S Binczak

T Sliwa

S Jacquir

J M Bilbault

Reaction-Diffusion Network For Geometric Multiscale High Speed Image Processing

Keywords: Image analysis, Multiscale geometry, Nonlinear signal processing PACS: 87.57.Nk, 07.05.Pj, 05.45.a

In the framework of heavy mid-level processing for high speed imaging, a nonlinear bi-dimensional network is proposed, allowing the implementation of active curve algorithms. Usually this efficient type of algorithm is prohibitive for real-time image processing due to its calculus charge and the inadequate structure for the use of serial or parallel architectures. Another kind of implementation philosophy is proposed here, by considering the active curve generated by a propagation phenomenon inspired from biological modeling. A programmable nonlinear reaction-diffusion system is proposed under front control and technological constraints. Geometric multiscale processing is presented and a discussion about electronic implementation is opened.

Introduction

Background framework of this work consists in the development of processing systems and their electronic implementation for high speed image intelligent sensors. Nowadays, many image processing techniques, particularly most of the linear or probabilistic ones, are included in real-time systems, but many families of mid-level techniques still remain unusable for such time processing requirements.

For high speed imaging applications, only some families of simple low-level techniques can be used, other techniques being applied on recorded data. For high speed imaging treatments, the approach of artificial retinas consisting in locating processing at the pixel stage gives some good results [START_REF] Kyuma | Artificial retinas -fast versatile image processors[END_REF][START_REF] Barbaro | A 100x100 pixel silicon retina for gradient extraction with steering filter capabilities and temporal output coding[END_REF][START_REF] Aubreton | Retina for pattern matching in standart 0.6 µm CMOS technology[END_REF]. However, an important disadvantage lies with this approach: Many treatments either remain very difficult to adapt to retinas architectures or imply development of specific architectures. To avoid this disadvantage, a generic way of image processing is proposed.

Mathematical morphology [START_REF] Serra | Image Analysis and Mathematical Morphology[END_REF][START_REF] Serra | Image Analysis and Mathematical Morphology[END_REF] has been specifically developed to meet image processing expectations. Therefore, it leads to solve a major part of image processing problems and is widely used. High speed electronic implementations of basic morphological operators as dilations have already been studied, for instance with the use of a nonlinear electronic network [START_REF] Binczak | Pattern dynamics in a nonlinear electrical lattice[END_REF]. However, the most important families of mathematical morphology treatments are based on two other main heavy operators which are geodesic reconstruction and watershed algorithm.

Different architectures have been built in order to implement these mid-level treatments [START_REF] Goldenberg | Fast Geodesic Active Contours[END_REF][START_REF] Paragios | Geodesic Active Contours and Level Sets for the Detection and Tracking of Moving Objects[END_REF][START_REF] Zarandy | Implementation of binary and gray-scale mathematical morphology on the CNN universal machine[END_REF], most of them using numerical technologies, able to do realtime image processing for usual speeds, but with a technological gap preventing high speed imaging applications.

In this context, a possible generalization of the geodesic dilation is explored by constraining its construction with compatibility regarding a second connexity notion linked to the regularity of the shape of the objects. It is not expressed algebraically, but through a more intuitive approach. In fact, geodesic dilation can be interpreted as a topological wave propagation starting from a marker whose evolution is defined by the structure of the image. PDE (Partial Differential Equations) are a very convenient tool to generate this propagation where features of the image are included as intrinsic parameters of the equations. Furthermore, some of the reaction-diffusion PDE include a notion of regularity for the propagation phenomenon. For some of them, it is even possible to adjust parameters defining the capacity of the wave to travel through straight zones, holes, breaks and so on. Therefore, it defines a kind of geodesicactive curve or region.

Another aspect is very important for the notion of objects' regularity: The scale from which the object is observed. But, carrying out multiscale analysis through successive multiple wave propagation is contrary to the high speed imaging technological gap. In order to reduce treatment times, the ideal case would be to achieve a multiscale analysis with only a one-pass wave propagation. In fact, a phenomenon producing propagation of wavefronts with increasing regularity along the height of the transition part is studied.

Besides, a systematic way of exploring dynamical systems described by PDE has been obtained by developing electronic circuits, which were very efficient for real-time analysis. These techniques led to analog computers, electrical lattices [START_REF] Scott | Active and nonlinear wave propagation in electronics[END_REF] or to the more general concept of Cellular Neural Network [START_REF] Chua | Cellular Neural Network: Theory[END_REF] (CNN). Although power computing has experienced an exponential growth, these dedicated systems have benefited from integrated electronics and still remain an alternative for high speed processing. Thus, it is possible to use this kind of electronic device to obtain propagation speeds allowing it to overcome the high speed imaging technological gap.

Therefore, the purpose of this study is to propose a reaction-diffusion system with interesting properties, defined under technological constraints in order to suggest an electronic implementation. This article is organized as follows: A choice of reaction-diffusion system is presented in section 2; then, the process of propagation of topological waves is studied according to the distribution of the local diffusive parameters. This provides a way to control the propagation paths of the travelling waves and to deduce a generic image processing method. In section 3, this image processing is applied on specific images, enabling edge restoration/ interpolation or one-pass multiscale approximation. This section is concluded by a preliminary result on grey level based segmentation, indicating that this system can lead to generic processing. Section 4 is devoted to open discussion on some possible implementation of an electronic circuit which could be able to perform high speed image processing. Finally, section 5 concludes and gives perspectives of this study.

A discrete bistable system as a Multiscale Regularity PDE

Not all interesting reaction-diffusion PDE have realistic electronic implementation. When dealing with regular lattice, the simplest way to connect nodes leads to the classical heat equation. Unfortunately, in this medium, no stable propagation waves can exist. In order to overpass this limitation, a possible modification is to use the most general reaction-diffusion equation :

dv n,m dt = D n,m v n-1,m + v n+1,m + v n,m-1 + v n,m+1 -4v n,m -f (v n,m ) . ( 1
)
From a dynamical system analysis, the minimum number of equilibrium points is three in order to assure the existence of stable propagating front wave with controllable shape. This leads naturally to the bistable equation.

In this section a study of the propagation in a system modeled by this equation is presented. It will be shown that, although this model is quite simple and its analog electronic implementation easily reachable, it allows the paths of propagating waves to be controlled, and therefore leads to deduce some interesting properties for image processing.

Let us consider a bi-dimensional regular discrete (N, M ) -length grid Ω on which the following bistable diffusive system is defined:

dv n,m dt = D n,m v n-1,m + v n+1,m + v n,m-1 + v n,m+1 - 4v n,m -v n,m (a -v n,m )(1 -v n,m ) , (2)
where D n,m is a local diffusion parameter, a a threshold parameter and v n,m corresponds to the information located at node (n, m) (for instance, the intensity value of the pixel (n, m)).

The system is completed by the Neumann conditions (zero-flux conditions) on the border ∂Ω of the definition domain Ω, so that

∂v n,m ∂η = 0 if (n, m) ∈ ∂Ω , (3)
where ∂ ∂η denotes the outer normale derivative at the boundary. In the following section, propagation phenomena emerging from this system are investigated, from which a generic image processing method is then deduced.

Wavefronts in the homogeneous grid case

For the sake of simplicity, we first consider the case where the local diffusion parameter is a constant so that

D n,m = D ∀(n, m) ∈ Ω . (4)
This particular system corresponds to a discrete version of the FitzHugh-Nagumo PDE (without recovery term) which was established to describe propagation phenomena in various biological systems. In a one-dimensional space, it allows the study of the electric propagation of the leading edge of an action potential, the neuronal information travelling along the membrane of the nerve fibers [START_REF] Scott | Neuroscience: A Mathematical Primer[END_REF][START_REF] Scott Edt | Encyclopedia of Nonlinear Science[END_REF]. Its discrete form (discrete Laplacian) corresponds to the myelinated nerve fibers case. In a continuous bi-dimensional space, it is widely used to study wavefront propagation in myocardial tissues [START_REF] Keener | Mathematical Physiology, Interdisciplinary applied mathematics[END_REF].

In the uncoupled case, i.e. when D = 0, v n,m = 0 and v n,m = 1, ∀{n, m} are two attracting steady states, while v n,m = a, ∀{n, m} is an unstable equilibrium point of the system, acting as a threshold.

In case of strong coupling, i.e. when D is large, we expect that a travelling wave will propagate depending on the value of a with a constant speed so that if a < 1/2 (a > 1/2 resp.), the steady state v = 1 (v = 0 resp.) will propagate at the expense of the steady state v = 0 (v = 1 resp.). When a = 1/2, no propagation occurs [START_REF] Binczak | Experimental propagation failure in a nonlinear electrical lattice[END_REF].

The response of the system, especially the shape of a wavefront, depends not only on the parameters of the system, but also on the initial conditions.

Let a marker be defined as a particular family of initial conditions for which v i,j (t = 0) = 1 for a set of (i, j) values, v k,l (t = 0) = 0 otherwise. The symmetry of the marker will determine the kind of travelling waves and its spatial shape. Among them, the two main propagating structures are the planar and the circular wavefronts. The following results are illustrated using numerical simulations obtained using a 4 th order Runge-Kutta algorithm.

Planar waves

They emerge from a rectangular marker, as illustrated in Fig. 1 and2 where two planar wavefronts propagate in opposing directions.

The symmetry induced by this choice of marker allows us to reduce the system to a one-dimensional space problem, expressed by:

dv n dt = D[v n-1 + v n+1 -2v n ] -v n (v n -a)(v n -1) . (5)
This system of equation has been widely investigated to study the neural propagation in myelinated nerve fibers. From these studies, some important results can allow us to characterize the process of propagation, although no explicit overall analytical expression of the wavefront is available.

In the first place, when the coupling between nodes is strong, the differentialdifference system (5) can be written, using a continuum approximation, so that

∂v ∂t = D∆v -v(v -a)(v -1) , (6)
where ∆ denotes the Laplacian operator. Using a travelling-wave analysis [START_REF] Binczak | Experimental propagation failure in a nonlinear electrical lattice[END_REF], one can express the propagation wave profile according to the travelling coordinate ξ = n -ut and initial conditions ξ 0 , and the unique velocity u of this topological wave as a function of D and a, so that

v(ξ) = 1 2 1 ∓ tanh[ ξ -ξ 0 √ 8aD ] (7)
u = ±(1 -2a) D 2 . ( 8
)
Eq. ( 7) indicates that the width of the wavefront decreases when D becomes smaller (this relationship remains valid even in a discrete system), while eq. ( 8) tells us how the parameter a controls the propagation, depending on its value in comparison with 1/2. In particular, it shows that the velocity increases when a decreases. Note also that the ± sign in eq. ( 8) corresponds to a bidirectional propagation. Qualitatively, these observations remain valid in the discrete case. For instance, Fig. 2 illustrates bidirectional wavefronts whose velocity is constant.

Nevertheless, a major feature due to discreteness is the failure of the propagation when D is smaller than a critical non-zero value D * > 0, which is missed in the continuum approximation. In this case, the wavefront is pinned [START_REF] Binczak | Experimental propagation failure in a nonlinear electrical lattice[END_REF][START_REF] Keener | Propagation and its failure in coupled systems of discrete excitable cells[END_REF][START_REF] Erneux | Propagating waves in discrete bistable reactiondiffusion systems[END_REF],

as illustrated in Fig. 4. From [START_REF] Erneux | Propagating waves in discrete bistable reactiondiffusion systems[END_REF], an asymptotic expression of this parameter when a -→ 0, is

D * = 1 4 a 2 , (9)
which is in accordance with the results presented (In this case D * = 0.0025).

Circular wave

This kind of travelling wave emerges when the marker tends to be circular, or has a circular symmetry, as illustrated in Fig. 3.

The spatial shape determines the velocity of the wavefronts, so that, in a continuous system [START_REF] Fast | Role of wavefront curvature in propagation of cardiac impulse[END_REF], a convex travelling wave propagates slower that a planar one. This behaviour matches the comparative results in Fig. 4 when the diffusive parameter D becomes large enough.

As D decreases, the wavefront width becomes smaller, emphazing the discreteness of the system. Therefore, a circular distribution along discrete nodes is no longer possible, and is transformed into a combination of planar waves with different wave vectors. As a consequence, "circular wave" and planar wave velocities eventually merge as D decreases. In addition, propagation fails for the same value D * of D. From now on, we will assume that D * is not a function of the kind of travelling waves, but only determined by the threshold parameter a.

Wavefronts in an inhomogeneous grid case

Dramatic in biological systems, the propagation failure phenomenon can be useful to develop new approaches in image processing. Contrary to classic cases, the point of interest is indeed the blocking case, allowing the path of the topological travelling wave to be controlled and leading to mid-level image

processing. An image is then defined as a discrete bi-dimensional grid where nodes correspond to pixel sites. Each node is coupled to its nearest neighbours in a diffusive manner weighted by the local intrinsic information of the image.

The main idea is to initiate a wavefront and let it propagate until it reaches an object Θ to be detected. In order to prevent further propagation, we now impose the following rule in eq. ( 2):

D n,m =                D p > D * if (n, m) / ∈ Θ 0 othervise. (10)
As D p > D * , propagation is possible if an appropriate marker is set outside the object. In a complementary way, D = 0 within the object, pins this wavefront at its borders, as illustrated in Fig. 5: The object is composed of two horizontal strands whose nodes are uncoupled. A rectangular marker is set at the top lines of the grid initiating a planar wave propagating along the vertical axis. Due to the propagation failure criterium, this wave stops at the border of Θ and can only extend through the corridor separating the two parts of the object. Because of this symmetry breaking, a circular wave emerges and propagates in the bottom part of the grid. Eventually, a stationary state is obtained so that the whole object is surrounded by the final state v = 1.

In addition, other new features appear from this inhomogeneous coupling. As presented in Fig. 6, a wavefront can not only be blocked due to the parameters of the system, but also to its geometry.

Compared to the case of Fig. 5, the wavefront is pinned in the corridor, leading to another final state, because of a larger diffusive parameter D p . The corresponding mathematical mechanism leading to this blockage is based on the existence of a stationary wave due to a maximum curvature prohibiting the emergence of a travelling wave. To put it simply, a larger width of the wave implies that the wave cannot propagate through narrow paths. Note that this result can also be observed in a bidimensional continuum space [START_REF] Fast | Role of wavefront curvature in propagation of cardiac impulse[END_REF][START_REF] Jacquir | A Theoretical Approach of the Propagation through Geometrical Constraints in Cardiac Tissue[END_REF].

A systematic study of the relationship between the diffusive parameter D, the width W and the thickness T of the corridor is presented in Fig. 7. The results indicate that there exists a critical value D m above which no propagation can emerge from the corridor. Obviously, the larger and thinner the corridor is, the wider a propagating wave can be, therefore, D m increases. As discussed in the following section, this property can be interesting to integrate objects or to delevop active curves.

In all the previous cases, it was implied that a marker necessarily generates a travelling wave. Actually, specific initial conditions are to be taken into account depending on the parameters of the system [START_REF] Neu | Initiation of propagation in a onedimensional excitable medium[END_REF]. More precisely, there exists a threshold surface for which the nodes must be above the excitation threshold a to ensure the initiation of a fully developed travelling wave. If an initial condition does not satisfy this requirement, the initial surface being smaller than the threshold one, then it decays to zero. Let us restrict this problem to initial conditions corresponding to a square marker of side W , as defined previously.

The results are presented in Fig. 8, showing that the size of the marker is a function of the diffusive parameter D. As the system becomes more diffusive, the marker is more spread on the grid, implying that fewer nodes will be above the excitation threshold. The purpose of our study is to initiate a propagation from a marker of whatever size. Therefore, we impose these initial conditions as Dirichlet ones, by setting the following Marker-rule:

D n,m = 0 if (n, m) ∈ M arker (11)
It corresponds to a forced propagation condition, implying the always successful initiation of a propagating wave [START_REF] Erneux | Propagating waves in discrete bistable reactiondiffusion systems[END_REF], if the local diffusive parameter D in the neighbourhood of the marker is above propagation failure criterium D * .

A Generic Image Processing Method

Now let us build a generic image processing method. For this, we will use the marker principles of geodesic mathematical morphology with the possibility of combining them with other image processing techniques.

A and B will denote sets or, with the same notation, indicate set functions, but they are more generally intended to be greyscale image quantities as different transforms of intensities, including duality to allow most possible types of operators, of the norms of local vectors of directional derivatives, or even of scalar-type results of other image processing as for example linear filtering.

A and B can be determined from the same image or from different images.

Here A will represent binary markers from which the propagation phenomenon starts, and B the topological constraint derived from the image. The couple of scalar discrete functions (A, B) defines the following equation:

E ε (A, B) =                                                                                          dv n,m dt = D(B) ε v n-1,m + v n+1,m + v n,m-1 + v n,m+1 -4v n,m -f a (v n,m ) f a (v) = v(a -v)(1 -v) with a < 1 2 D(B) = 1 + tanh(20B -12) 2 v| t=0 = A (12)
Here a will have the value 0.1 and the definition domain Ω will be the (n, m)length grid.

The system is completed by the Neumann conditions (zero-flux condtions) on the border ∂Ω of the definition domain Ω.

The Marker-rule expressed by eq. ( 11) is supposed set, otherwise specified.

This choice of constructing D(B) corresponds to a bimodal distribution of the local diffusive parameter separated by D * , allowing the control of the propagating paths.

The propagation phenomenon defined by E tends to a convergence state noted v ∞ ε (A, B), theoretically corresponding to infinite t but practically a millisecond value will be sufficient in most cases. v ∞ ε (., B) is idempotent if eq [START_REF] Chua | Cellular Neural Network: Theory[END_REF] is set or not, in the mean of

v ∞ ε (A, B) = v ∞ ε (v ∞ ε (A, B), B) . (13)
Depending on ε, several properties arise:

• v ∞ ε (., B) tends to identity, when ε -→ +∞, • v ∞ ε (A, B) -→ 1 Ω , when ε < min(D(B), D m ), if the marker rule is set, • v ∞ ε (A, B) -→ 1 ⊘ , when ε < min(D(B), D m ), if the marker rule is not set.
Then, let us define the main image processing operator as:

Φ ε,h (A, B) = {v ∞ ε (A, B) ≥ h} . ( 14
)
The propagation phenomenon is similar to the geodesic propagation, but with an additive scale of regularity constraint, defined by the couple variables (ε, h)

with ε defining the magnitude order of the scale of regularity of the one-pass propagation and h a thresholding along the scale regularity consequently to the choice of ε in the final result when the propagation is definitively blocked by the topological constraint. It is equivalent to fix ε and deduce h or to fix h and deduce ε. Eq. ( 14) leads to the immediate following properties:

• When ε -→ 1 + /D * , Φ ε,h (A, B)
approaches the geodesic reconstruction of B marked by A.

• Φ ε,h (., B) increases with fixed regularity scale parameters and increases with its two regularity scale parameters increasing independently.

• Φ ε,h (A, .) decreases with fixed regularity scale parameters and decreases with its two regularity scale parameters increasing independently.

It allows the generation of many morphological-type analysis techniques, constructed as classic techniques through the morphological theory, but with some advantages from the point of view of active curves (considering the evolving front) or regions (considering the interior of the evolving curve) as their greater regularity, without the topological problems of the deformable templates. Warning: if the Marker-rule is not imposed, there is no strict extensivity property but the authors think that a low extensivity property depending on the observation scale could be defined, extending algebraic closing, opening, granulometries, convexity spectra and so on.

As illustrated by the numerical study, ε plays the role of a main geometric scale parameter and h a secondary geometric scale parameter. The > sign produces an active geodesic region approach, < producing a dual region approach, whilst replacing it by = produces an active geodesic curve approach.

Other operators can be derived from the extrema of the Φ ε,h (A, B) function.

For the following section, c represents 1/ε.

Numerical Study

In this section, we characterize the propagation of waves in more complex and representative structures. The aim of this section is to extract from simple geometric cases the effects of topological and morphological structures on the propagation in order to illustrate (by using a 4 th order Runge-Kutta algorithm) its generic image processing possibilities. Among them, we focus on the ability of this system to reveal some multi-scale geometric information. Finally, we

show that segmentation processing can also be reached.

Scale and propagation blockage

First, we illustrate the effect of the scale factor on the propagation break. We turn to the geometrical aspect, so binary images are sufficient. In this case, D(B) is nearly equal to B which comes directly from the image. Figure 9 shows the sifter behaviour of the propagation: Its capacity to propagate through a corridor. For a given c, there exists a minimum corridor width above which waves can propagate though. The marker is the same in each case, but c is not the same for each propagation: It is growing from left image to right image.

It works as if we were looking at the corridor from a higher distance: It seems to become thinner and thinner. Then, we can see that the minimum corridor propagation width is growing with c.

For a given c, the Fig. 10 illustrates that the propagation blockage has an isotropic aspect, in the case where the size of the geometrical features of the image is sufficiently large compared to the size of the mesh of the system.

Figure 11 illustrates the same behaviour but with a rather porosity effect: the more c increases, the less propagation penetrates in the porous medium.

In a sense, propagation becomes more visquous. It could be interpreted as if each elementary part of the propagation front was blocked by a virtual dilation whose size is determined by the scale c. Therefore, c can also be denoted as the "scale of observation". Note that it acts as if this scale determines a size for a class of discrete negligible details. It is also true for the marker, if the Marker-rule is not used: If its measure is under this minimal size, it is equivalent to the null region and the propagation falls before disappearing to the null function.

This viscosity aspect induces an immediate property of interpolation or restora-tion of the geometric borders, with c determining the capacity of interiors/exteriors separation of the propagation phenomena, as illustrated in Fig. 12.

One-pass multi-scale approximation

Figure 13 shows that, when using sufficient c, the propagation acts like a viscous gauge, producing a viscous hull-like effect: The object is located between the two final states, allowing the definition of an area of interest in the image.

Then, we can see in the following Fig. 14, with levelling the result of this one pass propagation, that we obtain multiscale geometric information: Lower levelling produces higher level of details and higher levelling produces a higher level of approximation.

If we push the levelling to its limits, we can almost obtain the initial shape of the object for very low levelling and sorts of approximation hulls for levelling near one. This scale aspect of h depends on the primary scale determined by c: In fact, it is a secondary variation parameter around a sort of mean scale parameter. If c is higher, it produces a panel of viscous-hulls.

If c is smaller, it produces a panel of de-noised interiors/exteriors. A middle c produces a sort of progressive elimination of breaks of the initial shape. The value of c has to be adjusted depending on the application aim. An interpretation of means of measure of defects on manufactured objects on output of a production plant could be profitable: In a one go, it allows the quantification of noise, breaks and distortion/deformation, through a measure-function consisting in extracting one or more attributes for each h, giving a description of the shape. It can also be seen as a multiple pre-processing step between other treatments, leading to obtain more robust final results. With another kind of markers (grid-like ones for example), it could even be used for characterizing patterns. Moreover, identifying relationships between scale and length or surface of penetration (in the case of porous media for example), fractal spectrum-like descriptors could be obtained, leading to facilitate the distinction between rugosity and noise.

Note also that some fusion/separation aspects appear when h varies, allowing the subdivision of geometric parts of objects, as if successively adding the effects of several centrum of propagation. Therefore, we can view the object as with a multiple geometric description, all this in one go. Indeed, there is an effect of front touch which could certainly be used for SKIZ-like based image processing algorithms. In all situations, it can imply artificial retinas allowing the storage of multiple scale geometric analysis in the level of the output of one stationary state from an electronic network based only on variable couplings.

It is also possible to consider the multiscale geometrical analysis as a fuzzy segmentation function, as shown in Fig. 15. Here, the main scale parameter is high and the secondary scale parameter defines the connection between objects. As a first approach, we have a global group of objects, then divided into two groups with a large connection or not, and finally into four elementary objects. In fact we have multiple second connectivity distributed in a hierarchical structure due to its monotony regarding the level parameter, as for segmentation trees, but here stored in an image result. This can be considered as a fuzzy result and manipulated through fuzzy operators with other image results in order to obtain an analysis with multiple descriptions. This kind of technique could be used for sensor fusion information.

Grey level based segmentation

In order to obtain grey level based segmentation, it is straightforward to include an estimation of the gradient information in the topological constraint derived from image, that is B. B has naturally to vary in a monotonic way with gradient. For simplicity, the choice of B has been realized by including a normalization on a power function of the gradient magnitude. Finally, with the following Fig. 16, we illustrate the result produced with :

B = 1 - |g X + ig Y | 1/4 max Ω (|g X + ig Y | 1/4 ) , (15)
where g X is the numerical gradient of the image, corresponding to the differences in the row direction and g Y is the numerical gradient of the image, corresponding to the differences in the column direction. Note also that for a complete segmentation, we could, for instance, use a grid of markers. An important remark, when dealing with grey levels, is that the propagation depends not only on the density of the obstacle but also on its height, therefore the choice of B may not be trivial. To conclude, the choice of B and the evaluation of corresponding segmentation performance is a major point which has to be systematically explored in a future work.

Electronic Implementation

In order to reach high speed image processing, a specific programmable electronic device has to be conceived. However, it is not attended in this section to present an existing system but rather give a realistic scheme on how it could be realized. A possible electronic implementation for such tasks could be composed of a specific analog device controlled by a digital part. The major reasons are:

• to take advantage of the very fast signal processing character of analog circuits,

• to benefit from the fexibility of digital systems,

• to design it as a complement of classic numerical systems. The architecture of the analog network is presented in Fig. 18, details of which are shown in Fig. 19.

Initially, each capacity of each node is disconnected from the network, so that the markers can be introduced by loading the capacities (acting as analog V sync and resetting the digital counter. As the capacitors are now connected, using Kirchhoff's laws, the corresponding equations are

I n,m = g m (n, m) (V n-1,m -V n,m ) + (V n+1,m -V n,m ) + (V n,m-1 -V n,m ) + (V n,m+1 -V n,m ) (16)
I n,m = C dV n,m dt -I nl (V n,m ) , (17)
where I nl (V n,m ) is the current-voltage relationship of the nonlinear circuit. As the differential output voltage of the cascaded Gilbert cells [START_REF] Gilbert | A precise four-quadrant multiplier with subnanosecond response[END_REF] is connected to this input of an OTA, this current can be expressed so that, assuming that the devices are unsaturated,

I nl (V n,m ) = -g m K 2 V n,m (V n,m -a)(V n,m -1) , (18)
where K is a multiplicative intrinsic constant of the Gilbert cell.

Note that this cubic function could be also realized by a less precise but more compact low voltage circuit as in [START_REF] Cosp | Programmable VLSI Cubic-Like Function Implementation[END_REF]. From eqs ( 16) and [START_REF] Fast | Role of wavefront curvature in propagation of cardiac impulse[END_REF], and after normalization, the system of equations modeling the network becomes

dV n,m dτ = D n,m V n-1,m + V n+1,m + V n,m-1 + V n,m+1 - 4V n,m -V n,m (a -V n,m )(1 -V n,m ) , (19)
with D n,m = g m (n, m) g m K 2 and the rescaled time τ =

g m K 2 C .
The fact that K ≫ 1, g m ≫ 1 and C, chosen so that C ≪ 1 lead to obtain a very fast image processing network (τ ≫ 1). The treatment is stopped by switching off the analog commutators, after the counter reaches a specified value, as proposed in Fig. 17. Another possibility could be to compare the state of the system at periodic times to check if it reaches stationarity. The final result is then loaded by the digital board via ADC (Analog-to-Digital Converter).

Conclusion

The authors have proposed a nonlinear electronic network inspired from transmission phenomena in biological systems. It allows the conception of circuits for high speed image processing based on front propagation principles. This article illustrates this on an active region algorithm, making a parallel between the point of view of morphological geodesic reconstruction and a-priori the more robust active curve approach, with the idea of using the different scales of regularity of the bistable propagation along the height of its front. Even if this efficient method is rather heavy, the article shows that an adapted physical implementation can overcome a technological break point. Therefore, it could generalize, for instance, the use of deformable templates. Further works will concern on the one hand the generalization of electronic front propagation manipulation (how to determine B is the key point) in order to expand the field of applicable treatments and on the other hand the study of SOC (Systemon-Chip) possibilities, especially by adding FPGA based controller adapted to complex decompositions and allowing the completion of treatments by linear and probabilistic parts for example, mixing analog and numeric methods, in order to create a specific high-level programming and controlling system for "artificial retina"-type high speed image processing. High speed intelligent For this example, the marker rule is not set.

List of captions

  The subsequent values D n,m are shown in the bottom right inset of Fig. 16. In this example, two markers are imposed, one in the background between the two columns, and the second one, inside the right cheek (see the top left inset). The blocked frontwaves are presented in the top right inset and in superimposition with the initial image in the bottom left inset. The results indicate that this choice of B gives a very good greyscale segmentation for both areas.

Figure 17 shows

 17 Figure 17 shows how the different parts of the treatment can be shared out. This mixed-signal architecture is split into three different parts: Two digital and one analog. The diffusive coupling D n,m is extracted depending on the choice of B and the location of the marker(s). Because of multiple choices, this task is digital. The resulting values are then set in the analog network via DAC (Digital-to-Analog Converter).

  memories). The local diffusive couplings D n,m are set by a multiplexing logic, by controlling the forward transconductance g m (n, m) of the OTAs [21] (Operational Transconductance Amplifier) of the coupling circuit via the associ-ated polarization currents. The initialization part is finished by simultaneously switching on the analog commutators via a synchronization control voltage

Figure 1 :

 1 Figure 1: A planar wavefront propagation using a greyscale representation where white corresponds to v = 1 and black to v = 0. The top left inset shows the marker. The other insets illustrate the propagating wavefronts at different times (in arbitrary units). Parameters: a = 0.1 and D = 1. Results obtained from numerical simulations (4 th order Runge-Kutta algorithm) of eq. (6).

Figure 2 :

 2 Figure 2: v 100,n at different times corresponding to the insets of Fig. 1, illustrating the constant velocity. The dotted line shows the marker, the continuous lines, the propagating wavefront at t = 40, 80 and 120 a.u.. Parameters : a = 0.1, D = 1. Results obtained from numerical simulations (4 th order Runge-Kutta algorithm) of eq. (6).

Figure 3 :

 3 Figure 3: A circular wavefront propagation using a greyscale representation where white corresponds to v = 1 and black to v = 0. The top left inset shows the marker. The other insets illustrate the propagating wavefronts at different times (in arbitrary units). Parameters: a = 0.1 and D = 1. Results obtained from numerical simulations (4 th order Runge-Kutta algorithm) of eq. (2).

Figure 4 :

 4 Figure 4: Propagation velocity versus the diffusive parameter D. Numerical results comparison between planar wave speed (continuous line) and circular wave speed (dotted line). Parameter : a = 0.1.

Figure 5 :

 5 Figure 5: Propagation of a wavefront in an inhomogeneous grid. Inset (a) shows the initial marker and an object Θ. Inset (b) shows the wavefront crossing the corridor (of width W and thickness T) separating the two parts of Θ at t = 100 a.u.. Inset (c) shows the propagation of a circular wave emerging from the corridor at t = 200 a.u.. Inset (d) shows the final stationary state, obtained at t = 300 a.u.. Parameters: a = 0.1, D = 1, W = 6 nodes, T = 4 nodes.

Figure 6 : 2 Figure 7 : 1 Figure 8 :

 62718 Figure 6: Unsuccessful propagating wave via a corridor a=0.1, W=6 nodes, T=4, D=1.2

Figure 9 :

 9 Figure 9: Sifter effect (Top: shape, middle: marker, bottom: propagation blockage) for different values of c: From left to right: c = 0.25 to c = 4.75 by incremental steps of 0.75.

Figure 10 :

 10 Figure 10: Isotropy (Top: shape, middle: marker, bottom: propagation break) in the case where c = 2.

Figure 11 :

 11 Figure 11: Scale aspect of c: Porosity effect (up: shape and marker, down: propagation blockage for increasing values of c from left to right and from top to bottom: c = 0.1 to c = 1.75 by incremental steps of 0.15).

Figure 12 :

 12 Figure 12: A simple example of edge restoration/interpolation with an interior marker in the case where c = 3. Left: starting configuration, Right: final configuration.

Figure 13 :

 13 Figure 13: Scale aspect with high c: Hull effect (with interior and exterior markers). Left: Final state. Right: Shape and markers. Parameter: c = 8.

Figure 14 :

 14 Figure 14: Secondary geometrical scale aspect of h. From left to right, then top to bottom, h increases in a ratio-2 geometrical manner from h = 0.0078 to h = 0.996. c = 8.

Figure 15 :

 15 Figure 15: Multiscale segmentation in one-pass in the case where c = 8. The top insets show the marker and the starting configuration (right) composed of four parts separated by 11 nodes vertically and 15 nodes horizontally and the final state (left). The resulting fuzzy segmentation is obtained, from left to right then top to bottom, for h = 0.35, h = 0.5, h = 0.7 and h = 0.996.

Figure 16 :

 16 Figure16: Grey level segmentation of the noisy regions "background between columns" and "right cheek", starts with small markers. From left to right

Figure 17 :

 17 Figure 17: Scheme of the mixed-signal architecture.

Figure 18 :

 18 Figure 18: Analog network.

Figure 19 :

 19 Figure 19: Detail of the analog network.

  Fig. 1.

  Fig. 3.

  Fig. 6.

  Fig. 8.

Fig. 9 .

 9 Fig. 9.

Fig. 10 .

 10 Fig. 10.

Fig. 11 .

 11 Fig. 11.

Fig. 12 .

 12 Fig. 12.

Fig. 13 .

 13 Fig. 13.

Fig. 14 .

 14 Fig. 14.

Fig. 15 .

 15 Fig. 15.

sensors development for the industry is one aim for these works.


Mathilde S A Deloire

Aurélie Ruet

Delphine Hamel

Melissa C Bonnet

Vincent Dousset

Bruno Brochet

MRI predictors of cognitive outcome in early

Keywords: Adult, Biological Markers, Cognition, physiology, Cognition Disorders, etiology, pathology, physiopathology, Female, Humans, Longitudinal Studies, Magnetic Resonance Imaging, methods, Male, Middle Aged, Multiple Sclerosis, complications, pathology, physiopathology, Neuropsychological Tests, Predictive Value of Tests, Regression Analysis Multiple sclerosis, Brain atrophy, Ventricular fraction, Cognition, Magnetic resonance imaging

INTRODUCTION

Cognitive impairment is an important feature of Multiple Sclerosis (MS) and may affect everyday activities. Deficits in memory, information processing speed (IPS), attention, working memory, and executive functions are frequently seen . Cognitive dysfunction has 1 long been considered to be confined to patients at later stages of the disease but such impairments have been described in clinically isolated syndromes (CIS) and in early relapsing-remitting MS (RRMS) . 2 3 The association between cognitive deficiencies and several magnetic resonance imaging (MRI) markers, including lesion load (LL), diffuse brain abnormalities and brain atrophy, has been investigated . However, little is known about the value of these parameters at the 1 early stages of MS to predict cognitive decline over time and the value of magnetization transfer (MT) imaging parameters. We designed a longitudinal study in newly diagnosed clinically definite MS (CDMS) patients to investigate MRI markers predictive for deteriorating cognitive function. Cross-sectional data at baseline showed that cognitive impairment was associated with MR parameters evaluating diffuse brain damage . We hypothesized that diffuse brain damage outside lesions in early RRMS detected at baseline and their change 3 over 2 years predict the deterioration of cognitive performance over 7 years. Baseline values of various MR parameters, including LL, MT ratio (MTR) metrics, and global and central atrophy, and their change over 2 years were investigated for predicting the deterioration of cognitive performance over 7 years.

METHODS

Patients and controls

Fifty-eight patients, diagnosed with RRMS within the previous six months without other selection criteria, were included by the coordinating centre between November 2000 and November 2001. Patients were consecutively referred by practicing neurologists from a neurological network in south western France for the purpose of that study. None of these patients received disease-modifying therapies before the second exacerbation.

One patient was excluded from the study due to reconsideration of the MS diagnosis. Forty-four patients (77.2 ) completed all % evaluations during the 7-year study period and were used for the analysis. All patients underwent clinical and cognitive assessment at baseline (year 0) and after years (y) 1, 2, 5 and 7, and underwent brain MRI at y0 and y2. A sample of 56 healthy subjects matched for sex, age, and educational level was also studied at baseline. Baseline clinical, imaging, and cognitive characteristics of patients and controls have been published previously .

3

Standards Protocol Approvals and Patient consents

The study was approved by the institutional review board (CPP Bordeaux 2000/28) and patients gave written informed consent.

#

Clinical evaluation

Clinical evaluation included Expanded Disability Status Scale (EDSS), Multiple Sclerosis Functional Composite (MSFC), and Montgomery and Asberg Depression Rating Scale (MADRS).

Neuropsychological assessment

The neuropsychological assessment was previously described in detail . Stroop, similarities, Boston and RFF tests) and for all tests at y1, 2 and 5 follow-ups were not used in this report, because no alternate forms were used.

At baseline, patients were classified as patient cognitively impaired (PCI) if they performed less than the 5th percentile of matched controls on at least two tests of the battery (n 22) and patient cognitively unimpaired (PCU) if they did not (n 22).

= =

At each time point, the raw scores of each cognitive score were transformed to z scores using the mean and standard deviation (SD) baseline scores of the 44 patients as the reference data. Z scores were used to study longitudinal changes of cognitive tests and correlations. Additionally, two domain-specific z-scores were created for memory (SRT-LTS, SRT-CLTR, SRT-DR, SPART and SPART-DR) and IPS (SDMT, PASAT 3s and 2s).

MRI evaluation

Image acquisition

Methods for image acquisition and analysis have been detailed previously . Brain MRI scans were obtained on a Philips Gyroscan 3 ACS-NT 1.5 T scanner, including Fast Fluid-Attenuated Inversion-Recovery (FLAIR) images (TR/TE/TI: 11000/140/2725), MT images using a proton density sequence (TR/TE: 37/2.3 and flip angle 8) both with and without an MT saturation pulse, and T1-weighted images = (TR/TE: 450/12) before and after administration of gadolinium-DTPA (0.1 mmol/Kg). For all sequences, 26 contiguous interleaved axial slices were acquired with 5 mm slices, 256x256 matrices and 230 230 fields of view. The slices were positioned to run parallel to a line × joining the most inferoanterior and inferoposterior parts of the corpus callosum.

Native and pre-processed data were displayed on workstations running software developed by Bio-Clinica, Inc. (Lyon, France).

Following parameters were considered in the analysis: LL, Brain Parenchymal Fraction (BPF), which is defined as the ratio of whole brain parenchyma volume to the intracranial volume , Ventricular Fraction (VF), defined as the ratio of ventricular volume to the intracranial 4 volume , and means of lesion and normal-appearing brain tissue (NABT) MTR masks. 5

Statistical analysis

Statview version 5.0 (Windows) was used for statistical analysis. Matching between MS patients (n 44) and healthy controls (n 56)

= =
was verified using the Chi square test for gender and the t test for age and years of education. For each score, the percentages of patients deteriorating or improving more than 1.0 SD of controls scores or stable over 7 years were calculated in whole group, PCI and PCU groups. For IPS and memory domains, patients were classified in the deterioration group if they have more than one SD decrease based on baseline scores of healthy controls. Additionally, at the follow-up evaluations, the patients were considered cognitively deteriorated according to their deterioration score modified from Kujala . For each domain (IPS, memory), if the subject scored below 1.0 SD 6

compared with the norms, he/she received one deterioration point; if below 1.5 SD, two; if below 2.0 SD, three. All comparisons were -performed using the t test when distribution of values was normal or by non parametric Wilcoxon test when it was not.

Participants who fulfilled all follow-ups were compared to the original sample with regard to demographic data (age, gender, and years of education), baseline neuropsychological scores, EDSS, MSFC, MADRS, disease duration; LL, MTR means, BPF, and VF.

Differences were considered significant, for all analyses, when p values were less than 5 . Correlations between change in cognitive % scores and MADRS scores were studied by Pearson s correlation coefficient. Logistic regression analyses were also performed (see

[ ] [ -] [ -] = -
in both groups (in CI : 3.0 0 18 at baseline and 11 0 46 at y7, p 0.017, z 2.39, in CU : 4.0 0 21 at baseline and 10.5 0 31 at y7, p

[ -] [ -] = = - [ -]
[ -] = 0.004, z 2.80).

= -

Median EDSS deteriorated between y0 (2.0 0.0 5.5 ) and y7 (2.5 0.0 8.0 ) (p<0.001, z 3.586). but the MSFC did not change '

Regression analyses ( ) Tables 4

For memory or IPS z scores change over 7 years as dependent variable, two multiple regression models were performed with (i) baseline MRI parameters (LL, mean lesion MTR, BPF, VF and mean NABT MTR) as independent variables and (ii) MRI changes over 2 years (LL, mean lesion MTR, BPF, VF and mean NABT MTR). In univariate linear regression analyses, memory z score change over 7 years was associated with baseline LL and mean NABT MTR and with VF changes over 2 years. IPS z score change over 7 years was correlated with baseline MRI parameters (LL, BPF, VF and mean NABT MTR) and with VF and BPF changes over 2 years (all p value <0.05, see

). Parameters with p<0.25 in univariate analyses and the baseline EDSS were entered in the two multivariate models ( Table 4 ). After stepwise elimination, the only independent predictor of memory decline was the baseline NABT MTR. After stepwise Table 4 elimination, baseline NABT MTR and BPF and 2 years change of VF remained in the models for prediction of IPS decline.

No MR parameter predicted WLG z score change in multivariate analysis.

DISCUSSION

This study emphasizes the frequency of cognitive deterioration in the early stages of MS. This deterioration, which may have many impacts in the daily life of patients, including working and social activities, needs to be detected in order to adapt therapeutic strategies.

The present study was designed to determine which MR parameter, measured early in MS course, could help predict subjects who will deteriorate. The results showed that MRI parameters reflecting diffuse brain damage (BPF, VF and mean NABT MTR) predict more strongly cognitive deterioration than lesions.

The mechanisms of cognitive dysfunction in MS are not fully understood, but convergent evidence suggests that disconnection between cortical areas might be the basis of this dysfunction . Although focal lesions might contribute to this disconnection, several 9 cross-sectional studies using diffusion and MT imaging suggested that axonal damage largely contributes to cognitive alterations by interrupting critical networks , . In the present longitudinal study in early MS we observed that baseline NABT MTR, which 3 9 -15 reflects diffuse brain injury accumulated so far, but no MR parameters studying focal lesions, predicts cognitive changes over 7 years in the two main domains memory and IPS, in multivariate analyses. Although, LL was associated with cognitive outcome in univariate analyses, it did not remain in multivariate models. These results confirmed the importance of diffuse brain damage in cognition alteration in RRMS. Such disconnections could interfere to the allocation of brain resources for a specific task and may explain that the most common cognitive impairment in MS concerned IPS . [START_REF] Forn | Information-processing speed is the primary deficit underlying the poor performance of multiple sclerosis patients in the Paced Auditory Serial Addition Test (PASAT)[END_REF] Recent reports have shown correlations between cognitive disabilities and central atrophy and are in agreement with the hypothesis that disconnection between the sub-cortical and cortical structures involved in these networks may contribute to cognitive dysfunction 17 -

. Although atrophy measures did not correlate with cognitive functions at baseline , baseline BPF, a measure of global atrophy and 23 3

two-year VF change, a measure of central brain atrophy predict decline in IPS performance over 7 years. Although periventricular white-matter atrophy could contribute to VF change, and in particular corpus callosum atrophy, which has been implicated in cognitive impairment in MS , it is likely that damage of the deep gray-matter and the surrounding white matter is determinant in cognitive 24 deterioration affecting IPS in early RRMS. These results are in agreement with a recent study that analyzed the rates of atrophy in different parts of the brain and correlated them to various clinical indexes including the PASAT as part of the MSFC . The authors found that a 25 worse performance on the PASAT at follow-up was predominantly related to atrophy development around the ventricles and, to a lesser extent, brainstem atrophy.

Several studies investigated the association between MR parameters and cognition evolution in RRMS but none used MT imaging.

One study showed that one-year global atrophy rate was associated with cognitive deficiencies measured several years later . In that 26 study, prediction of cognitive deterioration could not be evaluated since cognitive data were only measured at the last follow-up. Another study that examined the relation between changes of LL and brain parenchymal volumes over 2 years together with change in cognition during the same time-frame and found that the best predictor was brain parenchymal volumes . These two studies did not specifically 27 evaluate central atrophy. Another study found that only neocortical volume changes, but not deep gray matter volume changes, were significantly associated with deteriorating cognitive performance over 2.5 years . It is possible that atrophy of the cerebral cortex 28 accounts for more of the cognitive deterioration when the disease progresses, since the mean disease duration was longer in that later study than in ours (4.0 2.8 vs. 2.0 / 2.2 years). It has been suggested that deep central atrophy may peak at earlier stages compared to whole

± + -
brain atrophy and that central atrophy progresses preferentially in the early stages of the disease . These data can explain that, 29 30 although baseline BPF which reflects brain whole atrophy developed so far is predictive of cognitive deterioration, it is only the central atrophy change which account for cognitive deterioration in attention/IPS domain. We hypothesized that disruption of deep central brain cognitive networks involved in attentional occurs in our population. It is worth mentioning that cortical atrophy also occurs in early MS31

, but appears to progress less rapidly than central atrophy . In our study, we did not specifically study neocortical volume. 32

Interestingly, it was recently shown that memory performance and mesial temporal volumes, in particular hippocampal atrophy, were correlated in MS , This suggests regional specificity of correlations between atrophy and alterations of a given cognitive domain. In 33 34 our study, we did not find correlation between memory change and atrophy measures although a trend was observed with VF change (data not shown). However baseline NABT MTR predicted memory changes over 7 years suggesting that diffuse alterations contribute also to the memory deficits by interrupting the relevant networks.

There are some limitations to this study. When performing imaging, it would have been informative to study regional changes in brain volume and MTR, for example, using voxel-based morphometry. Unfortunately those techniques were not available at the beginning of this study. Concerning cognition, the main limitation of longitudinal studies in MS is that relatively few patients deteriorate for cognitive scores and that a relatively large number of them remain stable. One possible reason is practice effect. To limit practice effect we used alternate forms at the 7 year evaluation, never used in the previous evaluations, but we cannot exclude that some practice effect remains.

Another explanation for the limited changes in cognitive performances is that cognitive skills deteriorate slowly at the early stages of MS because of the presence of compensatory mechanisms .

35

Further studies are needed to determine which therapeutics strategies could limit diffuse brain damage at the early stage of MS and therefore ongoing cognitive deterioration. 2.0 0.0 3.5

[ -]

1.5 0.0 5.5 Variables significantly correlated to cognitive change in multivariate analyses are in bold analyses but not significantly correlated with cognitive Z scores changes in final models were in italic police. police. For statistical analysis and further details, see methods.

'

  Univariate linear regressions were performed to assess correlation between individual baseline MR variables or changes over the first two years (LL, mean lesion MTR, BPF, VF and mean NABT MTR) and changes over 7 years of the domain specific cognitive z scores (memory and IPS) in the whole group. To determine which MRI parameters were the best predictors of cognitive change over 7 years in the whole group, we performed two stepwise multiple linear regression models for each cognitive change over 7 years (memory and IPS domains) as dependent variable. Independent variables were baseline MRI parameters (LL, mean lesion MTR, BPF, VF and mean NABT MTR) in the two first model and MRI parameters changes over 2 years (LL, mean lesion MTR, BPF, VF and mean NABT MTR) in the other models. In all models, we entered age, education level, gender and MADRS scores as independent variables and baseline EDSS was forced in all models as a covariate. Only independent variables with a conservative significance level of p<0.25 at the univariate analysis were entered simultaneously in the linear regression model. All parameters with p>0.05 were removed from the model by stepwise elimination.

7 (

 7 No statistical difference was observed for baseline demographics, clinical, and cognitive scores and MRI parameters between the 44 patients who completed all follow-ups over 7 years and the entire original cohort of 56 patients (all p values >0.05).The percentage of patients receiving disease-modifying therapies at any time during the study was 95.6 . During the follow-up % period, 9 of the 44 patients followed over 7 years converted from RRMS to secondary progressive MS.None of the patients reached the MADRS threshold for severe depression (MADRS>34) at baseline and only one patient at 7 years MADRS 46). Mild depression (MADRS score between 7 and 19) was diagnosed in 9 patients at baseline and in 16 patients at y7. = MADRS median range increased over the 7 years (3.0 0 21 at baseline and 10.5 0.0 46 at y7, p <0.001, z 3.712), and deteriorated

2

 2 seven years (p 0.20, t 1.31 ). The number of patients with EDSS <3 was 77.3 (34/44) at baseline and 59.1 (26/44) at y7. The = = % % number of patients with EDSS 6 was 0 at baseline and 3 at y7 (6.8 ). Median EDSS increase is 1.0 2.0 5.0 . During follow-up, noted in 21 (48 ) patients.% Over 2 years, all MR parameters deteriorated (p<0.05) in the whole group ( ). TableCognitive evolution during follow-upThe baseline results have been published . Differences were observed between RRMS patients and matched controls for memory, 3 attention, IPS, inhibition, and conceptualization.Nineteen out of 44 patients (43.18 ) had a global deterioration score >2 (sum of memory and IPS domains deterioration scores) and % 9/44 (20.45 ) a score >4. The proportions of patients deteriorating by cognitive domains more than 1.0 SD of controls scores, improving % more than 1.0 SD of controls scores and stable over 7 years are presented in for the three groups (all patients, PCI and PCU) Table3without any difference (Fisher test) between the PCI and PCU groups, for memory (p 0.37, OR 2.05; 95 CI 0.57 8.2) and IPS (p , OR 1.0, 95 CI 0.19 5.2). The proportion of patients deteriorating was 50 for memory (9 patients deteriorated for one score, 8 = % = -% patients for two score and 5 patients for more than 2 scores), 22.7 for IPS (5 for one score and 5 for at least 2 scores) and 13.6 for the % % Changes over 7 years in cognitive scores were not correlated with baseline MADRS scores or MADRS change over 7 years (whole, PCI, and PCU groups) (Pearson s correlation coefficient |r| <0.30, p >0.05).

  PCI patients cognitively impaired; PCU: patients cognitively unimpaired. For all clinical data, scores are expressed as mean (SD) except for EDSS and MADRS which are median (range). EDSS: = expanded disability status scale; MSFC: multiple sclerosis functional composite; MADRS: Montgomery and Asberg depression rating scale.

  It included the similarities test and the Brief Repeatable 3 Battery (BRB-N) with the Selective Reminding Test (SRT, and 3 subscores: SRT-LTS Long term storage; SRT-CLTR Consistent

= =

Long term retrieval ; SRT-DR delay recall; verbal memory), the 10/36 spatial recall test testing short-(SPART) and long-term = visuo-spatial memory (SPART DR), the Symbol Digit Modalities Test (SDMT, attention and IPS), the PASAT 3 and 2 second versions (PASAT 3s and PASAT 2s; working memory and IPS) and the Word List Generation test (WLG; verbal fluency). At y7, we applied alternate forms for all these neuropsychological tests to limit practice effect. Data concerning other tests used at baseline (Go/No-Go;

Table e

 e

	-1 at	www.neurology.org	).

RESULTS Demographics, clinical and MRI data summarizes

  demographics and disease characteristics of patients and controls at baseline. MS patients were matched to Table1healthy controls according to gender (p 0.16,

1.98), age (p 0.67, t 0.42), and mean number of years of education (p 0.72, t 0.36 ).

Table 1

 1 Demographic and clinical baseline characteristics of RRMS patients as well as separately for CPU and CPU groups included in the follow-up

	Patients

Table 2

 2

	MRI parameters
									Patients
	MRI parameters	Baseline	n 44 =	Y2			t-score	Baseline	PCI n 22 = Y2		t-score	Baseline	PCU n 22 = Y2	t-score
	LL (cm ) 3	9.57 11.26 ±	11.26 12.0 ±	**	-2.967	11.76 13.43 ±	12.78 12.59 NS ±	-1.313	7.38 8.34 ±	9.77 11.52 ± **	-2.851
	BPF	0.881 0.032 ±	0.865 0.045 ± ***	3.895	0.878 0.037 ±	0.861 0.052 ± **	2.879	0.883 0.027 ±	0.869 0.038 ± *	2.565
	VF	0.024 0.010 ±	0.027 0.012 ± ***	-5.051	0.025 0.010 ±	0.028 0.013 ± **	-3.790	0.023 0.009 ±	0.025 0.011 ± **	3.07
	Mean lesion MTR	46.66 2.29 ±	46.07 3.11 ±	*	1.973	46.24 2.64 ±	45.84 3.35 NS ±	1.153	47.08 1.84 ±	46.29 2.93 NS ±	1.584
	Mean NABT MTR	48.44 0.865 ±	47.64 0.954 ± ***	5.841	48.39 0.874 ±	47.64 0.927 ±	***	6.494	48.49 0.873 ±	47.63 1.00 ±	**	3.413

PCI patients cognitively impaired; PCU: patients cognitively unimpaired. MRI parameters are expressed as mean (SD). LL : lesion load; BPF : Brain Parenchymal Fraction; VF : Ventricular Fraction; = NABT : Normal-appearing brain tissue. MTR: Magnetization Transfer Ratio. P values and t-scores concerned comparison between baseline and y2. NS : p > 0.05; * p 0.05; ≤ ** p< 0.01; *** p < 0.001.

Table 3

 3 Number of patients with deterioration, no change or improvement for the two main cognitive domains over 7 years.

	All Patients (n 44) =	PCI (n 22)

=

PCU (n 22)

=

Improvement No

change Deterioration Improvement No change Deterioration Improvement No change Deterioration

	Memory domain (SRT-LTS, SRT-CLTR, SRT-DR, SPART, SPART-DR)	1	21	22	1	12	9	0	9	13
	IPS domain (SDMT, PASAT 3s & 2s)	0	34	10	0	17	5	0	17	5
	PCI patients cognitively impaired at baseline; PCU patients cognitively unimpaired at baseline (see methods).

= =

SRT, Selective Reminding Test; SRT-LTS, long-term storage; SRT-CLTR, consistent long-term retrieval; SRT-DR, delayed recall; SPART, Spatial Recall Test; SPART-DR, Delayed recall; SDMT, symbol digit modalities test; PASAT, paced auditory serial addition test.

TABLE 4

 4 Linear regression models predicting change in cognitive z scores over 7 years from MR parameters at baseline or changes over 2 years.

	Cognitive

z scores change (y7-baseline) MR parameters Included in models R Univariate analyses P values Univariate analyses Adjusted R model 2 P values multivariate analyses

	Memory domain	Baseline EDSS	-	0.095	0.54	0.144	<0.05
		Baseline LL	-	0.333	<0.05
		Baseline BPF	0.126	0.42
		Baseline VF	-0.175	0.26
		Baseline mean lesion MTR	0.253	0.10
		Baseline mean NABT MTR	0.377	<0.05
		Baseline EDSS	-	0.095	0.54	0.009	0.54
		LL change over 2 years	-0.085	0.59
		BPF change over 2 years	0.200	0.19
		VF change over 2 years	-	0.290	<0.05
		Mean lesion MTR change over 2 years	-0.090	0.57
		Mean NABT MTR change over 2 years	-0.057	0.72
	IPS domain	Baseline EDSS	-	0.273	0.07	0.416	<0.0001
		Baseline LL	-	0.425	<0.01
		Baseline BPF	0.551	<0.0001
		Baseline VF	-	0.414	<0.01
		Baseline mean lesion MTR	0.148	0.34
		Baseline mean NABT MTR	0.511	<0.001
		Baseline EDSS	-	0.273	0.07	0.326	<0.001
		LL change over 2 years	0.117	0.45
		BPF change over 2 years	0.435	<0.01
		VF

change over 2 years 0.545

  Memory domain includes the Selective Reminding Test (long-term storage; consistent long-term retrieval; delayed recall) and the Spatial Recall Test (recall score and Delayed recall). IPS domain includes the Symbol Digit Modalities Test, the Paced Auditory Serial Addition test (3 and 2 sec versions). LL : Lesion Load; MTR: Magnetization Transfer Ratio; NABT: normal appearing brain tissue; BPF; Brain Parenchymal Fraction; VF: Ventricular Fraction. Univariate analyses for age, MADRS scores, gender and educational levels showed not significant results (p>0.05). Variables with a p value <0.25 in univariate analyses were included in multivariate analyses. Variables included in multivariate

		-	<0.0001
	Mean lesion MTR change over 2 years	0.163	0.29
	Mean NABT MTR change over 2 years	-0.016	0.92

Acknowledgements:

The study received support from ARSEP (Association pour la Recherche contre la Scl rose en Plaques) and Schering France. Work was made

Sponsors did not participate in design and conduct of the study; collection, management, analysis, and interpretation of the data; and preparation, review, or approval of the manuscript.

Dr. Melissa C. Bonnet has participated as speaker to a symposium organized by Bayer.

Footnotes:

Statistical analysis were performed by Mathilde Deloire, PhD and Jeremy Jove, statistician, INSERM U657, University de Bordeaux, Bordeaux, France.

Dr Ruet reports no disclosure in relation with this study. She has been member of advisory boards or participate as speaker to symposia organized by Biogen-Idec. She is or has been investigator for studies promoted by Novartis, Bayer-Schering, Roche, Lilly, Peptimmune and Merck-Serono and has received subventions for this activity.

Dr Dousset reports no disclosure in relation with this study. He has been member of advisory boards or participate as speeker or chairman to symposia organized by Biogen-Idec. He is or has been investigator for studies promoted by Biogen-Idec, Novartis, Bayer-Schering, Teva, Peptimmune, Lilly and AB sciences and his institution received subventions for this activity Dr Deloire and Ms Hamel reports no disclosure.

Dr Brochet reports no disclosure in relation with this study. He has been member of advisory boards or participates as speaker or chairman to symposia organized by Merck-Serono, Bayer-Schering, Novartis, Biogen-Idec, Teva and Sanofi/Aventis. He is or has been investigator for studies promoted by Biogen-Idec, Novartis, Roche, Sanofi-Aventis, Bayer-Schering, Teva, Peptimmune, Lilly and AB sciences and his institution received subventions for this activity..