Jean-Philippe Thirion

Guillaume Calmon

Deformation Analysis to Detect and Quantify Active Lesions in Three-Dimensional Medical Image Sequences

Keywords: Lesion, mass effect, motion field analysis, multiple sclerosis, 3-D deformable grid, 3-D image processing, stereology, volume measurement

Evaluating precisely the temporal variations of lesion volumes is very important for at least three types of practical applications: pharmaceutical trials, decision making for drug treatment or surgery, and patient follow-up. In this paper we present a volumetric analysis technique, combining precise rigid registration of three-dimensional (3-D) (volumetric) medical images, nonrigid deformation computation, and flow-field analysis. Our analysis technique has two outcomes: the detection of evolving lesions and the quantitative measurement of volume variations. The originality of our approach is that no precise segmentation of the lesion is needed but the approximative designation of a region of interest (ROI) which can be automated. We distinguish between tissue transformation (image intensity changes without deformation) and expansion or contraction effects reflecting a change of mass within the tissue. A real lesion is generally the combination of both effects. The method is tested with synthesized volumetric image sequences and applied, in a first attempt to quantify in vivo a mass effect, to the analysis of a real patient case with multiple sclerosis (MS).

I. INTRODUCTION

T HE precise evaluation of lesion-volume variations along time is extremely important for the following reasons (see, for example, [START_REF] Wallace | Multiple sclerosis: The impact of MR imaging[END_REF], [START_REF] Thirion | Software to assist in monitoring treatment[END_REF]:

• for pharmaceutical research, to compare the effects of new drugs on different populations of patients; • for clinical applications, to determine the exact time when a potentially invasive drug is to be given, or surgery is to be performed; • for clinical follow up, to quantify the effects of the drug or surgery along time. The main source of in-vivo information about lesion growth is volumetric medical imaging such as three-dimensional (3-D) magnetic resonance images (MRI). Classical techniques (see, for example [START_REF] Roll | Volume estimation of synthetic multiple sclerosis lesions: An evaluation of methods[END_REF] and [START_REF] Roszmanith | Characterization and classification of brain tumours in three-dimensional mr image sequences[END_REF]) consist in delineating the Manuscript received August 8, 1997; revised December 1, 1998. This work was supported in part by the Institut National de Recherche en Informatique et Automatique, Sophia-Antipolis, France. The Associate Editor responsible for coordinating the review of this paper and recommending its publication was W. Higgins. Asterisk indicates corresponding author.

*J.-P. Thirion and G. Calmon are with FOCUS Imaging, "Les Genets," 449 Route des Cretes, Sophia Antipolis, 06560 Valbonne, France.

Publisher Item Identifier S 0278-0062(99)05465-8.

lesion in two volumetric images of the patient at two different time points and which gives two volumes and to be compared. The volume variation is an index of the lesion evolution. This measurement is difficult to perform for at least two reasons: the first is delineating in three dimensions and the second is delineation errors. Because hundreds or thousands of voxels are to be considered, (semi-) automatic segmentation tools are highly desirable for routine applications because they can offer an automation of tedious and repetitive tasks, as well as providing objective measurements. Among possible automatic segmentation tools are the mathematical morphological operators (erosion, dilation, connected components analysis, etc., or the 3-D extension of deformable models (3-D snakes, see [START_REF] Cohen | Using deformable surfaces to segment {3D} images and infer differential structures[END_REF]). In most practical cases, however, the a priori medical knowledge of the physician is indispensabl. Most of these methods incorporate an interactive initialization and a final interactive adjustment tool. Generally also, the accuracy of the delineation is not subvoxel, hence, the uncertainty on the total volume measurement can be higher than the volume variation itself . The main idea in this paper is to use an analysis method based on a volumetric deformation field to first detect the active lesions and then to evaluate their volume variations. In particular, our volume-variation measurement necessitates as input only the designation of a region of interest (ROI) surrounding the lesion (for example a sphere) or, when it is possible, a segmentation of the lesion which is not requested to be subvoxel. Because we use a precise 3-D rigid registration method, this ROI designation or rough segmentation needs to be performed only in (one) of the two volumetric images or one image of the time sequence to be analyzed, rather than at each time frame. Rather than a single value of volume variation, our method provides a kind of signature, or profile, associated to the lesion growth, from which we propose to quantify different effects that we call the tissue transformation and the (tissue deformation).

First we give a general description of the method and a definition of the tissue transformation and deformation effects. Then we concentrate on the description of the deformationfield analysis, which is the main contribution of our paper. Mainly, we have developed a new method of analysis based on the integration of the deformation field according to concentric shapes: either concentric spheres or shapes described as a set of 0278-0062/99$10.00 © 1999 IEEE isocontours. We present experimental results with synthesized images to evaluate the performance and test the robustness of our method. Last, we apply our method to sequences of volumetric images of a patient with multiple sclerosis (MS), to evidence and quantify a tissue deformation or mass effect at the level of the plaques: an effect which, to our knowledge, has never been quantified in vivo before.

II. GENERAL DESCRIPTION

The method consists of four steps (see also Fig. 1). 1) The 3-D rigid registration of the two successive images.

2) The computation of the deformation field between the two registered images.

3) The detection of evolving lesions. 4) The vector field analysis at the level of each detected lesion to quantify the volume variation. The most original part of the present work are the last two steps: the vector field analysis for both the detection and the quantification of evolving lesions.

For the first step, which is the computation of a rigid transformation between two volumetric images and , we use the automatic rigid matching method based on extremal points described in [START_REF]New feature points based on geometric invariants for 3D image registration[END_REF]. The accuracy of this method has been evaluated in [START_REF] Pennec | Validation of 3-d registration methods based on points and frames[END_REF] and is of the order of 1 10th of a voxel, assuming that the object which is scanned is really rigid. To fulfill this hypothesis, even when some part of the object are deformed (such as places containing lesions), the matching method is based on feature points extraction and outlier features are automatically discarded in the computation of the final transform. We then resample one of the two images (let say ) into to make it exactly superposable to except, of course, for the regions of the brain which have changed between the two acquisitions (that is, mainly the lesions). Note also that, for simplicity reasons, we are considering isotropic volumetric images. In our experiments we always resample the data into isotropic volumes before processing them. Typically, a 0.94 0.94 3.0-mm MR image is resampled into 0.94 mm before processing.

We then compute the nonrigid deformation between and using the nonrigid matching method described in [START_REF]Image matching as a diffusion process: an analogy with Maxwell's demons[END_REF]. It is a 3-D deformable grid technique which is very close to optical flow when small deformations are considered. The result is a dense (i.e., not restricted to contour points) deformation field , represented by a 3-D array of displacement vectors, one for each voxel in the image . As in many nonrigid matching methods, the result of the motion field estimation depends on a parameter which is a balance between the regularity of the deformation field and the similarity between and . It is very unlikely that this parameter , which is inherent to any nonrigid matching technique, can be eliminated. For the snakes methods [see [START_REF] Kass | Snakes: Active contour models[END_REF]] it is the balance between internal forces (regularity) and external forces (similarity).

This parameter has some influence on the volumevariation analysis. It can be interpreted to some extent as a blurring of the real deformation field, equivalent to a convolution with the Gaussian function of the vector field (see [START_REF] Burr | A dynamic model for image registration[END_REF]). This value is explicitly defined in the nonrigid matching method that we are using (see [START_REF]Image matching as a diffusion process: an analogy with Maxwell's demons[END_REF]).

The next sections describe in detail the detection of evolving lesions and the quantification of volume variation. First we must define precisely the effects that we want to measure.

III. TISSUE DEFORMATION AND TRANSFORMATION

We distinguish between two different models of lesion growth, real cases being generally a mix of these effects. Our model is crude with respect to many other works existing in the medical domain and concerning the biological aspects of lesion growth (see, for example, [START_REF] Young | The invasive growth of malignant tumours: An experimental interpretation based on elastic-jelly models[END_REF] and [START_REF] Cruywagen | The modeling of diffusive tumours[END_REF]). In particular, we consider explicitly neither the elastic properties of the brain tissues (see [START_REF] Demiray | Large deformation analysis of some soft biological tissue[END_REF]), nor the dynamic aspect of malignant cells growth, but only two fixed time frames, with no (or very few) biological a priori knowledge. We will see, however, that even with crude assumptions, solving the problem is not an easy task.

What changes can be observed in a medical image of a lesion? A lesion can be the inclusion or destruction of material within the tissue, or a localized change of the tissue properties, or a complex combination of those cases, which might or might not have the same appearance in MR images. Basically, we distinguish between deformation and transformation.

A. Tissue Deformation

Some lesions can be observed by way of a large deformation of the tissues (mass effect) without image intensity changes. Additional material is entering the tissue, but it may happen that the grey-level value representing the tissue in the MRI is unchanged, mainly because their proton density is the same. Hence, the only visible effect in that case is an expansion, contraction, or deformation of the tissue, which can be perceived only due to textural information. We call this effect (diffuse) deformation. But it also can be the addition of new untextured material in the central part of the lesion, which translates into two effects: the growing of a central spot (the lesion) and the displacement of the surrounding tissues (the deformation). We call this model central deformation.

B. Tissue Transformation

A lesion also can be detected by a change in intensity without any displacement of the tissues. The molecular structure of the tissue is changing in place: the tissue itself is not displaced. This type of lesion is, of course, much easier to delineate than in the previous case. The lesion volume is the area of the MR image where the tissue has a different composition and, therefore, a different gray value. It is a known phenomenon for the plaques in -weighted MR images of MS, which corresponds to demyelination of the axons and then glyosis. Most of the classical lesion-measurement methods are based on this model and are using segmentation tools exclusively.

C. Defining Volume-Variation Measurements

Of course, real lesions are always a complex combination of these effects and giving a clear definition the lesion volume or lesion growth is very difficult. If central deformation and tissue transformation might present the same appearance in the MRI within the lesion itself (i.e., translates into a contrasted central region), they have different influences on the nearest surrounding tissues. This leads to the idea of studying a lesion-evolution profile . A curve representing the volume-variation coefficient as a function of the distance to the approximate center of the lesion and up to a limiting bounding radius . The sphere defines an ROI centered on the lesion. By studying the profile outside the lesion (but inside the ROI), we might be able to distinguish deformation and outside the lesion) from transformation and outside the lesion) where is the vector field corresponding to the displacement of tissues.

D. An Ideal Mathematical Solution

Ideally, if we define a virtually closed surface in the image space enclosing a region of volume we can study the flux of tissues through , represented by the vector field produced by the nonrigid matching step. Intuitively, the summation of all that goes out minus the summation of all that enters is equal to the volume variation, which is a simplified version of the Ostrogradsky theorem which states that the integral over a closed surface of the flux of a vector field is equal to the integral over the encompassed volume of the divergence of the vector field. In practice, different factors prevent us from directly using this mathematically well-defined technique. We list now some of these problems with some possible (partial) solutions.

• The vector field produced by an intensity-based nonrigid matching is equally sensitive to a deformation or a simple intensity change (transformation). We can study precisely and separately ideal measurement models for tissue deformation and transformation, test these models on synthetic data, and compare the profiles with those obtained with real data.

• The estimated vector field is inevitably blurred by a regularity parameter .

We can quantify the effect of this blurring on ideal models and measure it in the synthesized models to extrapolate it to real data.

• A lesion can have a shape much more complicated than a sphere. We can study a family of embedded closed surface encompassing regions of volume , ranging in size from the approximate center point of the lesion to the complete ROI. It defines a profile of the lesion variation If the lesion can be approximately segmented, we can use a family of embedded surfaces whose shapes are much closer to the segmented lesion surface than spherical shells.

• is not a continuous field, but is sampled for a regular 3-D grid (the voxels). It is unclear how to integrate a discrete flow field over a sampled closed surface.

We develop in this paper a stochastic method to integrate the volume variation from a discrete deformation field.

• The displacement of surrounding tissues induced by a lesion evolution decreases in outside the lesion, and the vector field evaluation is inherently corrupted by measurement errors and discretization, hence, the evaluated flow becomes meaningless very rapidly when we get farther from the lesion. In addition, there might be several active lesions, as in the case of MS disease.

High-frequency noise is eliminated by the regularization of the vector field, but we must keep close to the lesion boundary for meaningful measurements.

• Different pathologies exist, corresponding to different models of lesions.

The usefulness of the discrimination power of each measurement has to be proved for each specific type of disease through in vitro studies and through clinical validations (coherence of the measurements along time, coherence with traditional clinical tests based on external symptoms, coherence with histology, etc. As we can see, the problem of defining and measuring a precise lesion volume variation is much more complex than simply counting voxels. But even if no complete mathematical formulation is at hand, the precise quantification and its impact on the development of new drugs is too important to simply abandon the effort when things become difficult. For example, in the case of MS, there are hundred thousands of patients throughout the world and the cost of therapy based on interferon is very high (today, approximately $10 000 per year per patient). In the following, we describe the solutions that we have explored to detect and quantify the evolution of such lesions.

IV. DETECTING EVOLVING LESIONS

In this section, first we present traditional methods based on segmentation to analyze lesion evolutions and then a more recent work based on the temporal analysis of the intensity signal ( [START_REF] Gerig | Exploring the discrimination power of the time domain for segmentation and characterization of lesions in serial mr data[END_REF]). Finally, we present our contribution, which is based on the evaluation and analysis of deformation fields and present an original method which evaluate volume variation through the integration of the deformation field in concentric shapes, which can be concentric spheres or embedded isosurfaces.

A. Segmentation

Detecting lesions in medical images is traditionally performed by segmentation and, therefore, relies on the local analysis of the intensity or texture in static images. Unfortunately, the intensity is generally not specific enough to automatically characterize a lesion and, in most cases, several modalities must be used to image the same brain. By combining those different images it is sometime possible to characterize the lesions in a more robust way, for example, by a component-classification method (see [START_REF] Gerig | Medical Image and Computer Vision: An Integrated Approach for Diagnosis and Planning[END_REF] and [START_REF] Cline | Threedimensional segmentation of mr images of the head using probability and connectivity[END_REF]). Once the lesions are characterized in each time frame, it is possible to analyze the whole sequence of segmented images as a fourdimensional (4-D) image (3-D time) and extract and analyze the lesions as 4-D connected components (see [START_REF] Kikinis | Quantitative follow-up of patients with multiple sclerosis using MRI part I: Technical aspects[END_REF] and [START_REF] Medcalf | 4d connected component labeling applied to quantitative analysis of ms lesion temporal development[END_REF]). On the one hand, this allows us to extract static as well as dynamic lesions. On the other hand, the motion information is not taken into account in the detection itself.

In the case of MS, there are several serious drawbacks in using segmentation methods. In -weighted MR images, the boundary of an MS plaque is fuzzy and sometimes surrounded by a halo. Hence, it is very difficult to segment. In [START_REF] Kikinis | Quantitative follow-up of patients with multiple sclerosis using MRI part I: Technical aspects[END_REF], this problem is partially overcome due to masking. In addition, thresholding and connected component analysis tools are very unstable operators. For example, an active plaque can merge with a neighboring passive plaque during the expansion. The estimated volume is suddenly and artificially increased due to the capture of the passive plaque or of another brain structure. This prevents us from studying precisely and automatically the evolution of individual plaques with segmentation, although it might be possible to obtain some global measurements. Even manually, segmentation is very difficult to perform in many cases. The final drawback of segmentation is that it totally ignores the mass effect (i.e., the effects on surrounding tissues).

B. Segmentation Based on Intensity Changes

A different approach is to consider a set of successive volumetric images of the same subject as being a temporal sequence (see Fig. 3).

A simple way to use the temporal domain is to consider the difference between two consecutive volumetric images (see Fig. 4). When a lesion is characterized by a hypersignal, that is, with an intensity locally larger than the intensity of the surrounding tissues, then a growing lesion appears as a white annulus in the difference of two consecutive images, and a shrinking lesion appears as a black annulus. Provided with an almost perfect registration of the images, the annulus can be isolated more easily in a difference image than a lesion in a single static image (compare Figs. 2 and4).

In [START_REF] Gerig | Exploring the discrimination power of the time domain for segmentation and characterization of lesions in serial mr data[END_REF] the intensity profile of the whole sequence of registered volumetric images is analyzed individually for each voxel position to characterize evolving regions. In this last work, no deformation due to lesions is considered, which might induce interpretation problems if there is indeed a displacement of the tissues.

If we are looking carefully at Fig. 3 (see also Fig. 2), we can perceive tissue displacements: the white spindle is the evolving (growing then shrinking) lesion. The first dark layer around the spindle is gray matter, followed by a lighter layer which is white matter, etc. As we can see, the widths of these layers remain fairly constant and the layers themselves are displaced by the evolving lesion. It has no visible effects farther from the lesion because, in 3-D, displacements due to mass effects are decreasing very rapidly (in . Such spatial displacement is even more apparent in Fig. 2(b) and [8, p. 474] (same patient but different lesion).

C. Flow-Field Analysis

We have developed a different way to characterize evolving lesions than simply analyzing image intensity evolutions. We analyze the deformation field computed between two consecutive images and (see Fig. 5). is represented by a discrete function where is a 3-D displacement vector defined at each voxel of . More precisely, being the position in corresponding to a point in we have [START_REF] Barrow | Parametric correspondence and chamfer matching: Two new techniques for image matching[END_REF] We are interested in places presenting large deformations large) and, in addition, because MS plaques have generally a rather spherical shape, places where the divergence is large (see Fig. 6). In some places can be large and low (in case of a translation, for example) or can be high and low (in noisy regions), but as the feature high magnitude high divergence is more specific to evolving lesions, we have tested successfully the following operator Besides, the sign of characterizes growing lesions from shrinking lesions. This operator makes active lesions very easy to detect (see Fig. 6). In addition, in the case of MS plaques we can use a mask representing the white matter in the brain, because most of the MS plaques appear in the white matter. We use thresholding and connected component analysis to finally extract automatically the centers and the approximative radii of the active lesions.

V. MEASURING THE VOLUME VARIATION PROFILE

For now, we assume that the approximate center and radius of an active lesion is determined and that we are looking for a precise volume-variation measure. We assume also that there is a single lesion present in the defined ROI. This assumption might restrain the applicability of the method for some pathologies.

div(f f f ). (d) kf f f kdiv(f f f ).
Each step corresponds to an image easier to segment automatically.

We describe now the method that we have applied in our experiments, which is based on the integration of the vector field for a set of concentric shapes, either spherical or defined by a set of isocontours.

A. The Method of Concentric Spheres

In this section we consider a family of spheres of increasing radii where is set by the user to entirely encompass the lesion and some of the surrounding tissues (but, hopefully, no other lesions). The aim of the concentric spheres is to obtain a volume-variation profile and to deduce from it the volume variation, without having to segment the lesion.

1) Integrating the Divergence: A first idea is to compute the integral of the divergence within each sphere or the integral of the flux on the surface of the sphere which is theoretically equivalent is the normal to the sphere)

(2)

For a growing lesion must increase when is increased until the lesion is entirely included into . At that point, remains constant (for the deformation model only, not for pure transformation). Up to now, however, we did not get good results in practice with such methods, probably because the noise in the vector field is amplified in the computation of the divergence which necessitates a differentiation.

2) A Stochastic Computation: We have then switched to a stochastic method to evaluate the volume variation which is the following.

Assume a shape , for example, a sphere, a cube, or any shape defined by a closed oriented surface in image . Assume also a regular grid [see Fig. 7(a)]. The number of grid nodes times the volume of a single voxel is an approximation of the total volume of , which tends to the exact value when the grid gets thinner. This method is close to stereological methods which are used to quantify the volumes of static lesions (see [START_REF] Roberts | Stereological estimation of the total volume of mr visible brain lesions in patients with multiple sclerosis[END_REF]). Similarly, the number of nodes of the regular grid within the deformed shape gives an approximation of [Fig. 7(c)]. As is the image in of the shape in is the volume variation between and of the shape represented by in (or by in . We could compute by computing stochastically and , which would necessitate the computation of the deformed shape . However, we note that computing the number of nodes of within the deformed shape is equivalent to computing the number of nodes of the deformed grid within the original shape [Fig. 7(b)], which is computationally much easier because the deformation is sampled for each node of and there is no need to compute the deformed shape . The method that we propose is fairly simple, but counterintuitive. Compute the number of nodes of within and the number of nodes of also within . The volume variation for the shape in is approximately . This approximation tends to the exact value when the grid gets thinner. If the volume variation is requested for a regular shape within instead of within , it suffices to use the same method with the inverted transformation obtained, for example, by the exchange of and within the nonrigid matching algorithm.

3) Practical Computation of the Profile: Suppose now that we have a family of embedded shapes such as, for example, a family of spheres with increasing radii . We propose an optimal algorithm (i.e., with a linear complexity) to compute the volume-variation profile. Suppose that we have defined a ROI containing grid nodes of .

• We define two arrays of numbers and , initialized to zero.

• For each node of (out of the nodes), we determine the index of the shell corresponding to the spheres and which contains (respectively, can be obtained in constant time with the distance and a lookup table. For each we increment the corresponding bucket (respectively, . • Once the arrays and are computed, we compute incrementally the arrays and

• At last, we compute the volume-variation profile The computational complexity of the arrays and is , as for the derivation of and from and , hence, the whole computation of the volume-variation profile is linear We shall note that this computation can also be performed with random positions throughout the ROI instead of with the nodes of a regular grid .

4) Computation of a Single Value of Volume Variation:

For the deformation model, must remain constant and equal to the searched as soon as is larger than the maximal extent of the lesion. However, because of the noise, moves with a Brownian motion around the true (each new error increments or decrements the estimated value randomly), which means in practice that oscillates around with larger and larger amplitudes when is increased. To avoid this phenomenon, we remove from the computation the effect of very small displacements (when we impose ). With this constraint, the noise is reduced but tends artificially to zero when becomes large, even for the deformation model, which is one of the reason which prevent us from directly using the volume profile to distinguish between transformation and deformation.

In order to get a single value of volume variation, we compute the maximal value of , which approximates the real . We have extensively validated this method with synthesized data, which constitutes an important part of the present paper.

B. Computing with Isointensity Surfaces

The advantage of using concentric spheres is that it doesn't necessitate any kind of segmentation and hence can be applied to invisible lesions (invisible meaning undetectable in a single frame). However, it can be improved seriously if we can take into account an approximate shape of the lesion by replacing concentric spheres by concentric shapes closer to the actual shape of the lesion.

If the lesion is sufficiently contrasted, it can be segmented as a set of labeled voxels in image . In the previous algorithm we have replaced the spheres with a family of embedded closed surfaces A simple way to obtain this family of surfaces is to consider a digital volumetric image where the voxels are labeled zero if they are outside , or one if they are inside. We then blur this image with a Gaussian filter. The isointensity surfaces for a set of increasing intensity constants have the requested properties (closed and embedded) and, furthermore, the intensity of at a point directly gives the index shell , which contains . Another equivalent solution is to precompute a 3-D distance map from using, for example, the chamfer distance (see [START_REF] Barrow | Parametric correspondence and chamfer matching: Two new techniques for image matching[END_REF]). The rest of the algorithm is exactly similar to the case of the embedded spheres and therefore the whole algorithm still has a linear complexity (a few seconds of computation on a workstation).

The segmentation of should be distinguished from the precise segmentation used to evaluate the volume variation in traditional methods. It can be much less precise (because it is then blurred) and, in addition, it must be performed only in one of the two images. If the lesion is well contrasted, using shells around a segmented lesion rather than simple spheres gives more reliable results because of the fast decrease ( ) of the deformation magnitude. Of course, a better segmentation leads to a better deformation analysis. We have verified this assumption with synthetic data.

VI. SYNTHETIC EXPERIMENTS

A. Tissue Transformation

We suppose (see Fig. 9) that the lesion evolution is simply a change of intensity without tissue displacement. Another assumption is that the image intensity saturates at the level of the lesion, that is, textural information is lost in those regions.

To produce a synthetic lesion, we have measured the average intensity of plaques in a real MRI, selected a region where the white matter of the brain is homogeneous, and implanted spherical synthetic lesions of known radii in it (see Fig. 10). The boundaries of the synthetic lesions are blurred to give a realistic appearance to the false MS plaque. In this model, the deformation field measured by our method is strictly due to intensity changes and not to tissue motion. We have compared the volume variation obtained by our deformation-field analysis method based on embedded spheres, embedded isosurfaces, and also with segmentation (see Table I). The segmentation used is based on thresholding and connected component analysis within an ROI defined by the user. The profile for the sphere and for the isosurface method is presented in Fig. 11. Note that , which should be zero outside , is in fact nonzero because of the regularization of the vector field. The measure which is finally retained is the maximum of , which in that case is a slight overestimation of the real value Segmentation seems to perform slightly better than deformation-field analysis in that case (see Table I).

B. Mathematical Model of the Expansion Field

We now suppose that the lesion is growing in a limited spherical region of radius lesion , which means that inside this region the Jacobian determinant of the deformation field is larger than one. We suppose also that the surrounding tissues are incompressible, which is reasonable brain,1 hence, the Jacobian determinant is one outside the lesion . With this model, the expression of the synthetic deformation field is if lesion

lesion if lesion (3)
The theoretical volume variation is then lesion (4)

The invert field (contraction) can be computed from this expression by replacing with and lesion with lesion . This computation is valid only in dimension three. The norm of the vector field is mathematically equivalent to outside lesion . It should be noticed that in a two-dimensional (2-D) world, this field would only decrease in , which can can be counterintuitive when looking at a 2-D slice of a volumetric image. We must also remember that we choose to keep the Jacobian constant inside the lesion, but in real cases, the Jacobian could have a complicated profile with respect to and can be specific to each pathology.

C. Central Deformation

Here we suppose that the lesion evolution is the addition of untextured extra material to the disk of the lesion (see Fig. 12), therefore, in contrast to tissue transformation, the lesion is pushing the surrounding tissues.

To generate synthetic data we have inlayed a synthetic lesion in the first image (central spot of radius lesion , computed a synthetic deformation field with a known Jacobian within lesion , and, finally, applied this field to the first image with a resampling algorithm (see Fig. 13). In the difference image we note a small motion at the boundary of the brain due to the expansion. This is the only noticeable visible difference with the case of the tissue transformation (compare Figs. 10 and13).

Table II presents experimental results comparing real and measured variations with embedded spheres, embedded isosurfaces, and segmentation. The segmentation underestimates the volume variation because the synthetic lesion is fuzzy and the intensity of its boundary is very similar to the one of the underlying image. In that case, the deformation-field method gives slightly better results than segmentation. Fig. 14 presents an example of measured profile.

D. Diffuse Deformation

In this last case, we apply a synthetic deformation field in a region of the image which does not present a particular intensity (see Fig. 15). No segmentation method can be applied at all: the lesion is invisible, even in the subtraction image. Only a slight displacement at the boundary of the brain can be observed (see Fig. 16). This small shift is the only evidence of an deformation of the tissue which, as we can see, can be partially retrieved thanks to the motion field analysis.

Table III shows that the measurements with the deformation-field techniques, although underestimating the real volume variation, are interesting indexes to evidence this type of deformation which is otherwise invisible. Fig. 17 shows the associated profile and Fig. 18 presents the retrieved deformation fields for both central and diffuse deformation.

E. Robustness with Respect to the Approximative Center

For the deformation model, a very interesting feature of the spheres method is that it is not very sensitive to the precise location of the center because once the sphere is larger than the lesion, the value is theoretically constant (but more and more noisy in practice). We have shifted the center up to a three-voxels distance (for a lesion with a diameter of ten voxels) and measured the performance for the case of central deformation. The results are degraded progressively, but the volume-variation measurement is still valuable (see Table IV).

F. Robustness with Respect to Shape

It is not an easy task to derive the theoretical deformation field of complex shapes. We have performed experiments with only ellipsoidal lesions and for central deformation, with volume . In that case, the results are much better for the isosurface technique than for the spheres, as one would expect (see Table V).

G. Conclusion on Synthetic Experiments

Segmentation is probably best suited for pure tissue transformation, that is, when the tissues are not displaced. However, this model is unlikely to be realistic for actual lesions. When there is a deformation, we can have a continuous variation of cases in between central and diffuse deformation. For central deformation, our method relying on deformation field and a segmentation method can give comparable results. However, the deformation-field method becomes much better when the deformation is more important than the intensity changes. In that case, segmentation underestimates much more the volume variation than the deformation-field method, up to the point when segmentation cannot be used anymore (no visible intensity changes).

Again, segmentation is operating on single frames and is unable to detect tissue deformations. Hence, in real cases we can expect that if, for a given lesion, the volume variation obtained with the deformation-field analysis is significantly larger than the one measured by segmentation, this is evidence of a deformation of the tissues, or mass effect, larger than the visible spot which can be segmented.

VII. MEASUREMENTS ON REAL MULTIPLE SCLEROSIS IMAGES

A close inspection on real MS plaques reveals that, in addition to a clearly visible bright spot in the center, some lesions are surrounded by a cloudy halo whose intensity can hardly be distinguished from the surrounding white matter. This strongly suggests that MS plaques are in fact larger than their visible central spots.

Another clue for this hypothesis is provided by dynamic sequences of accurately registered volumetric images. We have registered the volumetric images of a time sequence of 24 time frames (courtesy of Dr. R. Kikinis and C. Guttmann, see Fig. 19) and we have been able to evidence visually a deformation of the surrounding tissues induced by the lesion. The gyri of the brain are pushed when the lesion is growing, and return to place when it is shrinking (growing and shrinking is a normal course for active plaques). What is surprising is that this displacement is visible, even quite far from the central spot (up to ten voxels). Because the deformation effect decreases in in 3-D, the central spot alone cannot explain visible displacement that far from the center. It can be sensitive only two or three voxels apart, and the only explanation that we found is that a diffuse deformation, much larger in extension than the visible spot, is responsible for these displacements of tissues.

To give quantitative grounds to this assumption, we have compared the volume variation obtained by segmenting the plaque visible in the 20 images of Fig. 19 with the results of the spheres and the isosurfaces method (see Table VI or Fig. 20). The variations obtained by the deformation-field methods are much larger (about two times) than the ones obtained by segmentation, which justifies our hypothesis. We can see also that the spheres and the isosurfaces methods give coherent results and that, as in synthetic cases, the isosurface variations are generally slightly larger. The profiles obtained in the real case are qualitatively similar to the theoretical ones (compare Figs. 14 and21) which is an additional confirmation of the validity of our model. As the lesion is not spherical, we believe that the isosurfaces measurement method is the most reliable. In fact, even a volume variation twice as large as that measured by segmentation seems to us insufficient to fully explain the visual effect in the dynamic sequence. We saw previously that the isosurfaces method underestimates pure diffuse deformation in synthetic experiments (by about a factor of two), hence, we believe that the value which is provided by our method is a lower bound of an even larger diffuse deformation.

By integrating the volume variation (see Table VII or Fig. 22) we can estimate the absolute volume from both the spheres and the isosurfaces measurements and compare it to segmented volumes. The volume profile obtained from the segmentation and from the deformation-field methods are very coherent except for a multiplicative factor, which suggests that the mass effect is present at each stage of the evolution.

A. Some Validation Experiments with Real Images

These data enable us to perform some useful validation experiments 2 and check for the coherency of the results.

1) Temporal Coherency: As we have 20 time frames, a first experiment consists in comparing the integration of the results obtained between times 1 and 2, times 2 and 3, times and (relative volume variations, as in the previous section), with respect to the direct computation of the volume variation between times 1 and 2, times 1 and 3, times 1 and (absolute variations). In Fig. 23 we compare the absolute and relative variations, which shows a difference of only a few percent. These are nice results with respect to temporal coherency, because the integration of the relative volume variations accumulates, in the end, the errors of 20 independent measurements and is still very close to the absolute measurements.

2) Coherency Between Different Echos: For the same patient and for each time frame we have both the -weighted and the proton density volumetric images. An interesting experiment is to compare the computation performed independently in both types of images ( and proton density). The result is also presented in Fig. 23. The results of segmentation, absolute variation measurements, and relative variation measurements are not very sensitive to the change of MR sequence, which suggests that the measures are intrinsic to the tissue displacements and relatively independent of image contrast.

B. Comparison with Deformations Obtained with Cross-Correlation

One possible drawback of the method that we are using to evaluate the deformation field is that, because it is relying on the optical flow paradigm (conservation of image intensity), it can be influenced by intensity changes. Global intensity changes are taken into account because global linear transformations between the intensities of the two successive images of the sequence are estimated (using linear regression between the joint intensity map) and compensated for.

However, local intensity changes also have an influence which cannot be easily discarded. To evaluate this effect, we have implemented an independent way to evaluate a dense deformation field between two images. The principle is to search, for a subwindow defined around each voxel (typically a 5 voxels subwindow), a sub-window (of 5 voxels ) in the second image which correlate the most with this one. This subwindow is searched in a larger window (typically 12 voxels ) centered on the voxel having the same coordinate in the second image. It should be noted that this method works only for very small deformations and is highly time consuming. The following formula is the cross-correlation coefficient measured between two subwindows of voxels where are the intensities for locations in the first image and intensities in the second image [START_REF] Cruywagen | The modeling of diffusive tumours[END_REF] where and The principal advantage of cross correlation is that it is insensitive to local intensity variations (when the spatial extension of these variations is larger than the subwindow size). The principal drawback of cross correlation is computation time. Our implementation of cross correlation is 50 times slower than the implementation relying on optical flow.

The results are qualitatively very similar between both deformation measurement methods (see Fig. 24). This result shows some independence with respect to the method used to evaluate the deformation field and confirm our hypothesis of mass effect for some MS plaques.

C. Grounds for a Mass Effect for MS

The coherence of the results between real experiments and also with respect to synthetic experiments increase our confidence in our quantification of mass effects. We believe now that some MS plaques are subject to a mass effect of at least twice the volume of the visible plaque. Of course, we do not demonstrate that there is a mass effect for every plaque in MS. We now have a method to determine which plaque is active or inactive and, if active, whether it is subject to a mass effect. Such measurements open up new ways to evaluate the impact of drug treatments for this particular disease.

VIII. CONCLUSION

Thanks to a highly accurate 3-D registration algorithm and time sequences of volumetric images, we had visually observed in some patients' T2 MR images a diffuse deformation or mass effect in the case of MS (the eye being a precious tool to perform optical flow analysis). To our knowledge, the present paper is the first attempt to quantify a mass effect in vivo for MS. To achieve this, we have developed an original method to compute volume variations based on the integration of the deformation fields obtained between different time frames. The volume-variation profiles obtained from the segmentation and from deformation-field integration are very coherent except for a multiplicative factor, which suggests that the mass effect is present at each stage of the evolution and that it is at least twice as large as the visible plaque evolution. This applies to the studied cases, however, more experiments have to be made to determine the proportion of the MS diseased population which is presenting this kind of phenomenon (the cases that we have studied are presenting especially large plaques). This first result is extremely promising to better understand the disease. Our detection and quantification methods can help also to quantify more precisely the impacts of new drugs (such as Interferon) which are now tested in many ongoing clinical trials. The application of our tool, however, is not limited to MS plaques, but can be applied to the study of other pathologies such as cancer tumors.

Fig. 1 .

 1 Fig. 1. The general principle of the method.

Fig. 2 .

 2 Fig. 2. Two registered slices of a patient with MS, with a two-months interval (T 2 -weighted first echo MRI).

Fig. 3 .Fig. 4 .

 34 Fig. 3. Evolution of a lesion through time. The horizontal axis is a cross section of a 2-D image (itself extracted from a volumetric image). The vertical axis is time (20 different volumetric acquisitions for this subject). (a) The temporal sequence without volumetric image matching. (b) The evolution after image matching and 3-D resampling: the evolving lesion appears as a spindle shape. This sequence corresponds to a horizontal cross-section through the evolving lesion presented Fig. 2.

Fig. 5 .

 5 Fig.5. The 3-D deformation field measured between the two volumetric MRI's of the same patient, at the level of the lesion (this lesion is visible in Fig.2).

Fig. 6 .

 6 Fig. 6. (a) Difference of intensity. (b) Vector field norm kf f f k. (c) Divergence

Fig. 7 .Fig. 8 .

 78 Fig. 7. Stochastic computation of the volume variation. The main idea is that the stochastic computation of the volume of a shape f 01 (S ) with a regular grid G (a) is equivalent to the stochastic computation of S with a deformed grid f(G) (b).

Fig. 9 .Fig. 10 .Fig. 11 .

 91011 Fig. 9. Tissue transformation: intensity change without tissue displacement.

Fig. 12 .

 12 Fig. 12. Central deformation: addition of new material in the center of the lesion. The dashed lines in (b) represent the earlier positions of the lesion and textured tissues.

Fig. 13 .Fig. 14 .

 1314 Fig. 13. (a) Original image. (b) Synthesized central spot (I 1 ). (c) Synthesized deformation is applied (I 2 ). (d) Subtraction I 2 0 I 1 .

Fig. 15 .Fig. 16 .

 1516 Fig. 15. Diffuse deformation: deformation of the tissues without intensity changes.

Fig. 17 .

 17 Fig. 17. Profile of 1V i for diffuse (a) Spheres. (b) Isosurfaces.

Fig. 18 .

 18 Fig. 18. kf f f kdiv(f f f ) computed from the deformation fields. (a) Synthesized field. (b) Retrieved from central deformation images. (c) Retrieved from diffuse deformation images. Motion field analysis makes diffuse deformation clearly visible.

Fig. 19 .

 19 Fig. 19. The same ROI in the 20 successive images of the same patient (T2-weighted, first echo).

Fig. 20 .

 20 Fig. 20. Temporal volume variation (dV=dt) with a real plaque for the time series of 20 volumetric images (results in mm 3 per day): comparison of segmentation, spheres method, and isosurfaces method.

Fig. 21 .

 21 Fig. 21. Profile of 1V i for real images. (a) Measured with the spheres. (b)Measured with the isosurfaces (computed between frames one and four).

Fig. 22 .

 22 Fig. 22. Volume of a real plaque for the time series of 20 volumetric images: comparison of segmentation, spheres method, and isosurfaces method.

Fig. 23 .

 23 Fig. 23. Temporal coherency and coherency with a change of MR sequence: volume-variation profiles (plaque of Fig. 2) obtained by segmentation, by relative measurements, and by absolute measurements (isosurfaces method). (a) Results obtained with T 2 -weighted MR images. (b) Results obtained with proton density MR images.

Fig. 24 .

 24 Fig. 24. Comparison between volume-variation profiles obtained using a method close to optical flow (demons) and a method based on cross correlation for a time sequence in the case of an MS plaque presenting a mass effect. This result shows independence of results with respect to the method used to evaluate the deformation field.

TABLE III SYNTHETIC

 III EXPERIMENTS FOR DIFFUSE DEFORMATION

TABLE IV ROBUSTNESS

 IV WITH RESPECT TO THE DISPLACEMENT d OF THE CENTER

TABLE V ROBUSTNESS

 V WITH RESPECT TO SHAPE

TABLE VI MEASUREMENTS

 VI OF THE VOLUME VARIATION WITH A REAL PLAQUE (RESULTS IN mm 3 ); FOR THE TIME SERIES OF 20 VOLUMETRIC IMAGES, REPRESENTED IN FIG. 19

TABLE VII ESTIMATION

 VII OF THE VOLUME WITH A REAL PLAQUE (RESULTS IN mm 3 ); FOR A TIME SERIES OF 20 VOLUMETRIC IMAGES, REPRESENTED IN FIG. 19. NOTE THAT FOR THE DEFORMATION FIELD ANALYSIS TECHNIQUES (SPHERES AND ISOSURFACES), THIS VALUE IS OBTAINED BY INTEGRATION FROM THE FIRST VALUE GIVEN BY THE SEGMENTATION, HENCE IT CAN BE SUBJECT TO INCREASING ERRORS

In the brain, the ventricles can compensate for volume variations induced by tumors or lesions, except when they are totally compressed or when the ducts are obstructed. As long as they can compensate, there is no increase of the intracranial pressure and, therefore, the compression of the brain tissues is fairly reduced. For preliminary works about the study of the biomechanical properties of the brain, one can refer too[START_REF] Kyriacou | A biomechanical model of soft tissue deformation, with applications to nonrigid registration of brain images with tumor pathology[END_REF].

This does not replace other in vitro experiments and in vivo studies which are necessary for a complete medical validation, which is the subject of a collaboration that we have started with Dr. N. Roberts, University of Liverpool.

ACKNOWLEDGMENT The authors wish to thank Dr. R. Kikinis and Dr. C. Guttmann, Brigham and Women's Hospital, Harvard Medical School, Boston and Dr. N. Roberts, MARIARC, University of Liverpool, who provided us with temporal sequences of MS diseased patients.


Nadine Hagen

Michael Hans

Dieter Hartmann

Dieter Swandulla

Gerhild Van Echten- Deckert

Gerhild Van Echten-Deckert
email: g.echten.deckert@uni-bonn.de

Sphingosine-1-phosphate links glycosphingolipid metabolism to neurodegeneration via a calpain mediated mechanism Running title: Sphingoid-base phosphate induced neurotoxicity

We have recently reported that the bioactive lipid sphingosine-1-phosphate (S1P), usually signaling proliferation and anti-apoptosis induces neuronal death when generated by sphingosine-kinase2 and accumulating due to S1P-lyase deficiency. In the present study we identify the signaling cascade involved in the neurotoxic effect of sphingoid-base phosphates. We demonstrate that the calcium-dependent cysteine protease calpain mediates neurotoxicity by induction of the ER-stress specific caspase cascade and activation of cyclin dependent kinase5 (CDK5). The latter is involved in an abortive reactivation of the cell cycle and also enhances tau phosphorylation. Neuroanatomical studies in the cerebellum document for the first time that indeed neurons with abundant S1P-lyase expression are those, which degenerate first in S1Plyase-deficient mice.

We therefore propose that an impaired metabolism of glycosphingolipids, which are prevalent in the central nervous system, might be linked via S1P, their common catabolic intermediate, to neuronal death.

Introduction

Gangliosides, a class of sialic acid containing complex glycosphingolipids are characteristic components of neuronal cells. Neuronal ganglioside profiles vary in different regions of the brain and characteristically change during ontogenesis [START_REF] Van Echten-Deckert | Sphingolipid metabolism in neural cells[END_REF] . The possible physiological role of these complex molecules for neuronal function and neurodegeneration has been extensively studied [START_REF] Rk | The role of glycosphingolipids in neurological disorders. Mechanisms of immune action[END_REF] .

Reports on elevated expression and activity of enzymes involved in sphingolipid degradation in brain samples of patients suffering from Alzheimer's disease suggest that also less complex metabolic intermediates of these abundant brain lipids might contribute to neurodegeneration [START_REF] He | Deregulation of sphingolipid metabolism in Alzheimer's disease[END_REF] . Among these, ceramide, the central metabolic intermediate and S1P, the common degradation product of all glycosphingolipids (Figure 1) appear to be of specific interest given their diverse biological functions [START_REF] Hannun | Principles of bioactive lipid signalling: lessons from sphingolipids[END_REF] . In most cell types S1P and its metabolic precursor ceramide exert antagonistic effects on cell survival. Due to its tissue protective properties S1P turned out to be primarily a survival signal, whereas ceramide was shown to mediate cellular stress response [START_REF] Hannun | Principles of bioactive lipid signalling: lessons from sphingolipids[END_REF] .

Note that phosphorylation of sphingosine is catalyzed by sphingosine-kinase (SK) of which two distinct isoforms, SK1 and SK2, have been cloned and characterized [START_REF] Kohama | Molecular cloning and functional characterization of murine sphingosine kinase[END_REF][START_REF] Liu | Molecular cloning and functional characterization of a novel mammalian sphingosine kinase type 2 isoform[END_REF] . Degradation of S1P occurs either via reversible dephosphorylation to sphingosine or via irreversible cleavage by the ER resident S1P-lyase 1 (Figure 1), suggesting a tight regulation and maintenance of low cellular levels of this bioactive molecule. S1P exerts its functions either as a ligand for a family of five specific G-protein coupled receptors (S1P 1-5 ) or as an intracellular second messenger [START_REF] Hait | Sphingosine kinases, sphingosine 1-phosphate, apoptosis and diseases[END_REF] . In contrast to the well-characterized receptor-mediated effects of S1P, much less is known about its intracellular actions. One of the intracellular effects of S1P is its involvement in calcium homeostasis [START_REF] Ghosh | Sphingosine 1-phosphate generated in the endoplasmic reticulum membrane activates release of stored calcium[END_REF][START_REF] Meyer Zu Heringdorf | Photolysis of intracellular caged sphingosine-1-phosphate causes Ca2+ mobilization independently of G-protein-coupled receptors[END_REF] . The complex biological effects of S1P are cell type and differentiation specific. Thus S1P induces proliferation in neuronal progenitor cells [START_REF] Harada | Sphingosine-1-phosphate induces proliferation and morphological changes of neural progenitor cells[END_REF] but apoptosis in hippocampal neurons [START_REF] Moore | Sphingosine-1phosphate induces apoptosis of cultured hippocampal neurons that requires protein phosphatases and activator protein-1 complexes[END_REF] . We have recently shown that accumulation of S1P in S1P-lyase-deficient neurons induces apoptosis as well [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF] . This neurotoxic effect was independent of S1P receptors but involved dephosphorylation to sphingosine and rephosphorylation catalyzed by SK2 [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF] . A similar effect was observed with the synthetic sphingosine analog cis-4-methylsphingosine (cimes) [START_REF] Naetzker | Activation of p38 mitogen-activated protein kinase and partial reactivation of the cell cycle by cis-4-methylsphingosine direct postmitotic neurons towards apoptosis[END_REF] . Cimes is taken up by the cells and mainly phosphorylated by SK2 to form cis-4-methylsphingosine-phosphate (cimesP) [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF] . This semisynthetic S1P analog turned out to be metabolically stable, thus accumulating inside most cell types investigated so far [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF][START_REF] Naetzker | Activation of p38 mitogen-activated protein kinase and partial reactivation of the cell cycle by cis-4-methylsphingosine direct postmitotic neurons towards apoptosis[END_REF][START_REF] Van Echten-Deckert | cis-4-Methylsphingosine decreases sphingolipid biosynthesis by specifically interfering with serine palmitoyltransferase activity in primary cultured neurons[END_REF][START_REF] Van Echten-Deckert | Phosphorylated cis-4-methylsphingosine mimics the mitogenic effect of sphingosine-1-phosphate in Swiss 3T3 fibroblasts[END_REF] . Like S1P, cimesP stimulated proliferation of quiescent Swiss 3T3 fibroblasts [START_REF] Van Echten-Deckert | Phosphorylated cis-4-methylsphingosine mimics the mitogenic effect of sphingosine-1-phosphate in Swiss 3T3 fibroblasts[END_REF] .

S1P generated in the ER membrane has been shown to activate release of calcium from inositol 1,4,5-trisphosphate (InsP3)-sensitive calcium pools [START_REF] Ghosh | Sphingosine 1-phosphate generated in the endoplasmic reticulum membrane activates release of stored calcium[END_REF] . The neurotoxic effect of S1P and cimesP generated by SK2 in ER membranes [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF] might therefore be associated with the disruption of calcium homeostasis. This possibility is supported by experimental evidence indicating that the deregulation of the cysteine protease calpain is a key cytotoxic event in a variety of neurodegenerative processes [START_REF] Camins | Involvement of calpain activation in neurodegenerative processes[END_REF] .

Calpain activity triggered by elevated intracellular calcium levels is often associated with activation of cyclin-dependent kinase5 (CDK5) [START_REF] Camins | Involvement of calpain activation in neurodegenerative processes[END_REF] . Interestingly, several brain pathologies with neuronal CDK5 dysregulation also exhibit re-expression of different cell cycle markers in terminally differentiated neurons [START_REF] Hernandez-Ortega | Sequential expression of cell-cycle regulators and Alzheimer's disease-related proteins in entorhinal cortex after hippocampal excitotoxic damage[END_REF] . Indeed cell cycle reactivation is considered an important feature of neurological disorders [START_REF] Yang | Cell division in the CNS: protective response or lethal event in post-mitotic neurons?[END_REF] .

In this study we investigated the molecular mechanism of neuronal apoptosis elicited by S1P accumulation. Parallel experiments were conducted using S1P in S1P-lyase-deficient neurons or the semi-synthetic cimesP in wildtype neurons. Our results suggest that neuronal death induced by sphingoid-base phosphates is independent of mitochondria but involves calpain activation. This protease triggered the ER-stress specific caspase cascade and also CDK5 mediated cell cycle re-entry. Calpain dependent CDK5 activation could be correlated in addition with hyperphosphorylation of tau, that forms neurofibrillary tangles in AD and several other neurological disorders known as tauopathies [START_REF] Gendron | The role of tau in neurodegeneration[END_REF] . In this study we also provide evidence of the pathophysiological impact of sphingoid-base phosphate neurotoxicity. The apoptotic pathway described in this study may therefore be of particular interest for the development of new strategies in the treatment of neurodegenerative disorders that are triggered by sphingoid-base phosphates generated by SK2.

Results

Cimes fails to induce apoptosis in sphingosine-kinase2-deficient neurons

In a previous study we have shown that cimesP is mainly generated by SK2 [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF] . We have shown in addition that in S1P-lyase-deficient neurons S1P induces apoptosis only when generated by SK2 [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF] . We now compared the neurotoxicity of cimes in granule cells prepared from wildtype, SK1-and SK2-deficient mice, respectively. As depicted in Figure 2 cimes reduced viability of wildtype neurons as well as of SK1-deficient cells, whereas it did not affect viability of SK2deficient neurons (Figure 2a). Accordingly, effector-caspase activation was measured only in wildtype and SK1-deficient neurons (Figure 2b). Similarly DNA fragmentation occurred only in these two cell types (Figure 2c) whereas SK2-deficient neurons were unaffected (Figure 2). Therefore, the reader should keep in mind that throughout this study cells were incubated with cimes but the biologically active compound was, in fact, SK2-generated phosphate (cimesP).

Cimes induces intracellular calcium signaling without affecting mitochondrial function

Extra-cellular application of cimes or S1P leads to an increase in the intracellular calcium concentration [START_REF] Van Echten-Deckert | Phosphorylated cis-4-methylsphingosine mimics the mitogenic effect of sphingosine-1-phosphate in Swiss 3T3 fibroblasts[END_REF] , most likely due to release of calcium from the ER [START_REF] Ghosh | Sphingosine 1-phosphate generated in the endoplasmic reticulum membrane activates release of stored calcium[END_REF] . Prolonged incubation of cerebellar neurons with cimes, which leads to the intracellular accumulation of the metabolically stable cimesP, induced long-lasting and persistent increases in the resting [Ca] i which amounted up to 900 nM after 16 h of incubation (Figure 3a). As expected, incubation of neurons (up to 24 h) with the short-lived S1P had no effect on the resting [Ca] i (Figure 3a). Yet, brief applications of S1P induced a transient increase of intracellular calcium ([Ca] i ) (Figure 3b), a finding that is consistent with previous reports on different cell types [START_REF] Meyer Zu Heringdorf | Photolysis of intracellular caged sphingosine-1-phosphate causes Ca2+ mobilization independently of G-protein-coupled receptors[END_REF][START_REF] Van Echten-Deckert | Phosphorylated cis-4-methylsphingosine mimics the mitogenic effect of sphingosine-1-phosphate in Swiss 3T3 fibroblasts[END_REF] . To assure that neurons were capable to produce calcium signals cells were challenged with high extra-cellular potassium. As shown in Figure 3b more than 95% of the cells responded with robust transient increases in [Ca] i upon KCl-induced depolarization.

Disturbance of calcium homeostasis often affects mitochondrial functions [START_REF] Maceyka | SphK1 and SphK2, sphingosine kinase isoenzymes with opposing functions in sphingolipid metabolism[END_REF] . We therefore investigated whether mitochondria are involved in cimes-induced neuronal cell death by studying cytochrome c release into cytosol. However, cytochrome c could not be detected in the cytosolic fraction of cells treated with cimes (10 µM) indicating integrity of mitochondria (Figure 3c). To verify our findings we used neurons from S1P-lyase-deficient mice incubated with S1P (10 µM) and compared them to wildtype neurons treated alike. As illustrated in Figure 3d no cytochrome c could be detected in the cytosolic fraction of S1P-lyase-deficient mice in the presence of S1P. Furthermore, mitochondrial integrity was analyzed in the absence or presence of cimes using the fluorescent cationic dye JC-1. These measurements revealed that cimes does not reduce the number of intact mitochondria in terminally differentiated cerebellar neurons (Figure 3e). As positive control neurons were incubated in the presence of carbonyl-cyanide m-chlorophenyl hydrazone (CCCP), which abolishes mitochondrial membrane potential (Figure 3e).

Mitochondria independent apoptosis is promoted by caspase-9 and caspase-12

As shown in Figure 2b caspase activity is considerably increased in cells incubated with cimes.

We therefore examined which of the initiator-caspases was responsible for activation of effectorcaspase-3. As depicted in Figure 4a caspase-8 was not activated in the presence of the sphingoidbase phosphate. Instead of that caspase-9 was activated (Figure 4b), which is usually linked to the mitochondrial death pathway that we just excluded (see above). To confirm this unexpected result we used Z-LEHD-fmk, a specific caspase-9 inhibitor, which almost completely prevented cimes-induced effector-caspase-3 activation (Figure 4c). However, neuronal viability (Figure 4e) and DNA integrity (Figure 4d) were only partially improved by this inhibitor. Since caspase-9 was activated independently of cytochrome c release, we considered an alternative activation pathway, namely, the ER-stress specific apoptotic pathway involving particularly caspase-12 [START_REF] Nakagawa | Caspase-12 mediates endoplasmic-reticulum-specific apoptosis and cytotoxicity by amyloid-beta[END_REF][START_REF] Morishima | An endoplasmic reticulum stress-specific caspase cascade in apoptosis. Cytochrome cindependent activation of caspase-9 by caspase-12[END_REF] .

Consistent with this pathway, we found an activation of caspase-12 in the presence of cimesP (Figure 4f) that, in turn, activates caspase-9 in a cytochrome c independent manner.

Calpain mediates cimes-induced neurotoxicity

As shown in Figure 4 reduced cell viability and apoptotic DNA cleavage persisted even after almost complete abrogation of caspase activity. Based on the fact that sphingoid-base phosphates induce calcium release from the ER [START_REF] Ghosh | Sphingosine 1-phosphate generated in the endoplasmic reticulum membrane activates release of stored calcium[END_REF] and calpain was shown to induce caspase-9 independently of cytochrome c release [START_REF] Nakagawa | Cross-talk between two cysteine protease families. Activation of caspase-12 by calpain in apoptosis[END_REF] , we explored a possible involvement of this calcium-dependent regulatory protease in cimes-induced neurotoxicity. On the one hand, Western blot analysis revealed a strong up-regulation of calpain expression in neurons incubated with cimes (Figure 5a). On the other hand MDL28170, an effective pharmacological inhibitor shown to specifically suppress calpain activity [START_REF] Mehdi | Inhibition of the proteolysis of rat erythrocyte membrane proteins by a synthetic inhibitor of calpain[END_REF] , completely rescued neurons from cimes-induced toxicity (Figure 5b).

Accordingly, preincubation of cells with MDL28170 (10 µM) largely prevented caspase activation and DNA degradation (Figure 5c and5d). Interestingly, inhibition of calpain also prevented morphological changes induced by cimes (Figure 5e). As becomes clear from Figure 5e neurons treated with cimes (24 h, 10 µM) showed the typical changes in morphology, specifically cell-aggregates connected by radially running neurites, whereas MDL treated neurons retained the morphology of control cells.

Reactivation of cell cycle depends on calpain and CDK5/p25

We have shown previously that cimes-as well as S1P-induced neuronal apoptosis involves an inappropriate cell cycle reactivation [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF][START_REF] Naetzker | Activation of p38 mitogen-activated protein kinase and partial reactivation of the cell cycle by cis-4-methylsphingosine direct postmitotic neurons towards apoptosis[END_REF] . The fully protective effect of MDL encouraged us to investigate the role of calpain for cell cycle reactivation in these postmitotic neurons. First we examined whether depletion of cytosolic calcium affects cimes-induced expression of cyclin D1.

As depicted in Figure 6a the cell permeable calcium chelator Bapta-AM completely abrogated cyclin D1 expression induced by cimes. We observed the same result after incubation of the cells with the calpain inhibitor MDL (Figure 6b), suggesting once more the involvement of calciumdependent factors in the observed neurotoxic effects of sphingoid-base phosphates. We therefore aimed to identify downstream targets of calpain, which could promote cell cycle re-entry. As shown in Figure 6c and 6e MDL substantially abrogates cimes-induced up-regulation of CDK5 and of p25, suggesting their involvement in signaling downstream of calpain. Similar results were obtained with S1P in S1P-lyase-deficient neurons (Figure 6d). Furthermore, MDL completely abolished cimes-induced phosphorylation and thus inactivation of the inhibitory cell cycle regulator Rb (retinoblastoma protein) (Figure 6f). These results indicate that reactivation of neuronal cell cycle involves cytosolic calcium and a calpain-dependent formation of p25 accompanied by an up-regulation of CDK5 and phosphorylation of Rb.

Calpain mediates cimes-induced tau hyperphosphorylation

Hyperphosphorylation of the microtubule associated protein tau is a characteristic feature of neurodegenerative disorders (tauopathies) including Alzheimer's disease [START_REF] Lee | Neurodegenerative tauopathies[END_REF] . We therefore investigated whether sphingoid-base phosphates promote excessive phosporylation of tau. Indeed, incubation of wildtype and S1P-lyase-deficient neurons with cimes and S1P, respectively, results in an enhanced tau phosphorylation at the PHF-1 site (S396 and S404) (Figure 7a). Further studies with cimes revealed additional phosphorylation of tau at the 12E8 site (S262 and S214) (Figure 7b). PHF-1 recognizes phosphorylated motifs in the flanking region of the internal repeat domain while 12E8 binds to phosphorylated serine residues of the KXGS motifs within the repeat domain. In both cases the calpain inhibitor MDL reversed cimes-induced hyperphosphorylation of tau, whereas MDL alone did not affect tau phosphorylation.

Pathophysiological impact of S1P

To investigate the physiological relevance of accumulating sphingoid-base phosphates we compared sagittal sections through the cerebellar vermal region of S1P-lyase-deficient and wildtype mice. As shown in Figure 8, S1P-lyase immunoreactivity is mainly and regularly present in Purkinje cells as well as in (Bergmann) glial cell processes and some scattered interneurons (Figure 8a,b). Note that in corresponding regions from cerebella of S1P-lyasedeficient mice no immunoreactivity was detectable (Figure 8c,d). Analysis of the cerebellar cortex of wildtype (Figure 8e) and of S1P-lyase-deficient mice (Figure 8f) reveals the presence of scattered small groups of degenerating Purkinje cells only in S1P-lyase-deficient mice.

Discussion

In a recent study we have shown that in terminally differentiated neurons cimes is mainly phosphorylated by SK2 (90%) and only a poor substrate for SK1 [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF] . We now demonstrate that SK2 activity is indispensable for the apoptotic effect of cimes. Thus our results clearly show that cimes induces apoptosis in wildtype and SK1-deficient neurons whereas it fails to induce apoptosis in SK2-deficient neurons. It is well known that the two isoenzymes catalyzing sphingosine phosphorylation have opposite effects on cellular growth and apoptosis. While SK1 generates S1P, which promotes cell growth and rescues cells from ceramide-induced apoptosis, overexpression of SK2 suppresses growth and enhances cell death [START_REF] Hait | Sphingosine kinases, sphingosine 1-phosphate, apoptosis and diseases[END_REF] . Interestingly, structural analogues of sphingosine, including FTY720 [START_REF] Allende | Mice deficient in sphingosine kinase 1 are rendered lymphopenic by FTY720[END_REF] , FTY720 analogues [START_REF] Don | Essential requirement for sphingosine kinase 2 in a sphingolipid apoptosis pathway activated by FTY720 analogues[END_REF] and cimes [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF] are mainly phosphorylated by the less substrate specific SK2 [START_REF] Liu | Molecular cloning and functional characterization of a novel mammalian sphingosine kinase type 2 isoform[END_REF] . It was shown that some of them induced apoptosis [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF][START_REF] Don | Essential requirement for sphingosine kinase 2 in a sphingolipid apoptosis pathway activated by FTY720 analogues[END_REF] .

Despite some contradictory findings on localization of SK isoenzymes, it is generally accepted that SK1 is predominantly cytosolic and translocated to the plasma membrane upon activation [START_REF] Hait | Sphingosine kinases, sphingosine 1-phosphate, apoptosis and diseases[END_REF][START_REF] Spiegel | Sphingosine-1-phosphate: an enigmatic signalling lipid[END_REF] whereas SK2 is associated with internal membranes, predominantly the ER [START_REF] Maceyka | SphK1 and SphK2, sphingosine kinase isoenzymes with opposing functions in sphingolipid metabolism[END_REF][START_REF] Don | Essential requirement for sphingosine kinase 2 in a sphingolipid apoptosis pathway activated by FTY720 analogues[END_REF] . Interestingly, SK1 also promoted apoptosis when targeted to the ER [START_REF] Maceyka | SphK1 and SphK2, sphingosine kinase isoenzymes with opposing functions in sphingolipid metabolism[END_REF] indicating that ER localization rather than the enzyme by itself is essential for the apoptotic effect. Using fluorescent derivatives, it has been shown that sphingoid-base phosphate analogues generated by SK2 accumulate mainly in ER membranes [START_REF] Don | Essential requirement for sphingosine kinase 2 in a sphingolipid apoptosis pathway activated by FTY720 analogues[END_REF] . In light of these results and in agreement with an ER localization of SK2, it appears quite likely that cimes phosphorylated by SK2 also accumulates in ER membranes.

Moreover, we could show in this study that cimes downstream signaling is promoted by ER specific proteases including calpain and caspase-12. In addition we could exclude involvement of mitochondria in cimes-induced neuronal apoptosis. This was an unexpected finding given the clear activation of caspase-9, which has been shown to depend on cytochrome c release [START_REF] Li | Cytochrome c and dATP-dependent formation of Apaf-1/caspase-9 complex initiates an apoptotic protease cascade[END_REF] . Also, mitochondria permeabilization was proposed as part of the sphingoid-base phosphate-induced apoptotic pathway in immune cells [START_REF] Don | Essential requirement for sphingosine kinase 2 in a sphingolipid apoptosis pathway activated by FTY720 analogues[END_REF] . Cimes failed, however, to induce cytochrome c release and caspase-8 activation indicating that the sphingoid-base phosphate pro-apoptotic pathway in neurons is different.

The observation that caspase-9 was activated independently of cytochrome c release, prompted us to look for ER dependent factors that might be responsible for sphingoid-base phosphate-induced activation of procaspase-9. In agreement with previous findings [START_REF] Morishima | An endoplasmic reticulum stress-specific caspase cascade in apoptosis. Cytochrome cindependent activation of caspase-9 by caspase-12[END_REF] , our results indicate that cimes activates caspase-12, which then specifically cleaves procaspase-9 in a mitochondria-independent manner. Cleavage and hence activation of caspase-12 has been suggested to be catalyzed by calpain [START_REF] Nakagawa | Cross-talk between two cysteine protease families. Activation of caspase-12 by calpain in apoptosis[END_REF] . This cytosolic protease is activated by increased cytosolic calcium levels, which induce its translocation from the cytosol to ER membranes. As cimes promoted a persistent elevation of intracellular calcium concentration, activation of calpain appeared quite likely. Calpain activation has been described in several neuronal pathologies, many of them including also CDK5 dysregulation caused by calpain catalyzed cleavage of CDK5 regulatory subunit p35 [START_REF] Patrick | Conversion of p35 to p25 deregulates Cdk5 activity and promotes neurodegeneration[END_REF] . The resulting p25 subunit lacks the membrane anchor binding site generating a hyperactive and mislocalized CDK5/p25 complex [START_REF] Patrick | Conversion of p35 to p25 deregulates Cdk5 activity and promotes neurodegeneration[END_REF] . Note, that CDK5 is essential for normal brain development and function, but uncontrolled activity may lead to numerous neurodegenerative diseases [START_REF] Dhavan | A decade of CDK5[END_REF] .

Neurotoxicity caused by the CDK5/p25 complex has been suggested to be associated with hyperphosphorylation of tau [START_REF] Lee | Cdk5: one of the links between senile plaques and neurofibrillary tangles?[END_REF] and/or reactivation of the cell cycle [START_REF] Lopes | Cdk5 acts as a mediator of neuronal cell cycle re-entry triggered by amyloid-beta and prion peptides[END_REF] . Notably, cimes stimulates tau phosphorylation and induces cell cycle re-entry (Figure 9). Moreover, both effects are calpain and CDK5/p25 dependent. Hyperphosphorylation of tau caused by cimes strongly suggests that neurotoxicity of sphingoid-base phosphates might be related to an abnormal tau aggregation.

Interestingly, tau hyperphosphorylation was also reported in fetal tissue and in mitotic cells indicating that mitotic signals might be able to cause hyperphosphorylation of tau and hence apoptotic death in differentiated neurons [START_REF] Mandelkow | Tau in Alzheimer's disease[END_REF] . The mitogenic potential of cimes [START_REF] Van Echten-Deckert | Phosphorylated cis-4-methylsphingosine mimics the mitogenic effect of sphingosine-1-phosphate in Swiss 3T3 fibroblasts[END_REF] argues in favor of this hypothesis.

Collectively, our data indicate that sphingoid-base phosphates cause neuronal death by a calpainmediated mechanism involving CDK5/p25 and the ER-stress specific caspase cascade (Figure 9). Intriguingly, S1P dependent neurotoxicity described in the present study shows similarity to that of the amyloid beta-peptide in Alzheimer's disease. Thus amyloid beta-peptide neurotoxicity also involves procaspase-12 activation by disruption of ER calcium homeostasis but not by membrane-or mitochondria-targeted apoptotic signals [START_REF] Nakagawa | Caspase-12 mediates endoplasmic-reticulum-specific apoptosis and cytotoxicity by amyloid-beta[END_REF] . Furthermore, amyloid beta-peptide induces an aberrant reactivation of cell cycle events and activation of CDK5 [START_REF] Lopes | Neurodegeneration in an Abeta-induced model of Alzheimer's disease: the role of Cdk5[END_REF] . Notably, calpain emerged as a central player in the pathogenesis of neurological diseases [START_REF] Camins | Involvement of calpain activation in neurodegenerative processes[END_REF] thus suggesting a pathophysiological relevance of our results. Accordingly, an impaired metabolism of glycosphingolipids, which are highly abundant in the central nervous system, might be linked via S1P, their common catabolic intermediate, to neuronal death. Neuroanatomical studies document for the first time that indeed neurons with abundant S1P-lyase expression are those, which degenerate first in S1P-lyase-deficient mice. This finding suggests that S1P might be the missing link connecting impaired lipid metabolism and neurological disorders.

METHODS

Cell culture

Granule cells from cerebella of 6-days-old wildtype, S1P-lyase (sgpl1) -/-sphingosine-kinase1 (sphk1) -/-and sphingosine-kinase2 -/-mice were used. Sgpl1 +/-or sgpl1 -/-pups were inbred in a Swiss Webster genetic background. Heterozygous sgpl1 +/-non-inbred mouse was generated from gene trapped ES cells (OST 58278) by Lexicon Inc. (Texas) on a fee basis [START_REF] Vanveldhoven | Sphingosine 1-phosphate lyase deficient mice[END_REF] . To generate the sphk1 and sphk2 null mice, a genomic DNA fragment was cloned containing the sphk1 and sphk2 gene, respectively, from a 129/sv strain library inbred in a C57/BL6 background [START_REF] Allende | Mice deficient in sphingosine kinase 1 are rendered lymphopenic by FTY720[END_REF][START_REF] Mizugishi | Essential role for sphingosine kinases in neural and vascular development[END_REF] . For all transgenic mice, heterozygous matings were set up to generate homozygous mutant mice.

Mice were bred in the animal house of the University in Bonn (Germany).

The neuronal cells were cultured as described before [START_REF] Van Echten-Deckert | cis-4-Methylsphingosine decreases sphingolipid biosynthesis by specifically interfering with serine palmitoyltransferase activity in primary cultured neurons[END_REF] . Briefly, cells were isolated by mild trypsinisation (0.05% w/v) and dissociated by repeated passage through a constricted Pasteur pipette in a DNase solution (0.1% w/v). The cells were then suspended in Dulbecco´s modified eagle medium (DMEM) (containing 10% heat-inactivated horse serum, penicillin 100 U/l, and streptomycin 100 mg/l) and plated on to poly-L-lysine-coated 8 cm 2 Petri dishes (6 x 10 6 cells/dish). At day 5 in culture primary neurons were treated with 10 µM cis-4-methylsphingosine (synthesized as described [START_REF] Bar | Synthesis of Methyl-Branched Sphingosines[END_REF] ), S1P, or the caspase-9 inhibitor Z-LEHD-FMK (R&D Systems, Wiesbaden, Germany) for the indicated times. In some experiments preincubations with the calpain inhibitor MDL28170 (Sigma, Taufkirchen, Germany) or the cell permeable calciumchelator Bapta-AM (Invitrogen, Karlsruhe, Germany) were performed as indicated.

Calcium imaging

Neurons were loaded with the Ca 2+ sensitive dye Fura-2-AM (3 µM, Molecular Probes Europe BV, Leiden, The Netherlands) at 37°C in bicarbonate buffered saline solution containing (mM): 156 NaCl, 2 KCl, 2 CaCl 2 , 1 MgCl 2 , 26 NaHCO 3 , 1.25 NaH 2 PO 4 and 10 glucose, gassed with 5% CO 2 , pH 7.3. Background-corrected fluorescence was taken with a slow-scan CCD camera system with fast monochromator (TILL Photonics, Grafelfing, Germany) coupled on an Axiovert 100 microscope equipped with a Neofluar objective (10x, Zeiss, Oberkochen, Germany). Fura-2 was excited at 357 and 380 nm wavelengths, and fluorescence was collected between 500 and 540 nm at a frequency of 0.5 Hz. The change in [Ca 2+ ] i is presented as the change in the fluorescence ratio obtained at the two excitation wavelengths (F357/F380). This experimental set-up allowed for the two-dimensional representation of Ca 2+ signals in all cells simultaneously. Averages of fluorescence intensity from somatic regions were chosen for quantification (~50-80 pixels) and analyzed off-line with routines written in Igor Pro software (Wavemetrics, Eugene, OR, USA). A neuron was included in the analysis if the peak of the response from a 30 s reference application of 30 mM KCl was larger than threshold, defined as six standard deviations (S.D.) of the baseline noise [START_REF] Titz | Hyperpolarizing inhibition develops without trophic support by GABA in cultured rat midbrain neurons[END_REF] . The same baseline S.D. criterion was used to count cells responsive to other substances and to calculate the average peak amplitudes. All recordings were carried out at room temperature (22-25 °C) in Hepes buffered saline containing (mM): 145 NaCl, 2.5 KCl, 2 CaCl 2 , 1.3 MgCl 2 , 10 Hepes and 20 glucose, pH 7.3. In solutions with elevated KCl (20 mM), NaCl concentration was reduced by the same amount. Solutions were applied using a focal perfusion system (DAD-12, ALA Scientific Instruments, Westbury, NY, USA).

Caspase Assay

Caspase assays were performed according to provider's protocol (Invitrogen, Karlsruhe, Germany). Cell pellets were resuspended in 50 µl of cold lysis buffer and incubated on ice for 15 min. After addition of 50 µl reaction buffer, containing dithiotreitol (10 mM) and IETD-, LEHDor DEVD-p-nitroanilin substrate (50 µM), samples were incubated for 2 h at 37°C in the absence of light. Absorbance was measured at 405 nm. Caspase activities are expressed relative to untreated wildtype controls.

Cell viability assay

For quantification of cell death in cultured cells, we employed the CellTiter-Blue Cell Viability Assay (BD Pharmingen, Heidelberg, Germany), which is based on the conversion of resazurin to the fluorescent product resorufin exclusively by metabolically active (viable) cells. Following the indicated treatment of neurons, 100 µl of CellTiter-Blue reagent were added to each cell culture dish. After 1 h of incubation, fluorescence of resorufin was recorded in an aliquot (100 µl) culture medium at 544 Ex /590 Em .

Genomic DNA analysis

Genomic DNA analysis was performed as described previously [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF] . In brief, cells were harvested in the respective medium and centrifuged (2000 x g, 10 min, 4°C), thus collecting both adherent and detached cells. Cell pellets were then resuspended in 500 µl ice cold phosphate buffered saline (PBS) and centrifuged again (2000 x g, 10 min, 4°C). Genomic DNA was purified using QIAamp DNA Blood Mini Kits (Qiagen, Hilden, Germany) according to the protocol of the provider.

Finally, samples were loaded onto a 1.6% agarose gel. Following electrophoresis DNA was visualized under UV light using ethidium bromide.

Mitochondrial integrity

JC-1 (Cell Technology Inc, USA) is a common tool to assess the polarization status of mitochondrial membranes. This fluorescent dye forms so-called J-aggregates (red fluorescence) in intact negatively charged mitochondria. As soon as the mitochondrial membrane potential collapses, JC-1 is dispersed throughout the cell in a monomeric form (green fluorescence). Thus neurons were pretreated as indicated and incubated with JC-1 following provider's protocol.

Then cells were washed and JC-1 monomers assessed using excitation/emission wavelength of 485/530 nm, while J-aggregates were measured at 560/595 nm.

In addition cytochrome c release was analyzed using the cytochrome c release apoptosis assay kit from Calbiochem (Merck, Darmstadt, Germany) following provider's protocol.

Neuroanatomical studies

Mice (7 weeks of age) were killed by an overdose of chloroform and then perfused via the left ventricle with Sörensen phosphate buffer w/1% procaine followed by a further perfusion with either 6% glutardialdehyde (for epoxy resin embedding and semithin sectioning) or 2 % paraformaldehyde (for further vibratome sections and immunohistochemistry) in the same buffer.

For epoxy resin embedding, tissues were postfixed at least overnight, rinsed in buffer, and dissected tissue samples embedded in Epon / glycid ether after osmication following standard procedures. Sections were cut at 1 µm and stained with toluidine blue / pyronin G. For immunohistochemistry, brains were rinsed in Sörensen buffer, encased in agarose and cut on a high-frequency vibratome (Leica VT 1200 S, Leica, Wetzlar, Germany). After antigen retrieval and blocking, sections were incubated with an S1P-lyase antibody (Abcam, Cambridge, UK) at a 1:100 dilution, and the binding of the primary antibody was detected by the use of a HRPtagged secondary antibody using tyramide-FITC (NEN-Dupont) as a fluorescent substrate.

Nuclear counterstaining was done with bisbenzimide (Sigma, Deisenhofen, Germany).

Specimens were photographed on a Nikon 90i epifluorescence microscope equipped with a 4 channel EZ-C1 confocal laser system.

Western blotting

SDS-PAGE and Western blotting were performed as described earlier [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF] . Cells were lysed for 10 min at 4°C in Cell lysis buffer (Cell Signaling) containing protease inhibitors (Invitrogen). Cell extracts were centrifuged at 10,000 × g for 10 min at room temperature to separate insoluble material, followed by determination of protein concentration using the BCA assay (Sigma-Aldrich). Proteins from each sample were mixed with loading buffer (RotiLoad, Roth), boiled for 10 min and subjected to SDS-PAGE followed by transfer to nitrocellulose membranes for 6 min via the iBlot (Invitrogen). Membranes were blocked for 1 h with 5% non-fat milk in TBS at room temperature and subsequently probed with the desired primary antibody. Blots were revealed by ECL™ (Amersham Biosciences). The following primary antibodies were used: calpain1 (15C10), cyclin D1 (A-12), CDK5 (J-3), p35 (C-19) for p25, α-tubulin (H-300) from Santa Cruz Biotechnology (Heidelberg, Germany); caspase-12, pRb (Ser 807/811), Rb (4H1) from Cell Signalling (Danvers, USA); PHF-1 from P. Davies (Albert Einstein College, Bronx, NY), 12E8 from P. Seubert (Elan Pharma, South San Francimesco, CA) and K9JA from DAKO (Glostrup, Denmark); cytochrome c from cytochrome c release apoptosis assay kit. Primary antibodies were diluted in blocking solution in accordance with provider's protocol. Secondary antibodies were diluted 1: 40000 in TBST. To confirm equal amounts of protein loaded for each sample, blots were reprobed with respective antibody (Rb, α-tubulin). Some Western blots were densitometrically evaluated using the AlphaDigiDoc gel documentation system (Biorad, München, Germany). In each experiment the ratio of absorbance of the respective protein versus loading control was calculated.

Presentation of data and statistics

All experiments were repeated at least three times with consistent results in double determinations. Data are expressed as means ± S.D or SEM and normalized as indicated.

Statistical analysis was performed using Student's t test. Statistical significance was tested at 95% (p < 0.05) confidence level. Results presented as DNA or protein gels correspond to data obtained with at least three different cell preparations. Cerebellar neurons from wildtype (+/+) or S1P-lyase-deficient (-/-) mice were treated for 24 h with vehicle (ctrl, control), cimes or S1P (10 µM each). Cell lysates were probed for cytochrome c content. (e) Neurons were incubated for 24 h in the absence or presence of cimes (10 µM).

Title and legends to figures

Then JC-1 was added and as the ratio of J-aggregates to JC-1 monomers was determined. As a positive control, neurons were incubated with 100 μmol/l CCCP for 45 min prior to JC-1 staining. For quantification control cells were used as reference and set to 100%. Calpain is the central signaling molecule and mediates sphingoid-base phosphate-induced neuronal apoptosis by activation of ER-stress specific caspase cascade and initiation of cell cycle reactivation. In addition calpain/CDK5 dependent tau hyperphosphorylation is induced. The metabolic fate of exogenous cimes and S1P in wildtype and S1P-lyase-deficient mice, respectively, was described previously [START_REF] Hagen | Subcellular origin of sphingosine 1-phosphate is essential for its toxic effect in lyase-deficient neurons[END_REF] . CDK5, cyclin dependent kinase5; cimes, cis-4methylsphingosine; cimesP, cis-4-methylsphingosine phosphate; ER, endoplasmatic reticulum; Rb, retinoblastoma protein; SK2; sphingosine-kinase2; Sph, sphingosine; SPP, sphingosinephosphate phosphatase.

Figure 1

 1 Figure 1 Scheme of sphingolipid metabolism. Ceramide is formed either de novo starting from

Figure 2

 2 Figure 2 Cimes does not induce apoptosis in SK2-deficient neurons. Cerebellar neurons from

Figure 3

 3 Figure 3 Prolonged application of cimes induces gradual increases in intracellular calcium concentration ([Ca 2+ ] i ) without affecting mitochondrial function. (a) Neurons were incubated for

Figure 4

 4 Figure 4 Mitochondria independent apoptosis is promoted by caspase-9 and caspase-12.

Figure 5

 5 Figure 5 Calpain mediates cimes neurotoxicity. Cerebellar neurons were pre-incubated for 1 h

Figure 6

 6 Figure 6 Reactivation of the cell cycle by sphingoid phosphates depends on calpain and

Figure 7

 7 Figure 7 Calpain mediates cimes-induced tau hyperphosphorylation. (a) Cerebellar neurons from

Figure 8

 8 Figure 8 Correlation between S1P-lyase immunoreactivity and neuronal degeneration. Cerebella

Figure 9

 9 Figure 9Proposed signaling cascade of sphingoid-base phosphate-induced neurotoxicity.

Acknowledgement

We thank Eva-Maria Mandelkow for valuable discussions on tau phosphorylation, Paul P. Van Veldhoven for providing S1P-lyase-deficient mice, Richard L Proia for providing sphingosinekinase-deficient mice, Philip Hockberger for improving the English of the manuscript, Birgit Rau und Angelika Zoons for expert technical support and Tracy Klitz for her help in breeding mice.

Author contribution

NH designed, performed experiments and wrote the paper, MH designed and performed calcium measurements, DH performed neuroanatomical studies, DS supervised calcium measurements and contributed to writing of the paper, GvED designed experiments and wrote the paper.