,000 s, the harmonics of order m = 26 have periods as short as 150 s. The accuracy over 30 s of the range rate measurement can be, by Gaussian statistics, 3 × 10 -4 √ 1000/30 17 × 10 -4 cm/s, and the required accuracy in the computation of the difference r (t b + /2)r (t b -/2) is 0.05 cm. The distances can be as large as 2 × 10 13 cm, thus the relative accuracy in the difference needs to be 2.5 × 10 -15 . This implies that rounding off is a problem with current computers, with relative rounding off error of ε = 2 -52 = 2.2 × 10 -16 (Fig. 6); extended precision is supported in software, but it has many limitations. The practical consequences are that the computer program processing the tracking observables, at this level of precision and over interplanetary distances, needs to be a mixture of ordinary and extended precision variables. Any imperfection may result time, seconds from arc beginning Range-rate, cm/s in "banding", that is residuals showing a discrete set of values, implying that some information corresponding to the real accuracy of the measurements has been lost in the digital processing.

As an alternative, the use of a quadrature formula for the integral in (11) can provide a numerically more stable result, because the S/N of the range rate measurement is 1/ε. Figure 7 shows that a very small model change, generating a range rate signal ≤ 2 micron/s over one pass, can be computed smoothly by using a 7 nodes Gauss quadrature formula.

Conclusions

By combining the results of Milani et al. (2010) and of this paper, we have completed the task of showing that it is possible to build a consistent relativistic model of the dynamics and of the observations for a Mercury orbiter tracked from the Earth, at a level of accuracy and self-consistency compatible with the very demanding requirements of the BepiColombo Radio Science Experiment. In particular, in this paper we have defined the algorithms for the computation of the observables range and range rate, including the reference system effects and the Shapiro effect. We have shown which computations can be performed explicitly and which ones need to be obtained from an iterative procedure. We have also shown how to push these computations, when implemented in a realistic computer with rounding-off, to the needed accuracy level, even without the cumbersome usage of quadruple precision. The list of "relativistic corrections", assuming that we can distinguish their effects separately, is long, and we have shown that many subtle effects are relevant to the required accuracy. However, in the end what is required is just to be fully consistent with a post-Newtonian formulation to some order, to be adjusted when necessary. Interestingly, the high accuracy of BepiColombo radio system may require implementation of the second post-Newtonian effects in range.

previous one, Milani et al. (2010), have been performed within the scope of the contract ASI/2007/I/082/06/0 with the Italian Space Agency. BepiColombo is a scientific space mission of the Science Directorate of the European Space Agency. The work of DV was partially supported by the Czech Grant Agency (grant 202/09/0772) and the Research Program MSM0021620860 of the Czech Ministry of Education.

Fig. 1

 1 Fig.1Geometric sketch of the vectors involved in the computation of the range. SSB is the Solar System Barycenter, M is the center of Mercury, EMB is the Earth-Moon Barycenter, E is the center of the Earth

Fig. 2

 2 Fig.2The difference in the observables range and range rate for one pass of Mercury above the horizon for a ground station, by using an hybrid model in which the position and velocity of the orbiter have not transformed to TDB-compatible quantities and a correct model in which all quantities are TDB-compatible. Interruptions of the signal are due to spacecraft passage behind Mercury as seen for the Earth station. Top for an hybrid model with the satellite position and velocity not transformed to TDB-compatible. Bottom for an hybrid model with the position and velocity of the antenna not transformed to TDB-compatible

Fig. 3 Fig. 4

 34 Fig.3Total amount of the Shapiro effect in range over 2-years simulation. The sharp peaks correspond to superior conjunctions, when Mercury is "behind the Sun" as seen from Earth, with values as large as 24 km for radio waves passing at 3 solar radii from the center of the Sun. Interruptions of the signal are due to spacecraft visibility from the Earth station (in this simulation we assume just one station)

  from arc beginning Range-rate, cm/s

Fig. 6 Fig. 7

 67 Fig. 6Range and range rate differences due to a change by 10 -11 of the C 22 harmonic coefficient: the range rate computed as range difference divided by the integration time of 30 s is obscured by the rounding off

  the right hand side is weakly dependent upon dr do /dt r only through d S do /dt r , thus a moderately accurate approximation could be used in the computation of d S do /dt r , followed by a single iteration. For the other leg

	dr up dt r	= rup •	∂x Ms (t b ) ∂t b	1 -	dr do (t r )/dt r + d S do /dt r c	-	∂x Ea (t t ) ∂t t
		× 1 -	dr do (t r )/dt r + d S do /dt r + d S up /dt r c	1 -	1 c	∂t t ∂x Ea (t t )	• rup	-1

See the Resolution at http://www.iau.org/administration/resolutions/ga2006/.

Change in the observable time, days from arc beginning Range, cm

The computation of the observables, as presented in the previous section, is already complex, but still the list of subtle technicalities is not complete. A problem well known in radio science is that, for top accuracy, the range rate measurement cannot be the value

Acknowledgments

The authors thank the anonymous reviewer for his constructive comments useful to improve the presentation of the work. The results of the research presented in this paper, as well as in the


MD Alessandra ; Mangia
email: a.mangia@tin.it

Olav Dalgard

Nicola Minerva

Donato Bacca

Helmer Ring-Larsen

Massimiliano Copetti

Vito Carretta

Valeria Piazzolla

Raffaele Cozzolongo

Leonardo Mottola

Hans Verbaan

Donato Bacca

Valerio Piazzola

Angelo Andriulli

RIBAVIRN DOSAGE IN HCV GENOTYPES 2 AND 3 PATIENTS COMPLETING SHORT THERAPY WITH PEG-INTERFERON ALFA-2B AND RIBAVIRIN

Keywords: Viral hepatitis < Hepatology, Liver < Organ-based, Liver function ribavirin, peginterferon, HCV, antiviral therapy, chronic hepatitis C

des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Background. The optimal dose of ribavirin to be used in combination with Peg-IFN in HCV genotype 2 and 3 patients undergoing short treatment has not been established. Aim. To explore the relationship between starting ribavirin doses, expressed as mg/kg body weight and both rapid viral response at treatment week 4 [RVR] and sustained virological response [SVR] in patients treated for 12-14 weeks with peg-interferon alfa-2b and ribavirin.

Methods. A post-hoc analysis of data collected from two multicenter clinical trials was performed.

Multiple regression analyses were employed to identify independent baseline and on-treatment predictors of RVR and SVR. For each dose of ribavirin, the empirical estimated probability of response was computed and the continuous exposure index was dichotomized by using a recursive partitioning and amalgamation method.

Results. A non-linear relationship was ascertained between ribavirin dose and RVR but not SVR. A dose of 15.2 mg/kg was selected as the best splitting value for discriminating RVR versus non RVR.

Regression analysis identified low baseline viremia, genotype 2, and high ribavirin dose as independent prognostic factors for RVR. The likelihood of an SVR was not correlated with baseline ribavirin dose, but was independently predicted by adherence to the full dose throughout treatment and normal platelet counts.

Conclusions. Starting high ribavirin doses appeared capable to increase the rate of RVR in HCV genotype 2 and 3 patients undergoing short treatment. Maintenance of the full planned dose throughout treatment was essential for achieving optimal SVR rates.

INTRODUCTION

The benefit of short (12 or 14 weeks) therapy with Peg-Interferon (Peg-IFN) in combination with ribavirin for patients with chronic HCV genotypes 2 or 3 infection has been documented in recent clinical investigations [START_REF] Dalgard | Treatment with pegylated interferon and ribavirin in HCV infection with genotype 2 or 3 for 14 weeks: a pilot study[END_REF][START_REF] Mangia | Peginterferon alfa-2b and ribavirin for 12 vs 24 weeks in HCV genotype 2 or 3[END_REF][START_REF] Von Wagner | Peginterferon alfa 2a [40 kd] and ribavirin for 16 weeks in patients with genotype 2 or 3 chronic hepatitis C[END_REF][START_REF] Yu | A randomised study on PegInterferon and ribavirin for 16 versus 24 weeks in patients with genotype 2 chronic hepatitis C[END_REF][START_REF] Dalgard | A randomized controlled trial of pegylated interferon alfa and ribavirin for 14 vs 24 weeks in patients with HCV genotype 2 or 3 and rapid virological response[END_REF][START_REF] Andriulli | Meta-analysis: the outcome of anti-viral therapy in HCV genotype 2 and genotype 3 infected patients with chronic hepatitis[END_REF]. Patients who will benefit the most by short therapy are lean, noncirrhotic individuals capable to clear the virus at treatment week 4 [START_REF] Mangia | Determinants of relapse after a short [12 weeks] course of antiviral therapy and re-treatment efficacy of a prolonged course in patients with chronic HCV genotype 2 or 3 infection[END_REF]. This experimental evidence has been incorporated in some, but not all, treatment guidelines issued by scientific societies [START_REF] De Bruijne | For the Netherlands Association of Gastroenterologists and Hepatologists. Treatment of chronic hepatitis C virus infection -Dutch national guidelines[END_REF][START_REF] Zeuzem | Expert opinion on the treatment of patients with chronic hepatitis C[END_REF][START_REF] Ghany | Diagnosis, management, and treatment of hepatitis C: un update[END_REF], so that uncertainties still remain about implementing short therapy in everyday clinical practice. Indeed, a clear-cut benefit of short therapy in comparison with the standard 24 week treatment did not emerge in some other clinical trials [START_REF] Shiffman | Peginterferon alfa-2a and RBV for 16 or 24 weeks in HCV genotype 2 or 3[END_REF][START_REF] Lagging | for the NORdynamIC Study group. Randomized comparison of 12 or 24 weeks of paginterferon alpha 2a and ribavirin in chronic hepatitis C virus genotype 2/3 infection[END_REF].

A controversial issue in genotypes 2 and 3 therapy, that might explain part of previous inconsistencies across trials, is the optimal dose of ribavirin to be used in combination with Peg-IFN: whenever ribavirin was given at higher dosage (800-1400 mg daily, according to body weight) than the one currently recommended (800 mg daily), the benefit of short therapy appeared evident [START_REF] Dalgard | Treatment with pegylated interferon and ribavirin in HCV infection with genotype 2 or 3 for 14 weeks: a pilot study[END_REF][START_REF] Mangia | Peginterferon alfa-2b and ribavirin for 12 vs 24 weeks in HCV genotype 2 or 3[END_REF][START_REF] Von Wagner | Peginterferon alfa 2a [40 kd] and ribavirin for 16 weeks in patients with genotype 2 or 3 chronic hepatitis C[END_REF][START_REF] Yu | A randomised study on PegInterferon and ribavirin for 16 versus 24 weeks in patients with genotype 2 chronic hepatitis C[END_REF]; contrariwise, when administered dosage was the fixed 800 mg daily dosage [START_REF] Shiffman | Peginterferon alfa-2a and RBV for 16 or 24 weeks in HCV genotype 2 or 3[END_REF][START_REF] Lagging | for the NORdynamIC Study group. Randomized comparison of 12 or 24 weeks of paginterferon alpha 2a and ribavirin in chronic hepatitis C virus genotype 2/3 infection[END_REF], the benefit waned off.

The predominant mechanism(s) of ribavirin action against HCV are yet to be established. Although ribavirin monotherapy imposes a transient HCV decline early on therapy, the drug has no apparent long term effect on serum HCV RNA levels [START_REF] Dusheiko | Ribavirin treatment for patients with chronic hepatitis C: results of a placebo-controlled study[END_REF][START_REF] Pawlotsky | Antiviral action of ribavirin in chronic hepatitis C[END_REF]; however, in combination with interferon, it dramatically improves the success of therapy. In naïve patients undergoing treatment with conventional interferon and ribavirin, higher ribavirin concentrations were associated with a higher likelihood of response [START_REF] Jen | Population pharmacokinetic and pharmacodynamic analysis of ribavirin in patients with chronic hepatitis C[END_REF]. Plasma ribavirin concentrations have been shown to correlate with the starting dose of the drug [START_REF] Jen | Population pharmacokinetic and pharmacodynamic analysis of ribavirin in patients with chronic hepatitis C[END_REF], so that selecting appropriate starting dose and maintaining it throughout treatment impact positively on therapeutic outcome. In genotype 1 patients, the probability of achieving a sustained virological response (SVR) increased as a function of the ribavirin dose (mg/kg of body weight), with a 40-50% increase for a 12-16 mg/kg dose [START_REF] Snoeck | Predicting sustained virological response and anaemia in chronic hepatitis C patients treated with peginterferon alfa-2a [40 KD] plus ribavirin[END_REF]. Data are less clear for genotypes 2 and 3 infection, as a single study failed to prove a correlation between probability of SVR after 24 weeks of treatment and the ribavirin dose [START_REF] Snoeck | Predicting sustained virological response and anaemia in chronic hepatitis C patients treated with peginterferon alfa-2a [40 KD] plus ribavirin[END_REF]. Although debate is ongoing as to which ribavirin dosage should be administered in combination with Peg-IFN, it is clear that ribavirin activity is dose/exposure dependent [START_REF] Jen | Population pharmacokinetic and pharmacodynamic analysis of ribavirin in patients with chronic hepatitis C[END_REF][START_REF] Snoeck | Predicting sustained virological response and anaemia in chronic hepatitis C patients treated with peginterferon alfa-2a [40 KD] plus ribavirin[END_REF], and selecting and maintaining the optimal dose of the drug might be crucial for a successful therapy. This concept might apply particularly when considering short treatment duration. Objective of this analysis was to explore the relationship between starting ribavirin and both rapid viral response at treatment week 4 (RVR) and SVR in patients with genotypes 2 and 3 undergoing short (12 or 14 weeks) therapy with ribavirin and Peg-IFN alfa-2b.

PATIENTS AND METHODS

Study subjects

Data used in this analysis were collected from two multicenter clinical trials, run in Italy and Scandinavia, in naïve patients with genotypes 2 and 3. The complete inclusion and exclusion criteria, study design and primary results of which are available elsewhere [START_REF] Dalgard | A randomized controlled trial of pegylated interferon alfa and ribavirin for 14 vs 24 weeks in patients with HCV genotype 2 or 3 and rapid virological response[END_REF][START_REF] Mangia | Determinants of relapse after a short [12 weeks] course of antiviral therapy and re-treatment efficacy of a prolonged course in patients with chronic HCV genotype 2 or 3 infection[END_REF]. The primary efficacy objective of these trials was to compare SVR following Peg-IFN alfa-2b (Peg-Intron; Schering-Plough, Kenilworth, NJ, USA) plus ribavirin administered for short (12 or 14 weeks, respectively) or standard (24 weeks) duration. All patients received Peg-IFN alfa-2b 1.5 µg/kg subcutaneously weekly together with ribavirin administered orally. In the study by Mangia et al. [START_REF] Mangia | Determinants of relapse after a short [12 weeks] course of antiviral therapy and re-treatment efficacy of a prolonged course in patients with chronic HCV genotype 2 or 3 infection[END_REF], 718 patients were treated with Peg-IFN alfa-2b plus ribavirin 1000 or 1200 mg/day on the basis of body weight higher or lower than 75 kg; 496 patients with week 4 viral clearance (labelled as rapid virological responders, RVR) were allocated to 12 week treatment duration, whereas those without RVR were given therapy for 24 weeks.

Italian patients with missing serum creatinine values at baseline were not included in the present analysis. In the 428 patients enrolled in the trial by Dalgard et al [START_REF] Dalgard | A randomized controlled trial of pegylated interferon alfa and ribavirin for 14 vs 24 weeks in patients with HCV genotype 2 or 3 and rapid virological response[END_REF], ribavirin dose varied according to body weight, as follows: 800 mg for body weight <65 kg, 1000 mg for body weight ranging from 65 to 85 kg, 1200 for body weight ranging from 85 and 105 kg, and 1400 for body weight >105 kg. For sake of homogeneity with the design of the Italian study, of the original 428 Scandinavian patients only 148 individuals with RVR who were treated for 14 weeks, and 130 non-RVR patients whose treatment lasted for 24 weeks were considered eligible for the present investigation; the remaining 150 patients with RVR who were treated for the standard 24 weeks were excluded. Among Scandinavian patients considered eligible, only 10 had body weight > 105 kg and required 1400 mg, therefore the combined database allowed us to evaluate a large series of patients, including a comparable number of genotype 2 and 3, who received similar dosages of ribavirin.

Per protocol, the ribavirin dose had to be reduced by 200 mg daily in patients who experienced a decrease in haemoglobin level of more than 2 g/dl during treatment, and by 400 mg daily if haemoglobin levels decreased to less than 10 g/dl. Ribavirin was discontinued if haemoglobin levels decreased to less than 8.5 g/dl. The use of erythropoietin was not allowed. Anaemia was defined as haemoglobin concentration <10 g/dl documented on at least one occasion during the studies. For patients who were intolerant to Peg-IFN alfa-2b, dose reductions in decrements of 12% of the assigned dose were allowed.

Analytic Methods

Definitions. The HCV RNA level was measured using the COBAS AMPLICOR HCV Test [(Roche Molecular Systems, Branchburg, NJ, USA), version 2.0; limit of detection 50 IU/ml]. Rapid virologic response (RVR) was defined as undetectable serum HCV RNA at treatment week 4. End-of-treatment response (ETR) was defined as undetectable HCV RNA at weeks 12, 14 or 24 according to the different therapeutic regimens, and SVR was defined as undetectable HCV RNA at the end of a 24 week follow-up period.

Statistical analysis

As the primary objective of the present study was to explore the impact of ribavirin dose on both RVR and SVR, only patients who could tolerate antiviral drugs for the planned length of therapy were retained in the analysis. Patients who had reduction of ribavirin and/or Peg-IFN at some point during treatment but completed the planned treatment duration were retained. Consequently, of the total 905 eligible patients enrolled in the two previous trials, only 673 patients (405 from the Italian cohort and 268 from the Scandinavian cohort) were retained. Of the 232 excluded patients, 120 had no serum creatinine available for glomerular filtration (GFR) rate calculation, and 112 (10 among patients treated for 12-14 weeks and 102 among those treated for 24 weeks) had a premature treatment discontinuation for major side effects or were lost to follow up.

Baseline patients' characteristics were reported as frequencies and groups were compared with Pearson chi-square. Multiple logistic regression analyses were employed to identify independent baseline and on-treatment predictors of RVR and SVR, with age, sex, body mass index, genotype, baseline viremia, platelet count, aspartate aminotransferase-to-platelet ratio index (APRI) score [START_REF] Wai | A simple non invasive index can predict both significant fibrosis and cirrhosis in patients with chronic hepatitis C[END_REF][START_REF] Smith | Systematic review: non-invasive methods of fibrosis analysis in chronic hepatitis C[END_REF], and starting ribavirin dose as dependent variables. An exploratory analysis was made in order to assess the nature of the relationship between dose of ribavirin adjusted for GFR and response probability: for each dose, the empirical estimated probability of response was computed. Moreover, the continuous exposure index was dichotomized using the best splitting value by using a Recursive Partitioning and Amalgamation (RECPAM) method [START_REF] Cook | Empiric comparison of multivariate analytic techniques: advantages and disadvantages of recursive partitioning analysis[END_REF]. All analyses were performed using SAS® release 9.1. Two-tailed P-values <0.05 were considered significant.

RESULTS

Characteristics of patients

Baseline features of patients derived from the two studies are outlined in Table 1. There were differences in demographics, serum biochemistry, and virologic features of patients from the two cohorts: in the Scandinavian cohort, patients were as a mean 10 years younger, had a prevalent genotype 3 infection, and lower frequency of advanced liver damage, as indicated by the lower proportion of individuals with low platelet counts and APRI score >2. Conversely, a higher proportion of Italian patients received a high (≥15 mg /kg) dose of ribavirin, a finding that might be related to differences in the schedule of ribavirin administration between the two studies: a more stringent weight-related dosing in the Scandinavian trial, and a looser relation to body weight in the Italian study.

SVR rates and predictability of SVR by RVR in accordance with the different duration of treatment are reported in Table 2.

Impact of ribavirin dosing on rapid virologic response.

No patients had to reduce the ribavirin dose by treatment week 4, so that the relationship between starting ribavirin dose and the probability of RVR could be detailed. As shown in Figure 1, the dose of ribavirin, expressed in mg/kg of body weight, may be a determining factor of RVR in genotype 2 and 3 patients: the probability of RVR increased with increasing ribavirin dose. However, the relationship was a non-linear one and the probability increased from approximately 54% to 80% for a ribavirin dose increase from 13 to 15.2 mg/kg. The dose of 15.2 mg/kg was determined as the best splitting value for discriminating RVR versus non RVR: among the 147 patients receiving a dose of ribavirin higher than15 mg/kg an 80% probability of achieving an RVR was observed, while for the 528 patients who received a lower dose, the RVR rate was 67%. At the univariate analysis of predictors of RVR, body mass index, genotype, viral load, and ribavirin dose were significantly associated with RVR [Table 3]. Multiple logistic regression analysis identified low baseline viremia (<400.000 IU/ml) (OR = 2.5; 95% CI 1.6-3.8), genotype 2 (OR=1.7; 95% CI 1.2-2.5), and high ribavirin dose (15 mg/kg) (OR = 1.6; 95% CI 1.1-2.6) as independent prognostic factors.

Predictors of RVR at the univariate analysis are shown separately for HCV genotypes 2 and 3 in Table

Impact of ribavirin dosing on sustained virological response

As per protocol, antiviral therapy lasted 12-14 weeks in 473 patients with RVR, and 364 of them (77.0%) attained an SVR. The likelihood of an SVR was not correlated with baseline ribavirin dose, expressed in mg/kg of body weight but rather to the inability to adhere to the prescribed dose of the drug. Low viral load (p=0.033), normal platelet count (p=0.0001) and maintenance of full dose of ribavirin throughout treatment were associated with SVR (p=0.0001). Decreasing ribavirin dose relative to target during treatment was a predictor of relapse: of patients who achieved an SVR, only 7% had to reduce the dose of ribavirin after the initial 4 weeks of therapy with a consequent 25% of total amount of ribavirin reduction, whereas 19% of those who failed to clear the virus did so. At multivariate analysis, independent predictors of SVR in patients with RVR were no ribavirin dose reduction (OR =3.1; 95% CI 1.6-5.9) and normal platelet counts (OR = 2.75; 95% CI 1.6-4.7).

Two hundred patients without RVR were treated per protocol for the standard 24 weeks of therapy, and 134 of them achieved an SVR (67%). At univariate analysis, female sex (p=0.09) and high baseline ribavirin dose (p=0.05) emerged as the only two predictors of SVR. In particular, of 30 patients without RVR who received ribavirin at dose of ≥15 mg/kg of body weight, 23 (78.7%) individuals attained an SVR, as opposed to 110 of 170 patients in the lower ribavirin dose (64.7%). Dose reduction of ribavirin only occurred in 2% of those without RVR and was not associated with response.

At the multivariate analysis no factor was independently associated with SVR.

Ribavirin-related side effects

Sixty four of 673 patients with RVR required modification of the ribavirin dose due to a drop in haemoglobin levels below 10 g/dl. Anaemia was more frequently detected among patients treated with ribavirin dose of ≥15 mg/kg than in those who were treated with lower doses (9.5 vs 4.4%), but the difference was not significant (p=0.11). Other ribavirin related side effects as cutaneous rash, cough and dry skin were not differently distributed among patients in the low and high ribavirin dosage: 3% vs 2.4% (p=0.35).

DISCUSSION

Current analysis evaluated the impact of ribavirin dosing on the therapeutic outcome in patients with genotype 2 and 3 infection who received Peg-IFN alfa-2b in combination with ribavirin for a short treatment duration. Original data were derived from two clinical trials where patients were allocated to short or standard treatment duration depending on whether or not they attained an RVR [START_REF] Dalgard | A randomized controlled trial of pegylated interferon alfa and ribavirin for 14 vs 24 weeks in patients with HCV genotype 2 or 3 and rapid virological response[END_REF][START_REF] Mangia | Determinants of relapse after a short [12 weeks] course of antiviral therapy and re-treatment efficacy of a prolonged course in patients with chronic HCV genotype 2 or 3 infection[END_REF]. We could ascertain a relationship between the dose of ribavirin, expressed as mg/kg of body weight, and the likelihood of achieving an RVR. The relationship held true particularly for patients infected with HCV genotype 3.Furthermore, in RVR patients the SVR rate was higher among those who were compliant with the initially assigned ribavirin dose throughout treatment.

Weight-based dosing of ribavirin has been extensively utilized in patients with genotype 1, in whom a relationship between ribavirin dose and SVR has been established when the drug was administered in association with either Peg-IFN alfa-2a and alfa-2b [START_REF] Manns | Peginterferon alfa-2b plus ribavirin compared with interferon alfa 2b plus ribavirin for initial treatment of chronic hepatitis C: A randomized trial[END_REF][START_REF] Hadziyannis | Peginterferonalpha2a and ribavirin combination therapy in chronic hepatitis C: a randomized study of treatment duration and ribavirin dose[END_REF][START_REF] Fried | Peginterferon alfa2a plus ribavirin for chronic hepatitis C virus infection[END_REF][START_REF] Jacobson | for the WIN-R Study Group. Peginterferon alfa-2b and weight-based or flat-dose ribavirin in chronic hepatitis C patients: a randomized trial[END_REF][24][25]. Based on these data, the ribavirin dose of 15 mg/kg was selected as the best balance between efficacy and a manageable safety profile. Data are less clear for genotypes 2 and 3. When administered in combination with Peg-IFN alfa-2a for 48 weeks, ribavirin doses of 800 or 1000-1200 mg daily produced equivalent outcomes [START_REF] Fried | Peginterferon alfa2a plus ribavirin for chronic hepatitis C virus infection[END_REF]. Similarly, a comparative trial of fixed-(800 mg daily) or weight-based doses of ribavirin (800-1400 mg daily) in combination with Peg-IFN alfa-2b showed equal SVR rates: 67.7% vs 65.0% [START_REF] Jacobson | for the WIN-R Study Group. Peginterferon alfa-2b and weight-based or flat-dose ribavirin in chronic hepatitis C patients: a randomized trial[END_REF]. This study also documented that responses were consistent across all body weight categories in the weight-based group, but lower SVR were attained with increasing weight [START_REF] Fried | Peginterferon alfa2a plus ribavirin for chronic hepatitis C virus infection[END_REF]. However, a randomized study of Peg-IFN alfa-2a plus ribavirin for 24 weeks at doses of either 400 or 800 mg claimed no decrease in SVR rates in the lower dose group among genotype 3 infection, but SVR rates declined from the 67.5% rate in the 800 mg group to 63.9% in the 400 mg group [24].

It needs to be reminded that all previous trials administered therapy for at least 24 weeks. In principle, it might be conceivable that for the overall population of genotype 2 and 3 patients a fixed 800 mg/day dose of ribavirin could be enough to achieve optimal response rates after 24 weeks of therapy.

However, as shorter treatment courses may be viable in select genotype 2 and 3 patients, such as those with RVR, it could be speculated that much more promising results could be obtained by weight adjustment of ribavirin dose when considering abbreviated treatment. Indirect evidences support this claim. In the NORDynamIC trial, patients who achieved SVR had significantly lower body weight than those who did not; as a fixed dose of 800 mg of ribavirin was administered to all patients, it is plausible that SVR patients had been exposed to higher dose of ribavirin than those who did not achieve SVR [START_REF] Dusheiko | Ribavirin treatment for patients with chronic hepatitis C: results of a placebo-controlled study[END_REF]. A post-hoc analysis of the trial showed that the chance of achieving an SVR was associated with higher median serum ribavirin concentrations at week 4 [25].

In a study from Taiwan, a RVR rate of 86% was registered following therapy with Peg-IFN alpha-2a and weight-based ribavirin (1000-1200 mg daily); considering that the mean body weight of patients included into the study was 68 kg, a mean dose of 15 to 20 mg/kg was administered and could be one factor that might have impacted on the pronounced RVR rate [START_REF] Yu | A randomised study on PegInterferon and ribavirin for 16 versus 24 weeks in patients with genotype 2 chronic hepatitis C[END_REF]. In opposition, the ACCELERATE trial administered a fixed dose of 800 mg to patients whose mean body weight was 81.5 kg; consequently, they received a low ribavirin dose (9.8 mg daily, as a mean) and attained an RVR at a rate as low as 65.5% [START_REF] Lagging | for the NORdynamIC Study group. Randomized comparison of 12 or 24 weeks of paginterferon alpha 2a and ribavirin in chronic hepatitis C virus genotype 2/3 infection[END_REF]. We acknowledge that, although suggestive, all mentioned evidences should be interpreted with caution because they were derived from secondary analyses with potential confounding variables.

The present analysis has added new evidence to the ongoing debate on the optimal ribavirin dosage.

We found a relationship between body weight and RVR, an observation suggesting that the dose of ribavirin per kilogram may contribute substantially to response to therapy in patients undergoing short therapy. It is important to note that the type of the relationship was non-linear, but S-shaped, with a low and a high threshold value for dosing of ribavirin. From our analysis it turned out that a threshold value of ≥15.2 mg/kg was expected to result in better outcome of therapy when considering short treatment. In previous studies [START_REF] Snoeck | Predicting sustained virological response and anaemia in chronic hepatitis C patients treated with peginterferon alfa-2a [40 KD] plus ribavirin[END_REF] the concept that ribavirin clearance is linearly dependent on renal function was not incorporated into the analysis, at variance in our patients as suggested by Bruchfeld

[25], the renal effect could be excluded after the adjustment for GFR As a matter of fact, 80% of patients given ribavirin dose ≥15.2 mg/kg achieve an RVR, as compared to 54% of those who were given 13 mg/kg.

Reddy et al reported that as long as patients achieved RVR, ribavirin dose reduction had minimal impact on SVR after standard treatment duration [27]. Our findings on RVR patients who were treated with only 12-14 weeks of therapy demonstrate lower SVR rates when the initial dosage of ribavirin had to be reduced. Indeed, 46 of 473 patients with RVR required dose modification due to a drop in haemoglobin levels below 10 g/dl, and 54% of them attained an SVR as opposed to a 79%% rate in those who could tolerate the starting dose of ribavirin throughout treatment. Although data modelling suggests that RVR increases with ribavirin doses that equate to ≥15 mg/kg, there is also a simultaneous increase in the rate of anaemia. To contrast anaemia development, the use of off-label erythropoietin has been implemented [28-30], but the drug was not allowed in our patients for cost-saving considerations.

In summary, the results of our study suggest that in patients with HCV genotypes 2 and 3 infection completing short therapy with Peg-IFN alfa-2b in combination with weight-based doses of ribavirin, a high starting dose of ribavirin appeared one of the factors influencing the rate of RVR. We would recommend to administer ribavirin at a dose of ≥15 mg/kg when considering short treatment duration.

Larger prospective studies would be required to confirm the role of higher ribavirin doses on SVR.as both the need of maintaining the full planned dose of ribavirin throughout treatment to achieve an optimal SVR rate or the improvement of SVR in patients still viremic at treatment week 4 after an intensified ribavirin dosing suggest that higher ribavirin dosage affects SVR. Finally, the evidence that genotype 3 may derive more benefit from high dosages of ribavirin warrant further confirmation of the present post-hoc analysis.

(

  . Ferenci P, Laferl H, Schrzer TM, Gschwantler M, Maieron A, Brunner H, et al. A randomized prospective trial of ribavirin 400 mg/day versus 800 mg/day in combination with peginterferon alfa-2a in hepatitis C virus genotypes 2 and 3. Gastroenterology 2008¸ 47; 1816-23 [25]. Christensen PB, Alain AA, Buhl MR, Farkila M, Morch K, Sangfeld P, et al. Ribavirin concentration at week four is an independent predictor for sustained virological response after treatment of hepatitis C genotype 2/3 (NORDynamic trial). J Hepatol 2008; 48, S6 [26]. Bruchfeld A, Lindahl K, Schvarcz R, Stahle L. Dosage of ribavirin in patients with hepatitis C should be based on renal function: a population pharmacokinetic analysis Ther Drug Monit 2002; 24:701-8 [27]. Reddy KR, Shiffman M, Morgan T, Zeuzem S, Hadziyannis, Hamzeh FM et al. Impact of ribavirin dose reduction in HCV genotype 1 patients completing interferon alfa 2-a and ribavirin treatment Clin Gastroenterol Hepatol 2007;5:124-9 [28].McHutchison JG, Manns MP, Brown RS, Reddy R, Shiffman M, Wong J. Strategies for managing anaemia in hepatitis C patients undergoing antiviral therapy. Am J Gastroenterol 2007; 102:880-889 [29]. Afdhal NH, Dieterich DT, Pockros PJ, Schiff ER, Shiffman ML, Sulkowski MS, et al Epoetin alfa maintains ribavirin dose in HCV-infected patients: a prospective, double-blind, randomised controlled study. Gastroenterology 2004; 126:1302-11 [30]. Morreale A, Plowman B, DeLattre M. Boggie D, Schaefer M. Clinical and economic comparison of epoetin alfa and darbepoetin alfa. Curr Med Res Opin. 2004; 20:381-95 Probability of rapid virologic response [RVR] in patients with hepatitis C virus genotype 2 and 3 as a function of the ribavirin dose per kilogram of body weight after 12-14 weeks treatment. Observed values are presented as circles. The dashed lines are the 95% point-wise confidence intervals.

Figure 1 P r o b a b i l i t y o

 1 Figure 1

  4. At multivariate analysis, young age and low viremia were independent predictors of RVR in genotype 2 patients, OR =2.06, 95% CI 1.16-3.64 and OR= 2.01 (1.18-3.40), respectively. For independent predictors of RVR were low viremia (OR= 2.84, 95% CI 1.60-5.01) high ribavirin dose (OR= 2.13, 95% CI 1.07-4.26) and young age (OR= 2.91, 95% CI 1.77-4.80).

	PAGE 6
	genotype 3 patients
	F o
	r
	P
	e e r
	R e v i e w

Table 1 .

 1 Comparison of the demographic, biochemical, and virological profiles of 673 patients with genotype 2 and 3 infection, selected from the two original studies.

			Dalgard, 2008	Mangia, 2009
	Total number of patients	268	405
	Age:
	mean [years]		40.4 ±9.1	50.58±12.4
	range		[19-63]	[19-75]
	<45 years [no., %]	184(69)	146 (36]
	Gender: male [no., %]	166 (62]	240 (59)
	Body mass index:
	mean [kg/m 2 ]		25.7±4.3	25.9±3.6
	range		(16-41)	(16-40)
	<30 kg/m 2 [no., %]	225 (84)	345 (85)
	Body weight: [kg]
	<65	[no., %]	65 (24)	127 (31)
	<65-85	[no., %]	125 (47)	230 (57)
	>85-105	[no., %]	64 (24)	44 (11)
	>105	[no., %]	14 ( 5)	4 ( 1)
	Genotype 2 [no., %]		53 (20)	283 (70)
	Genotype 3 [no., %]		215 (80)	122 (30)
	Viral load:
	≥400.000 IU/ml [no., %]	204 (76)	247 (61)
	Platelet count: *
	>140.000 mm 3 [no., %]	244 (92)	310 (78)
	APRI : score >2 [no., %] **	32 (12)	89 (22)
	Ribavirin dose:
	≥15 mg/kg [no., %]	19 (7)	128 (32)
	* 8 missing values	** 16 missing values

Table 2 .

 2 Rates of RVR, EOT and SVR according to RVR

	Patients	All patients Patients with RVR	Patients without RVR
	group by		treated for 12 weeks	treated for 24 weeks
	time point
	Total	n=673	N=473	n=200
	EOT	606 (90.0)	425 (89.9)	181 (90.5)
	SVR	498 (74.0)	364 (77.0)	134 (67.0)

Table 3 .

 3 Univariate analysis of predictors of a rapid virological response (RVR) in 673 patients with

	HCV genotype 2 and 3 infection
		RVR	No RVR	P values
	Total number of patients	473	200
	Age: <45 yrs [no., %]	233 (49)	97 (48)	0.84
	Gender : male [no., %]	284 (60)	122 (61)	0.86
	Body Mass Index:
	<30 kg/m 2 [no., %]	410 (87)	160 (80)	0.035
	>30 kg/m 2 [no., %]	63 (13)	40 (20)
	Genotype 2 [no., %]	254 (54)	82 (41)
	Genotype 3 [no., %]	219 (46)	118 (59)	0.003
	Viral load:
	≥ 400.000 IU/ml [no., %]	292 (62)	159 (79)
	<400.000 IU/ml [no., %]	181 (38)	41 (20)	0.0001
	Platelet count:
	>140.000 mm 3 [no., %]	394 (83)	158 (79)	0.21
	APRI score: <2 [no., %]	399 (84)	161 (80)	0.18
	Ribavirin dose:
	≥15 mg/kg [no., %]	117 (25)	30 (15)
	< 15 mg/kg [no., %]	356 (75)	170 (85)	0.006

Table 4 .

 4 Univariate analysis of predictors of rapid virological response (RVR) in patients sorted out by

	the HCV genotype
		Genotype 2		Genotype 3
	Total number of patients	RVR	No	P	RVR	No	P
			RVR			RVR
		254	82		219	118
	Age: <45 yrs [no., %]	189 (74) 49 (60) 0.017 168 (77) 64 (54) 0.001
	Gender : male [no., %]	137 (54) 50 (61) 0.30 147 (67) 72 (61) 0.28
	Body Mass Index:
	<30 kg/m 2 [no., %]	221 (87) 62 (76) 0.022 189 (86) 98 (83) 0.42
	Viral load:
	>400.000 IU/ml [no., %]	100 (39) 20 (24) 0.017 138 (63) 97 (82) 0.0001
	Platelet count:
	≥140.000 mm 3 [no., %]	204 (81) 58 (72) 0.08 190 (88) 102 (87) 0.86
	APRI score:
	<2 [no., %]	217 (86) 60 (77) 0.06 182 (86) 103 (89) 0.60
	Ribavirin dose:
	≥15 mg/kg [no., %]	69 (27)	17 (21)	0.30 48 (22)	13 (61)	0.017
	< 15 mg/kg [no., %]	185 (73)	65 (79)		171 (78)	105 (89)


MD Philippe ; Zerbib
email: p-zerbib@chru-lille.fr

Dine Koriche

Stéphanie Truant

Ahmed Fouad Bouras

Gwenola Vernier-Massouille

David Seguy

François-René Pruvot

Antoine Cortot

MD Jean-Frédéric Frédéric Colombel
email: jean-frederic.colombel@chru-lille.fr

Bouras Af

Cortot Pruvot Fr

Colombel Jf

Pre-operative management is associated with low rate of post-operative morbidity in penetrating Crohn's disease

Keywords: Crohn's disease < Disease-based, Small intestine < Organ-based, General practice < Topics, Nutrition < Topics, Surgery < Default) Arial

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Crohn's disease (CD) is a chronic inflammatory disease associated with significant morbidity. The introduction of anti-TNF agents has improved outcome in CD [START_REF] Rutgeerts | Optimizing anti-TNF treatment in inflammatory bowel disease[END_REF][START_REF] Sands | Infliximab maintenance therapy for fistulizing Crohn's disease[END_REF] but there are still few data on their long-term efficacy beyond one year and their impact on the long-term outcome [START_REF] Sands | Long-term treatment of rectovaginal fistulas in Crohn's disease: response to infliximab in the ACCENT II Study[END_REF] . Despite improvement in medical care the rate of surgery remains high in CD [START_REF] Gardiner | Operative management of small bowel Crohn's disease[END_REF] . Penetrating CD, defined as subacute perforation with abscess formation and chronic perforation with internal fistula formation, is still a prominent indication for surgery [START_REF] Greenstein | Perforating and non-perforating indications for repeated operations in Crohn's disease: evidence for two clinical forms[END_REF] . Patients who had abdominal surgery for penetrating CD still experience a high rate of post-operative complications 6, 7 . A two-stage procedure including a temporary diverting stoma is often required in up to 39% to 51% of patients [START_REF] Goyer | Impact of complex Crohn's disease on the outcome of laparoscopic ileocecal resection: a comparative clinical study in 124 patients[END_REF][START_REF] Melton | Contemporary surgical management for ileosigmoid fistulas in Crohn's disease[END_REF] . Several risk factors have been associated with a poor outcome of surgery for penetrating CD such as the presence of an abscess at the time of surgery, the use of chronic corticosteroid medication and an impaired nutritional status.

We have implemented in our institution a systematic pre-operative management for penetrating CD consisting in bowel rest, nutritional therapy, intravenous antibiotics, weaning of steroids and percutaneous drainage of abscesses when appropriate. We here report the results of this approach focusing on the rate of post-operative major morbidities and need for faecal diversion for primary penetrating ileocecal CD.

Methods

Patients

We reviewed retrospectively the files of all consecutive patients who underwent a first ileocecal resection (ICR) for penetrating CD from December 1997 to January 2007 in a unique surgical department. Penetrating CD was defined according to Montreal's classification [START_REF] Satsangi | The Montreal classification of inflammatory bowel disease: controversies, consensus, and implications[END_REF] . In addition to medical history and physical examination, all patients were assessed before surgery with colonoscopy and computed tomography scanning (CT-scan • Drainage of abscesses Abdominal, pelvic or retroperitoneal abscesses > 5 cm in diameter were drained percutaneously under sonography or CT-scan guidance whenever possible or surgically drained. Repeat CT-scans were not systematically performed after drainage. Subsequently, ICR was performed 2 to 3 weeks after drainage of an abscess.

• Medical treatment

All patients received intravenous broad spectrum antibiotherapy for 15 days (metronidazole and fluoroquinolone or cephalosporin) directed against anaerobic bacteria and adapted to bacteriologic results. Presence of an abscess led to immediate withdrawal of immunosuppressors and/or anti-TNFα therapy and weaning of steroids was achieved before surgical resection. Steroids were decreased quickly before surgery i.e. at a rhythm of 10 mg of prednisolone / day until half dose and 5 mg / day after until 0. For patients being under a mean dose of 45 mg / day, the mean time for a complete weaning was 7 days. As patients were weaned of steroids at least 1 week before surgical resection, no steroid cover during the peri-operative period was necessary. Azathioprine and methotrexate were stopped as soon as the patient was hospitalized as well as Anti-TNFα therapy.

Surgical procedure

Ileocecal resection was performed using laparoscopic or open surgical resection.

Laparoscopic-assisted ileocecal resection

Patients were placed in the French position. A 3-trocar approach was used (subumbilical, 10 mm; right and left fossa, 5 mm). After full intracorporeally mobilization of the right colon, the distal ileum and the cecum were exteriorized through a 4-to 5-cm vertical midline incision. The whole small bowel was thoroughly

F o r P e e r R e v i e w Revised R1 6
Formatted: Font: (Default) Arial examined extracorporeally from the duodeno-jejunal flexure to the ileum. Vascular ligation, bowel division and a sutured end-to-end, or end-to-side anastomosis were performed extracorporeally with a handsewn technique using a single layer of interrupted resorbable sutures (Vicryl ® or Monocryl ® 4/0). In cases of fistula, the ileum and the victim organ (bowel or bladder) were divided intracorporeally. The defect of the victim organ was then closed laparoscopically or extracorporeally. Conversion to open surgery was defined as whenever any unplanned incision was performed, when any longer than 5 cm planned incision was made or earlier in the procedure than anticipated.

Open surgical resection

Through a sus-and sub-umbilical midline incision, the right colon was mobilized.

After vascular and bowel division, end-to-end or end-to-side ileo-colic anastomosis was performed with a handsewn technique using a single layer of interrupted resorbable sutures (Vicryl ® or Monocryl ® 4/0).

Faecal diversion by end ileocolostomy exteriorized in the right flank was performed after ICR, instead of the anastomosis, if an abscess was still present at the time of surgery or in case of complex ileo-sigmoid fistula requiring a large sigmoidectomy. In these cases, delayed ileo-colic anastomosis was performed 3 months later. Oral intake was started after surgery with clear liquids and enlarged as long as tolerated. Patients were discharged when a normal diet was possible.

Outcomes definitions

Post-operative morbidity and mortality were defined as any complication or death occurring within 3 months after ICR. Post-operative complications were classified using the morbidity scale proposed by Dindo et al. (Table 1) [START_REF] Dindo | Classification of surgical complications: a new proposal with evaluation in a cohort of 6336 patients and results of a survey[END_REF] . Hospital stay was defined as the time from the surgical intervention to hospital discharge. The post-operative course was considered as uneventful when ICR was performed with primary anastomosis, without any post-operative complication.

Statistical analysis

Continuous variables were expressed as mean (standard deviation, range).

Categorical variables, expressed as frequencies and percentages, were compared using the chi-square test or Fisher's exact test, as appropriate. All analyses were performed using SPSS, version 13.0 (SPSS Inc. Chicago, IL). • With fistula in 41 patients: entero-cutaneous fistula (n = 11), entero-bladder fistula (n = 11), ileo-sigmoid fistula (n = 21), entero-colic fistula (n = 3), ileo-ileal fistula (n = 7)

F

• With abscesses in 32 patients

• Or both abscesses and fistula in 5 patients.

Pre-operative management and surgical procedure are reported in Table 3.

For 50 patients (64%), a pre-operative TPN (n = 45) or EN (n = 5) was performed for 23 days (7 -69). Among 37 patients presenting with an abscess, percutaneous CT scan or surgical drainage was performed in 11 (29.7%) in association with antibiotic therapy. Eighteen patients were on steroids at their admission (mean dose, 45 mg/day). Sixteen patients were on immunosuppressors (azathioprine, methotrexate)

and one patient on anti-TNFα therapy. All patients were weaned off steroids, immunosuppressors and anti-TNFα therapy at the time of surgery.

Mean operating time was 155 minutes (SD, 45.7; 60 -300). Among 78 patients, 35 underwent laparoscopic ICR (45 %) of whom 11 (31.4 %) were

converted to an open approach for the following reasons: inflammatory pelvic adhesions ± complex fistula (n = 6), large inflammatory mass (n = 3), and ileosigmoid fistula (n = 2). Additional surgical procedures reported in Table 3

Discussion

The aim of this retrospective study on a large cohort of ICR for penetrating CD at a tertiary referral center was to assess the results of a standardized therapeutic strategy i.e. surgery after 2 to 3 weeks of pre-operative management consisting in bowel rest, nutritional therapy with intravenous antibiotics, weaning off steroids, immunosuppressors and anti TNFα therapy, and drainage of abscesses > 5 cm. This management is feasible and associated with low rate of post-operative morbidity of 18% and no mortality and had similar outcomes than those operated on for uncomplicated Crohn's ileitis.

The weakness of this current series is that it was uncontrolled. However, during the study period, our strategy of preoperative management was adopted as a standard of care based on our experience with Crohn's disease surgery resulting in a low number of patients undergoing planned ileo-colic resection for penetrating CD without preoperative management. Furthermore, such a prospective comparative trial or even a retrospective case-matched study seems in any case difficult if not impossible to perform.

These results are indeed comparable to those reported in a recent metaanalysis pooling data from 12 studies, in which the post-operative morbidity rate for surgery in CD was 12.8 % for laparoscopic surgery compared with 20.2 % for open surgery [START_REF] Tan | Laparoscopic surgery for Crohn's disease: a metaanalysis[END_REF] .

The low rate of temporary diverting stoma (7.7 %) is also remarkable. All of them were voluntarily performed in patients with residual abscess at the time of surgery or complex ileo-sigmoid fistula necessitating large sigmoidectomy. Indeed stoma diversion rate reported in previous series of ICR for penetrating CD was five times more elevated than in our series. In a retrospective study of ileosigmoid fistula in CD where 93% of patients underwent ICR, a stoma diversion was voluntarily performed in 51% of patients (53/104 patients) and was secondarily performed in 4% of patients (4/104 patients) due to anastomotic leakage [START_REF] Melton | Contemporary surgical management for ileosigmoid fistulas in Crohn's disease[END_REF] . In another recent prospective study comparing complicated and uncomplicated CD undergoing laparoscopic ICR, a two-stage procedure with a temporary diverting stoma was performed in 39 % for complex fistulizing CD (all of them being voluntarily performed)

8

. Operative findings evidenced that the inflammatory process in patients who initially had an abscess or phlegmon diminished after 2 weeks of bowel rest. It is therefore likely that our strategy of pre-operative management allowed ICR to be performed with primary anastomosis in circumstances that might have otherwise required a twostage procedure with diverting stoma. However, the optimal duration for bowel rest with nutritional assistance is yet unknown, the period of 2 to 3 weeks having been pragmatically chosen.

We believe that the good surgical outcome in this series is also linked to the impact of the pre-operative management on important risk factors for post-operative complications. Patients were weaned off corticosteroids, immunomodulators and anti-TNFα agents during the pre-operative period. The deleterious impact of steroids on the outcome of surgical resections in CD is well documented. A recent meta-analysis showed that pre-operative corticosteroids increased the likelihood of all postoperative complications (OR 1.41, 95% CI: 1.07-1.87) and of infectious complications (OR 1.68, 95%CI: 1.24-2.28). This higher risk of complications is dose dependent and therefore it is suggested to stop corticosteroids preoperatively or taper doses lower than 40 mg/day [START_REF] Subramanian | Preoperative steroid use and risk of postoperative complications in patients with inflammatory bowel disease undergoing abdominal surgery[END_REF] . Our policy was also to stop immunomodulators and anti-TNFα even though it is still debated whether or not they increase the likelihood of anastomotic leakage and infectious complications in CD patients [START_REF] Appau | Use of infliximab within 3 months of ileocolonic resection is associated with adverse postoperative outcomes in Crohn's patients[END_REF][START_REF] Colombel | Early postoperative complications are not increased in patients with Crohn's disease treated perioperatively with infliximab or immunosuppressive therapy[END_REF][START_REF] Marchal | The risk of post-operative complications associated with infliximab therapy for Crohn's disease: a controlled cohort study[END_REF] . Thiopurines can be related to a decrease in epithelial cell proliferation and T-cell-mediated suppression of the inflammatory reaction which could interfere with adequate collagen synthesis and wound healing resulting eventually in an impairment of anastomotic healing. In a recent prospective analysis, patients under thiopurine therapy had a significant increased risk for anastomotic leakage especially in case of intra-abdominal sepsis leading the authors to advice a two-stage procedure in this setting [START_REF] Myrelid | Thiopurine therapy is associated with postoperative intra-abdominal septic complications in abdominal surgery for Crohn's disease[END_REF] . In a retrospective study, thiopurines alone and the addition of thiopurines for patients under steroids was not found to significantly increase the risk of postoperative infectious complications [START_REF] Aberra | Corticosteroids and immunomodulators: postoperative infectious complication risk in inflammatory bowel disease patients[END_REF] .

Another important point of our preoperative management was to improve nutritional status when altered. Poor nutritional state and low serum albumin certainly increase post-operative morbidity and the risk of a two-stage procedure [START_REF] Post | Risks of intestinal anastomoses in Crohn's disease[END_REF][START_REF] Marceau | Laparoscopic subtotal colectomy for acute or severe colitis complicating inflammatory bowel disease: a casematched study in 88 patients[END_REF][START_REF] Yamamoto | Risk factors for intra-abdominal sepsis after surgery in Crohn's disease[END_REF] . Preoperative nutritional therapies can improve nutritional parameters and wound healing even before nutritional parameters show any change [START_REF] Gouma | Preoperative total parenteral nutrition (TPN) in severe Crohn's disease[END_REF][START_REF] Haydock | Improved wound healing response in surgical patients receiving intravenous nutrition[END_REF] . Recent calorie intake may be more important than nutritional status [START_REF] Windsor | Wound healing response in surgical patients: recent food intake is more important than nutritional status[END_REF] . Nutritional therapies alone in preoperative situation are probably insufficient to treat active CD [START_REF] Zachos | Enteral nutritional therapy for induction of remission in Crohn's disease[END_REF] , but, in association with antibiotherapy (and abscess drainage when appropriate) they seem to improve wound healing with a low rate of faecal diversion. In a prospective population-based study comparing handsewn and stapling anastomosis in patients with CD (where 98% of patients underwent ICR), the same preoperative management was reported before intestinal resection [START_REF] Smedh | Preoperative management is more important than choice of sutured or stapled anastomosis in Crohn's disease[END_REF] . The authors reported a very low complications rate (no anastomotic leakage) and conclude that the choice of anastomotic technique is not the most important factor for anastomotic healing but the crucial point is that patient was operated on under the optimal general conditions in terms of nutritional and healing capacity. Our study is, to our knowledge, the first which evaluated this preoperative management in a large series of penetrating CD.

The modalities of nutritional assistance have changed along our study. Initially, TPN appeared more fitted to the situation of penetrating CD since it insured a better bowel rest than EN, but with greater risks. Thus, in our initial experience, we attempted to put as much as possible patients under EN, but some of them aggravated their abscess under EN. Then, we decided to reserve EN to patients with a fistulizing form only (without abscess) and with a persistent intestinal transit.

This series further confirm that the laparoscopic-assisted approach to complex CD is feasible and safe. Abscess, phlegmon or fistulas are not contraindications to a successful laparoscopic ICR [START_REF] Goyer | Impact of complex Crohn's disease on the outcome of laparoscopic ileocecal resection: a comparative clinical study in 124 patients[END_REF][START_REF] Wu | Laparoscopic-assisted ileocolic resections in patients with Crohn's disease: are abscesses, phlegmons, or recurrent disease contraindications?[END_REF] . Several authors have reported fewer complications associated with the laparoscopic approach [START_REF] Wu | Laparoscopic-assisted ileocolic resections in patients with Crohn's disease: are abscesses, phlegmons, or recurrent disease contraindications?[END_REF][START_REF] Ludwig | Preliminary experience with laparoscopic intestinal surgery for Crohn's disease[END_REF][START_REF] Milsom | Prospective, randomized trial comparing laparoscopic vs. conventional surgery for refractory ileocolic Crohn's disease[END_REF] . Nevertheless, the nature of complicated CD can render surgery challenging, and the technical difficulties encountered are more pronounced with laparoscopic surgery [START_REF] Benoist | Laparoscopic ileocecal resection in Crohn's disease: a case-matched comparison with open resection[END_REF][START_REF] Hamel | Laparoscopic surgery for inflammatory bowel disease[END_REF][START_REF] Watanabe | Successful application of laparoscopic surgery to the treatment of Crohn's disease with fistulas[END_REF][START_REF] Zmora | Laparoscopy for Crohn disease[END_REF] . Penetrating CD (i.e., intra-abdominal abscess and fistula) was independent factors predicting conversion to open surgery [START_REF] Alves | Factors that predict conversion in 69 consecutive patients undergoing laparoscopic ileocecal resection for Crohn's disease: a prospective study[END_REF] . Our conversion rate of 34% was comparable to previous studies [START_REF] Goyer | Impact of complex Crohn's disease on the outcome of laparoscopic ileocecal resection: a comparative clinical study in 124 patients[END_REF][START_REF] Moorthy | Factors that predict conversion in patients undergoing laparoscopic surgery for Crohn's disease[END_REF][START_REF] Uchikoshi | Advantages of laparoscope-assisted surgery for recurrent Crohn's disease[END_REF] . According to other authors, the main reasons for conversion were the presence of complex inflammatory masses or fistula [START_REF] Tan | Laparoscopic surgery for Crohn's disease: a metaanalysis[END_REF][START_REF] Evans | Influence of experience on laparoscopic ileocolic resection for Crohn's disease[END_REF][START_REF] Maartense | Laparoscopic-assisted versus open ileocolic resection for Crohn's disease: a randomized trial[END_REF] .

In conclusion, pre-operative management for penetrating CD allowed to decrease dramatically faecal diversion rate than previously reported after ICR for penetrating CD with a low rate of post-operative morbidity. Most patients (64%) received intensive medical therapy including total parenteral nutrition or an elemental diet for more than 2 weeks. This policy might result in a longer hospital stay and higher overall costs. However, this needs to be balanced with a low rate of faecal

4 Formatted:

 4 Font: (Default) Arial

9 Formatted: 10 Formatted:

 910 , included liver biopsy (n = 2), cholecystectomy (n = 3), temporary faecal diversion (n = 6), closure of a fistula directed toward a victim organ (n = 29), additional small bowel Font: (Default) Arial resection (n = 4), sigmoidectomy (n = 3), stricturoplasties (n = 4), cesarean (n = 1) and closure of stoma (n =1). A temporary diverting stoma was performed in 6 patients (7.7%) due to presence of residual abscess at the time of surgery or in case of complex ileo-sigmoid fistula requiring a large sigmoidectomy. Faecal diversions were all temporary and always performed at time of open ICR and never for anastomotic leakage in post-operative period. Faecal diversions were all and always performed in open ICR.There was no post-operative death. According to the Dindo's classification[START_REF] Dindo | Classification of surgical complications: a new proposal with evaluation in a cohort of 6336 patients and results of a survey[END_REF] , post-operative morbidities were classified as 3 grades I, 7 grades II (including 3 patients who had conservative management of anastomotic leakage), 1 grade IIIa (percutaneous drainage of intra-abdominal collection) and 3 grade IIIb (cholecystitis, hemoperitoneum, occlusion that needed re-operation). Anastomotic leakage management never necessitated post-operative faecal diversion and was always managed through conservative treatment. The 6 patients necessitating diverting stoma were not included in the uneventful outcomes. Overall, the post-operative course was uneventful in 58 patients (74 %) (Table4).By univariate analysis, seven factors were tested in order to identify predictive factors of postoperative outcome, i.e the need for faecal diversion and/or occurrence of postoperative complications: previous laparotomy, BMI ≤ 20, albumin ≤ 30 before nutrition, preoperative enteral and/or parenteral nutrition, surgical approach (laparoscopic / open), abscess and/or fistula as indication for resection, additional surgical procedures. None of these factors was associated with the need for faecal diversion or occurrence of postoperative complications. Nevertheless, this could be a type-2 error due to the relatively small size of our population. Font: (Default) Arial

13 Formatted:

 13 Font: (Default) Arial

  ). Data collection included the following: patient characteristics such as gender, age, body mass index, smoking history, familial history of inflammatory bowel disease, and serum albumin level ; CD features

	Revised R1	5
	F o r
	P
	e
	e r
	R
	e
	v i e
	w
		Deleted:

such as extent of the disease, perianal involvement, time from diagnosis, indication for surgical treatment (i.e. abscess, fistula or both), medical treatment (i.e. steroids, immunosuppressors (azathioprine, methotrexate), anti-TNFα ).

Pre-operative management

• Nutritional therapies Enteral nutrition (EN) using preferentially elemental diet was applied for 2 weeks before surgery in 2 situations depending on the existence of an intestinal subocclusion: night enteral nutrition in addition to ordinary food if transit persisted or exclusive enteral nutrition (>30 kcal/kg ideal body weight / day) in sub-occluded patients. Patients with complete intestinal occlusion and complete food intolerance, patients with clinically or endoscopically severe colitis and patients with abdominal or pelvic abscesses received a Total Parenteral Nutrition (TPN) for 3 weeks before surgery.

Formatted: Font: (Default) Arial

Table 2 .

 2 Mean follow-up for the entire patient cohort was 23.2 months (SD, 24.9; 1 -86). Indications for resection were terminal ileitis associated:

	Revised R1	8
	o r
	P
	e
	e r
	R
	e
	v i e
	w

Formatted: Font: (Default) Arial

Results

Seventy eight patients (48 males) with a mean age of 29 years (SD, 8.8; 16 -70) underwent elective ICR for penetrating CD. Patients' characteristics are listed on

Table 1 .

 1 Classification of surgical complications[START_REF] Dindo | Classification of surgical complications: a new proposal with evaluation in a cohort of 6336 patients and results of a survey[END_REF] . If the patient suffers from a complication at the time of discharge, the suffix "d" (for "disability") is added to the respective grade of complication. This label indicates the need for a follow-up to fully evaluate the complication.

	diversion which is associated with decrease of quality of life and iterative

Table 2 .

 2 Patient's characteristics SD: Standard deviation; BMI: Body mass index Age, years, mean (SD, range) 29 (8.8, 16 -70)

	Gender (male / female)

Table 3 .

 3 Pre-operative management and surgical procedure TPN: Total parenteral nutrition; EN: Enteral nutrition ; ICR : Ileocecal resection ; IV :

	Intravenous ; SD : Standard deviation
	Penetrating ileitis, n	78
	Pre-operative Management
	• Nutritional therapies (2 weeks)		Formatted: Bullets and Numbering
	and IV antibiotic therapy (15 days)
	o TPN, n (%)	45 (58)	Formatted: Bullets and Numbering
	o EN, n (%)	5 (6)
	• Drainage of abscess > 5cm, n (%)	11 (30)	Formatted: Bullets and Numbering
	o Surgical, n	5
	o Radiological, n	6
	and anti TNFα therapy, n • Weaning of steroids, immunossupressors	35	Formatted: Bullets and Numbering
	Surgical procedure
	• Laparoscopic ICR, n (%)	35 (45)	Formatted: Bullets and Numbering
	• Open ICR, n (%)	43 (55)
	• Temporary diverting stoma, n (%)	6 (7.7)
	• Additional surgical procedures, n
	o Liver biopsy	2
	o Cholecystectomy	3
	o Closure of a victim organ	29
	o Additional small bowel resection	4
	o Sigmoidectomy	3
	o Stricturoplasties	4
	o Cesarean	1
	o Closure of a stoma	1

Formatted: Font: (Default) Arial

Formatted: Font: (Default) Arial