Method for determining an orthodontic treatment plan

Abstract

Disclosed is a method for generating a plan for the orthodontic treatment of a user's dental arch, comprising the following consecutive steps: a) generating an initial model and a final model representing the dental arch at an initial moment and a final moment; b) determining, using a computer, a deformation scenario that transforms, through the movement of the tooth models, the initial model into the final model; c) determining, using the computer, - a duration for performing the deformation scenario; and - intermediate moments between the initial moment and the final moment for performing the deformation of the dental arch according to the deformation scenario.

Description

[0001] Description

[0002] Title: METHOD FOR DETERMINING A TREATMENT PLAN

[0003] ORTHODONTIC

[0004] Technical field

[0005] The present invention relates to a method of determining an orthodontic treatment plan, which includes determining a complete orthodontic treatment plan or a portion of a complete orthodontic treatment plan.

[0006] The invention also relates to a computer program as well as a computer and a system for implementing this method.

[0007] Prior art

[0008] Orthodontic treatment is intended to change the arrangement of a user's teeth by means of an orthodontic appliance.

[0009] Among orthodontic appliances, we distinguish between arch and bracket orthodontic appliances on the one hand, and orthodontic aligners on the other.

[0010] An archwire and bracket orthodontic appliance consists of brackets fixed to the teeth and connected to each other by means of an archwire, typically made of a shape memory material. It exerts a rapid action on the movement of the teeth of the user being treated.

[0011] A aligner is typically a removable one-piece appliance, typically made of a transparent polymer material. It has a channel shaped to accommodate several teeth in an arch, usually all the teeth in an arch. The shape of the channel is designed to hold the aligner in position on the teeth, while also correcting the positioning of certain teeth. An orthodontic aligner has a slower initial action than an orthodontic appliance with arches and brackets. Advantageously, however, the aligner can be replaced by the user themselves. In addition, aligners are more discreet than appliances with arches and brackets. The implementation of orthodontic treatment requires the prior preparation of an orthodontic treatment plan in order to plan the stages of the upcoming orthodontic treatment.The orthodontic treatment plan thus defines times at which a check of the dental arch by a dental practitioner and / or a modification of an orthodontic appliance, for example a change of orthodontic appliance, for example an orthodontic splint, and / or a change of orthodontic arch, and / or a manufacture of an orthodontic appliance is / are planned.

[0012] Traditionally, an orthodontic treatment plan is created by the dental practitioner using a computer. The computer allows the practitioner to view a model of a dental arch and modify this model to determine a possible change in the position and orientation of each tooth, compatible with the change in the position and orientation of the other teeth, until the desired arrangement is achieved for all the teeth in the arch.The dental practitioner thus manages to determine a series of digital three-dimensional models comprising a model representing said arch at the start of the orthodontic treatment, a model representing said arch at the end of the orthodontic treatment, and one or more “intermediate” models representing said arch at intermediate times between the start and the end of the orthodontic treatment, the intermediate times being times at which a check of the arch by the dental practitioner and / or a modification of an orthodontic appliance and / or a manufacture of an orthodontic appliance is / are planned. This series of models, or “deformation scenario”, and the intermediate times thus define the orthodontic treatment plan.

[0013] Software for manipulating the arch model and generating an orthodontic treatment plan is well known. However, it requires learning how to use the software and requires orthodontic skills. Creating an orthodontic treatment plan can be laborious and time-consuming.

[0014] Furthermore, these software programs can lead to orthodontic treatment plans that result in rapid tooth movements, potentially detrimental to the user's health.

[0015] There is a continuing need for a method and system to improve the execution of an orthodontic treatment plan.

[0016] An object of the invention is to meet this need. Disclosure of the invention

[0017] Summary of the invention

[0018] According to a first main aspect, the invention provides a method for generating an orthodontic treatment plan for a dental arch of a user, the method comprising the following successive steps: a) generation or recovery of an “initial” model representing in three dimensions said dental arch at an initial time, said initial model being divided into tooth models, and optionally a gum model, and generation or recovery of a “final” model representing said dental arch with a “final” arrangement of the tooth models as desired at the end of the orthodontic treatment;b) determination, by a computer, of a set of successive elementary deformations transforming, by displacement of the tooth models, the initial model into a final model, said elementary deformations each respecting a respective set of constraints, the models resulting from the successive elementary deformations being called “transition models”, the succession of all the successive transition models being called “basic deformation scenario”; c) determination, by the computer,;

[0019] - a duration, called "treatment duration", to carry out, from the initial moment, the deformation of the dental arch according to the basic deformation scenario until obtaining the final arrangement, at a final moment; and

[0020] - intermediate moments between the initial and final moments to carry out the deformation of the dental arch according to the basic deformation scenario, the intermediate moments being moments at which a control of the arch by a dental practitioner and / or a modification of an orthodontic appliance and / or a manufacture of an orthodontic appliance is / are planned, the basic deformation scenario and said intermediate moments defining said orthodontic treatment plan, called "basic orthodontic treatment plan".

[0021] The instants at which, according to the basic orthodontic treatment plan, the dental arch is expected to have a shape according to the transition models are called "transition instants". As will be seen in more detail in the remainder of the description, the computer therefore creates, from only the initial and final models, the basic orthodontic treatment plan quickly and automatically, that is to say without human intervention. The automation of the creation of orthodontic treatment plans can be advantageously optimized, in particular with metaheuristic methods, which makes it possible to achieve performances that are very difficult to achieve manually, in particular by avoiding collisions or ensuring the most regular or fastest possible movements of the teeth.

[0022] Preferably, a method according to the first main aspect of the invention also has one or more of the following optional features:

[0023] - in step a), said computer determines the final model from the initial model;

[0024] - in step a), to determine the final model, said computer

[0025] - analyzes the shape of the initial model in order to determine the curvature and length of the dental arch and define a baseline having said curvature and length, then,

[0026] - for each of a plurality of tooth models, preferably for each tooth model of the initial model, determines a position and an orientation of said tooth model relative to said baseline, preferably from predefined rules and / or by assimilating the user's dental arch to a historical dental arch similar to the user's dental arch;

[0027] - preferably, prior to step a), said predefined rules are determined by statistical processing of historical data;

[0028] - in step b), said set of constraints comprises prescription constraints imposed by the user, preferably to specify the relative importance that the user gives to the speed of the orthodontic treatment, and / or to the pain generated by the orthodontic treatment, and / or to the comfort during the orthodontic treatment, and / or to the cost of the orthodontic treatment and / or to the aesthetic impact of the orthodontic treatment and / or to the reliability of the orthodontic treatment, i.e. to the probability that the orthodontic treatment leads to the intended result, and / or to a duration for wearing an orthodontic appliance, and / or to a predetermined functional, orthodontic or therapeutic objective;

[0029] - in step b), the computer displays a dynamic form suitable for the entry, preferably by the user, of at least part of the information necessary for the definition of said set of constraints, in particular necessary for the definition of prescription constraints;

[0030] - in step b), said set of constraints allows limited penetration of a tooth model into an adjacent tooth model, the limitation of said penetration preferably being determined by the possibility, preferably evaluated according to the rules of orthodontics, preferably by a dental practitioner, of filing, during the orthodontic treatment, at least one of the teeth modeled by said tooth models, in order to avoid a collision between said teeth resulting from said penetration;

[0031] - in step b), the computer implements an optimization algorithm, preferably a first optimization algorithm to determine a basic deformation scenario leading to a model as close as possible to the final model and / or a second optimization algorithm to determine a basic deformation scenario best meeting one or more prescriptions dictated by the user;

[0032] - in step b), the computer

[0033] - searches for a “coarse” deformation scenario with a coarse initial model comprising less than 5000 points, preferably less than 2000 points, preferably less than 1000 points, preferably less than 500 points, preferably less than 100 points, and / or more than 50 points, the coarse initial model resulting from a simplification of a fine initial model comprising more points than the coarse initial model, preferably comprising 1.1, or 1.5 or 2 or 5 or 10 or 100 times more points than the coarse initial model, then

[0034] - completes, at least partially, the transition and final models, i.e. adds points to these models,

[0035] - determines whether, in the coarse deformation scenario in which the transition and final models have been so completed, tooth models collide unacceptable, and, in the event of unacceptable collision, adds points to the initial coarse model, preferably at least in the collision areas, preferably at least the points added to the transition and final models in the collision areas, or even with all the points added to the transition and final models, and

[0036] - resumes said search with the initial coarse model to which the points have been added, the cycling preferably being continued until a deformation scenario is obtained without unacceptable collision, constituting the basic deformation scenario;

[0037] - at the beginning of step c), the computer

[0038] - determines, for each tooth model, the instant closest to the initial instant at which the tooth model can reach, following the basic deformation scenario determined in step b), its configuration in the final model, or “end of path instant”;

[0039] - determines, among the set of tooth models, a tooth model having the end of path time furthest from the initial time, or “limiting tooth model”;

[0040] - sets the final instant as the end instant of the path of the limiting tooth model;

[0041] - the computer preferably determines the end time of the path of a tooth model, preferably of each tooth model, by dividing a distance representative of the displacement of the tooth model during the basic deformation scenario, by a speed representative of the kinetic capabilities of said tooth model;

[0042] - in step c), the computer determines the intermediate instants by dividing said treatment duration according to the capacity of one or more orthodontic appliances, preferably according to the capacity of orthodontic aligners, to move the teeth modeled by the tooth models, and / or by dividing said treatment duration into intervals of the same duration, each interval preferably corresponding to a duration of use of an orthodontic aligner by the user intended for the orthodontic treatment, or corresponding to a frequency of checking the proper progress of the orthodontic treatment, said frequency preferably being predetermined;

[0043] - the method comprises, after step c), the following first step d): d) determination, by the computer, of a new deformation scenario, called “first smoothed deformation scenario”,

[0044] - in which the configuration of the limiting tooth model is, at any intermediate instant, preferably at any transition instant, that defined by the basic deformation scenario determined in step b), and

[0045] - wherein a movement speed, preferably each movement speed, of at least one tooth model other than the limiting tooth model, or "slowed tooth model", is smoothed between the initial instant and the final instant, i.e. wherein at least one speed parameter is reduced or optimized, preferably minimized, the first smoothed deformation scenario and said intermediate instants defining a new orthodontic treatment plan, called "first smoothed orthodontic treatment plan";

[0046] - the speed parameter is chosen from:

[0047] - the greatest value of a displacement speed of said slowed tooth model reached between the initial instant and the final instant, and / or

[0048] - the difference between said greatest value of said displacement speed and the smallest value of said displacement speed of said slowed tooth model between the initial instant and the final instant, and / or

[0049] - the variation of said speed of movement of said slowed tooth model, on average between the initial instant and the final instant;

[0050] - the first smoothed deformation scenario is determined so that the greatest value of said displacement speed between the initial instant and the final instant is less than the greatest value of said displacement speed between the initial instant and the final instant in the basic deformation scenario determined in step b);

[0051] - the method comprises, after said first step d), one or more successive additional steps d), each additional step d comprising the determination, by the computer, of an additional smoothed deformation scenario in which

[0052] - the limiting tooth model follows the path defined by the basic deformation scenario determined in step b), and

[0053] - the slowed-down tooth model(s) from step(s) d) prior to said additional step d) follow the path(s) defined by said smoothed deformation scenario(s) determined in said prior step d) or steps d), respectively, the additional smoothed deformation scenario being determined to reduce or optimize, preferably minimize said at least one speed parameter for at least one “additional” slowed-down tooth model different from the slowed-down tooth model(s) from step(s) d) prior, respectively, between the initial time and the final time, the orthodontic treatment plan thus modified being called “additional smoothed orthodontic treatment plan”;- the tooth model slowed down in the first step d) or in an additional step d) is chosen based on a criterion of usefulness for the dental practitioner and / or the user, preferably based on the risk that the application of the basic deformation scenario or the smoothed orthodontic treatment plan of the previous step d) represents for the user's health, respectively;

[0054] - the utility criterion defines a utility to limit a risk to the user's health and / or to meet the user's requirements;

[0055] - the tooth model slowed down during the first step d) or during an additional step d) is chosen according to the risk that the application of a high movement speed represents for the user's health, and in particular the application of a movement speed corresponding to the highest physiologically acceptable movement speed for the slowed down tooth that it models;

[0056] - the closer an additional step d) is to step c), the higher the said risk, that is to say that the computer proceeds as a priority to smoothing the movement speeds of the models of the teeth for which a rapid movement induces the highest risk;

[0057] - preferably, the method comprises a step d) for each tooth model, except the limiting tooth model;

[0058] - the method comprises, after step c) and, optionally after step d) or the additional step(s) d), the following step e): e) design and manufacture of at least one orthodontic appliance based on the basic orthodontic treatment plan obtained at the end of step c) or based on the smoothed orthodontic treatment plan obtained at the end of step d) or a cycle of steps d);

[0059] - said orthodontic appliance is an orthodontic splint and the intermediate moments are exclusively moments at which a change of orthodontic splint is planned;

[0060] - said orthodontic appliance is an orthodontic arch and / or an auxiliary appliance and the intermediate moments are exclusively moments at which a change of orthodontic arch and / or auxiliary appliance is planned;

[0061] - said auxiliary device is chosen from a hook, a button, a cleat, an elastomeric chain, a spring, an elastic band and a mini-screw;

[0062] - said orthodontic appliance is an assembly comprising an orthodontic arch and brackets for fixing said orthodontic arch to the teeth ("brackets" in English) and the intermediate moments are exclusively moments at which a change of the arch and / or one or more brackets is planned;

[0063] - the computer presents the basic orthodontic treatment plan and / or the smoothed orthodontic treatment plan to a dental practitioner for validation.

[0064] A complete orthodontic treatment typically comprises several phases. Each phase, or “partial orthodontic treatment”, may be the subject of an orthodontic treatment plan following a method according to the invention, the initial model representing the dental arch at the start of the phase in question and the final model representing said dental arch with an arrangement of the tooth models as desired at the end of said phase.

[0065] The invention thus also relates to a method for generating a plan for a complete orthodontic treatment of a user's dental arch, the complete orthodontic treatment consisting of a succession of several partial orthodontic treatments each corresponding to a respective phase of the complete orthodontic treatment, the method comprising the following successive steps:

[0066] A') generating or retrieving a first "start of phase" model representing said dental arch at a time at the beginning of the first phase of the complete orthodontic treatment, said first model being divided into tooth models, and generating or retrieving a last "end of phase" model representing said dental arch with a desired arrangement of tooth models at the end of the last phase of the complete orthodontic treatment, i.e. the end of the complete orthodontic treatment;

[0067] B') determination, preferably by a computer or by a computer-assisted dental practitioner, for each phase, from the first phase to the penultimate phase, of a respective end-of-phase model representing said dental arch with an arrangement of the tooth models desired at the end of said phase;

[0068] C) for each phase, implementation of a method comprising steps a) to c), and preferably a step d), preferably a cycle of steps d), the initial model being the start model of said phase and the final model being the end model of said phase.

[0069] The method implemented in step C') may include one or more of the optional features described in this description. The method for smoothing the speeds of the tooth models mentioned above may be generalized.

[0070] According to a second main aspect, the invention thus relates to a method for generating a plan for a partial or complete orthodontic treatment of a user's dental arch, the method comprising the following successive steps:

[0071] A) preferably following a step a),

[0072] - generation or recovery of an “initial” model representing in three dimensions said dental arch at an initial instant, said initial model being cut into tooth models, and

[0073] - generation or recovery of a “final” model representing in three dimensions said dental arch with a “final” arrangement of the tooth models as desired at a final moment marking the end of the orthodontic treatment, partial or complete;

[0074] B) for each tooth model,

[0075] - determination of a distance measuring a difference between the configurations of the tooth model in the initial model and in the final model;

[0076] - determining the shortest possible time for the tooth model to travel said distance, i.e. determining the shortest travel time to transit from the configuration of said tooth model in the initial model to the configuration of said tooth model in the final model, or “minimum travel time”;

[0077] (C) identification of the tooth model which exhibits said longest minimum travel time, or “limiting tooth model”;

[0078] D) determination of a “first smoothed deformation scenario” according to which the initial model is transformed into a final model by moving the tooth models, the first smoothed deformation scenario being determined so as to minimize, for at least one first “slowed down” tooth model different from the limiting tooth model, a speed parameter chosen from:

[0079] - the greatest value of a displacement speed of said slowed tooth model reached between the initial instant and the final instant, and / or

[0080] - a speed representative of the speed of movement of said slowed tooth model, preferably an average speed between the initial instant and the final instant, and / or

[0081] - the difference between said greatest value of said displacement speed and the smallest value of said displacement speed of said slowed tooth model between the initial instant and the final instant, and / or - the variation of said displacement speed of said slowed tooth model, on average between the initial instant and the final instant.

[0082] Preferably, one determines, preferably the computer determines intermediate instants, preferably marking instants at which orthodontic splint changes are planned, the first smoothed deformation scenario and said intermediate instants defining a first smoothed orthodontic treatment plan.

[0083] The generation of the final model can be carried out, from the initial model, by a dental practitioner using a computer adapted to the manipulation of tooth models.

[0084] In one embodiment, determining the distance measuring a difference between the tooth model configurations in the initial model and in the final model is performed without having to have previously determined the tooth arrangements between the initial and final models, for example by comparing the initial and final models.

[0085] Preferably, however, in step B), a "basic deformation scenario" of said arch is determined, preferably a computer determines, the basic deformation scenario comprising a succession of intermediate models modeling said arch in three dimensions at intermediate times between the initial time and the final time, the determination of said distance being based on said basic deformation scenario, the distance being for example the distance traveled by one or more points of the tooth model following the basic deformation scenario; then in step C), the limiting tooth model is determined, preferably a computer determines, as the tooth model having, following the basic deformation scenario, the last one reaching its configuration in the final model.

[0086] The basic deformation scenario and the intermediate moments form a “basic orthodontic treatment plan”.

[0087] Smoothing can be performed without necessarily having to define a base deformation scenario, but the prior generation of a base deformation scenario considerably improves the reliability or "predictability" of the orthodontic treatment plan, i.e., increases the probability that the teeth will move according to the orthodontic treatment plan. In one embodiment, to determine the base deformation scenario, the computer

[0088] - determines a set of successive elementary deformations transforming, by displacement of the tooth models, the initial model into a final model, said elementary deformations each respecting a respective set of constraints,

[0089] - determines, for each tooth model, said distance as a function of said set of elementary deformations, said distance preferably being the cumulative total of the elementary distances traveled by a point or a plurality of points of the tooth model during the elementary deformations.

[0090] The basic deformation scenario and / or the movement speeds of the tooth models can be determined by a dental practitioner using a computer suitable for handling tooth models, for example using the Treat software described at https: / / en.wikipedia.Org / wiki / Clear_aligners#cite_note-invisalignsystem-10.

[0091] The basic deformation scenario can alternatively be determined following step b).

[0092] Travel speeds can be calculated from

[0093] - distances measured by comparing the initial and final models and / or distances determined from the basic deformation scenario, preferably determined following step b), and

[0094] - time intervals determined from the treatment duration, preferably determined according to step c).

[0095] The first smoothed deformation scenario preferably results from a modification of a basic deformation scenario. Such a method can be advantageously used to smooth a conventionally defined basic orthodontic treatment plan, in particular for orthodontic treatment with a set of orthodontic aligners. Indeed, such a plan is conventionally defined manually by the dental practitioner, using a computer, by manipulating the tooth models from an initial model to the final model.

[0096] The dental practitioner may also use software, for example Treat, capable of providing the transition models and the intermediate models. The dental practitioner may then modify these models, the software recalculating the intermediate moments accordingly. The smoothing may alternatively relate to a basic deformation scenario determined by a computer, autonomously, as described according to the first main aspect of the invention.

[0097] Smoothing can be done by the computer, independently.

[0098] Preferably, the first slowed tooth is, among all the teeth modeled in the initial model and excluding the limiting tooth modeled by the limiting tooth model, the tooth in the arch that would be most useful to slow down, according to a utility criterion defined by the dental practitioner and / or the user and with regard to the basic orthodontic treatment plan.

[0099] The first tooth slowed down may be the tooth whose movement speed is most critical to the user's health

[0100] The first slowed tooth may be, for example, the tooth whose movement speed, following the basic orthodontic treatment plan, reaches a value closest to a predetermined "acceptable" value, in particular a value beyond which an unacceptable risk arises for the user's health.

[0101] Preferably, a method according to the second main aspect of the invention also has one or more of the following optional features:

[0102] - the intermediate times, preferably determined by the computer, are times at which a check of the arch by a dental practitioner and / or a modification of an orthodontic appliance and / or a manufacture of an orthodontic appliance is / are planned, preferably times at which a change of orthodontic splint is planned;

[0103] - the first slowed tooth is, among all the teeth modeled in the initial model and excluding the limiting tooth modeled by the limiting tooth model, the tooth in the arch whose speed of movement is the most critical for the health of the user, for example the tooth whose rapid movement generates the highest risk for the user;

[0104] - the method comprises, after determining the first smoothed deformation scenario, determining, preferably by a computer, a second smoothed deformation scenario reducing, preferably minimizing the speed parameter for a second slowed-down tooth model, modeling a second slowed-down tooth, different from the limiting tooth model and the first slowed-down tooth model, preferably reducing, preferably minimizing the greatest value of the displacement speed reached between the initial instant and the final instant by said second slowed-down tooth model, with the constraint that the limiting tooth model and the first slowed-down tooth model follow the paths defined by the first smoothed deformation scenario;

[0105] - preferably, the second slowed-down tooth is, among all the teeth modeled in the initial model and excluding the limiting tooth and the first slowed-down tooth, the tooth in the arch that would be most useful to slow down, according to said utility criterion defined by the dental practitioner and / or the user and with regard to the first smoothed orthodontic treatment plan, preferably the tooth that leads to the lowest risk for the health of the user, said utility criterion preferably being identical to the utility criterion used to choose the first slowed-down tooth;

[0106] - the second slowed tooth is the tooth whose movement speed, following the first smoothed orthodontic treatment plan, reaches a value closest to a value

[0107] predetermined “acceptable”, and in particular of a value critical to the health of the user;

[0108] - the first smoothed deformation scenario, and optionally the second smoothed deformation scenario, is / are determined in such a way as to respect:

[0109] - anatomical constraints preferably imposing an absence of penetration of a tooth model into an adjacent tooth model, and / or that the positions of one or more points of a tooth model are contained in an envelope defined around the tooth model, and / or that the translational speed of a tooth model in one direction and in one sense is lower than an upper limit for a translational speed, and / or that the rotational speed of a tooth model around an axis and in one direction is lower than an upper limit for a rotational speed; and / or

[0110] - clinical constraints imposed by the rules of orthodontics and / or the dental practitioner, preferably imposing immobility of one or more tooth models, and / or imposing technical constraints to be respected to move a tooth model, and / or favoring movements relative to others, and / or imposing an order for moving the tooth models, and / or imposing a correct occlusion, and / or authorizing or prohibiting filing of the teeth, i.e. authorizing or prohibiting penetration of a tooth model into an adjacent tooth model, and / or authorizing limited filing of the teeth, i.e. limiting the degree of penetration of a tooth model into an adjacent tooth model, and / or authorizing or prohibiting extraction of one or more teeth, and / or imposing a speed of movement of one or more teeth; and / or

[0111] - prescription constraints imposed by the user due, for example, to a need for orthodontic treatment generating limited pain and / or having a limited duration and / or having a limited cost, and / or having a limited aesthetic impact and / or having minimal reliability, and / or involving a limited duration for wearing an orthodontic appliance, in particular a maximum duration for wearing an orthodontic splint or an appliance with arch and brackets, and / or having a limited number of steps, and in particular limiting the number of orthodontic splints necessary for the orthodontic treatment associated with the first smoothed deformation scenario, or optionally with the second smoothed deformation scenario, and / or having a predetermined number of steps, and / or authorizing or prohibiting filing of the teeth, and / or authorizing limited filing of the teeth, and / or authorizing or prohibiting extraction of one or more teeth,and / or authorizing or prohibiting the use of one or more auxiliary orthodontic appliances.,

[0112] Generally, the method preferably comprises determining, preferably by a computer, successively for each of the tooth models considered as a “slowed-down tooth model”, except for the limiting tooth model, a smoothed deformation scenario (first smoothed deformation scenario for the first slowed-down tooth, second smoothed deformation scenario for the second slowed-down tooth, etc.), with each time the constraint that the limiting tooth model and the slowed-down tooth models following the previously defined smoothed deformation scenarios follow the paths defined by said previous smoothed deformation scenarios.

[0113] According to a third main aspect, the invention relates to a method for entering information into a computer, in particular in the context of a method for generating a plan for an orthodontic treatment of a dental arch, preferably according to the first or second main aspect of the invention, preferably at least for entering prescription constraints, said input method comprising the following steps: 01) a first user enters a first piece of information into the computer, for example in a first input field of a first form page displayed on a first screen of the computer;

[0114] 02) the computer analyzes said first information, then prepares and displays, on a second screen of the computer, a second form page comprising a second input field presenting a request to a second user to enter a second piece of information, the display or not of the second input field and / or the nature of the second piece of information accepted by the second input field depending on the first piece of information entered by the first user in the previous step;

[0115] 03) the second user enters the second information on the computer using the second input field,

[0116] 04) preferably, the computer uses the second information and preferably the first information to define an orthodontic treatment plan and / or to monitor the proper progress of an orthodontic treatment.

[0117] The second form page, used for entering the second information, can be a new page or result from an adaptation of the first page used in step 01) to enter the first information.

[0118] According to the invention, it belongs to a dynamic form.

[0119] As will be seen in more detail later in the description, a dynamic form comprising one or more said pages advantageously allows for much more efficient data entry than data entry with a static form. It avoids laborious reading of data entry pages unsuitable for the second user. A dynamic form therefore speeds up data entry by the second user. By facilitating understanding of the situation, it also limits the risk of incorrect data entry.

[0120] A dynamic form closely guides the entry, which advantageously allows entry without assistance, and in particular without the dental practitioner. Entry can notably be carried out remotely from the dental practitioner, and in particular with the mobile phone of the first and / or second user. For example, if several photos must be acquired under different acquisition conditions, the form can request the entry of the first photo and only request the entry of the second photo after analyzing the first photo and validating it.

[0121] The dynamic form is particularly useful when the computer is integrated into a mobile phone. It limits the exchange of information with the mobile phone.

[0122] The second form page may be from a refresh of the first form page, or it may be a new form page, especially when the first form page does not belong to the same form as the second form page, for example when the first form page was displayed more than 1 hour before the second form page.

[0123] The first user may be identical to the second user, and in particular may be an individual for whom orthodontic treatment is in progress or is to be planned. The first and second screens are then preferably identical. They may be, for example, the screen of the user's mobile phone.

[0124] The first user may be different from the second user. In particular, the first user may be a dental practitioner and the second user may be an individual for whom orthodontic treatment is in progress or is to be planned. The first and second screens are then preferably different. They may be, for example, the screen of a PC at the dental practitioner's home and the screen of the user's mobile phone, respectively. This embodiment advantageously allows the first user to enter "professional" information, which the second user is unable to determine alone. For example, a dental practitioner may analyze the dental situation of the individual, for example by analyzing photos of the individual's mouth that the latter has sent to him with his phone, and enter data characterizing this dental situation.The individual then has access to a form specifically adapted to their dental situation. More generally, this embodiment allows each user to enter information that the other user does not know, the input interface for one user depending on the entries made by the other user.

[0125] Preferably, a method according to the third main aspect of the invention further has one or more of the following optional features:

[0126] - the second input field only accepts a second piece of information if it meets a criterion, for example if it belongs to a predefined range or a predefined list, said criterion depending on the first piece of information;

[0127] - the format of the second input field depends on the first information;

[0128] - the first information includes at least one photo, preferably at least one photo with the mouth closed and at least one photo and / or at least one panoramic and / or cephalometric X-ray, with the mouth open, preferably at least one photo with the mouth closed, at least one photo with the mouth open, at least one photo with the front view, at least one photo with the right view and at least one photo with the left view, the right and the left being relative to the first user;

[0129] - the computer analyses said photo or photos and, depending on the result of said analysis, displays or not the second input field and / or determines the nature of the second information accepted by the second input field;

[0130] - as soon as the first user has entered the first information, the computer analyses the said first information and adapts the displayed page accordingly;

[0131] - the entry of the first information precedes the display of the second form page by less than 10 minutes;

[0132] - the first information and / or the second information are a prescription imposed by the first and / or second user expressing a need for an orthodontic treatment to be planned to generate limited pain and / or have a limited duration and / or have a limited cost, and / or have a limited aesthetic impact and / or have minimal reliability, and / or involve a duration for wearing a limited orthodontic appliance, and / or achieve a predetermined functional, orthodontic or therapeutic objective, in particular to define constraints for a generation of an orthodontic treatment plan according to the first and / or second main aspects of the invention.

[0133] Preferably, only input fields for which input is required are displayed. That is, if input is not always required, the computer queries the first user to determine whether the corresponding input field should be displayed.

[0134] For example, if the possibility of receiving anesthesia depends on the medical history of the second user, before displaying a second input field for the second user to enter their agreement or disagreement with anesthesia, the computer may display input fields for the first user to specify whether the second user has already had reactions to anesthesia, and only if the answer is negative, display a second input field for the second user to enter their agreement or disagreement with anesthesia.

[0135] In addition to one or more input fields, a form page typically includes navigation buttons to display the previous or next page of the form, or to exit the form. The first information and / or the second information may be of any nature, and in particular may be photos of said dental arch, X-ray images of said dental arch, data on planned or ongoing orthodontic treatment, models of said dental arch or views of models of said dental arch, or clinical prescriptions.

[0136] The first information and / or the second information may include information about the first and / or second user, for example data about the age or gender of the first user.

[0137] Preferably, it (they) comprises (they) photos, preferably extraoral, of at least one arch of the first user, preferably in the form of a film. Preferably, the photos comprise at least one open mouth photo, and at least one open mouth photo. Preferably, the photos comprise at least one front view photo, one right view photo and one left view photo, the right and left being relative to the user.

[0138] Preferably, the first information and / or the second information includes a clinical prescription defining a number of teeth to be moved and the number of teeth to be moved and / or kept immobile.

[0139] Preferably, the first information and / or the second information comprises a definition of treatment objectives and / or a definition of a maximum number of orthodontic aligners for an orthodontic treatment to be planned.

[0140] The computer preferably includes a memory defining a set of conditional rules determining the second input field, directly or indirectly based on the first information.

[0141] A conditional rule determining the second input field for the second information directly based on the first information is, for example, "if the first user entered an age less than 12 years, display the second input field asking if the first user has lost their baby teeth."

[0142] Conditional rules that determine the second input field indirectly based on the first information are, for example, "if analysis of a photo of the first user's dental arch reveals the presence of tartar, display the second input field asking for the date on which the first user underwent scaling." The photo constituting the first information needs to be analyzed in order to determine the presence of tartar. The second input field is only displayed if the analysis leads to the detection of tartar.

[0143] Preferably, the conditional rules also determine the presentation of the second input field, and more generally of the objects on the page containing the second input field. For example, the presentation may be different depending on the age of the first user.

[0144] Conditional rules can be ordered in the form of a decision tree.

[0145] In one embodiment, the method comprises, for each first information item of a set of first information items, a cycle of steps 01) to 03), said set of first information items preferably comprising more than 10, more than 50, more than 100 and / or less than 1000 first information items, the display or not of the input field of a step 02) of a said cycle and / or the nature of the second information item accepted by the input field of a step 02) of a said cycle depending not only on the first information item entered by the user in step 01) of said cycle, but also on at least one first information item and / or at least one second information item entered during one or more previous cycles.

[0146] The method preferably comprises a single step 04).

[0147] The shape of the second input field is not limited.

[0148] To the extent that a feature according to one aspect of the invention is technically compatible with another main aspect of the invention, it can be applied to that other aspect of the invention.

[0149] In particular, the smoothing-related features described according to the first main aspect of the invention are potentially applicable to the second main aspect, and vice versa. In particular, certain terms, such as "baseline deformation scenario" or "first smoothed deformation scenario" are used in the description of the two main aspects because they refer to similar objects, and possibly to the same objects when the two main aspects apply. For these objects in particular, the features according to the first main aspect of the invention are potentially applicable to the second main aspect, and vice versa. The invention also relates to:

[0150] - a computer program comprising program code instructions for execution

[0151] - steps b) and c), preferably steps a), b) and c), and optionally the first step d) and preferably additional steps d), and preferably an operation of designing an orthodontic appliance for a step e) and / or

[0152] - of a step C') and preferably of a step A') or B'), preferably of a step A') and of a step B') and of a step C'), and / or

[0153] - of a step 02), that is to say for the display of a dynamic form according to the invention, and preferably of an entry of the first information, and / or

[0154] - steps B), C) and D), and preferably A), when said program is executed by said computer;

[0155] - a computer medium on which such a program is recorded, for example a memory or a CD-ROM, and

[0156] - a computer in which such a program is loaded,

[0157] - an assembly comprising a said computer and a device for manufacturing an orthodontic appliance for implementing a step e).

[0158] Preferably, the computer program includes program code instructions to automate all operations that can be automated.

[0159] Preferably, the computer program further comprises program code instructions for slicing the initial model into tooth models and / or determining the final model from the initial model.

[0160] The invention also relates to a system comprising

[0161] - a three-dimensional scanner capable of producing a “raw” model of the first user’s arch, and

[0162] - a computer according to the invention, preferably optionally configured to transform said raw model into an initial model, optionally with the assistance of a dental practitioner.

[0163] Definitions

[0164] The term "user" means any person for whom a method according to the invention is implemented, whether or not that person is ill. The term "dental practitioner" means any dental practitioner in the broad sense, which includes in particular orthodontists and dentists.

[0165] A "complete orthodontic treatment" is a treatment intended to correct the arrangement of the teeth in a dental arch to a final position desired by the user. An orthodontic treatment that is part of a complete orthodontic treatment is called "partial". Without further specification, an "orthodontic treatment" generically refers to a complete or partial orthodontic treatment.

[0166] Orthodontic treatment requires the use of one or more orthodontic appliances. Retention treatment intended to keep teeth in a permanent position is not considered orthodontic treatment here.

[0167] Orthodontic treatment is planned with a "treatment plan". A distinction is made between "orthodontic treatment", which refers to a series of operations that take place in reality, and the "treatment plan", which is the result of the design of the orthodontic treatment. The treatment plan therefore predates the corresponding orthodontic treatment.

[0168] Orthodontic treatment using orthodontic aligners is the implementation of a treatment plan that defines models for the dental arch in anticipated shapes, before orthodontic treatment, for different times during orthodontic treatment. The generation of a treatment plan typically includes the design of one or more orthodontic aligners and their modeling. An example of aligner design is described in "History of Orthodontics" by Basavaraj Subhashchandra Phulari. The treatment plan thus defines models for the implemented orthodontic aligners, these models being used to manufacture the corresponding orthodontic aligners. The modeling of orthodontic aligners can be done automatically, by computer, or manually, typically by a dental practitioner.

[0169] More precisely, a series of models of the user's arch are conventionally determined, which represent consecutive arch configurations, and a series of corresponding orthodontic aligner models, making it possible to manufacture orthodontic aligners adapted for each one, modifying the configuration of the arch from a configuration represented by an arch model to the configuration represented by the following arch model. Each treatment plan therefore "corresponds" to an orthodontic treatment, models of the arch at the beginning and end of the associated orthodontic treatment, and, if the orthodontic treatment is implemented, one or more orthodontic aligners designed to achieve a configuration of the dental arch conforming to the model of the dental arch at the end of the orthodontic treatment.

[0170] An example of software for manipulating tooth models and creating a treatment plan is the Treat program, described at https: / / en.wikipedia.org / wiki / Clear_aligners#cite_note-invisalignsystem-lO. US5975893A also describes the creation of a treatment plan.

[0171] An "orthodontic appliance" is a device adapted for the implementation of orthodontic treatment. An orthodontic appliance can be intended for therapeutic or prophylactic treatment, but also for aesthetic treatment.

[0172] An orthodontic appliance may be, in particular, an arch and bracket appliance, or an orthodontic splint, or an auxiliary appliance of the Carrière Motion type. The configuration of an orthodontic appliance may be determined in particular to ensure its attachment to the teeth, but also according to a desired position for the teeth. More precisely, the shape is determined so that, in the service position, the orthodontic appliance exerts constraints tending to move the treated teeth towards their desired position.

[0173] A 3D scanner, or "scanner," is a device used to obtain a model of a dental arch.

[0174] The "service position" is the position of an orthodontic appliance, for example an orthodontic splint, when it has been fixed to the arch in order to treat this arch. Conventionally, the fixation of an orthodontic splint can be deactivated by the user, by simply pulling on the splint.

[0175] By "computer" is meant a computer processing unit, which includes a set of several machines, having computer processing capabilities. This unit can be integrated in particular in a scanner, or in a mobile phone, or be a PC type computer or a server, for example a server remote from the user, for example being the "cloud" or a computer placed at a dental practitioner's home. Conventionally, a computer comprises in particular a processor, a memory, a human-machine interface conventionally comprising a screen, a communication module via the internet, via WIFI, via Bluetooth® or via the telephone network. A computer program configured to implement, at least partially, a method of the invention is loaded into the computer's memory. The computer can also be connected to a printer.

[0176] In a method according to the invention, different computers communicating with each other can be implemented for different steps, or, preferably, the same computer is implemented for all steps. The computer is preferably integrated into a mobile phone.

[0177] A "computer form" means a set of pages, i.e. consisting of one or more pages, which are displayed on a computer screen and which allow the user to enter information.

[0178] A form is "dynamic" when it adapts based on previously acquired user information, on the displayed page or on previously displayed pages, for example by means of the dynamic form. It is therefore not predefined like a static questionnaire which requests the same information, in the same way, regardless of the information previously entered, in particular by the user.

[0179] An "input field" is an area on a form page used for the user to enter information into the computer. An input field can be, for example:

[0180] - a multiple-choice question, for example with check boxes;

[0181] - an input area for text or a number;

[0182] - a cursor to move;

[0183] - a button to click;

[0184] - an ordered set of buttons and / or check boxes and / or items to be selected, for example of the “dental map” type, or “teeth map”, as shown in Figure 8.

[0185] The adjectives "first" and "second" are used to distinguish the input fields on the first and second form pages. The first and second input fields can be different or the same, for example, if the first entry only changes the appearance of the first entry field.

[0186] A "model" is a digital three-dimensional model. A model is made up of a set of voxels, or "points." A model can be, for example, .stl or .obj, .DXF 3D, IGES, STEP, VDA, or Point Clouds. Advantageously, such a model, called "3D," can be viewed from any angle.

[0187] An "arch model" is a three-dimensional digital model that represents a user's arrangement of teeth. Preferably, the arch model also represents other organs of the mouth, and in particular the gums.

[0188] The number of points in an arch model is not limited. In one embodiment, an arch model, and in particular a final model, only includes the points strictly necessary for defining the arrangement of the teeth.

[0189] A "tooth model" is a three-dimensional digital model of a tooth in a user's arch. A model of an arch can be sliced ​​so as to define tooth models for at least some of the teeth, preferably for all the teeth represented in the arch model. The tooth models are therefore models within the arch model. Figure 3 shows an example view of an arch model sliced ​​into tooth models 32, with only the tooth models being represented. Computer tools exist for manipulating the tooth models of an arch model. These tools make it possible to impose constraints, in particular to limit the movements of the tooth models to realistic movements, for example to prevent adjacent tooth models from interpenetrating.

[0190] The number of points in a tooth model is not limited. In one embodiment, a tooth model only includes the points strictly necessary to define its configuration. In one embodiment, it includes points that may collide with other tooth models.

[0191] A point in a tooth model of the initial model is "in correspondence" with a point in a tooth model of the final model (or of a transition model) if the deformation scenario modifies the position of the point in the tooth model of the initial model so that it substantially coincides with that of the point in the tooth model of the final model at the final time (or of the transition model at the transition time). According to the international convention of the Fédération Dentaire Internationale, each tooth in a dental arch, and therefore each tooth model, has a predetermined "tooth number". The tooth numbers defined by this convention are recalled in Figure 4.

[0192] A "notable point" is a point on an arch or tooth model that can be identified, for example, the apex of the tooth or at the tip of a cusp, a point of interdental contact, that is, of a tooth with an adjacent tooth, for example, a point mesial or distal to the incisal edge of a tooth, or a point at the center of the tooth's crown, or "barycenter."

[0193] "Slicing" an arch model into "tooth models" is an operation that allows the representations of teeth (tooth models) in the arch model to be delimited and made autonomous. There are computer tools for manipulating the tooth models of an arch model. An example of software for manipulating tooth models is the Treat program, described on the page https: / / en.wikipedia.org / wiki / Clear_aligners#cite_note-invisalignsystem-10.

[0194] When an arch model is cut into tooth models, it is also possible to cut other models, for example a gum model.

[0195] A "reference frame" serves as a basis for locating points in space, in particular for measuring a distance or for measuring an orientation or position, for example of a tooth model. A reference frame may be, for example, a three-dimensional reference frame, for example orthonormal. To determine an arrangement of the teeth of an arch model or a configuration of a tooth in the arch, a reference frame fixed relative to the arch model is used. The reference frame may, for example, have its origin in the center of the user's oral cavity.

[0196] The "configuration" of a tooth or tooth model refers to its position and orientation in the frame of reference.

[0197] A "deformation scenario" is a set of transition models ordered chronologically. It is therefore the succession of transition models. It can be considered as a kind of 3D movie showing how the arch model deforms in the space between the initial model and the final model. The "fragmentation" of a deformation scenario consists of defining the intermediate moments, that is to say, specifying the moments at which, when the deformation scenario will take place, a control of the dental arch by a dental practitioner and / or a modification of an orthodontic appliance, in particular a change of orthodontic splint for orthodontic treatment with orthodontic splints, and / or a fabrication of an orthodontic appliance will have to be carried out.

[0198] An “orthodontic treatment plan” includes a deformation scenario and the intermediate moments defined for this deformation scenario.

[0199] A "stage" is a period of the orthodontic treatment plan defined between the initial time and the first intermediate time, between two consecutive intermediate times or between the last intermediate time and the final time.

[0200] A phase can typically include between 2 and 150 steps. For example, to correct a drift after orthodontic treatment to correct a malocclusion, or "relapse," 2 or 3 orthodontic aligners may be sufficient. A complex malocclusion correction phase may require several dozen orthodontic aligners.

[0201] The "path" of a tooth model following a deformation scenario is the set of successive representations of the tooth model in the transition models of the deformation scenario. It can be considered as a kind of 3D movie showing how the tooth model moves in space, in translation and / or in rotation, between the initial instant and the final instant. The determination of a deformation scenario by displacement of the tooth models thus involves the search for a set of paths for the models of the teeth of the arch.

[0202] The "kinetic capabilities" of a tooth model define the greatest physiologically acceptable values ​​for the movement speeds of that tooth model.

[0203] A physiologically acceptable maximum speed for a tooth model is therefore a speed beyond which a risk to the user's health appears, for example a risk of tooth loosening. It depends on the nature of the tooth, or the tooth number. For example, an incisor accepts higher movement speeds than a molar. A physiologically acceptable maximum speed for a tooth model can be defined according to the number of the tooth modeled, in particular on the basis of statistical data. It can also depend on the user, for example to take into account the presence of retainers.

[0204] A physiologically acceptable greatest value for a speed also depends on the type of movement considered, rotation or translation, and the direction of the movement considered, for example egression or ingression. Preferably, physiologically acceptable greatest values ​​are therefore defined for several movement speeds.

[0205] The "movement speeds" of a tooth model include a translational speed, for example the modulus of the velocity vector, and a rotational speed.

[0206] To account for the different behavior of a tooth depending on the type of movement, the movement speeds can include:

[0207] - the translation speeds along the different axes of a fixed reference frame relative to the arch model, of a point linked to the tooth model, preferably the barycenter of the tooth model, and

[0208] - the rotational speeds of the tooth model around each of said axes.

[0209] To take into account the different behavior of a tooth depending on the direction of movement, the displacement speeds can also include said translational and rotational speeds, distinguishing the direction of the speed each time, for example to distinguish egression and ingression.

[0210] A movement speed of a tooth model corresponds to an anticipated movement speed for the modeled tooth, following an orthodontic treatment plan.

[0211] We "smooth" a deformation scenario when we reduce, preferably minimize a speed parameter, preferably chosen from:

[0212] - the greatest value of a displacement speed of said slowed tooth model reached between the initial instant and the final instant, and / or

[0213] - a speed representative of the speed of movement of said slowed tooth model, preferably an average speed between the initial instant and the final instant, and / or

[0214] - the difference between said greatest value of said displacement speed and the smallest value of said displacement speed of said slowed tooth model between the initial instant and the final instant, and / or - the variation of said displacement speed of said slowed tooth model, on average between the initial instant and the final instant.

[0215] A "representative speed" of a tooth model is a speed determined from one or more speeds of movement of said tooth model, for example the modulus of the translational speed vector of the barycenter of the tooth model, or of the rotational speed vector of a notable point on the surface of the tooth model.

[0216] A "representative distance" of a tooth model's displacement is a distance calculated from the displacement of one or more points on the tooth model and / or one or more points related to the tooth model, such as its centroid. The length of the path traveled by the centroid of a tooth model following a deformation scenario is an example of a representative distance. The Euclidean distance between the position of the centroid of a tooth model in the final model and in the initial model is another example of a representative distance.

[0217] A "correct occlusion" is an arrangement of the teeth in both dental arches that allows for acceptable contact between the two arches according to the rules of orthodontics. In particular, with a correct occlusion, the cusps of the teeth in the upper arch are not in contact with the cusps of the teeth in the lower arch when the mouth is closed. The teeth in the two arches "fit together," with the cusps of the teeth in one arch penetrating the grooves or interdental spaces of the teeth in the other arch.

[0218] An "image" means a two-dimensional image, such as a photograph or a frame from a film. An image is made up of pixels.

[0219] By "image of an arch", "view of an arch", "representation of an arch", "scan of an arch", or "model of an arch" is meant an image, a view, a representation, a scan or a model of all or part of said dental arch, preferably representing at least 2, preferably at least 3, preferably at least 4 teeth. Figure 2 shows an example of a view of an arch model comprising 5000 points.

[0220] Metaheuristic methods are known optimization methods. They are preferably chosen from the group formed by

[0221] - evolutionary algorithms, preferably chosen from evolutionary strategies, genetic algorithms, differential evolution algorithms, distribution estimation algorithms, artificial immune systems, Shuffled Complex Evolution path recomposition, simulated annealing, ant colony algorithms, particle swarm optimization algorithms, taboo search, and the GRASP method;

[0222] - the kangaroo algorithm, the Fletcher and Powell method, the noise method, stochastic tunneling, random restart hill climbing, the cross-entropy method, and

[0223] - hybrid methods between the metaheuristic methods cited above.

[0224] A “statistical processing” is a processing which, when applied to a set of so-called “historical” data, makes it possible to determine characteristics specific to this set, for example an average, a standard deviation, or a median value. Statistical processing tools are well known to those skilled in the art.

[0225] "Deep learning devices," known as "deep learning" algorithms, are also well known to those skilled in the art. They include "neural networks" or "artificial neural networks."

[0226] A person skilled in the art knows how to choose and train a neural network according to the task to be performed. In particular, a neural network can be chosen from:

[0227] - les réseaux spécialisés dans la classification d’images, appelés « CNN » (« Convolutional neural network »), par exemple AlexNet (2012), ZF Net (2013), VGG Net (2014), GoogleNet (2015), Microsoft ResNet (2015), Caffe : BAIR Reference CaffeNet, BAIR AlexNet, Torch :VGG_CNN_S, VGG_CNN_M, VGG_CNN_M_2048, VGG_CNN_M_1024, VGG_CNN_M_128, VGG_CNN_F, VGG ILSVRC-2014 16-layer, VGG ILSVRC-2014 19-layer, Network-in-Network (Imagenet & CIFAR-10), Google : Inception (V3, V4),

[0228] - networks specialized in localizing and detecting objects in an image, called “Object Detection Networks”, for example R-CNN (2013), SSD (Single Shot MultiBox Detector: Object Detection network), Faster R-CNN (Faster Region-based Convolutional Network method: Object Detection network), Faster R-CNN (2015), SSD (2015), RCF (Richer Convolutional Features for Edge Detection) (2017), SPP-Net, 2014, OverFeat (Sermanet et al.), 2013, GoogleNet (Szegedy et al.), 2015, VGGNet (Simonyan and Zisserman), 2014, R-CNN (Girshick et al.), 2014, Fast R-CNN (Girshick et al.), 2015, ResNet (He et al.), 2016, Faster R-CNN (Ren et al.), 2016, FPN (Lin et al.), 2016, YOLO (Redmon et al.), 2016, SSD (Liu et al.), 2016, ResNet v2 (He et al.), 2016, R-FCN (Dai et al.), 2016, ResNeXt (Lin et al.), 2017, DenseNet (Huang et al.), 2017, DPN (Chen et al.), 2017, YQL09000 (Redmon and Farhadi), 2017, Hourglass (Newell et al.), 2016, MobileNet (Howard et al.), 2017, DCN (Dai et al.), 2017, RetinaNet (Lin et al.), 2017, Mask R-CNN (He et al.), 2017, RefineDet (Zhang et al.), 2018, Cascade RCNN (Cai et al.), 2018, NASNet (Zoph et al.), 2019, CornerNet (Law and Deng), 2018, FSAF (Zhu et al.), 2019, SENet (Hu et al.), 2018, ExtremeNet (Zhou et al.), 2019, NAS-FPN (Ghiasi et al.), 2019, Detnas (Chen et al.), 2019, FCOS (Tian et al.), 2019, CenterNet (Duan et al.), 2019, EfficientNet (Tan and Le), 2019, AlexNet (Krizhevsky and al.), 2012.

[0229] - networks specialized in image generation, for example Cycle-Consistent Adversarial Networks (2017), Augmented CycleGAN (2018), Deep Photo Style Transfer (2017), FastPhotoStyle (2018), pix2pix (2017), Style-Based Generator Architecture for GANs (2018), SRGAN (2018).

[0230] The above list is not exhaustive.

[0231] Training a neural network involves confronting it with a learning base containing information on the two types of object that the neural network must learn to "match", that is, to connect one to the other.

[0232] Training can be done from a learning base made up of recordings each comprising a first object of the first type and a corresponding second object of the second type.

[0233] Alternatively, training can be done from a learning base consisting of records each containing either a first object of the first type or a second object of the second type, each record however containing information relating to the type of object it contains. Such training techniques are for example described in the article by Zhu, Jun-Yan, et al. “Unpaired image-to-image translation using cycle-consistent adversarial networks.”

[0234] Training the neural network with these recordings teaches it to provide, from any object of the first type, a corresponding object of the second type.

[0235] The quality of the analysis performed by the neural network depends directly on the number of records in the training base. Preferably, the training base has more than 10,000 records and / or less than 10,000,000 records. “Understand,” “comprise,” or “present” should be interpreted broadly, without limitation, unless otherwise indicated.

[0236] Brief description of the drawings

[0237] Other characteristics and advantages of the invention will become apparent upon reading the detailed description which follows and upon examining the attached drawing in which:

[0238] - [Fig 1] Figure 1 schematically illustrates a method according to the first main aspect of the invention;

[0239] - [Fig 2] Figure 2 represents an example of a model acquired with a portable scanner integrated into a mobile phone and comprising 5000 points;

[0240] - [Fig 3] Figure 3 represents an example of an arch model cut into tooth models, referenced 32 (only the tooth models are represented);

[0241] - [Fig 4] Figure 4 illustrates the tooth numbering used in the dental field;

[0242] - [Fig 5] Figure 5 schematically illustrates a method according to the second main aspect of the invention;

[0243] - [Fig 6] Figure 6 schematically illustrates a form page for a method according to the third main aspect of the invention;

[0244] - [Fig 7] Figure 7 schematically illustrates a method according to the third main aspect of the invention;

[0245] - [Fig 8] Figure 8 represents an example of a dental card usable in a dynamic form according to the invention.

[0246] Other details and advantages of the invention are provided in the detailed description which follows, provided for illustrative and non-limiting purposes.

[0247] Detailed description

[0248] The method according to the first and second aspects of the invention aims to generate a plan for an orthodontic treatment which extends between an initial instant and a final instant. It can plan a complete or partial orthodontic treatment, that is to say insufficient to achieve, on its own, the desired configuration for the user.

[0249] A partial orthodontic treatment corresponds to a phase of a complete orthodontic treatment, for example a distalization phase intended to separate the teeth in order to then be able to reposition them, or a phase of alignment of the barycenters of the teeth following the curve of the arch which carries them, or a phase of rotation of the teeth around their barycenters.

[0250] In one embodiment, the method is implemented multiple times, for each phase of a complex orthodontic treatment.

[0251] In step A'), the computer determines the initial model for the first phase, or "first phase start model." This model represents the dental arch before the start of complex orthodontic treatment. The computer cuts it into tooth models, as in step a).

[0252] The computer, preferably a computer-assisted dental practitioner, also determines the final model for the last phase, or "final end-of-phase model", as in step a). This model represents the dental arch as desired at the end of the complex orthodontic treatment.

[0253] In step B'), the computer or a computer-assisted dental practitioner determines, by moving the tooth models, the end-of-phase models for each phase up to the penultimate phase, the end-of-phase model of the last phase having been determined in step A').

[0254] The end-of-phase model of a phase represents a goal to be achieved at the end of that phase. The start-of-phase model of a phase is the end-of-phase model of the phase that precedes it in time.

[0255] In a preferred embodiment, the computer defines the end-of-phase models, except possibly the last one, from the first start-of-phase model and the last end-of-phase model. For this purpose, the orthodontic rules necessary to define the phases are taught beforehand.

[0256] For example, in the previous example, after determining which tooth models need to be moved, by comparing the first early-stage model and the last late-stage model, the computer can move the tooth models of the first early-stage model until they are far enough apart so that their barycenters can then be aligned along the curve of the arch, and then rotated on themselves so that the extrados of the tooth models are substantially aligned. The resulting model can be considered the first late-stage model.

[0257] From this model, the computer can then move the tooth models to align them with the curve of the arch. The resulting model can be considered the second end-of-phase model.

[0258] From this model, the computer can then rotate the tooth models to align their extrados faces. The resulting model can be considered the third end-of-phase model.

[0259] To search for end-of-phase patterns, the computer can use optimization algorithms, particularly simulated annealing.

[0260] In step C'), the computer implements, for each phase, a method according to the first and / or second aspect(s) of the invention. For each occurrence of this method, the initial model used is the start model of said phase and the final model used is the end model of said phase.

[0261] An example of a method according to the first embodiment is now described in detail. In this example, it is assumed that the orthodontic treatment to be planned comprises only one phase.

[0262] In step a), we generate the initial and final models.

[0263] Initial model

[0264] The initial model is a digital three-dimensional model representing the teeth to be moved, in their arrangement on the dental arch planned at the start of orthodontic treatment, that is to say at the initial moment.

[0265] The initial model is preferably prepared from measurements taken on the user's teeth or on a physical model of their teeth, for example a plaster model.

[0266] The initial model is then preferably made less than one month before the initial time, preferably less than 2 weeks, preferably less than one week before the initial time, so that it corresponds well to the arrangement of the teeth at the start of orthodontic treatment.

[0267] The initial model is preferably created using a professional device, for example a 3D scanner, preferably implemented by a dental practitioner, for example an orthodontist or an orthodontic laboratory. In an orthodontic practice, the user or the physical model of their teeth can be advantageously arranged in a precise position and the professional device can be refined. This results in a very accurate initial model. The initial model preferably provides information on the positioning of the teeth with an error of less than 5 / 10 mm, preferably less than 3 / 10 mm, preferably less than 1 / 10 mm.

[0268] In one embodiment, the arrangement of the teeth may have changed between the time of initial model generation and the initial time. The initial model may, for example, have been generated more than one month or more than two months before the initial time. The initial model is then updated, preferably deformed, preferably by a displacement of one or more tooth models, to correspond to the arrangement of the teeth at the initial time. In particular, the initial model may be deformed to correspond to one or more photos of the dental arch taken less than one week before the initial time.

[0269] The number of points in the initial model is preferably greater than 5,000, 10,000 or 15,000 and / or less than 100,000. It then accurately represents the teeth. However, computer manipulation of an initial model can be slowed down if the number of points is high.

[0270] In one embodiment, the initial model comprises less than 5,000 points, or even less than 1,000 points, which makes it possible to accelerate the implementation of the method. In particular, the time required to generate a deformation scenario, in particular following the first optimization algorithm described below, depends on the number of points of the initial model used to determine the first distance.

[0271] An initial model comprising less than 5000 points, or "coarse model", may in particular result from a simplification of a fine initial model, preferably acquired with a 3D scanner, for example comprising more than 10,000 or 20,000 points. The number of points in the initial model is preferably greater than 1,000 and / or less than 500,000.

[0272] In one embodiment, the simplification of an initial model results from a random selection of points on the surface of the initial model. In one embodiment, the initial model comprises all the points that are in correspondence with a point of the final model. Preferably, the initial model only comprises points that are in correspondence with a respective point of the final model. In one embodiment, the initial model does not comprise points whose position cannot be affected by the orthodontic treatment. In one embodiment, the initial model only comprises a set of points strictly sufficient to define the position and orientation in space of each tooth model. For example, it only comprises, for each tooth model, three remarkable non-aligned points.Preferably, said set of points also includes points likely to collide with adjacent tooth models, for example points of a tooth model which, in the initial model, are close to an adjacent tooth model.

[0273] A match can be established between the tooth models in the fine model and in the coarse model, which allows, if a deformation scenario has been generated with a coarse initial model and thus includes coarse transition models, to reconstruct fine, high-precision transition models, for example usable for manufacturing an orthodontic splint.

[0274] To deform an initial model, the model is cut to generate a digital three-dimensional model for each tooth, or "tooth model." The tooth models are then moved.

[0275] Preferably, the initial model is also cut to generate a digital three-dimensional model for the gingiva, or "initial gingiva model."

[0276] Final model

[0277] The final model is a digital three-dimensional model representing the user's teeth in their arrangement on the dental arch as desired at the end of orthodontic treatment, i.e. at the final, future moment. It is therefore a theoretical model.

[0278] The objective of the final model is to provide the information necessary to define the orientation and position of each tooth in the arch at the final instant. The final model may be less precise than the initial model. The position of a tooth model may indeed be defined by the position of a remarkable point of this tooth model, for example by the position of its barycenter. The orientation of a tooth model may be defined by two non-parallel vectors, whose common origin is for example the barycenter of the tooth model. Three remarkable points, for example the barycenter and two points not aligned with the barycenter of a tooth model may therefore be sufficient to define the configuration of a tooth. The final model may thus be made up of a set comprising, for each tooth model, coordinates of three remarkable points of this tooth model.Determining the position of a tooth is for example described in the article “Dense Representative Tooth Landmark / axis Detection Network on 3D”, by Guangshun Wei, Zhiming Cui, Jie Zhu, Lei Yang, Yuanfeng Zhou, Pradeep Singh, Min Gu, Wenping Wang, https: / / arxiv.org / pdf / 2111.04212v2.pdf.

[0279] The final model may result from a deformation of the initial model by moving tooth models.

[0280] It can be determined classically by a dental practitioner, by moving tooth models, for example with the Treat program, described on the page https: / / en.wikipedia.org / wiki / Clear_aligners#cite_note-invisalignsystem-10.

[0281] In a preferred embodiment, in step a), the computer analyzes the initial model and deduces a final model. No manipulation of the tooth model is then necessary to define the final model. In one embodiment, however, the dental practitioner imposes constraints, for example depending on the orthodontic treatment envisaged.

[0282] In one embodiment, a memory of the computer contains a "historical" database comprising a set of records, each record associating a historical initial model and a historical final model. The historical initial and final models may in particular be models representing tooth arrangements of historical users at the beginning and end of "historical" orthodontic treatments.

[0283] The analysis of the initial model by the computer can then consist of

[0284] - search in the database for the closest historical initial model, i.e. the one which presents the form closest to that of the initial model for which a final model is sought, then

[0285] - choose, for said final model, the historical final model associated with the closest historical initial model.

[0286] The user's dental arch is thus assimilated to the closest historical initial model and the associated historical final model is considered to be usable for the user as well.

[0287] A historical database can also be used to train one or more neural networks to provide the position and / or orientation of tooth models in the final model. For example, one can provide - as input, records each containing a tooth number and data defining a configuration of a tooth with said number for a historical user, and

[0288] - at output, records each containing a tooth number and data defining an ideal configuration of a tooth bearing said number.

[0289] In particular, we can use a network specialized in image classification among those mentioned above.

[0290] In one embodiment, the computer uses predefined rules to transform the initial model into a final model. The predefined rules may, for example, specify that, in the final model, the teeth must be aligned, specify a gap between the vertices of adjacent tooth models, or specify an orientation for each tooth.

[0291] In one embodiment, the initial model is analyzed for

[0292] - determine a curved baseline following the curvature of the arch, for example connecting the barycenters of the teeth, as well as the length of the arch, for example the length of the baseline;

[0293] - determine, on said baseline, the theoretical position and orientation of each tooth, according to predefined rules.

[0294] Algorithms for determining a baseline and tooth configuration are well known, particularly for taking panoramic tomographic images. In particular, a mean square value can be used, with a typical function in ax 4 +bx 2 +c = 0.

[0295] Predefined rules can, for example, specify, depending on the length and curvature of the arch, how the different teeth should be distributed and oriented along the said baseline.

[0296] The predefined rules can be obtained, for example, by statistical processing of historical data providing, as a function of length and curvature, said distribution and orientation of "historical" teeth of historical arches of historical users.

[0297] The computer can advantageously determine the final model very quickly, without human intervention. Algorithms for comparing the shapes of two models are well known. For example, we know the ICP or "Iterative closest point" algorithm, described in particular in the online encyclopedia Wikipedia.

[0298] In a preferred embodiment, the initial model of the arch is cut so as to generate an initial gum model, and it is checked whether the arrangement of the tooth models in the final model is compatible with the initial gum model. This check can be carried out by a dental practitioner and / or by a computer, autonomously or controlled by an operator, for example a dental practitioner. Preferably, it is checked whether the tooth models in the final model penetrate the initial gum model and / or whether a physiologically unrealistic gap has appeared between the tooth models in the final model and the initial gum model. In the case of such a penetration or gap, the initial gum model is transformed into a final gum model so as to eliminate said penetration or gap.

[0299] In step b), the computer determines a series of successive deformations of the initial model leading to a final model.

[0300] The models resulting from successive elementary deformations before reaching the final model are called "transition models". Each transition model therefore represents the arrangement of the teeth at a respective transition instant.

[0301] The number of transition models is preferably greater than 3, preferably greater than 10 and / or less than 1000. It is preferably determined in such a way that no point of the arch model moves more than 1000 pm, 500 pm or 100 pm between two consecutive transition models and / or in such a way that at least one point of the arch model moves more than 10 pm, 50 pm or 100 pm between two consecutive transition models. The accuracy of the deformation scenario is thereby improved.

[0302] Each elementary deformation must respect a set of constraints. The constraints include:

[0303] - anatomical constraints, for example to impose that, during elementary deformation, a tooth model cannot penetrate into an adjacent tooth model, and / or that the positions of one or more points of a tooth model must be contained in an envelope defined around the tooth model, and / or that the translational speed of a tooth model in one direction and in one sense must remain below an upper limit defined for a translational speed, and / or that the rotational speed of a tooth model around an axis and in one direction must remain below an upper limit defined for a rotational speed;

[0304] - preferably, clinical constraints imposed by the rules of orthodontics and / or the dental practitioner, for example imposing, during elementary deformation, immobility of one or more tooth models, for example due to a gum problem, bone density or the presence of one or more dental implants, and / or imposing technical constraints to be respected to move a tooth model, for example due to the available orthodontic appliances, and / or favoring movements relative to others, and / or imposing an order for moving the tooth models, and / or imposing a correct occlusion, and / or authorizing or prohibiting stripping of the teeth, and / or authorizing limited filing of the teeth, and / or authorizing or prohibiting extraction of one or more teeth, and / or imposing a movement of one or more teeth as homogeneous as possible,that is to say limiting as much as possible the variations in the speed of movement of one or more teeth, and / or imposing an upper limit for a speed of movement of one or more teeth, and / or imposing the presence of one or more phases and / or an order of execution of said phases;,

[0305] - preferably, prescription constraints imposed by the user due, for example, to a need for orthodontic treatment generating limited pain and / or having a limited duration and / or having a limited cost, and / or having a limited number of steps and / or having a predetermined number of steps, and / or authorizing or prohibiting filing of the teeth, and / or authorizing limited filing of the teeth, and / or authorizing or prohibiting extraction of one or more teeth, and / or authorizing or prohibiting the use of one or more auxiliary orthodontic appliances.

[0306] The set of constraints imposed on an elementary deformation may be different depending on the arch model on which the elementary deformation is applied, or "model to be deformed", namely the initial model or a transition model. For example, the possible positions and orientations for a tooth model may be limited by the presence of adjacent tooth models, the positions and orientations of which may themselves be modified at each elementary deformation. In one embodiment, the set of constraints comprises constraints which may lead to an elementary deformation not directly applicable in reality. In particular, the set of constraints may allow limited penetration of a tooth model into an adjacent tooth model. The resulting elementary deformation then requires, in order to be operational, filing of one or both teeth whose tooth models penetrate into each other.Preferably, the computer informs the dental practitioner of the need to perform such filing.

[0307] All or part of the constraints may be determined from information entered by the user, preferably by means of a dynamic form. Figure 6 illustrates an example page of such a form. Figure 7 illustrates the use of a dynamic form according to the third main aspect of the invention.

[0308] The user can in particular specify

[0309] - a maximum number of orthodontic aligners for orthodontic treatment, i.e. a maximum number of intermediate moments;

[0310] - the numbers of the teeth that must remain immobile during orthodontic treatment, in particular by clicking on the boxes bearing the numbers of these teeth.

[0311] Figure 8 shows, for example, a dental map. The user can select one or more teeth by clicking on the representation of the number of said teeth on this map.

[0312] The page shown in Figure 6 still allows the user to specify treatment objectives, which can be used by the computer to determine a model of the arch at the end of orthodontic treatment.

[0313] The determination of the elementary deformations, and therefore of the deformation scenario, is preferably carried out by means of a computer program called a “generator”, implemented by the computer.

[0314] Preferably, the initial model is cut by the computer. Cutting the initial model to determine the models of the organs it represents is a well-known operation. Preferably, the initial model is cut to define at least the parts that represent the teeth, or "tooth models." The tooth models may be defined as described, for example, in international application PCT / EP2015 / 074896. To determine an elementary deformation, the generator moves tooth models, while respecting all the constraints. The elementary deformations include, and are preferably exclusively, movements of tooth models.

[0315] Determining an elementary deformation is fast, even if the tooth models are moved randomly, especially if the number of points in the initial model is low. However, determining a deformation scenario can be very time-consuming.

[0316] To speed up the search for a deformation scenario, the generator can implement rules used by dental practitioners to generate an orthodontic treatment plan. For example, it can

[0317] - promote movements of the tooth models along the shortest or fastest path to the final model, taking into account one or more tooth models, for example by defining said path as the sum of the paths taken by several tooth models, preferably taking into account all the tooth models, and

[0318] - only deviate from this path in case of collision with an adjacent tooth model.

[0319] Preferably, the generator implements a first optimization algorithm, preferably a metaheuristic method, preferably evolutionary, preferably by simulated annealing. The first optimization algorithm may in particular be chosen from the algorithms listed above in the definition of the metaheuristic methods.

[0320] The first optimization algorithm may implement the following steps: i) creation of a “to be tested” scenario, i.e. application, to the initial model, of a set of successive elementary “to be tested” deformations, preferably exclusively by moving tooth models, so as to obtain an arch model “to be tested”; ii) determination of a first distance measuring a difference in shape between the model to be tested and the final model; iii) comparison of said first distance with a first threshold so as to obtain a first score for the scenario to be tested; iv) if the first score is insufficient, for example higher than a first predetermined minimum score, modification of the scenario to be tested and return to step i).

[0321] The cycle of steps i) to iv) is thus repeated until the score of the scenario to be tested is satisfactory, i.e. the model to be tested can be considered sufficiently close to the final model. The scenario to be tested can then be considered as a "deformation scenario".

[0322] In step i), the scenario to be tested can be generated randomly.

[0323] It is preferably created taking into account the scores obtained in previous cycles, for example to avoid applying elementary deformations that do not produce good scores. Preferably, the creation of a scenario to be tested is guided by rules used by dental practitioners to generate an orthodontic treatment plan. For example, the scenario to be tested can be chosen to favor movements of the tooth models along the shortest path to the final model and only deviate from this path in case of collision with an adjacent tooth model.

[0324] In step i), the scenario to be tested may in particular be the scenario to be tested from the previous cycle to which an additional elementary deformation is added. In other words, the model to be tested results from an additional elementary deformation applied to the model to be tested from the previous cycle. The scenario to be tested thus “extends” from one cycle to the next until an acceptable scenario is reached. In one embodiment, such construction of the deformation scenario is stopped if said first distance becomes greater, with a predetermined deviation, possibly zero, than that of a previously determined scenario to be tested.

[0325] In step ii), said first distance is for example the sum of the Euclidean distances between points of the model to be tested and the corresponding points of the final model.

[0326] In step iii), the first score may be, for example, the inverse of the difference between the said first distance and the first threshold. The first threshold may be zero, so that the cycle of steps i) to iv) leads to the final model.

[0327] Preferably, the generator generates several arch deformation scenarios and then chooses the one that minimizes a distance with an ideal deformation scenario, for example inducing a minimum total deformation. Such a deformation scenario is called an "optimal deformation scenario".

[0328] More preferably, the generator implements a second optimization algorithm in order to search for an optimal deformation scenario. The second optimization algorithm is preferably a metaheuristic method, preferably evolutionary, preferably by simulated annealing. The second optimization algorithm can in particular be chosen from the algorithms listed above in the definition of the metaheuristic methods.

[0329] The second optimization algorithm may implement the following steps: i') creating a deformation scenario "to be tested", preferably by means of the first optimization algorithm; ii') measuring a second distance measuring a difference between the deformation scenario to be tested and an ideal arch deformation scenario; iii') comparing said second distance to a second threshold so as to obtain a second score for the deformation scenario to be tested, the second score being able for example to be the inverse of the difference between said second distance and the second threshold; iv') if the second score is insufficient, for example higher than a second predetermined minimum score, modifying the deformation scenario to be tested and returning to step i').

[0330] The cycle of steps i') to iv') is thus repeated until the score of the deformation scenario to be tested is satisfactory, i.e. the deformation scenario to be tested can be considered sufficiently close to the ideal deformation scenario. The deformation scenario to be tested is then an "optimal" deformation scenario.

[0331] The second distance may be, for example, the cumulative Euclidean distance traveled by a set of points of the initial model, for example, all the points of the initial model, during the deformation scenario to be tested. This Euclidean distance is preferably minimal in an ideal deformation scenario, so that the second threshold may be, for example, zero and the second score equal to the second distance. The set of points preferably comprises one, preferably more than 1, more than 2 points for at least one tooth model of the initial model, preferably at least two, preferably at least 3 tooth models of the initial model, preferably for each tooth model of the initial model. The second distance may give weights greater than the Euclidean distances traveled by certain points, for example by points belonging to tooth models representing teeth whose displacement must be particularly limited.

[0332] If the second threshold is zero, the second distance can define the second score. Step iii') is then unnecessary. It is therefore optional. Preferably, the second distance takes into consideration one or more prescriptions dictated by the user. For example, the user may have completed a computer questionnaire in the computer to specify these prescriptions, for example to specify the relative importance that he gives to the speed of the orthodontic treatment, and / or to the pain generated by the orthodontic treatment, for example measured by a pain coefficient, and / or to the comfort during the orthodontic treatment, for example measured by a comfort coefficient, and / or to the cost of the orthodontic treatment.

[0333] Comfort can particularly refer to the aesthetic impact of orthodontic treatment.

[0334] In one embodiment, the second distance therefore depends on the duration and / or a pain coefficient and / or a comfort coefficient and / or a cost associated with the deformation scenario to be tested. The duration, the pain coefficient and the cost are preferably minimal in an ideal deformation scenario, so that the basis for comparison of these criteria may be, for example, equal to 0. The comfort coefficient is maximal in the ideal deformation scenario, so that the basis for comparison of this criterion may be, for example, the maximum possible value for this coefficient.

[0335] The assignment of a duration (or a duration coefficient normalizing the duration) and / or a pain coefficient and / or a comfort coefficient and / or a cost (or a cost coefficient normalizing the cost) to a deformation scenario to be tested can be determined, by a dental practitioner or, preferably, by an evaluation module programmed in the computer implementing rules conventionally applied by dental practitioners or determined by the computer by means of statistical processing. The deformation scenario to be tested can be, for example, compared to historical arch deformation scenarios in a database in order to determine a similar historical deformation scenario, and inherit the information on the duration, the pain coefficient, the comfort coefficient and / or the cost.

[0336] The criteria (duration, pain coefficients, comfort coefficient, cost) for historical arch deformation scenarios can be evaluated from surveys conducted among people who have been treated according to said historical arch deformation scenarios and / or among dental practitioners who have carried out these treatments. A neural network can also be trained to assign a duration (or a duration coefficient) and / or a pain coefficient and / or a comfort coefficient and / or a cost (or a cost coefficient) to a deformation scenario to be tested. In particular, one can use a network specialized in image classification among those mentioned above, not trained to provide probabilities of occurrence of different predefined classes, but trained to provide a value in an infinite set of values, that is to say a continuous value.For training, one can thus provide a deformation scenario, or preferably only the initial and final models, as input and a duration (or a duration coefficient), a pain coefficient, a comfort coefficient or a cost (or a cost coefficient) associated with this deformation scenario.

[0337] For example, if

[0338] - li denotes the distance traveled by a point Pi of a tooth model of the arch following the deformation scenario to be tested,

[0339] - ki denotes a weight for a duration coefficient, for example between 1 and 10, preferably provided by the user, depending on the importance he places on the speed of orthodontic treatment,

[0340] - k2 denotes a weight for a pain coefficient, for example between 1 and 10, preferably provided by the user, depending on the importance he attaches to the pain that orthodontic treatment will possibly inflict on him,

[0341] - ks denotes a weight for a comfort coefficient, for example between 1 and 10, preferably provided by the user, depending on the importance he places on comfort during orthodontic treatment, and

[0342] - k4 denotes a weight for a cost coefficient, for example between 1 and 10, preferably provided by the user, depending on the importance he attaches to the cost that will be generated by the orthodontic treatment,

[0343] - C denotes a prescription factor taking into account the coefficients of duration Ci, and / or pain C2 and / or comfort C3, and / or cost C4, associated with a deformation scenario to be tested, for example equal to a polynomial function of these coefficients, for example equal to (ki*Ci + k2*C2+ k3*C3+ k4*C4), the second distance and / or the second score could be for example:

[0344] - the sum of the , for a set of N points “i”, N preferably being greater than 10; or - the product of the sum of the U, for a set of N points “i”, by the prescription coefficient.

[0345] In one embodiment, a deformation scenario is first searched for, preferably an optimal deformation scenario, with a coarse initial model, for example containing 100 points. Then the initial, transition and final models are completed in order to check for the absence of unacceptable collision, i.e., collisions that cannot be removed by filing, for the case where filing is authorized. In the event of an unacceptable collision, i.e., if the computer finds that the deformation scenario includes an interpenetration of adjacent tooth models beyond an acceptable limit, points are added to the initial model, and said search is repeated with the simplified initial model of the previous cycle to which the points were added.

[0346] In a preferred embodiment, the initial model of the arch is cut so as to generate an initial gum model, and, successively for each transition model, it is checked whether the arrangement of the tooth models in the transition model is compatible:

[0347] - with the initial gum model, for the first transition model, or

[0348] - with the gum model in the previous transition model, for the following transition models.

[0349] This verification can be carried out by a dental practitioner and / or by a computer, independently or controlled by an operator, for example a dental practitioner. Preferably, it is checked whether the tooth models in the transition model considered penetrate into the gum model and / or whether a physiologically unrealistic gap has appeared between the tooth models and the gum model. In the case of such penetration or gap, the gum model is modified so as to eliminate said penetration or gap. Each transition model thus has a representation of the gum compatible with the arrangement of the tooth models.

[0350] In step c), the computer determines the final time for the scenario determined in step b).

[0351] For this purpose, the deformation scenario can be compared, for example, to historical arch deformation scenarios from a database providing, for each historical arch deformation scenario, the associated processing time. The duration of the scenario, and thus the final time, can then be determined from the duration of a similar historical deformation scenario, for example being chosen as equal to the duration of the similar historical deformation scenario.

[0352] The stages of orthodontic treatment in the deformation scenario from stage b) are marked by the intermediate moments at which a check of the arch by a dental practitioner and / or a modification of an orthodontic appliance worn by the user and / or a manufacture of an orthodontic appliance intended for the user must be carried out.

[0353] Modifying an orthodontic appliance worn by the user may include modifying the structure or shape of the appliance, or replacing it with a new orthodontic appliance. In one embodiment, the intermediate times are the times at which orthodontic aligner replacements are planned.

[0354] The intermediate moments are preferably moments when a change of orthodontic aligner is planned.

[0355] The intermediate times may be chosen so that the time interval between two consecutive intermediate times, preferably between any two consecutive intermediate times, is within a predetermined range, preferably is constant and / or is equal to the maximum duration of use of an orthodontic appliance, for example the duration of use of an orthodontic splint.

[0356] The transition patterns at intermediate times are the “intermediate patterns.”

[0357] The number of intermediate models is preferably less than 0.1 times the number of transition models. It is preferably greater than or equal to 1 and / or less than 150.

[0358] In one embodiment, the number of intermediate models is equal to the number of transition models.

[0359] Preferably, the intermediate instants and the final instant are determined according to the movements of the tooth models following the deformation scenario and the orthodontic appliances considered. The possibilities of moving the teeth following the different possible translational and rotational movements are in fact different depending on the number of the tooth considered and the orthodontic appliance considered. For example, due to the capabilities of the polymer used to manufacture the orthodontic aligners, a translation for the intrusion or egression of a tooth between two stages can be limited to less than 0.1 mm, a rotation can be limited to less than 3° degrees of rotation, tip or torque, etc.These constraints linked to the properties of orthodontic gutters allow, by knowing the necessary displacements between the initial model and the final model, to calculate intermediate moments and a final moment compatible with the orthodontic gutters and the orthodontic treatment.

[0360] The method of determining the intermediate and final instants is not exhaustive. The rules conventionally used by dental practitioners to choose the most appropriate intermediate instants can be applied by the computer.

[0361] In a preferred embodiment, the computer proceeds as follows:

[0362] The initial model is divided into tooth models and the elementary deformations of the deformation scenario result from displacement of the tooth models, in translation and / or rotation. Preferably, the number of each tooth represented in the initial model is identified during the division of the initial model, by labeling carried out by an operator or, preferably, by shape recognition carried out by the computer, for example by means of a neural network. Such shape recognition carried out by the computer is well known to those skilled in the art.

[0363] A tooth has kinetic displacement capacities that are different depending on the nature of this tooth. In particular, the greatest physiologically acceptable values ​​of the displacement speeds, in translation or in rotation of a tooth, according to the different directions of space, depend on the number of the tooth. These displacement capacities make it possible to define constraints of each set of constraints imposed for each elementary deformation. In particular, these constraints can fix, for each tooth model, upper limits for displacement speeds, in translation and in rotation, according to the different axes of a reference frame, for example an orthonormal reference frame, fixed relative to the user's skull. The upper limit of a displacement speed can be in particular the greatest physiologically acceptable value for this speed.

[0364] The kinetic capacities of tooth movement can be determined by statistical analysis, in particular by analysis of panoramic X-rays and / or cephalometric X-rays of historical users. They can also be determined by analysis of panoramic X-rays and / or cephalometric X-rays of the user implementing the method. In one embodiment, kinetic capacities of tooth movement are determined by statistical analysis of historical data, i.e. relating to historical users, then the values ​​obtained are refined according to the user for whom the method is implemented, for example to take into account their bone density per tooth and / or the state of their gums.

[0365] From a computer table giving, for each tooth number, the upper limits of the speeds of movement, in translation and in rotation, according to the different axes of the reference system, the computer can therefore determine the said upper limits for each tooth model.

[0366] Furthermore, for a deformation scenario, the "path" of a tooth model includes all the configurations of the tooth model from the initial model to the final model, i.e. in the initial, transition and final models. It is thus possible to determine the distance traveled in space by each point of a tooth model during the course of the deformation scenario. It is also possible to determine the angular sector traveled, around each of the three axes of the reference frame, by each tooth model during the course of the deformation scenario.

[0367] For each tooth model, considering that it moves at the highest possible displacement speeds while respecting the constraints, that is to say as much as possible at the upper limits of these speeds defined by the constraints, it is thus possible to determine the smallest possible duration for this tooth model to modify its configuration from the initial model to the final model, following the deformation scenario.

[0368] The tooth model that imposes the longest duration is called the "limiting tooth model" because the deformation scenario cannot be executed any faster. This duration, which is the duration of the orthodontic treatment plan, can be added to the initial time to determine the final time and it is possible to date each moment of the deformation scenario.

[0369] The limiting tooth model can be defined by analyzing the paths of different tooth models, depending on the deformation scenario, preferably by computer. Alternatively, the limiting tooth model can be predefined, for example because it is classically identified as limiting for orthodontic treatment.

[0370] The deformation scenario is then fragmented so that the limiting tooth model can follow its path, the intermediate instants defining the fragmentation being determined according to the capabilities of the orthodontic appliance(s) to implement the deformation scenario. For example, it is possible to define the instants at which the orthodontic appliance worn by the user will have to be adapted so that the limiting tooth model can follow its path.

[0371] In particular, in the context of orthodontic treatment using orthodontic splints, an orthodontic splint only allows limited movement of a tooth. For example, its limited elasticity may impose a displacement of any point of any tooth always less than a limit of approximately 1 mm, or even always less than 0.5 mm. In other words, as soon as a point of a tooth has moved 1 mm since the orthodontic splint was fitted, the orthodontic splint must be changed. Knowing the tooth movement capacities possible with an orthodontic splint thus makes it possible to determine the intermediate moment at which the orthodontic splint must be changed.

[0372] For example, for an orthodontic treatment in which a molar must move 3 mm and a canine must move 4 mm, the upper limit for the molar movement speed being 1 mm per month and that of the canine 2 mm per month, it takes at least 3 months to move the molar and 2 months to move the canine. The molar model is therefore the limiting tooth model and the duration of the orthodontic treatment is 4 months. The intermediate moments can be chosen to mark each time a movement of 1 mm since the previous moment (intermediate or initial) if the orthodontic aligners are adapted to ensure a movement of 1 mm each. The intermediate moments are therefore, if to is the initial moment, to be at to + 1 month, to + 2 months, and to + 3 months.

[0373] The orthodontic treatment plan thus defined may, however, impose a path for a model of a molar which is very rapid, leading to pain for the user and / or an increased risk to the user's health. The following step d), and the second main aspect of the invention, make it possible to address this problem.

[0374] In step d), optional, in a particularly advantageous embodiment, the generator, preferably the first and second optimization algorithms, is / are used to search for a new deformation scenario, preferably optimal, called "smoothed", but with, for each elementary deformation, a new set of constraints imposing

[0375] - for the limiting tooth model, compliance with the path determined according to the deformation scenario determined in step b), and

[0376] - for at least one other tooth model than the limiting tooth model, called "slowed tooth model", a reduction, preferably an optimization of a said speed parameter.

[0377] Preferably, the new set of constraints imposes upper limits for the movement speeds lower than those obtained according to the orthodontic treatment plan resulting from step c). In other words, the set of constraints imposes that the speeds of said slowed tooth model, modeling a “slowed tooth”, cannot reach the maximum values ​​that the nature of said other tooth would allow. For example, it imposes, for one or more of the movement speeds of the slowed tooth, an upper limit lower than the upper limit imposed to establish the orthodontic treatment plan resulting from step c).

[0378] Smoothing advantageously improves treatment predictability, i.e. increases compliance between the orthodontic treatment plan and its subsequent translation in the user's mouth.

[0379] Preferably, the amplitude of the speed variation during the movement of the slowed-down tooth during the treatment period is limited, i.e. the difference between the highest and lowest speeds reached during the treatment period is reduced. For this purpose, the computer may also impose one or more minimum values ​​on one or more speeds of the slowed-down tooth model, i.e. lower limits for said speeds.

[0380] More preferably, the computer calculates at least one average speed of the slowed-down tooth model according to the deformation scenario obtained at the end of step c), for example an average speed of a point in translation or rotation around an axis, on average over the duration of the orthodontic treatment plan resulting from step c). The set of constraints then imposes that the instantaneous speed of said slowed-down tooth model cannot vary by more than a certain percentage of said average speed, for example by more than + / - 20% or + / - 10%. Advantageously, the movement of said slowed-down tooth model is thus more regular.

[0381] The smoothed deformation scenario advantageously limits the risks for the user. Smoothing can be carried out for several teeth simultaneously when the new set of constraints imposes that the speeds of several slowed tooth models cannot reach the maximum values ​​that the nature of the teeth they model would allow.

[0382] In a preferred embodiment, the smoothing is carried out successively for several slowed-down tooth models.

[0383] At each iteration of step d), the computer adds to the constraints the respect of a new path for a tooth model whose path was not imposed during the previous steps d). Smoothing is preferably done tooth by tooth, preferably starting with the teeth for which a rapid movement is most likely to be detrimental to the user. In other words, preferably, the first smoothing operations concern the teeth for which a rapid movement is most detrimental to the user.

[0384] In the example above, the generator can thus search for a smoothed, preferably optimal, deformation scenario, as described above, by imposing that the tooth model modeling the molar respects the path determined according to the deformation scenario determined in step b) and that the instantaneous speed of the tooth model modeling the canine does not exceed by more than 10% the upper limit defined for a canine, at any time. It then again searches for a new smoothed, preferably optimal, deformation scenario, as described above, by imposing that said tooth models modeling said canine and said molar respect their respective paths determined according to the previous smoothed deformation scenarios and that the instantaneous speed of a tooth model modeling for example an incisor does not exceed, for example, by more than 10% the upper limit defined for an incisor, at any time.

[0385] Smoothing can be repeated for each tooth. If a smoothing operation is unsuccessful, the speed constraint, for example limiting the speed variation to less than 10% of the average speed, can be relaxed. It is also possible to repeat smoothing operations previously carried out, by relaxing the speed constraints for these previous smoothing operations.

[0386] In one embodiment, the computer implements an optimization algorithm to test several sets of constraints to be imposed for the elementary deformations, and to deduce therefrom an optimally smoothed deformation scenario, i.e. in which the largest values ​​reached for the speeds of the slowed tooth model are the lowest possible. The amplitude of the range of possible speeds is advantageously reduced to a minimum.

[0387] The computer may also or alternatively present the different smoothed deformation scenarios to a dental practitioner so that the latter may choose the smoothed deformation scenario that he or she prefers. The dental practitioner's selection criteria may also be programmed into the computer so that the computer may choose a deformation scenario.

[0388] In step e), subsequent to step c), and possibly in step d), the intermediate models are used to design and manufacture one or more orthodontic appliances, for example one or more orthodontic splints. The design can be carried out by computer, possibly with a dental practitioner. The manufacturing can be carried out by any suitable manufacturing machine.

[0389] As is now clear, the invention allows for the creation of a partial or complete orthodontic treatment plan very quickly. Tests have shown that a deformation scenario can be determined by the computer in less than 10 minutes, then broken down by the computer to obtain a good quality treatment plan that meets the user's requirements. Smoothing the speeds also limits risks to the user's health.

[0390] Smoothing process

[0391] The smoothing method described above can be advantageously generalized to a method comprising steps A) to D), illustrated in Figure 5.

[0392] In step A), to generate or recover the initial and final models, we preferably proceed according to step a).

[0393] In step B), the definition of the measured distance for a tooth model can be arbitrary.

[0394] For example, after superimposing the initial and final models so that the immobile parts of the arch merge, we can measure

[0395] - the Euclidean distance between a point of the initial model, in particular a remarkable point, for example the barycenter, and the corresponding point of the final model; - the cumulative Euclidean distance between several points, preferably remarkable, of the initial model and the corresponding points of the final model.

[0396] A distance resulting from simple measurements measuring the difference in tooth model configurations between the initial model and the final model, for example the sum of the Euclidean distances between points of the tooth model in the initial model and the corresponding points of the tooth model in the final model, advantageously limits the calculations to search for the limiting tooth. In one embodiment, no deformation scenario is determined before the first smoothed deformation scenario.

[0397] After superimposing the initial and final models so that the immobile parts of the arch merge, it is possible, for example, to measure the distance traveled by one or more points, preferably remarkable ones, following a basic deformation scenario between the model and the final model, preferably as defined according to the first main aspect of the invention.

[0398] The distance traveled for a set of points of the tooth model following a basic deformation scenario, as for step d), is more complex since it requires defining said basic deformation scenario, preferably following a step b). However, it is more precise and advantageously allows limiting the risk of error when determining the limiting tooth.

[0399] The distance measurement is preferably carried out by a computer, autonomously.

[0400] The travel time of the distance for a tooth model can be roughly estimated, for example by dividing the distance measured for a tooth model by a constant speed fixed for said tooth model. The speed assigned to a tooth model is preferably determined as a function of the number of the modeled tooth and / or as a function of the physiological possibilities of displacement of the modeled tooth.

[0401] In an advantageous embodiment, the speed assigned to a tooth model is variable depending on the instant considered. In particular, it can increase from the initial instant, for example for more than 5 days from the initial instant, and / or it can decrease as an estimate of the final instant approaches, for example at least during the 5 days preceding the estimate of the final instant. Preferably, it is lower for instants close to the initial instant and the estimate of the final instant. Said constant speed can be a speed representative of one or more speeds of movement of one or more points of the tooth model. It can be for example the modulus of the vector of the translational speed of the barycenter of the tooth model.

[0402] The travel time of the distance for a tooth model can be evaluated more finely. For example, the speed of a tooth model can be variable, and in particular depend on the nature of the displacement considered, and therefore depend on the displacement considered during a path of the tooth model between its configurations in the initial and final models. The path of a tooth model can be determined by establishing a basic deformation scenario following a step b).

[0403] The elementary duration between two successive configurations of the tooth model can be determined, for example, by dividing the elementary distance traveled by this tooth model between these two configurations by a speed determined for this elementary distance. The travel time of the distance measuring the difference between the configurations of the tooth model in the initial model (initial configuration) and in the final model (final configuration) can then be the sum of the elementary durations determined between the different successive configurations from the initial configuration to the final configuration.

[0404] The duration of the distance is preferably carried out by a computer, autonomously, that is to say without human intervention, preferably by the computer having implemented the previous step.

[0405] In step C), the durations determined for each tooth model are then compared, and the limiting tooth model associated with the longest duration is retained. The displacement of the limiting tooth that it models sets the shortest possible duration for orthodontic treatment.

[0406] The duration associated with the limiting tooth model defines the duration of orthodontic treatment. It can be added to the initial time to define the final time.

[0407] The comparison of durations is preferably carried out by a computer, independently, preferably by the computer which implemented the previous steps.

[0408] In a preferred embodiment, for each tooth model and for each type of movement (ingression / egression, mesialization / distalization, lingualization / vestibularization, tip, torque and rotation) a distance to be traveled between the initial configuration and the final configuration is calculated, and this distance is divided by the maximum speed. The longest duration determines the limiting tooth model.

[0409] In step D), the computer determines the first smoothed deformation scenario, preferably in such a way as to reduce, preferably minimize a said speed parameter.

[0410] Preferably, the computer determines the first smoothed deformation scenario so as to reduce, preferably minimize, between the initial time and the final time, the largest value of at least one movement speed reached for at least one tooth model other than the limiting tooth model, or "first slowed-down tooth model".

[0411] The first slowed-down tooth model models a "first slowed-down tooth." The first slowed-down tooth is preferably, among all the teeth modeled in the initial model and excluding the limiting tooth modeled by the limiting tooth model, the tooth in the arch whose movement speed is most critical for the health of the user, i.e., the tooth whose rapid movement generates the highest risk for the user. In one embodiment, the computer determines the first smoothed deformation scenario so as to slow down all the tooth models other than the limiting tooth model.

[0412] Whatever the embodiment, step D) is preferably repeated by changing each time the tooth model which is slowed down, by imposing at each occurrence of step D) that the tooth models which have been slowed down during previous steps D) follow the path defined during these previous steps D), as described for step d).

[0413] The order in which the tooth models are successively slowed down is preferably determined based on utility criteria defined by the dental practitioner and / or user.

[0414] After step D), the method may include a step e) of designing and manufacturing at least one orthodontic appliance, in particular an orthodontic splint, based on the first smoothed orthodontic treatment plan.

[0415] Example

[0416] In step A), the computer retrieves an initial model resulting from a scan of the user's arch, with an optical scanner.

[0417] The computer-assisted dental practitioner, or the computer independently, determines a final model. In steps B) and C), the computer-assisted dental practitioner, or the computer independently, searches for a basic deformation scenario between the initial and final models as described in step b), i.e., paths for each of the tooth models. Then it determines the limiting tooth model and the final time based on the paths (to determine the traveled distance) and the kinetic capacities (to determine the travel time of the distance) of the tooth models.

[0418] Alternatively, the computer-assisted dental practitioner, or the computer alone, does not determine a basic deformation scenario, but determines the limiting tooth model by comparing distances between the initial and final configurations of the different tooth models.

[0419] Once the limiting tooth pattern is identified, the process preferably tries to move the other tooth patterns as slowly as possible.

[0420] In step D), the computer-assisted dental practitioner, or the computer independently, chooses the “slowed-down tooth model”, preferably the tooth model whose slowing down is most useful for health and / or to meet the user's prescriptions.

[0421] To determine the first smoothed deformation scenario, the computer searches for a set of successive elementary deformations transforming, by displacement of tooth models, the initial model at the initial time into the final model at the final time, and minimizing the speed parameter for the slowed down tooth model. It preferably implements a conventional optimization algorithm, preferably a metaheuristic method, preferably chosen from the methods described above.

[0422] The cost function to be minimized may in particular be the highest displacement speed reached by the slowed tooth model between the initial instant and the final instant. This speed can be determined as the highest instantaneous speed between these instants, the instantaneous speed being calculable by dividing a distance between two successive configurations of a tooth model by the time interval between these two configurations.

[0423] In a substantially equivalent manner, optimization can also be achieved by defining the sets of constraints imposed for the elementary deformations so that they all impose that the instantaneous speed (for said displacement speed) between two successive elementary deformations is less than a determined value. The computer then searches for a deformation scenario respecting these sets of constraints and then, if successful, reduces said determined value. Iteratively, the computer can thus determine the lowest possible value for the upper limit of the displacement speed between the initial instant and the final instant which makes it possible to define a deformation scenario. This deformation scenario is then a first smoothed deformation scenario.

[0424] Preferably, steps D) are then repeated, successively for other slowed-down tooth models, giving priority to the tooth models whose slowing-down is most useful for health and / or to meet user requirements.

[0425] Intermediate moments can be defined, preferably at the end of the process, depending on the action capabilities of the orthodontic appliance(s) envisaged for the orthodontic treatment.

[0426] In a preferred embodiment, when determining a smoothed deformation scenario, configurations are imposed at certain times for tooth models.

[0427] In particular, for the determination of the first smoothed deformation scenario, the constraint sets impose configurations on the limiting tooth model. The imposed configurations are preferably "transition" configurations in transition models of a basic deformation scenario, preferably configurations at intermediate times.

[0428] Similarly, for the determination of the second smoothed deformation scenario at the second occurrence of step D), the sets of constraints impose configurations on the limiting tooth model and on the first slowed tooth model. The imposed configurations are preferably "transition" configurations in transition models of the first smoothed deformation scenario, preferably configurations at intermediate times. A similar procedure is followed for the following occurrences of step D).

[0429] Preferably, steps B) to D) are carried out autonomously by a computer.

[0430] In one embodiment, the smoothing is performed to improve an existing orthodontic treatment plan. A dental technician or practitioner defines an orthodontic treatment plan with a computer, preferably in a conventional manner, for example with Treat software, from the initial model, by moving the tooth models from the initial model to a desired configuration at the end of the orthodontic treatment. He thus determines the intermediate times, in particular for orthodontic splint changes, the final time and a "conventional" deformation scenario comprising the intermediate models of the dental arch at the intermediate times.

[0431] From this data, preferably determined conventionally, the computer can implement steps B) to D), preferably autonomously. The dental practitioner or technician thus has a solution allowing him to perfect the orthodontic treatment plan that he has established.

[0432] As is now clear, the method according to the invention allows the computer to spread the path of the tooth models as much as possible in the time interval between the initial instant and the final instant, i.e. to smooth the movement of the tooth models as much as possible by reducing the instantaneous speeds of movement of the tooth models as much as possible.

[0433] Of course, the invention is not limited to the embodiments described in detail above.

Claims

CLAIMS Method for generating a plan for orthodontic treatment of a user's dental arch, the method comprising the following successive steps: a) generation or retrieval of an "initial" model representing said dental arch in three dimensions at an initial time, said initial model being cut into tooth models, and generation or retrieval of a "final" model representing said dental arch with a "final" arrangement of the tooth models desired at the end of the orthodontic treatment;b) determination, by a computer, of a set of successive elementary deformations transforming, by displacement of the tooth models, the initial model into the final model, said elementary deformations each respecting a respective set of constraints, the models resulting from the successive elementary deformations being called "transition models", the succession of the set of successive transition models being called "basic deformation scenario"; c) determination, by the computer,; - of a duration to achieve, from the initial moment, the deformation of the dental arch according to the deformation scenario until the final arrangement is obtained at a final moment; and - intermediate times between the initial and final times for performing the deformation of the dental arch according to the basic deformation scenario, the intermediate times being times at which an arch check by a dental practitioner and / or a modification of an orthodontic appliance and / or the fabrication of an orthodontic appliance is / are planned, the basic deformation scenario and said intermediate times defining said orthodontic treatment plan, referred to as the "basic orthodontic treatment plan". Method according to the preceding claim, wherein, in step a), said computer determines the final model from the initial model. A method according to the preceding claim, wherein in step a), to determine the final model, said computer - analyzes the shape of the initial model in order to determine the curvature and length of the dental arch, and defines a baseline having said curvature and said length, then, - for each of a plurality of tooth models, determines a position and orientation of said tooth model relative to said baseline based on predefined rules and / or by assimilating the user's dental arch to a historical dental arch similar to said user's dental arch. A method according to the immediately preceding claim, wherein, prior to step a), the predefined rules are determined by statistical processing of historical data. A method according to any one of the preceding claims, wherein, at the beginning of step c), the computer - determines, for each tooth model, the closest instant to the initial instant at which the tooth model can reach, following the basic deformation scenario determined in step b), its configuration in the final model, or "end of path instant"; - determines, among the set of tooth models, a tooth model having the end-of-path instant furthest from the initial instant, or "limiting tooth model"; - fixes the final instant as the end-travel instant of the limiting tooth model. A method according to the immediately preceding claim, wherein the computer determines the end-travel instant of a tooth model by dividing a distance representative of the tooth model's displacement during the basic deformation scenario by a velocity representative of the kinetic capacities of said tooth model. A method according to any one of the two immediately preceding claims, comprising, after step c), the following first step d): d) determination, by the computer, of a new deformation scenario called the "first smoothed deformation scenario," in which The limiting tooth model follows the path defined by the basic deformation scenario determined in step b), and in which at least one velocity parameter is optimized, the first smoothed deformation scenario and said intermediate instants defining a new orthodontic treatment plan, referred to as the "first smoothed orthodontic treatment plan". A method according to the immediately preceding claim, wherein the velocity parameter is chosen from: - the highest value of the speed of movement of said slowed-down tooth model reached between the initial instant and the final instant, and / or - the difference between the highest value of said displacement speed and the lowest value of said displacement speed of said slowed-down tooth model between the initial instant and the final instant, and / or - the variation of said speed of movement of said slowed-down tooth model, on average between the initial instant and the final instant. A method according to any one of the two immediately preceding claims, comprising, after said first step d), one or more successive additional steps d), each additional step d comprising the determination, by the computer, of an additional smoothed deformation scenario in which - the limiting tooth model follows the path defined by the basic deformation scenario determined in step b), and - the slowed tooth model(s) of the step(s) d) prior to said additional step d) follow the path(s) defined by the said smoothed deformation scenario(s) determined in said earlier step d) or in said earlier steps d), respectively, the additional smoothed deformation scenario being determined to optimize said at least one velocity parameter for at least one "additional" slowed tooth model, different from the slowed tooth model(s) of the earlier step(s) d), between the initial instant and the final instant, the additional smoothed deformation scenario and said intermediate instants defining an orthodontic treatment plan, referred to as the "additional smoothed orthodontic treatment plan". A method according to any one of the three immediately preceding claims, wherein the tooth model slowed down in the first step d) or in an additional step d) when claim 9 applies, is / are chosen according to a criterion of usefulness for the dental practitioner and / or the user, preferably according to the risk that the application of the basic deformation scenario or the smoothed orthodontic treatment plan of the preceding step d) represents to the user's health, respectively.A method according to any one of the preceding claims, comprising, after step c), or after the first step d) where claim 7 applies, or after the additional step(s) d) / s) where claim 9 applies, the following step e): e) designing and manufacturing at least one orthodontic appliance, based on the basic orthodontic treatment plan obtained at the end of step c) or, where claim 7 applies, based on the first smoothed orthodontic treatment plan, or, where claim 9 applies, based on the additional smoothed orthodontic treatment plan. A method according to the immediately preceding claim, wherein. - said orthodontic appliance is an orthodontic splint and the intermediate moments are exclusively moments at which a change of orthodontic splint is planned, or - The said orthodontic appliance is an assembly comprising an orthodontic archwire and attachments for fixing said orthodontic archwire to the teeth, and the intermediate moments are exclusively moments at which a change of the archwire and / or one or more attachments is planned. A method according to any one of the preceding claims, wherein said set of constraints includes user-imposed prescriptive constraints. A method according to any one of the preceding claims, wherein the computer displays a dynamic form adapted for entering at least some of the information necessary to define said set of constraints. A method according to any one of the preceding claims, wherein said set of constraints allows limited penetration of a tooth model into an adjacent tooth model, the limitation of said penetration being determined by the possibility of filing at least one of the teeth modeled by said tooth models in order to compensate for said penetration.A method according to any one of the preceding claims, wherein, in step b), the computer implements an optimization algorithm to determine a basic deformation scenario that best meets one or more user-defined requirements specifying the relative importance the user places on the speed of orthodontic treatment, and / or the pain generated by orthodontic treatment, and / or comfort during orthodontic treatment, and / or the cost of orthodontic treatment, and / or the aesthetic impact of orthodontic treatment, and / or the reliability of orthodontic treatment. A method according to any one of the preceding claims, wherein, in step b), the computer. - searches for a deformation scenario with a coarse initial model containing fewer than 5000 points, the coarse initial model resulting from a simplification of a fine initial model containing more points than the coarse initial model, then - adds points to the transition models of the deformation scenario and the final model, then, - determines whether, in the coarse deformation scenario in which the transition and final models were thus completed, tooth models collide in an unacceptable manner, and - In case of an unacceptable collision, add points to the initial rough model and resume the search with the initial rough model to which the points have been added. Method for generating a plan for a complete orthodontic treatment of a user's dental arch, the complete orthodontic treatment being composed a succession of several partial orthodontic treatments, each corresponding to a respective phase of the complete orthodontic treatment, the process comprising the following successive steps: A') generation or retrieval of a first "beginning-of-phase" model representing said dental arch at a time at the beginning of the first phase of the complete orthodontic treatment, said first model being cut into tooth models, and generation or retrieval of a final "end-of-phase" model representing said dental arch with a desired arrangement of tooth models at the end of the final phase of the complete orthodontic treatment; B') determination, preferably by a computer or by a computer-assisted dental practitioner, for each phase, from the first phase to the penultimate phase, of a respective end-of-phase model representing said dental arch with a desired arrangement of tooth models at the end of said phase; (c) for each phase, implementation of a method according to any one of the preceding claims, the initial model being the beginning model of said phase and the final model being the end model of said phase. Computer into which a program comprising program code instructions for execution is loaded - steps b) and c), preferably steps a), b) and c) of a process according to any one of claims 1 to 17, and optionally the first step d) where claim 7 applies or the additional step(s) d) where claim 9 applies, and / or - of a step C') and preferably of a step A') or B'), and preferably of a step A') and a step B'), of a method according to claim 18, when said program is executed by said computer. Computer according to the immediately preceding claim, wherein the program code instructions are adapted to determine the final model from the initial model, preferably according to claim 3 or claim 4, and / or, when claim 11 applies, to design said orthodontic appliance. System comprising - a three-dimensional scanner capable of producing a "raw" model of the arch the user, and - a computer according to any one of the two immediately preceding claims, said raw model being used as an initial model or the computer being configured to transform said raw model into an initial model, alone or with the assistance of a dental practitioner.

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