Computer-implemented method for orthodontic treatment planning

Abstract

A method for orthodontic treatment planning (50) using an orthodontic appliance (126). The method comprises determining an initial virtual path (140) for each model tooth (11-17, 21-27, 31-37, 41-48), calculating a space between adjacent pairs of model teeth at each stage (160), defining a minimum space between adjacent pairs of model teeth, and creating a key frame row (192, 194) when the calculated space is less than the minimum space, wherein each tooth position / orientation in the stage (160) is a key frame. Iterating each model tooth (11-17, 21-27, 31-37, 41-48) at the key frame row (192, 194) when the calculated space is less than the minimum space, changing the position and / or orientation of the model teeth (11-17, 21-27, 31-37, 41-48), and at each stage (160) using each model tooth in the key frame row (192, 194). 194) to calculate a space between adjacent pairs of model teeth based on the changed position and / or direction of the tooth elements (191, 192, 193, 194). The plurality of stages define an orthodontic treatment regimen. Each stage (160) corresponds to an orthodontic appliance (126) for orthodontic treatment of a patient.

Description

[0001] Cross-references

[0002] This application claims priority to U.S. patent application No. 17 / 722,447, filed on April 18, 2022, the disclosure of which is expressly incorporated herein by reference in its entirety. Technical Field

[0003] The present invention relates generally to the field of orthodontic treatment and, more particularly, to systems and methods for orthodontic treatment planning. Background Art

[0004] Orthodontics is the practice of manipulating the teeth to correct misalignment between the upper and lower dental arches. Typically, treatment for malocclusion involves the use of orthodontic devices that apply corrective forces to the teeth. Over time, these corrective forces force the teeth to move into their orthodontically correct positions.

[0005] One method of applying corrective forces to the teeth is with orthodontic devices known as "aligners." Aligners are typically provided as a series of removable devices that progressively reposition the patient's teeth from their initial orientation, in which the teeth may have been malformed, to an orthodontically correct and aesthetic orientation. Patients treated with braces can insert and remove the braces at will and therefore do not need to consult an orthodontist to advance treatment. Instead, when the braces currently being worn have moved the teeth to or close to the final orientation for that brace, the patient simply begins using the next brace in the series according to the treatment plan. In this respect, each brace in the series is different from all the other braces in the series.

[0006] To make the braces, the orthodontist first builds a computer model of the patient's dentition. For example, the model can be generated by taking an impression of the patient's dentition and then scanning the impression to digitize the impression for manipulation in the computer. Alternatively, the clinician can directly scan the patient's teeth using an intraoral scanner. The scan data is then used to build a computer model. In each case, the computer model includes one or more teeth, preferably all teeth, in the patient's upper and / or lower jaws. Once the computer model is built, the orthodontist can manipulate the individual teeth in the model teeth to ultimately determine the target orientation of each tooth, which provides a corrected dentition for each corresponding jaw, resolves any malocclusion, and ideally provides an aesthetic smile. Multiple computer models can be generated before treatment. Each model can include a unique orientation of one or more model teeth in the dentition, and one or more model teeth can be repositioned from the initial orientation to the target orientation step by step and continuously according to the treatment plan.

[0007] The stepwise repositioning of the model teeth is then replicated in a series of dental molds. An appliance is formed in each mold. Where multiple molds are present, a set of appliances are manufactured, each of which may be unique to one of the molds. For each appliance, forces are imposed on the patient's teeth during orthodontic treatment. The patient's teeth may be moved stepwise from an initial orientation to a target orientation according to a treatment plan determined by the computer model. In this manner, treatment moves the patient's teeth in a series of stages from an initial orientation that generally corresponds to the initial orientation of the computer model to a final orientation that generally corresponds to the target orientation of the computer model.

[0008] The entire process of manually planning each stage is labor-intensive and time-consuming, and requires a lot of training. In view of this, the planning process can be automated. In addition, the uniqueness of each patient is a major obstacle to full automation. The ongoing challenge of automation is to reduce the time required to develop a treatment plan that minimizes the patient's treatment period while successfully treating the patient. Minimizing the treatment period reduces costs because fewer treatment stages reduce material and model costs. However, unlike minimizing the time for treatment planning, during modeling, it is often necessary to manually manipulate the digital models of the patient's individual teeth. That is, the automatic, planned movement of one or more model teeth at their different treatment stages may require manual modification to make successful orthodontic treatment more likely. In other words, automatic tooth movement via software does not always result in a realistic orthodontic treatment plan.

[0009] For example, clinicians may need to manually resolve virtual tooth-to-tooth collisions that may occur when model teeth are moved from their initial to their final positions. The ability to identify tooth collisions during treatment planning and in the virtual environment allows such tooth collisions to be resolved prior to actual treatment. Manually resolving these collisions requires extensive training and practice, and is time-consuming for technicians.

[0010] Although orthodontic treatment planning is often successful, problems still exist in planning and designing before fabricating appliances according to the treatment plan.Therefore, there is a need for improved methods, systems, and computer program products in orthodontic treatment planning and appliance fabrication. Summary of the invention

[0011] The present invention overcomes the shortcomings and defects of the methods and systems for modeling and manufacturing of orthodontic appliances known to date. Although the present invention will be described in conjunction with certain embodiments, it should be understood that the present invention is not limited to these embodiments. On the contrary, the present invention includes all alternatives, modifications and equivalents that may be included in the spirit and scope of the present invention.

[0012] In one aspect of the present invention, there is a computer-implemented method for orthodontic treatment planning using one or more aligners. The method includes determining an initial virtual path for each model tooth in a patient's jaw to be moved during orthodontic treatment. Each initial virtual path is from a first position and / or orientation of a model tooth in a first arrangement to a second position and / or orientation of a model tooth in a second arrangement. Each initial virtual path is divided into a plurality of stages, each of the plurality of stages defining a position and / or orientation of a corresponding model tooth on the initial virtual path. The method also includes calculating the space between adjacent pairs of model teeth in each stage, defining the minimum space between adjacent pairs of model teeth allowed for orthodontic treatment, and when one or more of the calculated spaces are less than the minimum space, creating at least one critical framework row, wherein each tooth position and / or orientation in the stage is a critical framework. When one or more calculated spaces are less than a minimum space, the method includes iterating one or more of the following: for each model tooth on at least one key framework row, (i) changing the position and / or orientation of the model tooth from a first position and / or orientation, or from a previous position and / or orientation of a previous iteration; and (ii) calculating the space between adjacent pairs of model teeth at each stage using the changed position and / or orientation of each model tooth at at least one key framework row. After the iteration, the plurality of stages define an orthodontic treatment plan, each of the calculated spaces in the plurality of stages being greater than the minimum space, and each stage in the defined orthodontic treatment plan corresponding to an appliance for orthodontic treatment of the patient.

[0013] In an embodiment, the method further comprises manufacturing a series of aligners for the patient, each aligner corresponding to one of the plurality of stages.

[0014] In an embodiment, iterating comprises changing a position of at least one keyframe row in a plurality of stages.

[0015] In an embodiment, changing the position includes moving at least one key frame row one stage earlier or one stage later in the plurality of stages.

[0016] In an embodiment, the at least one keyframe row includes a first keyframe row and a second keyframe row, wherein iterating one or more times includes changing a position and / or orientation of each model tooth in each of the first keyframe row and the second keyframe row.

[0017] In an embodiment, the first key frame row and the second key frame row are not consecutive stages.

[0018] In an embodiment, the minimum space is in the range of 0.0 mm to 0.04 mm.

[0019] In an embodiment, the method further comprises defining a maximum space, wherein iteration occurs when one or more of the calculated spaces is less than the minimum space or greater than the maximum space.

[0020] In an embodiment, at each of the plurality of stages, the position and / or orientation of each model tooth is defined in at least two degrees of freedom.

[0021] In an embodiment, the position and / or orientation of each model tooth is described as a vector having at least two components. In an embodiment, the vector is Where X i,j is the position and / or orientation of model tooth i at stage j, N is the total number of model teeth in the patient's dental arch, K is related to the number of stage j among the multiple stages, α is the buccal / lingual movement of tooth i in stage j, and β is the mesial / distal movement of tooth i in stage j.

[0022] In an embodiment, the at least one key frame row includes a first key frame row (T p ) and the second key frame row (T p+1 ), the calculated space (S ij ) is represented as: The calculated space (S ij )yes as well as The function F at stage j j , is the position and / or orientation of the model tooth i in the first keyframe row, The position and / or orientation of the model tooth i in the second keyframe row, is the position and / or orientation of the model tooth i+1 in the first keyframe row, The position and / or orientation of the model tooth i+1 in the second keyframe row.

[0023] In an embodiment, stage j is at the first key frame row (T p ) and the second key frame row (T p+1 )between.

[0024] In an embodiment, defining the minimum space as zero further comprises defining the maximum space between adjacent pairs of model teeth according to the inequality:

[0025] in is the maximum space between adjacent teeth i and i+1.

[0026] In an embodiment, the method further comprises defining a maximum movement speed of each model tooth between any two consecutive stages. When one or more of the calculated spaces are less than the minimum space, the method comprises calculating a movement speed of each model tooth between each consecutive stage, and when the calculated movement speed is greater than the maximum movement speed, for each model tooth at at least one key framework row, changing a position and / or orientation of the model tooth from a first position and / or orientation or from a previous position and / or orientation of a previous iteration.

[0027] In an embodiment, the method further comprises defining a deviation constraint for a total movement of each model tooth from a first position and / or orientation. When one or more of the calculated spaces are less than a minimum space, the method comprises calculating a total movement of each model tooth from the corresponding first position and / or orientation. When the calculated total movement is greater than the deviation constraint, for each model tooth on at least one critical framework row, the method comprises changing a position and / or orientation of the model tooth from the first position and / or orientation or from a previous position and / or orientation of a previous iteration.

[0028] In one aspect of the invention, there is a computer-implemented method for orthodontic treatment planning using one or more aligners, wherein an initial staged plan includes a plurality of treatment stages and indicates one or more collisions between adjacent pairs of model teeth. The method includes defining a minimum space between adjacent pairs of model teeth and creating at least one critical framework row in the initial staged plan. In at least one critical framework row, each tooth position and / or orientation is a critical framework. When there is at least one collision in the staged plan, the method includes iterating one or more of the following: for each model tooth on at least one critical framework row, (i) changing the position and / or orientation of the model tooth from an initial position and / or orientation, or from a previous position and / or orientation of a previous iteration; and (ii) calculating the space between adjacent pairs of model teeth at each stage using the changed position and / or orientation of each model tooth at at least one critical framework row. After iteration, the plurality of stages define an orthodontic treatment plan, each calculated space in the plurality of stages is greater than the minimum space, and each stage in the defined orthodontic treatment plan corresponds to an aligner for orthodontic treatment of the patient.

[0029] In an embodiment, the method includes fabricating a series of aligners for the patient, each aligner corresponding to one of the plurality of stages.

[0030] In an embodiment, iterating includes moving at least one key frame row one stage earlier or one stage later from a position in the initial staged scheme.

[0031] In an embodiment, the at least one keyframe row includes a first keyframe row and a second keyframe row, and the iterating one or more times includes changing the position and / or orientation of each model tooth in each of the first keyframe row and the second keyframe row.

[0032] In an embodiment, the first key frame row and the second key frame row are not consecutive stages.

[0033] In an embodiment, the minimum space is in the range of 0.0 mm to 0.04 mm.

[0034] In an embodiment, the method further comprises defining a maximum space, wherein iteration occurs when one or more of the calculated spaces is less than the minimum space or greater than the maximum space.

[0035] In an embodiment, the position and / or orientation of each model tooth is described as a vector having at least two components. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and, together with the detailed description given below, serve to explain aspects of the invention.

[0037] Figure 1 is a flow chart of an embodiment of a method for planning orthodontic treatment of a patient.

[0038] Figure 2 is a schematic diagram of a system according to an embodiment of the present invention.

[0039] Figure 3A and Figure 3B It is a 3D digital tooth model of the patient's dentition with each tooth in its initial position before treatment. Figure 3A Depicts the upper dental arch, Figure 3B The lower dental arch is depicted.

[0040] Figure 4A and Figure 4B It is a 3D digital tooth model of the patient's dentition in its final position after treatment. Figure 4A Depicted with Figure 3A The 3D digital tooth model shown in the figure corresponds to the upper dental arch. Figure 4B Depicted with Figure 3B The 3D digital tooth model corresponds to the lower dental arch.

[0041] Figure 5 is a flow chart illustrating exemplary steps in a method of developing a treatment plan for a patient.

[0042] Fig. 6A and Figure 6B is a diagram showing the stages according to the orthodontic treatment plan, Fig. 6AThe tooth contact / spacing is listed, Figure 6B Listed with Figure 3A and Figure 4A Associated translation and rotational velocities.

[0043] Figure 6C and Fig.6D is a diagram showing the stages according to the orthodontic treatment plan, Figure 6C The tooth contact / spacing is listed, Fig.6D Listed with Figure 3B and Figure 4B Associated translation and rotational velocities.

[0044] Figure 7 is shown for reducing or eliminating Fig. 6A and Figure 6C Flowchart of an exemplary method for identifying inter-neighbor collisions in a hierarchical graph of FIG.

[0045] Fig. 8A and Figure 8B It is shown that according to Figure 3A and Figure 4A The orthodontic treatment plan associated with the model shown eliminates Fig. 6A An exemplary diagram of the stages of tooth positioning after an inter-tooth collision is shown in the example.

[0046] Figure 8C and Fig.8D It is shown that according to Figure 3B and Figure 4B The orthodontic treatment plan associated with the model shown eliminates Figure 6C An exemplary diagram of the stages of tooth positioning after an inter-tooth collision is shown in the example.

[0047] Fig. 9 is based on Figure 7 A table of exemplary objectives and constraints used in conjunction with an exemplary flowchart of an embodiment is shown.

[0048] Fig.10 is a perspective view of an orthosis made in accordance with an embodiment of the present invention.

[0049] Fig.11 is a schematic diagram of a computer device for determining a rank according to an embodiment of the present invention. DETAILED DESCRIPTION

[0050] Embodiments of the present invention relate to computer-implemented methods, systems, and computer program products for orthodontic treatment planning, and in particular, to computer-implemented methods, systems, and computer program products for planning treatment of a patient's teeth using one or more dental braces. In general, the goal of a treatment plan is to develop a plan to move a patient's teeth from an initial position before treatment (referred to as T1) to a final position after treatment (referred to as T2). Embodiments of the present invention are used to plan the movement of one or more teeth of a patient from one position to another position (such as, from any two positions between T1 and T2). Typically, the two positions may be any two positions of the tooth at different times during the planning of the movement of a single tooth using an orthodontic device such as an orthodontic appliance. For example, the two tooth positions may include an initial tooth position and a second tooth position in a continuous stage of an orthodontic treatment plan.

[0051] For this purpose, refer to Figure 1-4B , technicians and / or clinicians use the virtual environment of a computer system to plan orthodontic treatment for a patient. According to an embodiment of the present invention, treatment planning involves virtual manipulation of a 3D digital model of a patient's teeth. For example, treatment planning using an orthodontic appliance may include moving one or more virtual teeth from their positions in a T1 model to their positions in a T2 model, where the T1 model is a virtual model of the patient's teeth at T1 and the T2 model is a virtual model of the patient's teeth at T2. In this way, before manufacturing an orthodontic appliance to treat a patient, orthodontic treatment is first simulated with the aid of a computer system.

[0052] To plan virtual tooth movement according to an embodiment of the treatment planning method 50, refer to Figure 1 , a 3D digital model of the patient's dentition before orthodontic treatment is prepared at 100. This virtual model is referred to as a T1 model (an exemplary T1 model is shown in FIG. Figure 3A and Figure 3B are marked as 102 and 103 respectively). Figure 2 104 for preparing T1 models 102, 103. As shown, the system 104 includes a computer 106 and at least one imaging system 110. The computer 106 can receive a plurality of images 108 from the imaging system 110 and / or another imaging system. The imaging system 110 can include a wand 112 having an imaging sensor 114 and a light source 116. The imaging sensor 114 can be an intraoral camera that captures information about the patient's oral cavity when exposed to light from, for example, the light source 116.

[0053] The practitioner may insert at least a portion of the wand 112 into the patient's mouth. Using the light source 116 and the imaging sensor 114, the practitioner may capture data of all or selected crowns of the patient's teeth. The data may include a surface image 108 of one or more teeth of the patient or a surface image from an impression 118 of the patient's teeth, and / or a volumetric image (not shown) of volumetric data acquired by, for example, a cone beam computed tomography (CBCT) or similar device.

[0054] Computer 106 may include any suitable computing device, such as a personal computer, a server computer, a minicomputer, a mainframe computer, a blade computer, a tablet computer, a touch screen computing device, a telephone device, a cell phone, a mobile computing device, a dental device with a processor, etc. In some embodiments, computer 106 may provide a network service or a cloud computing service. More than one computer may also be used to store data on a hard drive or flash drive and / or perform operations performed by computer 106 according to embodiments of the present invention. Using surface image 108 and / or volume image, in Figure 1 A 3D digital model of the patient's teeth at position T1 is generated at position 100 in the figure, namely, T1 models 102 and 103 .

[0055] exist Figure 2 In the illustrated embodiment, although not limited to any particular network, the computer 106 is operably coupled to the imaging system 110 via one or more wired or wireless connections 120 through a network 122. The network 122 may include a local area network, the Internet, an intranet, a storage area network, or any other suitable network. The computer 106 may use a computer program to model the patient's teeth, design orthodontic treatments and devices, and model the patient's smile. Applicants have proposed computer programs and systems, examples of which are disclosed in U.S. Patent No. 9,529,970 filed on September 26, 2003 and International Application No. PCT / US2003 / 030917 and International Patent Application No. PCT / US2000 / 035558 filed on December 29, 2000, all of which are expressly incorporated herein by reference in their entirety. These systems provide an interface through which a treating orthodontist or other dental practitioner can view, manipulate, communicate treatments, design personalizations, and exchange patient data. As described herein, embodiments of the present invention provide enhancements to these systems that improve their functionality and utility, increasing treatment efficiency while reducing treatment costs.

[0056] Although embodiments of the present invention are not limited to the system 104 shown, the system 104 may also include a device capable of manufacturing an orthotic device 126 (e.g., Fig.101 (shown) or in electrical communication with a manufacturing system 124. The manufacturing system 124 includes a CNC machine 132 and a molding machine 130 for machining trim lines on each aligner 126 as necessary. By way of further example only, systems and methods for preparing 3D models of a patient's teeth are known at least according to U.S. Patent Publication Nos. 2018 / 0165818 and 2014 / 0272772, which have been assigned to Ormco Corporation and are incorporated herein by reference in their entirety.

[0057] Further references Figure 1 , at 134, the data in the T1 model is then used to calculate a digital orthodontic setup or T2 model. Figure 3A and Figure 3B ) corresponding to the exemplary T2 models are labeled 136 and 137 and are Figure 4A and Figure 4B . Like the T1 models 102, 103, the T2 models 136, 137 are virtual 3D models. The T1 models 102, 103 represent the pre-treatment virtual arrangement of the patient's teeth, while the T2 models 136, 137 represent the post-treatment arrangement of the virtual teeth shown in the T1 models 102, 103 minus any teeth that may be extracted before treatment. In other words, the T2 models 136, 137 are virtual representations corresponding to the expected results of orthodontic treatment. By way of example only and not limitation, the T2 models 136, 137 may be manipulated by operating a computer 106 ( Figure 2 ) on 3D Designer Software TM The image data 108 in the system was created using computer 106 which is available from Ormco, Inc. of Orange, California.

[0058] refer to Figure 1 At 140, a program (such as 3DDesigner Software) stored on and executable on the computer 106 is executed. TM system)( Figure 2 ) is configured to analyze the initial tooth position of each tooth in the T1 models 102 , 103 and the final position of each tooth in the T2 models 136 , 137 . Figure 3A An exemplary T1 model 102 of the patient's upper dental arch is shown, Figure 3B An exemplary T1 model 103 of a patient's lower dental arch is shown. Figure 4A and Figure 4B The corresponding T2 models are shown in Figure 4A Shown with Figure 3A The exemplary T2 model 136 of the upper dental arch corresponding to the T1 model 102 of the upper dental arch shown in FIG. Figure 4B Shown with Figure 3B The exemplary T2 model 137 of the lower dental arch corresponding to the T1 model 103 of the lower dental arch shown in FIG. 1 is shown in FIG. 106. A program running on the computer 106 automatically creates the position of each tooth from the T1 models 102, 130 (e.g., Figure 3A and Figure 3B ) to the positions in the T2 models 136 and 137 (as shown in Figure 4A and Figure 4B 136 , 137 . As an example only, the distance between the tooth at the T1 position in the T1 model 102 , 130 and the tooth at the T2 position in the T2 model 136 , 137 can be calculated based solely on the tooth movement speed. The movement speed can be a translation and / or rotation speed. For example, if the maximum allowed tooth movement speed (i.e., translation) for each stage is 0.25 mm, and the distance between the T1 position and the T2 position is 1 mm, then the virtual path between each stage will consist of a linear path with a length of 0.25 mm. Because the path can be improved as described herein, the calculated virtual path can be an initial calculation, in other words, it is only the starting point for subsequent calculations. For another example, the virtual path can be determined by linearly interpolating each degree of freedom of the virtual motion of each tooth from the T1 position to the T2 position. Thus, for translational movement, if the coordinate of the model tooth at its T1 position is equal to 5.0 mm and the coordinate of the model tooth at its T2 position is equal to 6.0 mm, then by linearly interpolating the coordinates, the virtual path of the coordinates will be 5.1 mm, 5.2 mm, ..., 5.9 mm, 6.0 mm, for a total of 10 movement stages. The virtual path is initially calculated and then an orthodontic treatment plan is prepared at 142. Once the orthodontic treatment plan is approved, typically by an orthodontist, the orthodontic treatment plan is prepared at 144, such as at Figure 2 The aligner 126 is manufactured in the manufacturing system 124 for delivery to the patient.

[0059] refer to Figure 5 , showing that according to Figure 1 142 of which is used to prepare Figure 3A and Figure 3B An exemplary process of orthodontic treatment planning for one or both of the T1 models 102 and 103 is shown. Figure 5At 146, a technician can check each T2 model 136, 137 to ultimately determine whether the final dental correction, interdental contact (i.e., intra-arch contact between adjacent teeth in the jaw), and space between adjacent teeth are appropriate. The inspection can include ensuring that the final contact in the T2 models 136, 137 is 0mm to 0.04mm, unless an interproximal repositioning (IPR) is planned. Regarding range, there may be some slight errors in the tooth positions in the T1 models 102, 103 reconstructed from scanned images of the patient's dentition. These errors may be on the order of 0.01mm and can be addressed by selecting a range (such as the range provided herein). For example, although 0.04mm within the range of this paragraph represents a slight overlap between adjacent model teeth, 0.04mm is selected as the lower limit of the overlap allowed in the virtual model to take into account slight errors in scanning and reconstruction. However, embodiments of the present invention are not limited to any range described herein.

[0060] At 150, in an embodiment, software running on a computer 106 can calculate an initial staging of one or both dental arches of a patient based on a virtual path for each tooth from the T1 model 102, 103 to the T2 model 136, 137. The tooth movement along the virtual path is planned in stages. Staging is the process of determining the order of tooth movement in a treatment plan, so staging is the time, path, and order of tooth movement. Each movement is planned from an initial tooth position (e.g., T1 model 102, 103) to a final tooth position (e.g., T2 model 136, 137). In situations where it is not possible or desirable to perform the entire tooth movement in a single stage, multiple stages of movement can be used. In other words, the virtual movement path can be divided into one or more shorter movements, depending on the total amount of virtual movement required for each tooth between two positions. The shorter movements completed in different stages add up to the total movement required for treatment. For example, a large movement (e.g., translation and / or rotation) can be divided into individual shorter translation and / or rotation movements that together equal the virtual movement path of each tooth from the T1 model 102, 103 to the T2 model 136, 137. Thus, by analyzing the virtual movement path of each tooth, one or more stages of tooth movement can be planned. Each stage is then associated with an appliance that is manufactured to move the patient's teeth according to the movement planned for that stage.

[0061] The stages determine successful orthodontic treatment, but are typically limited by physiological and material limitations. Exemplary physiological and material limitations include, but are not limited to, one or more of the maximum translation speed, the maximum rotation speed, and the maximum tilt / torque speed. These movement limits can be predetermined for a specific patient, for example, the maximum translation speed can be 0.25 mm per stage, the maximum rotation speed can be 2 degrees per stage, and the maximum tilt / torque speed can be 1 degree per stage. Therefore, for each stage, the clinician or software can limit the virtual tooth movement according to one or a combination of the maximum translation movement of 0.25 mm, the maximum rotation movement of 2 degrees, and the maximum tilt / torque of 1 degree. These limitations may be associated with the patient's pain tolerance, with larger movements at each stage typically associated with greater pain, and / or associated with material limitations of the appliance. The planning stages can be shown in the form of a diagram and can be referred to as a staged scheme.

[0062] Additionally, the material from which the appliance is made may only allow for limited movement within the time allotted for movement, so a maximum movement may be set if the maximum movement per stage is less than the patient's pain tolerance. The above constraints may be a factor in determining the total number of stages required for treatment. For example, the total number of stages may be determined by the tooth with the greatest movement from the position in the T1 model 102, 103 to the position in the T2 model 136, 137. This tooth may be referred to as the guide tooth and the treatment length may be determined because the tooth that moves the most dictates the total number of stages based on the maximum allowable tooth velocity, based on physiological and material limitations. Using these constraints, as well as other constraints that may be described below, an initial staging chart may be calculated.

[0063] Given the predetermined limitations and restrictions described herein, based on Figure 3A and Figure 3B The T1 models 102, 103 shown and based on Figure 4A and Figure 4B The T2 models 136 and 137 are respectively Fig. 6A and Figure 6B as well as Figure 6C and Fig.6D It is shown in Figure 5 FIG. 150 shows an initial staging diagram of an exemplary upper and lower dental arch for treatment. That is, via Fig. 6A (translation movement) and Figure 6B (rotational movement) shown in the initial stage, Figure 3A The T1 model 102 is converted to Figure 4A The T2 model 136 shown. And, via Figure 6C (translation movement) and Fig.6D (rotational movement) shown in the initial stage, Figure 3B The T1 model 103 is converted to Figure 4B T2 model 137 shown.

[0064] exist Figure 6A-6D In each of the examples, an exemplary diagram is shown with sequential stages 160 listed on the left side of the diagram and tooth numbers 162 listed from left to right across the top of the diagram. The tooth numbers 162 are labeled according to the International Dental Federation (FDI) tooth numbering system and are identical to the tooth numbers 162 of FIG. Figure 3A-Figure 4B The tooth markings in the reference Fig. 6A and Figure 6B , stage 0 represents the corresponding T1 models 102, 103 (e.g., Figure 3A and Figure 4A ) shows the tooth position. Fig. 6A and Figure 6C The values ​​in the graph of are the calculated spaces between the teeth. These values ​​can be positive (i.e., there is a gap between adjacent teeth), or negative, indicating overlap between virtual teeth. Stage 17 represents the corresponding T2 model 136, 137 (e.g., Figure 3B and Figure 4B ) shown in the tooth position. Therefore, the initial existence will Figure 3A The tooth arrangement is planned to Figure 4A There are 17 stages of tooth movement in the tooth arrangement. Figure 3B The tooth arrangement is planned to Figure 4B 22 stages of tooth movement for tooth arrangement. A vertical solid line with a solid circle extending from one stage and passing through one or more stages indicates tooth movement from the indicated stage to the indicated lower stage. For example, in Fig. 6A In the T2 model, tooth 17 starts to move at stage 1 and moves at each stage until stage 17, at which stage tooth 17 reaches its final position in the T2 model.

[0065] exist Fig. 6A and Figure 6C The calculated interproximal contacts or spaces between teeth are shown in the exemplary diagram of FIG. Fig. 6A In stage 9, the calculated contact between tooth 13 and tooth 12 is an overlap of 0.10 mm (see Fig. 6A 152). That is, according to the initial movement, tooth 13 and tooth 12 collide at stage 9. In an embodiment, as shown in the figure, if the value of stage 0 indicates overlap / collision with adjacent teeth, the interproximal contact in the T1 model (i.e., at the beginning of treatment corresponding to stage 0) can be adjusted to a value of 0. In the T1 model, there should not be any collision or overlap because the T1 model is constructed based on the patient's actual dentition. If the interproximal contact at stage 0 indicates severe collision (e.g., more than 0.2 mm), the quality of the T1 model can be re-evaluated and, if necessary, additional images 108 can be collected to determine the value of the collision. Figure 1The T1 model is constructed or reconstructed at 100 in Stage 0. Additional visual assessment of the interproximal contacts of the T1 model can be performed at Stage 0. As an additional example only, in cases where the patient's dental arch is considered "crowded", it is reasonable that the spaces between adjacent teeth should not be calculated. If the initial staged diagram (e.g., Fig. 6A and Figure 6C ) shows the space between adjacent teeth, the T1 model can be used to visually confirm the spacing shown in the diagram as a preliminary quality assessment of the T1 model relative to the initial staging calculation.

[0066] exist Fig. 6A and Figure 6C In the graph of , adjusted contact is shown. By adjusting contact, it is meant that the contact value of stage 0 is subtracted / added to all stages. Therefore, at stage 0, all contacts are shown as "0". Other information shown in the graph may include a visual indication of the interproximal contact or space between the virtual teeth at each stage. In this regard, ranges of different degrees of interproximal contact or space can be predetermined to facilitate visual assessment of the staged graph. For example, in an embodiment, normal contact is contact with a contact value of 0.00 mm to 0.04 mm (this range includes a slight virtual overlap of adjacent teeth), which may be within the error range of the imaging system 110. Fig. 6A For example, normal contacts with values ​​in the range of 0.00 mm to 0.04 mm are contacts that are not circled or underlined. Normal contacts generally do not require modification and are acceptable in orthodontic treatment planning. Although, as described above, the identified ranges represent slight overlaps, embodiments of the present invention are not limited to any preselected ranges, which may be related to errors in the tooth surfaces when scanning and / or reconstructing the scanned images. In addition, a range may be selected taking into account the desire to eliminate the space between each pair of adjacent teeth in the patient's dentition during planning treatment. Thus, a goal of treatment may be to zero all interproximal spaces in the T2 model.

[0067] Continue to refer Fig. 6A and Figure 6C , non-IPR contacts are contacts defined within the range of 0.05 mm to 0.14 mm. Non-IPR contacts are contacts involving significant virtual overlap of adjacent virtual teeth. Fig. 6AFor example, the area within the circle 152 (0.10 mm) is a non-IPR contact. In this regard, the non-IPR contact indicates significant inter-tooth collision during virtual tooth movement. That is, when a tooth moves along its virtual movement path, it may collide with another adjacent tooth. Because the teeth are virtual 3D representations, they may overlap with each other. This overlap is indicated as a non-IPR contact and can be referred to as an interproximal collision, that is, adjacent virtual teeth are in contact with each other and are therefore referred to as "colliding" in virtual space. According to an embodiment of the present invention, non-IPR contacts, such as contact 152, are resolved before approving an orthodontic treatment plan. Reference will be made below. Figure 5 Resolving non-IPR contacts is described at 170. Although not shown in the figure, Fig. 6A and Figure 6C In the chart, non-IPR contacts can be color-coded (e.g., red text) for easier visual identification. Fig. 6A and Figure 6C All non-IPR contacts in are underlined rather than color coded to facilitate comparison with subsequent step charts after collision avoidance calculations.

[0068] exist Figure 5 In the embodiment of the present invention, IPR contact can be checked at 164. IPR contact can be a contact greater than 0.14 mm, that is, the overlap is larger than that of non-IPR contact. For example, IPR contact can be defined in the range of 0.15 mm to 0.54 mm. Fig. 6A and Figure 6C Non-IPR contacts are shown in . These contacts are designated to be resolved by interproximal reduction at a predetermined stage of orthodontic treatment. IPRs can be assigned to selected teeth and all IPRs occur in a single stage.

[0069] In addition, Fig. 6A and Figure 6C , the open spaces between the teeth are shown at the circled area 156. All open spaces are circled and labeled 156. The distance between adjacent teeth can be displayed and distinguished from normal contact by colored text, such as green text or another visual text indicator (e.g., a plus sign). Fig. 6A and Figure 6C The staging diagram provides a visual quantitative analysis of the interproximal distances between adjacent teeth at each stage of initial staging.

[0070] Similarly, in Figure 6B and Fig.6D In the exemplary graph of FIG, the speed of tooth movement (i.e., translation and rotation) between stages is shown. For example, in Figure 6B In the , the crown and / or root velocity can be displayed. Figure 6BThe values ​​shown represent the absolute movement (in mm) of each tooth along its virtual path between consecutive stages. For example, between stages 2 and 3, tooth number 16 will move 0.14 mm (labeled 158). Figure 6B , teeth numbers 13 and 23 move at a maximum speed of 0.23 mm to 0.25 mm, so it is possible to determine the number of treatment stages as described below. Fig.6D In the embodiment, tooth number 47 rotates 0.30 degrees per stage, while tooth number 44 moves 0.25 mm per stage. Each of these teeth can determine the number of treatment stages in the orthodontic treatment plan.

[0071] refer to Figure 5 At 166, the clinician may check the movement speed against predetermined minimum and / or maximum thresholds and assess whether the tooth movement is too slow / too fast in a given situation. This may include the above Figure 6B and Fig.6D As described herein, if the tooth movement meets or exceeds one or more predetermined limits, such as one or more of the maximum translation speed, maximum rotation speed, and maximum tilt / torque speed described above, the clinician or the software can add one or more stages to reduce the movement speed of each stage below the predetermined limits.

[0072] In an exemplary embodiment, Figure 5 Any non-IPR contacts (referred to herein as inter-proximal collisions) at 170 are resolved. Fig. 6A , for example, non-IPR contacts 172, 174, and 176 are indicated. These occur at stage 11 (0.03 mm), stage 3 (0.03 mm), and stage 3 (0.03 mm), respectively, and must be resolved for successful orthodontic treatment. Although the non-IPR contacts 172, 174, and 176, as well as other contacts, can be resolved by manually resolving each contact by moving one or two affected virtual teeth, in accordance with an embodiment of the present invention, a hierarchical solver algorithm 180 can be utilized at 182 to resolve all non-IPR contacts. Advantageously, the hierarchical solver algorithm 182 reduces or eliminates manual repositioning, thereby reducing the clinician's involvement in orthodontic treatment planning.

[0073] Once any collisions are resolved according to step 182, in an embodiment, according to step 183, Figure 5 The treatment plan at 142 may include a predetermined constraint on the total number of stages. For example, at 184, by default, the number of stages for treating the patient's upper dental arch and the number of stages for treating the patient's lower dental arch may be the same. The dental arch requiring the most stages (e.g., the dental arch with the guide teeth) determines the number of stages for the other dental arch. For example, Fig. 6A and Figure 6C As shown, the lower dental arch ( Figure 3B ) requires 22 stages, while the patient's upper dental arch requires 17 stages to move all teeth in the patient's upper dental arch from the T1 position to the T2 position. In an embodiment, at 184, the treatment plan for the patient's upper dental arch is extended to 22 stages to match the number of stages required to treat the lower dental arch. However, the number of stages is not limited to a minimum number or a maximum number. For reference, the number of appliances 126 planned for treatment is 22 per dental arch (i.e., a total of 44 appliances), and then the number of appliances 126 can be adjusted based on the number of appliances 126 planned for treatment. Figure 1 These aligners are manufactured at 144. Thus, the number of aligners 126 corresponds to the number of treatment sessions for the corresponding dental arch.

[0074] In an exemplary embodiment, reference Figure 7 , at 182, the step-by-step solver algorithm 180 solves Fig. 6A and Figure 6C Most or all non-IPR contacts during, for example, orthodontic treatment planning Fig. 6A The non-IPR contacts 172, 174, and 176 of the exemplary T1 models 102 and 103 are shown in FIG. Fig. 8A and Figure 8C The resulting hierarchical sequences are shown separately, wherein all non-IPR contacts, including in particular non-IPR contacts 172, 174 and 176, are resolved. Figure 8B and Fig.8D Lists the Fig. 8A and Figure 8C speed.

[0075] To resolve non-IPR contacts using the hierarchical solver algorithm 180, Figure 7 186 in , the step-by-step solver algorithm 180 in Figure 6A-6D At least one key frame is created in the staged sequence shown. This is for example only and not for limitation. Fig. 8A shows a modified step diagram, where Fig. 6A A keyframe 186 is created at stage 6 of FIG. A keyframe represents a tooth position and / or orientation modified from its initial staged position and / or orientation at a stage. Each keyframe is described by two features: a stage number and a tooth position. Because the position and / or orientation of a tooth in a keyframe has changed, the virtual movement path of the tooth deviates from the reference Fig. 6A The initial virtual movement path described by . For example, the virtual path can be constructed via linear interpolation between two positions of the model tooth, such as between the T1 position and the T2 position. The key frame between these positions changes the path so that it is no longer a linear interpolation between the two positions. More generally, the new path is no longer a linear interpolation of each degree of freedom of the virtual movement of the model tooth from the T1 position to the T2 position.

[0076] refer to Fig. 8A , a keyframe can be created for each tooth in a stage. For example, keyframe 186 is a keyframe in stage 6, indicated by a solid circle. As shown, a solid circle is shown for each of stages 0, 6, 11, and 17 of tooth 17. Each circle is connected by a solid line, indicating that tooth 17 is moving at each stage. Keyframe 186 indicates that the position and / or orientation of tooth 17 deviated from the position and / or orientation of tooth 17 at stage 6 (keyframe 186). Fig. 6A The initial path shown. In each of Stages 1-5, the key frame 186 also changes the position and / or orientation of the tooth 17. From different perspectives, the position and / or orientation of the model tooth 11 at the key frame 186 modifies the position and / or orientation of the model tooth 11 in each of Stages 1-5. Fig. 8A In the example, stages 7-17 are relative to Fig. 6A The position and / or orientation of the model tooth 17 at stage 7-stage 17 is determined by the position and / or orientation of the model tooth 17 at the key frame 186 and the key frame (not labeled) at stage 11. Therefore, the key frame modifies the position and / or orientation of the tooth at one stage, and modifies the two virtual movement paths of the tooth (to the key frame and from the key frame) according to the new position and / or orientation of the tooth. For example, by changing Fig. 6A The grading shown is Fig. 8A Compared with the staged solver algorithm 180 shown in FIG. 1 , the key frame 190 is added at stage 11. At stage 11, the key frame 190 modifies the T1 model 102 ( Figure 3A ) of the tooth 11. Therefore, the virtual movement of the tooth 11 is modified from its initial virtual movement path from stage 6 (also a key frame) to stage 11 (i.e. to key frame 190) and from stage 11 to stage 17 (i.e. from key frame 190).

[0077] refer to Figure 7 and Fig. 8A At 186, in an embodiment, the hierarchical solver algorithm 180 adds at least one row of key frames at a stage of orthodontic treatment planning. That is, one key frame is added for each tooth position at the selected stage. This is referred to as a key frame row. Fig. 8A and Figure 8CIn the exemplary embodiment shown, two keyframe rows (including keyframe 190 at tooth 11) are created at stages 1 / 3 and 2 / 3 of the total number of stages. For example, keyframe row 192 is at stage 6 and second keyframe row 194 is at stage 11. Thus, the position and / or orientation of each tooth 11-17 and 21-27 is modified from stage 1 to stage 6 according to keyframe row 192 at stage 6. Thus, the position and / or orientation of each tooth 11-17 and 21-27 is modified to and from stage 11 according to keyframe rows 192 and 194. Thus, the movement of each tooth 11-17 and 21-27 to and from stage 6 and to and from stage 11 is modified. As described below, the hierarchical solver algorithm 180 optimizes each tooth position at stage 6 and stage 11 and may also change the hierarchical sequence of stage numbers associated with one or both of the keyframe rows 192 and 194. In other words, the hierarchical solver algorithm 180 may change the key frame row 192 from stage 6 to stage 5 or stage 7. The key frame row 194 may alternatively or similarly be modified. Fig. 8A The arrow 196 in FIG. 1 indicates the sequence of changing the key frame rows 192, 194. It is expected that the key frame rows 192, 194 can be changed in the sequence of changing the key frame rows 192, 194. Fig. 8A Move more than one stage in the staged sequence shown.

[0078] In the embodiments, reference Figure 7 , the hierarchical solver algorithm 180 resolves all non-IPR contacts. For example, the solver algorithm 180 resolves Fig. 6A The non-IPR contacts 172, 174 and 176 (and all other contacts) shown in FIG. 1 are adjusted in position and / or orientation so that these contacts do not occur during the movement. This is accomplished by Fig. 8A and Fig. 6A The comparison in shows that each non-IPR contact ( Fig. 6A ) are interpreted as normal contact range. Fig. 8ANon-IPR contacts are shown. Further, advantageously, the hierarchical solver algorithm 180 solves for the problem of misaligned key frames that are typically generated during manual manipulation of stages to correct interproximal tooth collisions. In other words, during manual manipulation, key frames may be added to different stages, with one key frame being added to fewer than all teeth at a single stage. The hierarchical solver algorithm 180 may eliminate individual key frames on a single tooth at multiple different stages. That is, the hierarchical solver algorithm 180 creates a key frame for each tooth at a particular stage, thereby, in embodiments, eliminating any necessity to create a single key frame for a single tooth at another stage. Further, one or the other or both of the key frame rows 192, 194 allow all key frames within a stage to be moved together with a single modification, such as Fig. 8A As shown by arrow 196 in FIG. This simplifies the movement of teeth by the doctor and simplifies the editing of the grading by the clinician.

[0079] More specifically, in the embodiments, reference is made to Figure 7 and Fig. 8A , the hierarchical solver algorithm 180 optimizes Figure 3A The position and / or orientation of each tooth 11-17 and 21-27 in each key frame row 192 and 194 in the embodiment of the present invention is determined, and the hierarchical sequence of key frame rows 192 and 194 in the entire stage sequence is optimized. Although not further described herein, the hierarchical solver algorithm 180 can additionally or alternatively optimize the key frame rows 192 and 194 in a similar manner. Figure 3B The position and / or orientation of each tooth 31-37 and 41-48.

[0080] In an embodiment, via Figure 7The hierarchical solver algorithm 180 at 182 resolves non-IPR contacts and optimizes tooth positions and / or orientations including using a sequential quadratic programming approach. In this regard, the position and / or orientation of each model tooth and the hierarchical sequence of key framework rows are defined in the hierarchical model. The position and / or orientation space between adjacent teeth is also defined. In an embodiment, the tooth position at each stage and the space between adjacent teeth are defined as a nonlinear problem. One or more inequality constraints on the nonlinear problem define a linear inequality system. The nonlinear problem is then solved under the constraints of the linear inequality system. The nonlinear problem is solved to converge the tooth position at each stage while maintaining the spacing between the teeth. This eliminates virtual tooth collisions in the sequence of stages. Constructing the linear inequality system includes linearizing the nonlinear problems by calculating the partial derivatives of the nonlinear problems. Using the coefficients derived from the partial derivative solutions replaced in the linear inequality system, the hierarchical solver algorithm 180 solves the hierarchical model constrained by the linear inequality system according to the priority of the constraints defining the linear inequality system. The tooth positions and / or orientations, spacings between teeth, and the key frame row order sequence determined from one iteration of the solution can be used as the starting point for subsequent iterations, so that the tooth positions and / or orientations, spacings between teeth, and the key frame row order sequence converge to a solution constrained by a system of linear inequalities, thereby resolving all interproximal collisions at each stage. Adri en Escande et al., "Fast Resolution of Hierarchized Inverse Kinematics with Inequality Constraints," filed May 19, 2010, (https: / / hal.archives-ouvertes.fr / hal-00484853), describes a sequential quadratic programming method, which is incorporated herein by reference in its entirety. As indicated, the disclosed method reduces computational time relative to inverse kinematics with inequality constraints.

[0081] refer to Figure 7 At 200, in an embodiment, a hierarchical model is defined. In the hierarchical model, the i-th tooth position X at stage j in the virtual space is described as a vector of at least two components (α and β) transposed and written as:

[0082]

[0083] Where N is the number of teeth, and K is related to the number of treatment stages in the treatment plan. For example, K is greater than the number of treatment stages.

[0084] The position of the key framework row in the staged sequence of orthodontic treatment phases is variable and is calculated according to the vector:

[0085]

[0086] Among them, T p is the floating point value position of the "p"th middle keyframe row, Where M is the number of keyframe rows between stage 0 (T1 model) and the last stage (T2 model). When in the range [0,1], it becomes:

[0087] 0.0 <T 1 <T 2 <… <T M <1.0

[0088] For K in (1) above, in order to determine the interproximal collisions in each stage, embodiments of the present invention control each tooth position and / or orientation in all stages, not just each tooth position and / or orientation in the critical framework row. The hierarchical solver algorithm 180 only determines the collisions between consecutive teeth in the jaw in all stages. To this end, the hierarchical solver algorithm 180 discretizes the virtual movement path of each tooth from the T1 model 102, 103 to the T2 model 136, 137. Each virtual movement path is parameterized as K discrete stages in the range [0,1]. K must be large enough to accurately monitor collisions along each virtual movement path. As an example and not a limitation, K can range from 70 to 100, because the treatment stages rarely (if ever) exceed 100 stages. After finding a solution, the unnecessary stages can be removed. Therefore, K may ultimately be related to the number of treatment stages. This is the relationship between K and the number of stages, that is, K is usually greater than the number of stages in the treatment plan. The hierarchical sequence of critical framework rows is described and solved in a variable space of dimension = N*Q*M. In summary, in the above equation,

[0089] 1) α is the buccal / lingual movement (translation perpendicular to the dental arch, in mm),

[0090] 2) β is the mesial / distal movement (translation along the dental arch, in mm),

[0091] 3) N is the total number of teeth in the patient's dental arch,

[0092] 4) Q is the degree of freedom for changing the position of the teeth, and

[0093] 5) M is the number of key frame rows.

[0094] The goal of the step solver algorithm 180 is to resolve the inter-neighbor collisions identified in the initial step. For example, the step solver algorithm 180 resolves the inter-neighbor collisions from the T1 model 102, 103 to the T2 model 136, 137, as shown in FIG. Fig. 6A and Figure 6C To construct the hierarchical model, a space S is defined between adjacent teeth i and i+1 at stage j.ij . Space S ij is defined as a nonlinear function F of the tooth position on each of the p and p+1 keyframe rows j (), where p is determined as T p <T j <T p+1 , T j It means that for each stage j, there are two key frame rows T p and T p+1 , these two key frame rows determine the key frame row T p and T p+1 The tooth positions and collisions at stage j in the hierarchical sequence of p and T p+1 are not consecutive stages. Instead, the two keyframe rows are separated by one or more stages. Space S ij Can be positive or negative, indicating interproximal space or adjacent tooth overlap, respectively. The collision at any stage depends only on the tooth positions on the two nearest critical framework rows for a given stage. Therefore, the tooth positions vary only on the critical framework rows. This determines the tooth positions for all other stages, thereby resolving tooth collisions for those stages. For each stage j, the hierarchical model includes a different nonlinear function F j (). For example, for each phase, each nonlinear function has two variables: α (buccal / lingual movement) and β (mesial / distal movement). Nonlinear functions F for different phases j () may be different. However, since there are six degrees of freedom, there are also factors that affect S ij These include, for example, tooth rotations, such as inclination and angle.

[0095] Based on the above, the space S between adjacent teeth i and i+1 at stage j is ij It is expressed as:

[0096]

[0097] In order to avoid collision between teeth on their respective virtual movement paths, the space S ij At each stage, the following inequality constraints are imposed.

[0098]

[0099] in, is the maximum space allowed between teeth i and i+1. For simplicity, a minimum space or lower limit of 0 is described, but the lower limit may vary based on the range of non-IPR contacts described herein (e.g., 0.0 mm to 0.04 mm). The maximum space may be determined based on the space between these teeth in the T1 model 102, 103 and the T2 model 136, 137.

[0100] In an embodiment, in addition to the above-mentioned linear inequality space constraint (4), the linear inequality system also includes a linear inequality speed constraint for tooth movement. This is a constraint that limits the movement amplitude of the tooth along its virtual movement path to below a threshold. In general, for the above-mentioned two degrees of freedom of buccal / lingual movement α and mesial / distal movement β, the speed constraint can be simplified and written as:

[0101]

[0102] in, Includes constraints on the degrees of freedom of each tooth motion used. By way of example and not limitation, velocity constraints may be set to (i.e., for each of α and β) 0.25 mm of translational movement, 2 degrees of rotational movement, and 1 degree of tilt / torque movement per stage. Embodiments of the present invention are not limited to Q=2 (degrees of freedom) as described above with respect to α and β. Thus, (5) may cover all degrees of freedom.

[0103] In an embodiment, additional or alternative linear inequality constraints limit the magnitude of the total tooth motion (i.e., deviation) in the T1 model 102, 103 from its original position and / or orientation. Thus, the linear inequality system may include deviation constraints. Thus, the distance that each tooth can move from its original position and / or orientation in the T1 model 102, 103 is limited. The deviation constraints are intended to keep the teeth in the patient's virtual jawbone. Simplified expressions for buccal / lingual motion α and mesial / distal motion β are:

[0104]

[0105] in, is the tooth position at T1.

[0106] In the embodiments, reference Figure 7 , at 202, the linear inequality system has multiple solution targets. Fig. 9, these objectives are prioritized before solving the hierarchical model. That is, in an exemplary embodiment, the solution objectives of the linear inequality constraints (4), (5), and (6) are prioritized. The established priorities ensure that the orthodontic treatment plan developed is a practical, patient-centered plan. Although a specific priority of objectives is described herein, the objectives may be prioritized in a different order. Furthermore, it should be understood that additional and / or alternative linear inequality constraints are possible. Therefore, unless otherwise stated, embodiments of the present invention are not limited to the specific priorities disclosed.

[0107] Therefore, reference Figure 7 and Fig. 9 , the hierarchical solver algorithm 182 will resolve the goal of neighbor collisions (i.e., S ij The patient's teeth should not collide during orthodontic treatment. This is the main goal for achieving efficient orthodontic treatment. For example, solving S ij The goal should not include collisions. To avoid this possibility, the grading should indicate that there is no collision between any two teeth at any stage (e.g., normal contact between 0 mm and 0.04 mm).

[0108] according to Fig. 9 In the embodiment, the deviation constraint (6) is in S ij It is then assigned a priority (ie, priority number 2 in this embodiment). Therefore, the total magnitude of tooth movement should be limited. The next priority target is the velocity constraint (5), which is assigned a priority number 3.

[0109] In the embodiments, reference Figure 7 At 204, after prioritizing the objectives of the linear inequality system, the order solver algorithm 180 linearizes the order model, which is the mathematical model described above, including the linear inequality system, the priorities, and the linearization iterations using partial derivatives. This may include F j () Initial linearization around some initial solution. This may include some initial estimates of tooth movement from the T1 model to the T2 model. For example, this may be Fig. 6A and Figure 6C A virtual path is shown, where linear interpolation is used to determine the stages between the starting position (T1) and the ending position (T2).

[0110] To this end, in an embodiment, the above (2) can be rewritten using a single vector as follows,

[0111]

[0112] For a single vector The step-by-step solver algorithm 180 linearizes S by determining partial derivatives at each iteration. ij ((3) above), as follows:

[0113]

[0114] in, is the spacing S of a particular iteration (“iter”) ij .variable The linear inequality spacing constraint (4) is written as:

[0115]

[0116] Velocity (5) and Deviation (6) can be used as simple inequalities without linearization. In an embodiment, all partial derivatives of (5) and (6) are equal to 1. Therefore, including the spacing (in ), the hierarchical model for each of the speed and deviation constraints is linearized.

[0117] In the embodiments, reference Figure 7 At 204, the step-wise solver algorithm 180 calculates the partial derivatives of the mesio-distal and bucco-lingual translations for each tooth in each keyframe row 192 and 194. For example, the step-wise solver algorithm 180 calculates the tooth position relative to each of the mesio-distal and bucco-lingual translations. The spatial partial derivative of .

[0118] exist Figure 7 At 206, the step solver algorithm 180 calculates the spatial partial derivatives of the time shift with respect to the key frame rows 192 and 194. This can be done by calculating the time shift of the key frame rows T p ,T p+1 The partial derivatives of all components of the collision vector of the position To solve the key frame line T p ,T p+1 Note that computing the partial derivatives of discrete values ​​of key frame rows 192 and 194 can be accomplished by representing a stage of the key frame row as a continuous variable, such as above,

[0119] 0.0 <T 1 <T 2 <… <T M <1.0

[0120] Determine (according to (2)) After obtaining a solution, the solution is discretized over a predetermined number (e.g., 100) of fixed discrete stages. Based on the speed, the number of stages is adjusted (e.g., reduced) to the number of stages required for the treatment.

[0121] At 210, the partial derivatives of 204 and 206 are substituted into a system of linear inequalities and the system is solved for each tooth in the critical frame row. In an embodiment, tooth collision (i.e., iteration spacing) ) and the speed of the key frame line (i.e., ) are calculated separately. It is expected that this is possible because the critical frame row includes all teeth in the corresponding jaw. After resolving the collision, the velocity violation can be resolved in one step by increasing the number of stages determined. In an embodiment, if the velocity constraint (5) remains too high or too low, the step-by-step solver algorithm 180 increases or decreases the number of stages by a predetermined amount (e.g., 3 to 7 orders), respectively, and then solves each of (4)-(6) until all each solution satisfies the constraint. In addition, in an embodiment, the step-by-step solver algorithm 180 not only changes the sequence of one or more critical frame rows, but the step-by-step solver algorithm 180 also changes the number of stages T associated with the T2 model. T2 In this way, as determined by the hierarchical solver algorithm 180, the speed constraint can be satisfied by adding or removing stages to increase or decrease the treatment length, respectively.

[0122] Once the hierarchical model is solved at 210, the hierarchical solver algorithm 180 applies the determined geometric and time shift solutions to the keyframe rows 192 and 194. i,j There is a collision between any adjacent teeth at Then the step solver algorithm 180 iterates at 214 until S ij According to (4), the convergence is within the constraints. As shown in the figure, during the iteration at 214, at the new tooth position X i,j The partial derivatives of the move are calculated to provide the new S ij , and so on, until This may be similar to the process in the Newton-Raphson method. During the iteration, if there is a tooth collision, the hierarchical solver algorithm 180 changes the tooth position X i,j Modify to a more ideal tooth position to avoid collision. This may initially result in an increase in the magnitude of tooth collision, i.e. a more negative S ij Once the hierarchical model converges, the stages of orthodontic treatment are as follows: Figure 8A-8D as shown in the example.

[0123] In an embodiment, additional technical constraints may be required to solve the linear inequality system. These may also be prioritized at 202. Fig. 9 , by way of example only, these might include (1) to sort the key frame rows in ascending order. This can be set as the highest priority for the technical constraints. As the second technical constraint (2), The increment step size is constrained at each iteration so that the linearization is applicable. This can be set to the lowest priority. The third technical constraint (3) is To avoid ambiguity in the case of an underdefined priority linear inequality system with the lowest priority. The order solver algorithm 180 can resolve collisions in any number of ways. Among multiple solutions, the optimal one is the minimum tooth motion. The third technical constraint is designed to achieve the minimum tooth motion during convergence.

[0124] In the embodiments, reference Figure 5 , at 184, once the hierarchical model converges to a solution, orthodontic treatment planning 142 includes accounting for any difference in the number of stages between the patient's upper arch and the patient's lower arch. If the difference is less than 5 appliances, the stages and appliances can be added to the arch with the fewest stages. Essentially, this extends the number of stages on the arch with fewer appliances to match the arch with the most appliances. If the difference is greater than 5, passive appliances can be created by adding stages after the last calculated treatment stage. The added stages cannot move teeth, but can provide some comfort value to the patient while treatment continues on the other side of the patient's jaw.

[0125] After proper orthodontic treatment planning, information about the phases can be used to create Figure 5 Although not shown, an exemplary process for forming the aligner 126 may include deforming a workpiece using a mold. At a certain stage of the orthodontic treatment plan, the mold may be manufactured based on a corresponding computer model of the patient's dentition. For example, the mold may be produced using a 3D digital model of the patient's teeth corresponding to the stage of the treatment plan. For example, Fig. 8A and Figure 8C A series of computer models corresponding to the stages of the process provide incremental steps from a T1 model to one or more intermediate dentition models, and ultimately a T2 model, which can be used to produce a corresponding mold. An exemplary method for forming a mold and manufacturing an orthotic appliance is described in co-owned U.S. Patent No. 10,935,958, the entire contents of which are incorporated herein by reference.

[0126] refer to Fig.10Thus, the aligner 126 includes a hollow shell 250 configured to enclose one or more crowns of a patient's teeth. The shell 250 is formed with a plurality of cavities 252 that collectively define a rim 254 that defines an opening 256. Each cavity 252 is shaped to receive a particular tooth of the patient's teeth through the opening 256 during use of the aligner 126. The shell 250 is made of one or more layers of resilient material and may include one or more receivers 258 configured to receive attachments (not shown) on the patient's teeth and / or one or more devices in the aligner 126.

[0127] During orthodontic treatment, the appliances 126 are selectively positioned on the patient's teeth and can fit tightly due to slight differences in the position of one or more cavities 252 relative to the corresponding teeth. Forced contact with the appliances 126 can move the patient's teeth toward a predetermined position according to the patient's treatment plan, which may ultimately end at T2. A set of appliances (not shown) may include one or more appliances 126. During orthodontic treatment, each treatment stage may include appliances that provide slightly different movements to the patient's teeth. The individual appliances are used in a predetermined order to complete the orthodontic treatment or move the patient's teeth to T2. Therefore, each appliance in the series can move one or more teeth by a specified amount. Although similar, each appliance is slightly different in shape. Over time, these individual amounts may result in complete treatment of the patient's malocclusion.

[0128] As described above, according to an embodiment of the present invention, a practitioner implements a computer 106 (e.g., such as a computer 106 ) using software capable of generating and manipulating 3D digital models according to the system 104 described above. Figure 2 and Fig.11 Now refer to Fig.11 , the above embodiments of the present invention or parts thereof (such as system 104) may be implemented using one or more computer devices or systems (such as exemplary computer 106). Computer 106 may include a processor 302, a memory 304, an input / output (I / O) interface 306, and a human-machine interface (HMI) 308, such as Figure 2 The computer 300 may also be operably coupled to one or more external resources 310, such as an intraoral scanner and a CBCT system or a manufacturing system 124, via the network 122 and / or the I / O interface 306. The external resources may include, but are not limited to, servers, databases, mass storage devices, peripheral devices, cloud-based network services, or any other resources that the computer 106 may use.

[0129] Processor 302 may include one or more devices selected from the group consisting of a microprocessor, a microcontroller, a digital signal processor, a microcomputer, a central processing unit, a field programmable gate array, a programmable logic device, a solid state machine, a logic circuit, an analog circuit, a digital circuit, or any other device that manipulates (analog or digital) signals based on operating instructions stored in memory 304. Memory 304 may include a single memory device or multiple memory devices, including but not limited to read-only memory (ROM), random access memory (RAM), volatile memory, non-volatile memory, static random access memory (SRAM), dynamic random access memory (DRAM), flash memory, cache memory, and / or a data storage device such as a hard drive, an optical drive, a tape drive, a volatile or non-volatile solid-state device, or any other device capable of storing data.

[0130] The processor 302 may operate under the control of an operating system 314 residing in the memory 304. The operating system 314 may manage computer resources so that computer program code embodied as one or more computer software applications or algorithms, such as an application 316 residing in the memory 304 including the hierarchical solver algorithm 180, may have instructions executed by the processor 302. In an alternative embodiment, the processor 302 may directly execute the application 316, in which case the operating system 314 may be omitted. One or more data structures 318 (e.g., the 3D digital models 102, 103, 136, and 137) may also reside in the memory 304 and may be accessed and modified by the processor 302, the operating system 314, or the application 316 (e.g., according to the hierarchical solver algorithm 180), and may be manipulated by a clinician.

[0131] The I / O interface 306 may provide a machine interface that operably couples the processor 302 to other devices and systems, such as external resources 310 or network 122. Thus, the application 316 may work in conjunction with the external resource 310 or network 122 via communication via the I / O interface 306 to provide various features, functions, applications, processes, or modules that comprise embodiments of the present invention. The application 316 may also have program code executed by one or more external resources 310, or otherwise rely on functions or signals provided by other systems or network components external to the computer 106. In fact, given the nearly endless possible hardware and software configurations, it will be appreciated by those of ordinary skill in the art that embodiments of the present invention may include applications that are located external to the computer 106, distributed between multiple computers or other external resources 310, or provided by computing resources (hardware and software) provided as services on the network 312, such as cloud computing services.

[0132] The HMI 308 can be operably coupled to the processor 302 of the computer 106 in a known manner to allow a practitioner to interact directly with the computer 106, for example, to operate a user interface. The HMI 308 can include a video or alphanumeric display, a touch screen, speakers, and any other suitable audio and visual indicators capable of providing data to a user. The HMI 308 can also include input devices and controls, such as an alphanumeric keyboard, a pointing device, a keypad, buttons, control knobs, a microphone, etc., which can accept commands or inputs from a user and transmit the inputted inputs to the processor 302.

[0133] The database 320 may reside in the memory 304 and may be used to collect and organize data used by the various systems and modules described herein. The database 320 may include data and supporting data structures that store and organize data, such as the 3D digital models 102, 103, 136, 137. In particular, the database 320 may be arranged with any database organization or structure, including but not limited to a relational database, a hierarchical database, a network database, or a combination thereof. A database management system in the form of a computer software application executed as instructions on the processor 302 may be used to access information or data stored in records of the database 320 in response to a query, wherein the query may be dynamically determined and executed by the operating system 314, other applications 316, or one or more modules.

[0134] In general, routines executed to implement embodiments of the present invention, whether implemented as part of an operating system or as a specific application, component, program, object, module or sequence of instructions, or a subset thereof, may be referred to herein as "computer program code," or simply "program code." Program code typically includes computer-readable instructions that reside at various times in various memories and storage devices in a computer, and that, when read and executed by one or more processors in a computer, cause the computer to perform the operations necessary to perform the operations and / or elements embodying aspects of embodiments of the present invention. The computer-readable program instructions for performing the operations of embodiments of the present invention may be source code or object code written, for example, in assembly language or in any combination of one or more programming languages.

[0135] Various program codes described herein can be identified based on the application implemented in a specific embodiment of the invention. However, it should be understood that any specific program naming below is only for convenience, so the present invention should not be limited to use in any specific application identified and / or implied by these naming. In addition, considering the generally endless ways in which computer programs can be organized into routines, processes, methods, modules, objects, etc., and the various ways in which program functions can be distributed between various software layers (e.g., operating systems, libraries, APIs, applications, applets, etc.) residing in classical computers, it should be understood that embodiments of the present invention are not limited to the specific organization and distribution of program functions described herein.

[0136] The program code embodied in any application / module described herein can be distributed separately or together as program products in various forms. In particular, the program code can be distributed using a computer-readable storage medium having computer-readable program instructions thereon to enable a processor to perform various aspects of the embodiments of the present invention.

[0137] Inherently non-transitory computer-readable storage media may include volatile and non-volatile, removable and non-removable tangible media implemented in any method or technology for storing data, such as computer-readable instructions, data structures (e.g., 3D digital models 102, 103, 136, and 137), program modules, or other data. Computer-readable storage media may also include RAM, ROM, erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other solid-state memory technology, portable compact disk read-only memory (CD-ROM) or other optical storage, cassettes, magnetic tapes, magnetic disk storage or other magnetic storage devices, or any other medium that can be used to store the desired data and can be read by a computer. Computer-readable storage media themselves should not be interpreted as transient signals (e.g., radio waves or other propagating electromagnetic waves, electromagnetic waves propagating through a transmission medium such as a waveguide, or electrical signals transmitted through a cable). Computer-readable program instructions can be downloaded from a computer-readable storage medium to a computer, another type of programmable data processing device, or another device, or downloaded to an external computer or external storage device via a network.

[0138] Computer-readable program instructions stored in a computer-readable medium can be used to direct a computer, other type of programmable data processing device, or other device to operate in a specific manner, so that the instructions stored in the computer-readable medium produce an orthodontic device that includes instructions to implement the functions, actions, and / or operations specified in the flowchart, sequence diagram, and / or block diagram. The computer program instructions can be provided to one or more processors in a general-purpose computer, a special-purpose computer, or other programmable data processing device to produce a machine, so that the instructions executed by the one or more processors cause a series of calculations to be performed to implement the functions, actions, and / or operations specified in the flowchart, sequence diagram, and / or block diagram.

[0139] Example

[0140] refer to Figure 3A , Figure 3B , Figure 4A , Figure 4B , Figure 6A-6D as well as Figure 8A-8D The results of the exemplary calculation are shown as Q = 2 (two degrees of freedom), M = 2 (the number of key frame rows is 2), and N = 14 (the number of teeth in the dental arch is 14). Figure 3A and Figure 3B The initial order scheme of the T1 model shown was calculated. Fig. 6A and Figure 6B Shows Figure 3A The initial ordering scheme of the T1 model. Figure 6C and Fig.6D Shows Figure 3B The initial ordering scheme for the T1 model is shown. Figure 6A-6D Each initial stage scheme is constructed by moving from stage 0 to the last stage (e.g. Fig. 6A and Figure 6B Stage 17 of Figure 6C and Fig.6D In stage 22) each degree of freedom of the virtual motion of each tooth is calculated by linear interpolation. Note that Fig. 6A and Figure 6C The initial staged solutions shown all include inter-tooth collisions (referred to as non-IPR contacts). Collisions are indicated by underlining of values ​​indicating negative space between adjacent teeth. As shown, collisions occur primarily between teeth 16 and 15, 13 and 12, and 12 and 11. Fig. 6A The collision started at stage 3 and lasted until stage 16. The maximum collision between teeth 13 and 12 occurred at stage 9, where a virtual overlap of 0.10 mm was observed. Figure 6CIn the 9th and 11th stages, collisions occurred between teeth 47 and 46, 46 and 45, 44 and 43, 43 and 42, 31 and 32, and 33 and 34. In stages 9-11, the maximum collision occurred between teeth 42 and 41, 0.13 mm.

[0141] Calculate the space S according to the hierarchical solver algorithm ij and speed Provided Figure 8A-8D The staged scheme shown, where Fig. 8A and Figure 8B Corresponds to Figure 3A The T1 model shown to Figure 4A The treatment phase scheme of the T2 model shown is Figure 8C and Fig.8D Corresponds to Figure 3B The T1 model shown to Figure 4B The treatment phase scheme for the T2 model is shown in Figure 1. As shown in the figure, the key frame rows appear in Fig. 8A Stages 6 and 11, and Figure 8C Stages 8 and 16. Fig. 6A and Figure 6C All collisions in are resolved. That is, Fig. 8A and Figure 8C There is no collision in either. Figure 8B and Fig.8D , the speed is within the range.

[0142] Although the present invention has been illustrated by the description of various embodiments, and these embodiments have been described in some detail, the inventors of the present invention do not intend to limit or in any way restrict the scope of the appended claims to such details. Therefore, additional advantages and modifications will be readily apparent to those skilled in the art. The various features of the present invention may be used alone or in any combination, depending on the needs and preferences of the user.

[0143] The required technical solutions are as follows:

Claims

1. A computer-implemented method for orthodontic treatment planning using one or more orthodontic appliances, the method comprising: determining an initial virtual path along which each model tooth in the patient's jaw is to be moved during orthodontic treatment, each initial virtual path being from a first position and / or orientation of the model teeth in the first arrangement to a second position and / or orientation of the model teeth in the second arrangement, wherein each initial virtual path is divided into a plurality of stages, each stage of the plurality of stages defining a position and / or orientation of a corresponding one of the model teeth on the initial virtual path; Calculate the space between adjacent model tooth pairs at each stage; Define the minimum space between adjacent model tooth pairs allowed for orthodontic treatment; as well as When one or more of the calculated spaces are less than the minimum space, creating at least one keyframe row, wherein each tooth position and / or orientation in the stage is a keyframe, and when one or more of the calculated spaces are less than the minimum space, iterating one or more times: for each model tooth on the at least one critical framework row, changing the position and / or orientation of the model tooth from the first position and / or orientation, or from a previous position and / or orientation of a previous iteration; as well as calculating the space between adjacent pairs of model teeth at each stage using the changed position and / or orientation of each model tooth at the at least one key framework row, Wherein, after iteration, the multiple stages define an orthodontic treatment plan, in which each calculated space is larger than the minimum space, and in the defined orthodontic treatment plan each stage corresponds to an orthodontic appliance for orthodontic treatment of the patient.

2. The method according to claim 1, further comprising: A series of aligners are manufactured for the patient, each aligner corresponding to one of the plurality of stages.

3. The method according to claim 1, wherein: Iterating includes changing a position of the at least one key frame row during the plurality of stages.

4. The method according to claim 3, wherein: Changing the position includes moving the at least one key frame row one stage earlier or one stage later among the plurality of stages.

5. The method according to claim 1, wherein: The at least one keyframe row includes a first keyframe row and a second keyframe row, wherein iterating one or more times includes changing a position and / or orientation of each model tooth in each of the first keyframe row and the second keyframe row.

6. The method according to claim 5, wherein: The first key frame row and the second key frame row are not consecutive stages.

7. The method according to claim 1, wherein: The minimum space is in the range of 0.0 mm to 0.04 mm.

8. The method according to claim 1, further comprising: A maximum space is defined, wherein iteration occurs when one or more calculated spaces are smaller than the minimum space or larger than the maximum space.

9. The method according to claim 1, wherein: At each stage of the plurality of stages, the position and / or orientation of each model tooth is defined in at least two degrees of freedom.

10. The method according to claim 1, wherein: The position and / or orientation of each model tooth is described as a vector having at least two components.

11. The method according to claim 10, wherein: The vector is: Among them, X i,j is the position and / or orientation of model tooth i at stage j, N is the total number of model teeth in the patient's dental arch, K is related to the number of stage j in the plurality of stages, α is the buccal / lingual movement of tooth i at stage j, and β is the mesial / distal movement of tooth i at stage j.

12. The method according to claim 11, wherein: The at least one key frame row includes a first key frame row (T p ) and the second key frame row (T p+1 ), the calculated space (S ij ) is represented as: Among them, the calculated space (S ij )yes as well as The function F at stage j j , is the position and / or orientation of the model tooth i in the first key frame row, is the position and / or orientation of the model tooth i in the second key frame row, is the position and / or orientation of the model tooth i+1 in the first key frame row, The position and / or orientation of the model tooth i+1 in the second key frame row.

13. The method according to claim 12, wherein: Stage j is in the first key frame row (T p ) and the second key frame row (T p+1 )between.

14. The method according to claim 12, wherein: Limiting the minimum space to zero also includes limiting the maximum space between adjacent model tooth pairs according to the inequality: in, is the maximum space between adjacent teeth i and i+1.

15. The method according to claim 1, wherein: The method further comprises: defining a maximum movement speed of each model tooth between any two consecutive stages, and when one or more calculated spaces are smaller than the minimum space, calculating the movement speed of each model tooth between each consecutive stage, and When the calculated movement speed is greater than the maximum movement speed, for each model tooth at the at least one key framework row, the position and / or orientation of the model tooth is changed from the first position and / or orientation or from a previous position and / or orientation of a previous iteration.

16. The method according to claim 1, wherein: The method further comprises: defining a deviation constraint for the total movement of each model tooth from said first position and / or orientation; When one or more of the calculated spaces are smaller than the minimum space, calculating a total movement of each model tooth from the corresponding first position and / or direction; and When the calculated total movement is greater than the deviation constraint, for each model tooth on the at least one critical framework row, the position and / or orientation of the model tooth is changed from the first position and / or orientation or from a previous position and / or orientation of a previous iteration.

17. A computer-implemented method for orthodontic treatment planning using one or more aligners, wherein an initial staged plan includes a plurality of treatment phases and indicates one or more collisions between adjacent pairs of model teeth, the method comprising: Define the minimum space between adjacent model tooth pairs; creating at least one keyframe row in the initial staged plan, wherein each tooth position and / or orientation in the at least one keyframe row is a keyframe; as well as When there is at least one collision in the ordered solution, iterate one or more times for each of the following: for each model tooth on the at least one critical framework row, changing the position and / or orientation of the model tooth from an initial position and / or orientation, or from a previous position and / or orientation of a previous iteration; as well as calculating the space between adjacent pairs of model teeth at each stage using the changed position and / or orientation of each model tooth at the at least one key framework row, Wherein, after iteration, a plurality of stages define an orthodontic treatment plan, in which each calculated space is larger than the minimum space, and in the defined orthodontic treatment plan, each stage corresponds to an orthodontic appliance for orthodontic treatment of the patient.

18. The method according to claim 17, further comprising: A series of aligners are manufactured for the patient, each aligner corresponding to one of the plurality of stages.

19. The method according to claim 17, wherein: Iteration includes moving the at least one key frame row one stage earlier or one stage later from a position in the initial staged solution.

20. The method according to claim 17, wherein: The at least one keyframe row includes a first keyframe row and a second keyframe row, wherein iterating one or more times includes changing a position and / or orientation of each model tooth in each of the first keyframe row and the second keyframe row.

21. The method according to claim 20, wherein: The first key frame row and the second key frame row are not consecutive stages.

22. The method according to claim 17, wherein: The minimum space is in the range of 0.0 mm to 0.04 mm.

23. The method of claim 17, further comprising: A maximum space is defined, wherein iteration occurs when one or more calculated spaces are smaller than the minimum space or larger than the maximum space.

24. The method of claim 17, wherein: The position and / or orientation of each model tooth is described as a vector having at least two components.

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