You Ding

Carlo Rovelli Cpt

The volume operator in covariant quantum gravity

A covariant spin-foam formulation of quantum gravity has been recently developed, characterized by a kinematics which appears to match well the one of canonical loop quantum gravity. In particular, the geometrical observable giving the area of a surface has been shown to be the same as the one in loop quantum gravity. Here we discuss the volume observable. We derive the volume operator in the covariant theory, and show that it matches the one of loop quantum gravity, as does the area. We also reconsider the implementation of the constraints that defines the model: we derive in a simple way the boundary Hilbert space of the theory from a suitable form of the classical constraints, and show directly that all constraints vanish weakly on this space.

Introduction

The spinfoam formalism [START_REF] Mp Reisenberger | World sheet formulations of gauge theories and gravity[END_REF][START_REF] Mp Reisenberger | Sum over surfaces' form of loop quantum gravity[END_REF][START_REF] Mp Reisenberger | A lattice worldsheet sum for 4-d Euclidean general relativity[END_REF][START_REF] Barrett | Relativistic spin networks and quantum gravity[END_REF][START_REF] Depietri | Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space[END_REF][START_REF] Oriti | Spacetime geometry from algebra: spin foam models for non-perturbative quantum gravity[END_REF] and canonical loop quantum gravity (LQG) [START_REF] Ashtekar | Background independent quantum gravity: A status report[END_REF][START_REF] Rovelli | Quantum Gravity[END_REF][START_REF] Rovelli | Knot theory and quantum gravity[END_REF] can ideally be viewed as the covariant and the canonical versions, respectively, of a background-independent quantum theory of gravity [START_REF] Rovelli | A new look at loop quantum gravity[END_REF]. This scenario is nicely realized in three dimensions [START_REF] Noui | Three dimensional loop quantum gravity: Physical scalar product and spin foam models[END_REF], and there are recent attempts to implement it in quantum cosmology [START_REF] Ashtekar | Loop Quantum Cosmology and Spin Foams[END_REF][START_REF] Mv Battisti | Triangulated Loop Quantum Cosmology: Bianchi IX and inhomogenous perturbations[END_REF]. An important step ahead towards the realization of this scenario in the complete four dimensional theory has been taken with the recent introduction of two spin-foam models whose kinematics appears to match the one of LQG rather well, which we refer to as the new model [START_REF] Engle | The loop-quantum-gravity vertex-amplitude[END_REF][START_REF] Engle | Flipped spinfoam vertex and loop gravity[END_REF][START_REF] Engle | LQG vertex with finite Immirzi parameter[END_REF][START_REF] Pereira | Lorentzian LQG vertex amplitude[END_REF][START_REF] Livine | Consistently solving the simplicity constraints for spinfoam quantum gravity[END_REF] and the Freidel-Krasnov-Livine-Speziale (FKLS) model [START_REF] Livine | A new spinfoam vertex for quantum gravity[END_REF][START_REF] Freidel | A New Spin Foam Model for 4d Gravity[END_REF]. The kinematics of canonical loop quantum gravity, indeed, is rather well understood; in particular, the properties of the geometrical operators, including the area and the volume operators [START_REF] Rovelli | Discreteness of Area and Volume in Quantum Gravity[END_REF][START_REF] Ashtekar | Quantum Theory of Geometry I: Area Operators[END_REF][START_REF] Ashtekar | Quantum Theory of Geometry II: Volume Operators[END_REF] are well established. (On the volume operator, see also [START_REF] Flori | Semiclassical analysis of the Loop Quantum Gravity volume operator: I. Flux Coherent States[END_REF].) The area operator of the new spinfoam model has been derived in [START_REF] Engle | LQG vertex with finite Immirzi parameter[END_REF][START_REF] Engle | Coherent states, constraint classes, and area operators in the new spin-foam models[END_REF] and shown to match the LQG one. Does the volume do so as well?

The volume observable in the covariant spinfoam language has not been constructed yet. The essential property of the volume operator is that it has contribution only from the nodes of a spin network state. Thus the only possible action of the volume operator is on the intertwiners. That's the reason why there is no generic well-defined volume operator in the old Barrett-Crane (BC) model [START_REF] Depietri | Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space[END_REF], based on the vertex amplitude introduced by Barrett and Crane [START_REF] Barrett | Relativistic spin networks and quantum gravity[END_REF], where intertwiners are fixed. In fact, the absence of the volume operator in the Barrett-Crane theory can be traced precisely to the key problem of the BC model: the fact that intertwiner quantum numbers are fully constrained. This follows from the SO(4) → SU (2) gauge fixing and the way certain second class constraints are imposed, arguably incorrectly, strongly. The new model [START_REF] Engle | The loop-quantum-gravity vertex-amplitude[END_REF][START_REF] Engle | Flipped spinfoam vertex and loop gravity[END_REF][START_REF] Engle | LQG vertex with finite Immirzi parameter[END_REF][START_REF] Pereira | Lorentzian LQG vertex amplitude[END_REF] imposes second class simplicity constraints weakly, rather than strongly as in the BC theory. This choice frees intertwiner degrees of freedom, and the volume operator can be nontrivial. In this model, the state space where the constraints vanish weakly turns also out to match that of LQG, providing a solution to the problem of connecting the covariant SO(4) spinfoam formalism with the canonical SU (2) spin-network one. To complete this identification, we construct here the volume operator in the covariant spinfoam picture, and show explicitly that it matches the corresponding LQG canonical operator.

As a first step, in the next section we review the derivation of the boundary state space of the spinfoam theory. We do so for completeness, but also in order to clean up and simplify previous derivations in the literature. In particular, we show explicitly and directly that all the constraints vanish in a weak sense in the physical boundary space. The form of the constraints that we write turns out to strongly simplify the study of the volume operator.

We work only in the Euclidean theory, on a fixed triangulation, and assume here that the Barbero-Immirzi parameter γ is positive. The paper is organized as follows. In section 2, we review the definition of the physical boundary Hilbert space. The volume operator is constructed and shown to match the LQG operator in Section 3.

The boundary space

Classical theory

Following [START_REF] Engle | Flipped spinfoam vertex and loop gravity[END_REF][START_REF] Engle | LQG vertex with finite Immirzi parameter[END_REF], we start with a Regge geometry [START_REF] Regge | General Relativity Without Coordinates[END_REF] on a fixed triangulation. Consider a 4d triangulation, which is formed by oriented 4-simplices, tetrahedra, triangles, segments and points. We call v, t and f respectively the 4-simplices, the tetrahedra and the triangles of the triangulation. For each simplex v, we introduce a variable e I µ (v): a right-handed tetrad one-form, constant over a coordinate patch covering the simplex v, with the determinant det(e) > 0 positive. Here µ = (0, a) and a = 1, 2, 3 are spacetime indices, while I = (0, i) and i = 1, 2, 3 are internal indices (the value 0 instead of 4 is for later convenience and does not indicate a Lorentzian metric). Without loss of generality, we can choose a linear coordinate system with basis vectors -→ X µ parallel with four edges of v emanating from the same point, and where the (coordinate) length of the four segments is 1. Consider in particular the tetrahedron t spanned by the three vectors -→ X a . To each triangle f a (coordinate-)normal to the coordinate basis vector -→ X a , we associate a bivector * B a (t) defined by:

* B IJ a = 1 2 bc a e I b e J c . (1)
B f (t) can be seen as elements in the algebra g = so(4), in the Euclidean case, and * stands for the Hodge dual in the internal indices. If we choose B f (t) as independent variables instead of the tetrads, and n I denotes the normal to the tetrahedron t, the simplicity constraints on B f (t), which assure that a tetrad field exist, can be stated as follows [START_REF] Engle | Flipped spinfoam vertex and loop gravity[END_REF][START_REF] Engle | LQG vertex with finite Immirzi parameter[END_REF]:

C J f := n I ( * B f (t)) IJ = 0. (2)
The usual quadratic diagonal

C f f := * B f (t) • B f (t) = 0 (3)
and off-diagonal

C f f := * B f (t) • B f (t) = 0 (4)
simplicity constraints can be easily shown to follow from [START_REF] Mp Reisenberger | Sum over surfaces' form of loop quantum gravity[END_REF]. Here the dot stands for the scalar product in the so(4) algebra. In addition, we should impose the closure constraint

f ∈∂t B f (t) = 0. ( 5
)
The new linear simplicity constraint (2) selects the solution of the quadratic constraints where

B f = f * (e ∧ e)
. This reformulation is central for the new model [START_REF] Engle | The loop-quantum-gravity vertex-amplitude[END_REF][START_REF] Engle | Flipped spinfoam vertex and loop gravity[END_REF][START_REF] Engle | LQG vertex with finite Immirzi parameter[END_REF][START_REF] Pereira | Lorentzian LQG vertex amplitude[END_REF]. In particular, if we choose a "time" gauge where n I = (0, 0, 0, 1), the simplicity constraint (2) turns out to be * B 0i f (t) = 0.

The classical discrete action is [START_REF] Engle | LQG vertex with finite Immirzi parameter[END_REF][START_REF] Engle | Coherent states, constraint classes, and area operators in the new spin-foam models[END_REF] S = -

f ∈int∆ Tr B f (t)U f (t) + 1 γ * B f (t)U f (t) - f ∈∂∆ Tr B f (t)U f (t, t ) + 1 γ * B f (t)U f (t, t ) , (7)
where U f (t, t ) is the group element of SO( 4), giving the parallel transport across each triangle f bounding t and t and U f (t) := U f (t, t) is the holonomy around the full link, starting at t. We use here unites where 2κ = 16πG = 1 and γ the Barbero-Immirzi parameter. This action, plus the simplicity and closure constraints defines a discretization of general relativity [START_REF] Engle | Flipped spinfoam vertex and loop gravity[END_REF][START_REF] Engle | LQG vertex with finite Immirzi parameter[END_REF]. From the action, we can read off the boundary variables as B f (t) ∈ so(4), U f (t, t ) ∈ SO(4). One can also see that the variable conjugate to U f (t, t ) is

J f (t) :=B f (t) + 1 γ * B f (t), (8)
inverting which gives

* B f (t) = γ 2 1 -γ 2 1 γ J f (t) - * J f (t) . (9)
Thus to each boundary triangle f in the boundary of the triangulation, we have an SO(4) group element U f and, as conjugate variable an so(4) algebra element J f . It is convenient to think these variables as associated with the links of the graph formed by the one-skeleton of the cellular complex dual to the boundary triangulation. Notice that these define precisely the same boundary phase space as the one of an SO(4) lattice Yang-Mills theory. As in Yang-Mills theory, the symplectic structure can be taken to be [START_REF] Engle | Flipped spinfoam vertex and loop gravity[END_REF]

{U f , U f } = 0, {(J f ) IJ , U f } = δ f f U f τ IJ , (10)
{(J f ) IJ , (J f ) KL } = δ f f λ IJ KL MN (J f ) MN ,
where τ IJ and λ IJ KL MN are, respectively, the generators and the structure constants of SO(4). In terms of the momentum variable J f , the constraints (2) and ( 5) read respectively:

C J f = n I ( * J f ) IJ - 1 γ J IJ f = 0, ( 11
)
f ∈∂t J f (t) = 0. ( 12
)
For the gauge-fixed version, introduce L j f := 1 2 j kl J kl f and K j f := J 0j f , which are respectively the generators of the SO(3) subgroup that leaves n I invariant, and the generators of the corresponding boosts. Then the simplicity constraint (2) becomes simply

K i f = γ L i f . (13)
This is the key constraint. In terms of (K i f , L i f ), the closure constraint ( 12) turns out to be

f ∈∂t L i f = 0, (14a)
and

f ∈∂t K i f = 0. ( 14b
)
If we further make the self-dual/anti-self-dual decomposition of J IJ f :

J (±)i f := 1 2 (L i f ± K i f ), (15)
the simplicity constraint [START_REF] Noui | Three dimensional loop quantum gravity: Physical scalar product and spin foam models[END_REF] implies

C i f = (1 -γ)J (+)i f -(1 + γ)J (-)i f . ( 16
)
In terms of J (±)i , the usual quadratic diagonal simplicity constraint (3), which follows from the new simplicity constraint (2) or ( 16), can be reexpressed as

C f f = (1 -γ) 2 J (+)2 f -(1 + γ) 2 J (-)2 f . ( 17
)

Quantization

From the discrete boundary variables and their symplectic structure, we can construct the Hilbert space associated with a boundary or 3-slice. To do this, it is simpler to switch to the dual, 2-complex picture, ∆ * . For each 3-surface Σ intersecting no vertices of ∆ * , let γ Σ := Σ ∩ ∆ * . The Hilbert space associated with Σ is then

H Σ = L 2 Spin(4) |L(γΣ)| , dµ Haar , (18)
where we replace SO(4) with its covering group Spin(4) = SU (2) × SU (2) and µ Haar is the Haar measure on the group Spin(4); |L(γ Σ )| denotes the number of links in γ Σ . Let Ĵf (t) IJ denote the right-invariant vector fields, determined by the basis J IJ of su(2) ⊕ su(2), on the copy of Spin(4) associated with the link l = f ∩ Σ determined by f , with orientation such that the node n = t ∩ Σ is the source of l.

By Peter-Weyl theorem, H Σ can be decomposed as follows

H Σ = j l l H * j l ⊗ H j l , (19)
where j l is an assignment of a Spin(4) representation to each link l and H j is the carrier space of the representation j. The two Hilbert spaces associated to the link l are naturally associated to the two nodes that bound the link l, because they transform under the action of a gauge transformation at one end of the link. Regrouping the four Hilbert spaces associated to each node n, the last equation can be rewritten in the form

H Σ = j l n H n . (20)
Here the Hilbert space associated to a node n is

H n = 4 a=1 H ja , (21)
where a = 1, 2, 3, 4 runs here over the four edges that join at the node n (that is, the four faces of the boundary tetrahedron), and we have identified the Hilbert space carrying a representation and its dual. We restrict our attention to a single boundary tetrahedron t, and its associated Hilbert space H n , which we call simply H in the following. The irreducible unitary representations of Spin( 4) are labelled by a couple of spins (j + , j -) and are given by the tensor product of two SU (2) irreducibles. That is H := H n has the structure

H = 4 a=1 H (j + a ,j - a ) = 4 a=1 H j + a ⊗ H j - a . (22)
The physical intertwiner state space K ph is a subspace of this space, where the constraints hold in a suitable sense. As a first step to impose the constraints, let us restrict the representations to the ones that satisfy

j + = 1 + γ 1 -γ j -, (23)
which satisfies the usual quadratic diagonal simplicity constraint (17) in the classical limit, and is what we need to recover the correct classical theory in the limit. We call γ-simple the Spin(4) representations that satisfy this relation.

Next, the Clebsch-Gordan decomposition for the single component of H associated with a single boundary face f gives

H j + ⊗j -= H j + H j -= j + +j - p=|j + -j -| H p . ( 24
)
Consider the highest spin term in each factor for γ < 1 and the lowest for γ > 1 respectively; this selects the "extremum" subspace

H max = 4 a=1 H j + +j -, for γ < 1; (25)
H min = 4 a=1 H j + -j -, for γ > 1. ( 26
)
We are now going to show that in this space (with (23) holding), the simplicity constraint ( 16) is satisfied weakly. That is, the action of the constraints on the states in H ext results in states orthogonal to H ext . Namely, Ψ| Ĉi f |Φ = 0, ∀ Ψ, Φ ∈ H ext . This follows from the following considerations. ∀Ψ, Φ ∈ H ext , consider the matrix element of the form ( 16) of the simplicity constraints

Ψ| Ĉi f |Φ = (1 -γ) Ψ| J + f |Φ -(1 + γ) Ψ| J - f |Φ (27)
and write the r.h.s. of this equation in a representation where elements of H j are symmetric spinors with 2j indices. The generators of SU (2) are then Pauli matrices σ A i B acting on each index. For γ < 1,

Ψ| Ĉi f |Φ =(1 -γ)Ψ (A1...A 2j + B1...B 2j -) 2j + p=1 σ Ap i e Ap Φ (A1... e Ap...A 2j + B1...B 2j -) -(1 + γ)Ψ (A1...A 2j + B1...B 2j -) 2j - p=1 σ Bp i e Bp Φ (A1...A 2j + B1... e Bp...B 2j -) =2 (1 -γ)j + -(1 + γ)j -Ψ (A1...A 2j + B1...B 2j -) σ A1 i e A1 Φ ( e A1...A 2j + B1...B 2j -) =0. ( 28
)
The first step is obtained by the symmetry of the highest spin states, and the last follows from [START_REF] Ashtekar | Quantum Theory of Geometry II: Volume Operators[END_REF]. Therefore the simplicity constraint is implemented weakly in H max for γ < 1. For γ > 1, the state |Ψ in H min can be expressed as Φ (A1...A 2j + )(B1...B2j -) = A1B1 ... A 2j -B 2j -Φ (A 2j -+1 ...A 2j + ) , on which the action of J (-) can be obtained as

J -Φ (A1...A 2j + )(B1...B2j -) = 2j - p=1 σ Bp i e Bp A1B1 ... Ap e Bp ... A 2j -B 2j -Φ (A 2j -+1 ...A 2j + ) = - 2j - p=1 σ Ap i e Ap A1B1 ... e ApBp ... A 2j -B 2j -Φ (A 2j -+1 ...A 2j + ) = - 2j - p=1 σ Ap i e Ap Φ (A1... f Ap...A 2j + )(B1...B2j -) . (29)
Hence the matrix elements of the simplicity constraint can be obtained as

Ψ| Ĉi f |Φ = 2 (1 -γ)j + + (1 + γ)j -Ψ (A1...A 2j + )(B1...B 2j -) σ A1 i e A1 Φ ( e A1...A 2j + )(B1...B 2j -) = 0
The last step follows again from [START_REF] Ashtekar | Quantum Theory of Geometry II: Volume Operators[END_REF]. Therefore the space H ert solves the simplicity constraint. The physical intertwiner space associated with a single node n is then obtained by solving the closure constraint ( 14) weakly in the space H ext , which turns out to be

K ph = Inv SU(2) [H ext ]. (30)
To show that the closure constraints ( 14) hold weakly on this space, observe the matrix elements [START_REF] Alexandrov | The new vertices and canonical quantization[END_REF] of the simplicity constraint implies

Ψ|K i f |Φ = γ Ψ|L i f |Φ . (31)
The l.h.s of (14a) is the generator of SU (2) transformations at the node and vanishes strongly on (30) by definition; the l.h.s of (14b) is proportional weakly to the one of (14a) by (31) and therefore vanishes weakly. Hence the SU (2)-invariant space turns out to be SO(4)-invariant space in the weak sense. Thus K ph is the intertwiner space as a solution of all the constraints: all the constraints hold weakly.

The total physical boundary space H ph of the theory is then obtained as the span of spin-networks in L 2 [Spin(4) L /Spin(4) N , dµ Haar ] with γ-simple representations on edges and with intertwiners in the spaces K ph at each node.

We have then the remarkable result that K ph is naturally isomorphic to the SU (2) intertwiner space, and therefore the constrained boundary space H ph can be identified with the SU (2) LQG state space H SU(2) associated to the graph which is dual to the boundary of the triangulation, namely the space of the SU (2) spin networks on this graph.

Since we have not proven that the physical Hilbert space considered is the maximal space where the constraints hold weakly, one might worry that the physically correct quantization of the degrees of freedom of general relativity could need a larger space. Also, it has been pointed out that imposing second class constraints weakly might lead to inconsistencies in some cases [START_REF] Alexandrov | The new vertices and canonical quantization[END_REF]. In the present case, however, these worries are not relevant, since the space obtained is directly related to the one of the canonical theory, which we can trust to capture the degrees of freedom of gravity correctly.

Let us now consider the geometrical operators in these two versions. Classically, the area A(f ) of a triangle f is given by A(f

) 2 = 1 2 ( * B f ) IJ • ( * B f ) IJ . If we fix the time gauge, we have A 3 (f ) 2 = 1 2 ( * B f ) ij • ( * B f ) ij .
These two quantities are equal up to a constrained term. As shown in [START_REF] Engle | LQG vertex with finite Immirzi parameter[END_REF][START_REF] Engle | Coherent states, constraint classes, and area operators in the new spin-foam models[END_REF],

using the constraints, the operator related to A 3 (f ) 2 can be obtained as A 3 (f ) 2 = κ 2 γ 2 L 2 f , which matches three-dimensional area as determined by LQG, including the correct Barbero-Immirzi parameter proportionality factor. Let us now turn to study the volume operator on this space H ph and its relation with the SU (2) volume in LQG.

The Volume

It is easy to see from the definition of e i a (v) given at the beginning of the previous section, that the volume of the tetrahedron t is given by

V (t) = 1 6 det(e(v)). ( 32
)
In terms of the variables * B defined in (1), the volume of a boundary tetrahedron t reads V related to the tetrahedra t as

V (t) = 1 27 abc Tr[ * B a * B b * B c ] ( 3 3 )
To see this, let the gauge-fixed simplicity constraint (6) hold, then the * B 0i f (t) vanish and the above quantity is equal to

V 3 (t) = 1 27 abc * B ij a * B jk b * B ki c = 1 6 det(e), (34)
which is exactly the expression (32) of the discrete volume. Note that the SO(4) volume V SO(4) (t) is gauge invariant, hence we can obtain eq (33) by the gauge-fixed version (34) without loss of generality.

Going to the variables J, and using ( 9), the volume reads

V (t) = 1 27 γ 2 1 -γ 2 3 abc Tr 1 γ J a - * J a 1 γ J b - * J b 1 γ J c - * J c (35)
The volume operator V (t) of the tetrahedron t is then formally given by (35) with J IJ replaced by the corresponding operators:

V (t) = 1 27 γ 2 1 -γ 2 3 abc Tr 1 γ Ĵa - * Ĵa 1 γ Ĵb - * Ĵb 1 γ Ĵc - * Ĵc . (36)
However, the physical volume should be defined on the physical boundary space H ph , satisfying the constraints. Since the volume operator does not change the graph of the spin network sates, nor the coloring of the links, its action can be studied on the Hilbert space associated to a single node. Consider the matrix element of the square of the volume operator between two states in the physical Hilbert space (we drop the hats):

i|V (t) 2 |j = 1 27 γ 2 1 -γ 2 3 abc i| 1 γ J ij a - * J ij a 1 γ J jk b - * J jk b 1 γ J ki c - * J ki c |j . ( 37
)
Writing this in terms of L and K components gives

i|V (t) 2 |j = 1 27 • 8 γ 2 1 -γ 2 3 abc ij m jk n ki p i| 1 γ L m a -K m a 1 γ L n b -K n b 1 γ L p c -K p c |j . ( 38
)
Notice that the intertwiner space is the subspace of the product of the space H a associated to the link a, and the action of (K a , L a ) is in fact on H a . Hence we can use the form (31) of the simplicity constraint to simplify Eq. (38), although the r.h.s seems a polynomial. Using the form (31) of the constraint, we can rewrite it as

i|V (t) 2 |j = 1 27 • 8 γ 2 1 -γ 2 3 1 γ -γ 3 abc ijk i|L i a L j b L k c |j (39)
and a little algebra gives i|V (t)

2 |j = γ 3 i| abc ijk L i a L j b L k c |j . (40)
That is

V (t) = γ 3 2 abc ijk L i a L j b L k c (41)
Now, the operator on the r.h.s. is precisely the LQG volume operator V LQC , as it acts on K ph including the correct dependence on the Barbero-Immirzi parameter γ.

Acknowledgments

Thanks to Eugenio Bianchi for enlightening discussions. We wish also to thank Jonathan Engle, Simone Speziale, Franck Hellmann, Roberto Pereira and Muxin Han for helpful comments and suggestions. Y. D. is supported by CSC scholarship No. 2008604080.


L Fatibene

M Ferraris

M Francaviglia

New Cases of Universality Theorem for Gravitational Theories *

New cases of the universality theorem for gravitational theories

L Fatibene, M Ferraris, M Francaviglia

Introduction

It is well-known that for almost any analytic function f (R) the metric-affine theory with Lagrangian L f (g, j 1 Γ) = √ gf (R(g, j 1 Γ)) is dynamically equivalent to standard GR with a suitably quantized cosmological constant (encoded by the function f ); see [START_REF] Borowiec | Universality of Einstein Equations for the Ricci Squared Lagrangians[END_REF] and [START_REF] Magnano | Nonlinear gravitational Lagrangians[END_REF]. Hereafter j 1 Γ refers to the fact that the Lagrangian depends on the connection Γ and its first derivatives.

The original universality theorem was established in vacuum in [START_REF] Borowiec | Universality of Einstein Equations for the Ricci Squared Lagrangians[END_REF]. In fact, matter coupling produces in f (R) theories new effects with respect to Einstein equations, since a new metric conformal to the original one can be defined (see [START_REF] Capozziello | From Dark Energy & Dark Matter to Dark Metric[END_REF]). The theory in these new variables is quite similar to standard GR though with the addition of an effective energy momentum tensor; see [START_REF] Magnano | Nonlinear gravitational Lagrangians[END_REF]. Such new effects have been recently investigated aiming to find a specific f (R) theory able to model dark energy and dark matter phenomenology; see e.g. [START_REF] Allemandi | Dark Energy Dominance and Cosmic Acceleration in First Order Formalism[END_REF], [START_REF] Capozziello | Cosmography of f (R) gravity[END_REF], [START_REF] Nojiri | Modified gravity as realistic candidate for dark energy, inflation and dark matter[END_REF], [START_REF] Capozziello | From Dark Energy and Dark Matter to Dark Metric[END_REF].

Models based on f (R) theories have been recently used also to semi-classically account for the quantum effect of standard LQG theories; see [START_REF] Olmo | New Cases of Universality Theorem for Gravitational Theories[END_REF].

The metric-affine formulation has been recently criticized. The most serious criticism is based on a theorem which shows that, under specific state equation hypotheses, internal and external solutions for a (stationary, spherically symmetric) polytropic star do not match on the boundary and produce singularities on the star surface; see [START_REF] Barausse | A no-go theorem for polytropic spheres in Palatini f (R) gravity[END_REF]. However, as it often happens when precise no-go theorems are formulated, it has been later argued that the hypotheses of this theorem are in fact physically unreasonable; see [START_REF] Olmo | Re-examination of polytropic spheres in Palatini f(R) gravity[END_REF]. In this particular case it has been shown that (at least for specific examples of f ) the singularity depends on matter densities far lower than the one that is reasonably expected. We shall not discuss further these aspects here.

Another criticism to f (R) theories (this time in purely-metric formulation; see [START_REF] Magnano | Nonlinear gravitational Lagrangians[END_REF]) is based on fixing the variation of first derivatives of field on the boundary; see [START_REF] Sotiriou | f (R) theories of gravity[END_REF]. This criticism seems to be based on a physically and also mathematically questionable method discussed [START_REF] Wald | General Relativity The University of[END_REF], that is meaningful only in standard GR; in standard purely-metric GR, one can in fact subtract a suitable boundary term from the action so that fixing first derivatives of the metric on the boundary (as it is prescribed by Calculus of Variations; [START_REF] Gelfand | Calculus of Variations[END_REF]) is not necessary any longer provided one accepts to modify the Hilbert Lagrangian by adding suitable ad-hoc boundary counterterms. The same unconventional procedure, however, cannot be carried over for a generic f (R). We argue that one cannot consider this a problem; see [START_REF] Fatibene | About Boundary Terms in Higher Order Theories[END_REF] for a detailed criticism of the method. In standard (higher order) variational calculus all derivatives of variations of fields are fixed up to one order less with respect to the effective order of the theory. The fact that first derivatives do not need to be fixed in GR, which is a second order gravitational theory when formulated in terms of the Hilbert Lagrangian, is just a consequence of the well-known fact that GR is in fact degenerate and can be formulated even covariantly as an equivalent first order theory; see [START_REF] Ferraris | Covariant first-order Lagrangians, energy-density and superpotentials in general relativity[END_REF]. Moreover, not fixing higher order variations causes unreasonable results in many cases, but we shall not discuss these aspects here, either; see [START_REF] Fatibene | About Boundary Terms in Higher Order Theories[END_REF].

We shall here establish the dynamical equivalence between f (R) theory à la Palatini and its Barbero-Immirzi formulation. The special case for f (R) = R is already well-known; see [START_REF] Barbero | Real Ashtekar variables for Lorentzian signature space-time[END_REF], [START_REF] Immirzi | Quantum Gravity and Regge Calculus[END_REF], [START_REF] Holst | Barbero's Hamiltonian Derived from a Generalized Hilbert-Palatini Action[END_REF], [START_REF] Fatibene | On a Covariant Formulation of the Barberi-Immirzi Connection[END_REF], [START_REF] Fatibene | Spacetime Lagrangian Formulation of Barbero-Immirzi[END_REF]. The extension to a generic f (R) is new, to the best of our knowledge.

Notation and Holst Formulation of GR

Holst formulation of GR is the classical basis of LQG formulation in terms of the Barbero-Immirzi connection.

Let us consider a 4 dimensional (paracompact, connected, orientable) manifold M which allows metrics in signature η = (3, 1) and global spin structures (i.e. with zero 1st and 2nd Stiefel-Whitney classes). Let P be a principal bundle over M with SO(η) as structure group. Notation follows [START_REF] Fatibene | Natural and gauge natural formalism for classical field theories. A geometric perspective including spinors and gauge theories[END_REF].

Let us denote by J 1 P the first jet prolongation of P ; there is a standard right action of SO(η) on J 1 P , namely the prolongation of the canonical right action R g : P → P on P ; see [START_REF] Fatibene | Natural and gauge natural formalism for classical field theories. A geometric perspective including spinors and gauge theories[END_REF]. The bundle C(P ) = J 1 P/SO(η) admits a global family of local coordinates (x µ , Γ ab µ ) and (global) sections are by definition (global) SO(η)-connections on P .

Let λ : (GL(4) × SO(η)) × GL(4) → GL(4) : (J, , e) → J • e • -1 be the natural action of the group GL(4)×SO(η) on the manifold GL(4). The associated bundle e(P ) = (L(M )×P )× λ GL(4) has coordinates (x µ , e µ a ) and (global) sections, that always exist under our hypotheses on M , are by definition (global) frames.

Here frame is meant in a non-standard sense. A global frame for us is not a global section of the frame bundle L(M ), that may not exist, but rather a global section of e(P ). A global frame is here a family of local sections of L(M ) defined on an open covering of M and such that transition functions are valued in SO(η) rather than in {I} as required for global sections of L(M ). This is done since generic manifolds do not allow global sections of L(M ); the topological condition for this is physically too strong in general, while e(P ) always allows global frames in the above hypotheses; see [START_REF] Fatibene | Natural and gauge natural formalism for classical field theories. A geometric perspective including spinors and gauge theories[END_REF].

Moreover, the standard covariant derivative of sections of e(P ) is the covariant derivative introduced ad hoc and used in literature for frames, which is not the standard covariant derivative for sections of L(M ); see [START_REF] Fatibene | Natural and gauge natural formalism for classical field theories. A geometric perspective including spinors and gauge theories[END_REF].

Vielbein e a µ are frame inverses; vielbein induce a metric on M

g µν = e a µ η ab e b ν (2.1)
where η ab is the standard diagonal matrix of signature η = (3, 1). Hereafter Greek indices are moved up and down by the metric g µν while Latin indices are moved by η ab .

Let us now define the curvature 2-form

R ab = 1 2 R ab µν dx µ ∧ dx ν (2.2)
where R ab µν (j 1 Γ) is the curvature tensor of Γ ab µ , the local representative of an arbitrary global section Γ of C(P ). The vielbein form is the 1-form

e a = e a µ dx µ (2.3)
For the Holst formulation (see [START_REF] Holst | Barbero's Hamiltonian Derived from a Generalized Hilbert-Palatini Action[END_REF], [START_REF] Fatibene | Spacetime Lagrangian Formulation of Barbero-Immirzi[END_REF], [START_REF] Ashtekar | Background Independent Quantum Gravity: a Status Report[END_REF]) let us set C = C(P )× M e(P ) for the configuration bundle; the Lagrangian is:

L H = 1 4κ R ab ∧ e c ∧ e d abcd -2 γ R ab ∧ e a ∧ e b (2.4)
where κ and γ are constants. For later covanience this Lagrangian can be written as Let us also set R := R ab µν e µ a e ν b and R b ν := R ab µν e µ a which are functions of (e, j 1 Γ). Let us stress that the additional term R ab µν e cµ e dν cdab in β R is peculiar of the Palatini formulation; if we assumed the connection to be metric from the beginning, the curvature would be the Riemann tensor of a metric and the additional term would vanish identically due to the symmetry properties of Riemann tensors, in particular the first Bianchi identity R α

L H = 1 8κ R ab µν e c ρ e d σ abcd -2 γ R
[βµν] = 0. One obtains the same result also using no frames, but allowing torsion; it is sufficient to use the correction µνρσ R µνρσ (j 1 Γ) which does not vanish identically if torsion is allowed. Here we have chosen to use frames in view of possible applications to LQG or possible applications with spinor couplings. We refer to [START_REF] Holst | Barbero's Hamiltonian Derived from a Generalized Hilbert-Palatini Action[END_REF] or [START_REF] Ashtekar | Background Independent Quantum Gravity: a Status Report[END_REF] for the equivalence between the Lagrangian (2.5) and standard GR; here it will follow from the universality result proved below, in the particular case f

( β R) = β R.
Before proceeding to consider these further extended gravitational theories let us first briefly review the standard results about metric-affine f (R) theories. The metric-affine formulation of f (R) models is described by the following Lagrangian:

L f (g, j 1 Γ, j 1 φ) = √ gf (R) + L mat (g, j 1 φ) (2.7)
where Γ is now a (torsionless) linear connection and φ is a set of matter fields; the matter Lagrangian does not depend on Γ (though it could depend on the Levi-Civita connection of the metric g).

The variation of the Lagrangian L f with respect to the metric g and the connection Γ is:

δL f = √ g -1 2 f g µν δg µν + f (δg µν R µν + g µν δR µν ) - √ gT µν δg µν = = √ g -1 2 f g µν δg µν + f δg µν R µν + 2g µν ∇ λ δu λ µν - √ gT µν δg µν = = √ g f R µν -1 2 f g µν -T µν δg µν -2∇ λ ( √ gf g µν ) δu λ µν + ∇ λ 2 √ gf g µν δu λ µν (2.8)
where f and f = df dR are understood to be evaluated at R and we set

u λ µν = Γ λ µν -δ λ (µ Γ α ν)α
and -√ gT µν = δL mat δg µν . One should also consider variations with respect to matter fields, which account for matter field equations; we are not interested here in that.

As usual the last boundary term in the variation vanishes because of boundary conditions (δu α βµ = 0 since δΓ α βµ = 0) and field equations are

f R (µν) -1 2 f g µν = T µν ∇ λ ( √ gf g µν ) = 0 (2.9)
By tracing the first equation with g, one obtains the master equation f (R)R -2f (R) = T , being T = g µν T µν ; except in degenerate cases this can be solved for R(T ).

Let us now set σ = sign(f ) and define a new metric gµν = |f |g µν ; accordingly one has σ √ gg µν = √ gf g µν . This can be used in the second field equation which implies that Γ λ µν are nothing but the Christoffel symbols of the metric g.

We can replace this information back into the first field equation and obtain

f Rµν -1 2 f g µν = T µν (2.10)
where Rµν is now the Ricci tensor of the metric g. Let us stress that f and f are still evaluated along the Ricci scalar R of the original metric g.

This equation can be recasted as an Einstein equation for the conformal metric g

Gµν := Rµν -1 2 R gµν = 1 f T µν -1 2 (f ) 2 R -f g µν = 1 f T µν + T (g) µν (2.11)
with an additional effective source T

(g) µν = -1 2f (f ) 2 R -f g µν .
The conservation laws for matter follow from Bianchi identities of g and read as follows

∇µ 1 f T µν + (T (g) ) µν = 0 (2.12)
where ∇ is the covariant derivative with respect to g. Let us stress that the effective energy-momentum tensor T (g) µν , being effective, does not need to obey other separated physical energy conditions which are usually required for matter energymomentun tensors. In this sense one can hope to choose f so that the effective energy-momentum tensor mimick dark energy/matter without needing to introduce extra exotic matter fields. Of course, the freedom in choosing matter fields to model the dark side of the universe is transformed into the freedom in choosing the function f . The standard universality result has been proved in the metric-affine formulation (2.7); it holds in vacuum (i.e. T µν = 0 and, more generally, when the trace T vanishes); the master equation reads thence as f R -2f = 0 (2.13) which, except few particular cases and the degenerate case f = R 2 that makes it an identity, has isolated zeros; by choosing ρ 0 to be one of the simple zeroes then one must have R = ρ 0 on-shell and the field equation can be recasted as

f Rµν -1 4 Rg µν = 0 ⇒ Rµν -1 2 Rg µν = -1 4|f | ρ 0 gµν = Λg µν (2.14)
which are in fact Einstein equations with cosmological constant Λ = -1 4|f | ρ 0 . Multiple zeroes are discussed in [START_REF] Borowiec | Universality of Einstein Equations for the Ricci Squared Lagrangians[END_REF].

Universality Theorem

Let us now consider the Lagrangian

L = ef ( β R) + L mat (e, j 1 φ) (3.1)
where e = det(e a µ ) denotes the determinant of the frame, f is an analytic function such that the so-called master equation β Rf ( β R) -2f ( β R) = T can be solved for β R(T ) as in Section 2. Here φ is a set of matter fields; the important issue is the hypothesis that the matter Lagrangian is independent of Γ ab µ (while it could depend on the spin connection ω ab µ (e) induced the frame). The variation of the matter Lagrangian defines the matter energy-momentum tensor As usual the boundary term vanishes because of the boundary conditions δΓ ab µ = 0 and field equations are

   f R a µ -1 2 f e a µ + βf R cd µν e ν b cd a • b • = T a µ ∇ µ (ef e µ c e ν d ) δ c [a δ d b] + β c • d •ab = 0 (3.4) Let us set Φ cd ab := δ c [a δ d b] + β c • d
•ab ; being it skew in both the upper and lower pair it defines an endomorphisms Φ : Λ 2 → Λ 2 in the space of skew 2-tensors. It can be proved (e.g. by explicit computation by Maple) that it is invertible. One can easily check that its inverse is

Φ -1 ab cd = (1 + 4β 2 ) δ a [c δ b d] -β a • b •cd (3.5)
Here we are discussing Lorentzian sector. In Euclidean signature the special cases β = ± 1 2 must be dealt with separately. They correspond to (anti)selfdual cases in which the map Φ cd ab is degenerate. Accordingly, the analysis needs extra care though it leads to similar results.

The second field equation is then We shall systematically denote by a tilde the quantities computed in the new frame.

∇ µ ef e µ [c
The second field equation is then

∇ µ ẽẽ µ [c ẽν d] = 0 (3.8)
which is the same equation obtained in the standard frame-affine framework; it implies that Γ ab µ ≡ ωab µ coincides with the spin connection induced by the frame ẽµ a .

Equation (3.8) can be recasted as: Hence equation (3.9) can be recasted as

∇ µ ẽẽ µ c ẽν d abcd = 0 ⇒ ∇ µ ẽa α ẽb β αβµν = 0 ⇒ ∇ [µ ẽa α ẽb β] = 0 (3.
∇ [µ ẽ[a α ẽb] β] = 0 ⇐⇒ k a cd ẽc [α ẽd µ ẽb β] -k b cd ẽc [α ẽd µ ẽa β] = 0 ⇐⇒ k a eg δ b f + k a f e δ b g + k a gf δ b e = k b eg δ a f + k b f e δ a g + k b gf δ a e ⇒ 3k a eg + 2k a ge = k b gb δ a e ⇒ 2k a ga = 4k a ga ⇒ k a ga = 0 (3.11)
and substituting back into the original equation we obtain

3k a eg + 2k a ge = 0 ⇒ k a eg = -2k a (ge) ⇒ k a [eg] = 0 (3.12)
Finally, we have the following lemma:

Lemma: if k abc = -k bac and k abc = k acb then k abc = 0
Proof: Let us simply notice that

k abc = -k bac = -k bca = k cba = k cab = -k acb = -k abc (3.13)
from which the thesis follows.

Hence since k ab µ = 0 then Γ ab µ = ωab µ .

This piece of information can be used to express the curvature tensor in terms of the Riemann tensor of the metric gµν induced by the frame ẽµ a :

R ab µν = Rα

gµρ gνσ gλβ = R -β(ẽ) -1 f Rα [λµν] gαβ µνβλ = R (3.16)
The first field equation in (3.4) can be now recasted as follows (f ) 2 gαβ Rβµ -1 2 f δ α µ e a α = T a µ (3.17)

f Rα • µ -1 2 f δ α µ = T a µ e α a =: T α • µ (3.18)
f Rµν -1 2 f g µν =: T µν (3.19) which coincides with the equation in standard metric-affine f (R)-theories (see equation (2.10)).

In fact, f and f are evaluated at the Ricci scalar R of the original metric g and if the matter Lagrangian depends on the frame through its associated metric (as assumed otherwise there is no metric affine formulation to compare with) one has -2eT a µ = δL mat δe µ a = 2 δL mat δg µν e aν = -2 √ gT µν e aν ⇒ T µν = T a µ e aν (3.20) We stress that equivalence holds both in vacuum and in the presence of matter.

Conservation Laws

We shall here compute and discuss conservation laws for f ( β R) theories, following [START_REF] Fatibene | Natural and gauge natural formalism for classical field theories. A geometric perspective including spinors and gauge theories[END_REF]. We shall use the formalism introduced in [START_REF] Fatibene | Augmented Variational Principles and Relative Conservation Laws in Classical Field Theory[END_REF] to which we refer for motivations. The case of standard Holst action has been already discussed in [START_REF] Fatibene | Entropy of SelfGravitating Systems from Holsts Lagrangian[END_REF].

The Lagrangian (3.1) is gauge-natural (see [START_REF] Fatibene | Natural and gauge natural formalism for classical field theories. A geometric perspective including spinors and gauge theories[END_REF]); any generator Ξ = ξ µ ∂ µ + ξ ab σ ab of automorphisms on P is thence a symmetry. Here σ ab is a right invariant pointwise basis of vertical vector fields on P . Accordingly, (in vacuum) the following Noether current is conserved where ds µν is the local basis of 2-forms on M induced by coordinates.

E = e 2f
Let us define the reduced current Ẽ and the superpotential U

   Ẽ = 2eξ λ f R c λ -1 2 f e c λ + βf e ν d c • d •ab R ab νλ e µ c -2∇ µ (ef e µ c e ν d ) Φ cd ab ξ ab (v) ds µ U = 2f ee µ c e ν d Φ cd ab ξ ab (v) ds µν = 2 ẽẽ µ c ẽν d Φ cd ab ξ ab (v) ds µν (4.3)
Accordingly, the Noether current is

E = Ẽ + Div (U) (4.4)
Notice that the reduced current vanishes on-shell (see equations (3.4)). Conserved quantities are then generated by integrating the superpotential.

As usual in gauge-natural theories which are equivalent to a natural theory the correspondence among conservation laws is established by means of the so-called Kosmann lift ξ ab (v) = ẽa α ẽbβ ∇β ξ α ; see [START_REF] Fatibene | Proceedings of "6th International Conference on Differential Geometry and its Applications[END_REF]. Then the superpotential is: which differs from the Komar superpotential computed for the frame ẽ by a pure divergence which does not contribute when integrated along closed regions and hence it does not contribute to conserved quantities.

U =2 ẽ ẽµ
Let us stress that one is forced to choose the Kosmann lift along the new frame ẽ in order to obtain a correspondence with the conservation laws of metric-affine formulation.

Conclusions and Perspectives

The result we obtained can be considered from two points of view. From the point of view of classical gravitational theories, it is interesting to have an equivalent formulation of the usual extended theories f (R) à la Palatini. Using frames allows coupling to spinors; one has just to extend the structure group from SO(η) to Spin(η). It is also interesting to know that the universality theorem extends further to f ( β R) theories. Moreover we obtained a non-trivial correspondence among conservation laws. This correspondence selects ẽ as preferred frame with respect to e.

From the point of view of Quantum Gravity these models allow a direct approach to quantization à la LQG of all f (R) theories; see [START_REF] Rovelli | Quantum Gravity[END_REF]. Classically these models are known to produce modified dynamics for gravitational physics, in particular in Cosmology. Even not considering the issue of whether f (R) theories better describe physics than standard GR, it is interesting from the theoretical viewpoint to explore the dynamics of such an infinite family of models. This could improve the understanding of the emergence of the classical dynamics from the quantum world. For example it would be interesting to explicitly see whether the formalism developed in these years is able to catch the classical difference of dynamics of these models when compared with standard GR. This is particularly relevant in Cosmology where the comparison could help in better understanding the relation between LQC and LQG; see [START_REF] Bojowald | Consistent Loop Quantum Cosmology Class[END_REF].

All f ( β R) are gauge-natural theories. As such the gauge and diffeomorphism constraint should be unchanged. Accordingly nothing should change in defining the Volume and Area operators together with their quantizations. Hence the modified dynamics should appear in Hamiltonian constraint. It will be interesting, at least from a theoretical viewpoint, to test the proposals for quantization techniques against therse extended models; see [START_REF] Thiemann | LoopQuantumGravity: An InsideView[END_REF].

A forthcoming paper will be devoded to study the Wheeler-DeWitt equation for the extended models introduced here.

  ds is the standard local volume form induced by coordinates, e is the (module of) the determinant of the vielbein e a µ and we set β = -

2 )

 2 Let us start computing the variation of the Lagrangian (3.1) with respect to the frame and the connection: δL =e -f e a µ δe µ a + f 2∇ µ δΓ ab ν

9 )

 9 Let us define k ab• c = Γ ab µ -ωab µ ẽµ c; this is the difference between the dynamical connection Γ and the spin connection induced by the frame ẽ. By construction k abc = -k bac . By considering the covariant derivative of the frame we have ẽµ

(

  Let us stress that in our notation Greek indices are moved by the metric g and not by g; hence Rα• µ means Rα • µ = g αβ Rβµ , not gαβ Rβµ as usual. This is a consequence of having two metrics around. One should specify which metric is involved at any step!) Before being ready to manipulate the first field equation we have to prove that the extra term in equation (3.4) vanishes: = = |f |ẽ Rα λµν ẽa γ αβρσ gλβ gγρ gσν = -|f |(ẽ) -1 Rα λµν ẽa γ gαβ βλγν = = -|f |(ẽ) -1 gµα ẽa that the scalar β R coindices with the Ricci scalar R of the metric g induced by the original frame e µ a : β R =R + βR ab µν e cµ e dν cdab = R + βf Rα λµν

  e µ c e ν d Φ cd ab £ Ξ Γ ab ν -ξ µ f ds µ (4.1)where ds µ is the local basis of 3-forms on M induced by coordinates and £ Ξ Γ ab µ = ξ ν R ab νµ + ∇ µ ξ ab (v) denotes the Lie derivative and we set ξ ab (v) = ξ ab + ξ µ Γ ab µ for the vertical part of the symmetry generator. Hence we haveE =e 2f e µ c e ν d Φ cd ab ξ λ R ab λν + ∇ µ ξ ab (v) -f ξ µ ds µ = =e ξ λ 2f e µ c Rab νλ e µ c -2∇ µ (ef e µ c e ν d ) Φ cd ab ξ ab (v) ds µ + + Div 2ef e µ c e ν d Φ cd ab ξ ab (v) ds µν (4.2)

  ds µν = =2 ẽ ∇ν ξ µ ds µν + 2 β µνβα ∇β ξ α ds µν = =2 ẽ ∇ν ξ µ ds µν + Div 2 3 β µνβα ξ α ds µνβ (4.5)

Acknowledgments

We wish to thank C. Rovelli for discussions about Barbero-Immirzi formulation. This work is partially supported by the contribution of INFN (Iniziativa Specifica NA12) the local research project Leggi di conservazione in teorie della gravitazione classiche e quantistiche (2010) of Dipartimento di Matematica of University of Torino (Italy).


Dr Richard Kay Russell
email: richardrussell@nhs.net

Michelle L Wilson

Sabarinathan Loganathan

Billy Bourke

Fevrionia Kiparissi

Franco Torrente

Gamal Mahdi

Astor Rodrigues

Adrian Thomas

Anthony Kwaku Akobeng

safety of adalimumab in children with inflammatory bowel disease

Keywords: Inflammatory bowel disease < Disease-based, Ulcerative colitis < Crohn's disease, adalimumab, Children

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.

Results: 72 patients (70 CD, 1 Ulcerative Colitis (UC), 1 IBD Unclassified (IBDU)) from 19 paediatric-centres received adalimumab at a median age of 14.8 (IQR 3.1, range 6.1-17.8) years; 66/70 CD (94%) had previously received infliximab. A dose of 80mg then 40mg was used for induction in 41(59%) and 40mg fortnightly for maintenance in 61 (90%). Remission rates were 24%, 58% and 41% at 1, 6 and 12 months respectively. Overall 43 (61%) went into remission at some point, with 24 (35%) requiring escalation of therapy. Remission rates were higher in those on concomitant immunosuppression cf. those not on immunosuppression [34/46 (74%) vs. 9/24 (37%) respectively (Χ 2 8.8, p=0.003)]. There were 15 adverse events (21%) including 4 (6%) serious adverse events with 2 sepsis related deaths in patients who were also on immunosuppression and home parenteral nutrition (3% mortality rate).

Conclusions:

Adalimumab is useful in treatment refractory paediatric patients with a remission rate of 61%. This treatment benefit should be balanced against side effects, including in this study a 3% mortality rate.

Introduction

The incidence of Crohn's disease (CD) in children continues to rise in the UK and throughout the world. [START_REF] Benchimol | Epidemiology of pediatric inflammatory bowel disease: A systematic review of international trends[END_REF][START_REF] Armitage | Incidence of juvenile-onset Crohn's disease in Scotland[END_REF][START_REF] Sawczenko | Prospective survey of childhood inflammatory bowel disease in the British Isles[END_REF] Despite early-onset CD being more extensive at diagnosis than adult-onset CD, and with more dynamic progression in location in the first years after diagnosis, 4 the evidence for effective treatment strategies in these children remains limited. 5;6 Initial induction of disease remission in UK practice is most commonly attempted with a course of exclusive enteral nutrition with steroids reserved for non-responders. 7 Disease relapse after induction of remission occurs frequently, requiring maintenance therapy with an immunomodulator, usually thiopurines initially. [START_REF] Mossop | Predicting the need for azathioprine at first presentation in children with inflammatory bowel disease[END_REF] In a large Scottish cohort, 50% of children needed immunosuppression within 1 year of diagnosis while more than 80% had received immunosuppression within 5 years of diagnosis. 4 Thiopurines are most commonly used as initial maintenance of remission treatment with Methotrexate remaining a useful alternative for patients who are intolerant/resistant to thiopurines. [START_REF] Turner | Methotrexate Following Unsuccessful Thiopurine Therapy in Pediatric Crohn's Disease[END_REF] Infliximab (IFX) is a chimeric anti-tumour necrosis factor (TNF) monoclonal antibody treatment that is useful for both induction and maintenance of remission in children. [START_REF] Hyams | Induction and maintenance infliximab therapy for the treatment of moderateto-severe Crohn's disease in children[END_REF] In line with adult studies, IFX use in UK children is predominantly as an adjuvant to other forms of immunosuppression. 11 It is also used in a small number of patients as a long term maintenance treatment in patients who are refractory or intolerant to other treatments and in whom more extensive surgery is not a viable option. IFX treatment allows catch up growth and reduces steroid use in paediatric patients with CD. [START_REF] Malik | Improvement In Growth Of Children With Crohn's Disease Following Anti-TNF-α Therapy Can Be Independent Of Pubertal Progress And Glucocorticoid Reduction[END_REF][13][START_REF] Bultman | Systematic review: steroid withdrawal in anti-TNF-treated patients with inflammatory bowel disease[END_REF] F o r P e e r R e v i e w v Adalimumab (Humira, Abbott UK) is a humanised anti-TNF therapy that has been shown to be efficacious for induction and maintenance of remission for adults with Crohn's disease. 15;16 Adalimumab is used primarily in clinical practice for patients who are are primary anti-TNF responders, but become intolerant or non responsive to IFX. [START_REF] Peyrin-Biroulet | Adalimumab maintenance therapy for Crohn's disease with intolerance or lost response to infliximab: an openlabel study[END_REF][START_REF] Ho | The use of adalimumab in the management of refractory Crohn's disease[END_REF][START_REF] Hinojosa | Efficacy and safety of short-term adalimumab treatment in patients with active Crohn's disease who lost response or showed intolerance to infliximab: a prospective, open-label, multicentre trial[END_REF] Adalimumab is not currently licensed for use in paediatric IBD patients. The published experience to date of adalimumab in children with the exception of one large retrospective study [START_REF] Rosh | Retrospective Evaluation of the Safety and Effect of Adalimumab Therapy (RESEAT) in Pediatric Crohn's Disease[END_REF] is limited mostly to case reports [START_REF] Veres | Adalimumab treatment in infliximab-resistant pediatric patient with Crohn's disease[END_REF][START_REF] Nguyen | Oropharyngeal and Proximal Esophageal Involvement During Adalimumab Treatment of Crohn Disease[END_REF][START_REF] Mian | Adalimumab, a Novel Anti-Tumor Necrosis Factor-[alpha] Antibody in a Child with Refractory Crohn's Disease[END_REF][START_REF] Hadziselimovic | Adalimumab Induces and Maintains Remission in Severe, Resistant Paediatric Crohn Disease[END_REF] and small clinical case series [START_REF] Viola | Efficacy of adalimumab in moderate-to-severe pediatric Crohn's disease[END_REF][START_REF] Wyneski | Safety and efficacy of adalimumab in pediatric patients with Crohn disease[END_REF][START_REF] Rosenbach | Adalimumab Treatment in Children with Refractory Crohns Disease[END_REF][START_REF] Noe | Short-term response to adalimumab in childhood inflammatory bowel disease[END_REF] . However it is increasingly clear that adalimumab is used widely in paediatric clinical practice.

In addition to limited information regarding paediatric efficacy there are continuing safety concerns around anti-TNF use, including that of adalimumab. Clinical experience outside the trial setting in adults has been mixed with reports of severe infective complications, malignancy and even death. 18;29 Specific concerns remain about the development of fatal Hepatosplenic T-cell lymphomas in young males with CD treated with thiopurines, infliximab or adalimumab. [START_REF] Kotlyar | A Systematic Review of Factors That Contribute to Hepatosplenic T-Cell Lymphoma in Patients With Inflammatory Bowel Disease[END_REF][START_REF] Mackey | Hepatosplenic T cell lymphoma associated with infliximab use in young patients treated for inflammatory bowel disease[END_REF][START_REF] Shale | Hepatosplenic T-Cell Lymphoma in Inflammatory Bowel Disease[END_REF] Evidence is awaited from prospective international clinical trials on the efficacy and safety of adalimumab in children with CD (in progress trials listed at clinical trials.gov). Here, we report our national experience on the indications and use of adalimumab in a survey of paediatric gastroenterology units across the United Kingdom and Republic of Ireland. patients aged <18 years of age at the time of commencing adalimumab in a paediatric centre with at least 4 weeks of follow up. Members who agreed to take part were sent a proforma to collect a standard dataset from case notes retrospectively (full proforma available on request). Data collected included; patient demographics, drug treatments (including previous IFX use) and details of any prior surgery. As an audit of routinely held clinical data, the Lothian Research Ethics Committee confirmed that informed consent from patients/families was not needed. Specific details on adalimumab use collected included; dosing schedule, need for dose escalation and documented adverse effects. Adalimumab effect was assessed using the Paediatric Crohn's Disease Activity Index (PCDAI) where available or Physicians Global Assessment (PGA) when PCDAI was not available. [START_REF] Hyams | Development and validation of a pediatric Crohn's disease activity index[END_REF] Standard definitions were used for PCDAI disease status and response (remission, PCDAI ≤10) and significant response in PCDAI was a decrease >12.5. [START_REF] Hyams | Development and validation of a pediatric Crohn's disease activity index[END_REF] PGA of clinical status in terms of response to induction doses of adalimumab was defined as "remission", "steroid-free remission", "response without remission" or "no response". Response to adalimumab was recorded at 1, 6 and 12 months and at study end. The study end point was defined as the last paediatric follow up visit (i.e. when seen in clinic last at data vii accrual or before transition to adult services, before transfer out of region, or prior to death). CD was diagnosed using standard criteria. 34;35 Disease location and behaviour at the time of commencing adalimumab treatment were defined using the Montreal classification. [START_REF] Silverberg | Towards an integrated clinical, molecular and serological classification of inflammatory bowel disease: Report of a Working Party of the 2005 Montreal World Congress of Gastroenterology[END_REF] Some data relating to 11 patients has been published previously as part of a Scottish adalimumab audit involving both children and adults. [START_REF] Ho | Efficacy and complications of adalimumab treatment for medically-refractory Crohn's disease: analysis of nationwide experience in Scotland (2004-2008)[END_REF] Two authors (RKR and DCW) reviewed the proformas from all centres for completeness and sense checking, and clarified missing or possibly incorrect data in all cases. One author (MLW) entered all data using double data entry to a dedicated database. Two authors (MLW, DCW) performed all statistical analyses.

Statistics

Continuous parametric data are presented as mean (standard deviation) and nonparametric data as a median followed by (range, interquartile range). Categorical data are presented as number of cases with percentage of total cases (%). Chi-squared analysis was used to compare frequencies and p<0.05 was considered significant.

Previous treatments

In terms of previous treatment 86% had at least one previous course of exclusive enteral nutrition, 90% at least one course of steroids (60% steroid dependent with inability to wean despite 3 months continuous treatment, 25% steroid-resistant and 27% having unacceptable steroid side effects) , 91% had prior thiopurines (azathioprine and/or 6-mercaptopurine; with 31% being resistant, 11% intolerant and

Adalimumab Baseline data

The induction dose of adalimumab used was 160mg then 80mg in 3 patients (4%), 80/40 in 41 patients (59%), 24mg/m 2 in 16 patients (23%) and 10 received other dosing regimens (14%). At baseline 1 patient was in remission. There were 26 (37%) patients on steroids when adalimumab was started and 46 (66%) on immunosuppression of whom 27 were on a thiopurine and 19 on methotrexate.

Remission (Table 1)

The number of patients in remission at 4 weeks, 6 and 12 months after starting therapy out of the total number assessed at each time point is listed in table 1.

Forty-three of 70 (61%) achieved remission on adalimumab at any point in the study period after a median of 0.2 (0.3, 0.04-0.76) years and after a median of 6 (6.5, 2-23) doses of adalimumab. Of the 50 patients (71%) who either entered remission (n=43, 61%) or had a significant clinical response (n=7) 15 had a subsequent loss of response x on maintenance adalimumab therapy after a median (IQR, range) of 17 (12, 7-40) adalimumab doses and at a median duration of 0.4 (0.4, 0.1-1.2) years.

Of the 46 patients taking concomitant immunosuppression at the start of the study a significantly higher number achieved remission compared to those with no concomitant therapy [34/46 (74%) vs. 9/24 (37%) respectively (Χ [START_REF] Armitage | Incidence of juvenile-onset Crohn's disease in Scotland[END_REF] Maintenance therapy and dosing changes during adalimumab treatment Sixty-eight (97%) CD patients went on to maintenance adalimumab therapy, of which 66 started on fortnightly therapy and 2 on weekly therapy, with an initial dose of 80mg in 1 patient (1%), 40mg in 61 patients (90%), 24 mg/m 2 in 3 patients (4%) and other dosing regimens in 3 patients (4%). Twenty-four (35%) required dose escalation of which 4 required an increased dose only, 17 the dosing interval shortened from fortnightly to weekly only, and 3 had both changes made. There was no influence of concomitant immunosuppressive usage on need for dose escalation (p=0.9). Nineteen of these 24 had dose escalation within 12 months of starting adalimumab. Five of xi these 24 patients then had reversal of escalation at a later stage, with 4 returning to fortnightly dosing and 1 also having a reduction of adalimumab dose. 8 patients with incomplete response had had maintenance therapy with dose escalation; of these 4 achieved remission and 4 did not. 5 patients with no response at all had maintenance therapy with dose escalation; 2 of these achieved remission and 3 did not.

Study outcomes

The median number of adalimumab doses given was 19 (22, 3-103). A total of 1662 doses were given in the 70 CD patients. These 70 CD patients were followed up for a median duration of 0.8 (0.8, 0.1-2.8) years with a total of 72.5 years of patient follow up. At study end, 22 had discontinued Adalimumab (primary non-response in 12, loss of effect in 6, a long drug holiday in 2 and allergic reaction in 2), 2 had died whilst receiving adalimumab and 46 were alive and receiving ongoing maintenance adalimumab therapy.

UC and IBDU

There were 2 patients both from one centre who responded to adalimumab for UC and IBDU having both lost response to infliximab and having failed/been intolerant to thiopurines previously.

Side effects/safety

There were 4 serious adverse events (SAE rate of 6%) including 2 deaths (mortality rate of 3%) in this cohort of 72 patients. The 2 deaths in the cohort were both from central venous catheter (CVC) sepsis leading to septic shock in patients requiring home parenteral nutrition and receiving multiple immunosuppressive therapies. This study has demonstrated that adalimumab is effective in treating children with otherwise treatment-resistant CD. In total 61% of patients achieved remission, but the time taken to reach remission was longer than that seen in prospective adult studies, particularly clinical trials. [START_REF] Colombel | Adalimumab for maintenance of clinical response and remission in patients with Crohn's disease: the CHARM trial[END_REF] Serious adverse events occurred in 6% of cases, with a mortality rate of 3%, the latter reflecting the severe disease spectrum of some children in this cohort.

Although there is a recognised morbidity and mortality rate in adult clinical studies, the combined mortality rate in clinical trials of adalimumab has not been reported to be higher than that expected of patients with CD overall. [START_REF] Colombel | Adalimumab safety in global clinical trials of patients with Crohn's disease[END_REF] However, deaths in young adults have been reported outside of clinical trials. [START_REF] Ho | Efficacy and complications of adalimumab treatment for medically-refractory Crohn's disease: analysis of nationwide experience in Scotland (2004-2008)[END_REF] With the exception of this study, there have been no reported deaths in short term follow up of paediatric adalimumab studies (all studies summarised in table 2). The other published paediatric studies have reported no increased safety concerns with adalimumab, but of note all except one have been smaller than the present study and the length of follow up to describe these potential complications has been relatively short. Both fatalities in this study occurred as a result of overwhelming sepsis, also reported in adult studies to be the most significant and serious side effect of patients treated with adalimumab. 37;38 The specific complication of Aspergillosis and death on adalimumab has also been reported by other groups. [START_REF] Manz | Fatal invasive pulmonary aspergillosis associated with adalimumab therapy[END_REF] A French group have recently reported 2 deaths in longterm follow up of paediatric patients, one as a result of colonic adenocarcinoma and the second due to multi-organ failure secondary to dehydration in a patient with a stoma. In contrast to the present study, these were both recorded many years (both >6 Another significant concern is the risk of malignancy especially lymphoma in paediatric patients treated with Adalimumab and other anti-TNF agents. 31;32 No such events were recorded in this study but the relatively small study population (n=72), the short length of total follow up (total 74.8 years in all 72 cases) and the rarity of this complication limit our ability to detect such complications in this study cohort.

The role of concurrent immunosuppression with thiopurines or methotrexate in most cases makes the association with anti-TNF therapy unclear; this remains an area of intense scrutiny, particularly following further reports of malignancies in paediatric rheumatology studies using anti-TNF agents. [START_REF] Diak | Malignancy in children and tumor necrosis factor-alpha blockers: Forty-eight cases reported to the food and drug administration[END_REF] Adalimumab studies in adults are now demonstrating longer term clinical benefits over years, [START_REF] Panaccione | Adalimumab sustains clinical remission and overall clinical benefit after 2 years of therapy for Crohn's disease[END_REF] but as shown in previous studies, a significant number of patients lose response to adalimumab over time, requiring either dose increase or reduction in dosing interval 20;43 Adalimumab studies in adult patients with CD suggested a longer delay to requiring treatment escalation in patients who received concomitant immunosuppression. [START_REF] Karmiris | Influence of trough serum levels and immunogenicity on long-term outcome of adalimumab therapy in Crohn's disease[END_REF] The need for treatment escalation in this study was not affected xvi by co-immunosuppression. However, concomitant use of immunosuppressants did significantly improve the chances of attaining initial remission on adalimumab therapy. By contrast, the other large paediatric study noted that clinical response rate was significantly lower with co-immunosuppression at 6 months into therapy. [START_REF] Rosh | Retrospective Evaluation of the Safety and Effect of Adalimumab Therapy (RESEAT) in Pediatric Crohn's Disease[END_REF] Adalimumab studies in adults with CD have not demonstrated a difference in initial response with co-immunosuppression but have in some suggested a longer time to treatment escalation in patients who are co-immunosuppressed. [START_REF] Karmiris | Influence of trough serum levels and immunogenicity on long-term outcome of adalimumab therapy in Crohn's disease[END_REF] Recent adult infliximab studies have supported the use of concurrent immunosuppression in the context of maintenance therapy with IFX. 11;45 Interestingly, the paediatric rheumatology trial of adalimumab (with or without methotrexate), resulted in significantly higher levels of adalimumab antibodies (26% vs. 6%) in the group not given methotrexate, although this was not associated with different clinical outcomes in the short term. [START_REF] Lovell | Adalimumab with or without Methotrexate in Juvenile Rheumatoid Arthritis[END_REF] This issue can only appropriately be addressed by prospective studies randomising children to either monotherapy or therapy with coimmunosuppression.

At present there are no published paediatric studies that adequately demonstrate the optimal dosing of adalimumab for paediatric patients with CD, either for the induction or maintenance of remission. Doses used in paediatric practice are therefore extrapolated from relevant adult studies, 15;47 , from paediatric rheumatology studies [START_REF] Lovell | Adalimumab with or without Methotrexate in Juvenile Rheumatoid Arthritis[END_REF] or from retrospective paediatric cases series (listed in table 2). Doses used in this retrospective study were heterogeneous, and hence it is difficult to draw any firm conclusions about optimal dosing. However, it may in part explain our longer time to treatment response, as a number of patients did not receive larger induction dosing before moving onto maintenance therapy. Although we found that time from demonstrated to be important in the pivotal paediatric infliximab trial compared to the corresponding adult study, 10;48 but not the North American retrospective paediatric adalimumab study nor in our study. [START_REF] Rosh | Retrospective Evaluation of the Safety and Effect of Adalimumab Therapy (RESEAT) in Pediatric Crohn's Disease[END_REF] In summary, we have demonstrated that adalimumab can be an effective treatment for paediatric CD patients unresponsive, intolerant to or with loss of effect to other therapies, including infliximab. This case series shows the high risk that patients are exposed to on immunosuppression, particularly on some combinations of therapies.

The study has also highlighted the need for prospective monitoring of these patients on a national and international basis via biological registries to most accurately contextualise the risk-benefit balance of adalimumab in children and young people with IBD, and allow seamless long term followup as transition to adult services occurs.

F

  of Paediatric Gastroenterology, Hepatology and Nutrition survey of the effectiveness and safety of adalimumab in children with inflammatory bowel disease Adalimumab is efficacious therapy for adults with Crohn's disease (CD). Aim: To summarise the United Kingdom and Republic of Ireland paediatric adalimumab experience. Methods: British Society of Paediatric Gastroenterology, Hepatology and Nutrition (BSPGHAN) members with Inflammatory Bowel Disease (IBD) patients <18 years old commencing adalimumab with at least 4 weeks follow up. Patient demographics and details of treatment were then collected. Response and remission was assessed using the Paediatric Crohn's Disease Activity Index (PCDAI) /Physicians Global Assessment (PGA).

  All members of the British Society of Paediatric Gastroenterology Hepatology and Nutrition (BSPGHAN) were approached by e-mail and invited to take part in the study during the summer of 2008 with a further follow up call for additional cases in early 2009. Members were asked to identify any Inflammatory Bowel Disease (IBD)

  19 centres returned at least one case or more (14 Manchester, 10 Edinburgh, 8 Dublin, 7 GOSH, 6 Bart's and the London, 5 Glasgow, 4 Dundee and Royal Free, 3 Oxford, 2 Cardiff), totalling 72 patients. Of these 70 had CD (47(67%) males), 1 Ulcerative Colitis (UC) and one Inflammatory Bowel Disease Unclassified (IBDU). Results are given below for patients with CD, while patients with IBDU and UC are described individually at the end of the results section. The median age at CD diagnosis was 10.5 years (3.6, 2.8-15.7), with a median age at start of adalimumab of 14.8 years (3.1, 6.1-17.8) with a median of 4.3 years (3.7, 0.1-10.5) duration from CD diagnosis to starting treatment. At start of adalimumab treatment the commonest disease location was L3 + L4 in 24 (34.3%) and behaviour type B1 37 (52.9%) with 29 (41%) having perianal disease. Surgery A total of 26 patients (37%) had 47 surgical procedures before or during the study period. Prior to adalimumab, 18 had surgery at a median (IQR, range) of 2.4 (1.7, 0.7-6.4) years post diagnosis. Eight patients required surgery at a median of 0.6 (0.4, 0.3-1.9) years after adalimumab commencement, with 5 requiring more than 1 procedure.

  of response) and 49% had prior methotrexate usage (with 15% being resistant, 12% intolerant and 50% developing loss of response. Sixty-six (94%) had prior infliximab usage, with 12 primary non-responders, 33 with loss of response, 3 a long drug holiday and 26 an allergic reaction necessitating discontinuation. The median (range) number of infliximab doses was 5 (1-27) with 17 (26%) had required a change in their dosing schedule. Two patients with juvenile arthritis developed CD whilst their arthritis was in remission on etanercept and were then changed to adalimumab therapy. Significant other therapies at adalimumab start included filgrastim (recombinant human G-CSF), parenteral nutrition, mycophenolate mofetil, sirolimus, thalidomide and basalixumab in 1 patient each.

  8.8, p=0.003)]. Thirteen received adalimumab within 2 years of CD diagnosis but were no more likely to achieve remission than those commencing adalimumab later in their course (p=0.53). PCDAI A PCDAI score was available for 48 patients at baseline with remission in 1, mild CD in 16 and moderate-severe CD in 31. The median PCDAI was 37.5 (20, 7.5-65) at baseline. Forty-two of the 48 who had a PCDAI at baseline also had one calculated at 4 weeks, with a median score of 15 (12.5, 0-45) and with 10 (24%) being in remission, 24 (57%) mild CD activity and 8 (19%) moderate-severe CD activity; 25 of 42 (60%) had a significant (≥12.5) change in PCDAI score.

  a boy who developed panenteric CD at 8.4 years of age who had thiopurine intolerance, methotrexate resistance and loss of response of infliximab despite dose alteration. He was receiving overnight supplementary enteral nutrition via gastrostomy tube and methotrexate therapy when also given 24mg/m 2 adalimumab at 15.5 years of age. Five days after starting adalimumab he had a CVC inserted and parenteral nutrition started. He achieved clinical remission after 7 doses (40mg fortnightly maintenance) in total but died seven months later after 20 doses of adalimumab plus ongoing methotrexate, due to coagulase-negative staphylococcal CVC sepsis. This escalated to invasive pulmonary aspergillosis, which in turn led to septic shock and multi-system organ failure. Death was not considered as a likely outcome by his clinical team prior to the development of septic shock.The second death was of a boy who developed ileo-colonic and perianal CD at 5.2 years of age complicated by stricturing disease. This was despite high dose steroids, azathioprine (with loss of effect), and sigmoid colostomy with mucous fistula formation at 6.4 years of age. He developed severe pelvic and perianal CD and proceeded to trials of filgrastim and infliximab (loss of response). He received 40mg/40mg induction dosing at 12.8 years of age when he was receiving azathioprine and filgrastim for severe CD with extensive perianal disease, growth and pubertal delay, and peristomal Pyoderma gangrenosum. Extensive investigations had shown no evidence of underlying immunodeficiency. He was commenced on home parenteral nutrition via CVC. He had a clinical response to adalimumab and proceeded to maintenance at 40mg fortnightly. He never achieved remission and died at age 13.5 years after 19 doses of adalimumab due to combined E. coli and Candida CVC sepsis. He developed septic shock and multi-system organ failure whilst azathioprine, filgrastim and hyperbaric oxygen. In contrast with the first case, death was considered as a possible outcome by his clinical team due to the severe and refractory disease with extensive skin and tissue loss.There was also one severe case of Clostridium Difficile needing hospitalisation, and one development of a stomal abscess with subsequent fistulisation and requiring prolonged hospitalisation. Other adverse events included 30 (43%) experiencing pain at the injection site, none of whom stopped treatment. A further 11 (16%) patients suffered minor adverse events that were not related to injection site pain -worsening colitis in 2, neutropaenia and lymphopaenia in 2, and 1 each of multisystem upset (dyspnoea, fatigue, arthritis), transient visual loss, nausea with pain, respiratory viral illness, stomal bleeding, rash and paronychia.Adalimumab was discontinued because of side effects in 8 (11%) of patients because of pyrexia in 2, sepsis in 4, rash in 1 and worsening diarrhoea in 1; 4 out of 8 (50%) required permanent discontinuation.

  the last dose of anti-TNF therapy.[START_REF] Crombé | Long-Term Outcome Of Treatment With Infliximab In Paediatric Crohn's Disease : A Population-based Study[END_REF] Children on a combination of adalimumab, multiple immunosuppressants and parenteral nutrition via a central line clearly have the most severe forms of CD. As such patients on a combination of adalimumab, other immunosuppressants and parenteral nutrition given via a central line represent an extremely high risk group. Whilst this combination of treatment should be avoided if at all possible, we recommend early and aggressive treatment of sepsis and also that appropriate prophylaxis in this group of patients should be mandatory.

  influence response to adalimumab the number of patients in our study treated within 2 years of diagnosis was small (n=13). Time from diagnosis was

Table 1 -

 1 RKR has received speaker's fees, travel support, or participated in medical board meetings with MSD Immunology, Abbott, Dr Falk, and Ferring Pharmaceuticals. PM has received speaker's fees from Nestle Nutrition. DCW has received speaker's fees, travel support, or participated in medical board meetings with MSD Immunology, Abbott Laboratories, Dr Falk, Warner Chilcott UK and Ferring Pharmaceuticals. GH has received support to attend academic meetings from Abbott, Schering-Plough, Shire and Proctor and Gamble, honoraria from Abbott, Shire, Otsuka Pharmaceuticals and Astra Zeneca for presentations at academic meetings and an educational grant from Shire. AR has received course fees and travel bursaries from Mead Johnson Nutritionals. MSM currently holds IBD research funding from Centocor and SHS International Ltd. ID has received course fees and travel sponsorship from Nutricia and Pfizer & speaker's fees from Astra Zeneca. Efficacy of Adalimumab at various time points *defined using Physicians global assessment # lists the number of patients who were in remission off steroids Overall 43/70 (61%) of patients went into remission at some point during study follow up which occurred for most patients between 4 weeks and 6 months.

	Conflict of interest:
	o r
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	xviii

Table 2 :

 2 Published Paediatric Adalimumab studies to dateIn addition to the case series listed there have been at least 4 published paediatric case reports.[START_REF] Veres | Adalimumab treatment in infliximab-resistant pediatric patient with Crohn's disease[END_REF][START_REF] Nguyen | Oropharyngeal and Proximal Esophageal Involvement During Adalimumab Treatment of Crohn Disease[END_REF][START_REF] Mian | Adalimumab, a Novel Anti-Tumor Necrosis Factor-[alpha] Antibody in a Child with Refractory Crohn's Disease[END_REF][START_REF] Hadziselimovic | Adalimumab Induces and Maintains Remission in Severe, Resistant Paediatric Crohn Disease[END_REF]

	Population	No of IBD	No of CD	Prior	Initial Dosing used	Clinical	Comments
		patients	patients	Infliximab	(mg)	response
	UK & ROI	72	70	94%	160 / 80 (3) , 80 /40 (41)	71%	2 deaths
	(current study)				24mg/m 2 (16) other (10)
	USA 28	10	7	100%	80/40 (4), 40 (5), 80 (1)	80%	Mean PCDAI 12 at
							start
	USA 26	15	15	100%	80/40 (11), 40(1), 80 (1),	64%	Included >18 years
					40/20(1), 160/80 (1)
	USA 20	115	115	95%	160 / 80 (22) , 80 /40 (51)	65%	Short follow up period
	(RESEAT)				40/40 (17) other/unknown (9)
	Israel 27	14	14	71%	Dosing schedule not available 85%	Included >18 years
	Italy 25	23	23	61%	160 / 80 (13), 120/80 (2),	91%	Prospective;80mg
							maintenance in most

Acknowledgements: We would like to thank all BSPGHAN members who took the time to contribute to this study, as well as all the paediatric and adult surgeons who were involved in the care of these children. DCW and RKR have received support from a Medical Research Council (MRC) patient research cohorts initiative grant (G0800675) for PICTS. MLW created the database and performed all analyses with support of CICRA (BSPGHAN quality initiative in biological agent usage for paediatric IBD grant 2010-2011). DCW/MLW have also received support from the GI-Nutrition Research Fund, University of Edinburgh. GH has a current MRC Clinician Scientist award.