METHOD FOR DETERMINING AN ORTHODONTIC TREATMENT PLAN

Abstract

A method for generating an orthodontic treatment plan for a user's dental arch, comprising the following successive steps: A) generating initial and final models representing the dental arch at initial and final times; B) for each tooth model in the initial model, determining a distance between the tooth model configurations in the initial and final models and the shortest possible time for the tooth model to travel said distance; C) identifying the limiting tooth model, which has the longest minimum travel time; D) determining a deformation scenario whereby the initial model is transformed into the final model by moving the tooth models so as to slow down at least one first slowed-down tooth model different from the limiting tooth model. No abstract figure

Description

Title of the invention: METHOD FOR DETERMINING AN ORTHODONTIC TREATMENT PLAN Technical field

[0001] The present invention relates to a method for determining an orthodontic treatment plan, which includes determining a complete orthodontic treatment plan or a part of a complete orthodontic treatment plan.

[0002] The invention also relates to a computer program as well as a computer and a system for implementing this method. Previous technique

[0003] Orthodontic treatment is intended to modify the arrangement of a user's teeth by means of an orthodontic appliance.

[0004] Among orthodontic appliances, a distinction is made between archwire and bracket orthodontic appliances on the one hand, and orthodontic aligners on the other.

[0005] An orthodontic appliance with archwires and brackets comprises 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 patient being treated.

[0006] An aligner, also known as a retainer, is typically a removable, one-piece appliance, usually made of a transparent polymer material. It has a channel shaped to accommodate several teeth of an arch, generally all the teeth of an arch. The shape of the channel is designed to hold the aligner in position on the teeth while simultaneously correcting the positioning of certain teeth. An orthodontic aligner has a slower initial action than a traditional archwire brace. Advantageously, however, the aligner can be replaced by the user. Furthermore, aligners are more discreet than traditional archwire braces.

[0007] The implementation of orthodontic treatment requires the prior preparation of an orthodontic treatment plan in order to plan the steps of the upcoming orthodontic treatment. The orthodontic treatment plan thus defines the 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 orthodontic aligner, and / or a change of orthodontic archwire, and / or the fabrication of an orthodontic appliance is / are planned.

[0008] Traditionally, an orthodontic treatment plan is created by the dental practitioner using a computer. The computer allows him, in particular, to visualize a The dental practitioner creates a model of a dental arch and modifies this model to determine a possible evolution of the position and orientation of each tooth, compatible with the evolution of the position and orientation of the other teeth, until the desired arrangement for all the teeth in the arch is achieved. The dental practitioner thus manages to determine a series of three-dimensional digital models comprising a model representing the said arch at the beginning of orthodontic treatment, a model representing the said arch at the end of orthodontic treatment, and one or more "intermediate" models representing the said arch at intermediate times between the beginning and the end of 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 the fabrication of an orthodontic appliance is / are planned.This series of models, or "deformation scenario", and the intermediate moments thus define the orthodontic treatment plan.

[0009] Software for manipulating the dental arch model and generating an orthodontic treatment plan is well known. However, it requires learning how the software works and demands orthodontic expertise. Creating an orthodontic treatment plan can be laborious and time-consuming.

[0010] Moreover, these software programs can lead to orthodontic treatment plans resulting in rapid tooth movement, potentially detrimental to the user's health.

[0011] There is a continuing need for a process and a system to improve the implementation of an orthodontic treatment plan.

[0012] One object of the invention is to meet this need. Summary of the invention

[0013] According to a first principal aspect, the invention provides a method for generating an orthodontic treatment plan for 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 optionally a gum model, and generation or retrieval of a "final" model representing said dental arch with a "final" arrangement of the tooth models as desired at the end of 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 final model, the said elementary deformations each respecting a respective set of constraints, the models resulting from successive elementary deformations being called "transition models", the succession of all successive transition models being called "basic deformation scenario"; c) determination, by computer, - of a duration, referred to as the "treatment duration", to carry out, from the initial moment, the deformation of the dental arch according to the basic deformation scenario until the final arrangement is obtained, at a final moment; and - intermediate moments between the initial and final moments to achieve 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".

[0014] The moments at which it is expected, according to the basic orthodontic treatment plan, that the dental arch will have a shape according to the transition models are called "transition moments".

[0015] As will be seen in more detail later in the description, the computer thus creates, from the initial and final models alone, the basic orthodontic treatment plan quickly and automatically, that is, without human intervention. The automation of orthodontic treatment plan creation can be advantageously optimized, particularly with metaheuristic methods, which makes it possible to achieve performance levels that are very difficult to achieve manually, especially by avoiding collisions or ensuring the smoothest or fastest possible tooth movements.

[0016] Preferably, a method according to the first main aspect of the invention also has one or more of the following optional features: - in step a), said computer determines the final model from the initial model; - 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 define a baseline having said curvature and said length, then, - for each of a plurality of tooth models, preferably for each tooth model of the initial model, determines a position and 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; - preferably, prior to step a), the said predefined rules are determined by statistical processing of historical data; - in step b), said set of constraints includes user-imposed prescription constraints, preferably to specify the relative importance that the user gives to the speed of orthodontic treatment, and / or to the pain generated by orthodontic treatment, and / or to the comfort during orthodontic treatment, and / or to the cost of orthodontic treatment, and / or to the aesthetic impact of orthodontic treatment, and / or to the reliability of orthodontic treatment, i.e. to the probability that orthodontic treatment will lead to the expected result, and / or to a duration for wearing orthodontic appliances, and / or to a predetermined functional, orthodontic or therapeutic objective; - in step b), the computer displays a dynamic form adapted for the input, preferably by the user, of at least part of the information necessary to define said set of constraints, in particular necessary to define prescription constraints; - in step b), said set of constraints permits a limited penetration of a tooth model into an adjacent tooth model, the limitation of said penetration being preferably determined by the possibility, preferably evaluated according to the rules of orthodontics, preferably by a dental practitioner, of filing, during 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; - In step b), the computer implements an optimization algorithm, preferably a first optimization algorithm to determine a baseline deformation scenario leading to a model as close as possible to the final model and / or a second optimization algorithm to determine a baseline deformation scenario that best meets one or more requirements dictated by the user; - In step b), the computer - searches for a "coarse" deformation scenario with an initial coarse model containing fewer than 5000 points, preferably fewer than 2000 points, preferably fewer than 1000 points, preferably fewer than 500 points, preferably fewer than 100 points, and / or more than 50 points, the initial coarse model resulting from a simplification of an initial fine model containing more points than the initial coarse model, preferably containing 1.1, 1.5, 2, 5, 10, or 100 times more points than the initial coarse model, then - completes, at least partially, the transition and final models, that is to say, adds points to these models, - 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, preferably at least in the collision zones, preferably at least the points added to the transition and final models in the collision zones, or even with all the points added to the transition and final models, and - resumes said research with the initial crude model to which the points have been added, the cycling being preferably continued until a deformation scenario without unacceptable collision is obtained, constituting the basic deformation scenario; - 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 time furthest from the initial time, or "limiting tooth model" »; - fixes the final instant as being the instant of the end of the path of the limiting tooth model; - the computer preferably determines the time of end of 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 capacities of said tooth model; - in step c), the computer determines the intermediate times by dividing said treatment time according to the capacity of one or more orthodontic devices, preferably according to the capacity of orthodontic aligners, to move the teeth modeled by the tooth models, and / or by dividing said treatment time into intervals of the same duration, each interval preferably corresponding to a duration of use of an orthodontic aligner by the user intended for orthodontic treatment, or corresponding to a frequency of checking the proper progress of the orthodontic treatment, said frequency being preferably predetermined; - the process comprises, 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 configuration of the limiting tooth model is, at any intermediate time, preferably at any transition time, that defined by the basic deformation scenario determined in step b), and - in which a travel speed, preferably each travel speed, of at least one tooth model other than the limiting tooth model, or "slowed-down tooth model", is smoothed between the initial and final instants, i.e. in which at least one speed parameter is reduced or optimized, preferably minimized, the first smoothed deformation scenario and the said intermediate moments defining a new orthodontic treatment plan, called the "first smoothed orthodontic treatment plan"; - The speed 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; - the first smoothed deformation scenario is determined so that the largest value of said displacement velocity between the initial and final instants is less than the largest value of said displacement velocity between the initial and final instants in the basic deformation scenario determined in step b); - the process 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 - 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 prior step d) or in said prior 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) of the previous step(s) d), respectively, between the initial instant and the final instant, the orthodontic treatment plan thus modified being called the "supplementary smoothed orthodontic treatment plan"; - the slowed-down tooth model in the first step d) or in an additional step d) is 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 previous step d) represents to the user's health, respectively; - the utility criterion defines a utility to limit a risk to the user's health and / or to meet the user's requirements; - the model of the slowed-down tooth during the first step d) or during an additional step d) is chosen according to the risk that the application of a high speed of movement represents for the user's health, and in particular the application of a speed of movement corresponding to the highest physiologically acceptable speed of movement for the slowed-down tooth that it models; - the closer an additional step d) is to step c), the higher the said risk, i.e. the computer prioritizes smoothing the movement speeds of the tooth models for which rapid movement induces the highest risk; - preferably, the process includes a step d) for each tooth model, except the limiting tooth model; - the process includes, 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 according to the basic orthodontic treatment plan obtained at the end of step c) or according to the smoothed orthodontic treatment plan obtained at the end of step d) or a cycle of steps d); - said orthodontic device is an orthodontic splint and the intermediate moments are exclusively moments at which a change of orthodontic splint is planned; - said orthodontic device is an orthodontic arch and / or an auxiliary device and the intermediate moments are exclusively moments at which a change of orthodontic arch and / or auxiliary device is planned; - said auxiliary device is chosen from a hook, a button, a cleat, an elastomeric chain, a spring, an elastic band and a mini-screw; - 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; - the computer presents the basic orthodontic treatment plan and / or the smoothed orthodontic treatment plan to a dental practitioner for validation.

[0017] A complete orthodontic treatment classically comprises several phases. Each phase, or "partial orthodontic treatment", can be the subject of an orthodontic treatment plan according to a method according to the invention, the initial model representing the dental arch at the beginning of the phase considered and the final model representing said dental arch with an arrangement of the tooth models as desired at the end of said phase.

[0018] The invention thus also relates to a method of generating a plan for a complete orthodontic treatment of a user's dental arch, the complete orthodontic treatment being made up 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: 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 last phase of the complete orthodontic treatment, i.e. the end 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 process 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.

[0019] The process implemented in step C') may include one or more of the optional features described in this description.

[0020] The tooth model velocity smoothing process mentioned above can be generalized.

[0021] 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: A) preferably following a step a), - generation or retrieval of an "initial" model representing in three dimensions said dental arch at an initial time, said initial model being divided into tooth models, and - generation or retrieval of a "final" model representing in three dimensions said dental arch with a "final" arrangement of tooth models as desired at a final moment marking the end of the orthodontic treatment, partial or complete; B) for each tooth model, - determination of a distance measuring a difference between the configurations of the tooth model in the initial model and in the final model; - determination of the shortest possible time for the tooth model to travel said distance, i.e. determination of the shortest travel time to transition 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"; C) identification of the tooth pattern that exhibits the longest said minimum displacement time, or "limiting tooth pattern"; D) determination of a "first smoothed deformation scenario" according to which the initial model is transformed into the final model by shifting 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 velocity parameter 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 - a speed representative of the speed of movement of said slowed-down tooth model, preferably an average speed between the initial and final instants, and / or - the difference between said highest value of said speed of movement and said lowest value of said speed of movement of said slowed-down tooth model between the initial and final instants, 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.

[0022] Preferably, intermediate times are determined, preferably the computer determines, preferably marking times at which changes of orthodontic splint are planned, the first smoothed deformation scenario and said intermediate times defining a first smoothed orthodontic treatment plan.

[0023] The generation of the final model can be carried out, from the initial model, by a dental practitioner using a computer adapted for the manipulation of tooth models.

[0024] In one embodiment, the determination of the distance measuring a difference between the configurations of the tooth model in the initial model and in the final model is carried out without it being necessary to have previously determined the arrangements of the teeth between the initial and final models, for example by comparing the initial and final models.

[0025] Preferably, however, in step B), a "basic deformation scenario" of said arch is determined, preferably by a computer, 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 a function of said basic deformation scenario, the distance being, for example, the distance traveled by one or more points of the tooth model according to the basic deformation scenario; then in step C), the limiting tooth model is determined, preferably by a computer, as the tooth model having, following the basic deformation scenario, the last one reaches its configuration in the final model.

[0026] The basic deformation scenario and the intermediate moments form a "basic orthodontic treatment plan".

[0027] Smoothing can be achieved without necessarily defining a basic deformation scenario, but the prior generation of a basic 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.

[0028] In one embodiment, to determine the basic deformation scenario, the computer - determines 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, - determines, for each tooth model, said distance as a function of said set of elementary deformations, said distance being preferably the sum of the elementary distances traveled by a point or a plurality of points of the tooth model during the elementary deformations.

[0029] The basic deformation scenario and / or the movement speeds of the tooth models can be determined by a dental practitioner using a computer adapted for manipulating tooth models, for example using the Treat software described on the page https: / / en.wikipedia.org / wiki / Clear_aligners#cite_note-invisalignsystem-10.

[0030] The basic deformation scenario can alternatively be determined following a step b).

[0031] The speeds of movement can be calculated from - distances measured by comparing the initial and final models and / or distances determined from the basic deformation scenario, preferably determined according to step b), and - time intervals determined from the treatment duration, preferably determined according to step c).

[0032] The first smoothed deformation scenario preferably results from a modification of a basic deformation scenario. Such a process can be advantageously used to smooth a conventionally defined basic orthodontic treatment plan, particularly 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 tooth models from an initial model to the final model.

[0033] The dental practitioner can also use software, for example Treat, capable of providing transition and intermediate models. The dental practitioner can then modify these models, with the software recalculating the intermediate times accordingly.

[0034] The smoothing can alternatively relate to a basic deformation scenario determined by a computer, autonomously, as described following the first main aspect of the invention.

[0035] The smoothing can be done by the computer, autonomously.

[0036] Preferably, the first slowed-down tooth is, among the set of modeled teeth in the initial model and apart from the limiting tooth modeled by the limiting tooth model, the tooth in the arch that it 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.

[0037] The first tooth slowed down may be the tooth whose speed of movement is most critical for the user's health

[0038] The first slowed-down tooth can be, for example, the tooth whose speed of movement, according to 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 health of the user.

[0039] Preferably, a method according to the second main aspect of the invention also has one or more of the following optional features: - the intermediate moments, preferably determined by the computer, are moments at which a dental practitioner checks the arch and / or modifies an orthodontic appliance and / or manufactures an appliance orthodontic treatment is / are planned, preferably times when a change of orthodontic aligner is planned; - the first slowed-down tooth is, among all the teeth modeled in the initial model and apart from the limiting tooth modeled by the limiting tooth model, the tooth in the arch whose speed of movement is the most critical for the user's health, for example the tooth whose rapid movement generates the highest risk for the user; - the process comprises, after determining the first smoothed deformation scenario, determining, preferably by a computer, a second smoothed deformation scenario reducing, preferably minimizing the velocity parameter for a second slowed tooth model, modeling a second slowed tooth, different from the limiting tooth model and the first slowed tooth model, preferably reducing, preferably minimizing the largest value of the displacement velocity reached between the initial instant and the final instant by said second slowed tooth model, with the constraint that the limiting tooth model and the first slowed tooth model follow the paths defined by the first smoothed deformation scenario; - 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 it 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 to the user's health, said utility criterion being preferably identical to the utility criterion used to choose the first slowed-down tooth; - the second slowed tooth is the tooth whose movement speed, following the first smoothed orthodontic treatment plan, reaches a value closest to a predetermined "acceptable" value, and in particular to a critical value for the user's health; - the first smoothed deformation scenario, and optionally the second smoothed deformation scenario, is / are determined in such a way as to respect: - anatomical constraints preferably imposing an absence of penetration of one tooth model into an adjacent tooth model, and / or that the positions of one or more points of a tooth model be contained within a defined envelope around the tooth model, and / or that the translational velocity of a tooth model along a direction and in a sense be less than an upper limit for a translational velocity, and / or that the rotational velocity of a tooth model around an axis and in a sense be less than an upper limit for a rotational velocity; and / or - 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 for moving a tooth model, and / or favoring certain movements over others, and / or imposing an order for moving tooth models, and / or imposing correct occlusion, and / or authorizing or prohibiting tooth filing, i.e., authorizing or prohibiting penetration of a tooth model into an adjacent tooth model, and / or authorizing limited tooth filing, i.e., limiting the degree of penetration of a tooth model into an adjacent tooth model, and / or authorizing or prohibiting the extraction of one or more teeth, and / or imposing a speed for moving one or more teeth; and / or - prescription constraints imposed by the user due, for example, to a need for orthodontic treatment that generates limited pain and / or has a limited duration and / or a limited cost, and / or has a limited aesthetic impact and / or minimal reliability, and / or involves a limited duration for wearing an orthodontic appliance, in particular a maximum duration for wearing an orthodontic aligner or an archwire appliance, and / or has a limited number of steps, and in particular limits the number of orthodontic aligners required for the orthodontic treatment associated with the first smoothed deformation scenario, or optionally the second smoothed deformation scenario, and / or has a predetermined number of steps, and / or allows or prohibits tooth filing, and / or allows limited tooth filing, and / or allows or prohibits the extraction of one or more teeth,and / or authorizing or prohibiting the use of one or more auxiliary orthodontic devices.

[0040] In general, the method preferably involves determining, preferably by a computer, successively for each of the tooth models considered as "slowed-down tooth model", apart from 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.

[0041] In one embodiment, for each of the tooth models other than the first and second tooth models, considered as "slowed-down tooth model", a said smoothed deformation scenario is successively determined, 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.

[0042] According to a third main aspect, the invention relates to a method of inputting information into a computer, in particular within the framework of a process for generating a plan for orthodontic treatment of a dental arch, preferably according to the first or second main aspect of the invention, preferably at least for capturing prescription constraints, said capture method comprising the following steps: 01) A first user enters initial information into the computer, for example in a first input field of a first form page displayed on a first screen of the computer; 02) the computer analyzes said first information, then prepares and displays, on a second computer screen, a second form page containing 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; 03) The second user enters the second piece of information on the computer using the second input field, 04) preferably, the computer uses the second piece of information and preferably the first piece of information to define an orthodontic treatment plan and / or to monitor the progress of orthodontic treatment.

[0043] The second form page, used for entering the second piece of information, can be a new page or result from an adaptation of the first page used in step 01) to enter the first piece of information.

[0044] According to the invention, it belongs to a dynamic form.

[0045] As will be seen in more detail later in the description, a dynamic form comprising one or more pages allows for much more efficient data entry than a static form. It avoids the laborious reading of input pages unsuitable for the second user. A dynamic form therefore speeds up data entry for the second user. By facilitating understanding of the situation, it also reduces the risk of incorrect entries.

[0046] A dynamic form closely guides data entry, which advantageously allows for unassisted entry, particularly without the involvement of the dental practitioner. Data entry can be performed remotely from the dental practitioner, notably using the mobile phone of the first and / or second user. For example, if several photos need to 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 and validating the first photo.

[0047] The dynamic form is particularly useful when the computer is integrated into a mobile phone. It effectively limits the exchange of information with the mobile phone.

[0048] The second form page may be from a refresh of the first form page, or be a new form page, in particular 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.

[0049] The first user may be the same as the second user, and in particular may be an individual for whom orthodontic treatment is underway or planned. The first and second screens are then preferably identical. They may be, for example, the user's mobile phone screen.

[0050] 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 underway or 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 office and the screen of the user's mobile phone, respectively. This embodiment advantageously allows the first user to enter "professional" information that the second user is unable to determine on their own. For example, a dental practitioner may analyze the individual's dental situation, for example, by analyzing photos of the individual's mouth that the individual has sent them with their phone, and enter data characterizing this dental situation.The individual then has access to a form specifically tailored to their dental situation. More generally, this implementation allows each user to enter information that the other user does not know, as the input interface for one user depends on the entries made by the other user.

[0051] Preferably, a method according to the third main aspect of the invention also has one or more of the following optional features: - 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; - the format of the second input field depends on the first piece of information; - the first item of information includes at least one photograph, preferably at least one photograph with the mouth closed, and at least one photograph and / or at least one panoramic and / or cephalometric radiograph with the mouth open, preferably at least one photograph with the mouth closed, at least one photograph with the mouth open, at least one photograph of the view of face, at least one photo viewed from the right and at least one photo viewed from the left, right and left being relative to the first user; - the computer analyzes 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; - as soon as the first piece of information has been entered by the first user, the computer analyzes said first piece of information and adapts the displayed page accordingly; - the entry of the first piece of information precedes the display of the second form page by less than 10 minutes; - the first piece of information and / or the second piece of 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 limited duration for wearing an 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.

[0052] Preferably, only input fields where input is required are displayed. In other words, if input is not always required, the computer queries the first user to determine whether the corresponding input field should be displayed.

[0053] 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.

[0054] 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.

[0055] The first piece of information and / or the second piece of information may be of any kind, and in particular may be photographs of said dental arch, X-ray radiographs 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.

[0056] The first piece of information and / or the second piece of information may include information about the first and / or second user, for example data on the age or sex of the first user.

[0057] Preferably, it / they include photos, preferably extraoral, of at least one eyebrow of the first user, preferably in the form of a film. Preferably, the photos include at least one photo of the mouth open, and at least one photo of the mouth open. Preferably, the photos include at least one photo viewed from the front, one photo viewed from the right, and one photo viewed from the left, with right and left being relative to the user.

[0058] Preferably, the first piece of information and / or the second piece of 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.

[0059] Preferably, the first piece of information and / or the second piece of information includes a definition of treatment objectives and / or a definition of a maximum number of orthodontic trays for an orthodontic treatment to be planned.

[0060] The computer preferably includes a memory defining a set of conditional rules determining the second input field, directly or indirectly depending on the first information.

[0061] A conditional rule determining the second input field for the second piece of information directly based on the first piece of 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".

[0062] Conditional rules that indirectly determine the second input field based on the first piece of information are, for example, "if the analysis of a photograph 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 had their teeth cleaned." The photograph, which constitutes the first piece of information, needs to be analyzed to determine the presence of tartar. The second input field is only displayed if the analysis leads to the detection of tartar.

[0063] 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 differ depending on the age of the first user.

[0064] Conditional rules can be ordered in the form of a decision tree.

[0065] In one embodiment, the process comprises, for each first piece of information in a set of first pieces of information, a cycle of steps 01) to 03), said set of first pieces of information preferably comprising more than 10, more than 50, more of 100 and / or less than 1000 first pieces of information, the display or not of the input field of a step 02) of said cycle and / or the nature of the second piece of information accepted by the input field of a step 02) of said cycle depends not only on the first piece of information entered by the user in step 01) of said cycle, but also on at least one first piece of information and / or at least one second piece of information entered during one or more previous cycles.

[0066] The process preferably comprises a single step 04).

[0067] The shape of the second input field is not limited.

[0068] Insofar as a feature following one aspect of the invention is technically compatible with another principal aspect of the invention, it can be applied to that other aspect of the invention.

[0069] In particular, the smoothing characteristics described according to the first main aspect of the invention are potentially applicable to the second main aspect, and vice versa. Specifically, certain terms, such as "basic deformation scenario" or "first smoothed deformation scenario," are used in the description of both main aspects because they refer to similar objects, and possibly to the same objects when both main aspects apply. For these objects in particular, the characteristics according to the first main aspect of the invention are potentially applicable to the second main aspect, and vice versa.

[0070] The invention also relates to: - a computer program comprising program code instructions for execution - steps b) and c), preferably steps a), b) and c), and optionally the first step d) and preferably additional steps d), and preferably an orthodontic appliance design operation for step e) and / or - a step C') and preferably a step A') or B'), preferably a step A') and a step B') and a step C'), and / or - 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 - of steps B), C) and D), and preferably A), when said program is executed by said computer; - a computer storage medium on which such a program is recorded, for example, a memory chip or a CD-ROM, and - a computer on which such a program is loaded, - a set comprising said computer and a device for manufacturing an orthodontic appliance for the implementation of step e).

[0071] Preferably, the computer program includes program code instructions to automate all operations that can be automated.

[0072] Preferably, the computer program further includes program code instructions for cutting the initial model into tooth models and / or determining the final model from the initial model.

[0073] The invention also relates to a system comprising - a three-dimensional scanner capable of creating a "raw" model of the first user's arcade, and - a computer according to the invention, preferably optionally configured to transform said raw model into initial model, optionally with the assistance of a dental practitioner. Definitions

[0074] By "user" is meant any person for whom a process according to the invention is implemented, whether that person is ill or not.

[0075] The term “dental practitioner” means any practitioner of teeth in the broadest sense, which in particular includes orthodontists and dentists.

[0076] 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 a "partial" orthodontic treatment. Without further specification, "orthodontic treatment" generically refers to either complete or partial orthodontic treatment.

[0077] Orthodontic treatment requires the use of one or more orthodontic appliances. Retention treatment intended to maintain teeth in a final position is not considered orthodontic treatment here.

[0078] Orthodontic treatment is planned using a "treatment plan." A distinction is thus made between "orthodontic treatment," which refers to a series of operations that take place in practice, and the "treatment plan," which is the result of the design of the orthodontic treatment. The treatment plan therefore precedes the corresponding orthodontic treatment.

[0079] Orthodontic treatment using orthodontic aligners is the implementation of a treatment plan that defines models for the dental arch in anticipated forms, prior to orthodontic treatment, for different points during the orthodontic treatment. Generating a treatment plan typically includes the design and modeling of one or more orthodontic aligners. An example of aligner design is described in "History of Orthodontics" by Basavaraj Subhashchandra Phulari. The treatment plan thus defines models for the orthodontic aligners to be used, and these models are used to fabricate the corresponding orthodontic aligners. The modeling of the orthodontic aligners can be performed automatically, by computer, or manually, typically by a dental practitioner.

[0080] More specifically, a sequence of models of the user's arch is classically determined, which represent consecutive arch configurations, and a corresponding sequence of orthodontic splint models is determined, allowing the manufacture of orthodontic splints adapted for each modification of the arch configuration from a configuration represented by an arch model to the configuration represented by the next arch model.

[0081] 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.

[0082] An example of software for manipulating tooth models and creating a treatment plan is the Treat program, described on the page https: / / en.wikipedia.org / wiki / Clear_aligners#cite_note-invisalignsystem-10. US5975893A also describes the creation of a treatment plan.

[0083] An "orthodontic appliance" is an appliance adapted for the implementation of orthodontic treatment. An orthodontic appliance may be intended for therapeutic or prophylactic treatment, but also for aesthetic treatment.

[0084] An orthodontic appliance may be, in particular, an archwire appliance, an orthodontic aligner, 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 positioning of the teeth. More specifically, the shape is determined so that, in the functional position, the orthodontic appliance exerts forces tending to move the treated teeth towards their desired positioning.

[0085] A 3D scanner, or "scanner", is a device that allows a model of a dental arch to be obtained.

[0086] The "service position" is the position of an orthodontic appliance, for example an orthodontic aligner, when it has been fixed to the dental arch in order to treat that arch. Typically, the fixation of an orthodontic aligner can be deactivated by the user by simply pulling on the aligner.

[0087] The term "computer" refers to a computing unit, which includes a set of several machines having computing capabilities. This unit may, in particular, be integrated into a scanner, or into a mobile phone, or be a PC-type computer or a server, for example a server remote from the user, for example the "cloud" or a computer located at a dental practitioner's office.

[0088] Typically, a computer includes, in particular, a processor, memory, a human-machine interface typically comprising a screen, and a communication module for internet, Wi-Fi, Bluetooth®, or telephone network connections. 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.

[0089] In a method according to the invention, different computers communicating with each other may be used for different steps, or, preferably, the same computer is used for all steps. The computer is preferably integrated into a mobile phone.

[0090] By "computer form" we mean a set of pages, that is to say consisting of one or more pages, which are displayed on a computer screen and which allow the user to enter information.

[0091] A form is "dynamic" when it adapts based on user information acquired previously, on the displayed page or on previously displayed pages, for example, by means of a dynamic form. It is therefore not predefined like a static questionnaire that requests the same information, in the same way, regardless of the information previously entered, particularly by the user.

[0092] An "input field" is an area on a form page used by the user to enter information into the computer. An input field can be, for example: - a multiple choice question, for example with checkboxes; - an input area for text or a number; - a cursor to move; - a button to click; - an ordered set of buttons and / or checkboxes and / or items to select, for example of the type "dental map", or "teeth map", as shown in figure 8.

[0093] 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 may be different or identical, for example, if the first piece of information only leads to a change in the appearance of the first input field.

[0094] By "model," we mean a three-dimensional digital model. A model consists of a set of voxels, or "points." A model can be, for example, of the type .stl or .Obj, .DXF 3D, IGES, STEP, VDA, or point cloud. Advantageously, such a model, called a "3D" model, can be observed from any angle.

[0095] A "model of an arch" is a three-dimensional digital model that represents an arrangement of a user's teeth. Preferably, the model of an arch also represents other organs of the mouth, and in particular the gums.

[0096] The number of points in an arch model is not limited. In one embodiment, an arch model, and in particular a final model, includes only the points strictly necessary for defining the arrangement of the teeth.

[0097] A "tooth model" is a three-dimensional digital model of a tooth in a user's dental arch. A model of an arch can be segmented 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 segmented into tooth models, with only the tooth models being represented. Computer tools exist for manipulating the tooth models of an arch model. These tools allow constraints to be imposed, in particular to limit the movement of the tooth models to realistic displacements, for example, to prevent adjacent tooth models from interpenetrating.

[0098] The number of points in a tooth model is not limited. In one embodiment, a tooth model includes only the points strictly necessary to define its configuration. In another embodiment, it includes points that may collide with other tooth models.

[0099] A point of a tooth model of the initial model is "in correspondence" with a point of a tooth model of the final model (or of a transition model) if the deformation scenario modifies the position of the point of the tooth model of the initial model so that it coincides substantially with that of the point of the tooth model of the final model at the final time (or of the transition model at the transition time).

[0100] 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 shown in [Fig. 4].

[0101] A "notable point" is a point on an arch or tooth model that can be identified, for example the apex of the tooth or the tip of a cusp, an interdental contact point, i.e. of a tooth with an adjacent tooth, for example a mesial or distal point on the incisal edge of a tooth, or a point at the center of the crown of the tooth, or "barycenter".

[0102] The "slicing" of an arch model into "tooth models" is an operation that allows the representations of the teeth (tooth models) within the arch model to be delimited and made autonomous. Computer tools exist for this purpose. to manipulate tooth models of an arch model. An example of software that allows manipulation of tooth models is the Treat program, described on the page https: / / en.wikipedia.org / wiki / Clear_aligners#cite_note-invisalignsystem-10.

[0103] When an arch model is cut into tooth models, it is also possible to cut other models, for example a gum model.

[0104] 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 can be, for example, a three-dimensional coordinate system, such as an orthonormal one. To determine the arrangement of teeth in an arch model or the configuration of a tooth in the arch, a reference frame fixed relative to the arch model is used. The reference frame can, for example, have its origin at the center of the user's oral cavity.

[0105] The “configuration” of a tooth or tooth model refers to its position and orientation in the reference frame.

[0106] A "deformation scenario" is a set of chronologically ordered transition models. It is therefore the succession of transition models. It can be considered as a kind of 3D film showing how the arcade model deforms in space between the initial model and the final model.

[0107] 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 aligner for orthodontic treatment with orthodontic aligners, and / or a fabrication of an orthodontic appliance will have to be carried out.

[0108] An “orthodontic treatment plan” includes a deformation scenario and the intermediate times defined for this deformation scenario.

[0109] A “stage” is a period in 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.

[0110] A phase can typically comprise between 2 and 150 steps. For example, to correct a drift after orthodontic treatment for malocclusion correction, or "relapse," 2 or 3 orthodontic aligners may be sufficient. A phase for correcting a complex malocclusion may require several dozen orthodontic aligners.

[0111] 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 film 3D modeling shows how the tooth model moves in space, in translation and / or rotation, between the initial and final moments. Determining a deformation scenario by displacement of the tooth models thus involves finding a set of paths for the tooth models in the arch.

[0112] The "kinetic capacities" of a tooth model define the largest physiologically acceptable values ​​for the movement velocities of that tooth model.

[0113] A higher physiologically acceptable 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 type of tooth, or the tooth number. For example, an incisor can tolerate higher movement speeds than a molar.

[0114] A higher physiologically acceptable value for the velocity of a tooth model can be defined based on the number of the modeled tooth, particularly on the basis of statistical data. It can also depend on the user, for example, to take into account the presence of rests.

[0115] A higher physiologically acceptable value for a velocity also depends on the type of motion considered, rotation or translation, and the direction of the motion considered, for example, egression or ingression. Preferably, therefore, higher physiologically acceptable values ​​are defined for several displacement velocities.

[0116] The "movement velocities" of a tooth model include a translational velocity, for example the magnitude of the velocity vector, and a rotational velocity.

[0117] To account for the different behavior of a tooth depending on the type of movement, the travel speeds may include: - the translational velocities along the different axes of a fixed reference frame relative to the arch model, from a point linked to the tooth model, preferably the centroid of the tooth model, and - the rotational speeds of the tooth model around each of said axes.

[0118] To take into account the different behavior of a tooth depending on the direction of movement, the speeds of movement can further include said speeds in translation and in rotation by distinguishing each time the direction of the speed, for example to distinguish egression and ingression.

[0119] A speed of movement of a tooth model corresponds to an anticipated speed of movement for the modeled tooth, according to an orthodontic treatment plan.

[0120] A deformation scenario is "smoothed" when a velocity parameter is reduced, preferably minimized, preferably 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 - a speed representative of the speed of movement of said slowed-down tooth model, preferably an average speed between the initial and final instants, and / or - the difference between said highest value of said speed of movement and said lowest value of said speed of movement of said slowed-down tooth model between the initial and final instants, 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.

[0121] A “representative velocity” of a tooth model is a velocity determined from one or more displacement velocities of said tooth model, for example the magnitude of the translational velocity vector of the barycenter of the tooth model, or of the rotational velocity vector of a notable point on the surface of the tooth model.

[0122] A "representative distance" of the displacement of a tooth model is a distance calculated from the displacement of one or more points of the tooth model and / or one or more points linked 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.

[0123] A "correct occlusion" is an arrangement of the teeth of the two dental arches that permits acceptable contact between these two arches according to the rules of orthodontics. In particular, with a correct occlusion, the cusps of the teeth of the upper arch are not in contact with the cusps of the teeth of the lower arch when the mouth is closed. The teeth of the two arches "interlock," with the cusps of the teeth of one arch fitting into the grooves or interdental spaces of the teeth of the other arch.

[0124] By "image" is meant a two-dimensional image, such as a photograph or an image extracted from a film. An image is made up of pixels.

[0125] The term “image of an arch,” “view of an arch,” “representation of an arch,” “scan of an arch,” or “model of an arch” means an image, view, representation, scan, or model of all or part of said dental arch, preferably representing at least 2, preferably at least 3, and preferably at least 4 teeth. [Fig. 2] shows an example of a view of an arch model comprising 5000 points.

[0126] "Metaheuristic" methods are known optimization methods. They are preferably chosen from the group formed by - 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, tabu search, and the GRASP method; - the kangaroo algorithm, the Fletcher and Powell method, the noise method, stochastic tunneling, random restart hill climbing, the cross-entropy method, and - hybrid methods between the metaheuristic methods mentioned above.

[0127] A "statistical processing" is a process which, when applied to a set of so-called "historical" data, makes it possible to determine characteristics specific to that set, for example, a mean, a standard deviation, or a median value. The tools of statistical processing are well known to those skilled in the art.

[0128] "Deep learning devices", also known as "deep learning" algorithms, are also well known to those skilled in the art. They include "neural networks" or "artificial neural networks".

[0129] The expert knows how to choose and train a neural network according to the task to be performed.Specifically, a neural network can be chosen from: - networks specialized in image classification, called "CNNs" ("Convolutional Neural Networks"), for example AlexNet (2012), ZFNet (2013), VGGNet (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), - networks specialized in the localization and detection of 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 (R-CNN). 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.), Dense et al., 2017), Hung et al. 2017, DPN (Chen et al.), 2017, YOLO9000 (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 et al.), 2012 - networks specializing 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).

[0130] The above list is not exhaustive.

[0131] Training a neural network consists of confronting it with a training base containing information on the two types of object that the neural network must learn to "match", that is to say, to connect one to the other.

[0132] Training can be done from a training base consisting of recordings each containing a first object of the first type and a corresponding second object of the second type.

[0133] Alternatively, training can be carried out using a training set consisting of recordings, each containing either a first object of the first type or a second object of the second type, each recording, however, containing information relating to the type of object it contains. Such training techniques are described, for example, in the article by Zhu, Jun-Yan, et al., “Unpaired image-to-image translation using cycle-consistent adversarial networks.”

[0134] 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.

[0135] The quality of the analysis performed by the neural network depends directly on the number of records in the training set. Preferably, the training set contains more than 10,000 records and / or fewer than 10,000,000 records.

[0136] “Understand”, “include” or “present” must be interpreted in such a way broad, non-limiting, unless otherwise indicated. Brief description of the drawings

[0137] Other features and advantages of the invention will become apparent from the reading of the detailed description which follows and from the examination of the attached drawing in which: - [Fig.1] the [Fig.1] schematically illustrates a method according to the first main aspect of the invention; - [Fig.2] [Fig.2] represents an example of a model acquired with a portable scanner integrated into a mobile phone and comprising 5000 points; - [[Fig.3]] [Fig.3] represents an example of an arch model cut into tooth models, referenced 32 (only the tooth models are shown); - [Fig.4] [Fig.4] illustrates the tooth numbering used in dentistry; - [Fig.5] Fig.5 schematically illustrates a method according to the second main aspect of the invention; - [[Fig.6]] Fig.6 schematically illustrates a form page for a process according to the third main aspect of the invention; - [Fig 7] Fig 7 schematically illustrates a process according to the third main aspect of the invention; - Figure 8 Figure 8 represents an example of a dental card usable in a dynamic form according to the invention.

[0138] Further details and advantages of the invention are provided in the detailed description that follows, which is provided for illustrative and not limiting purposes. Detailed description

[0139] The method according to the first and second aspects of the invention aims to generate a plan for orthodontic treatment extending from an initial time to a final time. It can plan a complete or partial orthodontic treatment, that is to say, insufficient to achieve, on its own, the configuration desired by the user.

[0140] 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 reposition them, or a phase of alignment of the barycentres of the teeth following the curve of the arch which supports them, or a phase of rotation of the teeth around their barycentres.

[0141] In one embodiment, the method is implemented several times, for each of the phases of a complex orthodontic treatment.

[0142] 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).

[0143] The computer, preferably a computer-assisted dental practitioner, also determines the final model for the last phase, or "final end-of-phase model", as for step a). This model represents the dental arch as desired at the end of the complex orthodontic treatment.

[0144] In step B'), the computer or a computer-assisted dental practitioner determines, by moving 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').

[0145] The end-of-phase model of a phase represents an objective to be achieved at the end of that phase. The beginning-of-phase model of a phase is the end-of-phase model of the phase preceding it in time.

[0146] In a preferred embodiment, the computer defines the end-phase models, except possibly the last one, based on the first beginning-phase model and the last end-phase model. For this purpose, the orthodontic rules necessary to define the phases are taught beforehand.

[0147] For example, in the preceding example, after determining which tooth models need to be moved, by comparing the first phase-start model and the last phase-end model, the computer can move the tooth models from the first phase-start model until they are sufficiently separated so that their centroids can then be aligned along the curve of the dental arch, and then rotated so that the extrados of the tooth models are substantially aligned. The resulting model can be considered the first phase-end model.

[0148] Starting 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-phase model.

[0149] Starting 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.

[0150] To search for end-of-phase patterns, the computer can use optimization algorithms, in particular by simulated annealing.

[0151] In step C'), the computer implements, for each phase, a process according to the first and / or second aspect(s) of the invention. For each instance of this process, the initial model used is the beginning model of said phase and the final model used is the end model of said phase.

[0152] An example of a procedure according to the first embodiment is now described in detail. In this example, the orthodontic treatment to be planned is considered to consist of only one phase.

[0153] In step a), the initial and final models are generated. Initial model

[0154] The initial model is a three-dimensional digital model representing the teeth to be moved, in their arrangement on the dental arch planned at the beginning of the orthodontic treatment, i.e. at the initial moment.

[0155] The initial model is preferably prepared from measurements taken on the user's teeth or on a physical model of his teeth, for example a plaster model.

[0156] 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 beginning of the orthodontic treatment.

[0157] The initial model is preferably created using professional equipment, for example, a 3D scanner, preferably operated by a dental practitioner, for example, an orthodontist or an orthodontic laboratory. In an orthodontic practice, the user or a physical model of their teeth can advantageously be positioned precisely, and the professional equipment can be refined. This results in a highly accurate initial model. The initial model preferably provides information on tooth positioning with an error of less than 0.5 mm, preferably less than 0.3 mm, and preferably less than 0.1 mm.

[0158] In one embodiment, the tooth arrangement 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 or two months before the initial time. The initial model is then updated, preferably by deforming, preferably by shifting one or more tooth models, to correspond to the tooth arrangement at the initial time. In particular, the initial model may be deformed to correspond to one or more photographs of the dental arch taken less than one week before the initial time.

[0159] 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, the computer manipulation of an initial model may be slowed down if the number of points is high.

[0160] In one embodiment, the initial model comprises fewer than 5,000 points, or even fewer than 1,000 points, which speeds up the implementation of the process. In particular, the time required to generate a deformation scenario, especially following the first optimization algorithm described below, depends on the number of points from the initial model used to determine the first distance.

[0161] An initial model with fewer than 5000 points, or a "coarse model," can in particular result from a simplification of a detailed initial model, preferably acquired with a 3D scanner, for example, with 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.

[0162] 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 includes all points that correspond to a point of the final model. Preferably, the initial model includes only points that correspond to a respective point of the final model. In one embodiment, the initial model does not include points whose position cannot be affected by orthodontic treatment. In one embodiment, the initial model includes only a set of points strictly sufficient to define the position and orientation in space of each tooth model. For example, it includes, for each tooth model, only three notable, non-aligned points.Preferably, said set of points also includes points that may collide with adjacent tooth models, for example points of a tooth model that, in the initial model, are close to an adjacent tooth model.

[0163] A concordance can be established between the tooth models in the fine model and in the coarse model, which makes it possible, if a deformation scenario has been generated with an initial coarse model and thus includes coarse transition models, to reconstruct fine, high-precision transition models, for example usable for manufacturing an orthodontic splint.

[0164] To deform an initial model, the latter is cut up so as to generate a digital three-dimensional model for each tooth, or "tooth model". Then the tooth models are moved.

[0165] Preferably, the initial model is also cut so as to generate a digital three-dimensional model for the gingiva, or "initial gingiva model". Final model

[0166] The final model is a three-dimensional digital 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.

[0167] 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 time. The final model may be less precise than the initial model. The position of a tooth model can indeed be defined by the position of a notable point of that tooth model, for example, by the position of its centroid. The orientation of a tooth model can be defined by two non-parallel vectors, whose common origin is, for example, the centroid of the tooth model. Three notable points, for example, the centroid and two points not aligned with the centroid of a tooth model, may therefore suffice to define the configuration of a tooth. The final model can thus consist of a set including, for each tooth model, coordinates of three notable points of that tooth model.

[0168] The determination of the positioning of a tooth is described for example 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.

[0169] The final model can result from a deformation of the initial model by displacement of tooth models.

[0170] 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.

[0171] In a preferred embodiment, at 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, based on the planned orthodontic treatment.

[0172] In one embodiment, a computer memory contains a "history" 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 the tooth arrangements of historical users at the beginning and end of "historical" orthodontic treatments.

[0173] The computer analysis of the initial model can then consist of - search the database for the closest historical initial model, that is, the one that most closely resembles the initial model for which a final model is being sought, then - choose, for the said final model, the historical final model associated with the closest historical initial model.

[0174] 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 also for the user.

[0175] 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 bearing said number for a historical user, and - the output consists of records, each containing a tooth number and data defining an ideal configuration for a tooth bearing said number.

[0176] In particular, a network specialized in image classification can be used from among those mentioned above.

[0177] 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 distance between the vertices of adjacent tooth models, or specify an orientation for each tooth.

[0178] In one embodiment, the initial model is analyzed for - 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; - determine, on said baseline, the theoretical position and orientation of each tooth, according to predefined rules.

[0179] Algorithms for determining a baseline and tooth configuration are well known, particularly for obtaining panoramic images by tomography. One can notably use a mean square value, with a typical function in ax4+bx2+c = 0.

[0180] Predefined rules may, for example, specify, according to the length and curvature of the arch, how the different teeth should be distributed and oriented along said baseline.

[0181] The predefined rules can, for example, be obtained by statistical processing of historical data providing, as a function of length and curvature, said distribution and said orientation of "historical" teeth from historical arches of historical users.

[0182] The computer can advantageously determine the final model very quickly, without human intervention.

[0183] Algorithms for comparing the shapes of two models are well known. For example, the ICP or "Iterative closest point" algorithm is well known, described in particular in the online encyclopedia Wikipedia.

[0184] In a preferred embodiment, the initial arch model is cut to generate an initial gingival model, and the arrangement of the tooth models in the final model is checked to ensure compatibility with the initial gingival model. This check can be performed by a dental practitioner and / or by a computer, autonomously or under the control of an operator, for example, a dental practitioner. Preferably, it is checked whether the tooth models in the final model penetrate the initial gingival model and / or whether a physiologically unrealistic gap has appeared. between the tooth models in the final model and the initial gingival model. In the case of such a penetration or gap, the initial gingival model is transformed into a final gingival model in such a way as to eliminate said penetration or gap.

[0185] In step b), the computer determines a series of successive deformations of the initial model leading to a final model.

[0186] 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.

[0187] The number of transition models is preferably greater than 3, preferably greater than 10, and / or less than 1000. It is preferably determined such that no point in the arch model moves more than 1000 pm, 500 pm, or 100 pm between two consecutive transition models, and / or such that at least one point in the arch model moves more than 10 pm, 50 pm, or 100 pm between two consecutive transition models. This improves the accuracy of the deformation scenario.

[0188] Each elementary deformation must comply with a set of constraints. The constraints include: - anatomical constraints, for example to impose that, during elementary deformation, a tooth model cannot penetrate an adjacent tooth model, and / or that the positions of one or more points of a tooth model must be contained within a defined envelope around the tooth model, and / or that the translational velocity of a tooth model along a direction and in a sense must remain below a defined upper limit for a translational velocity, and / or that the rotational velocity of a tooth model around an axis and in a sense must remain below a defined upper limit for a rotational velocity; - preferably, clinical constraints imposed by orthodontic rules and / or the dental practitioner, for example, imposing immobility of one or more tooth models during elementary deformation, 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 some movements over others, and / or imposing an order for moving tooth models, and / or imposing correct occlusion, and / or authorizing or prohibiting tooth stripping, and / or authorizing limited tooth stripping, and / or authorizing or prohibiting the extraction of one or more teeth, and / or imposing the most homogeneous possible movement of one or more teeth,that is to say, limiting as much as possible the variations in speed of movement of one or the other, several 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; - preferably, prescription constraints imposed by the user due to, for example, 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 allowing or prohibiting tooth filing, and / or allowing limited tooth filing, and / or allowing or prohibiting the extraction of one or more teeth, and / or allowing or prohibiting the use of one or more auxiliary orthodontic appliances.

[0189] The set of constraints imposed on an elementary deformation may differ depending on the arch model to 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, whose positions and orientations may themselves be modified with each elementary deformation.

[0190] In one embodiment, the set of constraints includes constraints that can lead to an elementary deformation not directly applicable in reality. In particular, the set of constraints may allow limited penetration of one tooth model into an adjacent tooth model. The resulting elementary deformation then requires, in order to be operational, the filing of one or both teeth whose tooth models interpenetrate each other. Preferably, the computer informs the dental practitioner of the need to perform such filing.

[0191] All or part of the constraints can be determined from information entered by the user, preferably using 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.

[0192] The user can in particular specify - a maximum number of orthodontic aligners for orthodontic treatment, i.e. a maximum number of intermediate moments; - the numbers of the teeth that must remain still during orthodontic treatment, in particular by clicking on the boxes bearing the numbers of these teeth.

[0193] Figure 8, for example, represents a dental chart. The user can select one or more teeth by clicking on the representation of the number of said teeth on this chart.

[0194] The page shown in [Fig.6] further enables 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.

[0195] The determination of 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.

[0196] Preferably, the initial model is sliced ​​by the computer. Slicing the initial model to determine the models of the organs it represents is a well-known operation. Preferably, the initial model is sliced ​​to define at least the parts that represent the teeth, or "tooth models." The tooth models can be defined as described, for example, in international application PCT / EP2015 / 074896.

[0197] To determine an elementary deformation, the generator displaces tooth models, while respecting all the constraints. The elementary deformations comprise, and are preferably exclusively, displacements of tooth models.

[0198] Determining an elementary deformation is rapid, even if the tooth models are moved randomly, particularly if the number of points in the initial model is small. However, determining a deformation scenario can be very time-consuming.

[0199] To accelerate 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 favor tooth model displacements 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 traveled by several tooth models, preferably taking into account all tooth models, and - only deviate from this path in case of collision with an adjacent tooth pattern.

[0200] Preferably, the generator implements a first optimization algorithm, preferably a metaheuristic method, preferably evolutionary, preferably by simulated annealing. The first optimization algorithm can in particular be chosen from among the algorithms listed above in the definition of metaheuristic methods.

[0201] The first optimization algorithm can implement the following steps: i) creation of a scenario "to be tested", i.e. application, to the initial model, of a set of successive elementary deformations "to be tested", preferably exclusively by displacement of 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 to a first threshold in order to obtain a first score for the scenario to be tested; (iv) if the first score is insufficient, for example higher than a predetermined minimum first score, modification of the scenario to be tested and resumption at step (i).

[0202] The cycle of steps i) to iv) is thus repeated until the score of the scenario to be tested is satisfactory, that is to say, until 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".

[0203] At step i), the scenario to be tested can be generated randomly.

[0204] It is preferably created taking into account the scores obtained during the cycles Previous scenarios, for example, can be used to avoid applying basic deformations that do not produce good scores. Ideally, the creation of a test scenario is guided by rules used by dental practitioners to generate an orthodontic treatment plan. For example, the test scenario might be chosen to favor tooth model movement along the shortest path to the final model, deviating from this path only in case of a collision with an adjacent tooth model.

[0205] In step i), the scenario to be tested can, 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 "lengthens" from one cycle to the next until an acceptable scenario is reached. In one embodiment, such a construction of the deformation scenario is stopped if said first distance becomes greater, by a predetermined margin, possibly zero, than that of a previously determined scenario to be tested.

[0206] 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.

[0207] In step iii), the first score can, for example, be the inverse of the difference between said first distance and the first threshold. The first threshold can be zero, so that the cycle from steps i) to iv) leads to the final model.

[0208] Preferably, the generator generates several arch deformation scenarios and then chooses the one that minimizes a distance from an ideal deformation scenario, for example, one inducing minimal total deformation. Such a deformation scenario is called the "optimal deformation scenario".

[0209] Preferably, the generator implements a second optimization algorithm to search for an optimal deformation scenario. The second optimization algorithm is preferably a metaheuristic method, of Evolutionary preference, preferably by simulated annealing. The second optimization algorithm can be chosen from among those listed above in the definition of metaheuristic methods.

[0210] The second optimization algorithm can implement the following steps: i') creation of a deformation scenario "to be tested", preferably using the first optimization algorithm; ii') measurement of a second distance measuring a difference between the deformation scenario to be tested and an ideal arch deformation scenario; iii') comparison of 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 for example 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 predetermined minimum second score, modification of the deformation scenario to be tested and resumption at step (i').

[0211] The cycle of steps i') to iv') is thus repeated until the score of the deformation scenario to be tested is satisfactory, that is to say, until 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.

[0212] The second distance can be, for example, the cumulative Euclidean distance traveled by a set of points in the initial model, for example, all the points in 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 can, for example, be zero and the second score equal to the second distance. The set of points preferably includes one, preferably more than one, more than two points for at least one tooth model in the initial model, preferably at least two, preferably at least three tooth models in the initial model, preferably for each tooth model in the initial model. The second distance can 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.

[0213] If the second threshold is zero, the second distance can define the second score. Step iii') is then unnecessary. It is therefore optional.

[0214] Preferably, the second distance takes into account one or more requirements dictated by the user. For example, the user may have filled out a computer questionnaire on the computer to specify these requirements, for example to specify the relative importance they place on the speed of processing orthodontic, and / or the pain generated by the orthodontic treatment, for example measured by a pain coefficient, and / or the comfort during the orthodontic treatment, for example measured by a comfort coefficient, and / or the cost of the orthodontic treatment.

[0215] Comfort can in particular refer to the aesthetic impact of orthodontic treatment.

[0216] 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, pain coefficient, and cost are preferably minimal in an ideal deformation scenario, so that the basis for comparison of these criteria can, for example, be equal to 0. The comfort coefficient is maximal in the ideal deformation scenario, so that the basis for comparison of this criterion can, for example, be the maximum possible value for this coefficient.

[0217] 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 into the computer implementing rules typically applied by dental practitioners or determined by the computer through statistical processing. The deformation scenario to be tested can, for example, be compared to historical arch deformation scenarios in a database in order to determine a similar historical deformation scenario and inherit information on the duration, pain coefficient, comfort coefficient, and / or cost.

[0218] 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.

[0219] 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 from 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, i.e., 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 cost coefficient) associated with this deformation scenario.

[0220] For example, if - li denotes the distance traveled by a point Pi of a tooth model of the dental arch according to the deformation scenario to be tested, - ki designates a weight for a duration coefficient, for example between 1 and 10, preferably provided by the user, depending on the importance they place on the speed of orthodontic treatment, - k2 designates a weight for a pain coefficient, for example between 1 and 10, preferably provided by the user, depending on the importance they attach to the pain that the orthodontic treatment will potentially inflict on them, - k3 designates a weight for a comfort coefficient, for example between 1 and 10, preferably provided by the user, depending on the importance they place on comfort during orthodontic treatment, and - kl designates a weight for a cost coefficient, for example between 1 and 10, preferably provided by the user, depending on the importance they attach to the cost that will be generated by the orthodontic treatment, - C designates a prescription factor taking into account the duration coefficients Ci, and / or pain coefficient C2, and / or comfort coefficient C3, and / or cost coefficient 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: - the sum of 11, for a set of N points "i", N preferably being greater than 10; or - the product of the sum of the 11, for a set of N points "i", by the prescription coefficient.

[0221] In one embodiment, a deformation scenario, preferably an optimal deformation scenario, is first sought using a crude initial model, for example, containing 100 points. Then, the initial, transition, and final models are completed to verify the absence of unacceptable collisions, i.e., collisions that cannot be eliminated by filing, in the case where filing is permitted. In the event of an unacceptable collision, i.e., if the computer detects that the deformation scenario includes an interpenetration of adjacent tooth models beyond an acceptable limit, points are added to the initial model, and the search is repeated with the simplified initial model from the previous cycle to which the points have been added.

[0222] In a preferred embodiment, the initial arch model is cut so as to generate an initial gingival model, and, successively for each model During the transition phase, we check if the arrangement of the tooth models in the transition model is compatible: - with the initial gum model, for the first transition model, or - with the gum model in the previous transition model, for subsequent transition models.

[0223] This verification can be performed by a dental practitioner and / or by a computer, either autonomously or under the control of an operator, for example, a dental practitioner. Preferably, it is checked whether the tooth models in the transition model under consideration penetrate the gingival model and / or whether a physiologically unrealistic gap has appeared between the tooth models and the gingival model. In the case of such penetration or such a gap, the gingival model is modified to eliminate said penetration or gap. Each transition model thus presents a representation of the gingiva compatible with the arrangement of the tooth models.

[0224] At step c), the computer determines the final time for the scenario determined in step b).

[0225] For this purpose, the deformation scenario can for example be compared to historical arch deformation scenarios from a database providing, for each historical arch deformation scenario, the associated treatment time.

[0226] The duration of the scenario, and therefore the final time, can then be determined from the duration of a similar historical deformation scenario, for example be chosen as equal to the duration of the similar historical deformation scenario.

[0227] The steps of orthodontic treatment in the deformation scenario from step 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 fabrication of an orthodontic appliance intended for the user will have to be carried out.

[0228] Modifying a user-worn orthodontic appliance may involve altering its structure or shape, or replacing it with a new orthodontic appliance. In one embodiment, the intermediate moments are the times at which orthodontic aligner replacements are planned.

[0229] The intermediate moments are preferably moments when a change of orthodontic aligner is planned.

[0230] The intermediate times can 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 constant and / or equal to the maximum duration of use of an orthodontic appliance, for example the duration of use of an orthodontic aligner.

[0231] The transition models at intermediate times are the "intermediate models".

[0232] 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.

[0233] In one embodiment, the number of intermediate models is equal to the number of transition models.

[0234] Preferably, the intermediate and final times are determined based on the movements of the tooth models according to the deformation scenario and the orthodontic appliances envisaged. The possibilities for tooth movement according to the various possible translational and rotational movements are indeed different depending on the tooth number considered and the orthodontic appliance envisaged. For example, due to the properties of the polymer used to manufacture the orthodontic aligners, a translation for the intrusion or extrusion of a tooth between two steps may be limited to less than 0.1 mm, a rotation may be limited to less than 3° of rotation, tip, or torque, etc.These constraints related to the properties of orthodontic aligners allow, by knowing the necessary displacements between the initial and final models, the calculation of intermediate times and a final time compatible with the orthodontic aligners and the orthodontic treatment.

[0235] The method for determining the intermediate times and the final time is not limiting. The rules conventionally used by dental practitioners to choose the most suitable intermediate times can be applied by the computer.

[0236] In a preferred embodiment, the computer proceeds as follows:

[0237] The initial model is cut into tooth models and the elementary deformations of the Deformation scenarios result from displacement of tooth models, in translation and / or rotation. Preferably, the number of each tooth represented in the initial model is identified during the cutting of the initial model, either by labeling performed by an operator or, preferably, by pattern recognition performed by a computer, for example, using a neural network. Such computer-based pattern recognition is well known to those skilled in the art.

[0238] A tooth exhibits kinetic displacement capacities that vary depending on the nature of that tooth. In particular, the highest physiologically acceptable values ​​for the displacement velocities, in translation or rotation, of a tooth in the different spatial directions depend on the tooth number. These displacement capacities allow for the definition of constraints for each set of constraints imposed for each elementary deformation. In particular, these constraints can establish, for each tooth model, upper limits for Speeds of movement, in translation and rotation, along the different axes of a reference frame, for example an orthonormal coordinate system fixed relative to the user's skull. The upper limit of a speed of movement can be, in particular, the highest physiologically acceptable value for that speed.

[0239] The kinetic capacities for tooth movement can be determined by statistical analysis, in particular by analyzing panoramic radiographs and / or cephalometric radiographs of historical users. They can also be determined by analyzing panoramic radiographs and / or cephalometric radiographs of the user implementing the method. In one embodiment, the kinetic capacities for tooth movement are determined by statistical analysis of historical data, i.e., data relating to historical users, and then the values ​​obtained are refined according to the user for whom the method is being implemented, for example, to take into account their bone density per tooth and / or the condition of their gums.

[0240] 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 frame, the computer can therefore determine the said upper limits for each tooth model.

[0241] 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, that is, 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 execution of the deformation scenario. It is also possible to determine the angular sector traversed, around each of the three axes of the reference frame, by each tooth model during the execution of the deformation scenario.

[0242] For each tooth model, considering that it moves at the highest possible speeds while respecting the constraints, i.e. as much as possible at the upper limits of these speeds defined by the constraints, it is thus possible to determine the smallest possible time for this tooth model to change its configuration from the initial model to the final model, according to the deformation scenario.

[0243] The tooth model that imposes the longest duration is called the "limiting tooth model" because the deformation scenario cannot be executed more quickly. 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.

[0244] The limiting tooth model can be defined by analyzing the paths of the different tooth models, according to the deformation scenario, preferably by the computer. Alternatively, the limiting tooth model can be predefined, for example because it is classically identified as limiting for orthodontic treatment.

[0245] The deformation scenario is then fragmented so that the limiting tooth model can follow its path, the intermediate moments 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 moments at which the orthodontic appliance worn by the user must be adjusted so that the limiting tooth model can follow its path.

[0246] In particular, in the context of orthodontic treatment using aligners, an aligner only allows limited tooth movement. For example, its limited elasticity may require that any point on any tooth always move less than approximately 1 mm, or even less than 0.5 mm. In other words, as soon as any point on a tooth has moved 1 mm since the aligner was fitted, the aligner must be changed. Knowing the maximum possible tooth movement with an aligner thus makes it possible to determine the intermediate point at which the aligner must be changed.

[0247] For example, in orthodontic treatment where a molar needs to move 3 mm and a canine needs to move 4 mm, with the upper limit for the molar's movement rate 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. Intermediate points can be chosen to mark each time a movement of 1 mm from the previous (intermediate or initial) point if the orthodontic aligners are designed to ensure a movement of 1 mm each. The intermediate points are therefore, if t0 is the initial point, t0 + 1 month, t0 + 2 months, and t0 + 3 months.

[0248] The orthodontic treatment plan thus defined may, however, impose a very rapid path for a molar model, 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, address this problem.

[0249] 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 - for the limiting tooth model, adherence to the path determined according to the deformation scenario determined in step b), and - for at least one other tooth model than the limiting tooth model, called "slowed-down tooth model", a reduction, preferably an optimization of said speed parameter.

[0250] Preferably, the new set of constraints imposes upper limits for movement velocities lower than those obtained according to the orthodontic treatment plan from step c). In other words, the set of constraints imposes that the velocities 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 velocities of the slowed tooth, an upper limit lower than the upper limit imposed for establishing the orthodontic treatment plan from step c).

[0251] Smoothing advantageously improves the predictability of treatment, i.e., increases the conformity between the orthodontic treatment plan and its subsequent translation in the user's mouth.

[0252] Preferably, the amplitude of the velocity variation during the movement of the slowed tooth is limited during the treatment period; that is, the difference between the highest and lowest velocities reached during the treatment period is reduced. To this end, the computer can further impose one or more minimum values ​​on one or more velocities of the slowed tooth model, i.e., lower limits for said velocities.

[0253] 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, averaged 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.

[0254] The deformation scenario thus smoothed advantageously limits the risks for the user.

[0255] Smoothing can be performed for several teeth simultaneously when the new set of constraints imposes that the speeds of several slowed-down tooth models cannot reach the maximum values ​​that the nature of the teeth they model would allow.

[0256] In a preferred embodiment, the smoothing is carried out successively for several slowed-down tooth models.

[0257] At each iteration of step d), the computer adds to the constraints the requirement to adhere to a new path for a tooth model whose path was not imposed in the previous steps d). Smoothing is preferably performed tooth by tooth, preferably starting with the teeth for which rapid movement is most likely to be detrimental to the user. In other words, preferably, the first smoothing operations concern the teeth for which rapid movement is most detrimental to the user.

[0258] In the example above, the generator can thus search for a smoothed deformation scenario, preferably optimal, as described above, by requiring that the tooth model representing the molar follow the path determined according to the deformation scenario determined in step b) and that the instantaneous velocity of the tooth model representing the canine does not exceed the upper limit defined for a canine by more than 10% at any time. It then searches for yet another smoothed deformation scenario, preferably optimal, as described above, by requiring that the tooth models representing the canine and the molar follow their respective paths determined according to the previous smoothed deformation scenarios and that the instantaneous velocity of a tooth model representing, for example, an incisor does not exceed, for example, the upper limit defined for an incisor by more than 10% at any time.

[0259] Smoothing can be repeated for each tooth. If smoothing is unsuccessful, the speed constraint, for example limiting the speed variation to less than 10% of the average speed, can be eased. It is also possible to reuse previously performed smoothing, by easing the speed constraints for those previous smoothing operations.

[0260] In one embodiment, the computer implements an optimization algorithm to test several sets of constraints to be imposed on the elementary deformations, and to deduce an optimally smoothed deformation scenario, that is, one in which the highest values ​​reached for the velocities of the slowed-down tooth model are as low as possible. The range of possible velocities is advantageously reduced to the maximum.

[0261] The computer can also, or alternatively, present the different smoothed deformation scenarios to a dental practitioner so that the latter can choose the smoothed deformation scenario he prefers. The dental practitioner's selection criteria can also be programmed into the computer so that the computer can choose a deformation scenario.

[0262] 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 aligners. The design It can be done by computer, possibly with a dental practitioner. Manufacturing can be carried out using any suitable manufacturing machine.

[0263] As is now clear, the invention makes it possible to carry out a partial or complete orthodontic treatment plan very quickly. Tests have shown that a deformation scenario of less than 10 minutes can be determined by the computer and then broken down by the computer to obtain a high-quality treatment plan that complies with the user's instructions. Furthermore, smoothing the speeds helps to limit the risks to the user's health. Smoothing process

[0264] The smoothing process described above can be advantageously generalized to a process comprising steps A) to D), illustrated in Fig 5.

[0265] In step A), to generate or retrieve the initial and final models, we preferably proceed by following step a).

[0266] In step B), the definition of the measured distance for a tooth model can be arbitrary.

[0267] For example, after superimposing the initial and final models so that the stationary parts of the arch coincide, one can measure - the Euclidean distance between a point of the initial model, in particular a notable point, for example the barycentre, and the corresponding point of the final model; - the cumulative Euclidean distance between several points, preferably notable ones, of the initial model and the corresponding points of the final model.

[0268] A distance resulting from simple measurements of the difference in tooth model configurations between the initial and final models, 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 for finding the limiting tooth. In one embodiment, no deformation scenario is determined before the first smoothed deformation scenario.

[0269] After superimposing the initial and final models so that the stationary parts of the arch merge, one can, for example, measure the distance traveled by one or more points, preferably notable ones, according to a basic deformation scenario between the model and the final model, preferably as defined according to the first main aspect of the invention.

[0270] The distance traveled for a set of points of the tooth model according to a basic deformation scenario, as in 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.

[0271] The distance measurement is preferably carried out by a computer, autonomously.

[0272] The travel time for a tooth model can be evaluated Roughly speaking, for example, by dividing the distance measured for a tooth model by a constant speed fixed for that tooth model. The speed assigned to a tooth model is preferably determined based on the number of the modeled tooth and / or based on the physiological movement capabilities of the modeled tooth.

[0273] In an advantageous embodiment, the speed assigned to a tooth model is variable depending on the time considered. In particular, it can increase from the initial time, for example for more than 5 days from the initial time, and / or it can decrease as an estimate of the final time approaches, for example at least during the 5 days preceding the final time estimate. Preferably, it is lower for times close to the initial time and the final time estimate.

[0274] Said constant velocity may be a velocity representing one or more displacement velocities of one or more points of the tooth model. It may, for example, be the magnitude of the translational velocity vector of the barycenter of the tooth model.

[0275] The travel time for a tooth model can be evaluated more precisely. 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).

[0276] The elementary time between two successive configurations of the tooth model can, for example, be determined 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 times determined between the different successive configurations from the initial configuration to the final configuration.

[0277] The travel time of the distance is preferably carried out by a computer, autonomously, that is to say without human intervention, preferably by the computer which implemented the previous step.

[0278] 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. moving the limiting tooth that it models fixes the shortest possible duration for orthodontic treatment.

[0279] The duration associated with the limiting tooth model defines the duration of the orthodontic treatment. It can be added to the initial time to define the final time.

[0280] The comparison of durations is preferably carried out by a computer, autonomously, preferably by the computer which implemented the previous steps.

[0281] In a preferred embodiment, for each tooth model and for each type of movement (intrusion / egression, mesialization / distalization, lingualization / vestibularization, tip, torque, and rotation), a distance to be traveled between the initial and final configurations is calculated, and this distance is divided by the maximum velocity. The longest duration determines the limiting tooth model.

[0282] At step D), the computer determines the first smoothed deformation scenario, preferably so as to reduce, preferably minimize a said velocity parameter.

[0283] 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 displacement velocity attained for at least one tooth model other than the limiting tooth model, or "first slowed-down tooth model".

[0284] The first slowed tooth model models a "first slowed tooth". The first slowed 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 speed of movement is most critical for the user's health, 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 tooth models other than the limiting tooth model.

[0285] Regardless of the embodiment, step D) is preferably repeated, changing each time the tooth model that is slowed down, imposing on each occurrence of step D) that the tooth models that were slowed down in previous steps D) follow the path defined in those previous steps D), as described for step d).

[0286] The order in which the tooth models are successively slowed down is preferably determined according to utility criteria defined by the dental practitioner and / or the user.

[0287] After step D), the process may include a step e) of designing and manufacturing at least one orthodontic appliance, in particular an orthodontic splint, according to the first smoothed orthodontic treatment plan. Examples

[0288] In step A), the computer retrieves an initial model resulting from a scan of the user's arcade, with an optical scanner.

[0289] The computer-assisted dental practitioner, or the computer operating autonomously, determines a final model.

[0290] In steps B) and C), the computer-assisted dental practitioner, or the computer operating autonomously, 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 distance traveled) and the kinetic capacities (to determine the travel time) of the tooth models.

[0291] Alternatively, the computer-assisted dental practitioner, or the computer in autonomy, 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.

[0292] Once the limiting tooth pattern has been identified, the process preferably tries to move the other tooth patterns as slowly as possible.

[0293] At step D), the computer-assisted dental practitioner, or the computer operating autonomously, selects the "slowed-down tooth model", preferably the tooth model whose slowing down is most useful for health and / or to meet user prescriptions.

[0294] To determine the first smoothed deformation scenario, the computer searches for a set of successive elementary deformations that transform, by shifting tooth models, the initial model at the initial time into the final model at the final time, and minimizes the velocity parameter for the decelerated tooth model. It preferably implements a conventional optimization algorithm, preferably a metaheuristic method, preferably chosen from among the methods described above.

[0295] The cost function to be minimized may, in particular, be the highest speed of movement reached by the slowed tooth model between the initial and final instants. 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.

[0296] In a substantially equivalent manner, optimization can also be achieved by defining the sets of constraints imposed for the elementary deformations such that they all require that the instantaneous velocity (for said displacement velocity) between two successive elementary deformations is less than one The computer then searches for a deformation scenario that respects these sets of constraints and, if successful, reduces the determined value. Iteratively, the computer can thus determine the lowest possible value for the upper limit of the displacement velocity between the initial and final times that allows it to define a deformation scenario. This deformation scenario is then a first smoothed deformation scenario.

[0297] Preferably, steps D) are then repeated successively for other slowed-down tooth models, giving priority to tooth models whose slowing is most useful for health and / or to meet user prescriptions.

[0298] Intermediate moments can be defined, preferably at the end of the procedure, according to the action capabilities of the orthodontic device(s) envisaged for the orthodontic treatment.

[0299] In a preferred embodiment, when determining a smoothed deformation scenario, configurations are imposed at certain times for tooth models.

[0300] In particular, for determining the first smoothed deformation scenario, the sets of constraints 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.

[0301] Similarly, for determining the second smoothed deformation scenario at the second occurrence of step D), the sets of constraints impose configurations on the limiting tooth model and the first slowed-down 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 subsequent occurrences of step D).

[0302] Preferably, steps B) to D) are carried out autonomously by a computer.

[0303] In one embodiment, smoothing is performed to improve an existing orthodontic treatment plan.

[0304] A dental technician or practitioner defines an orthodontic treatment plan using a computer, preferably in a conventional manner, for example with Treat software, starting from the initial model, moving tooth models from the initial model to a desired configuration at the end of orthodontic treatment. This determines the intermediate steps, particularly for changes in orthodontic splint, the final moment and a "conventional" deformation scenario including intermediate models of the dental arch at intermediate moments.

[0305] Based on this data, preferably determined conventionally, the computer can implement steps B) to D), preferably autonomously. The dental practitioner or technician thus has a solution enabling them to refine the orthodontic treatment plan they have established.

[0306] As is now clear, the method according to the invention allows the computer to spread out the path of the tooth models as much as possible in the time interval between the initial instant and the final instant, that is to say, 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.

[0307] Of course, the invention is not limited to the embodiments described in detail above.

Claims

1. Demands System for implementing a method for generating an orthodontic treatment plan for a user's dental arch, the method comprising the following successive steps: HAS) - generation or retrieval of an "initial" model representing said dental arch at an initial time, said initial model being divided into tooth models, and - generation or retrieval of a "final" model representing said dental arch with a "final" arrangement of tooth models as desired at a final moment marking the end of orthodontic treatment; B) for each tooth model, - determination of a distance measuring a difference between the tooth model configurations in the initial model and in the final model; - determination of the shortest possible time for the tooth model to travel said distance, or "minimum travel time" »; C) identification of the tooth pattern that has the longest minimum displacement time, or "limiting tooth pattern"; D) determination of a deformation scenario, called the "first smoothed deformation scenario" according to which the initial model is transformed into the 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 velocity parameter 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 - a speed representative of the speed of movement of said slowed-down tooth model, preferably an average speed between the initial and final instants, and / or - the difference between the highest value of the said speed of movement and the lowest value of the said speed of movement 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 deformation scenario being a set of transition models between the initial model and the final model, ordered chronologically, said system comprising: - a three-dimensional scanner to generate the "initial" and "final" models in step A), and - a computer programmed to execute at least steps B) to D) of the process.

2. System according to the preceding claim, comprising, - in step B), the determination of a "basic deformation scenario" of said arch, said 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 a function of said basic deformation scenario; then - in step C), the determination of the limiting tooth model as the tooth model having, following the basic deformation scenario, the last one reaches its configuration in the final model.

3. A system according to the immediately preceding claim, wherein, to determine the basic deformation scenario, a computer determines 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 comprising: - 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 be contained within a defined envelope around the tooth model, and / or that the translational velocity of a tooth model along a direction and in a sense be less than an upper limit for the translational velocity, and / or that the rotational velocity of a tooth model around an axis and in a sense be less than an upper limit for a rotational velocity; and / or- 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 some movements over others, and / or imposing an order to move the tooth models, and / or imposing a correct occlusion, and / or allowing or prohibiting the filing of teeth, and / or allowing limited filing of teeth, and / or allowing or prohibiting the extraction of one or more teeth, and / or imposing a speed of movement of one or more teeth;and / or - prescription constraints imposed by the user due to a need for orthodontic treatment generating limited pain and / or having a limited duration and / or limited cost, and / or having limited aesthetic impact and / or having minimal reliability, and / or involving a limited duration for wearing an orthodontic appliance and / or having a limited number of steps, and / or having a predetermined number of steps, and / or allowing or prohibiting tooth filing, and / or allowing limited tooth filing, and / or allowing or prohibiting the extraction of one or more teeth, and / or allowing or prohibiting the use of one or more auxiliary orthodontic appliances.;

4. System according to any one of claims 2 and 3, wherein the intermediate moments are moments at which a check of the arch by a dental practitioner and / or a modification of an orthodontic appliance and / or a fabrication of an orthodontic appliance is / are planned.

5. System according to the immediately preceding claim, wherein the intermediate times are times at which a change of orthodontic splint is planned.

6. System according to any one of the preceding claims, comprising, after determining the first smoothed deformation scenario, the determination, by the computer, of a second smoothed deformation scenario reducing said 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, 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.

7. A system according to the immediately preceding claim, wherein - the first slowed-down 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 it is 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, and / or the tooth whose movement velocity is most critical for the user's health, and / or - 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 it is most useful to slow down, according to a utility criterion defined by the dental practitioner and / or the user and with regard to the first smoothed orthodontic treatment plan,said utility criterion being preferably identical to the utility criterion used to choose the first slowed-down tooth, and / or the tooth whose speed of movement is most critical for the user's health,

8. A system according to any one of the two immediately preceding claims, wherein a smoothed deformation scenario is successively determined for each of the tooth models other than the first and second tooth models, considered as a "slowed-down tooth model", with 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.

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