This application a continuation-in-part of application Ser. No. 09/313,289, filed on May 13, 1999, now U.S. Pat. No. 6,318,994 the full disclosure of which is incorporated herein by reference and is related to two U.S. patent applications which are: Ser. No. 09/169,036, now U.S. Pat. No. 6,450,807 entitled System and Method for Repositioning Teeth; and Ser. No. 09/169,034, now U.S. Pat. No. 6,471,511 entitled Defining Tooth-Moving Appliances Computationally. Both of these applications were filed Oct. 8, 1998, and the full disclosures of which are incorporated herein by reference.

BACKGROUND

1. Field of the Invention

The invention relates generally to the field of orthodontics and, more particularly, to computer-automated development of an orthodontic treatment plan and appliance.

2. Description of the Background Art

Repositioning teeth for aesthetic or other reasons is accomplished conventionally by wearing what are commonly referred to as braces. Braces comprise a variety of appliances such as brackets, archwires, ligatures, and O-rings. Attaching the appliances to a patient's teeth is a tedious and time-consuming enterprise requiring many meetings with the treating orthodontist. Consequently, conventional orthodontic treatment limits an orthodontist's patient capacity and makes orthodontic treatment quite expensive. As such, the use of conventional braces is a tedious and time consuming process and requires many visits to the orthodontist's office. Moreover, from the patient's perspective, the use of braces is unsightly, uncomfortable, presents a risk of infection, and makes brushing, flossing, and other dental hygiene procedures difficult.

Tooth positioners for finishing orthodontic treatment are described by Kesling in the Am. J. Orthod. Oral. Surg. 31:297-304 (1945) and 32:285-293 (1946). The use of silicone positioners for the comprehensive orthodontic realignment of a patient's teeth is described in Warunek et al. (1989) J. Clin. Orthod. 23:694-700. Clear plastic retainers for finishing and maintaining tooth positions are commercially available from Raintree Essix, Inc., New Orleans, La. 70125, and Tru-Tain Plastics, Rochester, Minn. 55902. The manufacture of orthodontic positioners is described in U.S. Pat. Nos. 5,186,623; 5,059,118; 5,055,039; 5,035,613; 4,856,991; 4,798,534; and 4,755,139.

Other publications describing the fabrication and use of dental positioners include Kleemann and Janssen (1996) J. Clin. Orthodon. 30:673-680; Cureton (1996) J. Clin. Orthodon. 30:390-395; Chiappone (1980) J. Clin. Orthodon. 14:121-133; Shilliday (1971) Am. J. Orthodontics 59:596-599; Wells (1970) Am. J. Orthodontics 58:351-366; and Cottingham (1969) Am. J. Orthodontics 55:23-31.

Kuroda et al. (1996) Am. J. Orthodontics 110:365-369 describes a method for laser scanning a plaster dental cast to produce a digital image of the cast. See also U.S. Pat. No. 5,605,459.

U.S. Pat. Nos. 5,533,895; 5,474,448; 5,454,717; 5,447,432; 5,431,562; 5,395,238; 5,368,478; and 5,139,419, assigned to Ormco Corporation, describe methods for manipulating digital images of teeth for designing orthodontic appliances.

U.S. Pat. No. 5,011,405 describes a method for digitally imaging a tooth and determining optimum bracket positioning for orthodontic treatment. Laser scanning of a molded tooth to produce a three-dimensional model is described in U.S. Pat. No. 5,338,198. U.S. Pat. No. 5,452,219 describes a method for laser scanning a tooth model and milling a tooth mold. Digital computer manipulation of tooth contours is described in U.S. Pat. Nos. 5,607,305 and 5,587,912. Computerized digital imaging of the jaw is described in U.S. Pat. Nos. 5,342,202 and 5,340,309. Other patents of interest include U.S. Pat. Nos. 5,549,476; 5,382,164; 5,273,429; 4,936,862; 3,860,803; 3,660,900; 5,645,421; 5,055,039; 4,798,534; 4,856,991; 5,035,613; 5,059,118; 5,186,623; and 4,755,139.

SUMMARY

In one aspect, a computer-implemented method to prepare a malocclusion treatment plan includes selecting a tooth treatment pattern from a library of predetermined tooth treatment patterns; and generating the malocclusion treatment plan implementing the selected tooth treatment pattern.

Implementations of the above aspect may include one or more of the following. The generating the malocclusion treatment plan includes determining one or more tooth paths based on the selected tooth treatment pattern. The treatment pattern can be selected from one or more clinical treatment prescriptions. The clinical treatment prescription includes at least one of the following: space closure, reproximation, dental expansion, flaring, distalization, and lower incisor extraction. The determining a tooth path includes finding a collision free shortest path between an initial position and a final position for one or more teeth. The generating the malocclusion treatment plan includes specifying a series of treatment stages for one or more teeth. The method can include dividing a path for one or more teeth into the series of stages while keeping the movement of teeth in each stage below a predetermined range. The method can include generating an appliance for each treatment stage. The appliance can be either a removable appliance or a fixed appliance. The method can include generating a three-dimensional model for the teeth for each treatment stage. The method also can include generating dental diagnostic information from the three-dimensional model. Interproximal reduction, tooth size discrepancy information, and Bolton information, among others can be generated from the 3D model. The library of treatment patterns includes at least one or more of the following: all equal movement pattern, A-shaped movement pattern, V-shaped movement pattern, M-shaped movement pattern, W-shaped movement pattern, symmetric staircase pattern, asymmetric staircase pattern, and equal equal movement pattern. For the all equal movement pattern, the method includes subdividing paths while satisfying one or more constraints. The constraint can be minimizing tooth oscillation and tooth movement distance. For the equal equal pattern, the method includes dividing the teeth into a prestage movement group and a post stage movement group; and applying the all equal movement to the prestage movement group and subsequently applying the all equal movement to the prestage movement group. For the A-shaped movement pattern, the method includes sequentially moving each tooth from an incisor tooth toward a molar tooth. For the V-shaped movement pattern, the method includes sequentially moving each tooth from a molar tooth toward an incisor tooth.

In another aspect, a computer-implemented method prepares a malocclusion treatment plan by: selecting one tooth treatment pattern from a library of predetermined tooth treatment patterns; generating the malocclusion treatment plan in accordance with the selected treatment pattern; and producing a plurality of data sets representing a series of successive tooth arrangements progressing from a first tooth arrangement to a second tooth arrangement. Implementations of this aspect may include generating an appliance for each tooth arrangement.

In another aspect, a computer-readable medium executable by a computer to prepare a malocclusion treatment plan includes code to select one tooth treatment pattern from a library of predetermined tooth treatment patterns; and code to generate the malocclusion treatment plan in accordance with the selected treatment pattern.

Implementation of this aspect may include one or more of the following. The medium can include code to fabricate an appliance for each tooth arrangement. The code to fabricate appliances can include code to control a fabrication machine to produce successive positive models of the tooth arrangements; and code to produce the appliance as a negative of the tooth model. The code to control a fabrication machine includes code to provide a volume of non-hardened polymeric resin; and code to scan a laser to selectively harden a resin to produce the positive model. The medium can include code to control a fabrication machine to produce successive appliances for the tooth arrangements.

In yet another aspect, a computer-implemented method to automatically stage a series of tooth movements, by selecting one teeth treatment pattern from a plurality of predetermined teeth treatment patterns; generating a treatment plan for the teeth in accordance with the selected move pattern by: generating a treatment plan with a tooth path for each tooth; and determining a series of treatment stages for the teeth; and controlling a fabrication machine to produce successive appliances for the tooth arrangements.

Implementations of this aspect may include generating an appliance as a negative or a positive of a dental model.

In another aspect, an appliance to correct malocclusion, the appliance formed using computer readable code controlling a fabrication machine, the code comprising instructions to: select one teeth treatment pattern from a plurality of predetermined teeth treatment patterns; generate a treatment plan for the teeth in accordance with the selected move pattern by: generate a treatment plan with a tooth path for each tooth; and determine a series of treatment stages for the teeth; and control the fabrication machine to produce successive appliances for the tooth arrangements.

In another aspect, a computer system to prepare a malocclusion treatment plan includes a processor; a display coupled to the processor; and a data storage device coupled to the processor and containing code to select a tooth treatment pattern from a library of predetermined tooth treatment patterns; and code to generate the malocclusion treatment plan implementing the selected tooth treatment pattern.

In yet another aspect, a computer system to prepare a malocclusion treatment plan includes means for selecting a tooth treatment pattern from a library of predetermined tooth treatment patterns; and means for generating the malocclusion treatment plan implementing the selected tooth treatment pattern.

Yet other implementations of the above aspects can include one or more of the following. The constraints relates to teeth crowding, teeth spacing, teeth extraction, teeth stripping, teeth rotation, and teeth movement. The teeth can be rotated approximately five and ten degrees (per stage) and can be incrementally moved in one or more stages (per stage), each stage moving each tooth approximately 0.2 mm to approximately 0.4 mm. The constraints can be stored in an array with one dimension of the array identifying each stage in the teeth movement. The treatment paths can include determining the minimum amount of transformation required to move each tooth from the initial position to the final position and creating each treatment path to require only the minimum amount of movement. Additionally, intermediate positions can be generated for at least one tooth between which the tooth undergoes translational movements of equal sizes. Further, intermediate positions can be generated for at least one tooth between which the tooth undergoes translational movements of unequal sizes. A set of rules can be applied to detect any collisions that will occur as the patient's teeth move along the treatment paths. Collisions can be detected by calculating distances between a first tooth and a second tooth by establishing a neutral projection plane between the first tooth and the second tooth, establishing a z-axis that is normal to the plane and that has a positive direction and a negative direction from each of a set of base points on the projection plane, computing a pair of signed distances comprising a first signed distance to the first tooth and a second signed distance to the second tooth, the signed distances being measured on a line through the base points and parallel to the z-axis, and determining that a collision occurs if any of the pair of signed distances indicates a collision. Where the positive direction for the first distance is opposite the positive direction for the second distance, a collision is detected if the sum of any pair of signed distances is less than or equal to zero. Information indicating whether the patient's teeth are following the treatment paths can be used to revise the treatment paths. More than one candidate treatment path for each tooth can be generated and graphically displayed for each candidate treatment path to a human user for selection. A set of rules can be applied to detect any collisions that will occur as the patient's teeth move along the treatment paths. Collisions can be detected by calculating distances between a first tooth and a second tooth by: establishing a neutral projection plane between the first tooth and the second tooth, establishing a z-axis that is normal to the plane and that has a positive direction and a negative direction from each of a set of base points on the projection plane, computing a pair of signed distances comprising a first signed distance to the first tooth and a second signed distance to the second tooth, the signed distances being measured on a line through the base points and parallel to the z-axis, and determining that a collision occurs if any of the pair of signed distances indicates a collision. A collision can also be detected if the sum of any pair of signed distances is less than or equal to zero. A set of rules can be applied to detect any improper bite occlusions that will occur as the patient's teeth move along the treatment paths. A value for a malocclusion index can be computed and the value displayed to a human user. The treatment paths can be generated by receiving data indicating restraints on movement of the patient's teeth and applying the data to generate the treatment paths. A three-dimensional (3D) graphical representation of the teeth at the positions corresponding to a selected data set can be rendered. The graphical representation of the teeth to provide a visual display of the movement of the teeth along the treatment paths can be generated. A graphical interface, with components representing the control buttons on a videocassette recorder, which a human user can manipulate to control the animation, can be generated. A portion of the data in the selected data set may be used to render the graphical representation of the teeth. A level-of-detail compression can be applied to the data set to render the graphical representation of the teeth. A human user can modify the graphical representation of the teeth and the selected data set can be modified in response to the user's request. A human user can select a tooth in the graphical representation and, in response, information about the tooth can be displayed. The information can relate to the motion that the tooth will experience while moving along the treatment path. The information can also indicate a linear distance between the tooth and another tooth selected in the graphical representation. The teeth can be rendered at a selected one of multiple viewing orthodontic-specific viewing angles. A user interface through which a human user can provide text-based comments after viewing the graphical representation of the patient's teeth can be provided. The graphical representation data can be downloaded to a remote computer at which a human view wishes to view the graphical representation. An input signal from a 3D gyroscopic input device controlled by a human user can be applied to alter the orientation of the teeth in the graphical representation.

Advantages of the system may include one or more of the following. The system facilitates automated staging after final setup. The system eliminates manual staging, saves time and is convenient to use. An easy to use graphical user interface supports the entry of treatment planning requirements such as particular staging pattern(s), anchorage requirement(s) (low, mid, high), and the minimum allowable tooth movements.

DESCRIPTION OF THE DRAWINGS

FIG. 1 is an elevational diagram showing the anatomical relationship of the jaws of a patient.

FIG. 2A illustrates in more detail the patient's lower jaw and provides a general indication of how teeth may be moved by the methods and apparatus of the present invention.

FIG. 2B illustrates a single tooth from FIG. 2A and defines how tooth movement distances are determined.

FIG. 2C illustrates the jaw of FIG. 2A together with an incremental position adjustment appliance which has been configured according to the methods and apparatus of the present invention.

FIG. 3 is a block diagram illustrating a process for producing incremental position adjustment appliances.

FIG. 4 is a flow chart illustrating a process for optimizing a final placement of the patient's teeth.

FIG. 5 is a flow chart illustrating the positioning of teeth at various steps of an orthodontic treatment plan.

FIG. 6 is a flow chart of a process for determining a tooth's path among intermediate positions during an orthodontic treatment plan.

FIG. 7 is a flow chart of a process for optimizing the path of a tooth from an initial position to a final position during an orthodontic treatment plan.

FIG. 8 is a diagram illustrating a buffering technique for use in a collision detection algorithm.

FIG. 9 is a flow chart for a collision detection technique.

FIG. 10 shows an exemplary X-type movement.

FIG. 11 shows an exemplary A-type movement.

FIG. 12 shows an exemplary V-type movement.

FIG. 13 shows an exemplary XX-type movement.

FIG. 14 shows an exemplary process to determine tooth path.

FIG. 15 shows an exemplary process to determine an all-equal path.

FIG. 16 shows an exemplary process to recursively determine frame movement as used in FIG. 15.

FIG. 17 shows an exemplary process to determine mid-frame movements as used in FIG. 16.

FIG. 18 shows an exemplary process to determine an A-shape path.

FIG. 19 shows an exemplary process to determine an equal path.

FIGS. 20A-20B show an exemplary process to determine a V-shape path.

FIG. 21 is a block diagram illustrating a system for generating appliances in accordance with the present invention.

DESCRIPTION

FIG. 1 shows a skull 10 with an upper jaw bone 22 and a lower jaw bone 20. The lower jaw bone 20 hinges at a joint 30 to the skull 10. The joint 30 is called a temporomandibular joint (TMJ). The upper jaw bone 22 is associated with an upper jaw 101, while the lower jaw bone 20 is associated with a lower jaw 100.

A computer model of the jaws 100 and 101 is generated, and a computer simulation models interactions among the teeth on the jaws 100 and 101. The computer simulation allows the system to focus on motions involving contacts between teeth mounted on the jaws. The computer simulation allows the system to render realistic jaw movements which are physically correct when the jaws 100 and 101 contact each other. The model of the jaw places the individual teeth in a treated position. Further, the model can be used to simulate jaw movements including protrusive motions, lateral motions, and tooth guided motions where the path of the lower jaw 100 is guided by teeth contacts rather than by anatomical limits of the jaws 100 and 101. Motions are applied to one jaw, but may also be applied to both jaws. Based on the occlusion determination, the final position of the teeth can be ascertained.

Referring now to FIG. 2A, the lower jaw 100 includes a plurality of teeth 102, for example. At least some of these teeth may be moved from an initial tooth arrangement to a final tooth arrangement. As a frame of reference describing how a tooth may be moved, an arbitrary centerline (CL) may be drawn through the tooth 102. With reference to this centerline (CL), each tooth may be moved in orthogonal directions represented by axes 104, 106, and 108 (where 104 is the centerline). The centerline may be rotated about the axis 108 (root angulation) and the axis 104 (torque) as indicated by arrows 10 and 112, respectively. Additionally, the tooth may be rotated about the centerline, as represented by an arrow 114. Thus, all possible free-form motions of the tooth can be performed.

FIG. 2B shows how the magnitude of any tooth movement may be defined in terms of a maximum linear translation of any point P on a tooth 102. Each point P1 will undergo a cumulative translation as that tooth is moved in any of the orthogonal or rotational directions defined in FIG. 2A. That is, while the point will usually follow a nonlinear path, there is a linear distance between any point in the tooth when determined at any two times during the treatment. Thus, an arbitrary point P1 may in fact undergo a true side-to-side translation as indicated by arrow d1, while a second arbitration point P2 may travel along an arcuate path, resulting in a final translation d2. Many aspects of the present invention are defined in terms of the maximum permissible movement of a point P1 induced on any particular tooth. Such maximum tooth movement, in turn, is defined as the maximum linear translation of that point P1 on the tooth which undergoes the maximum movement for that tooth in any treatment step.

FIG. 2C shows one adjustment appliance 111 which is worn by the patient in order to achieve an incremental repositioning of individual teeth in the jaw as described generally above. The appliance is a polymeric shell having a teeth receiving cavity. This is described in U.S. application Ser. No. 09/169,036, filed Oct. 8, 1998, now U.S. Pat. No. 6,450,807 which claims priority from U.S. application Ser. No. 08/947,080, filed Oct. 8, 1997, now U.S. Pat. No. 5,975,893 which in turn claims priority from provisional application No. 06/050,352, filed Jun. 20, 1997 (collectively the prior applications), the full disclosures of which are incorporated by reference.

As set forth in the prior applications, each polymeric shell may be configured so that its tooth receiving cavity has a geometry corresponding to an intermediate or final tooth arrangement intended for the appliance. The patient's teeth are repositioned from their initial tooth arrangement to a final tooth arrangement by placing a series of incremental position adjustment appliances over the patient's teeth. The adjustment appliances are generated at the beginning of the treatment, and the patient wears each appliance until the pressure of each appliance on the teeth can no longer be felt. At that point, the patient replaces the current adjustment appliance with the next adjustment appliance in the series until no more appliance remains. Conveniently, the appliances are generally not affixed to the teeth and the patient may place and replace the appliances at any time during the procedure. The final appliance or several appliances in the series may have a geometry or geometries selected to overcorrect the tooth arrangement, i.e., have a geometry which would (if fully achieved) move individual teeth beyond the tooth arrangement which has been selected as the final. Such overcorrection may be desirable in order to offset potential relapse after the repositioning method has been terminated, i.e., to permit some movement of individual teeth back toward their precorrected positions. Overcorrection may also be beneficial to speed the rate of correction, i.e., by having an appliance with a geometry that is positioned beyond a desired intermediate or final position, the individual teeth will be shifted toward the position at a greater rate. In such cases, the use of an appliance can be terminated before the teeth reach the positions defined by the appliance.

The polymeric shell 111 can fit over all teeth present in the upper or lower jaw. Often, only certain one(s) of the teeth will be repositioned while others of the teeth will provide a base or an anchor region for holding the appliance 111 in place as the appliance 111 applies a resilient repositioning force against the tooth or teeth to be repositioned. In complex cases, however, multiple teeth may be repositioned at some point during the treatment. In such cases, the teeth which are moved can also serve as a base or anchor region for holding the repositioning appliance.

The polymeric appliance 111 of FIG. 2C may be formed from a thin sheet of a suitable elastomeric polymer, such as Tru-Tain 0.03 in, thermal forming dental material, available from Tru-Tain Plastics, Rochester, Minn. Usually, no wires or other means will be provided for holding the appliance in place over the teeth. In some cases, however, it will be desirable or necessary to provide individual anchors on teeth with corresponding receptacles or apertures in the appliance 100 so that the appliance can apply an upward force on the tooth which would not be possible in the absence of such an anchor.

FIG. 3 shows a process 200 for producing the incremental position adjustment appliances for subsequent use by a patient to reposition the patient's teeth. As a first step, an initial digital data set (IDDS) representing an initial tooth arrangement is obtained (step 202).

In some implementations, the IDDS includes data obtained by scanning a physical model of the patient's teeth, such as by scanning a positive impression or a negative impression of the patient's teeth with a laser scanner or a destructive scanner. The positive and negative impression may be scanned while interlocked with each other to provide more accurate data. The initial digital data set also may include volume image data of the patient's teeth, which the computer can convert into a 3D geometric model of the tooth surfaces, for example using a conventional marching cubes technique. In some embodiments, the individual tooth models include data representing hidden tooth surfaces, such as roots imaged through x-ray, CT scan, or MRI techniques. Tooth roots and hidden surfaces also can be extrapolated from the visible surfaces of the patient's teeth. The IDDS is then manipulated using a computer having a suitable graphical user interface (GUI) and software appropriate for viewing and modifying the images. More specific aspects of this process will be described in detail below.

Individual tooth and other components may be segmented or isolated in the model to permit their individual repositioning or removal from the digital model. After segmenting or isolating the components, the user will often reposition the tooth in the model by following a prescription or other written specification provided by the treating professional. Alternatively, the user may reposition one or more teeth based on a visual appearance or based on rules and algorithms programmed into the computer. Once the user is satisfied, the final teeth arrangement is incorporated into a final digital data set (FDDS) (step 204).

In step 204, final positions for the upper and lower teeth in a masticatory system of a patient are determined by generating a computer representation of the masticatory system. An occlusion of the upper and lower teeth is computed from the computer representation; and a functional occlusion is computed based on interactions in the computer representation of the masticatory system. The occlusion may be determined by generating a set of ideal models of the teeth. Each ideal model in the set of ideal models is an abstract model of if idealized teeth placement which is customized to the patient's teeth, as discussed below. After applying the ideal model to the computer representation, and the position of the teeth is optimized to fit the ideal model. The ideal model may be specified by one or more arch forms, or may be specified using various features associated with the teeth.

The FDDS is created by following the orthodontists' prescription to move the teeth in the model to their final positions. In one embodiment, the prescription is entered into a computer, which automatically computes the final positions of the teeth. In alternative other embodiments, a user moves the teeth into their final positions by independently manipulating one or more teeth while satisfying the constraints of the prescription. Various combinations of the above described techniques may also be used to arrive at the final tooth positions.

One method for creating the FDDS involves moving the teeth in a specified sequence. First, the centers of each tooth model may be aligned using a number of methods. One method is a standard arch. Then, the teeth models are rotated until their roots are in the proper vertical position. Next, the teeth models are rotated around their vertical axis into the proper orientation. The teeth models are then observed from the side, and translated vertically into their proper vertical position. Finally, the two arches are placed together, and the teeth models moved slightly to ensure that the upper and lower arches properly mesh together. The meshing of the upper and lower arches together is visualized using a collision detection process to highlight the contacting points of the teeth.

Based on both the IDDS and the FDDS, a plurality of intermediate digital data sets (INTDDSs) are defined to correspond to incrementally adjusted appliances (step 206). Finally, a set of incremental position adjustment appliances are produced based on the INTDDs and the FDDS (step 208).

After the teeth and other components have been placed or removed to produce a model of the final tooth arrangement, it is necessary to generate a treatment plan which produces a series of INTDDS's and FDDS as described previously. To produce these data sets, it is necessary to define or map the movement of selected individual teeth from the initial position to the final position over a series of successive steps. In addition, it may be necessary to add other features to the data sets in order to produce desired features in the treatment appliances. For example, it may be desirable to add wax patches to the image in order to define cavities or recesses for particular purposes, such as to maintain a space between the appliance and particular regions of the teeth or jaw in order to reduce soreness of the gums, avoid periodontal problems, allow for a cap, and the like. Additionally, it will often be necessary to provide a receptacle or aperture intended to accommodate an anchor which is to be placed on a tooth in order to permit the tooth to be manipulated in a manner that requires the anchor, e.g., to be lifted relative to the jaw.

In the manner discussed above, information on how the patient's teeth should move from an initial, untreated state to a final, treated state is used to generate a prescription, or treatment plan. The prescription takes into consideration the following:

1. Initial Position: a detailed description of the initial maloclussion.

2. Final Position: a detailed description of treatment goals for the patient.

3. Movement: a detailed, sequential description of how the patient's teeth should be moved in order to accomplish the desired goals for final placement.

1. Initial Position

The initial position section describes in detail the patient's malocclusion. Considerations include:

1. Crowding

2. Spacing

3. Extraction

4. Stripping

Additionally, considerations for the Final Position discussed below may also be used.

2. Final Position

This section is a detailed description of final position objectives and treatment goalsboth static and functional. These considerations include

1. Overjet

2. Overbite

3. Midlines

4. Functional Occlusion

5. Classification

6. Torque

7. Tip

8. Rotations

9. Lingual/Palatal

10. Buccal/Facial

11. Intercuspation

12. Initial Position of the OcclusionCR/CO Considerations

13. Interarch Issues

14. Intra-arch Issues

15. Space

3. Movement

The movement section specifies an order in moving the patient's teeth in order to achieve the goals for final placement. In this process, the orthodontist has precise control over which teeth the orthodontist wants to move and which teeth to anchor (not move), thereby breaking the treatment down into discrete stages. The movement order information is captured for both the upper and the lower arches.

At each stage, major and minor tooth movements are analyzed. Major movements usually occur at the beginning of a tooth's movement. Minor movements usually occur as detailing movements that occur toward the end of treatment. On average, each aligner should be able to accomplish move about 0.25-0.33 mm and to rotate about 5-10 degrees within a 2-week period. However, biologic variability, patient and clinician preferences are also taken into consideration. Additionally, various movements such as distalization, tip, and torque can have separate parameters.

Based on these considerations, a plan is generated for moving teeth. FIG. 4 illustrates a process 300 for generating tooth movements while minimizing teeth indices, as discussed in copending U.S. application Ser. No. 09/169,034, now U.S. Pat. No. 6,471,511 the content of which is hereby incorporated by reference. First, the process 300 automatically or, with human assistance, identifies various features associated with each tooth to arrive at a model of the teeth (step 302). An ideal model set of teeth is then generated either from casts of the patient's teeth or from patients with a known acceptable occlusion (step 303).

From step 302, the process 300 positions the model of the teeth in its approximate final position based on a correspondence of features to the ideal model (step 304). In that step, each tooth model is moved so that its features are aligned to the features of a corresponding tooth in the ideal model. The features may be based on cusps, fossae, ridges, distance-based metrics, or shape-based metrics. Shape-based metrics may be expressed as a function of the patient's arches, among others.

Next, the process 300 computes an orthodontic/occlusion index (step 306). One index which may be used is the PAR (Peer Assessment Rating) index. In addition to PAR, other metrics such as shape-based metrics or distance-based metrics may be used. The PAR index identifies how far a tooth is from a good occlusion. A score is assigned to various occlusal traits which make up a malocclusion. The individual scores are summed to obtain an overall total, representing the degree a case deviates from normal alignment and occlusion. Normal occlusion and alignment is defined as all anatomical contact points being adjacent, with a good intercuspal mesh between upper and lower buccal teeth, and with nonexcessive overjet and overbite.

In PAR, a score of zero would indicate good alignment, and higher scores would indicate increased levels of irregularity. The overall score is recorded on pre- and posttreatment dental casts. The difference between these scores represents the degree of improvement as a result of orthodontic intervention and active treatment. The eleven components of the PAR Index are: upper right segment; upper anterior segment; upper left segment; lower right segment; lower anterior segment; lower left segment; right buccal occlusion; overjet; overbite; centerline; and left buccal occlusion. In addition to the PAR index, other indices may be based on distances of the features on the tooth from their ideal positions or ideal shapes.

From step 306, the process 300 determines whether additional index-reducing movements are possible (step 308). Here, all possible movements are attempted, including small movements along each major axis as well as small movements with minor rotations. An index value is computed after each small movement and the movement with the best result is selected. In this context, the best result is the result that minimizes one or more metrics such as PAR-based metrics, shape-based metrics or distance-based metrics. The optimization may use a number of techniques, including simulated annealing technique, hill climbing technique, best-first technique, Powell method, and heuristics technique, among others. Simulated annealing techniques may be used where the index is temporarily increased so that another path in the search space with a lower minimum may be found. However, by starting with the teeth in an almost ideal position, any decrease in the index should converge to the best result.

In step 308, if the index can be optimized by moving the tooth, incremental indexreducing movement inputs are added (step 310) and the process loops back to step 306 to continue computing the orthodontic/occlusion index. Alternatively, in the event that the index cannot be further optimized, the process 300 exits (step 312).

In generating the index reducing movements of step 310, the process considers a set of movement constraints which affect the tooth path movement plan. In one embodiment, movement information for about fifty discrete stages is specified. Each stage represents a single aligner, which is expected to be replaced about every two weeks. Thus, each stage represents about a two-week period. In one embodiment, a two-dimensional array is used to track specific movements for each tooth at a specific period of time. One dimension of this array relates to teeth identification, while the second dimension relates to the time periods or stages. Considerations on when a tooth may be moved include the following:

1. Mesial

2. Distal

3. Buccal/Facial

4. Lingual/Palatial

5. Expansion

6. Space

7. Teeth moving past each other

8. Intrusion

9. Extrusion

10. Rotations

11. Which teeth are moving when

12. Which teeth move first

13. Which teeth need to be moved before others are moved

14. What movements are easily done

15. Anchorage

16. The orthodontist user's philosophy on distalization of molars and minor expansion in adults

In one embodiment, the user can change the number of desired treatment stages from the initial to the target states of the teeth. Any component that is not moved is assumed to remain stationary, and thus its final position is assumed to be the same as the initial position (likewise for all intermediate positions, unless one or more key frames are defined for that component).

The user may also specify key frames by selecting an intermediate state and making changes to component position(s). In some embodiments, unless instructed otherwise, the software automatically linearly interpolates between all user-specified positions (including the initial position, all key frame positions, and the target position). For example, if only a final position is defined for a particular component, each subsequent stage after the initial stage will simply show the component an equal linear distance and rotation (specified by a quatemion) closer to the final position. If the user specifies two key frames for that component, the component will move linearly from the initial position through different stages to the position defined by the first key frame. It will then move, possibly in a different direction, linearly to the position defined by the second key frame. Finally, it will move, possibly in yet a different direction, linearly to the target position.

These operations may be done independently to each component, so that a key frame for one component will not affect another component, unless the other component is also moved by the user in that key frame. One component may accelerate along a curve between one pair of stages (e.g., stages 3 and 8 in a treatment plan having that many stages), while another moves linearly between another pair of stages (e.g., stages 1 to 5), and then changes direction suddenly and slows down along a linear path to a later stage (e.g., stage 10). This flexibility allows a great deal of freedom in planning a patient's treatment.

In some implementations, non-linear interpolation is used instead of or in addition to linear interpolation to construct a treatment path among key frames. In general, a non-linear path, such as a spline curve, created to fit among selected points is shorter than a path formed from straight line segments connecting the points. A treatment path describes the transformation curve applied to a particular tooth to move the tooth from its initial position to its final position. A typical treatment path includes some combination of rotational and translational movement of the corresponding tooth, as described above.

FIG. 5 shows step 310 in more detail. Initially, a first tooth is selected (step 311). Next, constraints associated with the tooth is retrieved for the current stage or period (step 312). Thus, for the embodiment which keeps a two-dimensional array to track specific movements for each tooth at a specific period of time, the tooth identification and the time period or stage information are used to index into the array to retrieve the constraints associated with the current tooth.

Next, a tooth movement plan which takes into consideration the constraints is generated (step 313). The process of FIG. 5 then detects whether the planned movements would cause collisions with neighboring teeth (step 314). The collision detection process determines if any of the geometries describing the tooth surfaces intersect. If there are no obstructions, the space is considered free; otherwise it is obstructed. Suitable collision detection algorithms are discussed in more detail below.

If a collision occurs, a push vector is created to shift the path of the planned movement (step 315). Based on the push vector, the current tooth bounces from the collision and a new tooth movement is generated (step 316). From step 314 or 316, the movement of the current tooth is finalized.

Next, the process of FIG. 5 determines whether tooth movement plans have been generated for all teeth (step 317), and if so, the process exits. Alternatively, the next tooth in the treatment plan is selected (318), and the process of FIG. 5 loops back to step 312 to continue generating tooth movement plans.

The resulting final path consists of a series of vectors, each of which represents a group of values of the interpolation parameters of the translational and rotational components of the transformations of the moving teeth. Taken together, these constitute a schedule of tooth movement which avoids tooth-to-tooth interferences. Pseudo code for generating the tooth path in view of specified constraints is shown below:

For each tooth path model

For each path increment

Load constrains associated with each tooth

Move the tooth in view of constraint

Perform tooth collision detection

If collision occurs, for associated colliding teeth create push vector

and bounce back from collision to avoid collision

end for

end tooth path model

FIG. 6 is a flow chart of a computer-implemented process for generating non-linear treatment paths along which a patient's teeth will travel during treatment. The non-linear paths usually are generated automatically by computer program, in some cases with human assistance. The program receives as input the initial and final positions of the patient's teeth and uses this information to select intermediate positions for each tooth to be moved (step 1600). The program then applies a conventional spline curve calculation algorithm to create a spline curve connecting each tooth's initial position to the tooth's final position (step 1602). In many situations, the curve is constrained to follow the shortest path between the intermediate positions. The program then samples each spline curve between the intermediate positions (step 1604) and applies the collision detection algorithm to the samples (step 1606). If any collisions are detected, the program alters the path of at least one tooth in each colliding pair by selecting a new position for one of the intermediate steps (step 1608) and creating a new spline curve (1602). The program then samples the new path (1604) and again applies the collision detection algorithm (1606). The program continues in this manner until no collisions are detected. The routine then stores the paths, e.g., by saving the coordinates of each point in the tooth at each position on the path in an electronic storage device, such as a hard disk (step 1610).

The path-generating program, whether using linear or non-linear interpolation, selects the treatment positions so that the tooth's treatment path has approximately equal lengths between each adjacent pair of treatment steps. The program also avoids treatment positions that force portions of a tooth to move with more than a given maximum velocity.

Orthodontic constraints that may be applied by the path-generating program include the minimum and maximum distances allowed between adjacent teeth at any given time, the maximum linear or rotational velocity at which a tooth should move, the maximum distance over which a tooth should move between treatment steps, the shapes of the teeth, the characteristics of the tissue and bone surrounding the teeth (e.g., ankylose teeth cannot move at all), and the characteristics of the aligner material (e.g., the maximum distance that the aligner can move a given tooth over a given period of time). For example, the patient's age and jaw bone density may dictate certain safe limits beyond which the patient's teeth should not forced to move. In general, a gap between two adjacent, relatively vertical and non-tipped central and lateral teeth should not close by more than about 1 mm every seven weeks. The material properties of the orthodontic appliance also limit the amount by which the appliance can move a tooth. For example, conventional retainer materials usually limit individual tooth movement to approximately 0.5 mm between treatment steps. The constraints have default values that apply unless patient-specific values are calculated or provided by a user. Constraint information is available from a variety of sources, including text books and treating clinicians.

In selecting the intermediate positions for each tooth, the path-generating program invokes the collision detection program to determine whether collisions will occur along the chosen paths. The program also inspects the patient's occlusion at each treatment step along the path to ensure that the teeth align to form an acceptable bite throughout the course of treatment. If collisions or an unacceptable bite will occur, or if a required constraint cannot be satisfied, the program iteratively alters the offending tooth path until all conditions are met. The virtual articulator described above is one tool for testing bite occlusion of the intermediate treatment positions.

As shown in FIG. 7, once the path-generating program has established collision-free paths for each tooth to be moved, the program calls an optimization routine that attempts to make the transformation curve for each tooth between the initial and final positions more linear. The routine begins by sampling each treatment path at points between treatment steps (step 1702), e.g., by placing two sample points between each treatment step, and calculating for each tooth a more linear treatment path that fits among the sample points (step 1704). The routine then applies the collision detection algorithm to determine whether collisions result from the altered paths (step 1706). If so, the routine resamples the altered paths (step 1708) and then constructs for each tooth an alternative path among the samples (step 1710). The routine continues in this manner until no collisions occur (step 1712).

In some embodiments, as alluded to above, the software automatically computes the treatment path, based upon the IDDS and the FDDS. This is accomplished using a path scheduling algorithm which determines the rate at which each component, i.e., each tooth, moves along the path from the initial position to the final position. The path scheduling algorithm determines the treatment path while avoiding round-tripping, i.e., while avoiding moving a tooth along a distance greater than absolutely necessary to straighten the teeth. Such motion is highly undesirable, and has potential negative effects on the patient.

One implementation of the path scheduling algorithm attempts first to schedule or stage the movements of the teeth by constraining each tooth to the most linear treatment path between the initial and final positions. The algorithm then resorts to less direct routes to the final positions only if collisions will occur between teeth along the linear paths or if mandatory constraints will be violated. The algorithm applies one of the path-generation processes described above, if necessary, to construct a path for which the intermediate treatment steps do not lie along a linear transformation curve between the initial and final positions. Alternatively, the algorithm schedules treatment paths by drawing upon a database of preferred treatments for exemplary tooth arrangements. This database can be constructed over time by observing various cou