FR2974001A1 - METHOD FOR DESIGNING AND MANUFACTURING A POSITIONING GUTTER FOR USE IN REPOSITIONING THE MAXILLARY OF A PATIENT DURING OPERATION OF ORTHOGNATHIC SURGERY - Google Patents

Abstract

A method of designing and manufacturing a positioning gutter for use in repositioning the maxillary (1) of a patient during an orthognathic surgery operation, characterized in that a dental reference frame (SRD) is defined to estimate the displacements and the rotations of the bone structures starting from an imagery of the patient's anatomy, carried out either in 2D, or in 3D, by choosing said reference dental (SRD) starting from the sagittal plane of the articulator and the following three points: * the inter-incisal point (Ii) of the maxillary (1) which will constitute, preferably, the origin of the reference frame; * the vestibulomésial cusp point of the first left molar (M1G); * the vestibulomésial cusp point of the first right molar (M1D); and in that a particular treatment of the data obtained from these points and the data acquired on the plaster maxillary model of the patient (5) is carried out.

Description

The present invention relates to the field of orthognathic surgery. More specifically, it relates to the realization of positioning gutters used to reposition the bones of the jaws of the patient, after an operation by which the practitioner has cut fractions of the jaws (upper jaw) and / or the mandible (lower jaw). After this cutting and repositioning, one obtains configurations and respective positions of the maxillary and the mandible that no longer have the jaw offset that motivated the operation for functional reasons (such as remedy poor chewing) or aesthetic. Orthognathic surgery is performed when an orthodontic treatment alone would be ineffective in correcting a severe dento-skeletal abnormality. It consists of performing an osteotomy of the maxillary and mandibular bone bases according to various methods that may be associated with: - the Maxillary Lefort 1 maxillary osteotomy, which consists in completely separating the upper dental arch and the palate from the rest of the face, by cutting the arch above the roots of the upper teeth, then mobilizing the arch by placing it in its ideal position and performing osteosynthesis by means of plates and screws; - the sagittal cleavage of the ascending branches of the mandibular ramus, which consists in moving the mandible according to the patient's needs in the three directions of space to obtain an advance, a recoil, a derotation (advanced on one side, recoil of the other), an elevation or a lowering; - a bone genioplasty that aims to correct the anomalies of position and morphology of the chinus symphysis in the frontal, vertical or sagittal direction. The orthognathic surgical treatment is preferably preceded by orthodontic treatment to achieve good dental alignment ensuring accurate corrections in all directions, especially in the vertical direction. Postoperative orthodontic treatment can also be performed to perfect the outcome of the treatment. The surgeon bases the prediction of his operative gestures on a bone analysis based on lateral and lateral teleradiographies, or on an image traditionally performed on a CT scan, and on the examination of the soft parts of the face. The treatment objectives that he deduces from his analyzes are transcribed on plaster models in the prosthesis laboratory, so as to have occlusal guides in

2 preoperative to place the bone elements in their desired optimal positions. But the positioning, particularly vertical bone segments has different degrees of inaccuracy due to inaccuracies accumulating during the many steps of the procedure.

Computer assisted surgery has made significant progress in the implementation of these techniques, in particular Lefort 1 maxillary osteotomy in the context of bimaxillary osteotomies. A technique frequently used by surgeons is that known as "two-dimensional planning". The surgery is simulated by computer on the profile teleradiography, possibly using the teleradiography of face. The given movement is transcribed on plaster models of the jaws of the patient, and a positioning gutter is made to place, in the first place, the maxillary previously detached from the rest of the facial mass, based on the non-osteotomized mandible. It is more particularly to this method that the present invention is addressed.

The movements to be imposed on the objects concerned must be defined in relation to a repository. The choice of reference axes can be varied. The so-called "Frankfurt Plan" can be used for this purpose. This is the plane passing through the two external auditory canals and the two suborbital margins. In this case, the axis X of the reference is included in the transfer plane and is parallel to said straight lines, the Y axis is also in the plane of Frankfurt and is perpendicular to the X axis, and the Z axis is perpendicular to the plane of Frankfurt. The position of the origin point of the landmark is irrelevant. The displacement of the bone elements can be represented by indicating on a rectangle (representing the palatal plateau) the anteroposterior and vertical movement of the anterosuperior nasal spine (ENA) and the vertical movement of the posterior nasal spine (ENP). This gives us a good idea of the movement made at the osteotomy line. Also, dental castings are made of plaster of the patient that will allow to simulate the preoperative intervention on these moldings.

The castings are mounted on an articulator intended to reproduce the occlusion of the patient, as well as the mandibular kinetics by condylar rotation, at least in the first degrees of the mouth opening. The patient's reference system (such as the Frankfurt reference system described above) is reproduced on the articulator, as is the relationship between the two dental arches. The casts are positioned relative to the reference frame that is reproduced on the articulator, as well as the relationship between the two dental arches.

The osteotomy operations that would be necessary to restore a correct positioning of the arches are then simulated by cutting the plaster according to registration lines and various measurements. There is no very standardized methodology for this purpose, as the surgeon's know-how plays a crucial role at this stage. Then we make a thin resin positioning gutter that will help, during surgery, to obtain the desired relative positioning of the arches in the occlusal position. The maxilla is then osteosynthesized in the position thus determined, and serves as a reference for the subsequent positioning of the mandible.

This method is simple to implement. It is inexpensive, the only consumable material being the resin constituting the gutter. It makes it possible to precisely check the occlusal ratios in space, in particular the final occlusion by adjusting the dental arches of the casts. It allows three-dimensional movements. If necessary we can add to the plaster simulation a lateral translation or a frontal rotation to align interincistive points or restore a latch occlusal plane. We can associate with the global movement of the maxilla segmental surgery with correction of the transverse dimension by maxillary disjunction performed on the cast. Finally, ergonomics during surgery is perfect, with a maxillary attached to the mandible in the occulal ratio guided by the gutter. It is only necessary to impact the maxillomandibular assembly upward to ensure a stable position suitable for osteosynthesizing the maxilla in good conditions, without parasitic movements. However, the operations involve multiple factors of inaccuracies: - possibility of differences of inclination of several degrees between the referential of the teleradiography and the frame of reference of the articulator; - Quantification difficult to reproduce and insufficiently reliable movements between the starting position and the final position, especially on the vertical dimension; - inaccuracies related to the operation of teleradiography itself: sometimes insufficiently uniform enlargement, radiation not enough or too penetrating to obtain a precise image of the organs to consider, possible misdirection of the patient's head in the cephalostat; also surgeons may be wrong in the choice of reference points; - imprecision on the realization of the wax impressions of the jaws from which plaster castings will be made; - approximation in the positioning of the moldings on the articulator; - errors during the preparatory surgery carried out on the plaster models, the realization of which is artisanal, without rigorously standardized protocol, thus extremely dependent on the know-how of the operator; these errors may relate to the placement of reference lines on the molding, which will serve as benchmarks for the reproduction of the quantified movement in the preoperative planning, but do not correspond to cephalometric lines, osteotomy or any surgical reference; the cutting plane of the molding is defined with a certain approximation, in particular because the ENA and the ENP are not materialized on the molding; - Finally, the realization of the positioning gutter, which is self-or photopolymerisable resin, may be inaccurate if the gutter is removed too early castings; a deterioration of the molding also risks creating points in superocclusion pushing the intermaxillary ratios when it is put in place postoperatively. Finally, positioning inaccuracies can occur during the operation itself. There may also be bone interferences in the posterior part of the jawbone that are not anticipated in the preoperative phase, which may lead to a relaxation of the condyles of the glenoid fossa and lead to an incorrect positioning of the jaw during the execution of the Lefort technique 1 .

The osteotomy line is not made in a single plane but rather has a "sloping roof" aspect whose ridge would be parallel to the palatal plateau. The posterior contacts in case of maxillary advancement are weak and there may be parasitic movements of sagittal rotation during positioning. The mandibular rotation around a bicondylar axis, which is the movement theoretically performed by the mandible during its repositioning, is parasitized by possible autorotations around various points, and the semi-adaptable articulator will only give a rough approximation of the autorotation movement in relation to the real movement preoperatively. To reduce or compensate for these cumulative errors, the dexterity and experience of the surgeon and others are obviously fundamental to the success of the operation. Improvements to this technique include, among other things, the realization of positioning gutters by computer-aided design (CAD). But there is still a lack of possibility of adjustment in the vertical dimension.

The use of internal or external markers can be practiced, without constituting an ideal solution by the known techniques.

Techniques using "surgical navigation" (the branch of computer-assisted surgery) have been a significant advance in the success of maxillofacial surgery. The computer will, in real time preoperatively, help the operator by providing various types of information about his actions (anatomical guidance ...) and possible operational planning. The interfaces between the surgeon and the operator make it possible to accurately repair the specific instruments used during the operation in space relative to the patient. Optical tracking tracking systems are most often used. A simple and original measurement technique has been developed and is described in the document "Interest of navigation in orthognathic surgery: assessment of preoperative precision, development of a positioning aid", F.JALBERT thesis, University Toulouse III, supported on 7.10.2008, to which the reader can refer for more information. It is based on the spatial identification of different characteristic points and on the three-dimensional measurement of the relative displacements of the structures studied. It requires an optical navigation system based on the triangulation of two 2D images. The two infrared cameras in the location system, placed side by side, each capture a 2D view of the reflection of infrared flashes emitted by the system and sent by reflective markers. Thanks to computer processing of these images, the system evaluates the positioning of the sensors with an accuracy of less than 1 mm. It is necessary first to establish the dental reference system of the maxillary with respect to which the movements in translation and in rotation of the different elements of the jaws can be planned and realized. This repository must make it possible to define spatially the object, and the three points necessary and sufficient for this purpose which are chosen are: - point Ii (interincistive); - the point M1 G (vestibulomésial cusp of the first left molar); - the point M1 D (vestibulomésial cusp of the first right molar). The maxillary is represented by a dihedron whose vertex is the point Ii.

The maxillary thus defined undergoes a displacement between an initial position and a final position by the application of a transformation combining for each characteristic point a translation and a rotation, ie a total of six degrees of freedom. This transform is quantified with respect to a fixed reference oriented with respect to the cranial planes of the patient. During the operative planning, on each point one considers an earlier translation A expressed in mm, a vertical translation V expressed in mm and a sagittal rotation RS expressed in degrees. This schedule is a translation of the objectives calculated on the teleradiography of the profile. Thanks to the associated software, we visualize the displacement of the maxilla by juxtaposition of the dihedrals corresponding to the different compositions. One can also compare in real time the positions obtained at different times of the surgical procedure: starting position, theoretical planning, displacement during molding simulation, and finally displacement actually performed. The procedure begins in the prosthesis laboratory by the creation of an individual gutter, for example photopolymerizable resin, and comprising a surgical stainless steel rod. This groove has the impression of the maxillary teeth and, before curing the resin, reference holes are formed opposite points Ii, M1 D and M1G. A pin is included in the resin. A patient file is then created where the planning data is entered into the software in dental coordinates in the sagittal plane. For this purpose, a reference frame M is attached to the gutter in the form of a rigid registration body, and the three points Ii, M1G and M1D are palpated so as to mount the maxilla in the M (O, x, y, z). We then record the position of the molding of the maxillary arch in the starting position on the articulator, and thus locate the points Ii, Ml D and M1G in the cranial reference of the patient. For this purpose, it is necessary to know only the sagittal plane, which the articulator can give in a sufficiently reliable way. The measure to determine this is to palpate four well-defined, symmetrical landmarks at the upper level of the facial arc, so as to define the median sagittal plane. Once this registration has been made and the starting position is known, the standard procedure of "model surgery" is performed by cutting the plaster molding of the maxillae after having previously defined cutting lines thereon. The molding thus cut and reassembled is then put back on the articulator. Finally, a second series of measurements is performed by palpating exactly the same four previous reference points at the top of the articulator. We obtain an intermediate situation, where these points appear in different positions of their original positions since the measurement reference is attached to the maxillary by the navigation gutter. The maxillary points Ii, M1G and Ml D are in the same position and it is the articulator that seems to have been moved. The registration software then recalculates a rigid registration of the four preceding reference points, before and after the displacement of the molding without modifying their geometry, so as to associate them and confuse them at best. This step is necessary to know the displacement of the maxilla. The shift observed at the positions of the three dental dots before (Ii, M1G and M1 D) and after the cutting and repositioning procedure of the model, their positions after the procedure being designated by Ii ', M1G' and M1 D 'respectively. The software registration operation aims to superimpose the four maxillary cue points by bringing the points from their initial positions to their final positions. This causes the points Ii, M1 D and M1G to shift in their positions Ii ', M1 G' and M1 D 'of which we have spoken, and the transform between the two maxillary marks associated with Ti and Ii' makes it possible to calculate the various degrees of translation and rotation that were applied following the surgery of the models carried out on the molding of the maxilla.

The surgery can then be performed on the patient. After exposing the maxillary and before performing the osteotomy, the operator performs a slight bone sharing to form the four points of reference that have been mentioned, located above the osteotomy line, and thus representing the repository Fixed cranial in relation to which will be measured the maxillary movement.

Then it records the initial position of the maxilla by palpating the three points li, M1G and M1 D by means of the rigid register body M, which allows to calibrate the gutter on which the body M is fixed. The gutter is put in place by ensuring good tooth meshing, and at that moment the four maxillary landmarks are palpated. The gutter can then be removed.

Then the Lefort 1 osteotomy is performed, the maxillary elements are repositioned using an intermediate gutter, and osteosynthesis is performed by rigid plates. A second series of measurements indicates, directly during the operation, the replacement made in the maxillary with respect to the interincistive point Ii, and compares it in real time to the theoretical planning, to the movement on the molding and to the initial position in a visual way following the three axes of the repository associated with Ii, by means of encrypted values. One of the factors that can affect the success of the operation is the accuracy and reproducibility of the construction of the positioning gutter preoperatively. The inventors have found that the difference between the displacement made on the molding that made the gutter and the preoperative was certainly identified by practitioners as representing a significant problem, but that its importance was undervalued. The interferences involved are mainly an improper simulation of the mandibular autorotation during the design of the gutter, a malposition of the condyles in the glenoid fossa during the osteosynthesis, the presence of badly evaluated bone interference hindering and modifying the movement. during the impaction of the maxillomandibular block. The translation error can thus reach ± 4 mm, both in anterior translation and in vertical translation, and the error in rotation can reach ± 5 ° or more. The errors are mainly in the sagittal plane with a random repositioning of the incisal point Ii and a palatal plateau flip-flop. Devices made in CAD (stereolithographic positioning gutters) put on the market by companies marketing simulation software are not always reliable enough to assume the required accuracy. The object of the invention is to propose a method leading to the manufacture of a positioning gutter having a better accuracy than the methods conventionally used, thus ensuring better chances of success in the maxillofacial surgery undergone by the patient.

To this end, the subject of the invention is a method of designing and manufacturing a positioning gutter intended to be used for repositioning the maxillary (1) of a patient during an orthognathic surgery operation, characterized in that that we define a dental reference system (SRD) allowing to estimate the displacements and the rotations of the bone structures starting from an imagery of the patient's anatomy, carried out either in 2D, or in 3D, by choosing said referential dental ( SRD) from the sagittal plane of the articulator and the following three points: * the inter-incisal point (Ii) of the maxillary (1) which will constitute, preferably, the origin of the reference frame; * the vestibulomésial cusp point of the first left molar (M1 G); * the vestibulomésial cusp point of the first right molar (M1 D); and in that a processing of the data obtained from these points is carried out comprising the following steps: if a 2D image is available, a reference frame (Ii, À, L, V) is determined by selecting on the radiography the points (Ii, M1 G and M1 D); * taking the interincistive point (Ii) as the origin of the repository; defining the anteroposterior vector ()) by = = Ii - / M1G + M1Dv 2 * by defining the lateral vector (L) as being perpendicular to the plane of the radiography; * by defining the vertical vector (17) as being perpendicular to (A); * and by normalizing these three vectors (Â, É, 17); if a 3D reconstruction of the maxillary (1) is available, a reference frame (Ii, À, É,: * is determined by generating the sagittal plane of the head from several selected points on the virtual model (2) of the patient's head: * by selecting on the 3D reconstruction these points (Ii, M1 G and M1 D); * by projecting these points on the sagittal plane of the head, to create new points (Iip, M1 Gp, and M1 Dp); * by defining Ii as the origin of the frame of reference; 10 * by defining the anteroposterior vector (A) as A = fi pp / MlGp + M1Dp 2 * by defining the lateral vector (L) as being perpendicular to the sagittal plane of the head: * by defining the vertical vector (V) by V = Ax L; 15 * and by normalizing the vectors (V, L and Å); - we simulate on the computer representation of the maxillary (1) the operative gesture by to the previously determined dental reference system, by calculating the position and the orientation r elative of the dental reference after simulation (SRD1) compared to the dental reference before simulation (SRDo); A new reference frame (SRD1_o) is defined as: SRD1, = A 1, 4, Vi-o)), Po being the position vector whose coordinates (A, L, V) respectively correspond to the movements on the anteroposterior, lateral axes and vertical, and (Al_, V_o) being the three orthogonal unit vectors; from these three orthogonal unit vectors, a rotation matrix [λ1_0 Li-o V_o] is generated which is used to calculate the Euler angles (RL, RA and Rv) corresponding to the rotations around each axis. The default values of the constants L, Rv and RA will be zero if one starts from a 2D image, but it is possible to change these parameters by relying on plaster models of the maxillary and the mandible; 30 - trace and mark on the plaster model (3) of the patient's maxillary lines and reference points: * a first cutting line (4), parallel to the base of the model (9). This route will serve as a reference to the prosthetist to perform the first cut; * four lines perpendicular to the base of the model (9), starting from points located at the base and on the same plane parallel to the coronal plane of the articulator, respectively a line (5) on the rightmost edge, a line (6) on the anterior side, a line (7) on the leftmost edge, and a line (8) on the posterior side, the lines (6, 8) drawn on the anterior and posterior edges of the model (3). ) each starting from a point on the sagittal plane of the articulator; - twelve reference points are marked on the model, located on each of the preceding lines (5, 6, 7, 8) at the base of the model (9), at the intersection with the first cutting line (4) and at the above the first section line (4), four of said points (p1, p4, p7, p10) being situated on the same plane at the level of the base and making it possible to define the coronal sagittal and frontal planes associated with the articulator, another four of said points (p2, p5, p8, p11) being located on the section line, four others of said points (p3, p6, p9, p12) being located above the section line; all the reference points of the model, as well as the interincistive point (ii), the vestibulomésial cusp point of the first left molar (m1g) and the vestibulomésial cusp point of the patient are digitized with the aid of a 3D localization system. first right molar (m1d) of the model, and a 3D numerical model of the plaster model is generated; a reference system associated with the articulator (SRA) is calculated according to: tmpZ = ((p4-p10) x (p1-p10)) + ((p7-p10) x (p4-p10)) eax = ( p4 - p10) eay = tmpz x eax eaz = eax x eay pa = (p4 + p10) * 0.5-0 - one normalizes eax, eay and eaz, which correspond to the three unit vectors of the reference frame (SRA), pa corresponding to the vector position; the sagittal, coronal and frontal planes of the articulator are defined by the vectors eay, eaz and eax perpendicular to the respective planes, and the position of the planes is defined

11 by the point pa whose coordinates have the same values as the components of the vector pa; the first section plane (PPC) is then calculated by adjusting the points p2, p5, p8 and p11 to a plane, the vector vppc perpendicular to the obtained section plane and the center of gravity m of the four points, by defining the first plane of cut (PPC) as the plane passing through m and at which vppc is perpendicular; the orientation of vppc is then modified so as to orient it towards the teeth of the plaster model, by making the dot product between vppc and eaz; * if this scalar product is positive, vppc is not modified compared to the previous determination, so, so, that PPC; * if this scalar product is negative, we modify vppc by multiplying it by a factor (-1,0), and we modify PPC accordingly; * then the cutting thickness "ec; eight reference axes are then generated, calculated from the reference points p1 to p12, said axes being represented by a vector indicating the direction of the axis and a point on the axis, and being: AxlnfD "Lower Right Axis ": AxlnfD = (p2 - pl, pl) AxInfA" Lower Anterior Axis ": AxlnfA = (p5 - p4, p4) AxlnfG" Lower Left Axis ": AxlnfG = (p8 - p7, p7) AxlnfP" Lower Posterior Axis ": AxlnfP = (pliOp, p10) AxSupD "Upper Right Axis": AxSupD = (p3 - p2, p2) AxSupA "Upper Anterior Axis": AxSupA = (p6 - p5, p5) AxSupG "Upper Left Axis": AxSupG = (p9 - p8, p8) AxSupP "Posterior Upper Axis": AxSupP = (p12 - fold, pl l) - we then generate intersection points associated with the coronal plane of the articulator (PCA), calculating the intersection between the coronal plane of the articulator PCA = (eaz, pa) and the axes AxInfA, AxlnfP, AxlnfD and AxlnfG, the four points obtained being respectively named piaa "point int ersection anterior articulator ", piap" point of intersection posterior articulator ", piad" point of intersection right articulator "and piag" point of intersection articulator left "- one simulates then the first cut made on the model in plaster and one generates reference frames and intersection points associated with this section, using the section plane PPC = (vppc, m), the section thickness "ec" and the eight axes previously calculated to generate two frames, one SRS = (ps, (esx es)), esz)) located above the section plane, the other SRI = (pi, (eix, eiy, eiz)) located below the section plane, and eight points intersection, by calculating these parameters as follows: * for SRS we set: ps - = m - 0 + vppc * (ec * 0.5) then we calculate the points of intersection between the axes AxSupA, AxSupP, AxSupD, AxSupG and the plane (vppc, ps) where ps is the point whose coordinates have the same values as the components of the ps vector, naming the points of intersection respectively pisa "anterior superior intersection point", pisp "posterior superior intersection point", pisd "right upper intersection point" and pisg "left upper intersection point" , and by defining and then normalizing the vectors: esx = (pria - pisp) esy = vppc x esx es, = es, x esy; * for SRI, one puts: pi - = m - 0 - vppc * (ec * 0.5) then one calculates the points of intersection between axes AxInfA, AxlnfP, AxlnfD, AxlnfG and the plane (vppc, pi), pi being the point whose coordinates have the same values as the components of the vector pi, by naming the points of intersection respectively pila "lower intersection point", piip "lower intersection point", piid "intersection point lower right "and piig" lower left intersection point ", and by defining and then normalizing the vectors: eix - = (pua - paap) eiy = vppc x ei ei = ei x eiy; zx - we determine the rectangle which includes the points of intersection and whose sides are parallel to the esx and esy vectors, by naming the vertices of the rectangle pad "right front point", pag "left anterior point", ppd "right posterior point ", and ppg" left posterior point "; the dental reference system SRD = (pdt, (edtx, edty, edtz)) is generated and four points of intersection associated with the dental plane, using the reference SRA = (pa, (eax, eay, eaz)) associated with the articulator, the points ii, mi g, mid acquired on the teeth of the model in plaster, and axes AxSupA, AxSupP, AxSupD, AxSupG: * to generate SRD one poses pdt = ii -0, then one defines the sagittal plane of the articulator as PSA = (eay, pa); * we project the points ii, mig and mid on the PSA plane; the new points thus obtained are called iip, m 1 gp and m 1 dp; and then the following vectors are defined and normalized: ## EQU1 ## where edt, edty and edtz respectively corresponding to the anteroposterior, lateral and vertical vectors; * to generate the points of intersection, we calculate them between axes AxSupA, AxSupP, AxSupD, AxSupG and the dental plane PDent = (edtz, ii), by naming the points of intersection respectively pida "point of previous dental intersection ", Pidp" point of posterior dental intersection ", pidd" point of right dental intersection "and pidg" point of left dental intersection "; - two control reference frames are generated, one called "superior control reference system" SRCS = (pcs, ecsx, ecsy, ecsz)) for the structures (points, reference frames and axes) located above the line of cut, and the other says "lower control reference system" SRCI = (17;, (i> cx, eciy, eciz)); * for SRCS we define its different vectors as follows and we normalize them: pcs = p6-0 ecsx = p3- p6 ecsz - = ecsx x (p9 - p6) ecs - = ecs x ecs yzx * for SRCI, we define its different vectors as follows and we normalize them: pci = p4-0 ecix = p1- p4 eciz = ecix x (p7 - p4) eciy = eci x eci Z x - we generate a numerical 3D representation of the plaster model; a numerical simulation of the operations to be performed on the plaster model is performed to obtain the bone movements planned by the surgeon, by: a) calculating the transformation in translation and in rotation for the simulation of the movements, using the displacement values (A, L, V) on the antero-posterior, lateral and vertical axes and the angles of rotation (RA, RL and Rv) around these same axes, the transformation being defined as TRXyZ = (TXyZ, RZXy), where TXyZ = (A, L, V) and RZXy correspond to the rotation matrix in the order of rotation yxz obtained by: 14 R = ay cos0ycos0 - sinexsineysine -cosexsinez cos 9ZsinexsinGy + cos GysinOz cosexcos9Z -cosexsiney sinex cosessine + coseysinexsine -cos 9ycos 9Zsinex + sineysine z cosexcosGy where 6Ç, Gy and 9Z correspond respectively to RA, RL and Rv. b) motion simulation, in which all parameters above the section are first referenced in the SRD repository, then the TRXyZ transformation is applied to the SRD dental repository to thereby obtain the simulated SRDS dental repository; the transformation associated with SRDS (translation and rotation matrix) is then applied to the parameters referenced to SRD; c) optimization of the 3D representation of the model and calculation of the height of the possible second cutting line; * In the case where the upper part of the 3D representation intersects the lower part in various areas, the optimization is performed by: selecting the point located below the xy plane of the SRI frame;

Then generating an axis using the point obtained previously and the z unitary vector of the SRSS reference frame; then calculating the point of intersection pdc "reference point for the second section" between the previously calculated axis and the xy plane of the SRI repository, then generating a plane P parallel to the xy plane of the SRSS reference frame at the point pdc; then cutting the upper part of the 3D representation using the plane P obtained previously, followed by the elimination of the portion situated below this plane P, replacing the points pisas, pisps, pisds and pisgs respectively by the intersection between the axes AxSupAs, AxSupPs, AxSupDs, AxSupGs and plane P; then calculating the distance between the point pdc and the xy plane of the SRSS reference frame, this distance corresponding to the height of the second section "hdc" (15) to be performed by the prosthetist with respect to the first section line (4) marked on the plaster model (3); then plotting the second cutting line "hdlc" on the plaster model (3), hdlc being obtained according to the equation hdlc = hdc - ec * 0.5 where ec corresponds to the thickness of the cut; * in the case where it is not necessary to make a second cut, the values of hdc "height of the second cut" and hdlc "height of the second cut line" are taken as zero; the instruction document for the prosthetist is generated from nine parameters associated with the marking made on the plaster model: * hdlc; * ha "height of the front side of the plaster model"; * hp "height of the posterior side of the plaster model"; * hd "height of the right side of the plaster model"; * hg "height of the left hand side of the plaster model"; * dla "lateral displacement of the front side of the plaster model"; * dlp "lateral displacement of the posterior side of the plaster model"; * dad "antero-posterior displacement of the right side of the plaster model"; * dag "antero-posterior displacement of the left side of the plaster model"; - a repository change is made using SRCI as the main repository: * the SRCS repository is computed with respect to the SRCI repository and a new SRM repository is obtained, "maxillary reference system in the initial position"; the SRCSS repository is computed with respect to the SRCI repository and a new SRMS repository "maxillary reference system in the simulated position" is obtained; the SRD repository is computed with respect to the SRCS repository and a new reference SRDR "relative dental reference system" equal to the SRDS repository is obtained relative to the SRCSS repository; the position and orientation of the SRD dental reference frame with respect to SRCI is calculated before and after simulation, by applying to the SRDR the transformation associated with SRM, and the transformation associated with SRMS to obtain the SRDI reference frames respectively "initial dental reference system "and SRDS" simulated dental referral system "; - saving the calculated parameters in a file; - the gutter is built on the basis of the instruction document previously generated and the plaster model. These points (p1-p12) can be embodied by holes. After the manufacture of the gutter, one can proceed to the control of its conformity with the command by: - palpation of points and generation of the two reference frames of control by using a system of 3D localization to carry out the numerical acquisition on the maxillary model in plaster six control points (p1, p4, p7, p3, p6 and p9); - use of these control points to generate two control references SRCS0 "superior control reference system obtained" for the part of the plaster model above the section and SRCIo "lower control reference system obtained" for the part below the cup. - quantification of the movements performed by the prosthetist using the SRCS0 and SRCIo repositories, to obtain a reference SRDO "obtained dental reference system" and an SRDI reference system "initial dental reference system"; - Calculation of the SRDO repository with respect to the SRDI repository, to obtain a new reference system SRG "gutter reference system" whose axes (x, y, z) correspond respectively to the anteroposterior, lateral and vertical axes; - Definition of the movements performed by the prosthetist by the coordinates of the SRG reference position vector with respect to the displacement, and by the Euler angles in the y-x-z rotation order of the rotation matrix associated with the SRG reference frame; - comparison of the movements performed by the prosthetist with those that had been planned. The inventors worked simultaneously on three points which appeared to them crucial for the success of the design of the gutter: - the correspondence between the plane of the radiography (in 2D imaging) or the sagittal plane of the head (in 3D imaging) and the sagittal plane of the articulator, obtained thanks to the device called "facial bow" used to build the plaster model; - the ability to identify the sagittal plane of the articulator on the plaster model of the morphology of the patient; - The parallelism between the upper coronal plane of the articulator and the base of said plaster model. The method according to the invention is based on the use of the maxillary plaster model of the patient and on the choice of three particular reference points of this model from which a suitable data processing is carried out. A 3D three-dimensional location system is also used. Data from 2D or 3D imaging used in the planning stage of the surgical procedure are used as input to the treatment.

The invention will be described with reference to the following appended figures: FIG. 1 which shows a maxillary and locates the three reference points used in the construction of the dental reference system; FIG. 2, which shows a radiograph of the skull of the patient on which the dental reference frame chosen has been reported; FIG. 3 which shows an image of the 3D generation of the maxillary repository from a virtual model derived from a scanner imaging; - Figure 4 which shows the possible movements for the dental reference; FIG. 5, which shows an example of plotting of the first cutting line on the plaster model of the maxillary of the patient; - Figures 6, 7, 8 and 9 which show the four lines and locations of twelve reference points plotted on the plaster model; - Figure 10 which shows a simplified 3D representation of the plaster model and several parameters in the initial position after the first cut; - Figure 11 shows an improved 3D representation of the plaster model and several parameters in the initial position after the first cut; FIG. 12 which shows an example of a 3D representation of the plaster model and of several parameters, before and after the simulation of the movements; FIG. 13 shows in a sagittal view examples of cases obtained after numerical simulation of the movements, when there is an intersection between the upper and lower parts of the model; FIG. 14, which shows in sagittal view examples of cases obtained after digital simulation of the movements, when there is no intersection between the upper and lower parts of the model; FIG. 15 which shows examples of optimization of the 3D representation in cases where there is an intersection between the upper and lower parts of the model; - Figure 16 shows the methodology for calculating the parameters to be included in the document for the prosthetist. - Figure 17 which shows the methodology for the change of the main repository before and after the numerical simulation. - Figures 18 and 19 show the methodology to quantify the movements performed by the prosthetist on the plaster model. - Figure 20 which shows an example of instruction document sent to the prosthetist. The method according to the invention comprises the following steps; In step 1, we first define a frame of reference for estimating the movements and rotations of the bone structures from the patient's anatomy imagery, performed either in 2D (in particular by radiography), or in 3D (notably by scanner or MRI). The repository to be defined must be easily identifiable on the 2D or 3D imagery and also on the maxillary plaster model of the patient. As stated above, said reference frame is chosen from the sagittal plane of the articulator and from three points, illustrated in FIG. 1: the interincistive point Ii of the maxillary 1 which will preferably constitute the origin of the reference frame; - the vestibulomésial cusp point of the first left molar M1G; the vestibulomésial cusp point of the first right molar M1 D. If only 2D imaging is available, as shown in FIG. 2, a reference frame (Ii, À, É, fi: - is selected by selecting on the radiograph the points Ii, M1 G and M1 D - by taking the point Ii as the origin of the reference frame - by defining the anteroposterior vector À by = = Ii - / M1G + M1Dv 2 - by defining the lateral vector L as being perpendicular to the plane of the radiography (thus not visible in Figure 2) - and defining the vertical vector 17 as being perpendicular to Å.

The three vectors are then normalized. In the case where we have a 3D reconstruction of the bone structure of the head (FIG. 3) resulting from a 3D imaging, a reference frame (Ii, À, É, 17) is determined by: - generating the sagittal plane of the head from several points selected by the surgeon on the virtual model 2 of the patient's head; the plane can be calculated by adjusting the acquired points to a plane by a least squares method; selecting the points III, M1 G and M1 D on the 3D reconstruction as in FIG. 1; projecting these points on the sagittal plane of the head, to create new points which will subsequently be called Iip, M1 Gp, and M1 Dp; - defining Ii as the origin of the repository; defining the anteroposterior vector A as A = Iip - / M1Gp + M1Dp 2 - defining the lateral vector L as being perpendicular to the sagittal plane of the head; in the example described and shown, its direction is positive on the right side of the head on the virtual model; - defining the vertical vector V by V = ÂxL; it therefore has its positive direction downwards in the example shown; standardizing the V, L and A vectors as shown in FIG. 3. In step 2, the surgeon simulates on the radiography (FIG. 2) or on the 3D reconstruction (FIG. 3) the operative gesture (osteotomies and translation and / or rotation of the bone structures) relative to the previously determined dental reference system. The quantification of the movements is performed by calculating the position and the relative orientation of the dental reference after simulation SRD1 with respect to the dental reference before simulation SRDo. We obtain a new repository SRD1_0 which is defined as: SRD1_0 = 4-0 vi-o)) P_o is the position vector whose coordinates (A, L, V) correspond respectively to displacements on the anteroposterior, lateral and vertical axes, and I7_o, V_o) are the three orthogonal unit vectors. From these, one generates a matrix of rotation [Âl_ovi-o] used to calculate the angles of Euler

RL, RA and Rv (in that order), corresponding to the rotations around each axis. Figure 4 schematizes these displacements and rotations. In the case where only 2D imaging is available, L, Rv and RA constants equal to zero are defaulted. But the surgeon can, if he wishes, modify these parameters by basing himself, for the estimation of their values, on plaster models of the maxillary and the mandible. In step 3, the surgeon traces and marks on the plaster model 3 of the maxilla of the patient the lines and the reference points. These lines and points will make it possible to generate a numerical representation with which it will be possible to define and quantify the gestures to be performed on the plaster model 3 of the maxilla of the patient to make the positioning gutter: 1) The surgeon traces the outline of the first cutting line 4, parallel to the base of the model 3. The path 4 serves as a reference for the prosthetist to perform the first cut. The pattern 4 can be made by means of a device rotating on a plate 10 the model 3 facing the pencil which bears on the surface of the model 3. The height of the pencil is adjustable so that the trace is carried out at the desired height regardless of the height dimension of the model 3. It also ensures the perfect registration of the route 4 in the appropriate plan. FIG. 5 shows an example of the result of this plot 4. 2) The surgeon draws four lines perpendicular to the base of the model 3 starting from points situated at the base of the model 3 and on the same plane parallel to the coronal plane of the articulator . These lines are drawn respectively on the rightmost, leftmost, anterior and posterior edges of the model 3. The lines drawn on the anterior and posterior edges of the model 3 each start from a point situated on the sagittal plane of the articulator which is easily identifiable on the model 3. Figures 6, 7, 8, 9 show these four lines: that 5 on the right side, the 6 on the anterior side, the 7 on the left side and the 8 on the posterior side of the model 3. 3) The surgeon marks twelve reference points on the model, which are also visible in Figures 6 to 9. The points are located on each of the preceding lines 5 (points p1, p2, p3), 6 (points p4, p5, p6), 7 (points p7, p8, p9), 8 (points p10, p11, p12) respectively at the base of the model, at the intersection with the first line of cut 4 and above the first line 4. These points are advantageously materialized by small holes for easy ter their identification. The points p1, p4 p7 and p10 must be located on the same plane at the level of the base they will allow among other things to define the coronal sagittal and frontal planes associated with the articulator, the points p2, p5, p8 and p11 must be located on the section line, the points p3, p6, p9 and p12 are located above the section line and do not need to be on the same plane. In step 4, all the reference points are digitized and a 3D numerical model of the plaster model 3 is generated. A 3D location system is used to perform the numerical acquisition on model 3 of points p1 to p12 and points Ii, M1GetM1D. Then a reference system associated with the articulator (SRA) is calculated, according to: tmpZ = ((p4-p10) x (p1-p10)) + ((p7 -p10) x (p4-p10)) eax = ( p4 - p10) eay = tmpZ x eax

eaZ = eax x eay pa = (p4 + p10) * 0.5-0 eax, eay and eaZ are then normalized. They correspond to the three unit vectors of the SRA reference and pa corresponds to the position vector. The sagittal, coronal and frontal planes of the articulator are defined by the vectors eay, eaZ and eax (vectors perpendicular to the respective planes). The position of the planes is defined by the point pa whose coordinates have the same values as the components of the vector pa. The first section plane is then calculated by adjusting the points p2, p5, p8 and p11 to a plane, the vector vppc perpendicular to the section plane obtained and the center of gravity m of the four points. The first plane of PPC cut is thus defined as the plane passing through m and vppc is perpendicular. The orientation of vppc is then modified so as to direct it towards the teeth of the plaster model, by making the dot product between vppc and eaZ. If this scalar product is positive, vppc is not modified with respect to the previous determination, so, as well as PPC. On the other hand, if this scalar product is negative, we modify vppc by multiplying it by a factor (-1,0). PPC is modified accordingly. This scalar product is never zero.

The cut thickness "ec" is then estimated. This is associated with the type of tool used by the prosthetist to cut the plaster model. If the prosthetist uses a saw of a model conventionally used for this purpose, it can be estimated that ec is 1.0 mm. Then eight reference axes are generated: these axes are calculated from the points p1 to p12. They are represented by a vector (indicating the direction of the axis) and a point on the axis. The axes are: AxlnfD "Lower Axis Right": AxInfD = (p2 -pl, pl) AxInfA "Lower Anterior Axis": AxInfA = (p5 - p4, p4) AxlnfG "Lower Left Axis": AxInfG = (p8 - p7, p7) AxlnfP "Posterior Lower Axis": AxInfP = (pl l -p10, plO) AxSupD "Upper Axis Right": AxSupD = (p3 - p2, p2) AxSupA "Upper Anterior Axis": AxSupA = (p6 -p5, p5 ) AxSupG "Upper Left Axis": AxSupG = (p9 - p8, p8) AxSupP "Upper Posterior Axis": AxSupP = (p12 - pl 1, fold) We then generate intersection points associated with the coronal plane of the articulator . These points are generated by calculating the intersection between the coronal plane of the PCA = (en,, pa) articulator and the axes AxInfA, AxlnfP, AxlnfD and AxlnfG. The four points obtained are named piaa "joint articulator intersection point", piap "posterior articulator intersection point", piad "right articulator intersection point" and piag "left articulator intersection point". The first cut made on the plaster model is then simulated and references and points of intersection associated with this section are generated. In this step, the section plane PPC = (vppc, m), the section thickness "ec" and the eight axes previously calculated are used to generate two frames, one SRS = (ps, (esx, esy, es,)) located above the section plane, the other SRI = j): j, "located below the section plane, and eight points of intersection. These parameters are calculated as follows. For SRS, we set: ps = m-0 + vppc * (ec * 0.5) then we calculate the points of intersection between the axes AxSupA, AxSupP, AxSupD, AxSupG and the plane (vppc, ps), ps being the point whose coordinates have the same values as the components of the vector ps, by naming the points of intersection respectively pisa "anterior superior intersection point", pisp "posterior superior intersection point", pisd "right upper intersection point" And pisg "upper left intersection point". Then we define the vectors: esx = (pria - pisp) esy - = vppc x esx es, - = esx x esy esx, esy and es, are then normalized. For SRI, we set: pi = m-0-vppc * (ec * 0.5) then we calculate the points of intersection between the axes AxInfA, AxlnfP, AxlnfD, AxlnfG and the plane (vppc, pi), where pi is the point whose coordinates have the same values as the components of the vector pi, by naming the points of intersection respectively pila "lower inferior intersection point", piip "lower inferior intersection point", piid "right inferior intersection point "and piig" lower left intersection point ". Then we define the vectors: eix - = (pua - paap) eiy = vppc x eix el = axis' Z x y eix, eiy and eiz are then normalized. Then we determine the rectangle which includes the points of intersection and whose sides are parallel to the esx and esy vectors. The vertices of the rectangle are named pad "right front point", pag "left front point", ppd "right back point", and ppg "left back point". Then we generate the dental reference system and the points of intersection associated with the dental plane: in this part, the reference SRA = (pa, (eax, eay, eaz)) associated with the articulator, the points ii, mi g, mid acquired on the gypsum model teeth, and the AxSupA, AxSupP, AxSupD, AxSupG axes are used to generate the dental reference SRD = (pdt, (edt ,, edty, edtz)) and four points of intersection. These parameters are calculated as follows. For SRD we put pdt = ii -0, then we define the sagittal plane of the articulator 5 as PSA = (eay, pa) we project the points ii, mig and mid on the PSA plane; the new points thus obtained are called iip, m 1 gp and m 1 dp. Then the following vectors are defined: edtx = llp- / mlgp + mldp 2 edtz = edtx x eay edty = edtz x edtx edtx, edty and edtz are then normalized edtx, edty and edtZ correspond to the anteroposterior, lateral and vertical. For the points of intersection, they are calculated between axes AxSupA, AxSupP, AxSupD, AxSupG and the dental plane PDent = (edtZ, ii), naming the points of intersection respectively pida "point of previous dental intersection" , pidp "posterior dental intersection point", pidd "right dental intersection point" and pidg "left dental intersection point". Then we generate the control repositories. The objective of this operation is to create the tools to be able to quantify the work done by the prosthetist or the person who builds the repositioning gutter and to compare it with what was planned by the surgeon before. For this, two frames of reference are generated, one called "superior control reference system" SRCS = (pcs, (ecsx, ecsy, ecs,)) for the structures 25 (points, references and axes) located above the line of cut and the other called "lower control reference system" SRCI = (pci, (ect ,, eciy, eciz)) for the structures located below the section line. For SRCS we define its different vectors as follows: pcs = p6-0 ecsx = p3-p6 ecsz - = ecsx x (p9 - p6) ecsy - = ecsz x ecsx ecsx, ecsy and ecsz are then normalized.

For SRCI, we define its different vectors as follows: pci = p4-0 ecix = plp4 eciz = ecix x (p7-p4) eciy = eciz ecix x ecix, eciy and eciz are then normalized. Finally, a digital 3D representation of the plaster model is generated. The aim is to allow the user to visualize a numerical representation of the plaster model. The degree of complexity of this representation depends on the parameters used in its design and previously calculated parameters (reference frames, points, thickness of the first section, etc.). This representation also makes it possible to visualize the two rigid structures obtained after having simulated the first cut. Fig. 10 shows an example of a simplified 3D representation of the plaster model and several parameters in the initial position, after the first cut, and Fig. 11 shows an improved 3D representation of the same model. In step 5, a numerical simulation of the operations to be performed on the plaster model is performed to obtain the bone movements planned by the surgeon. This simulation is performed using the parameters obtained in step 4 and the displacement and rotation values obtained in step 2 as input data. The procedures performed on the basis of this information are: a) Calculation of the transformation (translation and rotation) for motion simulation. This transformation is obtained by using the displacement values (A, L, V) on the antero-posterior, lateral and vertical axes and the rotation angles RA, RL and Rv around these same axes. The transformation is defined as TRXyZ = (TXyZ, RZXy) where TXyZ = (A, L, V) and RZXy correspond to the rotation matrix in the order of rotation y-xz. It is obtained as follows: 25

26 coseycosez - sinexsineysinez -cosexsinez cosezsiney + coseysinexsine cosesinexsiney + coseysine cosexcose -coseycosesinex + sineysinez -cosexsiney sinex cosexcosey

where G, 9 and O respectively correspond to RA, RL and Rv. b) Simulation of movements. To perform the motion simulation, all the parameters (points, references and axes) above the section, as shown in Figures 10 and 11, are first referenced to the SRD repository. Then the TRXy transformation is applied to the SRD dental repository to obtain the SRDS simulated dental reference. The transformation associated with SRDS (translation and rotation matrix) is then applied to the parameters referenced to SRD. Figure 12 shows a 3D representation of the plaster model and several parameters before and after the motion simulation. c) Optimization of the 3D representation of the model and calculation of the height of the second section line. Following the previous simulation of the movements, two situations can arise. The first, as shown in Figure 13 in sagittal view, when the upper part of the 3D representation intersects the lower part in various areas and in more or less significant proportions, as shown by the three cases shown, and the second, as shown in Figure 14 in sagittal view, when the two parts do not intersect. The first case is identified when at least one of the points pads, pags, ppds or ppgs is below the xy plane of the SRI repository, and the second case when these four points are above this same plane. In the second case, an optimization is not necessary because the two portions do not intersect, and it is therefore not necessary to perform a second cut on the 3D representation and, therefore, on the plaster model.

In the first case mentioned above, we must optimize the upper part so that it does not cut the lower part. To do this, the following procedures must be performed: a) selection of the point located below the xy plane of the SRI repository; b) generating an axis using the point obtained previously and the unit vector in z of the SRSs reference frame; c) calculation of the intersection point between the previously calculated axis and the xy plane of the SRI frame; this point will be named pdc "reference point for the second cut" (figure 15 on the left); R = ay

D) generation of a plane P parallel to the xy plane of the SRSS reference frame at the point pdc (FIG. 15, left-hand side); e) cutting of the upper part of the 3D representation using the plane P obtained previously, followed by the elimination of the portion situated below this plane P (FIG. 15 on the right); the points pisan, pisps, pisds and pisgs are respectively replaced by the intersection between the axes AxSupAs, AxSupPs, AxSupDs, AxSupGs and the plane P; f) calculating the distance between the point pdc and the xy plane of the SRSS; this distance corresponds to the height of the second cut "hdc" (figure 15 on the left) which will be performed by the prosthetist with respect to the first cut line 4 marked on the plaster model 3. The height of the second cutting line "hdlc" which will be plotted on the plaster is obtained according to the equation hdlc = hdc - ec * 0.5 where ec corresponds to the thickness of the section. FIG. 15 shows the examples of optimization of the 3D representation in the three intersection cases represented in FIG. 13. In the second case, where it is not necessary to perform a second cut, the values of hdc " height of the second cut "and hdlc" height of the second cut line "are equal to zero. In step 6, the second cutting line hdlc is marked on the plaster model 3, if this second cutting line is necessary. In step 7, the instruction document for the prosthetist is generated. This document, associated with the marking performed on the plaster model, helps guide the prosthetist and improve the accuracy and reproducibility of the classic technique for the construction of the gutter. To generate this document, nine parameters are needed. These parameters are associated with the marking performed on the plaster model 3. The first, hdlc "height of the second cut line" was presented in part 5) and the other eight, presented in figure 16, are: ha " height of the anterior side ", hp" height of the posterior side ", hd" height of the right side ", hg" height of the left side ", dla" lateral displacement of the anterior side ", dlp" lateral displacement of the posterior side ", dad" anteroposterior displacement of the right side "and dag" anteroposterior displacement of the left side ". FIG. 16 shows the methodology for calculating each of the 8 parameters and the possible combinations for each of the sides of the plaster model 3. It is defined, as can be seen in FIG. 16, the various parameters other than hdlc by: height of the front side of the plaster model "; if the upper part of the plaster model moves in the negative direction of the X axis of the SRI reference, ha is

28 calculated as the vertical distance (in the Z axis of the SRI reference) between the point pisas and the X-Y plane of SRI; if the upper part of the plaster model moves in the positive direction of the X axis or if its displacement is zero on this axis, ha is calculated as the vertical distance between the pila point and the plane P formed by the pisas points, pisds, pisps and pisgs; - hp "height of the posterior side of the plaster model"; if the upper part of the plaster model moves in the negative direction of the X axis of the SRI reference, ha is calculated as the vertical distance between the point piip and the plane P; if the upper part of the plaster model moves in the positive direction of the X axis or if its displacement is zero on this axis, ha is calculated as the vertical distance between the point pisps and the X-Y plane of SRI; - hd "height of the right side of the plaster model"; if the upper part of the plaster model moves in the positive direction of the Y axis of the SRI reference, hd is calculated as the vertical distance between the point piid and the plane P; if the upper part of the plaster model moves in the negative direction of the Y axis or if its displacement is zero on this axis, hd is calculated as the vertical distance between the point pisds and the X-Y plane of SRI; - hg "height of the left hand side of the plaster model"; if the upper part of the plaster model moves in the positive direction of the Y axis of the SRI reference, hg is calculated as the vertical distance between the point pisgs and the X-Y plane of SRI; if the upper part of the plaster model moves in the negative direction of the Y axis or if its displacement is zero on this axis, hg is calculated as the vertical distance between the piig point and the plane P; - dla "lateral displacement of the front side of the plaster model"; we calculate the projection of the pila and pisas points on the SRI frame and then we calculate dla as the difference between the Y coordinate of the pisas projection and the Y coordinate of the pila projection; - dlp "lateral displacement of the posterior side of the plaster model"; we calculate the projection of the piip and pisps points on the SRI frame and then we calculate dlp as the difference between the Y coordinate of the pisps projection and the Y coordinate of the piip projection; - dad "anteroposterior displacement of the right side of the plaster model"; we calculate the projection of the points piid and pisds on the reference SRI and then we calculate dad as the difference between the X coordinate of the projection of pisds and the coordinate X of the projection of piid;

29 - dag "antero-posterior displacement of the left side of the plaster model"; we calculate the projection of the points piig and pisgs on the reference SRI and then we calculate dag as the difference between the X coordinate of the projection of pisgs and the X coordinate of the projection of piig.

From the nine parameters mentioned above, the instruction document for the prosthetist can thus be generated and transmitted. Figure 20 shows an example of such a document sent to the prosthetist. In step 8, a repository change and a data backup are performed. The repository changes are performed, as shown in Figure 17, using SRCI as the primary repository. The SRCS repository is computed against the SRCI repository. The new repository, which is the SRCS projection on SRCI, is named SRM, "maxillary referral system in the initial position". The SRCSs repository is computed against the SRCI repository. The new repository, which is the projection of SRCSs on SRCI, is named SRMs "maxillary referral system in the simulated position". The SRD repository is computed against the SRCS repository. The new repository, which is the SRD projection on SRCI, is named SRDR "relative dental reference system". It is also equal to the SRDs repository with respect to the SRCSs repository. To calculate the position and the orientation of the dental reference system with respect to the SRCI before and after simulation, it suffices to apply to the SRDR the transformation associated with SRM, and the transformation associated with SRMs to obtain respectively the SRDI reference systems "dental reference system initial "and SRDS" simulated dental referral system ".

Finally we save the calculated parameters in a file. In step 9 we proceed to the construction of the gutter. For this purpose, the previously generated instruction document and the maxillary cast model of the patient are transmitted to the prosthetist. The latter thus builds the gutter in a conventional manner on the basis of the instructions presented in the document and guided by the plots made on the plaster model. To materialize the value of the height parameters presented in the document, the prosthetist can use small blades of different thicknesses and choose the most suitable combination to the height required for each side of the plaster model. Once the gutter is built, it is sent to the surgeon who checks its compliance with the order. For this purpose, he can use a software that manages the data stored in step 8) and also manages the 3D location system to palpate points on the plaster model above and below the cut made by the prosthetist. These points will make it possible to quantify the displacements actually performed by the prosthetist and to compare them with planned movements during the simulation of the surgical procedure. In case of non-compliance, the gutter must be rectified or redone. In this control step, the procedures performed are: 1) Palpation of points and generation of the two control repositories. In this part, the 3D localization system is used to perform the digital acquisition on the plaster model of maxillary six easily identifiable control points p1, p4, p7, p3, p6 and p9. These points are then used to generate two control repositories according to the method described in the previous section 4). These two repositories will be named SRCSo "upper control reference system obtained" for the plaster model part above the cut and SRCIo "lower control reference system obtained" for the part below the cut. 2) Quantification of the movements performed by the prosthetist. To quantify these motions, the methodology developed in step 8 is applied using the SRCSo and SRCIo repositories, thus obtaining Figure 18 where SRDO is the "dental reference system obtained" and SRDI is the "system of reference". initial dental reference ". Then, the SRDO repository is computed against the SRDI repository. The new repository is named SRG "Gutter Reference System" (Figure 19).

The x, y, and z axes correspond respectively to the antero-posterior, lateral and vertical axes. The movements made by the prosthetist are defined by the coordinates of the SRG reference position vector with respect to the displacement, and by the Euler angles in the rotation order y-x-z of the rotation matrix associated with the SRG reference frame. 3) Comparison of results and possible decision to return the gutter to the prosthetist. In this part, the surgeon can compare the movements performed by the prosthetist with what has been planned. If the movements do not correspond to the planning, the surgeon can return the plaster to the prosthetist for correction or re-execution of the gutter. Otherwise, the gutter meets the expectations of the surgeon, who can use it during the operation. In addition to the use of the repositioning gutter resulting from the design process according to the invention in conventional procedures of orthognathic surgery, this method can be used to design a gutter that can be used as a tool for monitoring and 3D control of the surgical procedure intraoperatively. This is possible by combining the gutter thus obtained and the information resulting from the steps of change of reference and control with the methodology presented in the JALBERT thesis mentioned in the introduction. This application makes it possible to improve the precision and the reproducibility of the surgical procedure by combining a more precise gutter made by the method according to the invention with a follow-up and a 3D control of the surgical gesture intraoperatively. 10

Claims (1)

CLAIMS1.- A method of designing and manufacturing a positioning gutter for use in repositioning the jawbone (1) of a patient during an orthognathic surgery operation, characterized in that a dental reference system is defined ( SRD) for estimating the movements and rotations of bone structures from an imagery of the patient's anatomy, performed either in 2D or in 3D, by choosing said dental reference system (SRD) from the sagittal plane of the patient. the articulator and the following three points: * the inter-incisal point (Ii) of the maxillary (1) which will constitute, preferably, the origin of the reference frame; * the vestibulomésial cusp point of the first left molar (M1G); * the vestibulomésial cusp point of the first right molar (MID); and in that a processing of the data obtained from these points is carried out which comprises the following steps: if a 2D image is available, a reference frame (Ii, λ, L, V) is determined: selecting on the radiography the points (Ii, M1 G and M1 D); * taking the interincistive point (Ii) as the origin of the repository; defining the anteroposterior vector (A) as A = I 1 -MILG + MlD "2 ~ * by defining the lateral vector (L) as being perpendicular to the plane of the X-ray; * by defining the vertical vector (V) as being perpendicular to ()), * and normalizing these three vectors (λ, L, V); if we have a 3D reconstruction of the maxillary (1), we determine a reference (Ii, Â, L, V) 25 * by generating the sagittal plane of the head from several selected points on the virtual model (2 ) of the patient's head * by selecting on the 3D reconstitution said points (Ii, M1G and MI D); * projecting these points on the sagittal plane of the head, to create new points (Iip, M1Gp, and MlDp); 30 * defining Ii as the origin of the repository; defining the anteroposterior vector (A) as A = lip ~ M1Gp + M1Dp 2 * by defining the lateral vector (L) as being perpendicular to the sagittal plane of the head; * by defining the vertical vector (V) by V = Âx L; * and by normalizing the vectors (V, Let)); on the computerized representation of the maxillary (1), the operative gesture is simulated with respect to the previously determined dental reference, by calculating the position and the relative orientation of the dental reference after simulation (SRD) with respect to the dental reference system before simulation (SRD0 ); a new repository (SRD1.o) is defined as SRD1_0 = G_0)), where Po is the position vector whose coordinates (A, L, V) correspond respectively to displacements on the anteroposterior, lateral and vertical axes, and (Δl-o , 4-0, Vo) being the three orthogonal unit vectors; from these three orthogonal unit vectors, a rotation matrix [A, _o V-o] used to calculate the Euler angles (RL, RA and Rv), corresponding to the rotations about each axis, is generated; - On the plaster model (3) of the maxillary of the patient, the lines and the reference points are marked and marked: a first cutting line (4), parallel to the base of the model (9); * four lines perpendicular to the base of the model (3), starting from points located at the base and on the same plane parallel to the coronal plane of the articulator, respectively a line (5) on the rightmost edge, a line (6) on the anterior side, a line (7) on the leftmost edge, and a line (8) on the posterior side, the lines (6, 8) drawn on the anterior and posterior edges of the model (3). ) each starting from a point on the sagittal plane of the articulator; - twelve reference points are marked on the model, located on each of the preceding lines (5, 6, 7, 8) at the base of the model (9), at the intersection with the first cutting line (4) and at the above the first section line (4), four of said points (p1, p4, p7, p10) being situated on the same plane at the level of the base and making it possible to define the coronal sagittal and frontal planes associated with the articulator, another four of said points (p2, p5, p8, p11) being located on the section line, four others of said points (p3, p6, p9, p12) being located above the section line; all the reference points of the model, as well as the interincistive point (ii), the vestibulomésial cusp point of the first left molar (m1g) and the vestibulomésialcuspid point of the first right molar (m1d) of the model are digitized, and a 3D digital model of the plaster model (3); a reference system associated with the articulator (SRA) is calculated, according to tmpZ = ((p4 - p10) x (p1 - p10)) + ((p7 - p10) x (p4 - p1)) eax = ( p4 - pl 0) eay = tmpZ x eax eaZ = ea, x eay pa = (p4 + plO) * 0.5-0 - one normalizes eax, eay and eaZ, which correspond to the three unit vectors of the frame of reference (SRA), pa corresponding position vector; the sagittal, coronal and frontal planes of the articulator are defined by the vectors eay, eaZ and eax perpendicular to the respective planes, and the position of the planes is defined by the point pa whose coordinates have the same values as the components of the vector pa; the first section plane (PPC) is then calculated by adjusting the points p2, p5, p8 and p11 to a plane, the vector vppc perpendicular to the obtained section plane and the center of gravity m of the four points, by defining the first plane of cut (PPC) as the plane passing through m and at which vppc is perpendicular; the orientation of vppc is then modified so as to orient it towards the teeth of the plaster model, by making the dot product between vppc and eaZ; * if this scalar product is positive, vppc is not modified compared to the previous determination, so, so, that PPC; * if this scalar product is negative, we modify vppc by multiplying it by a factor (-1,0), and we modify PPC accordingly; * the cut thickness "ec" is then estimated; eight reference axes are then generated calculated from the reference points (p1 to p12) and represented by a vector indicating the direction of the axis and a point on the axis, said axes being: AxlnfD "Lower Right Axis" : AxlnfD = (p2 - pl, pl) AxInfA "Lower Anterior Axis": AxInfA = (p5 - p4, p4) AxlnfG "Lower Left Axis" AxInfG = (p8- p7, p7) AxlnfP "Posterior Lower Axis": AxInfP = (pl 1- p10, p10) AxSupD "Upper Right Axis": AxSupD = (p3 - p2, p2) AxSupA "Upper Anterior Axis": AxSupA = (p6 - p5, p5) AxSupG "Upper Left Axis": AxSupG = ( p9- p8, p8) AxSupP "Posterior Upper Axis": AxSupP = (p12 - pl 1, pl 1) - we then generate intersection points associated with the coronal plane of the articulator (PCA), calculating the intersection between the coronal plane of the PCA articulator (eaZ, pa) and axes AxInfA, AxlnfP, AxlnfD and AxInfG, the four points obtained being respectively named piaa "articulated intersection point" anterior lenght ", piap" point of intersection posterior articulator ", piad" point of intersection right articulator "and piag" point of intersection left articulator "- one simulates then the first cut made on the model in plaster and one generates reference points and intersection points associated with this section, using the PPC = (vppc, m) section plane, the section thickness "ec" and the eight axes previously calculated to generate two frames, one SRS = (ps, (esx, esÇ, es,)) located above the section plane, the other SRI = (pi, (eiy, eZ)) below the section plane, and eight points of intersection , calculating these parameters in the following way: * for SRS one poses: ps = m-0 + vppc * (ec * 0.5) then one calculates the points of intersection between axes AxSupA, AxSupP, AxSupD, AxSupG and the plane (vppc, ps), where ps is the point whose coordinates have the same values as the components of the vector ps, by naming the p intersection anoints respectively pisa "anterior superior intersection point", pisp "posterior superior intersection point", pisd "right upper intersection point" and pisg "left superior intersection point", and defining, then normalizing the vectors: esx = (pisa - pisp) esy - = vppc x esx es, - = esxxesy; * for SRI, one puts: pi = m - 0 - vppc * (ec * 0.5) then one calculates the points of intersection between axes AxlnfA, AxInfP, AxlnfD, AxlnfG and the plane (vppc, pi), pi being the point whose coordinates have the same values as the components of the vector pi, by naming the points of intersection respectively plia "lower inferior intersection point", piip "lower inferior intersection point", piid "inferior intersection point right "and piig" lower left intersection point ", and by defining and then normalizing the vectors: eix = (pua - piip) eiy = vppc x ei ei x ei x x x - the rectangle which includes the points of intersection and whose sides 15 are parallel to the esx and esy vectors, by naming the vertices of the rectangle pad "right fore-point", pag "left fore-point", ppd "right-rearward point", and ppg "left-posterior point " the dental referential SRD = (pdt, (edtx, edty, edt,)) is generated and four points of intersection associated with the dental plane, using the associated referential 20 SRA = (pa, (eax, eay, eaZ)) to the articulator, the points ii, ml g, ml d acquired on the teeth of the plaster model, and the axes AxSupA, AxSupP, AxSupD, AxSupG: * to generate SRD we set pdt = ii - 0, then we define the sagittal plane of the articulator as PSA = (eay, pa); * we project the points ii, mlg and m1d on the PSA plane; the new points thus obtained are called iip, mlgp and m1dp; * then we define and standardize the following vectors: edtx = ii - (mlgp + m1d; 2 Edt, = edtx x eayedty = edtZ edtx x edtx, edty and edtZ respectively corresponding to the anteroposterior, lateral and vertical vector; * for generate the points of intersection, we calculate them between axes AxSupA, AxSupP, AxSupD, AxSupG and PDent dental plane = (edtZ, ii), by naming the points of intersection respectively pida "point of previous dental intersection", pidp "posterior dental intersection point", pidd "right dental intersection point" and pidg "left dental intersection point" - two control reference frames are generated, one called "superior control reference system" SRCS = (pcs, ecsx, ecsy, ecsZ)) for the structures (points, references and axes) located above the section line, and the other called "lower control reference system" SRCI = (pci, This: eciy, eciZ)); * for SRCS we define its different vectors as follows and we normalize them: pcs = p6-0 ecsx = p3 - p6 ecsZ = ecsx x (p9 - p6) ecsy = ecsZ x ecsx * for SRCI, we define its different vectors as follows and we normalize them: pci = p4-0 ecix = pl - p4 eciZ = ecix x (p7 - p4) eciy = eciZ x ecix - we generate a numerical 3D representation of the plaster model; a numerical simulation of the operations to be performed on the plaster model is performed to obtain the bone movements planned by the surgeon, by: a) calculating the transformation in translation and in rotation for the simulation of the movements, using the displacement values (A, L, V) on the anteroposterior, lateral and vertical axes and the angles of rotation (RA, RL and Rv) around these same axes, the transformation being defined as TRx, Z = (TxyZ, R, xy), where Txy, Z = (A, L, V) and Rz, ~ correspond to the rotation matrix in the order of rotation yxz obtained by: coseycos9Z - sin9xsinOysin9Z -cosOxsin9Z cos9Zsiney + cos9ysinOxsin9Z RZxY = cos9ZsinOxsinOy + cosOysin9Z cosexcos9Z -cosOycos9Zsin9x + sinOysin9Z cosoxsiney sinex cosexcosoy where 9x, ey and 9Z correspond respectively to RA, RL and Rv. b) motion simulation, in which all the parameters above the section are first referenced in the SRD repository, and then the TRxy transformation, is applied to the SRD dental repository to thereby obtain the SRDS simulated dental referential; the transformation associated with SRDS (translation and rotation matrix) is then applied to the parameters referenced to SRD; c) optimization of the 3D representation of the model and calculation of the height of the possible second cutting line; * in the case where the upper part of the 3D representation intersects the lower part in various zones, the optimization is carried out by selecting the point located below the xy plane of the SRI frame and then generating an axis using the point obtained previously and the unitary vector in z of the SRSS reference frame; then calculating the point of intersection pdc "reference point for the second section" between the previously calculated axis and the xy plane of the SRI repository, then generating a plane P parallel to the xy plane of the SRSS reference frame at the point pdc; then cutting the upper part of the 3D representation using the plane P obtained previously, followed by the elimination of the portion situated below this plane P, replacing the points pisan, pisps, pisds and pisgs respectively by the intersection between the axes AxSupAs, AxSupPs, AxSupDs, AxSupGs and plane P; then calculating the distance between the point pdc and the xy plane of the SRSS, this distance corresponding to the height of the second section "hdc" which will be performed by the prosthetist with respect to the first section line (4) marked on the plaster model (3); then plotting the second cutting line "hdlc" on the plaster model (3), hdlc being obtained according to the equation hdlc = hdc - ec * 0.5 where ec corresponds to the thickness of the cut; * in the case, where it is not necessary to make a second cut, the values of hdc "height of the second cut" and hdlc "height of the second cutting line" are taken as zero; the instruction document for the prosthetist, based on nine parameters associated with the marking performed on the plaster model (3): * hdlc; * ha "height of the front side of the plaster model"; * hp "height of the posterior side of the plaster model"; * hd "height of the right side of the plaster model"; * hg "height of the left hand side of the plaster model"; * dla "lateral displacement of the front side of the plaster model"; * dlp "lateral displacement of the posterior side of the plaster model"; * dad "antero-posterior displacement of the right side of the plaster model"; * dag "antero-posterior displacement of the left side of the plaster model"; - a repository change is made using SRCI as the main repository: * the SRCS repository is computed with respect to the SRCI repository and a new SRM repository is obtained, "maxillary reference system in the initial position"; * We calculate the SRCSS repository with respect to the SRCI repository and we obtain a new repository SRMs "maxillary reference system in the simulated position"; the SRD repository is computed with respect to the SRCS repository and a new "relative dental reference system" SRDR repository is obtained equal to the SRDs repository with respect to the SRCSS repository; the position and orientation of the SRD dental referential with respect to SRCI are calculated before and after simulation, by applying to SRDR the transformation associated with SRM1 and the transformation associated with SRMs to obtain respectively the SRDI references "initial dental reference system" and SRDS "simulated dental referral system"; - saving the calculated parameters in a file; the gutter is manufactured on the basis of the previously generated instruction document and the plaster model (3); 2.- Method according to claim 1, characterized in that a 2D imaging is used and in that one takes by default the constants (L, Rv, RA) equal to zero. 3. A method according to claim 1 or 2, characterized in that materializes said points (p1-p12) by holes. 4.- Method according to one of claims 1 to 3, characterized in that, after the manufacture of the gutter, one proceeds to the control of its conformity with the control by: - palpation of points and generation of the two control reference points in using a 3D location system to perform digital acquisition on the plaster maxillary model of the six control points (p1, p4, p7, p3, p6 and p9); use of these control points to generate two SRCSo control references "superior control reference system obtained" for the plaster model part above the cut and SRCIo "lower control reference system obtained" for the part in below the cup. - quantification of the movements performed by the prosthetist using the SRCSo and SRCI0 repositories, to obtain a SRDO reference "obtained dental reference system" and an SRDI reference system "initial dental reference system" (18); - the SRDO repository is computed with respect to the SRDI repository, to obtain a new reference SRG "gutter reference system" whose axes (x, y, z) correspond respectively to the anteroposterior, lateral and vertical axes (19) the movements made by the prosthetist are defined by the coordinates of the position vector of the SRG reference frame with respect to the displacement, and by the Euler angles in the rotation order yxz of the rotation matrix associated with the SRG reference frame; - we compare the movements performed by the prosthetist with those that had been planned.