Romain Postoyan

Dragan Nešić

A framework for the observer design for networked control systems

This paper proposes a framework for the observer design for networked control systems (NCS) affected by disturbances, via an emulation-like approach. The proposed model formulation allows us to consider various static and dynamic time-scheduling protocols, in-network processing implementations and encompasses sampled-data systems as a particular case. Provided that the continuous-time observer is robust to the measurement errors (in an appropriate sense) we derive bounds on the maximum allowable transmission interval (MATI) that ensure the convergence of observation errors under network-induced communication constraints. The stability analysis is trajectory-based and utilizes small-gain arguments.

A number of observers can be combined and used within our approach to obtain estimators for NCS.

I. INTRODUCTION

Networked control systems (NCS) are systems in which the sensors and the actuators are spatially distributed and communicate with the control structure via a network. At each transmission instant, only a subset of sensors and/or actuators, collocated into a node, is chosen to transmit their data over the communication channel according to a scheduling rule called protocol. The growing interest for NCSs is motivated by the fact that they have lower costs, easier maintenance and installation, greater flexibility as well as lower weight and volume in comparison to the classical control systems. On the other hand, the communication constraints induced by the use of a serial channel cannot be ignored and require novel observation and control design methods. R. Postoyan is with the Centre de Recherche en Automatique de Nancy, UMR 7039, Nancy Université, CNRS, 2 avenue de la forêt de Haye, 54516 Vandoeuvre-lès-Nancy, France. E-mail: romain.postoyan@cran.uhp-nancy.fr. Supported by the French Ministère de l'Education Nationale de la Recherche et de la Technologie (MENRT) and the LSS-CNRS, SUPELEC. D. Nešić is with the Department of Electrical and Electronic Engineering, University of Melbourne, Parkville 3010, Victoria, Australia. E-mail: d.nesic@ee.unimelb.edu.au. Supported by the Australian Research Council under the Future Fellow and Discovery Project programs.

In this paper, we focus on the design of a centralized observer that receives data from sensors through a shared communication medium. Related available studies in the literature have addressed this problem for particular classes of systems or protocols. In [START_REF] Dačić | Observer design for linear networked control systems using matrix inequalities[END_REF], a methodology for the mutual design of weighted dynamic protocols and observer gains is developed for linear systems using matrix inequalities. The existence of a round-robin protocol that preserves the observability of linear discrete-time NCS is ensured in [START_REF] Zhang | Stabilization of networked control system: designing effective communication sequence[END_REF] under mild conditions. Using linear time-varying periodic systems analysis tools, a linear observer is then derived for such a protocol.

The observer design originally developed for sampled-data systems in [START_REF] Karafyllis | From continuous-time design to sampled-data design of observers[END_REF] has been extended to NCS in [START_REF] Postoyan | Observers for classes of nonlinear networked systems[END_REF]. Assuming a continuous-time observer is known and satisfies some robustness properties with respect to output disturbances, the observation error convergence is ensured under network-induced constraints by replacing the unavailable continuous-time output by an auxiliary variable which flows along the same vector fields between transmission instants and is reset when measurements are received.

In this study, we propose a framework for the observer design for nonlinear NCS via an emulation-like approach, for plants whose dynamics are affected by disturbances. Modeling the problem like in [START_REF] Nešić | Input-output stability properties of networked control systems[END_REF], our approach allows to study various types of observers, time-scheduling protocols and in-network processing implementations. We notably recover the designs in [START_REF] Karafyllis | From continuous-time design to sampled-data design of observers[END_REF], [START_REF] Postoyan | Observers for classes of nonlinear networked systems[END_REF] as particular cases by showing that it corresponds to a specific choice of in-network processing algorithm. The stability analysis is trajectory-based and carried out using small-gain arguments which allow us to derive easy computable bounds on the maximum allowable transmission interval (MATI). We believe that this is the first time that this problem is addressed with such generality and that our model formulation can be the starting point for other observer designs.

An important remark is that our results are also new for the observer design for sampleddata systems. Thus, we provide an alternative to [START_REF] Arcak | A framework for nonlinear sampled-data observer design via approximate discrete-time models and emulation[END_REF] where the emulation of observers for sampled-data systems is investigated based on discrete-time approximate models, noting that we ensure different stability properties here and provide explicit bounds on the maximum allowable sampling period contrary to [START_REF] Arcak | A framework for nonlinear sampled-data observer design via approximate discrete-time models and emulation[END_REF].

The paper is organized as follows. After having defined the notations and recalled some stability definitions in Section II, the problem is stated in Section III and the model formulation is developed. The main results are given in Section IV and applied to a class of globally Lipschitz observers in Section V.

II. PRELIMINARIES

Let R = (-∞, ∞), R ≥0 = [0, ∞), R >0 = (0, ∞), Z ≥0 = {0, 1, 2, . . .}, Z >0 = {1, 2, . . .}. Let a ∈ R >0 ∪ {∞}, a function γ : [0, a) → R ≥0 is of class K if it is continuous, zero at zero and strictly increasing. By extension, for a, b ∈ R >0 ∪ {∞}, γ : [0, a) × [0, b) → R ≥0 is of class KK if, for any (s 1 , s 2 ) ∈ [0, a) × [0, b), γ(s 1 , •) and γ(•, s 2 ) are of class K. A continuous function γ : [0, a) × R ≥0 -→ R ≥0 is of class KL if for each t ∈ R ≥0 , γ(•, t) is
of class K, and, for each s ∈ [0, a), γ(s, •) is decreasing to zero. The initial time is denoted t 0 ∈ R ≥0 and the initial condition of a variable x is denoted x 0 = x(t 0 ). The Euclidean norm of a vector or a matrix is denoted by | • | and λ min (•), λ max (•) respectively stands for the minimum, maximum eigenvalue of a symmetric positive definite matrix. Let f : R → R n , n ∈ Z >0 , be a (Lebesgue) measurable function and define, for

t 1 ≤ t 2 ∈ R, f [t 1 ,t 2 ) = ess. sup τ ∈[t 1 ,t 2 ) |f (τ )| and f ∞ = ess. sup τ ∈[t 0 ,∞) |f (τ )|. The set L n
∞ denotes the set of functions f : R ≥0 → R n such that f ∞ < r, r ∈ R ≥0 . For (x, y) ∈ R n+m , the notation (x, y) stands for [x T , y T ] T .

Consider the system:

ẋ = f (x, u), y = h(x), (1)
where x ∈ R nx , y ∈ R ny , u ∈ R nu are, respectively, the state, the output and the input,

n x , n y , n u ∈ Z >0 .
Definition 1: System (1) is input-to-output stable (IOS) from u to y with linear gain γ if there exist β ∈ KL and γ ∈ R >0 such that, for any

x 0 ∈ R nx , u ∈ L nu ∞ : |y(t)| ≤ β(|x 0 |, t -t 0 ) + γ u [t 0 ,t] for t ≥ t 0 ≥ 0. If y = x, then system (1) is input-to-state stable (ISS) w.r.t. u.
Definition 2: System (1) is said to be bounded-input-bounded-state (BIBS) with input u if there exist α, γ ∈ K, such that, for any

x 0 ∈ R nx , u ∈ L nu ∞ : |x(t)| ≤ α(|x 0 |) + γ( u [t 0 ,t]
), for t ≥ t 0 ≥ 0. When no input acts on system (1) (i.e. u = 0), we say that the system is globally stable (GS).

III. PROBLEM STATEMENT

The analysis follows the emulation approach adopted for the control of NCS in [START_REF] Walsh | Asymptotic behavior of nonlinear networked control systems[END_REF], [START_REF] Nešić | Input-output stability properties of networked control systems[END_REF].

The approach consists in first designing the observer while ignoring communication constraints.

Thus, for the plant modeled by equations:

ẋ = f P (x, w), y = h P (x), (2)
where x ∈ R nx is the plant state, y ∈ R ny is the plant output, w ∈ R nw is an exogenous disturbance input, an observer is synthesized:

ż = f O (z, y), x = h O (z), (3)
where z ∈ R nz is the observer state and x ∈ R nx is the system state estimate. Notice that we allow for immersion-based observers since the dimension of the observer, n z , may be bigger than the dimension of the plant, n x .

Remark 1: Although in practice, the system output is likely to be corrupted by noise, ( 2) is disturbance-free here. This model can be justified by the use of a filter whose dynamics are already embedded into (2).

Communication constraints are then taken into account. The variable y is no longer available but ŷ, which is the generated variable from the most recent system output sent through the network. The problem can be modeled in the following form:

ẋ = f P (x, w) ∀t ∈ [t i-1 , t i ] y = h P (x) ż = f O (z, ŷ) ∀t ∈ [t i-1 , t i ] x = h O (z) ẏ = fP (ŷ, z) ∀t ∈ [t i-1 , t i ] ŷ(t + i ) = y(t i ) + h(i, e(t i ), z(t i ))                          (4)
where e = ŷy ∈ R ne (n e = n y ) is the network-induced error and the sequence t i , i ∈ Z >0 , of monotonically increasing transmission times satisfies υ ≤ t i -t i-1 ≤ τ for some fixed τ ∈ [υ, ∞), t 0 ∈ R ≥0 being the initial time 1 . We refer to τ as the MATI. The network implementation can be described as follows. Grouping sensors into l sensor nodes, where l ∈ {1, . . . , n y }, the system output is partitioned into l corresponding subvectors, y = (y 1 , . . . , y l ). At each transmission instant, exactly one sensor node is chosen to transmit its packet according to the protocol defined by the function h. For instance, if the node k ∈ {1, . . . , l} is selected at time

t i , we have ŷk (t + i ) = y k (t i ) and ŷj (t + i ) = ŷj (t i ) for j = k, in other words e k (t + i ) = 0 and e j (t + i ) = e j (t i ).
The function h can be used to model several common protocols in the literature such as round-robin (RR) and try-once-discard protocols (TOD) (see [START_REF] Nešić | Input-output stability properties of networked control systems[END_REF] for more details) for instance, or to describe sampled-data systems by setting h ≡ 0. The network may also contain an arbitrary number of passive nodes which can only receive packets. They may be used for hosting distant observers and/or actuators for plants with inputs. Without loss of generality, it is assumed that there is only one passive node in the network where an observer is run.

Remark 2: Dynamical protocols such as TOD require the use of smart sensors that have sufficient computational capacities to run a copy of the observer located in the passive node (see Fig. 1 in [START_REF] Dačić | Observer design for linear networked control systems using matrix inequalities[END_REF]). At each node j ∈ {1, . . . , l + 1} (where the index l + 1 denotes the passive node), the observer below is run:

żj = f O (z j , ŷ), xj = h O (z j ). They are synchronized (z j (t) = z k (t)
for all t and j, k ∈ {1, . . . , l + 1}) by assuming that they start with the same initial condition and thank to the assignment procedure, which is modeled by a piecewise constant function σ : R ≥0 → {1, . . . , l} so that when node k has been assigned at time

t i-1 , σ(t) = k for t ∈ [t i-1 , t i ] and y σ(t i-1 ) (t i-1 ) = y k (t i-1
). In that way, at time t ∈ [t i-1 , t i ], the following signals are available at sensor node j ∈ {1, . . . , l}: σ(t i-1 ), y σ(t i-1 ) (t i-1 ), y j (t), z j (t); at the passive node: σ(t i-1 ), y σ(t i-1 ) (t i-1 ), z l+1 (t). Since each observer receives y σ(t i-1 ) (t i-1 ), they all have the same input signal ŷ(t) and are synchronised for all time (unless a computational glitch occurs) and the stability analysis reduces to studying a single observer.

Between the transmission instants, ŷ is generated according to the in-network processing implementation. Usually zero-order-hold (ZOH) devices are implemented: fP = 0 i.e. the output ŷ is kept constant during the transmission intervals. Nevertheless, it has to be noted that more general algorithms can be utilized like the predictive-type used in [START_REF] Karafyllis | From continuous-time design to sampled-data design of observers[END_REF] for sampled-data systems: fP (z) = ∂h P ∂x (h O (z))f P (h O (z), 0), that may help ensuring stronger convergence properties as we will show it in Section V. Model (4) can be written in a more compact way that is appropriate to our study:

ξ = f ξ (ξ, e, z, w) ∀t ∈ [t i-1 , t i ] (5)
ż = f z (ξ, e, z) ∀t ∈ [t i-1 , t i ] (6)
ė = g(ξ, e, z, w) ∀t ∈ [t i-1 , t i ] (7)
ξ(t + i ) = ξ(t i ) (8)
z(t + i ) = z(t i ) (9)
e(t + i ) = h(i, e(t j ), z(t i )), (10)
where ξ = x-x ∈ R n ξ (n ξ = n x ) is the observation error and f ξ (ξ, e, z, w) = f P (ξ +h O (z), w)- w). Remark 3: Variables ξ and z could have been embedded into one single vector to be consistent with [START_REF] Nešić | Input-output stability properties of networked control systems[END_REF], however we will need to distinguish them in the sequel since we are not interested in the same properties. Indeed, contrary to ξ, no convergence property is desired for z but only some well definition or bounded behaviour for all time.

∂h O ∂z (z)f O (z, e + h P (ξ + h O (z))), f z (ξ, e, z) = f O (z, e + h P (ξ + h O (z))), g(ξ, e, z, w) = fP (e + h P (ξ + h O (z)), z) -∂h P ∂x (ξ + h O (z))f P (ξ + h O (z),
The main problem of this study is to ensure the convergence of the observation error when the plant outputs are transmitted through a serial communication channel.

IV. MAIN RESULTS

In this section, we propose guidelines for the design of observers for NCS. Assuming the observer (3) ensures some global asymptotic stability properties in the absence of network, we distinguish the cases where the convergence of the observer is maintained practically w.r.t. MATI or asymptotically under communication constraints. We will see in Section V that this difference typically comes from the choice of the in-network processing algorithm.

A. Practical stability

First, design a continuous-time observer (3) robust to measurement errors in the following sense.

Assumption 1: System (5)-( 6) is IOS from (e, w) to ξ with linear gains γ e 1 , γ w 1 . This type of condition was already used for the observer design for sampled-data systems and NCS respectively in [START_REF] Karafyllis | From continuous-time design to sampled-data design of observers[END_REF], [START_REF] Postoyan | Observers for classes of nonlinear networked systems[END_REF] and is similar to the IOS assumption for the control of NCS in [START_REF] Nešić | Input-output stability properties of networked control systems[END_REF] (condition 2 in Theorem 7).

Second, select a scheduling protocol that satisfies the following property.

Assumption 2: Protocol (10) is uniformly globally exponentially stable (UGES) (see Definition 7 in [START_REF] Nešić | Input-output stability properties of networked control systems[END_REF]) with Lyapunov function W : Z ≥0 ×R ne → R ≥0 that is locally Lipschitz in e and uniformly in i, i.e. there exists ρ ∈ [0, 1) and (a 1 , a 2 ) ∈ R 2 >0 such that, for all i ∈ Z ≥0 , (e, z) ∈ R ne+nz :

a 1 |e| ≤ W (i, e) ≤ a 2 |e| (11)
W (i + 1, h(i, e, z)) ≤ ρW (i, e). ( 12
)
It has been shown in [START_REF] Nešić | Input-output stability properties of networked control systems[END_REF] that the round-robin and the try-once-discard protocols are UGES with locally Lipschitz Lyapunov functions, respectively in view of Propositions 4 and 5 in [START_REF] Nešić | Input-output stability properties of networked control systems[END_REF]. The sampled-data case also satisfies Assumption 2 with W (e) = |e| for instance, then a 1 = a 2 = 1 and ρ = 0.

Third, make sure the e-system (7) grows exponentially between two successive transmission instants.

Assumption 3: There exist L, γ ξ 2 , γ z 2 , γ w 2 ∈ R ≥0 , such that, for all (i, ξ, z, w) ∈ Z ≥0 × R n ξ +nz+nw and almost all e ∈ R ne :

∂W (i, e) ∂e , g(ξ, e, z, w) ≤ LW (i, e) + γ ξ 2 |ξ| + γ z 2 |z| + γ w 2 |w|. ( 13
)
This condition is linked to the forward completeness of system [START_REF] Karafyllis | From continuous-time design to sampled-data design of observers[END_REF] in view of [START_REF] Angeli | Forward completeness, unboundedness observability, and their Lyapunov characterizations[END_REF] and is reminiscent of condition (27) in [START_REF] Nešić | Input-output stability properties of networked control systems[END_REF] for the control of NCS.

Fourth, guarantee the boundedness of the states of system (5).

Assumption 4: There exist α 3 ∈ K and γ e 3 , γ w 3 ∈ R ≥0 such that, for all z 0 ∈ R nz , (ξ, e, w) ∈ L n ξ +ne+nw ∞ , the following holds along solutions to (6):

|z(t)| ≤ α 3 (|(ξ 0 , z 0 )|) + γ e 3 e [t 0 ,t] + γ w 3 w [t 0 ,t] ∀t ≥ t 0 ≥ 0. ( 14
)
This condition is typically used to guarantee the boundedness of the states of ( 5)-( 10) when using zero-order-hold devices. It is very related to the stability of system (2): we usually prove it by assuming system (2) is BIBS with input w and using Assumption 1 as shown in Section V.

We are now ready to state the main theorem. Its proof is provided in Appendix A. The main idea is to consider system (5)- [START_REF] Postoyan | Commande et construction d'observateurs pour les systèmes non linéaires à données échantillonnées et en réseau[END_REF] as the interconnection of three subsystems in ξ, z and e and to apply small-gain arguments to conclude about the stability. Due to the fact that we are dealing with three subsystems (and not two) and that one of them is not expected to converge (z-subsystem ( 6),( 9)), the analysis in [START_REF] Jiang | Small-gain theorem for ISS systems and applications[END_REF] had to be modified.

Theorem 1: Under Assumptions 1-4, if τ ∈ [υ, τ 1 ) where τ 1 = 1 L ln La 1 +γ e 1 γ ξ 2 +γ z 2 γ e 3 Lρa 1 +γ e 1 γ ξ 2 +γ z 2 γ e 3 (τ 1 = a 1 (1-ρ) γ e 1 γ ξ 2 +γ z 2 γ e 3 if L = 0), then: • there exist β ∈ KL, σ ∈ K, σ, ε ∈ KK such that, for any ∆ ∈ R ≥0 , (ξ 0 , e 0 , z 0 ) ∈ R n ξ +ne+nz with |(ξ 0 , e 0 , z 0 )| < ∆, w ∈ L nw ∞ , this holds for all t ≥ t 0 ≥ 0 |(ξ(t), e(t))| ≤ β (|(ξ 0 , e 0 , z 0 )|, t -t 0 ) + σ( w ∞ ) + σ(τ, w ∞ ) + ε(τ, ∆). ( 15
)
• system ( 5)-( 10) is BIBS with w as input.

It has to be noticed that ( 15) is a global property in the sense that the MATI does not depend on the bound on the initial condition ∆. On the other hand, it can be seen that when w = 0, the observation error does not asymptotically converge to the origin but to the ball centered in 0 of radius ε(τ, ∆). This is mainly due to the fact that γ z 2 = 0 in (13) which typically arises when ZOH devices are implemented, as shown in Section V. The use of other in-network processing algorithms such as the predictive-type implementation may overcome this issue as they may satisfy slightly different conditions that will ensure the asymptotic convergence to the origin.

B. Asymptotic stability

We propose an alternative to Section IV-B to guarantee the asymptotic convergence of (ξ, e) to the origin in the absence of disturbances. We slightly strengthen Assumption 1 as follows.

Assumption 5: There exist

β 1 ∈ KL, γ e 1 , γ w 1 ∈ R ≥0 such that, for any ξ 0 ∈ R n ξ , (e, w) ∈ L ne+nw ∞ , solutions to (5) satisfy: |ξ(t)| ≤ β 1 (|ξ 0 |, t -t 0 ) + γ e 1 e [t 0 ,t] + γ w 1 w [t 0 ,t]
for t ≥ t 0 ≥ 0. Remark 4: Assumption 5 implies that system ( 5) is ISS w.r.t. (z, e, w) with linear gains.

When Assumption 5 holds and Assumption 3 is satisfied with γ z 2 = 0, the stability of ξand e-dynamics can be investigated separately from the whole system ( 5)- [START_REF] Postoyan | Commande et construction d'observateurs pour les systèmes non linéaires à données échantillonnées et en réseau[END_REF]. In that way, Assumption 4 can be relaxed as follows.

= 0. If τ ∈ [υ, τ 2 ) where τ 2 = 1 L ln La 1 +γ e 1 γ ξ 2 Lρa 1 +γ e 1 γ ξ 2 (τ 2 = a 1 (1-ρ) γ e 1 γ ξ 2 if L = 0), then:
• there exist β ∈ KL, σ ∈ K, σ ∈ KK such that, for all (ξ 0 , z 0 , e 0 ) ∈ R n ξ +nz+ne , w ∈ L nw ∞ :

|(ξ(t), e(t))| ≤ β (|(ξ 0 , e 0 )|, t -t 0 ) + σ( w ∞ ) + σ(τ, w ∞ ) ∀t ≥ t 0 ≥ 0. (16)
• system ( 5)-( 10) is forward complete with input w ∈ L nw ∞ .

V. APPLICATIONS

In this section, we illustrate the generality of our approach to the observer emulation for NCS.

We show that a general class of globally Lipschitz observers which covers the designs in [START_REF] Farza | Observer design for a class of MIMO nonlinear systems[END_REF], [START_REF] Gauthier | A simple observer for nonlinear systems -applications to bioreactors[END_REF], [START_REF] Rajamani | Observers for Lipschitz nonlinear systems[END_REF] to mention a few, can be implemented over networks ruled by the RR or the TOD protocol, using ZOH devices or predictive-type implementations and we derive explicit MATI bounds. The case where the system outputs are simply sampled is also considered.

Consider the system:

ẋ = Ax + ̺(x), y = Cx, (17)
where x ∈ R nx , y ∈ R ny , A and C are real matrices of appropriate dimensions and ̺ : R nx → R nx is globally Lipschitz. The following observer is synthesized:

ẋ = Ax + ̺(x) + Λ(y -ȳ), ȳ = C x, (18)
where x ∈ R nx , ȳ ∈ R ny and Λ is a real matrix, which is of the form of (3) with z = x. The convergence of the observation error ξ = x -x is usually proved using a quadratic Lyapunov function.

Assumption 7: There exists a Lyapunov function V : ξ → ξ T P ξ where P is symmetric and positive definite such that: ∂V ∂ξ Ax + ̺(x) -Ax -̺(x) -Λ(y -ȳ) ≤ -αV where α ∈ R >0 . We now implement observer (18) over a network as described in Section III. Consider the sequence of monotonically increasing transmission instants t i , i ∈ Z >0 , that satisfies υ ≤ t it i-1 ≤ τ for all i ∈ Z >0 and some fixed υ, τ ∈ R >0 . The problem is modeled as:

ξ = (A -ΛC)ξ + ̺(ξ + z) -̺(z) -Λe ∀t ∈ [t i-1 , t i ] (19)
ż = Az + ̺(z) + Λ(e + Cξ) ∀t ∈ [t i-1 , t i ] (20)
ė = fP (z) -CA(ξ + z) -C̺(ξ + z) ∀t ∈ [t i-1 , t i ] (21)
ξ(t + i ) = ξ(t i ) (22)
z(t + i ) = z(t i ) (23)
e(t + i ) = h(i, e(t i ), z(t i )), (24)
where z = x, fP (z) = 0 or fP (z) = CAz + C̺(z) whether ZOH devices or the predictive-type algorithm introduced in Section III are implemented. Function h depends whether the protocol is round-robin, try-once-discard (explicit definitions can be found in [START_REF] Nešić | Input-output stability properties of networked control systems[END_REF]) or plant outputs are simply sampled (h ≡ 0). We now follow the guidelines of Section IV.

First, we verify that observer (18) is robust to measurement errors as required by Assumptions 1 or 5. Under Assumption 7, we have that along solutions to (19), using the fact that and γ e 1 = 2 α 1 λ min (P ) |P Λ|. Remark 5: It has to be emphasized that we only provide here one possible expression for γ e 1 . Others can be determined using different tools, see for instance in Section V in [START_REF] Postoyan | A framework for the observer design for networked control systems[END_REF] for linear systems or Chapter 5.3.2 in [START_REF] Postoyan | Commande et construction d'observateurs pour les systèmes non linéaires à données échantillonnées et en réseau[END_REF] for the observers in [START_REF] Farza | Observer design for a class of MIMO nonlinear systems[END_REF] (that belong to the studied class of observers).

λ min (P )|ξ| 2 ≤ V (ξ) ≤ λ max (P )|ξ| 2 : V ≤ -αV -2ξ T P Λe ≤ -αV + 2|ξ||P Λ||e| ≤ -αV + 2 1 √ λ min (P ) √ V |P Λ||e|. Using the formula 2ab ≤ α 2 a 2 + 2 α b 2 for a, b ∈ R, we get: V ≤ -α 2 V +
Second, we have seen in Section IV-A that Assumption 2 holds for RR and TOD protocols and the sampled-data case.

Third, we prove that the e-system satisfies the exponential growth condition between transmission instants stated in Assumption 3. The idea is to combine the fact that globally Lipschitz Lyapunov functions are available in [START_REF] Nešić | Input-output stability properties of networked control systems[END_REF] for the RR and the TOD protocol (and as a consequence for the sampled-data case) and that the vector field of the e-system is globally Lipschitz. We explicitly show it only for the RR protocol, the coefficients for the other network configurations are given in Table I. We consider the following Lyapunov function as done in [START_REF] Nešić | Input-output stability properties of networked control systems[END_REF]. For i ∈ Z ≥0 and e ∈ R ne , W (i, e) = j∈{1,...,l}

a 2 j (i)|e j | 2 = |D(i)e|, where D(i) = diag (a 1 (i)I n 1 , . . . , a l (i)I n l )
with a j (i) some time-varying coefficients which are such that for any i ∈ Z ≥0 and j ∈ {1, . . . , l} there exists a unique k ∈ {1, . . . , l} such that a

γ ξ 2 = γ z 2 = √ l(|CA| + K).
For the predictive-type implementation, i.e. f (z) = CAz + C̺(z), we obtain: ∂W (i,e) ∂e , g(ξ, e, z) ≤ √ l(|CA| + K)|ξ|, so Assumption 3 is satisfied with L = 0,

γ ξ 2 = √ l(|CA| + K)
where γ z 2 = 0. Fourth, we identify an appropriate sufficient condition on system (17) that ensures that the z-system is bounded according to Assumption 4 when using ZOH devices. Using the fact that ξ = xz, system (20) can be written as: ż = (A -ΛC)z + ̺(z) + Λ(e + Cx). As a consequence, ZOH predictive-type

RR protocol L = 0, γ ξ 2 = √ l(|CA| + K), γ z 2 = √ l(|CA| + K) L = 0, γ ξ 2 = √ l(|CA| + K), γ z 2 = 0 TOD protocol L = 0, γ ξ 2 = |CA| + K, γ z 2 = |CA| + K L = 0, γ ξ 2 = |CA| + K, γ z 2 = 0 Sampled-data L = 0, γ ξ 2 = |CA| + K, γ z 2 = |CA| + K L = 0, γ ξ 2 = |CA| + K, γ z 2 = 0 TABLE I COEFFICIENTS OF ASSUMPTION 3 FOR SYSTEM (21)
by following the same arguments as for proving that ( 19) is ISS, we get:

|z(t)| ≤ β 1 (|z 0 |, t) + γ e 1 ( e [0,t] + |C| x [0,t] ). (25)
Now suppose the plant (17) is GS, i.e. there exists

α ∈ K such that |x(t)| ≤ α(|x 0 |) = α(|ξ 0 + z 0 |) ≤ α(2|(ξ 0 , z 0 )|).
In view of (25), we deduce that:

|z(t)| ≤ β 1 (|z 0 |, t) + γ e 1 |C|α(2|(ξ 0 , z 0 )|) + γ e 1 e [0,t] ≤ β 1 (|(ξ 0 , z 0 )|, 0) + γ e 1
|C|α(2|(ξ 0 , z 0 )|) + γ e 1 e [0,t] . Thus, Assumption 4 is satisfied with γ e 3 = γ e 1 . Note that we do not need to know α to compute γ e 3 . We are now ready to apply the results of Section IV. The first proposition is a direct consequence of Theorem 1.

Proposition 1: Consider system (19)-( 24) with ZOH in-network processing. Suppose Assumption 7 holds and system (17) is GS. If MATI satisfies τ ∈ [υ, τ * ) where τ * is defined in Table II depending on the protocol, then (15) holds and system (19)-( 24) is GS.

Since the nonlinearity of system (20) is globally Lipschitz, Assumption 6 always applies (see Theorem 3.2 in [START_REF] Khalil | Nonlinear Systems[END_REF]). The following proposition follows from Theorem 2.

Proposition 2: Consider system (19)-( 24) with the predictive-type in-network processing and suppose Assumption 7 holds. If MATI satisfies τ ∈ [υ, τ * ) where τ * is defined in Table II depending on the protocol, then (16) holds and system (19)-( 24) is forward complete.

VI. CONCLUSION

We have developed a framework for the observer design for NCS affected by disturbances, via an emulation-based approach. The proposed model allows us to study various observers, time-scheduling protocols and in-network processing implementations. Sufficient conditions on the system are given and explicit MATI bounds are deduced which ensure the convergence of the observation error under network-induced communication constraints. The extension of this study to the case where the ISS / IOS assumptions hold with nonlinear gains and the protocol is uniformly globally asymptotically stable is available in [START_REF] Postoyan | On emulation-based observer design for networked control systems[END_REF]. A consequence is that the obtained stability properties are no longer global but semiglobal and practical in general and the computation of the MATI bounds becomes more involved.

Assumption 6 :Theorem 2 :

 62 System (6) is forward complete with input (ξ, e, w) ∈ L n ξ +ne+nw ∞ . The following theorem can then be derived. Its proof follows similar lines to the proof of Theorem 1, see Appendix B. Under Assumptions 2,5,6 and suppose Assumption 3 holds with γ z 2

2 j

 2 (i) = k. It can then be deduced that |D(i)| = √ l, therefore, for i ∈ Z ≥0 and e ∈ R ne (with g(ξ, e, z) = fP (z) -CA(ξ + z) -C̺(ξ + z)), ∂W (i, e) ∂e , g(ξ, e, z) ≤ |D(i) ė| = D(i) fP (z) -CA(ξ + z) -C̺(ξ + z) , this gives for the ZOH implementation: ∂W (i,e) ∂e , g(ξ, e, z) ≤ √ l(|CA| + K)(|ξ| + |z|) where K stands for the Lipschitz constant of C̺. We see that Assumption 3 holds with L = 0,

  |P Λ| 2 |e| 2 . Invoking the comparison principle (seeLemma 3.4 in[START_REF] Khalil | Nonlinear Systems[END_REF]), we have that:V (t) ≤ e -α 2 t V (0)+ 4 |P Λ| 2 e 2 [0,t] , therefore |ξ(t)| ≤ β 1 (|ξ 0 |, t)+γ e1 e [0,t] and Assumption 5 (equivalently Assumption 1) is satisfied with β 1 (s, t) = λmax(P ) λ min (P ) e -α 4 t s for (t, s) ∈ R 2

	2	1
	α	λ min (P ) α 2	1 λ min (P ) ≥0

TABLE II MATI

 II

BOUNDS FOR SYSTEM (19)-(24)

[START_REF] Rajamani | Observers for Lipschitz nonlinear systems[END_REF] DRAFT

Note that υ is arbitrary and it is used to prevent Zeno solutions in[START_REF] Farza | Observer design for a class of MIMO nonlinear systems[END_REF].July 8,

DRAFT

PROOF OF THEOREM 1

The proof follows the main lines of the proof of Theorem 2.1 in [START_REF] Jiang | Small-gain theorem for ISS systems and applications[END_REF] under appropriate modifications due to the fact that we consider the interconnection of three systems (and not two) and that the z-system (6),( 9) exhibits a boundedness property and not an ISS / IOS property.

Step 1: BIBS property. Let (ξ 0 , e 0 , z 0 ) ∈ R n ξ +ne+nz , w ∈ L nw ∞ and τ ∈ [υ, τ * ). Let [t 0 , t max ) denote the maximum existence interval for system (5)- [START_REF] Postoyan | Commande et construction d'observateurs pour les systèmes non linéaires à données échantillonnées et en réseau[END_REF], where t max ∈ (t 0 , ∞]. Let t ∈ [t 0 , t max ). Since Assumptions 2-3 hold, according to Proposition 6 in [START_REF] Nešić | Input-output stability properties of networked control systems[END_REF] and using the fact that 11), there exists β 2 ∈ KL such that:

where

L ln ρ -1 so that ζ is well defined). On the other hand, in view of Assumption 1, there exists β 1 ∈ KL such that:

Thus, in view of (26), (27) and Assumption 4, we have that:

where M e (τ, ξ 0 , e 0 , z 0 , w

It can then be shown that:

with (for the purpose of clarity, we omit the arguments of functions M ξ and M z ):

where α ∈ K and ϑ ∈ R ≥0 . Therefore, system (5)-( 10) is BIBS in view of Definition 2 and

Step

in view of (26), ( 28), ( 29), ( 29) and (31):

Considering (34) and noticing that

) that there exist λ 2 ∈ (1, ∞) and β2 ∈ KL such that:

Similarly, in view of (31), it can be shown that there exist β1 ∈ KL and λ 1 ∈ (1, ∞) such that,

(36) By combining ( 35) and (36) and introducing β = β1 + β2 , it follows that:

According to (30) and using the fact that β(a+b, t) ≤ β(2a, t)+ β(2b, t) for any a, b, t ∈ R ≥0 since β(•, t) ∈ K, we have that:

, 0), consequently, in view of (30) and (37), taking any ∆ ∈ R ≥0 and (ξ 0 , e 0 , z 0 ) ∈ R n ξ +ne+nz with |(ξ 0 , e 0 , z 0 )| < ∆, t ∈ [t 0 , ∞) we have that:

where, noting that We then obtain that ε is equal to 0 and appropriate σ and ς can be deduced.


V E P P Lemmens
email: v.lemmens@ikz.nl

A E Dassen

A A M Van Der Wurff

J W W Coebergh

K Bosscha

Lymph node examination among patients with gastric cancer: variation between departments of pathology and prognostic impact of lymph node ratio

Keywords: gastric cancer, lymph nodes, pathology, surgery, survival No conflict of interest, no financial support

Lymph node examination among patients with gastric cancer: variation between departments of pathology and prognostic impact of lymph node ratio

Introduction

At least 15 lymph nodes should be retrieved for proper TNM-staging in gastric cancer. We evaluated nodal harvest and examined its relation to stage distribution and survival at a population-based level, including the value of N-ratio (metastatic/evaluated) as a staging modality.

Methods

All patients resected for primary M0 gastric cancer diagnosed in 1999-2007 in the Dutch Eindhoven Cancer Registry area were included (N=880). Determinants of lymph node evaluation and their relationship with stage and survival were assessed in multivariable regression analyses. N-ratio categories were determined (N ratio 0, 0%; N ratio 1, 0.1%-19%; N ratio 2, 20%-29%; N ratio 3, ≥ 30%)

Results

The median number of lymph nodes examined was 7, dependent on N-category (N0: 7; N+: 8). It varied between departments of pathology from 5 to 9. This variation remained after adjustment for relevant patient-and tumour factors. Stage distribution differed between pathology departments (proportion N0 ranging from 14% to 21%, p=0.003). Among resected patients with N0M0 disease and <7 nodes examined, 5-year survival was 56%, compared to 69% among patients with ≥7 nodes examined (p=0.012). Five-year survival for N-ratio 0 was 58%, N-ratio 1 50%, N-ratio 2 18% and Nratio 3 11% (p<0.0001), while 5-year survival ranged from 58% for N0, 17% for N1, and 11% for N2/3 (p<0.0001).

Conclusion

In this series of patients with a relatively low number of evaluated lymph nodes, a high prognostic accuracy of N-ratio was found. However, improvement in nodal assessment is mandatory.

Introduction

Gastric cancer is still one of the leading cancers in incidence and mortality throughout the world.

Mortality of gastric cancer ranks fourth in Europe for males and fifth in females [START_REF] Ferlay | Estimates of cancer incidence and mortality in Europe in 2008[END_REF]. Although mortality and incidence declined since the second half of the previous century, survival rates remained dismal in Europe with a relative 5-year survival of 14-32% [START_REF] He | Recent trends of cancer in Europe: a combined approach of incidence, survival and mortality for 17 cancer sites since the 1990s[END_REF]. In the southern Netherlands, overall 5-year survival is 18% [START_REF] Dassen | Trends in incidence, treatment and survival of gastric adenocarcinoma between 1990 and 2007: a population-based study in the Netherlands[END_REF]. The only curative treatment is surgery with (partial) gastric resection and lymph node dissection. The type of lymph node dissection is still under discussion. Japan and some other countries perform an extended lymphadenectomy, the so-called D2-or D3-dissection. Several large studies have been conducted to evaluate the outcome of patients after a D2-dissection in the West [START_REF] Cuschieri | Patient survival after D1 and D2 resections for gastric cancer: long-term results of the MRC randomized surgical trial. Surgical Co-operative Group[END_REF][START_REF] Hartgrink | Extended lymph node dissection for gastric cancer: who may benefit? Final results of the randomized Dutch gastric cancer group trial[END_REF]. As they found no survival benefit for this type of dissection, with higher post-operative morbidity a D2-dissection is therefore no general practice in our country. The long-term results after a median survival of 15 years did find lower regional recurrence and gastric cancer related deaths after a D2 dissection. It was suggested that a D2 dissection should be recommended, especially in view of the availability of a spleen-saving (and therefore safer) D2-dissection [START_REF] Songun | Surgical treatment of gastric cancer: 15-year follow-up results of the randomised nationwide Dutch D1D2 trial[END_REF].

It is widely accepted that lymph node status and lymph node ratio, together with T and M category, are the most important prognostic factors [START_REF] Siewert | Relevant prognostic factors in gastric cancer: tenyear results of the German Gastric Cancer Study[END_REF][START_REF] Marchet | The ratio between metastatic and examined lymph nodes (N ratio) is an independent prognostic factor in gastric cancer regardless of the type of lymphadenectomy: results from an Italian multicentric study in 1853 patients[END_REF]. According to several studies and guidelines (UICC) a resection with at least 15 lymph nodes should be performed for proper staging and disease control. As in most countries where a D1-dissection is performed these numbers cannot be met, N-ratio (metastatic/evaluated) is proposed as a new N-staging modality.

In this perspective, we conducted a retrospective study in the southern part of the Netherlands to evaluate the amount of lymph nodes dissected and examined its relation to stage distribution and survival.

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

Patients and methods

Data collection

The Eindhoven Cancer Registry collects data on all patients with newly diagnosed cancer in a large part of the southern Netherlands. The registry area grew from an area covering 850,000 to about 2.3 million inhabitants. This population-based registry was notified by 6 pathology departments, 10 community hospitals (20 at

Analyses

Differences between the departments of pathology according to the number of lymph nodes evaluated and the postoperative nodal status were tested by means of a Kruskal Wallis test. The independent influence of institution or patient and tumour characteristics on the number of lymph nodes evaluated was analyzed by means of a logistic regression analysis. To examine the hypothesis that the number of lymph nodes examined is related to survival, 5-year crude overall survival differences between patients with the median number or less versus more than the median number of nodes examined were tested using a log-rank test, stratified for N status. Furthermore, the ratio between the number of metastatic and evaluated lymph nodes was determined. Cutoff values for N-ratio intervals were determined based on the prognosis of patients and the number of patients included within each category. Patients were categorised into 4 groups: N-ratio 0 (number of metastatic nodes / number of evaluated nodes * 100%=0%), N-ratio 1 (0.1-19%), N-ratio 2 (20-29%), and N-ratio 3 (≥30%). Fiveyear survival was compared between these groups using a log-rank test. A multivariable proportional hazards regression analysis was used to discriminate independent risk factors for death. To compare the prognostic value of nodal status and N-ratio, the model was first built with inclusion of nodal status and lymph node count, and then repeated with N-ratio instead of the aforementioned variables.

All tests were two-sided. P-values <0.05 were considered statistically significant. All analyses were performed using SAS/STAT ® statistical software (SAS system 9.1.3, SAS Institute, Cary, NC).

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

6

Results

General characteristics and departments of pathology

Three out of the six departments of pathology served one hospital, while two departments covered 3 hospitals each. One hospital has been served by two departments of pathology during the study period for logistic reasons.

The general characteristics of all patients are shown in table 1. The median age was 69 years. The majority of patients was male, and presented with comorbidity. A large proportion of patients had poorly differentiated tumours. Few patients received neoadjuvant treatment; the most commonly performed resection was a subtotal gastrectomy. Twelve percent of patients had 15 or more lymph nodes examined.

Nodal evaluation

The median number of lymph nodes evaluated varied between 5 in department #6 to 9 in departments #1 and #4 (p<0.0001) (table 2). In total, a median number of 7 nodes was evaluated between 1999 and 2007. There was also a large variation between the departments concerning the proportions of patients with no exact number of evaluated nodes stated in the pathology report. Often, terms were used such as 'a few' or 'a number of', indicating that lymph nodes were indeed evaluated.

Five out of six departments of pathology showed an increasing trend over time in the number of evaluated lymph nodes. In total, the median number of evaluated nodes increased from 6 in the period 1999-2001, to 8 in 2004-2007. Within the last period, the median number of nodes evaluated continued to rise to 13 in department #3 and to 14 in department #4 in 2007 (results not shown).

Among patients with N+ disease, there was a larger proportion of patients with an unknown exact number of nodes evaluated, but also a larger proportion of patients with 15 or more nodes evaluated (median 8 nodes compared to 7 among N0 patients). Postoperative N category differed between the departments of pathology (p=0.003) (table 2). In the departments with a higher median number of lymph nodes evaluated, a smaller proportion of patients was diagnosed with N0 disease. Compared to the other departments, in department #1 a higher proportion of patients was diagnosed with N3 disease, and a smaller proportion with unknown N category.

In table 3, the results of a multivariable logistic regression analysis (adjusting for all variables listed)

show that patients with two or more comorbid conditions, patients with a T1 or T4 tumour, and patients whose resection specimen was examined in department of pathology #2 had a significantly lower

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 7
chance of having 7 or more nodes evaluated compared to the respective reference groups. Patients with N+ disease and patients undergoing a total gastrectomy or a multi-organ resection had a higher chance of having 7 or more nodes examined. Patients being diagnosed more recently also had a higher odds of having more nodes evaluated, but this reached borderline significance only (p=0.06).

Survival

Five-year survival was significantly higher among patients with N0, M0 disease which had 7 or more nodes evaluated compared to patients with less than 7 nodes evaluated (figure 1a). Among patients with N+, M0 disease, no prognostic effect of lymph node count could be noted (figure 1b). Five-year survival clearly differed according to nodal status, ranging from 58% for patients with N0 disease, 17%

for patients with N1 disease, and 11% for patients with N2/3 disease (figure 1c). Classifying patients according to lymph node ratio yielded a comparable survival gap between patients with N-ratio of 0 and patients with an N-ratio of 2 or 3 (figure 1d). Patients with an N-ratio of 1 however, only fared slightly less well than patients with an N-ratio of 0 (50% vs. 58%). After adjustment for relevant patient and tumour characteristics, the risk of death (hazard ratio (HR)) was strongly correlated with nodal category and with lymph node count (table 4). Exchanging these two variables for N-ratio yielded comparable effects, but note again the only borderline significant worse survival of patients with Nratio 1 compared to N-ratio O. To a lesser degree, T-category and having two or more comorbid conditions also were of prognostic importance.

Without inclusion of N-ratio or lymph node count and nodal status in the model, patients who had their resection specimen examined in department of pathology #2 exhibited a significant increased risk of death (HR 1.3, 95% confidence limits 1.01-1.7) (results not shown).

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

8

Discussion

Nodal category (N-category) is one of the most important prognostic factors in gastric cancer. Proper N-staging is therefore needed to predict outcome in patients. According to UICC guidelines in gastric cancer at least 15 lymph nodes should be investigated to correctly assess N-category (6 th and 7 th edition). Additionally, several studies have shown the importance of N-ratio in staging gastric cancer [START_REF] Siewert | Relevant prognostic factors in gastric cancer: tenyear results of the German Gastric Cancer Study[END_REF][START_REF] Costa | Prognostic score in gastric cancer: the importance of a conjoint analysis of clinical, pathologic, and therapeutic factors[END_REF]. In this retrospective study we investigated the amount of lymph nodes evaluated and N-ratio after surgery for gastric carcinoma, and its relationship to survival in the Southern part of the Netherlands.

Nodal evaluation

This region is served by 10 community hospitals, all draining on 6 departments of pathology; the median number of investigated lymph nodes between departments of pathology varied between 5 and 9 lymph nodes per patient, with a median number of 7 in the whole region. These results are confirmed by other studies, where the median number of lymph nodes examined also varied between different geographical regions [START_REF] Baxter | Inadequacy of lymph node staging in gastric cancer patients: a population-based study[END_REF][START_REF] Coburn | Significant regional variation in adequacy of lymph node assessment and survival in gastric cancer[END_REF]. The region is characterised by the absence of an academic hospital in our region. Recent Dutch studies showed that hospital characteristics also influenced nodal yield in colon cancer; especially academic centres showed a higher median lymph node yield [START_REF] Elferink | Large variation between hospitals and pathology laboratories in lymph node evaluation in colon cancer and its impact on survival, a nationwide population-based study in The Netherlands[END_REF][START_REF] Lemmens | Pathology practice patterns affect lymph node evaluation and outcome of colon cancer: a population-based study[END_REF].

Volume did not seem to have an effect. Also after adjustment in a multi-level analysis for these and other relevant factors, differences between departments of pathology remained, probably suggesting variation in diligence and effort put in these time-consuming examinations. Fat-clearing agents are not widely used in the Netherlands. Although a minimum number of at least 15 lymph nodes is considered mandatory for proper staging, more studies reported an insufficient number of investigated lymph nodes [START_REF] Baxter | Inadequacy of lymph node staging in gastric cancer patients: a population-based study[END_REF][START_REF] Coburn | Significant regional variation in adequacy of lymph node assessment and survival in gastric cancer[END_REF]. Factors associated with a higher amount of lymph nodes in these studies were younger age, female gender, Asian race, and more radical surgery [START_REF] Baxter | Inadequacy of lymph node staging in gastric cancer patients: a population-based study[END_REF][START_REF] Bouvier | How many nodes must be examined to accurately stage gastric carcinomas? Results from a population based study[END_REF]. Obesity has been suggested to be of influence as well [START_REF] Lee | Abdominal shape of gastric cancer patients influences shortterm surgical outcomes[END_REF]. In the present study, we did not find an effect of age or gender, but we did find an effect of more radical surgery. Obviously, in a total gastric resection more surrounding tissue is removed, resulting in more lymph nodes retrieved. Other factors associated with the amount of lymph nodes found were comorbidity, T-and N-category, and department of pathology. Practice of surgeons and pathologists can influence the amount of lymph nodes found. In the Netherlands, mostly a D1 resection is performed. Several prospective studies have proven no benefit of a D2 resection over a D1 resection with high postoperative morbidity and mortality [START_REF] Cuschieri | Patient survival after D1 and D2 resections for gastric cancer: long-term results of the MRC randomized surgical trial. Surgical Co-operative Group[END_REF][START_REF] Hartgrink | Extended lymph node dissection for gastric cancer: who may benefit? Final results of the randomized Dutch gastric cancer group trial[END_REF], although latest analyses showed lower gastric cancer related deaths and locoregional recurrence 15 years after a D2 dissection. [START_REF] Songun | Surgical treatment of gastric cancer: 15-year follow-up results of the randomised nationwide Dutch D1D2 trial[END_REF] The Besides treatment and patient-and tumour-related characteristics, inadequate lymph node harvesting might be related to the pathological examination. Different techniques of pathologic examination influences the total number of lymph nodes found. One retrospective study found more lymph node metastases when they retrospectively sectioned lymph nodes at three levels instead of one [START_REF] Mcgrath | Histopathological assessment of lymph nodes in upper gastrointestinal cancer: does triple levelling detect significantly more metastases?[END_REF]. Using fat clearing technique instead of conventional techniques increased nodal yields [START_REF] Bunt | Lymph node retrieval in a randomized trial on western-type versus Japanese-type surgery in gastric cancer[END_REF]. As mentioned before, a previous report from the Eindhoven Cancer Registry, pathology practice was linked to the adequacy of nodal assessment in colon cancer [START_REF] Lemmens | Pathology practice patterns affect lymph node evaluation and outcome of colon cancer: a population-based study[END_REF]. However, the increasing median number of lymph nodes in 5 out of 6 departments of pathology in our study suggests a rise in awareness of the importance of an adequate nodal examination. There also is a role for the surgeon as well in improving quality of treatment by performing a more thorough lymph node dissection. In the end, it remains a joint responsibility of pathologist and surgeon, and communication and feedback are essential in increasing and maintaining quality of nodal assessment.

Survival

Five-year survival was significantly higher when 7 or more lymph nodes were investigated among N0M0 patients. In most other studies, the threshold was set at 15 resected lymph nodes as in concordance with the UICC/AJJC guidelines, with hazard ratios of ~0.50 in favour of evaluation of more than 15 lymph nodes [START_REF] Coburn | Significant regional variation in adequacy of lymph node assessment and survival in gastric cancer[END_REF][START_REF] Bouvier | How many nodes must be examined to accurately stage gastric carcinomas? Results from a population based study[END_REF][START_REF] Siewert | Benefits of D2 lymph node dissection for patients with gastric cancer and pN0 and pN1 lymph node metastases[END_REF][START_REF] Smith | Impact of total lymph node count on staging and survival after gastrectomy for gastric cancer: data from a large US-population database[END_REF]. In our region, only 12% of patients had > 15 investigated

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 10
lymph nodes, making evaluations at this cut-off point less reliable. Several hypotheses have been mentioned to explain the positive correlation between survival and the number of evaluated lymph nodes. One hypothesis is understaging. Understaging can be a result of a minimum amount of lymph nodes retrieved. Another hypothesis is reduction of tumour burden. With an extended lymphadenectomy, tumour burden is reduced. Even pN0 patients with a lymph node count of more than 15 are found to have better survival [START_REF] Siewert | Relevant prognostic factors in gastric cancer: tenyear results of the German Gastric Cancer Study[END_REF]. This can be attributed partly to the removal of lymph nodes with micrometastasis, which are difficult to detect in normal pathological evaluation [START_REF] Siewert | Benefits of D2 lymph node dissection for patients with gastric cancer and pN0 and pN1 lymph node metastases[END_REF]. The fact that in our study the number of lymph nodes examined had a larger influence on survival among nodenegative than among node positive patients confirms this hypothesis. Where the effect of reduction of tumour burden becomes more important than understaging is not clear, although a prospective study of Siewert et al suggested a threshold around 15 to 20 lymph nodes [START_REF] Siewert | Relevant prognostic factors in gastric cancer: tenyear results of the German Gastric Cancer Study[END_REF]. This was confirmed by other, retrospective studies [START_REF] Coburn | Significant regional variation in adequacy of lymph node assessment and survival in gastric cancer[END_REF][START_REF] Smith | Impact of total lymph node count on staging and survival after gastrectomy for gastric cancer: data from a large US-population database[END_REF]. Unfortunately we were not able to adjust for radicality of resection, since this item was not routinely collected during the whole study period. Also, we could not discriminate between resections with curative versus palliative intent. However, since we included only patients who were metastasis-free at time of diagnosis (M0), we assume that the proportion of patients undergoing a tumour resection with strict palliative intent was very low, and has therefore probably not influenced our results.

Lymph node ratio

To overcome the problem of inadequate nodal harvest in staging, the lymph node ratio (N-ratio) has been suggested This is defined as the amount of positive lymph nodes divided by the total amount of retrieved lymph nodes. It gives information about the N-category and about the extent of lymph node dissection. In breast, colon and rectal cancer it has proven its superior prognostic information over Ncategory according to the TNM classification [START_REF] Moug | Positive lymph node retrieval ratio optimises patient staging in colorectal cancer[END_REF][START_REF] Peschaud | The ratio of metastatic to examined lymph nodes is a powerful independent prognostic factor in rectal cancer[END_REF][START_REF] Van Der Wal | Axillary lymph node ratio and total number of removed lymph nodes: predictors of survival in stage I and II breast cancer[END_REF][START_REF] Vinh-Hung | Lymph node ratio as an alternative to pN staging in node-positive breast cancer[END_REF]. In all studies evaluating N-ratio in gastric cancer, as we know of, it has proven to be an important independent prognostic factor in multivariate analysis, as confirmed by the results of our study [START_REF] Siewert | Relevant prognostic factors in gastric cancer: tenyear results of the German Gastric Cancer Study[END_REF][START_REF] Marchet | The ratio between metastatic and examined lymph nodes (N ratio) is an independent prognostic factor in gastric cancer regardless of the type of lymphadenectomy: results from an Italian multicentric study in 1853 patients[END_REF][START_REF] Costa | Prognostic score in gastric cancer: the importance of a conjoint analysis of clinical, pathologic, and therapeutic factors[END_REF][START_REF] Lemmens | Pathology practice patterns affect lymph node evaluation and outcome of colon cancer: a population-based study[END_REF][START_REF] Ceelen | Peritoneal minimal residual disease in colorectal cancer: mechanisms, prevention, and treatment[END_REF][START_REF] Huang | Prognostic impact of metastatic lymph node ratio in advanced gastric cancer from cardia and fundus[END_REF][START_REF] Persiani | Ratio of metastatic lymph nodes: impact on staging and survival of gastric cancer[END_REF]. We found a 5-year survival of 50% in Nratio group 1, while these patients would have been assigned to at least the N1 group using the traditional TNM classification (6 th edition), with an expected 5-year survival of maximum 17%, These results suggest a higher prognostic value of the N-ratio system in comparison to the traditional TNM classification, although more analyses should be performed to confirm this. One of the drawbacks of the N-ratio is that there are no standardized categories in literature; N-ratio groups can therefore be fit

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

to the used dataset. Because of the low number of patients with a low N-ratio we used a higher cut-off point. This can bias our results and give a seemingly higher prognostic value than the TNMclassification; some authors have questioned the clinical usefulness in case of low numbers of nodes [START_REF] Pedrazzani | Ratio between metastatic and examined lymph nodes (N ratio) may have low clinical utility in gastric cancer patients treated by limited lymphadenectomy: results from a single-center experience of 526 patients[END_REF]. In the new AJCC/UICC TNM classification (7 th

  and mortality data were obtained from Statistics Netherlands (CBS) (CBS, 2007. Voorburg/Heerlen).

  nodes evaluated in our region reflects the type of lymph node dissection performed.Only in 21 patients a D2 resection was reported in the study period. Although the amount of harvested lymph nodes can partly be accounted to the type of surgery, patient characteristics can be of influence as well. In a D2 resection on cadavers a range from 17 to 44 lymph nodes per patient was reported[START_REF] Wagner | Lymph node counts in the upper abdomen: anatomical basis for lymphadenectomy in gastric cancer[END_REF]. Considering the inter-individual variation in nodal count, this might lead to an inadequate lymph node dissection among certain patients. Furthermore, as patients grow older the amount of lymph nodes decreases. Differences in immunologic reaction can play a role as well. The immune reaction against neoplastic cell products alters the shape and morphology of lymph nodes. An advanced T-category might as well stimulate immune reaction, but the larger size of the tumour also might stimulate surgeon and pathologist for more aggressive lymph node harvesting. In addition, in advanced T-category, the risk of lymph node metastases rises. Metastatic lymph nodes have a greater size, which makes harvesting and examining them easier. The positive association between Ncategory and the number of lymph nodes evaluated reflects this as well.

  the beginning of the 1970's but many of them have merged) at 15 locations, and 2 radiotherapy institutions.All patients resected for primary gastric cancer (ICD-O (International Classification of Diseases for Oncology) code C16 ) without evidence for distant metastasis, diagnosed between 1999 and 2007 in the Dutch Eindhoven Cancer Registry area were included (N=880). Information on diagnosis, staging, and treatment is routinely extracted from the medical records by specially trained administrators of the cancer registry. Registration takes place 6 to 18 months after diagnosis. By means of an independent case ascertainment method, the completeness of the registration is estimated to exceed 95%.

	Stage distribution is based on the Tumour Node Metastasis (TNM) system (International Union
	Against Cancer (UICC) classification 6 th edition). Subsite distribution is divided as follows: cardia
	(comprising gastro-esophageal junction, C16.0), middle part (fundus, corpus, lesser curvature, and
	greater curvature (the two latter not classifiable to C16.0 -C16.4], C16.1, C16.2, C16.5, and C16.6),
	pyloric part (antrum and pylorus, C16.3 and C16.4), overlapping lesions (C16.8), and not otherwise
	specified (C16.9). Tumour characteristics registered furthermore include number of lymph nodes
	examined, number of positive lymph nodes, and grade of tumour differentiation. Prognostically
	relevant concomitant conditions are recorded from the medical records according to a slightly adapted
	version of the Charlson Index. This item was not registered before 1993; since 1995 these data are
	reliable and validated[8,9]. Socio-economic status (SES) of the patient was defined at neighborhood
	level (based on postal code of residence area, 17 households on average) combining mean
	household income and mean value of the house/apartment. The latter was derived from individual
	fiscal data made available at an aggregated level. Postal codes were assigned to one of 3 SES
	categories: low (1st-3 rd decile), intermediate (4 th -7 th decile), and high (8	th -10 th decile)[9]. For patients
	residing in nursing homes, a special SES category was assigned. Vital status of all patients diagnosed
	until 1 st of January 2007 was assessed on 1 st of January 2008 through merging with the Municipal
	Administrative Databases, where all deceased and emigrated persons in the Netherlands are

Table 2 .

 2 Median number of lymph nodes evaluated and proportion N0, according to department of

	pathology
		Median		Proportion of patients with	%N0
	Dep. of pathology	number of nodes	Range	unknown number of evaluated nodes
		evaluated
				Unknown	At least 1 node
				whether any	evaluated, but exact
				nodes have been	number not stated in medical file a
				evaluated
	1	9	0-31	0%	0%	15%
	2	6	0-21	1%	28%	20%
	3	7	0-35	1%	27%	20%
	4	9	0-41	2%	12%	17%
	5	7	0-36	1%	8%	20%
	6	5	0-21	3%	45%	22%
	total	7	0-41	1%	19%	19%
	Difference of median numbers of lymph nodes evaluated across departments of pathology: Kruskal
	Wallis test p<0.0001
	Differences in postoperative nodal status between departments of pathology: chi 2 test p=0.003

a Often stated in the pathology report as: 'a few', or 'a number of'.

Table 3 .

 3 Odds of having 7 or more lymph nodes evaluated, calculated by means of a multivariable logistic regression analysis (model including all listed variables).

						n	Odds ratio	95% CL
	Age (yrs) <70 a		447	1.0
	70+			433	0.8	0.6-1.1
	Gender Males	a		574	1.0
	Females Comorbidity a No comorbidity	a	306 265	1.3 1.0	0.9-1.8
	One comorbid condition	248	0.7	0.5-1.2
	Two or more comorbid conditions	313	0.5	0.3-0.7
	Unknown		54	1.3	0.6-2.9
	T-category
	T1 T2	a			132 488	0.4 1.0	0.2-0.7
	T3				205	0.9	0.6-1.5
	T4				35	0.4	0.2-0.9
	N-category N0 a		449	1.0
	N+				431	2.3	1.6-3.2
	Tumor site
	Cardia		168	1.6	0.8-3.3
	Middle part Pyloric part	a	222 323	1.1 1.0	0.7-1.7
	Overlapping/unknown	167	1.1	0.7-1.9
	Tumour grade Moderately/well differentiated	a	269	1.0
	Poorly differentiated	520	1.3	0.9-2.0
	Unknown		91	0.8	0.4-1.5
	Neoadjuvant treatment No a	851	1.0
	Yes			29	0.8	0.3-1.7
	Type of resection
	Total gastrectomy Subtotal gastrectomy	a	192 509	1.9 1.0	0.1-3.0
	Oesophageal-cardiac resection	118	1.3	0.6-2.8
	Multi-organ resection	29	5.0	1.4-14.5
	Department of pathology
	1					78	1.0	0.6-1.9
	2					185	0.3	0.2-0.5
	3					108	0.9	0.5-1.5
	4 5	a				178 238	1.5 1.0	0.9-2.3
	6					93	0.5	0.3-1.1
	Period of diagnosis 1999-2003 a	426	1.0
	2004-2007		454	1.4	1.0-1.9
	a Reference category
	CL=confidence limits

Table 4 .

 4 Multivariable proportional hazard regression analysis for patients who underwent resection for gastric cancer between 1999 and 2006 in the south of the Netherlands (model including all listed variables).

							Model including N-category	Model including N-ratio
							and number of evaluated
							lymph nodes separately
							Hazard ratio	95% CL	Hazard ratio	95% CL
	Age (yrs) <70 a			1.0	1.0
	70+				1.1	0.9-1.3	1.1	0.9-1.4
	Gender Males	a			1.0	1.0
	Females Comorbidity a No comorbidity	a	0.9 1.0	0.7-1.1	0.9 1.0	0.7-1.1
	One comorbid condition	1.1	0.9-1.4	1.1	0.9-1.4
	Two or more comorbid conditions	1.3	1.0-1.7	1.3	1.0-1.7
	Unknown			0.9	0.6-1.5	0.9	0.5-1.4
	T-category
	T1 T2	a				0.6 1.0	0.4-0.8	0.6 1.0	0.4-0.9
	T3					1.1	0.9-1.5	1.2	0.9-1.5
	T4					1.7	1.0-2.7	1.8	1.0-2.9
	N-category N0 a			1.0	n.a.
	N1					2.9	2.2-3.6
	N2/3				4.5	3.1-6.2
	Number of evaluated lymph nodes <7 a	1.0	n.a.
	≥7					0.7	0.6-0.9
	N-ratio Ratio 0 (0%)	a	n.a.	1.0
	Ratio 1 (0.1-19%)	1.5	1.0-2.2
	Ratio 2 (20-29%)	3.1	2.0-4.6
	Ratio 3 (≥30%)	3.8	2.9-4.9
	Tumor site
	Cardia			0.9	0.6-1.4	0.9	0.6-1.3
	Middle part Pyloric part	a		0.9 1.0	0.7-1.2	0.9 1.0	0.7-1.2
	Other/unknown	1.4	1.0-1.9	1.3	1.0-1.8
	Tumour grade Moderately/well differentiated	a	1.0	1.0
	Poorly differentiated	1.0	0.8-1.3	0.9	0.7-1.2
	Unknown			1.0	0.7-1.6	0.9	0.7-1.5
	Neoadjuvant treatment No a	1.0	1.0
	Yes				0.8	0.4-1.4	0.9	0.5-1.6
	Type of resection
	Total gastrectomy Subtotal gastrectomy	a	1.2 1.0	0.9-1.6	1.2 1.0	0.9-1.7
	Oesophageal-cardiac resection	1.0	0.7-1.6	1.0	0.6-1.6
	Multi-organ resection	1.4	0.7-2.6	1.4	0.7-2.6
	Department of pathology
	1						0.8	0.6-1.1	0.8	0.6-1.1
	2						1.1	0.8-1.5	1.1	0.8-1.4
	3						0.9	0.6-1.2	0.9	0.6-1.2
	4 5	a					1.0 1.0	0.7-1.3	1.0 1.0	0.7-1.3
	6						0.9	0.6-1.4	1.0	0.6-1.5
	Period of diagnosis 1999-2002 a	1.0	1.0
	2003-2006			1.0	0.8-1.3	1.0	0.8-1.3

a Reference category

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


Marcello P Riggio
email: marcello.riggio@glasgow.ac.uk

Alan Lennon

David J Taylor

David Bennett

Molecular identification of bacteria associated with canine periodontal disease

Keywords: canine periodontal disease, bacteria, microbiological culture, 16S rRNA, polymerase chain reaction

Periodontal disease is one of the most common diseases of adult dogs, with up to 80% of animals affected. The aetiology of the disease is poorly studied, although bacteria are known to play a major role. The purpose of this study was to identify the bacteria associated with canine gingivitis and periodontitis and to compare this with the normal oral flora. Swabs were obtained from the gingival margin of three dogs with gingivitis and three orally healthy controls, and subgingival plaque was collected from three dogs with periodontitis. Samples were subjected to routine bacterial culture. The prevalent species identified in the normal, gingivitis and periodontitis groups were uncultured bacterium (12.5% of isolates), Bacteroides heparinolyticus / Pasteurella dagmatis (10.0%) and Actinomyces canis (19.4%), respectively. Bacteria were also identified using culture-independent methods (16S rRNA gene sequencing) and the predominant species identified were Pseudomonas sp. (30.9% of clones analysed), Porphyromonas cangingivalis (16.1%) and Desulfomicrobium orale (12.0%) in the normal, gingivitis and periodontitis groups, respectively. Uncultured species accounted for 13.2%, 2.0% and 10.5%, and potentially novel species for 38.2%, 38.3% and 35.3%, of clones in the normal, gingivitis and periodontitis groups, respectively. This is the first study to use utilise culture-independent methods for the identification of bacteria associated with this disease. It is concluded that the canine oral flora in health and disease is highly diverse and also contains a high proportion of uncultured and, in particular, potentially novel species.

A c c e p t e d M a n u s c r i p t 3

Introduction

Periodontal disease (gingivitis and periodontitis) is one of the most common infectious diseases affecting adult dogs, with up to 80% of animals of all breeds affected (Golden et al., 1982;Harvey & Emily, 1993;[START_REF] Harvey | Periodontal disease in dogs. Etiopathogenesis, prevalence, and significance[END_REF]. The incidence of the disease increases markedly with advancing years and causes significant oral pain and suffering. Periodontal disease has been described as a multi-factorial infection [START_REF] Lindhe | Experimental periodontitis in the Beagle dog[END_REF], and plaque bacteria are known to be an important causative factor. Gingivitis is completely reversible and is recognised by the classic signs of halitosis, bleeding, inflammation, redness and swelling of the gingivae. Periodontitis is irreversible and attacks the deeper structures that support the teeth, permanently damaging the surrounding bone and periodontal ligament and resulting in increased periodontal pocket depth and tooth loss. The aetiology of canine periodontal disease remains unknown, although gramnegative anaerobic bacteria have been implicated in the disease (Hennet & Harvey, 1991a, b;[START_REF] Boyce | Occurrence of gram-negative black-pigmented anaerobes in 15[END_REF].

In recent years, the use of culture-independent (bacterial 16S rRNA gene sequencing) methods has supplemented traditional culture-dependent methods to detect bacteria in clinical specimens. 16S rRNA gene sequencing has permitted the identification of bacteria which are uncultivable, fastidious in their growth requirements and even novel, in addition to detecting known cultivable species (Clarridge, 2004;[START_REF] Spratt | Significance of bacterial identification by molecular biology methods[END_REF]. In the current study, the bacteria associated with canine periodontal disease, and with the normal canine oral cavity, were identified using both culture-dependent and culture-independent methods.

A c c e p t e d M a n u s c r i p t 4

Materials and methods

Sample collection and processing

Ethical approval for the study was obtained from the Local Research Ethics Committee.

Samples were classified into normal and diseased groups as follows: no gingival inflammation, no periodontal pockets (normal); gingival inflammation and/or periodontal pockets less than 3 mm in depth (gingivitis); periodontal pockets at least 4 mm in depth (periodontitis). Dental plaque was collected using sterile swabs from the gingivae of periodontally healthy dogs (three samples) and animals with gingivitis (three samples). For the periodontitis cases (three samples), subgingival plaque was collected using a sterile curette from the periodontal pocket. Swabs were placed into sterile reduced transport medium and subgingival plaque was immersed into 1 mL of fastidious anaerobe broth (FAB) and immediately sent for laboratory analysis. Each swab was then immersed into 1 mL of FAB. All samples were mixed for 30 s to remove bacteria.

Bacterial culture

Ten-fold serial dilutions (to 10 -6 ) were prepared for each sample and spiral plated onto both Columbia agar containing 7.5% (v/v) defibrinated horse blood (for aerobic culture) and fastidious anaerobe agar (FAA) (BioConnections, Wetherby, UK) containing 7.5% (v/v) defibrinated horse blood (for anaerobic culture). Columbia blood agar plates were incubated in 5% CO 2 at 37°C, and FAA plates were incubated at 37°C in an anaerobic chamber with an atmosphere of 85% N 2 / 10% CO 2 / 5% H 2 at 37°C. Plates were incubated for up to seven days, and up to eight morphologically distinct colonies (visually representing the most abundant colony types) were A c c e p t e d M a n u s c r i p t 5 then subcultured in order to obtain pure cultures. Bacterial isolates were identified by 16S rRNA gene sequencing as described below.

Extraction of DNA from samples

A bacterial DNA extract was prepared from each sample by digestion with 1% SDS and proteinase K (100 ug/mL) at 60ºC for 1 h, followed by boiling for 10 min. Extraction of DNA from bacterial isolates was carried out using the same method.

PCR amplification of bacterial 16S rRNA genes

Bacterial 16S rRNA genes were amplified by PCR using the universal primers 5′-CAGGCCTAACACATGCAAGTC-3′ (63f) and 5′-GGGCGGWGTGTACAAGGC-3′ (1387r) [START_REF] Marchesi | Design and evaluation of useful bacterium-specific PCR primers that amplify genes coding for bacterial 16S rRNA[END_REF]. PCR reactions were carried out in a total volume of 50 μL containing 5 μL of the extracted DNA and 45 μL of reaction mixture comprising 1 x GoTaq ® PCR buffer (Promega, Southampton, UK) 1.25 units of GoTaq ® polymerase (Promega), 1.5 mM MgCl 2 , 0.2 mM dNTPs (New England Biolabs, Hitchin, UK), and each primer at a concentration of 0.2 μM.

The PCR cycling conditions comprised an initial denaturation phase of 5 min at 95ºC, followed by 35 cycles of denaturation at 95ºC for 1 min, annealing at 58ºC for 1 min and primer extension at 72ºC for 1.5 min, and finally a primer extension step at 72ºC for 10 min.

A c c e p t e d M a n u s c r i p t 6

PCR quality control

Stringent procedures were adhered to in order to prevent contamination during the PCR process [START_REF] Riggio | Detection of Helicobacter pylori DNA in recurrent aphthous stomatitis tissue by PCR[END_REF]. Negative and positive control reactions were included with every batch of samples being analysed. The positive control comprised a standard PCR reaction mixture containing 10 ng of Escherichia coli genomic DNA instead of sample, whereas the negative control contained sterile water instead of sample. PCR products (10 μL) were electrophoresed on 2% (w/v) agarose gels, stained with ethidium bromide (0.5 μg/mL) and visualised under ultraviolet light.

Cloning of 16S rRNA PCR products

PCR products were cloned into the pSC-A-amp/kan plasmid vector using the StrataClone ™ PCR Cloning Kit (Stratagene) in accordance with the manufacturer's instructions. For each library, clones were initially sorted into groups based upon the RsaI restriction digestion profiles and further discrimination was achieved by digestion of clones with MnlI. Clones with identical 16S rRNA gene restriction profiles for both enzymes were assigned to distinct restriction fragment length polymorphism (RFLP) groups.

PCR amplification of 16S rRNA gene inserts

Sequencing of bacterial 16S rRNA genes

The 16S rRNA gene insert of a single representative clone from each RFLP group was sequenced. Sequencing was performed with the SequiTherm EXCEL™ II DNA Sequencing Kit (Cambio, Cambridge, UK) and IRD800-labelled 357f sequencing primer (5′-CTCCTACGGGAGGCAGCAG-3′) using the following cycling conditions: (i) initial denaturation at 95ºC for 30 s; (ii) 10 s at 95ºC, 30 s at 57ºC and 30 s at 70ºC, for 20 cycles and

(iii) 10 s at 95ºC and 30 s at 70ºC for 15 cycles. Formamide loading dye (6 μL) was added to each reaction mixture after thermal cycling and 1.5 μL of each reaction mixture was run on a LI-

Statistical analysis

To determine whether the observed differences in the microflora between each of the three groups were of statistical significance, a cross-tabulation using Fisher's exact test was performed.

A level of statistical significance was indicated by p<0.0167 (Bonferroni correction).

Results

Culture-dependent identification of bacteria

Bacterial isolates obtained following microbiological culture of samples were identified by 16S rRNA gene sequencing, and the results are shown in Table 1. All isolates had identities of at least 98% with a known database sequence. Of the 32 isolates obtained from the normal samples, the predominant bacteria identified were uncultured bacterium (4 isolates, 12.5%) and Neisseria A c c e p t e d M a n u s c r i p t 9 weaveri (three isolates, 9.4%). Thirty isolates were obtained from the gingivitis samples, of which three (10%) were identified as Bacteroides heparinolyticus and three (10%) as Pasteurella dagmatis. For the periodontitis samples, 36 isolates were identified and the predominant species was Actinomyces canis (seven isolates, 19.4%).

Culture-independent identification of bacteria

Following 16S rRNA PCR analysis, all nine samples were shown to be positive for the presence of bacteria. For the three normal samples, 152 clones were analysed and 83 clones were sequenced. Bacteria with identities of at least 98% with a known database sequence are grouped according to species in

Statistical analysis

In order to determine if the differences in the microflora observed in each of the three groups was statistically significant, a three-way comparison between groups using cross-tabulation with a Fisher's exact test was performed for the data presented in Tables 123.

For bacteria identified by culture-dependent methods (Table 1) statistically significant differences were observed between the gingivitis and periodontitis groups (p=0.0090) and the normal and periodontitis groups (p=0.0043). However, no statistical difference was observed between the normal and gingivitis groups (p=0.181).

For known bacteria identified by culture-independent methods (Table 2) statistically significant differences were observed between all three groups (p<0.000001).

For potentially novel bacteria identified by culture-independent methods (Table 3), statistically significant differences were observed between all three groups (p<0.00020).

Discussion

Canine periodontal disease is one of the most common infectious diseases of companion animals and is characterised by gingival inflammation and tooth loss [START_REF] Hennet | Natural development of periodontal disease in the dog: a review of clinical, anatomical and histological features[END_REF][START_REF] Harvey | Periodontal disease in dogs. Etiopathogenesis, prevalence, and significance[END_REF]. Black pigmenting anaerobic bacteria, in particular Porphyromonas and Prevotella species, have been isolated from the periodontal pockets of dogs with periodontal disease [START_REF] Watson | Diet and periodontal disease in dogs and cats[END_REF]Gorrel and Rawlings, 1996). [START_REF] Isogai | Ecology of genus Porphyromonas in canine periodontal disease[END_REF] Porphyromonas denticanis) associated with the disease have also been described (Collins et al., 1994;[START_REF] Hirasawa | Porphyromonas gingivicanis sp. nov. and Porphyromonas crevioricanis sp. nov., isolated from beagles[END_REF][START_REF] Love | Porphyromonas canoris sp. nov., an asaccharolytic, blackpigmented species from the gingival sulcus of dogs[END_REF]Fournier et al., 2001;Hardham et al., 2005).

Our current study is the first to use molecular cloning and sequencing of bacterial 16S rRNA genes, in addition to conventional microbiological culture methods, to identify the bacteria associated with canine gingivitis, periodontitis and oral health. Given the relatively small number of samples analysed, it was not possible to age-and sex-match the animals used in the study, although this would be desirable in future large-scale studies. Despite the relatively small number of samples analysed in each group in our current study, clear correlations were seen to emerge between disease status and the prevalence of specific bacterial species, and differences in the microflora between the three groups was statistically significant. The most prevalent species found in the normal, gingivitis and periodontitis groups were Pseudomonas sp. (30.9%),

Porphyromonas cangingivalis (16.1%) and Desulfomicrobium orale (12.0%), respectively.

Porphyromonas cangingivalis was first isolated from cases of canine periodontitis (Collins et al., 1994) and Desulfomicrobium orale has been isolated from cases of human periodontitis [START_REF] Langendijk | Isolation of Desulfomicrobium orale sp. nov. and Desulfovibrio strain NY682, oral sulfate-reducing bacteria involved in human periodontal disease[END_REF]. Other prevalent species identified included Porphyromonas canoris, Tannerella forsythensis and Capnocytophaga cynodegmi (gingivitis), and Actinomyces sp. and Capnocytophaga cynodegmi (periodontitis). The association of Tannerella forsythensis with human periodontal disease is well documented, Capnocytophaga cynodegmi is found in the oral cavity of the vast majority of dogs [START_REF] Van Dam | Molecular characterization of Capnocytophaga canimorsus and other canine Capnocytophaga spp. and assessment by PCR of their frequencies in dogs[END_REF] and Porphyromonas canoris has been isolated from canine dental plaque samples [START_REF] Allaker | Prevalence of Porphyromonas and Prevotella species in the dental plaque of dogs[END_REF]. Culture-independent methods showed that microbial diversity was similar in all three groups (19 to 24 phylotypes). Uncultured bacteria were found at a higher proportion in the normal samples (13.2%) compared to the gingivitis (2.0%) and periodontitis (10.5%) samples. Potentially novel species were found at high proportions in all three groups (35.3% to 38.3%), a finding that is unsurprising when one A c c e p t e d M a n u s c r i p t 12 considers that this is the first study to use culture-independent methods to identify bacteria in the canine oral cavity. However, sequencing of the entire 16S rRNA gene would be required to confirm these species as being novel.

The finding that Pseudomonas sp., Porphyromonas cangingivalis and Desulfomicrobium orale were the predominant species identified by culture-independent methods in the normal, gingivitis and periodontitis samples, respectively, is not corroborated by the culture data obtained. However, some concordance does exist between the data since some species were detected by both identification methods (three, nine and five species in the normal, gingivitis and periodontitis samples, respectively). In addition, previously uncultured bacteria were identified by both methods in all three groups. However, many bacteria were identified by cultureindependent methods but not by culture methods. A possible explanation for this anomaly is the use of standard culture media and incubation conditions, which were adopted to ensure that as many different types of bacteria as possible were cultured. However, this approach may not have been suitable for the culture of many species, particularly those with fastidious growth requirements. Consequently, we advocate that culture-independent methods should be used in conjunction with conventional culture methods in order to identify the total microflora in clinical samples. Conversely, some bacteria isolated by culture methods were not identified by cultureindependent methods. The most likely explanation for this additional anomaly is PCR primer bias, which is caused by self-annealing of the most abundant templates in the late stages of amplification [START_REF] Suzuki | Bias caused by template annealing in the amplification of mixtures of 16S rRNA genes by PCR[END_REF] or as a result of differences in the amplification efficiency of different templates [START_REF] Polz | Bias in template-to-product ratios in multitemplate PCR[END_REF]. This results in the differential amplification of PCR products, leading to an inaccurate reflection of the true numbers of species present within the sample.

Following

  cloning of the 16S rRNA gene products amplified by PCR for each sample, approximately 50 clones from each library were selected at random. The 16S rRNA gene . The M13SIF binding site is located 61 base pairs downstream of the M13 reverse primer-binding site, and the M13SIR binding site is located 57 base pairs upstream of the M13 20 primer-binding site, in the pSC-A-amp/kan plasmid vector.

  enzyme analysis 16S rRNA gene inserts amplified by PCR were subjected to restriction enzyme analysis.Approximately 0.5 μg of each PCR product was digested in a total volume of 20 µL with 2.0 units of each of the restriction enzymes RsaI and MnlI (Fermentas Life Sciences, York, UK) at 37ºC for 2 h and the generated restriction fragments visualised by agarose gel electrophoresis.

  the development of canine periodontal disease. Clinical Infectious Diseases 20 (Suppl 2), S317-S319.

  Sequence data were compiled using LI-COR Base ImagIR 4.0 software, converted to FASTA format and compared with bacterial 16S rRNA gene sequences from the EMBL and GenBank sequence databases using the advanced gapped BLAST program, version 2.1[START_REF] Altschul | Gapped BLAST and PSI-BLAST: a new generation of protein database search programs[END_REF]. The program was run through the National Centre for Biotechnology Information website (http://www.ncbi.nlm.nih.gow/BLAST). Clone sequences with at least 98% identity with a known sequence from the database were designated the same species as the matching sequence with the highest score. Clone sequences with less than 98% identity were tentatively classified as putative novel phylotypes.

	2.10. Sequence analysis
	M a n u s c r i p t
	A c c e p t e d
	COR Gene ReadIR 4200S automated DNA sequencing system
	8

Table 2

 2

	Uncultured

, with a total of 19 phylotypes being identified. The predominant species was Pseudomonas sp. (30.9% of clones analysed). Uncultured species (three phylotypes) accounted for 20 (13.2%) of clones analysed. Fifty-eight (38.2%) of clones analysed (17 phylotypes) represented potentially novel species (Table

3

).

In total, 149 clones were analysed and 96 clones were sequenced across the three gingivitis samples. The bacteria identified (24 phylotypes) are grouped according to species in Table

2

. The predominant species was Porphyromonas cangingivalis (16.1% of clones analysed).

Table 2 .

 2 The predominant species was Desulfomicrobium orale (12.0% of clones analysed).

Uncultured species (four phylotypes) accounted for 14 (10.5%) of clones analysed. Forty-seven (35.3%) of clones analysed (17 phylotypes) represented potentially novel species (Table

3

).

Table 1

 1 Bacterial species identified by 16S rRNA gene sequencing of isolates obtained from three normal, three gingivitis and three periodontitis samples (all at least 98% identity). Unable to distinguish between species: 1 Family; 2 Phylum.

	Clarridge, J.E. III, 2004. Impact of 16S rRNA gene sequence analysis for identification of
	bacteria on clinical microbiology and infectious diseases. Clinical Microbiology Reviews 17,
	840862.
	Collins, M.D., Love, D.N., Karjalainen, J., Kanervo, A., Forsblom, B., Willems, A., Stubbs, S.,
	Sarkiala, E., Bailey, G.D., Wigney, D.I., Jousimies-Somer, H., 1994. Phylogenetic analysis of
	members of the genus Porphyromonas and description of Porphyromonas cangingivalis sp.
	nov. and Porphyromonas cansulci sp. nov. International Journal of Systematic Bacteriology
	44, 674-679.
	Fournier, D., Mouton, C., Lapierre, P., Kato, T., Okuda, K., Ménard, C., 2001. Porphyromonas
	gulae sp. nov., an anaerobic, Gram-negative coccobacillus from the gingival sulcus of various
	animal hosts. International Journal of Systematic and Evolutionary Microbiology 51, 1179-
	1189.
	Golden, A.L., Stoller, N., Harvey, C.E., 1982. A survey of oral and dental diseases in dogs
	anesthesized at a veterinary hospital. Journal of the American Animal Hospital Association
	18, 891-899.
	Gorrel, C., Rawlings, J.M., 1996. The role of a 'dental hygiene chew' in maintaining periodontal
	health in dogs. Journal of Veterinary Dentistry 13(1), 31-34.
	Hardham, J., Dreier, K., Wong, J., Sfintescu, C., Evans, R.T., 2005. Pigmented-anaerobic
	bacteria associated with canine periodontitis. Veterinary Microbiology 106, 119-128.
	Harvey, C. E., Emily, P.P., 1993. Periodontal disease. In: Harvey, C.E., Emily, P.P. (Eds.), Small
	Animal Dentistry. Mosby, St. Louis, USA, pp. 89-144.

*

Table 2

 2 Bacterial species identified by 16S rRNA sequencing of clones from three normal, three 397 gingivitis and three periodontitis samples: at least 98% identity. 398

		Normal	Gingivitis	Periodontitis
	Species	No. of clones	No. of clones	No. of clones
		analysed	analysed	analysed
		(% of total)	(% of total)	(% of total)
		n=152	n=149	n=133
	Acinetobacter junii			1 (0.8)
	Acinetobacter sp.	1 (0.7)
	Actinomyces hordeovulneris		1 (0.7)
	Actinomyces sp.	1 (0.7)	1 (0.7)	11 (8.3)
	Bergeyella sp.	5 (3.3)	6 (4.0)
	Capnocytophaga canimorsus		1 (0.7)	2 (1.5)
	Capnocytophaga cynodegmi		6 (4.0)	10 (7.5)
	CDC Group NO-1		1 (0.7)
	Clostridiales bacterium (oral) 3			6 (4.5)
	Clostridium sporogenes / botulinum*	1 (0.7)
	Desulfomicrobium orale			16 (12.0)
	Filifactor villosus		4 (2.7)
	Fusobacterium russii		2 (1.3)
	Gemella palaticanis	1 (0.7)
	Klebsiella pneumoniae	1 (0.7)
	Methylobacterium radiotolerans	1 (0.7)
	Moraxella bovoculi		3 (2.0)	3 (2.3)
	Moraxella canis			1 (0.8)
	Moraxella nonliquefaciens	1 (0.7)
	Neisseria canis		1 (0.7)
	Orodibacter denticanis		2 (1.3)
	Pasteurella canis		5 (3.4)	4 (3.0)
	Pasteurella dagmatis			5 (3.8)
	Peptococcus sp. (oral)		3 (2.0)
	Peptoniphilus sp. 'Oral Taxon 386'			2 (1.5)
	Peptostreptococcus sp. (oral)			5 (3.8)
	Porphyromonas cangingivalis		24 (16.1)	2 (1.5)
	Porphyromonas canis		1 (0.7)
	Porphyromonas canoris		8 (5.4)	1 (0.8)
	Pseudomonas sp.	47 (30.9)
	Psychrobacter pulmonis	2 (1.3)
	Salibacillus sp.	1 (0.7)
	Serratia grimesii	3 (2.0)
	Serratia proteomaculans	2 (1.3)
	Serratia proteomaculans quinovora	1 (0.7)
	Simonsiella steedae	2 (1.3)

Acknowledgements

We thank the Royal College of Veterinary Surgeons Trust for their financial support and Dr David Lappin for carrying out the statistical analysis.

A c c e p t e d M a n u s c r i p t 13 In conclusion, a wide range of bacteria is present in the oral cavity of healthy dogs and those with gingivitis and periodontitis and a distinct microbial flora appears to be associated with each of the three groups. Potentially novel bacterial species may play a significant role in gingivitis and periodontitis.

Conflict of interest statement

The authors have no conflicts of interest.

A c c e p t e d M a n u s c r i p t