AN ANATOMICAL-BASED 3D REGISTRATION SYSTEM OF M U L T I M O D A L I T Y AND ATLAS DATA IN NEUROSURGERY D. I~moine t, C. Barillot t, B. Gibaud t, E. Pasqualini ~; i'INSERM U-335, Laboratoire SIM, Facult6 de Mtdecine, 35043 Rennes Cedex, France. :~Servicede Neurochirurgie,H6pital de Pontchailou, 35033 Rennes Cedex, France. Abstract The knowledge of patient neuro-anatomy is key information, at least in the understanding of the pathological processes and in the elaboration of precise treatment strategies in neurosurgery. In addition to classical radiology systems like angiography, CT scanner or MRI have greatly contributed to the improvement of the patient anatomy investigation. Each examination modality still carries its own information and the need to make a synthesis between them is obvious but still makes different problems hard to solve. There is no unique imaging facility which can bring out the whole set of known anatomical structures, brought together in a neuro-anatomical atlas. Nevertheless, it is very important for the physician to assign location to these structures from the images delivered by the studies. Only an accurate fusion of these data may help the physician to recognize the precise anatomical structures involved in the therapeutic process he has to set up. The aim of this study is to provide an understanding of heterogeneous data. We propose a method to register multimodality data according to a common referential system called Proportional Squaring. Upon this geomelrical basis, the deformation model is built up allowing the transfer of different patient data including the atlas within the same referential. Keywords Image Registration, Data Fusion, Brain Atlas, Multimodality Imaging, Stereotactic Neurosurgery, Deformation Model, MRI, CT, Angiography. 1. I N T R O D U C T I O N Modem neurology and neurosurgery make extensive use of medical images for both diagnostic and therapeutic purposes. Imaging modalities are now quite numerous, since the new ones have not always replaced the former ones: namely, they are complementary because they are suitable to display the various anatomical structures: CT and conventional radiology are relevant for the skull and ventricular system, angiography (film-based or digital) is used to display the blood vessels, MRI is suitable to visualize cerebral tissues and nuclear medecine (PET, SPECT) for functional imaging. Nevertheless, this large number of imaging modalities (we have only mentioned the major ones) can only bring a partial answer to the problem of localizing cerebral structures. On the one hand, no single modality can actually provide information to accurately identify cerebral structures like, for instance, the brain stem or the gyri of the cortex; complex fusion of several modalities (mainly angiography and MRI data) is necessary to reach this latter goal. A common geometrical reference is needed in order to be able to mix data from the various modalities. Furthermore, the ability to correlate in-vivo data with an anatomical model, for instance a 3D atlas, brings additional information that significantly helps the understanding of brain anatomy (Bookstein 1988, Chen et al. 1985, Christopher et al. 1991, Dann et al. 1988, Evans et al. 1991, Fox et al, 1985). Our objective is to propose solutions to these problems : our approach consists of validating and quantitatively assessing the use of anatomical references; this choice offers the advantage of remaining independent of any external landmarks leading in most cases to study protocols which may be difficult to carry out and unpleasant for the patient. The second objective is to be able to refer to anatomical models 155 by means of a comprehensive deformation model which enables the transfer of 3D points from a patient's data set to the atlas or from the atlas to a patient's data set or between two patient data sets. The registration and deformation models are intrinsically 3D : the actual representation made by means of 2D sections, coming either from in-vivo studies or from the arias, is only related with the capabilities of the workstation currently used to run the application ~ C AT). Namely, the algorithms can be @plied to 3D volumetric data sets (with an isotropic resolution in the 3 directions of space) without modification. We also made a choice for the Talairach Proportional Squaring Model (PSM). It is based on a very simple principle and has proven to be quite accurate, especially for the deep cerebral structures, as demonstrated by Talairach's statistical study on cerebral anatomy. Our primary aim was to realize a computer platform in order to facilitate and to increase the accuracy of the registration procedures which are currently manually performed by superposing films, drawing proportional squarings and reading atlas plates. Beyond this straightforward application in surgical practice, this platform could be used for research purposes, especially for quantitatively evaluating the variability of cerebral structures with the final aim of managing this information within a computerized 3D brain atlas. 2. P R ~ C I P L E OF THE TALAIRACH'S PROPORTIONAL SQUARING MODEL 2.1. Use of a Ventricular-Based Line Cerebral anatomy studies have demonstrated that bone based lines were not very accurate in modelling the proportions existing between the intra-cerebral structures. As an example, a skull with a large antero-posterior dimension does not automatically imply a wide thalamus, equally the angle between the Francfon line and the bi-commissural line is too inconstant to be used as a good reference among patients (between 11°5 ' and 18°5' for a sample of 5 people). Thus, bone based lines can not provide an accurate anatomical referential system (Longuet and Higgins, 1981). On the contrary, the ventricular system is a good referential since its shape and its orientation are tightly related to brain stem motion. The necessity to find out a general orientation map of the structures and to define individual ratios for the structure dimensions resulted in the choice of a ventricular and proportional base line : the bi-commissural line AC-PC (Naidich et aL 1986, Talairach et al. 1967-1988, Vanier et al. 1985). X PC AC ZBM Figure 1 : Definitionof the ProportionalSquaringModel 2.2. Definition of the Proportional Squaring Model The AC-PC line is defined as a straight line tangent to the upper border of the anterior commissura and tangent to the lower border of the posterior commissura within the sagittal mid-plane. From this line, two verticals are defined, i) VAC as the perpendicular to AC-PC at the posterior border of AC and ii) VPC as the perpendicular to AC-PC at the anterior border of PC as shown in Figure 2. These three lines and the mid-plane divide the cerebral volume into 12 parts (6 per hemisphere) with regards to the brain dimensions (Figure I). For each hemisphere, we define : • the upper point of the parietal cortex (along VAC) : zhm, • the most posterior point of the occipital cortex (along AC-PC) : xpm, • the lower point of the temporal cortex (along VAC) : zbm, • the most anterior point of the frontal cortex (along AC-PC) : xam, • the most lateral point of the parieto-temporal cortex (along the perpendicular to the mid-plane): ydm for the right hemisphere and ygm for the left hemisphere. 156 Within each of these sub-volumes, the deformation model defines the location of a structure as statistically proportional to the size of this sub-volume. It is a piecewise linear deformation model. For a particular patient, the calculation of the PSM from the brain extrema enables the computation of anamorphosis coefficients which make the transfer of information between a patient and a reference possible. 2.3. Computation of the Proportional Squaring Model Let Ppatient = ( Xpat,Ypat, Zpat) be the coordinates of a point according to the referential centered at the anterior c ommissura A C wliere the a x e s XpatYpa t and Zpat are respectively defined along the AC-PC and VAC lines and the normal to the mid-plane (Figure 1); let Pmoaet = (Xmoaet,Ymodet,Zmoaet) be the coordinates of the corresponding point within the referential built upon a model; let Mp~aient-moaet be the transformation matrix between the "patient" referential and the "model" referential and considering VJi as the sub-volumes of the Proportional Squaring Model, where j = r and j = l for the right and the left hemisphere respectively, and i = (0 ..... 5 ), the sub-volume number which includes the current point; the transfer of information between the "patient" and the "model" can be calculated as : Pmodel = Mpatient-model" Ppatient with : [sxi00 I o ,io ,iI i o o z.zil Mp~a~ra°~=l ^ ^ ~ J ~ J l 1oool 1 r l JJ whereSi=lSxiSyiSzi/J isthe scahng " vector andTi= J [TxiTyiTzi] J J J is the translation vector. L J The Mpatient-moaet transformation matrix is computed according to the sub-volume the point Ppatlent belongs to. Thus, for the Vi's of the right hemisphere, the computation is performed as follows: V0~S0=[Cto,a3, Cts] , ,[ . ,[ ] T I = [ 0 , 0 , 0] ] T3--[0, o , 0] Vl ~ $1= al,ct3, 0~5 V3=:~ S3= ~1~2,0~3, f2 6 T0=[-(ac-pc)moa~a+(ac-pc)~t.o~o, 0 , O] • r T,=[O, 0 , 0] V 5 :::~ S 5 = ~0,0~3, ~6 T;=[-(ac-pC)modd+(ac-lX:)p,ll,t.Oto, 0, 0] where: aO= ~3= xpmmo,~l+(ac-Pc)~oa,a xpmp,a~t+ (ac- p c ) ~ yd'nmodea - - ydn p.e~ ~1 = O~ 4 (ac- pC)model (ac- pc)p,~t ygmmoaa ygmp~e~t ~2 = ~5 = Xammode1 xamp,e~ zhmmoaca zhmp~e~t 016~ - Zbmrnodd - zbmv~i~t 157 H Zmri Zpatient = V A C ~ Xl~ti~ac ~pc vpc F Figure 2 : Definitionof the AC-PCbase-lineupon the mid-planesagittalslice 3. REGISTRATION OF MULTIMODAL STUDIES A registration procedure consists of defining the 3D geometrical relationships between in-vivo studies (CT, MRI, angiograms,...) and the proportional squaring system previously defined. MRI is actually the only modality upon which the bi-commissural line as well as the brain extrema can be detected. For this reason, the proportional squaring of a particular patient, including the definition of the AC-PC line and the computation of the scaling coefficients, are set up during the MRI registration procedure. In the work described below and according to the hardware limitations (PC workstation under MS-DOS), we have chosen to use directly (without preprocessing) non-isotropic sets of images which may have been acquired from multiple incidences (transaxial, sagittal or coronal orientation for MRI). It should be noted that the registration stage between multi-incidence data from the same modality would no longer be necessary if 3D isotropic data were available. The following text presents the registration principles for different modalities (MRI, CT, angiography). 3.1. R e g i s t r a t i o n o f a M R I S t u d y 3.1.1. Princinle As sl~ecified before, a standard MRI study may involve several analysis incidences. Several data are necessary to accurately define the patient referential. Consequently this study procedure requires specific data : a sagittal mid-plane slice, a sagittal or coronal slice including zhm, a sagittal or coronal slice including zbm, an axial or sagittal slice including xam, an axial or sagittal slice including xpm, an axial or coronal slice including ydm and an axial or coronal slice including ygm. The registration of the different MRI incidences with respect to each others is performed by using the numerical values carried out by the MRI system along with the images. These data make computation of the geometrical transformations between an image and a basic referential attached to the machine (called "machine referential") easy. This directly issues the transformation matrix between one image of one series (I of S) and another image of another series (1"of $3. 3.1.2. Definition of the "Patient Referential" The registration problem under consideration is to define as exactly as possible the base lines of the patient geometrical reference (AC-PC line and the two vertical lines VAC and VPC). The geometrical referential, as defined in §2-2, cannot be detected by using an automatic procedure involving image processing algorithms. Consequently, we made a choice for an interactive designation of the PS referential, whatever the MRI data base is (isotropic or multi-incidence). Obviously, the accuracy of this procedure will be highly dependent on the sampling quality of the cerebral volume resulting from the MRI study. The methodology proposed here involves four stages : 1. Definition of approximated base lines (Figure 2) : The AC-PC line and its two associated vertical lines are interactively defined upon a sagittal slice showing the anterior and posterior commissuras (as explained on §2-2), (Figure 9: Colour Plate, p. 2). 158 A Z~i H Zml.i - ~ . .~._Xmri R F Xmri P (a) Co) Figure 3 : Correctionof the geometricalbase lines a : rotation of VAC about the AC-PC line on a coronal slice b : rotation of AC-PCabout the VAC line on a transaxialslice. 2. Translation of the AC location (Figure 3a) : A translation of the AC location can be performed (if necessary) in order to replace it into the mid-plane estimated from a coronal slice containing (or very close to) the anterior commissura (trans2 on Figure 3a). 3. Rotation of the VAC base line about the AC-PC line (Figure 3a) : On the same coronal slice, the VAC and mid-plane orientation are corrected by making a rotation of VAC about the ACPC axis (rot3 on Figure 3a). 4. Correction of the AC-PC line (Figure 3b) : A correction of the mid-plane defined by the ACPC and VAC lines is performed by estimating a rotation of this plane about VAC upon a transaxial slice containing (or very close to) AC (rot4 on Figure 3b). The four respective transformation matrices involved in the processing can be summerized as follows : Mpa~at_MRi= M p . ~ t - ~ " Mp.~i,,~t.r,~= 1 000 Mpa~cnt-i~¢I'[ 000 1 l O00 1 The transfer of information between the "patient referential" and MRI data is calculated as : Ppafiexlt -- Mpatient-MRl • Pm~ Once the geometrical basis of the patient referential is defined, the last stage consists of determining the 3D box encasing the brain. This is done by using the slices previously selected during the MRI study protocol (Figure 10" Colour Plate,p.2 ). Finally, the transfer of information between the "model" referential and MRI data is calculated as : Pmodel -- Mmodd-patient* Mt~ent-Mgl * P r ~ 159 A H Xih Zih i R )l ........ ) - ! ,Xcr P . R . , . ~ ~ Xc r F (a) Co) Figure 4: Definition of the C T mid-plane upon an axial plane (a) and a coronal plane (b) 3.2. Registration of a C T Study 3.2.1. Princivle Cerel~ral structures such as the anterior and posterior commissuras are not visible on transaxial CT slices. The reconstruction of the mid-plane from CT has not proven suitable to deduce the AC-PC line, especially when using a standard 5mm slice thickness. The method proposed here is based on the localization of some specific information which can be localized upon both the CT and the MRI midplanes. The registration of these data will effect the geometrical transformation between CT and MRI. The registration between CT data and the "patient referential" is performed by using the results of the MRI registration as linking information. 3.2.2. Estimation of the CT Sagittal Mid-Plane The definition of the CT sagittal mid-plane is interactively performed by the designation of the estimated mid-plane position on each slice. Three steps are involved in this definition : 1. Learning stage: On a reference slice, the estimation of the position and the orientation of the mid-plane is performed by using two parameters A and ~ (Figure 4a). The initial value of 00 is set to zero. 2. Update stage : On the other slices, new values (oi, Oi) can be assigned for correction of the mid-plane orientation (Figure 4b). 3. Optimization stage : The set of the estimated parameters to and 0 allows the estimation of an average position of the CT mid-plane by using the following relations : 1 N 1 N o = - - ]~ coi N i=l 0 = N55]~ 0i ' , where N is the number of CT slices. i-2 3.2.3. CT-MRI Assienment On the mid-piane defined as above, a set of points featuring structures, which can be seen on both MRI and CT, is interactively designated. These structures can be the skin, the middle of the bone, the limits of the ventricles, or others. The registration between CT and MRI is then performed by interactively carrying the graphical representations of structures of interest from CT over to their corresponding position on the MRI mid-plane. The geometrical transformation is directly derived from this procedure (Figure 11: Colour Plate, p. 2 ). It seems rather difficult to use automatic pattern recognition techniques to detect reference structures. The selection of these structures may change from one CT study to another since the sampling of cerebral volume (by the CT) may also change (the CT study does not usually cover the entire head). Nevertheless, it is still possible to think about particular procedures which would help the assignment stage between CT and MRI. 160 0 l i ! E ! / .... -T i / .................,, .............. /:/ [ ! Figure 5 : Geometricalconditionsof the stereotacticangiographystudy protocol 3.3. Registration of Angiographic Data As opposed to the two other modalities, the angiography study protocol is strict and its completion, in stereotactic conditions, rather awkward. Pairs of radiographs at a distance of 5 metres (face and profile) are performed from two co-planar and perpendicular sources. An instrumental framework (on which referential landmarks can be attached) is fixed to the patient's head (Figure 5). The advantage of taking film at a distance of 5 metres is that the X-Rays beams are almost parallel (in a first approximation), since the magnification ratio varies between 1.02 and 1.08 from side to side of the frame. The referential associated to the patient, called the object referential, is composed of referential elements. These elements are flat plates including radio-opaque landmarks shaped as N's and crosses allowing the neurosurgeon to correctly position the frame. Under scopy, it is possible to check along the face and profile orientations whether the crosses are correctly placed and aligned or not. This procedure makes the determination of the transformation matrices between the object referential and the two film referentials easier. These matrices are a function of the geometrical features of the stereotactic room and have been experimentally determined ~ Gall 1990, Longuet and Higgins 1981, Metz et al. 1989). Since no particular caution is taken during the film digitization (by using a video camera connected to the PC), the first stage consists of computing the transformation matrices between the radiograph referentials and the projection referentials, which are considered as the acquisition referentials (one for each incidence). Three coins have been placed on the two film holders which can be automatically detected after digitization in order to perform this preliminary 2D registration. As for CT, the AC and PC structures can not be recognized on the angiograms, thus the registration of the patient AC-PC referential can not be done directly. The MRI mid-plane slice is used once again as the connection between angiography and the patient referential. The structures used to carry the angiography information over to MRI are bone contours (to get a good idea of the general shape) along with blood vessels elements (arteries and veins) like the pericalleus artery or the great cerebral vein of Galeus which surround the extremities of the corpus caUosum, easily identified on MRI. 3.3.1. Definition of the Angiographic Mid-Plane Concerning the definition of a 3D point within the object referential, two corresponding points upon face and profile films have to be designated in order to find out the correct 3D position. The way to find out the 3D location of a point within the object referential is to firstly select its position on the face or profile view and then to adjust this position along the epipolar line upon the other view (profile or face) (Figure 6). 161 x,~ A F A ....................... tf "~11! t I • . . . . . . . . . . !.L__/ i ] / objectreference / / ..................... L//i / z~ H L / zf F x~--~ Figure 6 : Principleof the projectiongeometrybetweenthe objectreferentialand the two orthogonalprojections(face and profile). The location of the mid-plane is interactively defined on a face view angiogram. This method has a drawback : the face incidence is supposed to be perpendicular to the real mid-plane, which is usually the case in most studies. A slight rotation cannot be easily detected. Further work is needed to estimate its influence with regards to the registration accuracy. The projection matrices between the object referential and the orthogonal views are : and [ x:] [xoq tt~ =[F d . [Y°bJlwithi = {1,2,3} and j = {1,2,3,4} p'J 3.3.2. ReaJstration between Aneioa'raDhv and MRI As with CT, several points viewed on both angiography and MRI are used to transfer the information between both modalities : i) the pericalleus artery and the great cerebral vein of Galeus which are attached to the corpus calleus extremas and ii) the bone contours can be viewed on angiography and estimated upon the MRI mid-plane slice. From this registration, the geometrical transformation between angiography and MR/and then between angiography and patient can be derived. This work was intentionaly done without involving segmentation techniques in vessel detection on angiograms. This domain is widely discussed in the literature and the complexity of the anatomical structures to be dealt with does not simplify this problem (spatio-temporal filtering, segmentation of overlapping vascular structures, ...). Nevertheless, as for CT, it can be possible to work out automatic processes to carry pre-recognized vessel structures over MR/(registration of vessels surrounding cortex gyri for instance). 3.4. Registration of 3D Representations The aim of this part is to make possible the use of 3D representation of pre-registered M R / o r CT data sets. This is not exactly a registration problem in the sense of detecting reference structures and registering them. Nevertheless, it is necessary to compute the geometrical transformations making up the relation between a point on a 3D representation and its position within the registered data base. The 162 actual solution is to compute the 3D representations of pre-registered 3D data sets by means of external software (Barillot 1988, Robb and Barillot 1989). These CT or MRI data bases have to be re-sampled in order to make isotropic volumes. The 3D display software performs the surface segmentation and brings out a "3D image" which includes a 2D projection (with surface shading) and the depth inforrhation of the displayed points (Z-buffer). In addition with the "3D image", the display software carries out a transformation matrix which makes the transfer of a "3D image" point possible (xi, Yl, Zbuffi) to the referential system of the original data base. /N--,,. /% patient or itt~l 2K lerl~ In~IKe Figure 7 : ArchivingDataHierarchy. 4. APPLICATION 4.1. Multimodality Images Fusion In order to validate and actually exploit these registration techniques we built a multi-modal point transfering application : this application allows point to point coordinate transfer between data related to a patient and a digitized atlas or between the atlas and the patient data, or between a patient data set and another patient. These assignments are performed by using the proportional squaring deformation model. This application is made of two parts : /) an acquisition and registration module and i/) a point to point transfer module. Concerning the second one, the principle consists of selecting an input and output data from the patient/study / series/image hierarchy (Figure 7) (BariUot et al. 1989). The display screen is split into four parts, the upper left quadrant is used to display the input image. A point is then selected by moving a cursor with the mouse on this image in order to define a point in the 3D space, then the system computes the 3 output images, by selecting within three series the closest planes to the selected 3D point; planes are displayed and cursors show the localization of the transfered points upon the output images. This application has been implemented on a PC AT with a 512 x 512 x 12 bits bit map ( 8 bits + 4 bits for graphics) and connected to a video camera. 4.2. Data Acquisition The Talairach atlas is composed of anatomical plates in the three orthogonal planes : sagittal, axial and coronal. The application considers this atlas as a particular patient with only one study and three series. All data (except for angiographic images which have to be digitized on the workstation) are retrieved from the central database of the SIRENE PACS (CT, MR, 3D images) (Gibaud et al. 1989). 4.3. Results All software developments have already been done, this actually makes the registration of all of the imaging modalities previously mentioned possible. The completion of all kinds of point to point assignments can also be done as patient to atlas, atlas to patient or patient to patient (Figures 12, 13, 14: Colour Plates, p. 2). A number of additional tools have been developed in order to enhance the readability of the images and to facilitate the use of the system • zoom of an area of interest, full screen display, superposition of the proportional squaring, printing of geometric data and others. The primary use of the system has produced good results and no obvious registration errors could be detected. However, a major concern is how to assess the accuracy of the registration and to study how inaccuracies may be propagated. Any application, and especially in neurosurgery, which uses such registration techniques must be able to give quantitative measurements of the uncertainty related to any point transfer between the registered data sets. 163 ¢ ) t~ ( I TP ¢ ~ll,. ] assignment~ ¢ t patientx ) "registered data a'sslgnment~ x~ latlasor ~ ~ I TP+IMOD - Figure 8 : Relationshipsbetweenthe differentinaccuracyand error sources 5. EVALUATION 5.1. Position of the Problem The assessment of registration has to be considered at two levels. With respect to the registration of data concerning one patient, the problem is essentially related to the accuracy of the registration between modalities. Namely, the anamorphosis coefficients are obviously the same for all modalities and do not introduce additional errors. Regarding the registration between different patients, the problem is also to evaluate the accuracy of the deformation model itself. It is well known that the proportional squaring model is quite suitable for the deep cerebral structures but can only provide approximate statistical information about cerebral gyri, for instance. 5.2. Errors and Inaccuracy Causes (Figure 8) In order to measure registration uncertainties, we have designed a model showing the various error origins and the way they cumulate (Figure 8). A primary cause of errors concerns the pixel size (field of view / number of pixels) : E TP, the pixel size in the third direction has also to be considered. Such an error apples to all modalitie~ Additional distorsion may come up with some modalities, like a geometric distorsion in MR due to the non homogeneity of the magnetic field, or like distorsions due to the digitization camera for angiographic images. The second origin is related to user interaction. The designation of anatomical structures is obviously subjective : an expert may vary in designating a single structure as well as different experts may also vary in designating the same structure (Dann et al. 1988, Seitz et al. 1990). Studies on consistency and variability will helps us to quantitatively evaluate this uncertainty (I._REC). Such an error may induce a bad definition of a structure or a plane, especially when the study does not perfectly fit the study protocol (for instance, designation of the inter-hemispheric plane in a coronal angiogram). Finally, it is clear that the registration accuracy of a CT or an angiographic data set is highly dependent on the MR registration quality. Consequently, a cumulative effect has to be taken into account (IPROG). Another issue is to evaluate the quality of the deformation model itself, and the intrinsic quality of the digitized Talairach arias. 6. CONCLUSION We have described in this paper a straightforward way to register multimodality and multipatient data by means of anatomical reference structures. This geometrical referential is widely acknowledged as one of the most accurate, in the anatomical sense, in the context of stereotactic neurosurgery. We have focused our work on finding reliable procedures which help to define this referential using data gathered from a patient. Beyond the prevalence given to the MRI modality in this approach, we wanted to put stress on the establishment of systematic procedures which take into account the particularity of the 164 different modalities (nature of the information carried out, sampling of the cerebral medium, etc...) and ensure maximum exactness along the different registration stages. Further research is needed concerning the validation of these procedures, It is actually crucial to be able to quantify the uncertainty of the registration processes between modalities and between patients. This project is going to be the main part of our work during the coming months. Based on these validations, a more fundamental study will be to improve the deformation model in order to extend its application field, which is usually limited to the central region of the brain. The application field of such a system is huge. It could be helpful in the neurosurgical domain (biopsy, definition o f intra-cerebral entry ways, etc...), in the functional anatomy domain (concerning the localization of epilepsy crises generators), in radiotherapy for the treatment of cerebral lesions or even in the research domain like, for instance, the constitution (or the improvement) of an anatomical brain arias. 7. REFERENCES Barillot C. (1988). 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