Automatic aligner design using robust parameter optimization method

Abstract

Provided herein are methods and systems for producing orthodontic appliances that utilize iterative modeling techniques to improve the efficiency and efficacy of the appliances. Further disclosed herein are orthodontic appliances manufactured by such methods.

Description

[0001] This application is a divisional application of Chinese patent application number 2019800936262 (corresponding to PCT international application number PCT / US2019 / 069131), filed on December 31, 2019, entitled "Automatic Orthodontic Appliance Design Using Robust Parameter Optimization Method".

[0002] Cross-references

[0003] This application claims the benefit of U.S. Provisional Patent Application No. 62 / 788,043, filed January 3, 2019, the entire contents of which are incorporated herein by reference. Technical Field

[0004] This technical field relates to the design of dental appliances, and more specifically to the design of dental appliances by optimizing the physical properties of dental appliances according to the requirements of a prescribed treatment plan. Background Technology

[0005] Orthodontic treatment typically involves addressing misaligned teeth and may include the diagnosis, prevention, and / or correction of malocclusion. Many forms of orthodontic treatment involve an initial consultation and diagnosis of the malocclusion by a dental professional (e.g., an orthodontist, a professional with specialized training such as a dental school graduate, or a dentist), a treatment plan, and the use of dental appliances (e.g., braces, brackets, wires, etc.) to implement the treatment plan. Some forms of orthodontic treatment involve the application of a set of removable dental appliances to progressively reposition the patient's teeth from their initial positions to their final positions through an intermediate arrangement. The basic treatment plan for orthodontic treatment can be developed after the initial consultation or at other times, and in many cases (especially those involving braces, wires, and brackets), the basic treatment plan for orthodontic treatment may be modified at different times during examinations and / or throughout the treatment process.

[0006] While convenient, removable appliance systems may not be able to implement treatment plans as effectively as possible. In many cases, the thickness or physical geometry of the appliance may not provide the forces required to move teeth beyond or incompletely to the intended position specified for the stage of the treatment plan. Furthermore, the physical properties of the appliance may be susceptible to stress or strain in different areas, potentially limiting the types of forces it can exert. Systems using removable appliances of uniform thickness may be too thick or too thin in some places, potentially causing discomfort and / or being overly restricted in the types of forces they can exert. While it is desirable to personalize appliances for patients and / or their treatment plans, existing systems make this difficult. Summary of the Invention

[0007] A method for determining the geometry of an orthodontic appliance is disclosed. The method may include providing a treatment plan including: an initial position of a patient's teeth, a final position of the patient's teeth, multiple stages for moving the patient's teeth from the initial position to the final position, and a treatment force for each of the multiple stages for moving the patient's teeth. The method may further include: generating an initial 3D model of the appliance, the initial 3D model including multiple tooth-receiving cavities for accommodating the patient's teeth being positioned to generate the treatment force; generating a finite element shell model including multiple shell elements based on the initial 3D model; determining a first modeling force based on the finite element shell model; modifying at least one shell element of the finite element shell model to generate at least one intermediate 3D model including a second modeling force for moving the patient's teeth to the final position; comparing at least one of the first and second modeling forces with the treatment force to provide a similarity value; and repeating the modification until a threshold shell element value, a threshold similarity value, or a combination thereof is obtained.

[0008] In some embodiments, modifying at least one shell element of a 3D model includes: using a topology algorithm to change the discrete element density map. Modifying at least one shell element of a 3D model may include: using a sizing algorithm to change the discrete thickness map.

[0009] Modifying at least one shell unit of the 3D model includes: using a parametric algorithm to modify the parametric thickness map. A similarity value can compare a first modeling force, a second modeling force, or any combination thereof with a therapeutic force, wherein the similarity value is greater than 50%.

[0010] The method may further include the step of generating instructions for manufacturing orthodontic appliances. The method may also include the step of manufacturing orthodontic appliances.

[0011] A method for determining the geometry of an orthodontic appliance is also disclosed. This method may include providing a treatment plan that includes: an initial position of the patient's teeth, a final position of the patient's teeth, multiple stages for moving the patient's teeth from the initial position to the final position, and treatment forces for each of the multiple stages for moving the patient's teeth. The method may further include: generating an initial 3D model of an orthodontic appliance, the initial 3D model including multiple tooth-accommodating cavities for accommodating a patient tooth being positioned to generate a therapeutic force; generating a finite element shell model including multiple shell elements based on the initial 3D model; determining a first modeling force based on the finite element shell model; modifying at least one shell element of the finite element shell model to generate a first intermediate 3D model, the first intermediate 3D model including a second modeling force for moving the patient tooth to its final position; modifying at least one shell element of the first intermediate 3D model to generate a second intermediate 3D model, the second intermediate 3D model including a third modeling force for moving the patient tooth to its final position; comparing at least one of the first modeling force, the second modeling force, and the third modeling force with the therapeutic force to provide a similarity value; and repeating the modification until a threshold shell element value, a threshold similarity value, or a combination thereof is obtained.

[0012] In some embodiments, modifying at least one shell element of a 3D model includes: using a topology algorithm to modify a discrete element density map. In some embodiments, modifying at least one shell element of a 3D model includes: using a size adjustment algorithm to modify a discrete thickness map. In some embodiments, modifying at least one shell element of a 3D model includes: using a parametric algorithm to modify a parametric thickness map.

[0013] In some embodiments, the similarity value compares the first modeling force, the second modeling force, the third modeling force, or any combination thereof with the therapeutic force, and wherein the similarity value is greater than 50%.

[0014] In some embodiments, the method may further include the step of generating instructions for manufacturing orthodontic appliances. In some embodiments, the method may further include the step of manufacturing orthodontic appliances.

[0015] Orthodontic appliances constructed using the methods described herein are disclosed.

[0016] Orthodontic appliances may contain no more than 90% of the amount of material used in comparable conventional orthodontic appliances with therapeutic power.

[0017] An orthodontic appliance can be one of several orthodontic appliances.

[0018] A method for designing dental appliances is also disclosed. The method may include: identifying the expected outcome for at least a portion of a patient's dentition at the end of at least one phase of a treatment plan, wherein the treatment plan includes a plan for treating at least a portion of the dentition; identifying one or more forces applied to the at least a portion of the dentition during the at least one phase of the treatment plan; identifying one or more clinical acceptability criteria for the at least one phase, the one or more clinical acceptability criteria providing criteria for assessing conformity with the expected outcome; and collecting appliance models for the at least one phase, wherein the appliance models include models of appliances used for the at least a portion of the dentition at the beginning of the at least one phase, and... The orthodontic appliance model has a thickness parameter representing the thickness of at least a portion of the orthodontic appliance model; iteratively models the application of one or more forces to the at least portion of the dentition at the beginning of the at least one stage using the orthodontic appliance model with the thickness parameter at an iteratively decreasing thickness until a result thickness for the thickness parameter is found, the result thickness being less than or equal to the initial thickness, and the result thickness being associated with a satisfactory result of the at least portion of the dentition at the end of the at least one stage, the satisfactory result satisfying one or more clinical acceptability criteria; and provides instructions for manufacturing dental appliances using the orthodontic appliance model with the result thickness assigned to the thickness parameter.

[0019] Iterative modeling of applying one or more forces to at least a portion of the dentition at the beginning of at least one stage may include: assigning an initial thickness to a thickness parameter; determining whether applying one or more forces to at least a portion of the dentition at the beginning of at least one stage meets one or more clinical acceptability criteria; and using the initial thickness as the resulting thickness if applying one or more forces to at least a portion of the dentition at the beginning of at least one stage using an orthodontic model with an initial thickness assigned to a thickness parameter meets one or more clinical acceptability criteria.

[0020] Iteratively modeling the application of one or more forces to at least a portion of the dentition at the beginning of at least one stage may include: assigning an initial thickness to a thickness parameter; determining whether the application of one or more forces to at least a portion of the dentition at the beginning of at least one stage meets one or more clinical acceptability criteria; and if the application of one or more forces to at least a portion of the dentition at the beginning of at least one stage using an orthodontic model with an initial thickness assigned to the thickness parameter does not meet one or more clinical acceptability criteria, then: assigning one or more intermediate thicknesses to the thickness parameter, the one or more intermediate thicknesses being less than the initial thickness, and iteratively determining whether the application of one or more forces to at least a portion of the dentition at the beginning of at least one stage using an orthodontic model with one or more intermediate thicknesses assigned to the thickness parameter meets one or more clinical acceptability criteria.

[0021] In some embodiments, if one or more forces are applied to at least a portion of the dentition at the beginning of the at least one phase using an orthodontic appliance model having one of one or more intermediate thicknesses assigned to a thickness parameter, and one or more clinical acceptability criteria are met, then that one of the one or more intermediate thicknesses is used as the resulting thickness.

[0022] The method may also include using one of one or more intermediate thicknesses as the resulting thickness.

[0023] Iterative modeling of applying one or more forces to at least a portion of the dentition at the start of at least one phase may include: identifying the maximum number of modeling operations; assigning an initial thickness to a thickness parameter; and determining whether applying one or more forces to at least a portion of the dentition at the start of at least one phase meets one or more clinical acceptability criteria. In some embodiments, if applying one or more forces to at least a portion of the dentition using an orthodontic model with an initial thickness assigned to a thickness parameter at the start of at least one stage does not meet one or more clinical acceptability criteria, then: one or more intermediate thicknesses are assigned to the thickness parameter, the one or more intermediate thicknesses being less than the initial thickness; iteratively determining whether applying one or more forces to at least a portion of the dentition using an orthodontic model with one or more intermediate thicknesses assigned to the thickness parameter at the start of at least one stage meets one or more clinical acceptability criteria; if applying one or more forces to at least a portion of the dentition using an orthodontic model with one or more intermediate thicknesses assigned to the thickness parameter at the start of at least one stage does not meet one or more clinical acceptability criteria, then: identifying the closest intermediate thickness among the one or more intermediate thicknesses, the orthodontic model with the closest intermediate thickness being closer to meeting one or more clinical acceptability criteria than an orthodontic model with an initial thickness or any one of the one or more intermediate thicknesses other than the closest intermediate thickness; and using the closest intermediate thickness as the resulting thickness.

[0024] In some embodiments, the method may include collecting a treatment plan and identifying at least one stage of the treatment plan. In some embodiments, the starting thickness includes one or more of the following: 0.5 mm, 0.6 mm, 0.7 mm, 0.8 mm, 0.9 mm, 1.0 mm, 1.1 mm, 1.2 mm, 1.3 mm, 1.4 mm, and 1.5 mm.

[0025] Iteratively modeling the application of one or more forces to at least a portion of the dentition at the start of at least one stage may include: simulating the placement of an orthodontic appliance model on at least a portion of the dentition and simulating the response of at least a portion of the dentition to the virtual placement.

[0026] Iterative modeling of applying one or more forces to at least a portion of the dentition may include using finite element techniques to solve partial differential equations representing one or more clinical acceptability criteria.

[0027] In some embodiments, one or more clinical acceptability criteria may include a clinical acceptability score representing the probability of statistical relevance to the expected outcome. One or more clinical acceptability criteria may indicate an acceptable biomechanical outcome at the end of at least one phase. An acceptable biomechanical outcome may include an acceptable position of at least a portion of the dentition at the end of the at least one phase or acceptable forces on at least a portion of the dentition during the at least one phase. One or more clinical acceptability criteria may indicate acceptable physiological stresses on at least a portion of the dentition during the at least one phase. One or more clinical acceptability criteria may indicate acceptable appliance structural characteristics of the device used to achieve the at least one phase.

[0028] In some embodiments, at least a portion of the dentition may include portions of one or more teeth of the dentition, and at least a portion of the orthodontic appliance is configured to receive the one or more teeth and apply one or more forces to the one or more teeth.

[0029] In some embodiments, the dental appliance includes a variable thickness appliance that has a resulting thickness over at least a portion of the dentition.

[0030] In some embodiments, the method may include directly manufacturing dental appliances.

[0031] At least one phase may include one or more of the following: the initial phase of the treatment plan, the final phase of the treatment plan, the intermediate phase of the treatment plan, and multiple phases of the treatment plan.

[0032] In some embodiments, dental appliances include polymer appliances configured to accommodate a patient’s dentition and apply one or more forces thereon.

[0033] Merging by reference

[0034] All publications, patents and patent applications mentioned in this specification are incorporated herein by reference as if each individual publication, patent or patent application were specifically and individually indicated for inclusion by reference. Attached Figure Description

[0035] The novel features of the invention are particularly set forth in the appended claims. The features and advantages of the invention will be better understood by referring to the following detailed description and accompanying drawings, which illustrate illustrative embodiments utilizing the principles of the invention, as shown in the drawings:

[0036] Figure 1 A schematic diagram depicts a method for determining the geometry of orthodontic appliances.

[0037] Figure 2A An example finite element shell model of an orthodontic appliance is depicted. Figure 2B Depicting Figure 2A The cross-section of the shell model is shown in the figure, and an example thickness function is provided. Figure 2C The cross-section of the orthodontic appliance is depicted and an example solid cross-section is provided, the thickness of which is limited by a parameterized function.

[0038] Figure 3A A tooth repositioning appliance that can be manufactured using the methods disclosed herein is described. Figure 3B A tooth repositioning system comprising multiple instruments is described.

[0039] Figure 4 A data processing system that can be used in performing the methods and processes described herein is described.

[0040] Figure 5 An example flowchart of a method for designing dental appliances according to some embodiments is shown.

[0041] Figure 6 An example flowchart of a method for iteratively modeling forces applied to the dentition to obtain an orthodontic appliance model with a resulting thickness, according to some embodiments, is shown.

[0042] Figure 7 An example flowchart of a method for iteratively modeling forces applied to the dentition to obtain an orthodontic appliance model with a resulting thickness, according to some embodiments, is shown.

[0043] Figures 8A to 8E An example of topology optimization used to provide optimization forces for teeth is shown. Figure 8A The 3D depiction of the canine teeth is shown; Figure 8B The initial geometry of a portion of an orthodontic appliance for canines is shown; Figure 8C An example 3D model of a portion of an orthodontic appliance with canines using volumetric units is shown; Figure 8D An example of a topology-optimized profile of a modeled portion of an orthodontic appliance to reduce canine tilt is shown, and the exponent provides the size of the profile at the location; and Figure 8E The optimized portion of the orthodontic appliance is shown, which provides reduced canine tilt.

[0044] Figure 9A It shows that it has a source Figure 8D The initial model of the canine part of the orthodontic appliance, and the index provides the size of the contour at the location; Figure 9BAn example canine intermediate with a reduced tilt and an orthodontic appliance is shown; Figure 9C An example final model of a canine with reduced tilt and an orthodontic appliance is shown; and Figure 9D An example of minimizing the tilt angle through modeling iterations is shown.

[0045] Figure 10A An example shell unit 3D model of an orthodontic appliance with modified unit thickness to optimize tooth movement is shown; Figure 10B An alternative view of the example shell unit model is shown.

[0046] Figure 11A An example orthodontic appliance model is shown using a thickness map with corresponding forces for arch expansion; Figure 11B A second example of an orthodontic appliance model is shown, in which the thickness diagram and the resultant force for arch expansion vary; Figure 11C A third example of an orthodontic appliance model is shown, in which the thickness diagram and the resultant force for arch expansion vary; and Figure 11D A fourth example of an orthodontic appliance model is shown, in which the thickness diagram and the resultant force for arch expansion have variations.

[0047] Figure 12A An example is shown of the desired unidirectional movement of multiple consecutive teeth by an invasive force applied unidirectionally from canine to canine; and Figure 12B An example model region from the first premolar to the first premolar is shown.

[0048] Figure 13A An example of upper anterior tooth overbite is shown; Figure 13B An example of mesio-distal tooth movement is shown; and Figure 13C An example of applying force to control root tilt is shown.

[0049] Figure 14 A schematic diagram is depicted of a method for determining the geometry of orthodontic appliances using topology optimization and volumetric elements.

[0050] Figure 15 A schematic diagram depicts a method for determining the geometry of orthodontic appliances using sizing optimization and shell or beam units. Detailed Implementation

[0051] The systems, methods, and computer-readable media described herein address important technical problems related to the effective design of dental appliances having geometries that effectively achieve one or more stages of a treatment plan. The systems, methods, and computer-readable media described herein can use one or more automated techniques to identify optimal physical properties of the dental appliance that achieve the force system specified by the treatment plan. As noted herein, automated techniques can model the application of dental appliances with various geometries to the dentition and can evaluate whether these geometries effectively achieve the expected outcomes of the stages of the treatment plan. Through automated simulation, the solution can focus on the appliance geometry that most effectively achieves the stages of the treatment plan. These techniques can be advantageous when appliances are directly manufactured (e.g., via 3D printing technology), including appliances with variable thickness.

[0052] This paper describes a method for optimizing the geometry of orthodontic appliances. A fast and robust algorithm for orthodontic appliance design is provided, which can be further enhanced by controlling the thickness of the appliance. Furthermore, a method for generating variable-thickness appliances is provided.

[0053] Although the detailed description contains many specific details, these details should not be construed as limiting the scope of this disclosure, but merely as illustrating different examples and aspects of this disclosure. It should be understood that the scope of this disclosure includes other embodiments not discussed in detail above. Various other modifications, variations, and modifications that will be apparent to those skilled in the art in terms of the arrangement, operation, and details of the methods, systems, and apparatuses provided herein without departing from the spirit and scope of the invention described herein.

[0054] As used herein, “patient” can include anyone, including people seeking dental / orthodontic treatment, people who have undergone dental / orthodontic treatment, and people who have previously undergone dental / orthodontic treatment. “Patient” can include customers or potential customers of orthodontic treatment, such as people who are using the visualization tools in this article to inform them of their decision to fully undergo orthodontic treatment or to choose an orthodontic treatment plan.

[0055] As used herein, a “treatment plan” or “orthodontic treatment plan” may include a plan for moving a patient’s teeth from an initial alignment to a desired alignment using dental appliances. A treatment plan may specify a set of intermediate (e.g., progressive) stages that define the alignment of the teeth between the initial alignment through which they can be moved and the desired alignment. A treatment plan and each of its stages may have an “expected outcome,” such as the position or other physical property expected to be achieved by that stage, and an “actual outcome,” such as the position or other physical property actually achieved by the appliances when that stage is performed. As described herein, the actual outcome of a treatment plan / stage may be the same as or different from the expected outcome of the treatment plan / stage. A stage of a treatment plan may apply one or more forces to the teeth to achieve the desired position. A stage of a treatment plan may be associated with one or more “clinically acceptable criteria” (e.g., criteria used to assess conformity to the expected outcome of that stage). Clinically acceptable criteria may indicate an acceptable biomechanical outcome of the stage, such as an acceptable position, acceptable force, etc., which need not be the same as the expected position but are acceptable to one or more clinicians. An example of a clinical acceptability criterion includes one or more clinical acceptability scores, which represent the probability of statistical relevance to the expected outcome (e.g., if the expected outcome of a phase of the treatment plan is a displacement of 1 millimeter (mm) from the tooth, then a clinical acceptability criterion could include a clinical acceptability score representing the standard deviation of various distances from the expected displacement).

[0056] As used herein, a “dental positioning appliance” or “orthodontic appliance” may include a set of dental appliances configured to progressively change the position of a patient’s teeth over time. As described herein, dental positioning appliances and / or orthodontic appliances may include polymer appliances configured to move a patient’s teeth according to an orthodontic treatment plan. As used herein, the terms “dental appliance” and “tooth-accommodating appliance” are considered synonyms. As used herein, a “dental positioning appliance” or “orthodontic appliance” may be considered synonyms and may include any dental appliance configured to change the position of a patient’s teeth according to a plan (e.g., an orthodontic treatment plan). One type of dental appliance is an orthodontic appliance. As used herein, a “variable thickness appliance” or “variable thickness dental appliance” may include an appliance having a non-uniform thickness (e.g., having different thicknesses in different sections). Examples of variable thickness orthodontic appliances can be found in at least the following documents: U.S. Patent Publication No. 2017 / 0007359, U.S. Provisional Patent Application No. 62 / 189,291, U.S. Provisional Patent Application No. 62 / 189,312, and U.S. Provisional Patent Application No. 62 / 189,317, the disclosures of which are incorporated herein by reference in their entirety as if they were fully set forth herein. The appliances can be manufactured using indirect or direct manufacturing techniques, examples of which are further discussed herein. Examples of materials used in the manufacture of appliances include those described in the following documents: U.S. Patent No. 9,655,693 (titled “Multilayer dental appliances and related methods and systems”); U.S. Provisional Patent Application Serial No. 62 / 677,354 (titled “CURABLE COMPOSITION FOR USEIN A HIGH TEMPERATURE LITHOGRAPHY-BASED PHOTOPOLYMERIZATION PROCESS AND METHOD OF PRODUCING CROSSLINKED POLYMERS THEREFROM”); and U.S. Provisional Patent Application Serial No. 62 / 677,364 (titled “POLYMERIZABLE MONOMERS AND METHOD OF POLYMERIZING THE SAME”), all of which are incorporated herein by reference as if they were fully set forth herein.

[0057] As used herein, an "orthodontic appliance model" may include a virtual representation of a physical orthodontic appliance used for a phase of treatment planning. An orthodontic appliance model may include a virtual representation of a tooth-accommodating cavity that, at a portion of a phase of treatment planning (e.g., at the beginning or end), accommodates the patient's dentition. An orthodontic appliance model may have one or more parameters characterizing its physical counterpart. Examples of such parameters include one or more "thickness parameters" that characterize the thickness of various portions of the physical orthodontic appliance corresponding to the appliance model. For example, in the case of a uniform thickness appliance, the thickness parameter of the appliance model may represent the expected thickness of the physical orthodontic appliance corresponding to the appliance model. As another example, for a variable thickness appliance, one or more thickness parameters may represent the thickness of various regions of the physical orthodontic appliance, including but not limited to the region surrounding a particular tooth and / or portion of the dentition. An orthodontic appliance model may, but is not necessarily, the basis for a virtual object used to directly form the physical orthodontic appliance. As an example, as used herein, an orthodontic appliance model may, but is not necessarily, differ from the file used for 3D printing the appliance.

[0058] Orthodontic appliance models can be used to model the forces applied to the dentition. In some implementations, the difference geometry between the appliance model and a virtual model of the dentition receiving a physical appliance corresponding to the appliance model can form the basis for the forces the physical appliance might apply to the dentition during phases of treatment planning. The force model can include an "iterative" force model (where the parameters of the appliance model are varied (e.g., iterative)) and the resulting forces applied to the modeled dentition until a condition is met. Examples of conditions include finding a satisfactory outcome, such as the outcome of a phase that meets clinical acceptability criteria. Other examples of conditions include, for a given number of modeling operations, identifying a single parameter value that, compared to other parameter values, the appliance model is closer to meeting clinical acceptability criteria.

[0059] As used herein, the term “and / or” can be used as a function word to indicate that two words or expressions are together or separately. For example, the phrase “A and / or B” includes A alone, B alone, and A and B together. Depending on the context, the term “or” does not necessarily exclude one of several words / phrases. For example, the phrase “A or B” does not exclude A and B together.

[0060] As used in this article, the terms “torque” and “moment” are considered synonymous.

[0061] As used herein, “torque” can include a force acting on an object (e.g., a tooth) at a distance from the center of resistance. For example, torque can be calculated by the cross product of vector forces applied to a location corresponding to a displacement vector from the center of resistance. Torque can include a vector pointing in one direction. A torque relative to another torque can include one of a torque vector pointing toward a first side of the object (such as a tooth) and another torque vector pointing toward an opposite side of the object (such as a tooth). Any discussion herein regarding the application of forces to a patient's teeth applies equally to the application of torques to teeth, and vice versa.

[0062] As used herein, "multiple teeth" can include two or more teeth. Multiple teeth may, but are not required to, include adjacent teeth. In some embodiments, one or more posterior teeth include one or more of molars, premolars, or canines, and one or more anterior teeth include one or more of central incisors, lateral incisors, canines, first premolars, or second premolars. A "part" of the dentition can include a portion of the dentition, such as an area around a particular tooth, an area around a particular interproximal area, an area near a particular occlusal area, etc.

[0063] The embodiments disclosed herein are well applicable to moving one or more teeth in a first group or moving one or more teeth in a second group, and combinations thereof.

[0064] In some embodiments, a method for determining the geometry of an orthodontic appliance is provided, the method comprising the steps of (i) providing a treatment plan, wherein the treatment plan includes an initial position of a patient's teeth, a final position of a patient's teeth, multiple stages for moving the patient's teeth from the initial position to the final position, and a treatment force for each of the multiple stages for moving the patient's teeth; (ii) generating an initial 3D model of an orthodontic appliance (also referred to as a brace) including multiple tooth-receiving cavities for accommodating the patient's teeth being positioned to generate the treatment force; (iii) generating a finite element shell model including multiple shell elements based on the initial 3D model; (iv) determining a first modeling force based on the finite element shell model to generate at least one intermediate 3D model including a second modeling force for moving the patient's teeth to the final position; (v) comparing at least one of the first and second modeling forces with the treatment force to provide a similarity value; and (vi) repeating the changes until a threshold shell element value, a threshold similarity value, or a combination thereof is obtained.

[0065] In some embodiments, the method for determining the geometry of an orthodontic appliance further includes the step of generating instructions for manufacturing the orthodontic appliance.

[0066] Figure 1A schematic diagram of a method 100 for determining the geometry of an orthodontic appliance is depicted. Method 100 provides an example process for determining the geometry of an orthodontic appliance using an initial 3D model and a finite element shell model. At box 110, a treatment plan is developed. At box 120, a dentition assessment is obtained. At box 120, a dentition assessment is obtained for each stage of the treatment plan. In some embodiments, the dentition assessment is used to generate a model of the patient's teeth, and at box 140, an initial 3D model of the orthodontic appliance can be generated. Furthermore, at box 140, a finite element shell model of the orthodontic appliance can be generated. In some embodiments, the finite element shell model at box 140 can be a topological discrete element density map, a parametric analysis thickness map, a size-adjusted discrete thickness map, or a shell element model.

[0067] In some embodiments of method 100, at block 130, a therapeutic force system is obtained to provide movement of teeth and / or multiple teeth, allowing the patient's teeth to progress from an initial stage to final alignment. In some embodiments of method 100, the finite element shell model at block 140 has a force system that is compared with the therapeutic force system from block 130. At block 170 of method 100, parameters and / or values ​​of the finite element shell model from block 140 are modified to improve the orthodontic appliance. At block 150, additional inputs can be added to the variant of the element shell model, such as providing manufacturing constraints, providing aesthetic parameters, providing input functions or algorithmic variables, etc. At block 160, additional manufacturing constraints can be added as needed, such as adding variables to improve the calculations generated by the changes in parameters. In some embodiments of block 160, the additional constraints include topological values ​​of the discrete element diagram, parameter values ​​of the parameterized thickness diagram, dimensional adjustment values ​​of the discrete thickness diagram, or values ​​of the finite element shell model.

[0068] Providing constraints at point 160 can improve modeling efficiency, patient comfort, and treatment efficiency. As a non-limiting example, a model of an orthodontic appliance without constraints provided at point 160 might take several days to process, while input constraints at point 160 can reduce this time. Inputs at box 160 may include providing a baseline local thickness that is relatively greater than or less than the thickness of the rest of the orthodontic appliance being modeled. As a non-limiting example, an orthodontic appliance including a missing tooth may include increased thickness around the missing tooth to provide increased and / or sufficient force to nearby target teeth. Another example input at point 160 is a constraint for patient comfort, such as a constraint that may form spikes that cause pain or discomfort.

[0069] In some embodiments, at 160, a penalty parameter is provided as an additional constraint, such as a penalty for an orthodontic surface that includes spikes or too many spikes. The penalty parameter can address surface roughness (e.g., the maximum difference between peak height and valley depth on a surface within a radius) and can reduce or eliminate the formation of spikes.

[0070] In some embodiments, the additional constraint at 160 improves the smoothness of the orthodontic appliance. In some embodiments, the additional constraint includes local and / or focused forces of the appliance in one force direction. In some embodiments, the additional constraint at 160 and / or the input function at 150 removes material from the outer surface of the modeled orthodontic appliance before removing material from the inner surface (e.g., the patient mold may cover the modeled appliance shell, and the outer surface of the modeled orthodontic appliance is optimized so that no new gaps appear between the optimized appliance shell and the patient mold). In some embodiments, the additional constraint at 160 and / or the input function at 150 removes material only from the outer surface of the modeled orthodontic appliance.

[0071] In some embodiments, the input function at 150 and / or the additional constraints at 160 comprise unidirectional movement of multiple teeth. In some embodiments, unidirectional movement of multiple teeth comprises multiple consecutive teeth. As a non-limiting example, it may be desirable for multiple teeth to move in the same direction (e.g., multiple teeth indentation, expansion, or extension), and the input function, algorithmic variables, or additional constraints to maximize the minimum force in the direction of movement; see, for example, Figure 12A In some embodiments, an optimization objective is used in the model, and in some embodiments, the optimization objective is to maximize the minimum amount of force required to move multiple consecutive teeth in one direction. In some embodiments, the constraint may be limited such that the unidirectional movement design region includes a region of multiple consecutive teeth, multiple consecutive teeth plus one adjacent tooth on each side, multiple consecutive teeth plus two adjacent teeth on each side, or multiple consecutive teeth plus three adjacent teeth on each side. As a non-limiting example, modeling an orthodontic appliance for canine-to-canine intrusion can have a design region that optimizes the minimum force in the direction of movement, and the design region may include from the first premolar to the first premolar (i.e., multiple consecutive teeth plus one adjacent tooth on each side); see, for example Figure 12A (unidirectional movement from canine tooth to canine tooth) and Figure 12B (Example model area from the first premolar to the first premolar).

[0072] In some embodiments of method 100, at block 170, variations in the parameters and / or values ​​of the finite element shell model may continue until the geometry of the orthodontic appliance with a threshold or threshold fraction is determined. At block 180, instructions for manufacturing the orthodontic appliance are generated.

[0073] Develop a treatment plan

[0074] At box 110 of method 100, a treatment plan with the desired therapeutic force system is developed. A certain amount of force and torque can directionally induce planned movement of the patient's teeth. At box 120, a dentition assessment can be obtained, and the desired force system can be arranged based on the patient's dentition. In some embodiments of box 130, an appropriate torque-to-force ratio can be determined to provide therapeutic movement of the patient's teeth. The therapeutic force can be part of the therapeutic force system, also referred to as the ideal force system and the therapeutic force system.

[0075] In some embodiments, the treatment plan formulated at box 110 may include only the initial and final positions of the patient's teeth. In some embodiments, the treatment plan at box 110 may include an initial position, a final position, and multiple intermediate positions between the initial and final positions. In some embodiments, each intermediate position is considered a "stage" in which the patient's teeth can be moved toward the final position. In some embodiments, the treatment plan includes multiple stages (also referred to herein as multiple steps). Each of the multiple stages may have its own initial and final positions. In some embodiments, the treatment plan may include multiple stages for continuously moving the patient's teeth from the initial position to the final position. At box 130, each stage of the treatment plan may provide a therapeutic force (also referred to herein as a "therapeutic force" and "ideal force"), which may be applied to at least one of the multiple teeth to provide a mobilizing force to move the patient's teeth toward the final position. The therapeutic force at each stage may include one or more force systems applied to the patient's teeth and / or multiple teeth.

[0076] In some embodiments, the treatment plan may include a 3D model of an orthodontic appliance and a 3D model of the patient's teeth. Placing an initial 3D model of the orthodontic appliance onto the 3D model of the patient's teeth applies therapeutic forces to gradually move the teeth into a new configuration. This process is repeated using successive 3D models of the orthodontic appliance, including the new configuration, ultimately moving the teeth into the final desired configuration through a series of intermediate configurations or alignment patterns.

[0077] In some cases, only certain teeth accommodated by the 3D-modeled orthodontic appliance will be repositioned by the appliance, while other teeth can provide base or anchor areas to hold the appliance in place as it applies force to one or more teeth targeted for repositioning. In some cases, at some point during treatment, some, most, or even all of the teeth will be repositioned. The moved teeth can also serve as bases or anchors to hold the appliance in place while the patient wears it. In some embodiments, no wires or other means will be provided to hold the appliance in place on the teeth. However, in some cases, it may be necessary or required to provide separate attachments or other anchoring elements on the teeth, with corresponding receptacles or holes in the appliance so that the appliance can apply selected forces on the teeth.

[0078] The target final alignment of teeth (e.g., the expectation and anticipated end result of orthodontic treatment) can be received from the clinician in the form of a prescription, calculated based on the fundamental principles of orthodontics, and / or calculated from an outpatient prescription. By specifying the expected final position of the teeth and a digital representation of the teeth themselves, the final position and surface geometry of each tooth can be specified to form a complete model of the tooth alignment at the end of the desired treatment.

[0079] With the initial and target positions of each tooth, a movement path can be defined for the movement of each tooth. In some embodiments, the movement path is configured to move the tooth in the fastest manner with minimal round trips to bring the tooth from its initial position to its desired target position. Optionally, the tooth path can be segmented, and the segments can be calculated such that the movement of each tooth within a segment remains within thresholds of linearity and rotational translation. In this way, the endpoints of each path segment can constitute a clinically feasible repositioning, and the set of segment endpoints can constitute a clinically feasible sequence of tooth positions, so that moving from one point in the sequence to the next does not result in tooth collision.

[0080] At box 130, a healing force system can be defined that enables movement paths defined by a treatment plan. In some embodiments, a healing force system can be defined for each of the multiple phases of a treatment plan.

[0081] In some embodiments, the treatment plan includes unidirectional movement of multiple consecutive teeth (e.g., unidirectional movement for anterior tooth intrusion), tooth tilting (e.g., anterior tooth tilting), root control (e.g., mesial-distal root control), root torque (e.g., lingual root torque), or any combination thereof.

[0082] Initial 3D model

[0083] At box 140 of method 100, an initial three-dimensional (3D or 3-D) model of the orthodontic appliance may be generated. In some embodiments, the initial 3D model of the orthodontic appliance is based on a model of the patient's teeth. In some embodiments, the initial 3D model of the orthodontic appliance is based on a 3D model of the patient's teeth. In some embodiments, an initial 3D model of the orthodontic appliance is generated for each step of a treatment plan developed at box 110, the treatment plan including multiple stages for moving the patient's teeth from an initial position to a final position.

[0084] Dental models of a patient's teeth and oral cavity can be obtained in a variety of ways. In some embodiments of box 120, dental models of a patient's teeth are obtained through dentition assessment. Known techniques (e.g., X-rays, 3D X-rays, computer-aided computed tomography images or datasets, and magnetic resonance imaging) can be used to scan or image a patient's teeth to construct a 3D surface model of the patient's teeth. These models are typically 3D mesh models of the patient's upper and lower dental arches (including teeth and gingiva).

[0085] After constructing a 3D model of the tooth surface, models of the patient's individual teeth can be exported. In one approach, the individual teeth and other components are segmented to allow for individual repositioning or removal of teeth in or from digital data. As is known in the art, teeth in the model can be segmented manually or automatically. Each tooth can then be represented by a 3D mesh model. In some embodiments, a computed model of the patient's dentition can be used to reduce memory and computational requirements when manipulating, comparing, or otherwise using the digital model.

[0086] In some embodiments of box 140, the initial 3D model of the orthodontic appliance (referred to in some embodiments as the initial 3D model of the appliance) includes multiple tooth-receiving cavities for receiving the patient's teeth and / or a 3D model of the patient's teeth. In some embodiments, the initial 3D model of the orthodontic appliance has multiple tooth-receiving cavities positioned to generate therapeutic forces that move the patient's teeth from an initial position to a final position (also referred to as the "target position"). For example, the initial 3D model of the orthodontic appliance may be shaped such that placement of the appliance on the patient's teeth applies controlled forces to progressively move the teeth into a new configuration. This process is repeated using successive appliances (each process including a new configuration based on the 3D model) ultimately moving the teeth to the final desired configuration through a series of intermediate configurations or alignment patterns. Repeating this process using successive appliances can be based on the treatment plan established at box 110.

[0087] In some embodiments, the initial 3D model may be based on known orthodontic positioning principles. In some embodiments, the initial 3D model may be based on multiple known orthodontic positioning principles.

[0088] The initial 3D model of the appliance can have a layout adapted to the patient's teeth (e.g., the shape of the tooth cavity matches the shape of the patient's teeth) and can be manufactured based on a positive or negative model of the patient's teeth generated by impression, scanning, etc.

[0089] Generate finite element shell model

[0090] At box 140 of method 100, a finite element shell model can be generated. Simulation of an initial 3D model of an orthodontic appliance and / or patient's teeth may involve complex calculations. In simulations using finite element analysis, a system or object can be represented by a geometrically similar model consisting of numerous interconnected and simplified regions (also referred to as "volume elements" or "shell elements") of discrete regions that constitute the finite element. Using this approach, complex calculations can be decomposed into calculations of smaller sub-computations representing discrete regions. The finite element shell model can divide the surface of the finite element model into multiple shell elements to provide a 3D surface with polygonal shapes. In some embodiments, the 3D surface with polygonal shapes is a planar 3D surface (e.g., the shell elements may be 2D but have geometry to provide a 3D representation).

[0091] In some embodiments, a finite element shell model comprising multiple shell elements is provided based on an initial 3D model of an orthodontic appliance. The finite element shell model may include a 2D mesh model represented in 3D space (also referred to herein as a “3D mesh model”). The 3D mesh model can be characterized by nodes and / or by utilizing the nodes that are interconnected with other finite shell elements. As a non-limiting example, the finite element shell model may be a mesh model of shell elements formed according to an initial 3D model of an orthodontic appliance.

[0092] Compared to other modeling techniques, the use of the finite element shell model of box 140 disclosed herein can provide unexpected benefits, such as reduced modeling computation time, in part because feature modeling can be represented by fewer variables. In some cases, the finite element shell model provided herein can provide more than 100 times faster processes and computations when compared to traditional solid orthodontic appliance models. This allows for iterative searches without tedious and time-consuming computations. In some embodiments, the finite element shell model is a thick shell model. In other embodiments, the finite element shell model is a thin shell model.

[0093] At box 140 of method 100, an initial finite element shell model can be approximated based on an initial 3D model of the orthodontic appliance. Modifications to the finite element shell model at box 170 can generate multiple intermediate 3D models.

[0094] Based on the input parameters, a finite element shell model can represent a classification of shell elements. As a non-limiting example, a finite element shell model can represent a parametric thickness map, a topological density map, a discrete thickness map, or a combination thereof.

[0095] In some embodiments, at block 140, the finite element shell model is represented by a parametric thickness map. Shell elements may have initial values ​​based on representative thicknesses, and the finite element shell model may utilize initial parameters to represent a thickness map function. The parametric thickness map describes the thickness of the orthodontic appliance in a 3D model based on point coordinates in a local tooth coordinate system. In some embodiments, the parametric thickness map describes the thickness of the orthodontic appliance in an initial 3D model based on point coordinates in a local tooth coordinate system. The point coordinates in the local tooth coordinate system may be based on coordinates set by at least one patient tooth, as represented by a 3D model of the patient tooth.

[0096] In some embodiments, at block 140, the parametric thickness map of the finite element shell model may be based on point coordinates in a local coordinate system, and as a non-limiting example, the coordinates may represent the position relative to the buccal, labial, vestibular, or lingual side of a tooth, the proximity of the point to the incisal edge or gingiva, the proximity of the point to the cusp or gingival margin, the proximity to the interproximal margin, or the proximity of the point to adjacent teeth (e.g., mesial, mesial, and / or distal). In some embodiments, the thickness map may be based on point coordinates in a local coordinate system, and as a non-limiting example, the coordinates may represent the position relative to the quadrants of the two dental arches, the relative position to the right maxillary quadrant, the relative position to the left maxillary quadrant, the relative position to the right mandibular quadrant, the relative position to the left mandibular quadrant, the relative position to the midline, the relative position to the facial side of the dental arch, the relative position to the lingual side of the dental arch, the relative position to the occlusal plane, or the relative position to the dental arch.

[0097] Parametric thickness maps can be parameterized based on each coordinate point on a finite element shell model. An example of a parametric thickness function is provided in... Figure 2A The Chinese side indicated that... Figure 2A An example finite element shell model of an orthodontic appliance (e.g., the surface of an aligner) is shown. A cross-section of the finite element shell model shows the local coordinate system of a representative tooth. Figure 2B ). Figure 2B A cross-sectional view of the surface in the sagittal plane passing through the central incisor is shown, and an example thickness function is provided. A parameterized thickness map can have a thickness determined in a coordinate system, which can be provided by selected parameters. In Figure 2, the thickness (t) at point P is a function of the height (z) and the surface normal angle (a). The thickness function can be expressed as:

[0098] t=Az+Bsin(a) Equation (1)

[0099] Coefficients A and B can be parameters used for optimization. Figure 2C A surface cross-section through the sagittal plane of the central incisor is shown, and an example solid cross-section is provided, represented by the values ​​selected for parameters A and B.

[0100] In some embodiments, the initial finite element shell model at box 140 includes a uniform thickness map (i.e., representing a uniform thickness orthodontic appliance). In other embodiments, the initial finite element shell model includes variations of the thickness map, which may be provided, for example, according to a parametric function. In some embodiments, the thickness map may have unconditional convergence when calculating the force system on at least one tooth. A thickness map with unconditional convergence when calculating the force system on at least one tooth can be more robust than models typically used in conventional solid orthodontic appliance models.

[0101] In some embodiments, at box 140, a finite element shell model using a parametric thickness map provides a smooth orthodontic appliance. The properties of the parametric thickness map and modifications made thereon can provide an orthodontic appliance that is both aesthetically pleasing and comfortable for the patient.

[0102] In some embodiments, at block 140, the finite element shell model represents a topological discrete element density map. Shell elements may have initial values ​​based on representative densities, and the finite element shell model may utilize the element density of each shell element to represent a density map function. The topological discrete element density map describes an initial 3D model of the density of the orthodontic appliance based on the positions of the shell elements in the tooth local coordinate system. The tooth local coordinate system may be based on coordinates set by at least one patient tooth, as represented by a 3D model of the patient tooth. In a particular embodiment, the initial topological density map represents an orthodontic appliance with more material than required. Each point of the shell mesh of the finite element shell model is provided with an element density number, and each element density number has a value from 0 to 1. In some embodiments, the value of each element density number is 1 before a change in value at block 170 of method 100. In some embodiments, the value of at least one element density number is 1 before a change in value at block 170 of method 100.

[0103] The topological discrete element density map can be based on the position of the shell element in the local coordinate system, and as a non-limiting example, the coordinates can represent the position relative to the buccal, labial, vestibular, or lingual side of the tooth, the proximity of the point to the incisal edge or gingiva, the proximity of the point to adjacent teeth (e.g., proximal, mesial, and / or distal), the quadrant of the two dental arches, the proximity of the point to the cusp or gingival margin, the proximity to the interproximal margin, or the position of the dental arch.

[0104] In some embodiments, at box 140, the finite element shell model represents a discrete thickness map for dimensional adjustment. Shell elements may have initial values ​​based on representative thicknesses, and the finite element shell model may utilize the element thickness of each shell element to represent a discrete thickness map function for dimensional adjustment. The thickness map is an initial 3D model describing the thickness of the orthodontic appliance based on the element values.

[0105] In some embodiments, at block 140, the initial sizing adjustment discrete thickness map represents an orthodontist with more material than required. Each point of the shell mesh of the finite element shell model is provided with an element thickness number, and each element thickness number has a value from 0 to 1. In some embodiments, the value of each element thickness number is 1 before the change in value at block 170 of method 100. In some embodiments, at least one element thickness number has a value of 1 before the change in value at block 170 of method 100. In some embodiments, the element thickness numbers can be scaled to actual thickness values. As a non-limiting example, the element density numbers can be scaled to an actual thickness value of 1 mm, such that a thickness number of 1 represents an actual thickness of 1 mm, a thickness number of 0 represents an actual thickness of 0 mm, and a thickness number of 5 represents an actual thickness of 0.5 mm. In some embodiments, the thickness numbering can be scaled such that thickness number 1 represents 5.0 mm, 4.9 mm, 4.8 mm, 4.7 mm, 4.6 mm, 4.5 mm, 4.4 mm, 4.3 mm, 4.2 mm, 4.1 mm, 4.0 mm, 3.9 mm, 3.8 mm, 3.7 mm, 3.6 mm, 3.5 mm, 3.4 mm, 3.3 mm, 3.2 mm, 3.1 mm, 3.0 mm, 2.9 mm, 2.8 mm, 2.7 mm, 2... 0.6 mm, 2.5 mm, 2.4 mm, 2.3 mm, 2.2 mm, 2.1 mm, 2.0 mm, 1.9 mm, 1.8 mm, 1.7 mm, 1.6 mm, 1.5 mm, 1.4 mm, 1.3 mm, 1.2 mm, 1.1 mm, 1.0 mm, 0.9 mm, 0.8 mm, 0.7 mm, 0.6 mm, 0.5 mm, 0.4 mm, 0.3 mm, 0.2 mm, 0.1 mm, or values ​​less than 0.1 mm but greater than 0 mm.

[0106] A change to the finite element shell model at box 170 provides a different force modeled by the treatment plan for box 110. For example, a change in the value from the finite element shell model at box 140 can result in a change in the modeling force, thereby increasing or decreasing the amount of force applied to the patient's teeth. At box 140 of method 100, the finite element shell model of the initial 3D model of the orthodontic appliance has a first modeling force. In some embodiments, this first modeling force at box 140 is substantially similar to the treatment force at box 130 for a stage of the treatment plan for box 110. In some embodiments, the first modeling force is determined and / or calculated. In some embodiments, the first modeling force is determined by computational modeling.

[0107] In some embodiments, the similarity between the first modeling force and the healing force is greater than 99%, greater than 98%, greater than 97%, greater than 96%, greater than 95%, greater than 94%, greater than 93%, greater than 92%, greater than 91%, greater than 90%, greater than 85%, greater than 80%, greater than 75%, greater than 70%, greater than 65%, greater than 60%, greater than 55%, or greater than 50%.

[0108] Change of value or parameter

[0109] In some embodiments of method 100, at block 170, the finite element shell model from block 140 can be altered by providing variations in the shell elements. In some embodiments of block 170, a finite element analysis platform is used to analyze the modeled force system. In some embodiments, at least one shell element is modified. In some embodiments, at least one shell element is modified randomly. In some embodiments of block 170, the resulting intermediate 3D mesh model (also referred to herein as the “intermediate 3D model”) takes the modified finite element shell model as input, determines the forces on at least one tooth, and compares them with the corresponding therapeutic forces from block 130.

[0110] In some embodiments, at box 170, a change to the finite element shell model introduces a force system, and then at box 175, this force system is compared to the therapeutic force at box 130. In some embodiments, the comparison provides a score, and the score or multiple scores can be used to determine whether the force system achieves the therapeutic goal. As a non-limiting example, the intermediate 3D model at box 170 may have a force system more similar to the therapeutic force system at box 130 (also referred to as an "intermediate force system" or "second modeling force") compared to the force system provided by the initial 3D model at box 140. In some embodiments, at box 175, a similarity value is determined, comparing the modeling force system to the therapeutic force system. In some embodiments, a score is determined.

[0111] In some embodiments, at block 170, a change to the finite element shell model introduces a force system, which is then compared to the treatment force at block 130, and at block 175, the accuracy of the force system for at least one tooth is determined. As a non-limiting example, for a tooth, a finite element shell model that introduces the same force system as at said tooth can be considered 100% accurate. In some embodiments, the accuracy of the force system for a single tooth is determined. In some embodiments, the accuracy of the force system for multiple teeth is determined. In some embodiments, the accuracy of the entire treatment force system is determined.

[0112] In some embodiments of box 175, changes to the finite element shell model provide a material fraction corresponding to the amount of material used to manufacture the corresponding orthodontic appliance. In some embodiments, the material fraction has values ​​between 0 and 1, scaled to the actual mass value. As a non-limiting example, a material fraction with a value of 1 is scaled to 5 grams, and a value of 0 represents 0 grams, which would have a corresponding value of 0.5 representing 2.5 grams. In some embodiments, a material fraction value of 1 represents a range from 5 grams to 1 milligram, from 4 grams to 1 milligram, from 3 grams to 1 milligram, from 2 grams to 1 milligram, from 1 gram to 1 milligram, from 500 milligrams to 1 milligram, from 250 milligrams to 1 milligram, or from 125 milligrams to 1 milligram; and a material fraction value of 0 is scaled to the value of 0 grams.

[0113] In some embodiments of box 175, multiple comparisons can be used in the development of orthodontic appliances. As a non-limiting example, changes to the values ​​of the finite element shell model can result in the formation of more than one model that provides greater than 99% similarity to the treatment force system, but each model has a different material fraction; thus, orthodontic appliances with similar force systems can be created while using a reduced amount of material.

[0114] At box 170 of method 100, a finite element analysis can be performed to determine how many changes can be made before representing the desired orthodontic appliance. For example, a parametric thickness map can be represented at box 140, and changes to the shell element in box 170 can generate an intermediate force system, which is then evaluated at box 175 for similarity to the desired therapeutic force system in box 130. Based on the output of this intermediate force system at box 170, calculations can be performed to determine which shell element should be changed next, or whether random perturbation should be attempted. The calculations at box 175 and the comparisons with the intermediate 3D model and intermediate force system in box 170 can be repeated until a threshold score, similarity value, material score, or any combination thereof is obtained.

[0115] In some embodiments of block 170, at least one discrete finite shell element is modified. In some embodiments, the entire finite element shell model from block 140 is modified at block 170. As a non-limiting example, a finite element shell model with a uniform parametric thickness map can be modified to generate an intermediate 3D model with a non-uniform parametric thickness map. In some embodiments, a parametric algorithm is used to modify the parametric thickness map.

[0116] The modified shell element model at box 170 can provide a second modeling force, which can be compared at box 175 with the first modeling force (i.e., the modeling force based on the initial finite element shell model at box 140). In some embodiments of box 170, modifying at least one shell element of the finite element shell model generates at least one intermediate 3D model, which includes the second modeling force for moving the patient's tooth to its final position. In some embodiments, the second modeling force from box 170 is more similar to the therapeutic force from box 130 than the first modeling force from box 140.

[0117] In some embodiments of box 170, an algorithm, optionally software, is used to modify at least one shell element of the finite element shell model from box 140. In some embodiments, gradient-based methods and / or secant methods can be used to modify the finite element shell model of the parameterized thickness map. In some embodiments, the finite element shell model of the parameterized thickness map can be modified using software known in the art (e.g., Artelys Knitro, MATLAB Optimization Toolbox, and the pyOpt platform). In some embodiments, a moving asymptote method can be used to modify the finite element shell model of the topological density map and / or the finite element shell model of the discrete thickness map. In some embodiments, the moving asymptote method includes an iterative method for solving and / or approximating at least one value at box 175 (e.g., generating the minimum material value required for an orthodontic appliance having at least 95% similarity to the therapeutic force system). In some embodiments, the moving asymptote method includes an iterative process for generating subproblems to be solved. In some embodiments, the moving asymptote method iteratively solves for functions associated with the finite element shell model.

[0118] The modeling force of box 170 can be modified based on the input function (e.g., an asymptote moving function) until a threshold is achieved at box 175, or until further iterations of the function at box 175 do not produce a threshold change (e.g., a convergence value is observed), or a combination thereof.

[0119] In some embodiments of box 170, an explicit time-stepping method can be used to modify the finite element shell model. An explicit method can calculate the state of the system at a later time based on the system's state at the current time, as opposed to an implicit time-stepping method, which finds a solution by solving equations involving both the current and future states of the system. As a non-limiting example, an explicit time-stepping method provides the initial positions and orientations of all objects in the model, including the positions and orientations of shell elements, and their positions and orientations after a time step (e.g., to a known or calculated value). Using an explicit time-stepping method can reduce computation and increase method throughput. In some embodiments, an explicit time-stepping method utilizes mass scaling to accelerate simulation runs. In some embodiments, an implicit time-stepping method can be used.

[0120] In some embodiments of block 170, the finite element shell model can be modified using additional constraints, such as those provided at block 160. In embodiments, a constrained search space can be used to modify the finite element shell model. For example, a reduced number of parameters can be used to limit the parametric thickness map, thereby reducing the search space. Reducing the number of parameters can provide improved computational performance. Increasing the number of parameters can provide a more accurate representation, such as a more accurate representation of the modeling forces of the finite element shell model.

[0121] In some embodiments of block 170, the finite element shell model can be modified using additional input functions or algorithms, such as those provided at block 150. In embodiments, the technique used to modify the finite element shell model can employ sensitivity-based algorithms. For example, to maximize the strength of an orthodontic appliance (e.g., where accurate force and / or accurate torque are not the primary objectives), the method can be optimized to avoid using gradients. By modifying the method in this way, a reduction in computation time can be achieved.

[0122] Parametric thickness map

[0123] In some embodiments of box 140, the initial 3D model includes a generated finite element shell model having a parametric thickness map defined by a parametric function. In some embodiments of box 150, the input function for modifying the parametric thickness map includes a parametric algorithm. The thickness map can be modified by changing the parameters of the parametric algorithm and / or the sizing function, thereby generating an intermediate 3D model of the orthodontic device at box 170.

[0124] In some embodiments of box 170, the finite element shell model of box 140 is modified in multiple iterations, further transforming the parametric thickness map defined by a parametric function. As a non-limiting example, at box 175, the modification may end when further iterations do not provide the benefit of reducing the size of the 3D model of the orthodontic appliance, and / or when a threshold (e.g., a value of similarity between a first modeling force, a second modeling force, a therapeutic force, or any combination thereof) is met.

[0125] Non-limiting examples of using parametric thickness maps to model orthodontic appliances include modeling of orthodontic appliances. In some embodiments, the orthodontic appliance provides arch expansion force. In some embodiments, the appliance may be modeled for a patient missing at least one tooth, which results in reduced contact between the orthodontic appliance and the tooth compared to a patient with said missing at least one tooth. Such missing teeth lead to a reduced level of anchorage, and parametric modeling using parametric thickness maps can be used to iteratively optimize the force system. If a patient has missing teeth, an appliance designed using conventional methods may not provide sufficient force to move the target tooth (or multiple teeth) and may not provide treatment (e.g., missing teeth may result in an appliance that cannot adequately move molars in the distal direction). Parametric models can be used to model locally increased wall thickness, which can increase the force on the target tooth (or multiple teeth). As a non-limiting example, an orthodontic appliance providing arch expansion force may be designed to converge within a design region of the two missing teeth, and the model can maximize the expansion force on the target tooth (or multiple teeth), which can simplify computation and computer modeling. Figure 11A -D).

[0126] In some embodiments, the parametric thickness map and algorithm are provided with inputs having higher thickness levels in the region to reduce the processing required in areas with high stress concentration. As a non-limiting example, the thickness map of an orthodontic appliance with arch expansion force may include an increased baseline thickness for the expansion region, which can reduce computation time compared to a randomized algorithm.

[0127] In some embodiments, parametric thickness maps and / or models can be used to generate orthodontic appliances for patients with missing teeth, orthodontic appliances that provide arch expansion, orthodontic appliances that include gap closure, orthodontic appliances that address breakage issues, or any combination thereof.

[0128] In some embodiments, the parametric thickness map begins with a "fat" or overly thick orthodontic appliance and iteratively thins it during the modeling process. In some embodiments, the parametric thickness model uses random perturbations on the thickness, which can impose artificial distortion and thereby allow for optimization. In a preferred embodiment, the parametric thickness model includes constraints (e.g., Figure 1 (See box 160 in the image). A so-called "fat" thickness map can be a map where the thickness is greater than the expected final thickness at each location.

[0129] Topology density map

[0130] In some embodiments of block 140, the initial 3D model includes a generated finite element shell model having a topology density map defined by a topology algorithm. In some embodiments of block 150, the input function for changing the topology density map includes a topology algorithm. The topology density map can be changed by altering the parameters of the topology algorithm, thereby generating an intermediate 3D model of the orthodontic device at block 170.

[0131] In some embodiments, the topology density map is uniform, and the change to the value of the shell cell at box 170 is applied to all shell cells. In other embodiments, the topology density map is non-uniform after the change. In some embodiments, each individual shell cell has a value from 0 to 1. In some embodiments, each individual shell cell has a value between 0 and 1. In some embodiments, none of the individual shell cells have a value of 0.

[0132] In some embodiments of box 170, the discrete element density map defined by a topology function is modified to generate an intermediate 3D model of the orthodontic apparatus. The intermediate 3D model of the orthodontic apparatus at box 140 has a second modeling capability.

[0133] At box 175, a comparison can be made between the first modeling force of box 130, the second modeling force of box 170, the healing force provided by the treatment plan of box 110, or any combination thereof.

[0134] Optionally, the finite element shell model at box 140 is modified in multiple iterations, further transforming the discrete element density map defined by the topological function. As a non-limiting example, the modification may end when further iterations do not provide the benefit of reducing the size of the 3D model of the orthodontic appliance, and / or when a threshold (e.g., the value of similarity between the first modeling force, the second modeling force, the therapeutic force, or any combination thereof) is met.

[0135] In some embodiments, the topology density model moves material in a non-parametric manner. In some embodiments, the topology density model may trade off volume between one location and another during optimization. For example, a maximum material mass for a given mass can be used for the orthodontist, and once or if that mass is reached during optimization, instead of adding additional volume during optimization, the mass or volume is conserved during modeling, such that adding volume or mass at one location results in removing volume or mass at another location. In some embodiments, the topology density model uses a random perturbation to the thickness, which can impose artificial distortion and thus allow for optimization.

[0136] Figure 14A schematic diagram of a method 1400 for determining the geometry of an orthodontic appliance using topology optimization is depicted. Method 1400 provides an example procedure for determining the geometry of an orthodontic appliance using an initial 3D model and a finite element model. At box 1410, a treatment plan is developed. At box 1420, a dentition assessment is obtained. At box 1420, a dentition assessment is obtained for each stage of the treatment plan. In some embodiments, the dentition assessment is used to generate a model of the patient's teeth, and at box 1440, an initial 3D model of the orthodontic appliance can be generated. Furthermore, at box 1440, a finite element model of the orthodontic appliance can be generated.

[0137] In some embodiments, Figure 14 Box 1410 corresponds to and / or merges Figure 1 Box 110. In some embodiments, Figure 14 Box 1420 corresponds to and / or merges Figure 1 Box 120. In some embodiments, Figure 14 Box 1430 corresponds to and / or merges Figure 1 Box 130. In some embodiments, Figure 14 Box 1450 corresponds to and / or merges Figure 1 Box 150. In some embodiments, Figure 14 Box 1460 corresponds to and / or merges Figure 1 Box 160. In some embodiments, Figure 14 Box 1475 corresponds to and / or merges Figure 1 Box 175. In some embodiments, Figure 14 Box 1480 corresponds to and / or merges Figure 1 The frame is 180.

[0138] In some embodiments of method 1400, at box 1470, the volumetric element model from box 1440 can be altered by providing variations in the volumetric elements. Topology optimization can begin with a homogeneous material and can be optimized by changing the properties of each element. In some embodiments, the model at box 1440 has a uniform thickness. In some embodiments of box 1470, the volumetric elements are modified from one location to another, resulting in a heterogeneous model. In some embodiments of box 1470, an element analysis platform is used to analyze the modeled force system. In some embodiments, at least one volumetric element is modified, for example, by utilizing a different density. In some embodiments, at least one volumetric element is modified randomly. In some embodiments of box 1470, the resulting intermediate 3D model (also referred to herein as the “intermediate 3D model”) takes the modified finite volumetric element model as input, determines the forces on at least one tooth, and compares them with the corresponding therapeutic forces from box 1430.

[0139] In some embodiments of box 1470, the force system applied by the change in the finite volume element model is then compared at box 1475 with the therapeutic force of box 1430. In some embodiments, the comparison provides a score, and the score or multiple scores can be used to determine whether the force system achieves the therapeutic goal. As a non-limiting example, the intermediate 3D model at box 1470 may have a force system more similar to the therapeutic force system at box 1430 (also referred to as the "intermediate force system" or "second modeling force") compared to the force system provided by the initial 3D model at box 1440. In some embodiments of box 1475, a similarity value is determined, comparing the modeling force system with the therapeutic force system. In some embodiments, a score is determined.

[0140] In some embodiments of block 1470, a modification to the finite volume element model results in a force system, which is then compared to the treatment force at block 1430, and at block 1475, the accuracy of the force system for at least one tooth is determined. As a non-limiting example, for a tooth, a finite volume element model that produces the same force system as the force system at said tooth can be considered 100% accurate. In some embodiments, the accuracy of the force system for a single tooth is determined. In some embodiments, the accuracy of the force system for multiple teeth is determined. In some embodiments, the accuracy of the entire treatment force system is determined.

[0141] In some embodiments of box 1475, changes to the finite volume element model provide a material fraction corresponding to the amount of material used to manufacture the corresponding orthodontic appliance. In some embodiments, the material fraction has a value between 0 and 1, which is scaled to the actual value of the mass.

[0142] In some embodiments of box 1475, multiple comparisons can be used in the development of orthodontic appliances. As a non-limiting example, changing the values ​​of a finite volume element model can result in the formation of more than one model that provides greater than 99% similarity to the treatment force system, but each model has a different material fraction; thus, orthodontic appliances with similar force systems can be created while using a reduced amount of material.

[0143] At box 1470 of method 1400, a finite volume element analysis can be performed to determine how many changes can be made before representing the desired orthodontic appliance. For example, topology optimization can be represented at box 1440, and changes to the volume elements in box 1470 can produce an intermediate force system, which is then evaluated at box 1475 for similarity to the desired therapeutic force system of box 1430. Based on the output of this intermediate force system at box 1470, calculations can be performed to determine which volume element should be changed next, or whether random perturbation should be attempted. The calculations at box 1475 and the comparisons with the intermediate 3D model and intermediate force system of box 1470 can be repeated until a threshold score, similarity value, material score, or any combination thereof is obtained.

[0144] In some embodiments of block 1470, at least one discrete finite volume element is modified. In some embodiments, the entire finite volume element model from block 1440 is modified at block 1470. As a non-limiting example, a finite element shell model with a uniformly parameterized thickness map can be modified to generate an intermediate 3D model with a non-uniform thickness map. In some embodiments, an algorithm is used to modify the thickness map.

[0145] The modified volumetric element model at frame 1470 can provide a second modeling force, which can be compared at frame 1475 with a first modeling force (i.e., a modeling force based on the initial finite volumetric element model at frame 1440). In some embodiments of frame 1470, modifying at least one volumetric element of the finite volumetric element model generates at least one intermediate 3D model, which includes a second modeling force for moving the patient's tooth to its final position. In some embodiments, the second modeling force from frame 1470 is more similar to the therapeutic force from frame 1430 than the first modeling force from frame 1440.

[0146] In some embodiments of block 1470, an algorithm, optionally software, is used to modify at least one volume element of the finite volume element model from block 1440. In some embodiments, gradient-based methods and / or secant methods can be used to modify the finite volume element model of the thickness map. In some embodiments, the finite volume element model of the thickness map can be modified using software known in the art (e.g., Artelys Knitro, MATLAB Optimization Toolbox, and the pyOpt platform). In some embodiments, a moving asymptote method can be used to modify the finite volume element model of the topology density map. In some embodiments, the moving asymptote method includes an iterative method for solving and / or approximating at least one value at block 1475 (e.g., generating the minimum material value required to generate an orthodontic appliance with at least 95% similarity to the therapeutic force system). In some embodiments, the moving asymptote method includes an iterative process for generating subproblems to be solved. In some embodiments, the moving asymptote method iteratively solves for a function associated with the finite volume element model.

[0147] The modeling force of box 1470 can be modified based on the input function (e.g., an asymptote shift function) until a threshold is achieved at box 1475, or until further iterations of the function at box 1475 do not produce a threshold change (e.g., a convergence value is observed), or a combination thereof.

[0148] In some embodiments of block 1470, an explicit time-stepping method can be used to modify the finite volume element model. In some embodiments of block 1470, additional constraints, such as those provided at block 1460, can be used to modify the finite volume element model. In embodiments, a constrained search space can be used to modify the finite element shell model. For example, a thickness map can be defined using localized portions including teeth or multiple teeth to reduce the search space. Reducing the size of the localized portions can provide improved computational performance. Increasing the size of the localized portions can provide a more accurate representation, for example, a more accurate representation of the modeling forces of the finite element shell model.

[0149] In some embodiments of block 1470, the finite volume element model can be modified using additional input functions or algorithms, such as those provided at block 1450. In embodiments, the technique for modifying the finite volume element model can use sensitivity-based algorithms. For example, to maximize the strength of an orthodontic appliance (e.g., where accurate force and / or accurate torque are not the primary objectives), the method can be optimized to avoid using gradients. By modifying the method in this way, a reduction in computation time can be achieved.

[0150] Discrete thickness map

[0151] In some embodiments of block 140, the initial 3D model includes a generated finite element shell model having a discrete thickness map defined by a sizing algorithm. In some embodiments of block 150, the input function for modifying the discrete thickness map includes a sizing algorithm. The discrete thickness map can be modified by changing the parameters of the sizing algorithm, thereby generating an intermediate 3D model of the orthodontic device at block 170.

[0152] In some embodiments of block 150, the discrete thickness map can be used with an algorithm to change the value of at least one shell element from block 170. In some embodiments, the discrete thickness map is changed in block 170 using a sizing algorithm provided by block 150. In some embodiments, the discrete thickness map is uniform, and the change in the value of the shell element is applied to all shell elements. In other embodiments, the discrete thickness map is non-uniform after the change. In some embodiments, each individual shell element has a value from 0 to 1. In some embodiments, each individual shell element has a value between 0 and 1. In some embodiments, none of the individual shell elements has a value of 0.

[0153] In some embodiments of box 170, the discrete element thickness map defined by a topological function is modified to generate an intermediate 3D model of the orthodontic apparatus. The discrete element thickness map can be modified by changing the sizing function to generate the intermediate 3D model of the orthodontic apparatus. The intermediate 3D model of the orthodontic apparatus at box 140 has a second modeling force.

[0154] At box 175, a comparison can be made between the first modeling force of box 130, the second modeling force of box 170, the healing force provided by the treatment plan of box 110, or any combination thereof.

[0155] Optionally, the finite element shell model at box 140 is modified in multiple iterations, further transforming the discrete element density map defined by the size adjustment function. As a non-limiting example, the modification may end when further iterations do not provide the benefit of reducing the size of the 3D model of the orthodontic appliance, and / or when a threshold (e.g., a value of similarity between the first modeling force, the second modeling force, the therapeutic force, or any combination thereof) is met.

[0156] In some embodiments, a discrete thickness map is used in conjunction with a size adjustment optimization model, wherein the shell representing the thickness parameter is optimized. In some embodiments, the size adjustment optimization model may adjust the shell values ​​during optimization. In some embodiments, the size adjustment optimization model uses random perturbations on the shell thickness values, which may impose artificial distortion and thereby enable optimization.

[0157] Figure 15A schematic diagram of method 1500 for determining the geometry of an orthodontic appliance using size adjustment optimization is depicted. Method 1500 provides an example process for determining the geometry of an orthodontic appliance using an initial 3D model and a finite shell element model, where the shell represents a thickness parameter. At box 1510, a treatment plan is developed. At box 1520, a dentition assessment is obtained. At box 1520, a dentition assessment is obtained for each stage of the treatment plan. In some embodiments, the dentition assessment is used to generate a model of the patient's teeth, and at box 1540, an initial 3D model of the orthodontic appliance can be generated. Furthermore, at box 1540, a finite volume element model of the orthodontic appliance can be generated.

[0158] In some embodiments, Figure 15 Box 1510 corresponds to and / or merges Figure 1 Box 110. In some embodiments, Figure 15 Box 1520 corresponds to and / or merges Figure 1 Box 120. In some embodiments, Figure 15 Box 1530 corresponds to and / or merges Figure 1 Box 130. In some embodiments, Figure 15 Box 1550 corresponds to and / or merges Figure 1 Box 150. In some embodiments, Figure 15 Box 1560 corresponds to and / or merges Figure 1 Box 160. In some embodiments, Figure 15 Box 1575 corresponds to and / or merges Figure 1 Box 175. In some embodiments, Figure 15 Box 1580 corresponds to and / or merges Figure 1 The frame is 180.

[0159] In some embodiments, method 1500 discloses a housing unit. In some embodiments, beam units may be used instead of housing units. In some embodiments, beam units replace housing units throughout method 1500.

[0160] In some embodiments of method 1500, at block 1570, the shell element model from block 1540 can be modified by providing a change in the shell thickness value. Size adjustment optimization can begin with a homogeneous representation of thickness and can be optimized by changing the thickness value. In a preferred embodiment, changing the values ​​of the finite element shell model maintains a constant total thickness value. In some embodiments, the model at block 1540 has a shell model where the shell has homogeneous thickness values ​​(i.e., identical). In some embodiments of block 1570, shell element values ​​are moved from one location to another, thus forming a non-homogeneous model. In some embodiments of block 1570, an element analysis platform is used to analyze the modeled force system. In some embodiments, at least one shell element value is modified. In some embodiments, at least one shell element value is randomly modified. In some embodiments of block 1570, the resulting intermediate 3D mesh model (also referred to herein as the “intermediate 3D model”) takes the modified finite shell element model as input, determines the forces on at least one tooth, and compares them with the corresponding treatment forces from block 1530.

[0161] In some embodiments of box 1570, the modification of the finite volume element model results in a force system that is then compared at box 1575 with the therapeutic force of box 1530. In some embodiments, the comparison provides a score, and the score or multiple scores can be used to determine whether the force system achieves the therapeutic goal. As a non-limiting example, the intermediate 3D model at box 1570 may have a force system more similar to the therapeutic force system at box 1530 (also referred to as an "intermediate force system" or "second modeling force") compared to the force system provided by the initial 3D model at box 1540. In some embodiments of box 1575, a similarity value is determined by comparing the modeled force system with the therapeutic force system. In some embodiments, a score is determined.

[0162] In some embodiments of block 1570, a modification to the finite volume element model results in a force system, which is then compared to the treatment force at block 1530, and at block 1575, the accuracy of the force system for at least one tooth is determined. As a non-limiting example, for a tooth, a finite shell element model that produces the same force system as at said tooth can be considered 100% accurate. In some embodiments, the accuracy of the force system for a single tooth is determined. In some embodiments, the accuracy of the force system for multiple teeth is determined. In some embodiments, the accuracy of the entire treatment force system is determined.

[0163] In some embodiments of block 1575, variations in the finite shell element model provide a material fraction corresponding to the amount of material used to manufacture the corresponding orthodontic appliance. In some embodiments, the material fraction has a value between 0 and 1, which is scaled to the actual mass value.

[0164] In some embodiments of box 1575, multiple comparisons can be used in the development of orthodontic appliances. As a non-limiting example, changing the values ​​of a finite shell unit model can result in the formation of more than one model that provides greater than 99% similarity to the therapeutic force system, but each model has a different material fraction; thus, orthodontic appliances with similar force systems can be created while using a reduced amount of material.

[0165] At box 1570 of method 1500, a finite shell element analysis can be performed to determine how many changes can be made before representing the desired orthodontic appliance. For example, sizing optimization can be represented at box 1540, and changes to the shell elements in box 1570 can produce an intermediate force system, which is then evaluated at box 1575 for similarity to the desired therapeutic force system of box 1530. Based on the output of this intermediate force system at box 1570, calculations can be performed to determine which shell element should be changed next, or whether random perturbation should be attempted. The calculations at box 1575 and the comparisons with the intermediate 3D model and intermediate force system of box 1570 can be repeated until a threshold score, similarity value, material score, or any combination thereof is obtained.

[0166] In some embodiments of block 1570, at least one discrete finite shell element is modified. In some embodiments, the entire finite shell element model from block 1540 is modified at block 1570. As a non-limiting example, a finite element shell model with a uniform thickness parameter can be modified to generate an intermediate 3D model with a non-uniform thickness map. In some embodiments, an algorithm is used to modify the non-parametric thickness map.

[0167] The modified shell element model at frame 1570 can provide a second modeling force, which can be compared at frame 1575 with a first modeling force (i.e., a modeling force based on the initial finite volume element model at frame 1540). In some embodiments of frame 1570, modifying at least one volume element of the finite volume element model generates at least one intermediate 3D model, which includes a second modeling force for moving the patient's tooth to its final position. In some embodiments, the second modeling force from frame 1570 is more similar to the therapeutic force from frame 1530 than the first modeling force from frame 1540.

[0168] In some embodiments of block 1570, an algorithm, optionally software, is used to modify at least one shell element of the finite shell element model from block 1540. In some embodiments, gradient-based methods and / or secant methods can be used to modify the finite shell element model of the nonparametric thickness map. In some embodiments, the finite shell element model of the nonparametric thickness map can be modified using software known in the art (e.g., Artelys Knitro, MATLAB Optimization Toolbox, and the pyOpt platform). In some embodiments, a moving asymptote method can be used to modify the finite shell element model of the nonparametric thickness map. In some embodiments, the moving asymptote method includes an iterative method for solving and / or approximating at least one value at block 1575 (e.g., for generating a minimum material value for an orthodontic appliance having at least 95% similarity to the therapeutic force system). In some embodiments, the moving asymptote method includes an iterative process for generating subproblems to be solved. In some embodiments, the moving asymptote method iteratively solves for a function associated with the finite shell element model.

[0169] The modeling force of box 1570 can be modified based on the input function (e.g., an asymptote shift function) until a threshold is achieved at box 1575, or until further iterations of the function at box 1575 do not produce a threshold change (e.g., a convergence value is observed), or a combination thereof.

[0170] In some embodiments of block 1570, an explicit time-stepping method can be used to modify the finite shell element model. In some embodiments of block 1570, additional constraints, such as those provided at block 1560, can be used to modify the finite shell element model. In embodiments, a constrained search space can be used to modify the finite element shell model. For example, a nonparametric thickness map can be defined using localized portions including teeth or multiple teeth to reduce the search space. Reducing the size of the localized portions can provide improved computational performance. Increasing the size of the localized portions can provide a more accurate representation, for example, a more accurate representation of the modeling forces of the finite element shell model.

[0171] In some embodiments of block 1570, the finite shell element model can be modified using additional input functions or algorithms, such as those provided at block 1550. In embodiments, the technique for modifying the finite shell element model can use sensitivity-based algorithms. For example, to maximize the strength of an orthodontic appliance (e.g., where accurate force and / or accurate torque are not the primary objectives), the method can be optimized to avoid using gradients. By modifying the method in this way, a reduction in computation time can be achieved.

[0172] Complete the change

[0173] In some embodiments, at least one of the shell units of the intermediate 3D model is modified to generate a second intermediate 3D model of the orthodontic device having a third modeling force. In some embodiments, the intermediate 3D shell model has at least one shell unit that has been modified, and the resulting third modeling force is compared with a first modeling force, a second modeling force, and / or a therapeutic force.

[0174] In some embodiments, at least one of the first modeling force, second modeling force, third modeling force, and therapeutic force is compared with any one of the first modeling force, second modeling force, third modeling force, and therapeutic force to determine whether further changes are needed. For example, some embodiments of method 100 provide a similarity comparison at block 175, wherein the first modeling force, second modeling force, third modeling force, and therapeutic force according to the treatment plan are compared until a value or parameter has been satisfied. In some embodiments, the finite element shell model is modified until a threshold similarity value is obtained. In some embodiments, the finite element shell model is modified until a threshold score is obtained. In some embodiments, the finite element shell model is modified until no improvement is observed in the score and / or similarity value.

[0175] In some embodiments, at least one of the first modeling force, the second modeling force, and the third modeling force is compared with the therapeutic force to provide a similarity value (e.g., at box 175). In some embodiments, the similarity value is a percentage match with the therapeutic force. For example, the first modeling force, the second modeling force, or both the first modeling force and the second modeling force may have a similarity greater than 50%, greater than 60%, greater than 70%, greater than 80%, greater than 90%, greater than 91%, greater than 92%, greater than 93%, greater than 94%, greater than 95%, greater than 96%, greater than 97%, greater than 98%, or greater than 99%.

[0176] In some embodiments, the finite shell model is modified until a threshold similarity value is obtained (e.g., at box 175). In some embodiments, the threshold similarity value is when the first modeling force, the second modeling force, the third modeling force, or any combination thereof has a similarity to the therapeutic force greater than 50%, greater than 60%, greater than 70%, greater than 80%, greater than 90%, greater than 91%, greater than 92%, greater than 93%, greater than 94%, greater than 95%, greater than 96%, greater than 97%, greater than 98%, or greater than 99%.

[0177] In some embodiments, the finite shell model is modified until a threshold score is obtained (e.g., at box 175).

[0178] In some embodiments, the finite shell model is modified until a threshold shell element value is obtained (e.g., at box 175). The shell element value can be the minimum value of the map. For example, for a parametric thickness map, a threshold shell element value can be selected such that the thickness does not reach zero at any point in the aligner, thereby preventing unwanted holes in the aligner design. In some embodiments, the threshold shell element value is the thickness of the orthodontic appliance. In some embodiments, the threshold shell element value is less than 1 mm, less than 900 μm, less than 800 μm, less than 700 μm, less than 600 μm, less than 500 μm, less than 400 μm, less than 300 μm, less than 200 μm, less than 100 μm, or less than 50 μm.

[0179] In some embodiments, the finite shell model is purposefully modified to increase the similarity to the intermediate 3D model in each iteration (e.g., at box 175). In some embodiments, the finite shell model is modified until no further improvement is obtained through further modifications (e.g., a high similarity value is reached). Orthodontic appliances can be fabricated using the intermediate finite element shell model that provides the desired similarity value or score.

[0180] Using the methods disclosed herein, the geometry of orthodontic appliances can be determined with reduced computation time compared to conventional solid orthodontic appliance modeling. In some embodiments, the method for determining the geometry of orthodontic appliances provides a reduction in computation time of greater than 40%, greater than 45%, greater than 50%, greater than 55%, greater than 60%, greater than 65%, greater than 70%, greater than 75%, greater than 80%, greater than 85%, greater than 90%, or greater than 95% compared to conventional solid orthodontic appliance models.

[0181] In some embodiments, the 3D model of the orthodontic appliance is an idealized model in which characteristics can be ignored. In some embodiments, idealization may ignore material properties, manufacturing defects, density gradients, thickness gradients, variations in shell elements of a finite element shell model, etc.

[0182] Additional process

[0183] In some embodiments, upon obtaining a threshold shell unit value, a score, a threshold similarity value, or a combination thereof (e.g., at box 175), a final model is generated (e.g., at box 180). The final model is a 3D model of an orthodontic appliance having a desired force system substantially similar to the therapeutic force. Further modifications can be made to the final model. As a non-limiting example, the final model providing the desired force system can be further modified to provide aesthetically pleasing features. Manufacturing instructions can be generated at box 180.

[0184] In some embodiments, a manufactured product is created based on the final model provided by box 180. Various embodiments of orthodontic appliances can be manufactured in a variety of ways. In some embodiments, the orthodontic appliance (or portions thereof) described herein can be produced using direct manufacturing techniques, such as additive manufacturing (also referred to herein as “3D printing”) or subtractive manufacturing techniques (e.g., milling). In some embodiments, direct manufacturing involves forming an object (e.g., an orthodontic appliance or a portion thereof) without using physical templates (e.g., molds, masks, etc.) to define the object's geometry.

[0185] In some embodiments, the orthodontic appliances described herein may be manufactured using a combination of direct and indirect manufacturing techniques, such that different parts of the appliance may be manufactured using different manufacturing techniques and assembled to form the final appliance. For example, the appliance housing may be formed by indirect manufacturing (e.g., thermoforming), and one or more structures or components described herein (e.g., auxiliary components, power arms, etc.) may be added to the housing by direct manufacturing (e.g., printing onto the housing).

[0186] The configuration of the orthodontic appliances described herein can be determined based on the patient's treatment plan using the methods described above. Computer-based treatment planning and / or appliance manufacturing methods can be used to facilitate the design and manufacture of the appliances. For example, one or more appliance components described herein can have geometries digitally determined and manufactured with the aid of computer-controlled manufacturing apparatus (e.g., computer numerical control (CNC) milling, computer-controlled additive manufacturing, such as 3D printing, etc.). The computer-based methods proposed herein can improve the accuracy, flexibility, and convenience of appliance manufacturing.

[0187] In some embodiments, computer-based 3D planning / design tools, such as Treat from Align Technology, Inc. TM The software can be used to design and manufacture the orthodontic appliances described in this article.

[0188] Instructions for manufacturing orthodontic appliances can be generated (e.g., at box 180). These instructions can be configured to control a manufacturing system or apparatus to produce orthodontic appliances having desired appliance geometry and material composition. In some embodiments, these instructions are configured to manufacture orthodontic appliances using direct manufacturing methods (e.g., stereolithography, selective laser sintering, fused deposition modeling, 3D printing, continuous direct manufacturing, multimaterial direct manufacturing, etc.). Optionally, these instructions can be configured to cause a manufacturing machine to directly manufacture orthodontic appliances having a tooth-receiving cavity with a variable gable bend. In alternative embodiments, the instructions can be configured to indirectly manufacture the appliance, for example, by thermoforming. Any suitable manufacturing system or apparatus can be used in the manufacture of orthodontic appliances described herein.

[0189] Compared to comparable conventional orthodontic appliances with the same therapeutic force system, orthodontic appliances can be constructed using less material using the methods disclosed herein. Orthodontic appliances manufactured according to the methods disclosed herein can use less than 5 grams of material, less than 4.5 grams of material, less than 4 grams of material, less than 3.5 grams of material, less than 3 grams of material, less than 2.5 grams of material, less than 2 grams of material, less than 1.5 grams of material, less than 1.4 grams of material, less than 1.3 grams of material, less than 1.2 grams of material, less than 1.1 grams of material, less than 1.0 grams of material, less than 0.9 grams of material, less than 0.8 grams of material, less than 0.7 grams of material, less than 0.6 grams of material, less than 0.5 grams of material, less than 0.4 grams of material, less than 0.3 grams of material, less than 0.2 grams of material, or less than 0.1 grams of material.

[0190] Figure 3AAn exemplary tooth repositioning appliance or orthodontic appliance 300 is illustrated, which can be manufactured using the methods disclosed herein and worn by a patient to achieve progressive repositioning of individual teeth 302 in the jaw. The appliance may include a housing (e.g., a continuous polymer housing or a segmented housing) having tooth-receiving cavities that accommodate and resiliently reposition the teeth. The appliance, or one or more portions thereof, may be indirectly manufactured using a solid model of the teeth. For example, the appliance (e.g., a polymer appliance) may be formed using a solid model of the teeth and sheets of polymer material with an appropriate number of layers. The solid model of the teeth (e.g., a solid mold) may be formed using various techniques, including 3D printing. The appliance may be formed by thermoforming the appliance on the solid model. In some embodiments, the solid appliance is manufactured directly based on a digital model of the appliance, for example using additive manufacturing techniques. In some embodiments, the solid appliance may be manufactured using various direct forming techniques such as 3D printing. The appliance may be mounted on all teeth present in the maxilla or mandible, or not on all teeth. The appliance may be constructed to fit the patient's teeth (e.g., the topography of the tooth-receiving cavity matches the topography of the patient's teeth) and may be manufactured based on a positive or negative model of the patient's teeth generated by impression, scanning, etc. Alternatively, the appliance may be a general-purpose appliance configured to receive teeth but not necessarily shaped to match the topography of the patient's teeth. In some cases, only certain teeth received by the appliance are repositioned by the appliance, while other teeth may provide a base or anchorage region to hold the appliance in place when the appliance applies force to one or more teeth that become the repositioning target. In some cases, at some point during treatment, some teeth, most teeth, or even all teeth will be repositioned. The moved teeth may also serve as a base or anchorage to hold the appliance in place when the appliance is worn by the patient. In some embodiments, no thread or other means for holding the appliance on the teeth are provided. However, in some cases, it may be desirable or necessary to provide separate attachments or other anchorage elements 304 on the teeth 302, having corresponding apexes or holes 306 in the appliance 300, so that the appliance can apply selected forces on the teeth. Numerous patents and patent applications assigned to Align Technology, Inc. (including, for example, U.S. Patent Nos. 6,450,807 and 5,975,893) and on the company's website accessible on the World Wide Web (see, for example, the url "invisalign.com") describe the inclusion of Exemplary appliances, including those used in the system. Examples of attachments suitable for use with orthodontic appliances are also described in patents and patent applications assigned to Allianz Technologies, including, for example, U.S. Patent Nos. 6,309,215 and 6,830,450.

[0191] Alternatively, in cases involving more complex mobility or treatment options, it may be advantageous to use auxiliary components (e.g., features, accessories, structures, devices, components, etc.) in conjunction with orthodontic appliances. Examples of these accessories include, but are not limited to, elastics, wires, springs, bars, arch expanders, palatal expanders, twin blocks, occlusal blocks, bite ramps, mandibular advancement splints, biteplates, pontics, hooks, brackets, headgear tubes, springs, bumper tubes, palatal bars, frameworks, pin-and-tube apparatuses, buccal shields, buccinator bows, wire shields, lingual flanges and pads, lippads or bumpers, protrusions, and divots. In some embodiments, the appliances, systems, and methods described herein include modified orthodontic appliances having integrally formed features that are shaped to couple with or replace these auxiliary components.

[0192] Figure 3BA tooth repositioning system 310 comprising multiple appliances 312, 314, and 316 is illustrated. Any orthodontic appliance described herein can be designed and / or provided as part of a set of multiple appliances for use in a tooth repositioning system. Each appliance can be configured such that the tooth receiving cavity has a geometry corresponding to the intermediate or final tooth alignment intended by that appliance. By placing a series of progressive position adjustment appliances on the patient's teeth, the patient's teeth can be progressively repositioned from an initial tooth alignment toward a target tooth alignment. For example, the tooth repositioning system 310 may include a first appliance 312 corresponding to the initial tooth alignment, one or more intermediate appliances 314 corresponding to one or more intermediate alignments, and a final appliance 316 corresponding to the target alignment. The target tooth alignment may be the planned final tooth alignment selected for the patient's teeth at the end of all planned orthodontic treatment. Alternatively, the target alignment can be one of several intermediate alignments of the patient's teeth during orthodontic treatment, which may include a variety of different treatment scenarios, including but not limited to: recommendations for surgery, the suitability of interproximal resection (IPR), scheduling of progress checks, optimal anchoring placement, the need for palatal expansion, involvement of dental restorations (e.g., inlays, onlays, crowns, bridges, implants, veneers, etc.). Thus, it should be understood that the target tooth alignment can be any planned alignment of the patient's teeth following one or more progressive repositioning stages. Similarly, the initial tooth alignment can be any initial alignment of the patient's teeth followed by one or more progressive repositioning stages.

[0193] Data processing system Figure 4 This can be used to perform the methods and processes described herein. Data processing system 400 typically includes at least one processor 402 that communicates with one or more peripheral devices via a bus subsystem 404. These peripheral devices typically include a storage subsystem 406 (memory subsystem 408 and file storage subsystem 414), a set of user interface input and output devices 418, and an interface 416 to an external network. This interface is schematically shown as a "network interface" box 416 and is coupled to corresponding interface devices in other data processing systems via a communication network interface 424. Data processing system 400 may include, for example, one or more computers, such as personal computers, workstations, mainframes, laptops, etc.

[0194] The user interface input device 418 is not limited to any particular device and can generally include, for example, a keyboard, a pointing device, a mouse, a scanner, an interactive display, a touchpad, a joystick, etc. Similarly, various user interface output devices can be used in the system of the present invention and may include one or more of, for example, a printer, a display (e.g., visual, non-visual) system / subsystem, a controller, a projection device, an audio output, etc.

[0195] Storage subsystem 406 maintains the basic programming requirements, including computer-readable media with instructions (e.g., operation instructions, etc.) and data structures. The program modules discussed herein are typically stored in storage subsystem 406. Storage subsystem 406 typically includes memory subsystem 408 and file storage subsystem 414. Memory subsystem 408 typically includes multiple memories (e.g., RAM 410, ROM 412, etc.), including computer-readable storage for storing fixed instructions, instructions and data during program execution, basic input / output systems, etc. File storage subsystem 414 provides permanent (non-volatile) storage of program and data files and may include one or more removable or fixed drives or media, hard disks, floppy disks, CD-ROMs, DVDs, optical disc drives, etc. One or more of the storage systems, drives, etc., may be located remotely, for example, coupled via a server on a network or via the Internet / World Wide Web. In this context, the term "bus subsystem" is generally used to include any mechanism for enabling various components and subsystems to communicate with each other as intended, and may include various suitable components / systems that would be known or considered suitable for use therein. It should be recognized that the various components of the system may, but are not necessarily, in the same physical location, but may be connected via various local area network or wide area network media, transmission systems, etc.

[0196] Scanner 420 includes any means for acquiring a digital representation (e.g., images, surface topography data, etc.) of a patient's teeth (e.g., by scanning a physical model of a tooth such as a casting 421, by scanning an impression of the acquired teeth, or by directly scanning the intraoral cavity), which may be obtained from the patient or from a professional therapist (e.g., an orthodontist), and scanner 420 also includes means for providing the digital representation to data processing system 400 for further processing. Scanner 420 may be located at a remote location relative to other components of the system and may transmit image data and / or information to data processing system 400, for example, via network interface 424. Manufacturing system 422 manufactures orthodontic appliance 423 based on a treatment plan that includes dataset information received from data processing system 400. For example, manufacturing system 422 may be located at a remote location and receive dataset information from data processing system 400 via network interface 424. Camera 425 may include any image capture means configured to capture still images or video. Camera 425 may help capture various views of the patient's dentition. In some implementations, camera 425 can help capture images at different focal lengths at different distances from the patient.

[0197] The data processing aspects of the methods described herein can be implemented in digital electronic circuits, or in computer hardware, firmware, software, or suitable combinations thereof. The data processing apparatus can be implemented in a computer program product, which is physically embodied in a machine-readable storage device for execution by a programmable processor. Data processing blocks can be executed by a programmable processor that executes program instructions to perform functions by manipulating input data and producing output. The data processing aspects can be implemented as one or more computer programs executable on a programmable system including one or more programmable processors operatively coupled to a data storage system. Typically, the processor receives instructions and data from read-only memory and / or random access memory. Suitable storage devices that physically contain computer program instructions and data include all forms of non-volatile memory, such as: semiconductor memory devices, such as EPROM, EEPROM, and flash memory devices; disks, such as internal hard disks and removable disks; magneto-optical disks; and CD-ROM disks.

[0198] Design dental appliances

[0199] Figure 5 A schematic diagram of a method 500 for designing dental appliances according to some embodiments disclosed herein is depicted. Method 500 provides an example process for designing dental appliances using an appliance model iteratively modeled with an iteratively decreasing thickness. At box 502, a treatment plan is gathered. As disclosed in method 100, the treatment plan may include multiple stages for moving a patient's teeth from an initial position to a final position. A dentition assessment may be obtained, and a desired force system may be arranged based on the patient's dentition. At box 504 of method 500, one or more stages of the treatment plan are identified. In some embodiments, the treatment plan is formulated with a desired therapeutic force system that can directionally induce planned movement of the patient's teeth. In some embodiments, the treatment plan includes a desired therapeutic force system that can directionally induce planned movement of at least a portion of the patient's teeth.

[0200] In some embodiments, a dentition assessment is obtained at the end of at least one phase of the treatment plan. At box 506 of method 500, the expected outcome for at least a portion of the patient's dentition at the end of at least one phase of the treatment plan is identified. As further discussed at box 110 of method 100, the expected outcome for at least a portion of the patient's dentition at the end of at least one phase of the treatment plan may be the final position of the patient's teeth at said phase. At box 506, the treatment plan includes a plan for treating at least a portion of the dentition. In some embodiments, the plan for treating at least a portion of the dentition includes applying therapeutic forces to said portion of the dentition. In some embodiments, the plan for treating at least a portion of the dentition includes applying forces to provide adjustment to the patient's teeth or dentition. At box 508, one or more forces applied to at least a portion of the dentition during at least one phase of the treatment plan are identified. In some embodiments, at least one force applied to at least a portion of the dentition during at least one phase of the treatment plan is identified. In some embodiments, multiple forces applied to at least a portion of the dentition during at least one phase of the treatment plan are identified. In some embodiments, at least a portion of the dentition includes portions of one or more teeth of the dentition, and at least a portion of the orthodontic appliance is configured to receive the one or more teeth and apply one or more forces to the one or more teeth.

[0201] In some embodiments, at least one stage of the treatment plan includes an initial stage of the treatment plan. In some embodiments, at least one stage of the treatment plan includes a final stage of the treatment plan. In some embodiments, at least one stage of the treatment plan includes an intermediate stage of the treatment plan. In some embodiments, at least one stage of the treatment plan includes multiple stages of the treatment plan. In some embodiments, at least one stage includes at least one of the following: an initial stage of the treatment plan, a final stage of the treatment plan, an intermediate stage of the treatment plan, multiple stages of the treatment plan, or any combination thereof.

[0202] In some embodiments, at least one criterion identifies clinical acceptability for at least one stage of a treatment plan. In some embodiments, multiple criteria identify clinical acceptability for at least one stage of a treatment plan. Clinical acceptability criteria provide standards for assessing conformity with expected outcomes. In some embodiments, one or more clinical acceptability criteria identify at least one stage of a treatment plan, and these one or more clinical acceptability criteria provide standards for assessing conformity with expected outcomes. Some non-limiting examples of criteria for assessing conformity with expected outcomes are provided in the above discussion of threshold scores, similarity values, material scores, or any combination thereof. In some embodiments, one or more clinical acceptability criteria include a clinical acceptability score that represents the probability of statistical correlation with the expected outcome. In some embodiments, the expected outcome corresponds to a treatment force system established in the treatment plan. In some embodiments, one or more clinical acceptability criteria indicate an acceptable biomechanical outcome for the completion of at least one stage of the treatment plan. In some embodiments, one or more clinical acceptability criteria indicate an acceptable biomechanical outcome for the completion of the treatment plan. In some embodiments, an acceptable biomechanical outcome includes an acceptable position of at least a portion of the dentition at the end of the at least one stage or acceptable forces on at least a portion of the dentition during the at least one stage. In some embodiments, an acceptable biomechanical outcome includes an acceptable position of at least a portion of the dentition at the end of the at least one phase, an acceptable force on at least a portion of the dentition at the end of the at least one phase, or any combination thereof. In some embodiments, one or more clinical acceptability criteria indicate acceptable physiological stress on at least a portion of the dentition during the at least one phase. In some embodiments, the acceptable physiological stress corresponds to at least one force determined in the treatment force system of block 130 of method 100. In some embodiments, one or more clinical acceptability criteria indicate acceptable appliance structural characteristics for the apparatus used to implement the at least one phase of the treatment plan. In some embodiments, acceptable appliance structural characteristics for dental appliances include variable thickness appliances having an resulting thickness on at least a portion of the dentition. The resulting thickness is further defined below.

[0203] As further disclosed herein, an orthodontic appliance model can be generated. At box 510 of method 500, an orthodontic appliance model is collected for at least one stage. The orthodontic appliance model includes a model of an appliance for at least a portion of the dentition at the start of at least one stage. The orthodontic appliance model has a thickness parameter representing the thickness of at least a portion of the orthodontic appliance model. As described above, the thickness parameter of the orthodontic appliance model can represent the expected thickness of the physical orthodontic appliance corresponding to the orthodontic appliance model. For variable-thickness appliances, one or more thickness parameters can represent the thickness of various regions of the physical orthodontic appliance, including but not limited to the region surrounding specific teeth and / or portions of the dentition. In some embodiments, modeling the application of one or more forces to at least a portion of the dentition at the start of at least one stage of the treatment plan includes simulating the placement of the orthodontic appliance model on said at least a portion of the dentition and simulating the response of said at least a portion of the dentition to the virtual placement (i.e., the simulated placement).

[0204] At box 512, iterative modeling is performed on applying one or more forces to at least a portion of the dentition at the start of at least one stage using an orthodontic appliance model with a thickness parameter. In some embodiments, the iterative model has an iteratively decreasing thickness. In some embodiments, modeling is performed on applying at least one force to at least a portion of the dentition using an orthodontic appliance model with a thickness parameter at the start of at least one stage using an iteratively decreasing thickness of at least a portion of the orthodontic appliance model. The iterative reduction of thickness may continue until a result thickness is found that satisfactorily meets one or more clinically acceptable criteria for the thickness parameter. In some embodiments, iterative modeling on applying one or more forces to at least a portion of the dentition includes solving partial differential equations using finite element techniques, which represent one or more clinically acceptable criteria. Such finite element techniques (e.g., using a finite element shell model) are further provided herein. For example, a satisfactory result may be obtaining a threshold score, a similarity value, a material score, or any combination thereof in the orthodontic appliance model at at least one stage. The result thickness has a thickness parameter, and the result thickness is less than or equal to the initial thickness of the orthodontic appliance model. The result thickness is associated with a satisfactory outcome of at least a portion of the dentition at the end of at least one phase of the treatment plan, which meets one or more clinical acceptability criteria.

[0205] At box 514 of method 500, instructions are provided for manufacturing a dental appliance using an orthodontic appliance model having a resulting thickness assigned to a thickness parameter. At box 516, the dental appliance is manufactured. The orthodontic appliance model having a resulting thickness assigned to a thickness parameter is used. Further disclosure relating to instructions and manufacturing of dental appliances is provided herein (see above discussion relating to 180 of method 100 as a non-limiting example). In some embodiments, the dental appliance is manufactured directly. In some embodiments, the method includes directly manufacturing the dental appliance.

[0206] In some embodiments, dental appliances include polymer appliances configured to receive a patient's dentition and apply one or more forces thereon. Further discussion of polymer appliances is provided herein (see, for example, above). Figure 3A (Discussion).

[0207] exist Figure 6 Examples of methods for iteratively modeling the application of forces to the dentition to obtain an orthodontic appliance model are provided. At box 602 of method 600, iteratively modeling the application of one or more forces to at least a portion of the dentition at the start of at least one phase of treatment planning includes assigning an initial thickness to a thickness parameter. In some embodiments, iteratively modeling the application of one or more forces to at least a portion of the dentition at the start of at least one phase includes simulating placing an appliance model on at least a portion of the dentition and simulating the response of at least a portion of the dentition to the virtual placement. At box 604, it is determined whether the application of one or more forces to at least a portion of the dentition at the start of at least one phase of treatment planning meets one or more clinical acceptability criteria.

[0208] In some embodiments, the initial thickness includes one or more of the following values: 0.5 mm, 0.6 mm, 0.7 mm, 0.8 mm, 0.9 mm, 1.0 mm, 1.1 mm, 1.2 mm, 1.3 mm, 1.4 mm, and 1.5 mm. In some embodiments, the initial thickness is less than 1.5 mm, less than 1.4 mm, less than 1.3 mm, less than 1.2 mm, less than 1.1 mm, less than 1.0 mm, less than 0.9 mm, less than 0.8 mm, less than 0.7 mm, less than 0.6 mm, or less than 0.5 mm. In some embodiments, the initial thickness is greater than 0.1 mm and less than 2.5 mm, greater than 0.2 mm and less than 2.0 mm, greater than 0.3 mm and less than 1.8 mm, greater than 0.4 mm and less than 1.6 mm, or greater than 0.5 mm and less than 1.5 mm. In some embodiments, the initial thickness is between 0.1 mm and 2.5 mm, between 0.2 mm and 2.0 mm, between 0.3 mm and 1.8 mm, between 0.4 mm and 1.6 mm, or between 0.5 mm and 1.5 mm.

[0209] If the determination at box 604 is positive (i.e., the initial thickness meets one or more clinically acceptable criteria), the initial thickness is used as the resulting thickness of the thickness parameter assigned to the appliance model. In box 610 of method 600, if one or more forces are applied to at least a portion of the dentition at the start of at least one stage using an appliance model with an initial thickness assigned to the thickness parameter, meeting one or more clinically acceptable criteria, the initial thickness is used as the resulting thickness. As a non-limiting example, if the initial thickness provides forces within a threshold of force similarity values ​​(as further disclosed herein) for a stage of the therapeutic treatment plan, the initial thickness may be used as the resulting thickness of the thickness parameter assigned to the appliance model.

[0210] If the determination at box 604 is negative (i.e., applying one or more forces to at least a portion of the dentition at the start of at least one stage does not meet one or more clinical acceptability criteria), then one or more intermediate thicknesses are assigned to the thickness parameter. At box 606 of method 600, one or more intermediate thicknesses are assigned to the thickness parameter. One or more intermediate thicknesses are less than the initial thickness (i.e., the thickness parameter decreases). At box 608, iteratively determining whether applying one or more forces to at least a portion of the dentition at the start of at least one stage using an orthodontic model with one or more intermediate thicknesses assigned to the thickness parameter meets one or more clinical acceptability criteria. In some embodiments, iterative determination continues until an intermediate thickness that meets one or more clinical acceptability criteria is provided. In some embodiments, iterative determination continues until all iterations for each variable have been tried. In some embodiments, if applying one or more forces to at least a portion of the dentition at the start of at least one stage of the treatment plan using an orthodontic model with one or more intermediate thicknesses assigned to the thickness parameter meets one or more clinical acceptability criteria, then that one or more intermediate thicknesses are used as the resulting thickness. In some embodiments, one or more intermediate thicknesses of box 608 of method 600 are used as the resulting thickness of box 512 of method 500.

[0211] In some embodiments, the maximum number of modeling operations is established before iterative modeling. Figure 7 An example of a method with a maximum number of modeling operations is provided. At block 702 of method 700, the maximum number of modeling operations is identified. In some embodiments, the maximum number of modeling operations is less than 100, less than 1,000, less than 10,000, less than 100,000, less than 1 million, less than 2 million, less than 3 million, less than 4 million, less than 5 million, or less than 10 million modeling operations.

[0212] At box 704 of method 700, iteratively modeling the application of one or more forces to at least a portion of the dentition at the start of at least one stage of treatment planning includes assigning an initial thickness to a thickness parameter. At box 706, determining whether the application of one or more forces to at least a portion of the dentition at the start of at least one stage of treatment planning meets one or more clinical acceptability criteria.

[0213] If the determination at box 706 is positive (i.e., the initial thickness meets one or more clinically acceptable criteria), the initial thickness is used as the resulting thickness of the thickness parameter assigned to the appliance model. At box 712 of method 700, if applying one or more forces to at least a portion of the dentition at the start of at least one stage using an appliance model with an initial thickness assigned to the thickness parameter satisfies one or more clinically acceptable criteria, the initial thickness is used as the resulting thickness. As a non-limiting example, if the initial thickness provides forces within a threshold of force similarity values ​​(as further disclosed herein) for a stage of the therapeutic treatment plan, the initial thickness may be used as the resulting thickness of the thickness parameter assigned to the appliance model.

[0214] If the determination at box 706 is negative (i.e., applying one or more forces to at least a portion of the dentition at the start of at least one stage does not meet one or more clinical acceptability criteria), then one or more intermediate thicknesses are assigned to the thickness parameter. At box 708 of method 700, one or more intermediate thicknesses are assigned to the thickness parameter. This one or more intermediate thickness is less than the initial thickness (i.e., the thickness parameter is reduced). At box 710, iteratively determining whether applying one or more forces to at least a portion of the dentition at the start of at least one stage using an appliance model with one or more intermediate thicknesses assigned to the thickness parameter meets one or more clinical acceptability criteria. The number of iterations is limited by the maximum number of identified modeling operations. At box 714, determining whether clinical acceptability criteria have been met within the maximum number of modeling operations from box 702.

[0215] If the determination at box 714 is positive (i.e., one or more intermediate thicknesses meet one or more clinical acceptability criteria), then at box 720, the orthodontic model having said one or more intermediate thicknesses is used as the resulting thickness of box 512. As a non-limiting example, if the intermediate thickness provides force within a threshold of force similarity values ​​(as further disclosed herein) for a stage of a therapeutic treatment plan, then said intermediate thickness may be used as the resulting thickness assigned to the thickness parameter of the orthodontic model.

[0216] If the determination at box 714 is negative (i.e., no intermediate thickness meets one or more clinical acceptability criteria) and the maximum number of modeling operations has been satisfied, the closest intermediate thickness is identified at box 716. In some embodiments, the closest intermediate thickness among one or more intermediate thicknesses is identified, and the orthodontic model with the closest intermediate thickness is closer to meeting one or more clinical acceptability criteria than an orthodontic model with a starting thickness or any of one or more intermediate thicknesses other than the closest intermediate thickness. As a non-limiting example, if modeling operations are performed with a similarity threshold of 95% similarity to the therapeutic force system, and after the maximum number of modeling operations, the closest similarity value observed among all intermediate thicknesses is 94% similarity to the therapeutic force system, then the intermediate thickness parameter providing a model with 94% similarity to the therapeutic force system will be used as the resulting thickness. At box 718 of method 700, the closest intermediate thickness identified from box 716 is used as the resulting thickness of box 512 of method 500.

[0217] In some embodiments, the method of designing dental appliances further includes the steps of collecting treatment plans and identifying at least one stage of the treatment plan.

[0218] Example

[0219] Example 1

[0220] Parametric model of orthodontic appliances for dental arch expansion with missing teeth

[0221] An orthodontic appliance providing arch expansion force was designed using parametric thickness maps. This model can be used to account for missing teeth.

[0222] Providing arch expansion force to areas with missing teeth is challenging due to the lack of anchorage caused by the absence of contact between the orthodontic appliance and the teeth. When adjacent teeth are missing, conventionally designed appliances may not provide sufficient expansion force to move, for example, molars in the distal direction. Parametric thickness mapping was used to locally and iteratively increase the wall thickness of appliances for patients with missing teeth, and an increase in the force used for arch expansion was observed. Figure 11A As shown in Figure -D, the arch expansion force increases from approximately 0.5 N to approximately 1.2 N as the thickness map changes. Figure 11A The first model is shown, where the thickness map provides the corresponding force of 0.67 N for dental arch expansion; Figure 11B The second model is shown, where the thickness map provides the corresponding force of 1.02 N for dental arch expansion; Figure 11C The third model is shown, where the thickness diagram provides the corresponding force of 0.76 N for dental arch expansion; Figure 11DThe fourth model is shown, where the thickness map provides the corresponding force for 1.18 N of dental arch expansion. By providing optimized and increased force, a substantially similar level of dental arch expansion force is provided in the model with missing teeth compared to the model without missing teeth.

[0223] Example 2

[0224] Model for correcting anterior overbite

[0225] Orthodontic appliances are modeled to correct overly prominent front teeth (e.g., upper front teeth).

[0226] To correct overbite ( Figure 13A A treatment plan is developed to indent and straighten the upper anterior teeth. Orthodontic appliances are designed to provide active forces and torques to pull and rotate the teeth lingually. The process includes: (i) determining which teeth need to be tilted back (usually, but not necessarily, the anterior teeth); (ii) calculating the center of root (COR) position for each tooth; (iii) simulating the force system of the orthodontic appliance and extracting force and torque data at the COR points; and (iv) starting with a thick appliance geometry, allowing for topology optimization of the orthodontic appliance during which material can be selectively removed from the outer surfaces (non-tooth-facing surfaces) of the appliance, and optimizing the geometry using a design objective that maximizes the lingual torque on the COR while limiting the forces on the COR to the lingual direction.

[0227] Example 3

[0228] Model used to control mesial-distal root tilt

[0229] Orthodontic appliances are modeled to control mesial-distal root movement.

[0230] Canines and premolars can move in the mesial-distal direction to close the gap. Figure 13B Traditionally, translational forces are applied to the crown. Improved treatment is achieved by also applying torques to the tooth to prevent root tilting. During model optimization, simulated forces and torques from the modeled orthodontic appliance can be used to reduce root tilting torques on the crown. Figure 1 The input function at 150 and / or the constraint at 160 can maximize the anti-tilting moment on the crown while designing orthodontic appliances using constrained amounts of material.

[0231] Example 4

[0232] Model for controlling torque on the lingual tooth root

[0233] Orthodontic appliances are modeled to control the torque on the lingual tooth roots.

[0234] Teeth can move lingually, but may tilt. Figure 13C Improved treatment is provided by applying torque to the crown of the tooth to be moved. Using the model disclosed herein, the orthodontic appliance is designed to have control over the root torque. In the model, input functions and / or constraints are provided to control the tilting torque. The input functions and / or constraints may include bubble-like features (power ridge features) designed to control the tilting torque. Further constraints on appliance displacement being less than a threshold may be introduced to avoid flaring problems with the orthodontic appliance.

[0235] Teeth programmed to move lingually can be modeled, and tilting can be avoided by applying torques to the crowns of the modeled teeth. Dynamic ridge features (e.g., bubble-like features) are placed to control the tilting torque. During optimization, constraints are introduced that define how the dynamic ridge features can be modified. Constraining displacements on orthodontic appliances to be less than a threshold helps in the production of orthodontic appliances without causing outward spread issues after geometry optimization.

[0236] Example 5

[0237] Model for unidirectional movement of multiple teeth

[0238] Orthodontic appliances are modeled to provide unidirectional movement to multiple teeth.

[0239] When using traditional orthodontic appliances to move multiple consecutive teeth in the same direction (e.g., during multiple tooth intrusion, tilting, or expansion), some teeth have been observed to lose force, leading to reduced effectiveness of the orthodontic appliance. By modeling the unit thickness of the orthodontic appliance, the optimization goal could be to provide sufficient force to move the teeth along the desired path.

[0240] The treatment plan involves applying force to move consecutive teeth in a unidirectional direction, applying the desired indentation force from one canine to another. Figure 12A A model of an orthodontic appliance is generated that provides optimized force for the intrusion of successive teeth. The optimization objective is set to maximize the minimum force required in the direction of movement. The modeling design region is constrained to facilitate computational speed and efficiency. The design region is set from the first premolar to the first premolar (…). Figure 12B Furthermore, the design area is used to perform optimization to generate optimized orthodontic appliances.

[0241] Example 6

[0242] Optimization of shell element diagram

[0243] Orthodontic appliances are modeled using shell element diagrams that represent thickness.

[0244] Size adjustment and optimization can be combined with housing unit Figure 1The thickness of orthodontic appliances is optimized using shell elements. Shell element modeling, which uses shell elements to represent thickness, is faster than topology optimization using solid elements. This sizing optimization of the shell element diagram can be used to optimize the thickness distribution of orthodontic appliances to provide therapeutic forces, such as tooth translation and rotation.

[0245] Orthodontic appliances modeled using shell element diagrams (using shell elements to represent thickness) are optimized to provide therapeutic force with an optimized thickness distribution. Figure 10A (Front view of the model) Figure 10B (Back of the model)). Modify the component thickness to achieve the force required for the desired tooth movement. For example... Figure 10A and Figure 10B As shown, the resulting shell element diagram has a non-homogeneous thickness distribution, and a model orthodontic appliance with optimized thickness is generated to provide target forces for desired tooth movement. Topology optimization, size adjustment optimization, and bead optimization can be applied.

[0246] Example 7

[0247] Topology optimization of solid cells

[0248] Topology optimization is used to optimize orthodontic appliances.

[0249] Topology optimization is a method for optimizing the layout of materials within a given set of loads, boundary conditions, and constraints, with the goal of providing defined properties such as strength, displacement, and rotation. An example of topology optimization performed on a single tooth to generate a localized portion of an optimized orthodontic appliance (…). Figure 8A -E).

[0250] like Figure 8A As shown, a single canine tooth is modeled. The tooth is modeled using a shell element diagram. Figure 8B As shown, a localized portion of the orthodontic appliance is modeled, which has an initial geometry conforming to the modeled canine tooth. For example... Figure 8C As shown, the modeled canines match the modeled portion of the orthodontic appliance, and the modeled portion of the orthodontic appliance is decomposed into volumetric elements. Figure 8D As shown, the modeling portion of the orthodontic appliance is optimized to reduce tilting during tooth movement. This reduction in tilting is achieved by optimizing the contour of the modeling portion of the orthodontic appliance. Figure 8E As shown, an optimized orthodontic appliance is generated using the modeling portion of the orthodontic appliance.

[0251] Perform multiple modeling iterations to generate Figure 8E Optimized orthodontic appliances. Example optimized contour models are as follows: Figures 9A-9C As shown. Figure 9AAn early-stage model of a canine tooth modeled in the modeling area of ​​an orthodontic appliance with a relatively high tilt angle is shown. Figure 9B An intermediate stage model is shown, in which the modeled canine teeth have a reduced tilt angle; Figure 9C A model of the later stage is shown, in which the modeled canines have a near-minimized tilt angle. Figure 9D The results show that the tilt angle decreases with the number of model iterations, thus stabilizing.

[0252] In a specific example, direct manufacturing is used to produce optimized orthodontic appliances with altered thicknesses.

[0253] Example 8

[0254] Parameter implementation in the model

[0255] Functional parameterization is used during the design of orthodontic appliances. Using the modeling systems or methods further described herein, parameters can be incorporated into the formation of orthodontic appliances to improve functionality.

[0256] Generate a 3D tooth model that has a thickness function (e.g., Figure 2A-2C The thickness function is calculated incorporating parameters implemented into the dental model. In some embodiments, these parameters include clinical features such as the spatial arrangement, proximity, and orientation of nearby teeth and soft tissue relative to points on the appliance model. Local thicknesses at points can be calculated, incorporating functional parameterization to provide the desired effect. As a non-limiting example, functional parameterization is used to map clinical features (e.g., features providing forces for tooth movement) onto the surface of the orthodontic appliance in a manner that provides a smooth surface, which can improve the patient's experience with the appliance by taking into account the proximity of soft tissue.

[0257] While preferred embodiments of the invention have been shown and described herein, it will be apparent to those skilled in the art that these embodiments have been provided by way of example only. Many modifications, variations, and substitutions will now be made by those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in the practice of the invention. The following claims are intended to define the scope of the invention, and methods and structures within the scope of these claims and their equivalents will be covered therein.

Claims

1. A method for determining the geometry of an orthodontic appliance, the method comprising: Receive a treatment plan for the patient's teeth, the treatment plan including: Multiple stages used to move a patient's teeth from their initial to their final position, and The therapeutic force used for each of the plurality of stages; An initial 3D model of an orthodontic appliance is generated, the initial 3D model including a plurality of tooth cavities configured to position patient teeth according to at least one of the plurality of phases; A finite element shell model comprising multiple shell elements is generated based on the initial 3D model; The first modeling force is determined based on the finite element shell model; Modify at least one shell element of the finite element shell model to generate an intermediate 3D model, the intermediate 3D model corresponding to the second modeling force; At least one of the first modeling force or the second modeling force is compared with the therapeutic force of the at least one stage to provide a force similarity value; and The changes are repeated until a threshold shell unit value, a threshold of the force similarity value, or a combination thereof is obtained, wherein the threshold shell unit value represents the minimum thickness of the orthodontic appliance.

2. The method according to claim 1, wherein, Changing at least one shell element of the finite element shell model includes: using a topology algorithm to change the discrete element density map.

3. The method according to claim 1, wherein, Changing at least one shell element of the finite element shell model includes: using a size adjustment algorithm to change the discrete thickness map.

4. The method according to claim 1, wherein, Changing at least one shell element of the finite element shell model includes: using a parametric algorithm to change the parametric thickness map.

5. The method according to claim 1, wherein, The force similarity value compares the first modeling force, the second modeling force, or any combination thereof with the therapeutic force, and wherein the threshold of the force similarity value is greater than 50%.

6. The method of claim 1, further comprising generating instructions for manufacturing the orthodontic appliance.

7. The method of claim 1, further comprising the step of manufacturing an orthodontic appliance.

8. The method of claim 1, wherein the change is repeated until a threshold of the force similarity value is obtained, and wherein the threshold of the force similarity value is greater than 50%.

9. The method of claim 1, wherein repeating the change comprises generating one or more additional intermediate 3D models, each additional intermediate 3D model corresponding to a corresponding modeling force.

10. The method of claim 9, further comprising: The corresponding modeling force of each additional intermediate 3D model is compared with the healing force to provide a corresponding force similarity value, and Select the intermediate 3D model that provides the desired force similarity value.

11. The method of claim 10, further comprising generating instructions for manufacturing the orthodontic appliance using the selected additional intermediate 3D model.

12. The method of claim 1, wherein the initial 3D model comprises a finite element model, and wherein generating the finite element shell model comprises dividing the surface of the finite element model into a plurality of shell elements.

13. The method according to claim 1, wherein the finite element shell model includes a parameterized thickness map defined by a parameterized function, a topological density map defined by a topology algorithm, or a discrete thickness map defined by a size adjustment algorithm.

14. A system comprising: processor, and The memory includes instructions that, when executed by the processor, cause the system to perform operations including the method according to any one of claims 1-13.

15. An orthodontic appliance constructed using the method according to any one of claims 1-13.

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