CROSS-REFERENCE

[0001] This application claims the benefit of U.S. Provisional Application No.

62/099,965, filed January 5, 2015, the full disclosure of which is incorporated herein by reference.

BACKGROUND

[0002] Prior methods and apparatus for aligning teeth can be less than ideal in at least some instances. While braces can be used to move teeth into alignment, braces can be cumbersome to wear and can require expertise to place on the subject. Also, complex movements can be difficult to achieve and orthodontic placement may less than ideally address the complex movements of several teeth in at least some instances.

[0003] Transparent shell appliances have been used to successfully move teeth. For example a user can be provided with a series of transparent shell appliances. Each shell of the series of shells may correspond to a stage of the treatment. For example, a fourth shell in a series of ten shells may correspond to the fourth state of treatment. Although transparent shell appliances can be used to successfully reposition teeth, the transparent shell appliances can provide less than ideal results in at least some instances. For example, complex movements of teeth, such as to fill an extraction, can be difficult to treat with transparent shell appliances. Also, in at least some instances, a wearer of a transparent shell appliance may not complete treatment, for example when teeth do not move sufficiently with the appliance and the user stops treatment.

[0004] Prior methods and apparatus of aligning teeth with transparent shell appliances can rely on providing shells with cavities shaped to the tooth profile at a final intended position and orientation at a stage of the treatment. Work in relation to embodiments suggests cavities shaped to position a tooth at a final intended position and orientation at a stage of the treatment can provide less than ideal movement. Although attachments can be placed on teeth to facilitate movement of the teeth with polymeric shell appliances, the resulting movements can be less than ideal in at least some instances. For example, the force applied to the tooth can decrease as the tooth moves toward the target position. Also, the movement of a tooth may not be uniform, and the tooth may move more easily along some dimensions than others. For example, the movement of a tooth can occur along six degrees of freedom, and relative movement compared to a target movement can differ among the degrees of freedom of the tooth. Further the movement of teeth can be coupled, such that movement of a first tooth can affect movement adjacent teeth.

[0005] Prior user interface software can provide the user with teeth shown at target positions for each stage of treatment. The polymeric shell appliance can be manufactured in accordance with target positions of the teeth. Although

manufacturing appliances in accordance with target positions of the teeth at the end of each stage of treatment can be effective, work in relation to some embodiments suggests that the amount of force applied to each tooth can differ from that which would be ideal, and the corresponding movement of the tooth can be less than ideal in at least some instances.

[0006] In light of the above, it would be desirable to provide improved methods and apparatus for moving teeth to target positions with polymeric shell appliances.

Ideally such methods and apparatus would more accurately move teeth to target positions with decreased forces.

SUMMARY

[0007] Embodiments of the present disclosure improved methods and apparatus for moving teeth. In many embodiments, appliances such as polymeric shell appliances are provided in which the appliances are configured to provide one or more activation forces to facilitate tooth movement. In many embodiments, the activation forces provided by each appliance are arranged to provide force in a direction opposite to an intended direction of tooth movement for each of a plurality of teeth, and the tooth movement may comprise a movement vector composed of translations and rotations of the tooth for each of the plurality of teeth. The activation forces may comprise one or more of a force to urge a tooth in target direction of tooth movement, or a counter force opposite the force. In many embodiments, a tooth moves about a center of resistance, and the tooth is urged with the force in the targeted direction of tooth movement so as to generate a moment about the center of resistance. The counter force can generate a counter moment about the center of resistance, such that the tooth can be moved with a differential moment comprising a differential of the moment and the counter moment. The differential moment can be related to tipping of the tooth along the targeted direction of movement, and tipping of the tooth along the targeted direction of movement can be controlled in order to facilitate movement and may decrease an amount of force to move the tooth along the targeted direction for each of the plurality of teeth.

[0008] In many embodiments, each polymeric shell appliance comprises a plurality of engagement structures shaped to engage a plurality of attachments to generate a plurality of counter forces and counter moments for a stage of treatment. The polymeric shell appliance may comprise a plurality of tooth receiving cavities with an inner surface profile shaped so as to correspond to a surface profile of a received tooth, in which each of the plurality of tooth receiving cavities is positioned and/or oriented away from a corresponding target position and orientation of the received tooth for the corresponding stage of treatment.

[0009] In many embodiments, a processor comprises a user input and display for a user to position and orient a plurality of teeth at target positions and orientations for each stage of a treatment. The processor may comprise instructions to position teeth receiving cavities of the appliance at positions away from the target positions and orientations for each stage of the treatment in order to provide activation energy to the appliance. The processor may comprise instructions to manufacture a plurality of appliances with indirect manufacturing comprising thermoforming or direct manufacturing comprising one or more of 3D printing, stereolithography, or fused deposition modeling.

[0010] Other objects and features of the present disclosure will become apparent by a review of the specification, claims, and appended figures.

INCORPORATION BY REFERENCE

[0011] All publications, patents, and patent applications mentioned in this

specification are herein incorporated by reference to the same extent as if each individual publication, patent, or patent application was specifically and individually indicated to be incorporated by reference. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The novel features of the invention are set forth with particularity in the appended claims. A better understanding of the features and advantages of the present disclosure will be obtained by reference to the following detailed description that sets forth illustrative embodiments, in which the principles of the invention are utilized, and the accompanying drawings of which:

[0013] FIG. 1A shows a jaw, a plurality of teeth, and a polymeric shell appliance to align teeth, in accordance with embodiments;

[0014] FIG. IB shows a cross-sectional diagram of an appliance engaging a tooth crown and positioned attachment, in accordance with embodiments;

[0015] FIG. 2 shows components of an alignment apparatus and corresponding forces, in accordance with embodiments;

[0016] FIG. 3A shows a tooth position prior to completion of a stage of treatment, a target position upon completion of the stage, and a position and orientation of a tooth receiving cavity to complete the stage of treatment, in accordance with embodiments;

[0017] FIG. 3B shows a polymeric shell appliance configured with one or more activation sites to store energy with a tooth at a target position and orientation comprising a non-extruded position and orientation of the tooth, wherein the force is oriented in an intrusive direction and insufficient to intrude the tooth and sufficient to inhibit extrusion of the tooth, in accordance with embodiments.

[0018] FIG. 4 shows a method of determining tooth receiving cavities of an appliance away from the target locations, in accordance with embodiments;

[0019] FIG. 5 shows a simplified block diagram of a data processing system, in accordance with embodiments;

[0020] FIG. 6A shows an alignment apparatus with an external force producing mechanism, in accordance with embodiments;

[0021] FIG. 6B shows an alignment apparatus with an external force producing mechanism, in accordance with embodiments; and

[0022] FIG. 7 shows an alignment apparatus with an external force producing mechanism, in accordance with embodiments.

DETAILED DESCRIPTION

[0023] As used herein the terms "torque" and "moment" are treated synonymously. [0024] As used herein the term "and/or" is used as a functional word to indicate that two words or expressions are to be taken together or individually. For example, A and/or B encompasses A alone, B alone, and A and B together.

[0025] As used herein a "plurality of teeth" encompasses two or more teeth.

[0026] As used herein a "moment" encompasses a force acting on an object such as a tooth at a distance from a center of resistance. The moment may be calculated with a vector cross product of a vector force applied to a location corresponding to a displacement vector from the center of resistance, for example. The moment may comprise a vector pointing in a direction. A moment opposing another moment may encompass one of the moment vectors oriented toward a first side of the object such as the tooth and the other moment vector oriented toward an opposite side of the object such as the tooth, for example.

[0027] As used herein a "differential moment" encompasses two or more moments coupled to each other to provide opposing moments to one or more teeth. The differential moment may comprise a first moment and a second opposing moment applied to a tooth. Alternatively or in combination, the differential moment may comprise a first moment of a first one or more teeth of the arch coupled to a second, opposing moment of a second one or more teeth of the arch. The first one or more teeth of the arch may comprise a first segment of the arch and the second one or more teeth of the arch may comprise a second segment of the arch, in which the first moment of the first segment of the arch is coupled to the second, opposing moment of the second segment of the arch. The first one or more teeth may comprise a first plurality of adjacent teeth of the first segment of the arch, and the second one or more teeth may comprise a second plurality of adjacent teeth of the second segment of the arch, in which the first moment of the first plurality of adjacent teeth of the arch opposes the second, counter moment of the second plurality of adjacent teeth of the arch.

[0028] As used herein, a tooth comprising a moment refers to a tooth with a force acting on the tooth about a center of resistance. The force can be generated by an appliance coupled to the tooth, either directly or with an attachment on the tooth, and combinations thereof.

[0029] The counter moments as disclosed herein can be used to accurately control movement of one or more teeth, and can be used to provide anchoring of one or more teeth. In many embodiments, a plurality of posterior teeth comprises counter moments to improve anchoring of the posterior teeth, and one or more anterior teeth comprise a lesser counter moment and are moved toward the plurality of posterior anchor teeth. Alternatively, counter moments of one or more of the plurality of posterior teeth can be configured to allow the one or more posterior teeth to move toward the anterior tooth or teeth.

[0030] The moments of a plurality of groups of one or more teeth can be coupled to each other in order to control movement of the teeth, and the moments of the one or more groups of teeth can be coupled to each other in many ways. The moments of the groups of one or more teeth can be coupled to each other with offset moments and/or balanced moments in order to provide preferential movement to one or more of the groups of one or more teeth. For example, posterior teeth can be provided with a larger counter moment than anterior teeth in order to move the anterior teeth to the posterior teeth.

[0031] The moments and counter moments as disclosed herein are well suited for moving many types of teeth and conditions of teeth, and are well suited for use with many conditions of teeth. The embodiments disclosed herein can be used to treat one or more of: cant of an occlusal plane, to raise teeth on one side of the mouth and lower teeth on an opposite side of the mouth, en masse expansion of teeth along an arch, closure of an extraction site, intrusion, extrusion, rotation, or tipping, or combinations thereof, for example.

[0032] In many embodiments, one or more posterior teeth comprise one or more of a molar, a premolar, or a canine, and one or more anterior teeth comprise one or more of a central incisor, a lateral incisor, a cuspid, a first bicuspid or a second bicuspid. For example, "posterior teeth" may be used herein to refer to the molars and premolars and "anterior teeth" may be used herein to refer to the incisors and canines. It shall be appreciated that "posterior" and "anterior" may also refer to the relative positioning of groups of one or more teeth, e.g., "posterior teeth" may refer to any teeth that are disposed posteriorly relative to one or more "anterior teeth," and "anterior teeth" may refer to any teeth that are disposed anteriorly relative to one or more "posterior teeth."

[0033] The embodiments disclosed herein can be used to couple groups of one or more teeth to each other. The groups of one or more teeth may comprise a first group of one or more anterior teeth and a second group of one or more posterior teeth. The first group of teeth can be coupled to the second group of teeth with the polymeric shell appliances as disclosed herein.

[0034] The first group of teeth can be coupled to the second group of teeth in many ways, and in many embodiments the first group of one or more teeth comprises a first moment and a first counter moment, and the second group of one or more teeth comprises a second moment and a second counter moment. The first moment and the first counter moment may comprise a combined first moment and a combined first counter moment of the first group of one or more teeth, and the second moment and the second counter moment may comprise a combined second moment and a combined second counter moment of the second group of teeth. The combined first moment, combined first counter moment, combined second moment and combined second counter moment can be coupled to each other with the polymeric shell appliance in order to move the first group of one or more teeth, the second group of one or more teeth, or combinations thereof.

[0035] In many embodiments, each of the first group of one or more teeth comprises a first moment and a counter moment, and each of the second group of one or more teeth comprises a second moment and a second counter moment. The first moment can be generated with a first force to one or more of the first teeth at a first region or location of the first tooth and the counter moment generated with a counter force to the one of the first teeth at a counter location. The second moment can be generated with a second force to one or more of the second teeth at a region of the second tooth and the counter moment generated with a counter force to the one of the second teeth at a counter location.

[0036] The center of resistance of an individual tooth can be located near the bifurcation or trifurcation of the root of the tooth, for example. For a single rooted tooth, the center of resistance can be located somewhere between about 25% and about 70% of the distance from the alveolar crest to the apex of the root, for example about 40% of the distance.

[0037] The center of resistance of a group of a segment of teeth comprising a plurality of teeth can be determined in one or more of many ways. The center of resistance can be determined with finite element modeling, published values in the scientific literature, bench testing with experimental loads, mathematical formula and approximations, and/or combinations thereof, for example. The center of resistance can be determined in response to supporting dental structures such as the periodontal ligaments, soft tissue, and bony supporting structures, for example. Although the center of resistance of a group of teeth may change with the direction of movement, a person of ordinary skill in the art can determine the center of resistance in accordance with embodiments disclosed herein.

[0038] The embodiments disclosed herein are well suited for moving one or more teeth of the first group of one or more teeth or moving one or more teeth of the second group of one or more teeth, or combinations thereof.

[0039] The embodiments disclosed herein are well suited for combination with one or known commercially available tooth moving components such as attachments and polymeric shell appliances. In many embodiments, the appliance and one or more attachments are configured to move one or more teeth along a tooth movement vector comprising six degrees of freedom, in which three degrees of freedom are rotational and three degrees of freedom are translational. Embodiments disclosed herein can provide differential moment vectors based on a moment and a counter moment to each of a plurality of teeth. The differential moment vector can provide improved accuracy of movement of the teeth and may result in decreased amounts of force to move one or more teeth.

[0040] The present disclosure provides orthodontic systems and related methods for designing and providing improved or more effective tooth moving systems for eliciting a desired tooth movement and/or repositioning teeth into a desired arrangement.

[0041] In one aspect, a method of moving a plurality of teeth with an appliance is provided. The method comprises: providing an appliance shaped for placement on the plurality of teeth, the appliance comprising a plurality of tooth receiving cavities shaped to receive each of the plurality of teeth and provide a differential moment to the plurality of teeth in order to move and/or anchor the teeth, the plurality of teeth comprising a first one or more teeth and a second one or more teeth, the first one or more teeth comprising a first counter moment and the second one or more teeth comprising a second counter moment, the first counter moment opposite the second counter moment. [0042] In many embodiments, the differential moment of said each of the plurality of teeth comprises a moment and a counter moment opposite the moment, the moment generated with a force about a center of resistance, the counter moment generated with a counter force about the center of resistance, the counter force opposite the force, the force greater than the counter force for said each of the plurality of teeth in order to move the teeth.

[0043] In many embodiments, each of the plurality of tooth receiving cavities is shaped and arranged to produce a summed moment comprising a sum of the moment and the counter moment for said each of the plurality of teeth.

[0044] In many embodiments, the appliance is shaped to urge a first portion of the first one or more teeth and a second portion of the second one or more teeth away from each other in order to move the first one or more teeth toward the second one or more teeth. The appliance can be shaped to urge a first portion of the first one or more teeth and a second portion of the second one or more teeth away from each other in order to move the first one or more teeth and the second one or more teeth toward each other.

[0045] In many embodiments, the first one or more teeth comprise a first plurality of teeth and the appliance comprises a shape to generate the first counter moment with each of the first plurality of adjacent teeth, the first counter moment comprising a combination of similarly oriented moments from said each of the first plurality of adjacent teeth.

[0046] In many embodiments, the second one or more teeth comprise a second plurality of teeth and the appliance comprises a shape to generate the second counter moment with each of the second plurality of adjacent teeth, the second counter moment comprising a combination of similarly oriented moments from said each of the second plurality of adjacent teeth.

[0047] In many embodiments, the plurality of tooth receiving cavities is shaped and arranged to balance the differential moment between the first one or more teeth and the second one or more teeth and to balance the first counter moment and the second counter moment between the first one or more teeth and the second one or more teeth.

[0048] In many embodiments, the first one or more teeth comprises an anterior group of one or more teeth and the second one or more teeth comprises a posterior group of one or more teeth, wherein the first counter moment of the anterior group of one or more teeth opposes the second counter moment of the posterior group of one or more teeth. The anterior group of one or more teeth can comprise a single anterior tooth, the appliance shaped to generate the first counter moment with the single anterior tooth. The posterior group of one or more teeth can comprise a plurality of adjacent posterior teeth, the appliance shaped to generate the second counter moment with the plurality of adjacent posterior teeth. The appliance can be shaped to generate the second counter moment with each of the plurality of adjacent posterior teeth, the second counter moment comprising a combination of similarly oriented moments from said each of the adjacent posterior teeth. The first counter moment can be less than the second counter moment in order to move the anterior group of one or more teeth toward the plurality of adjacent posterior teeth. The plurality of adjacent posterior teeth can comprise three adjacent posterior teeth, the appliance shaped to generate the second counter moment with the three adjacent posterior teeth. The three adjacent posterior teeth can comprise three adjacent posterior anchor teeth coupled together as a block of teeth having a combined center of resistance away from the center of resistance of each tooth of the three adjacent posterior teeth.

[0049] In many embodiments, the first one or more teeth comprises a posterior group of one or more teeth and the second one or more teeth comprises an anterior group of teeth, and the first counter moment of the anterior group of one or more teeth opposes the second counter moment of the anterior group of one or more teeth. The group of one or more anterior teeth can comprise a plurality of adjacent anterior teeth and the plurality of adjacent tooth receiving cavities can comprise a plurality of adjacent anterior tooth receiving cavities shaped to generate the first counter moment.

[0050] In many embodiments, the method further comprises providing an external force or anchorage producing mechanism coupled to the plurality of teeth, wherein the external force or anchorage producing mechanism is arranged to apply a force and/or anchorage to the posterior group of one or more teeth so as to reduce movement of the posterior group of one or more teeth. The force applied to the posterior group of one or more teeth by the external force producing mechanism can comprise a distal force component. The external force or anchorage producing mechanism can comprise a class II or class III elastic.

[0051] In many embodiments, each of the plurality of tooth receiving cavities comprises an inner surface profile corresponding to a surface profile of the tooth in order to generate a moment and a counter moment with said each of the plurality of teeth.

[0052] In many embodiments, the plurality of tooth receiving cavities comprises a first one or more cavities shaped to receive the first one or more teeth and a second one or more cavities shaped to receive the second one or more teeth, the first one or more tooth receiving cavities shaped to generate the first counter moment and the second one or more tooth receiving cavities shaped to generate the second counter moment with the first counter moment opposite the second counter moment.

[0053] In many embodiments, the first counter moment of the first one or more teeth is sufficient to move first one or more roots of the first one or more teeth toward the second one or more teeth.

[0054] In many embodiments, the differential moment to said each of the plurality of teeth comprises a moment and a counter moment opposite the moment, wherein a force at a location generates the moment about a center of resistance and a counter force at a counter location generates the counter moment about the center of resistance for said each of the plurality of teeth and wherein a sum of the force and the counter force comprises a combined overall force to the tooth for said each of the plurality of teeth. A combined overall force of the first one or more teeth can urge the first one or more teeth toward the second one or more teeth. The combined overall force can be lower than each of the force and the counter force for said each of the plurality of teeth in order to move the first one or more teeth toward the second one or more teeth with decreased amounts of force.

[0055] In many embodiments, the one or more of the plurality of tooth receiving cavities comprise one or more engagement structures shaped to receive one or more attachments and urge the first one or more teeth away from the second one or more teeth with a counter force in order to facilitate movement of the first one or more teeth toward the second one or more teeth. The one or more engagement structures shaped to receive the one or more attachments can generate a force opposite the counter force to move the first one or more teeth in a target direction toward the second one or more teeth. The force can be greater than the counter force to move the one or more target teeth in the target direction and the counter force can decrease a total amount of force to the one or more target teeth and generate the first counter moment. [0056] In many embodiments, the appliance comprises a plurality of structures shaped to receive a plurality of attachments and urge a first tooth away from a second tooth in order to facilitate movement of the first tooth toward the second tooth.

[0057] In many embodiments, the appliance comprises a polymeric shell, the polymeric shell comprising a plurality of activation sites to store energy with a plurality of deflections of the polymeric shell in order to direct movement of the teeth. One or more of the plurality of deflections can store energy with a force against the tooth, the force can be insufficient to move the tooth in a direction opposite the deflection when the tooth comprises a target position and orientation, and additional deflection can generate sufficient increased force to move the tooth in response to the tooth moving away from the target position and orientation. The target position and orientation can comprise a non-extruded position and orientation of the tooth and the force can be oriented in an intrusive direction and insufficient to intrude the tooth and sufficient to inhibit extrusion of the tooth. The target position and orientation can comprise a non-intruded position and orientation of the tooth corresponding to a stage of the appliance and the force can be oriented in an extrusive direction and

insufficient to extrude the tooth and sufficient to inhibit intrusion of the tooth.

[0058] In many embodiments, the plurality of teeth comprises a plurality of adjacent teeth and a target tooth to be moved toward the plurality of adjacent teeth, the plurality of appliance cavities shaped to receive each of the plurality of adjacent teeth and the target tooth in order to move the target tooth toward the plurality of adjacent teeth, wherein the plurality of cavities is shaped and arranged to provide opposing forces to the plurality of adjacent teeth and the target tooth in order to distribute forces among the plurality of adjacent teeth and inhibit movement. The plurality of adjacent teeth can comprise a plurality of adjacent molars and the target tooth can comprise an anterior tooth retracted toward an extraction site. The target tooth can move in a sagittal direction.

[0059] In many embodiments, a user adjusts positions and orientations of the teeth shown on a display with user input for a stage of treatment corresponding to the appliance, wherein each of the plurality of tooth receiving cavities comprises a cavity shape profile corresponding to a tooth shape profile of a tooth to be received in the cavity, and wherein each cavity shape profile is positioned and/or oriented away from a corresponding tooth shape profile position and orientation shown on the display in order to provide activation energy to the appliance when placed on the plurality of teeth.

[0060] In many embodiments, each cavity shape matches at least a portion of a surface of the received tooth. For example, each cavity shape can match opposing surfaces of the received tooth in order to engage each of the opposing surfaces of the tooth. Each cavity shape profile can comprise first and second opposing surfaces to engage said each of the opposing surfaces of the tooth, wherein said first and second opposing surfaces are shaped to contact the tooth together along a direction of tooth movement.

[0061] In many embodiments, the first one or more teeth and a second one or more teeth move toward each other in order to provide differential space closure to a space extending between the first one or more teeth and the second one or more teeth. The first one or more teeth can comprise a plurality of anterior teeth and the second one or more teeth can comprise a plurality of posterior teeth, and the plurality of posterior teeth can comprise a combined center of resistance away from a center of resistance of each of the plurality of posterior teeth.

[0062] In many embodiments, the first counter moment corresponds to a first force to the first one or more teeth from the appliance at a first location about a first center of resistance and the second counter moment corresponds to a second counter force to the second one or more teeth about a second center of resistance.

[0063] In many embodiments, the appliance comprises a polymeric shell appliance. The appliance can comprise a polymeric shell appliance directly manufactured with one or more of 3D printing, stereo lithography, or fused deposition modeling.

[0064] In many embodiments, the plurality of teeth receiving cavities provide the differential moment to the plurality of teeth in order to increase anchorage of one or more of the plurality of teeth.

[0065] In another aspect, an appliance shaped for placement on a plurality of teeth is provided. The appliance comprises a plurality of tooth receiving cavities shaped to receive each of the plurality of teeth and provide a differential moment to the plurality of teeth in order to move and/or anchor one or more teeth of the plurality of teeth, the plurality of tooth receiving cavities comprising a first one or more tooth receiving cavities shaped to receive a first one or more teeth and a second one or more tooth receiving cavities shaped to receive a second one or more teeth, the first one or more tooth receiving cavities shaped to provide a first counter moment to the first one or more teeth, the second one or more tooth receiving cavities shaped to provide a second counter moment to the second one or more teeth, the first counter moment opposite the second counter moment.

[0066] In many embodiments, each of the plurality of tooth receiving cavities is shaped and arranged to provide the differential moment comprising a moment and a counter moment opposite the moment to a received tooth, the moment generated with a force about a center of resistance, the counter moment generated with a counter force about the center of resistance, the counter force opposite the force, the force greater than the counter force for said each of the plurality of teeth.

[0067] In many embodiments, the first one or more tooth receiving cavities is shaped and arranged to receive one or more anterior teeth and generate the first counter moment and the second one or more tooth receiving cavities is shaped and arranged to receive posterior teeth and generate the second counter moment, the second counter moment greater than the first counter moment.

[0068] In many embodiments, each of the plurality of tooth receiving cavities is shaped and arranged to produce a summed moment comprising a sum of the moment and the counter moment for said each of the plurality of teeth.

[0069] In many embodiments, the first one or more tooth receiving cavities comprises a plurality of adjacent teeth receiving cavities shaped and arranged to receive a plurality of adjacent teeth, wherein the first counter moment comprises a combined counter moment of the plurality of adjacent teeth about a center of resistance away from a center of resistance of said each of the plurality of adjacent teeth.

[0070] In many embodiments, the second one or more tooth receiving cavities comprises a plurality of adjacent teeth receiving cavities shaped and arranged to receive a plurality of adjacent teeth, wherein the second counter moment comprises a combined counter moment of the plurality of adjacent teeth about a center of resistance away from a center of resistance of said each of the plurality of adjacent teeth.

[0071] In many embodiments, each of the plurality of tooth receiving cavities comprises a cavity shape profile corresponding to a tooth shape profile of a tooth to be received in the cavity, wherein each cavity shape profile is positioned and/or oriented away from a corresponding tooth shape profile position and orientation in order to provide activation energy to the polymeric shell appliance when placed on the plurality of teeth. Each cavity shape profile can comprise first and second opposing surfaces to engage said each of the opposing surfaces of the tooth and said first and second opposing surfaces can be shaped to contact the tooth together along a direction of tooth movement.

[0072] In many embodiments, the polymeric shell appliance is shaped to urge a first portion of the first one or more teeth and a second portion of the second one or more teeth away from each other in order to move the first one or more teeth toward the second one or more teeth. The polymeric shell appliance can be shaped to urge a first portion of the first one or more teeth and a second portion of the second one or more teeth away from each other in order to move the first one or more teeth and the second one or more teeth toward each other. The first one or more teeth can comprise a first plurality of teeth and the polymeric shell appliance can comprise a shape to generate the first counter moment with each of the first plurality of adjacent teeth, the first counter moment comprising a combination of similarly oriented moments from said each of the first plurality of adjacent teeth. The second one or more teeth can comprise a second plurality of teeth and the polymeric shell appliance can comprise a shape to generate the second counter moment with each of the second plurality of adjacent teeth, the second counter moment comprising a combination of similarly oriented moments from said each of the second plurality of adjacent teeth.

[0073] In many embodiments, the plurality of tooth receiving cavities is shaped and arranged to balance the differential moment between the first one or more teeth and the second one or more teeth and to balance the first counter moment and the second counter moment between the first one or more teeth and the second one or more teeth. The first one or more teeth can comprise an anterior group of one or more teeth and the second one or more teeth can comprise a posterior group of teeth, wherein the first counter moment of the anterior group of one or more teeth opposes the second counter moment of the posterior group of one or more teeth. The posterior group of one or more teeth can comprise a plurality of adjacent posterior teeth, the polymeric shell appliance being shaped to generate the second counter moment with the plurality of adjacent posterior teeth. The plurality of adjacent posterior teeth can comprise three adjacent posterior teeth, the polymeric shell appliance being shaped to generate the second counter moment with the three adjacent posterior teeth. The three adjacent posterior teeth can comprise three adjacent posterior anchor teeth coupled together as a block of teeth having a combined center of resistance away from the center of resistance of each tooth of the three adjacent posterior teeth. The anterior group of one or more teeth can comprise a single anterior tooth, the polymeric shell appliance being shaped to generate the first counter moment with the single anterior tooth.

[0074] In many embodiments, the polymeric shell appliance is shaped to generate the second counter moment with each of the plurality of adjacent posterior teeth, the second counter moment comprising a combination of similarly oriented moments from said each of the adjacent posterior teeth. The first counter moment can be less than the second counter moment in order to move the anterior group of one or more teeth toward the plurality of adjacent posterior teeth.

[0075] In many embodiments, the first one or more teeth comprises a posterior group of one or more teeth and the second one or more teeth comprises an anterior group of teeth, wherein the first counter moment of the anterior group of one or more teeth opposes the second counter moment of the anterior group of one or more teeth. The group of one or more anterior teeth can comprise a plurality of adjacent anterior teeth and the plurality of adjacent tooth receiving cavities can comprise a plurality of adjacent anterior tooth receiving cavities shaped to generate the first counter moment.

[0076] In many embodiments, the appliances further comprises an external force or anchorage producing mechanism coupled to the plurality of teeth, wherein the external force or anchorage producing mechanism is arranged to apply a force and/or anchorage to the posterior group of one or more teeth so as to reduce movement of the posterior group of one or more teeth. The force applied to the posterior group of one or more teeth by the external force producing mechanism can comprise a distal force component. The external force or anchorage producing mechanism can comprise a class II or class III elastic.

[0077] In many embodiments, each of the plurality of tooth receiving cavities comprises an inner surface profile corresponding to a surface profile of the tooth in order to generate a moment and a counter moment with said each of the plurality of teeth.

[0078] In many embodiments, the plurality of tooth receiving cavities comprises a first one or more cavities shaped to receive a first one or more teeth and a second one or more cavities shaped to receive a second one or more teeth, the first one or more tooth receiving cavities shaped to generate the first counter moment and the second one or more tooth receiving cavities shaped to generate the second counter moment with the first counter moment opposite the second counter moment.

[0079] In many embodiments, the first counter moment of the first one or more teeth is sufficient to move first one or more roots of the first one or more teeth toward the second one or more teeth.

[0080] In many embodiments, the differential moment to said each of the plurality of teeth comprises a moment and a counter moment opposite the moment, wherein a force at a location generates the moment about a center of resistance and a counter force at a counter location generates the counter moment about the center of resistance for said each of the plurality of teeth and wherein a sum of the force and the counter force comprises a combined overall force to the tooth for said each of the plurality of teeth. A combined overall force of the first one or more teeth can urge the first one or more teeth toward the second one or more teeth. The combined overall force can be lower than each of the force and the counter force for said each of the plurality of teeth in order to move the first one or more teeth toward the second one or more teeth with decreased amounts of force.

[0081] In many embodiments, one or more of the plurality of tooth receiving cavities comprises one or more engagement structures shaped to receive one or more attachments and urge the first one or more teeth away from the second one or more teeth with a counter force in order to facilitate movement of the first one or more teeth toward the second one or more teeth. The one or more engagement structures shaped to receive the one or more attachments can generate a force opposite the counter force to move the first one or more teeth in a target direction toward the second one or more teeth, and the force can be greater than the counter force to move the one or more target teeth in the target direction, and the counter force can decrease a total amount of force to the one or more target teeth and generates the first counter moment. In many embodiments, the appliance further comprises the one or more attachments.

[0082] In many embodiments, the polymeric shell appliance comprises a plurality of engagement structures shaped to receive a plurality of attachments and urge a first tooth away from a second tooth in order to facilitate movement of the first tooth toward the second tooth. In many embodiments, the appliance further comprises the plurality of attachments. [0083] In many embodiments, the appliance comprises a polymeric shell, the polymeric shell comprising a plurality of activation sites to store energy with a plurality of deflections of the polymeric shell in order to direct movement of the teeth. One or more of the plurality of deflections can store energy with a force against the tooth, wherein the force is insufficient to move the tooth in a direction opposite the deflection when the tooth comprises a target position and orientation corresponding to a stage of the polymeric shell, and wherein additional deflection generates sufficient increased force to move the tooth in response to the tooth moving away from the target position and orientation. The target position and orientation can comprise a non-extruded position and orientation of the tooth and the force can be oriented in an intrusive direction and insufficient to intrude the tooth and sufficient to inhibit extrusion of the tooth. The target position and orientation can comprise a non- intruded position and orientation of the tooth and the force can be oriented in an extrusive direction and insufficient to extrude the tooth and sufficient to inhibit intrusion of the tooth.

[0084] In many embodiments, the plurality of teeth comprises a plurality of adjacent teeth and a target tooth to be moved toward the plurality of adjacent teeth, the plurality of polymeric shell appliance cavities shaped to receive each of the plurality of adjacent teeth and the target tooth in order to move the target tooth toward the plurality of adjacent teeth and wherein the plurality of cavities is shaped and arranged to provide opposing forces to the plurality of adjacent teeth and the target tooth in order to distribute forces among the plurality of adjacent teeth and inhibit movement. The plurality of adjacent teeth can comprise a plurality of adjacent molars and the target tooth can comprise an anterior tooth retracted toward an extraction site. The target tooth can move in a sagittal direction.

[0085] In many embodiments, a user adjusts positions and orientations of the teeth shown on a display with user input for a stage of treatment corresponding to the polymeric shell appliance, wherein each of the plurality of tooth receiving cavities comprises a cavity shape profile corresponding to a tooth shape profile of a tooth to be received in the cavity, and wherein each cavity shape profile is positioned and/or oriented away from a corresponding tooth shape profile position and orientation shown on the display in order to provide activation energy to the polymeric shell appliance when placed on the plurality of teeth. Each cavity shape profile can match opposing surfaces of the received tooth in order to engage each of the opposing surfaces of the tooth. Each cavity shape profile can comprise first and second opposing surfaces to engage said each of the opposing surfaces of the tooth and said first and second opposing surfaces can be shaped to contact the tooth together along a direction of tooth movement.

[0086] In many embodiments, the appliance is configured to move the first one or more teeth and the second one or more teeth toward each other in order to provide differential space closure to a space extending between the first one or more teeth and the second one or more teeth. The first one or more teeth can comprise a plurality of anterior teeth and the second one or more teeth can comprise posterior teeth and the plurality of posterior teeth can comprise a combined center of resistance away from a center of resistance of each of the plurality of posterior teeth.

[0087] In many embodiments, the first counter moment corresponds to a first force to the first one or more teeth from the appliance at a first location about a first center of resistance and the second counter moment corresponds to a second counter force to the second one or more teeth about a second center of resistance.

[0088] In many embodiments, the appliance comprises a polymeric shell appliance. The appliance can comprise a polymeric shell appliance directly manufactured with one or more of 3D printing, stereo lithography, or fused deposition modeling.

[0089] In many embodiments, the plurality of teeth receiving cavities provide the differential moment to the plurality of teeth in order to increase anchorage of one or more of the plurality of teeth.

[0090] In another aspect, a system to generate a plurality of appliances for moving a plurality of teeth of a subject is provided. The system comprises: an input; a display; and a processor coupled to the display and the input. The processor can comprise instructions embodied on a tangible medium to: display the plurality of teeth of the subject at a plurality of stages of a treatment, each stage corresponding to an appliance of the plurality of appliances, adjust each of the plurality of teeth on the display to a position and an orientation in response to user input to position the teeth at each of a plurality of stages of the treatment, and determine a shape profile of a polymeric shell appliance shaped for placement on the plurality of teeth at a corresponding stage of treatment, the polymeric shell appliance comprising a plurality of tooth receiving cavities, each of the plurality of tooth receiving cavities comprising a shape profile corresponding to a shape profile of a received tooth, wherein the shape profile of said each of the plurality of tooth receiving cavities is one or more of located or oriented away from the position and orientation shown on the display for the corresponding stage of treatment.

[0091] In many embodiments, the processor comprises instructions to include an attachment on one or more of the plurality of teeth in response to a force to the one or more of the plurality of teeth.

[0092] In many embodiments, the processor comprises instructions to generate one or more attachment engaging structures on the polymeric shell appliance.

[0093] In many embodiments, the shape profile of said each of the plurality of tooth receiving cavities matches the shape profile of the received tooth. The shape profile of said each of the plurality of tooth receiving cavities can be configured to engage opposing surfaces of the received tooth. Each cavity shape profile can comprise first and second opposing surfaces to engage said each of the opposing surfaces of the received tooth and said first and second opposing surfaces can be shaped to contact the tooth together along a direction of tooth movement.

[0094] In many embodiments, the processor comprises instructions to determine a center of resistance of each of a plurality of individual teeth, wherein the processor comprises instructions to determine a center of resistance of a group of adjacent teeth, in which the center of resistance of the group of adjacent teeth is located away from a center of resistance of each of the group of adjacent teeth.

[0095] In many embodiments, the processor comprises instructions to determine a differential moment about a center of resistance for each of the plurality of teeth. The differential moment can comprise a first moment about the center of resistance in response to a first force and a second moment about the center of resistance in response to a second force opposite the first force for said each of the plurality of teeth. The differential moment can be related to tipping along a direction of tooth movement for said each of the plurality of teeth.

[0096] In many embodiments, the processor comprises instructions to generate an appliance as in any one of the embodiments herein.

[0097] In another aspect, a method of moving teeth with a polymeric shell appliance is provided. The method comprises: providing a first force to a first crown of a first tooth and a second force to a second crown of a second tooth in order to move the first tooth toward the second tooth, the force resulting in a first moment on the first tooth and a second moment on the second tooth; and providing a first counter force to the first crown opposite the first force and a second counter force to the second crown opposite the second force in order to inhibit the first moment in the first tooth and the second moment in the second tooth, the first force greater than the first counter force and the second force greater than the second counter force in order to move one or more of the first tooth toward the second tooth or the second tooth toward the first tooth.

[0098] In another aspect, a method comprises providing a polymeric shell appliance. The polymeric shell appliance is configured to provide: a first force to a first crown of a first tooth and a second force to a second crown of a second tooth in order to move the first tooth toward the second tooth, the force resulting in a first moment on the first tooth and a second moment on the second tooth; and a first counter force to the first crown opposite the first force and a second counter force to the second crown opposite the second force in order to inhibit the first moment in the first tooth and the second moment in the second tooth, the first force greater than the first counter force and the second force greater than the second counter force in order to move one or more of the first tooth toward the second tooth or the second tooth toward the first tooth.

[0099] In many embodiments, the polymeric shell appliance is configured to couple the first force to the first crown and the second force to the second crown with the polymeric shell extending between the first crown and the second crown and the polymeric shell appliance is configured to provide the first counter force to the first crown with a first attachment on the first crown engaging the polymeric shell appliance and to provide the second counter force to the second crown with a second attachment on the second crown engaging the polymeric shell.

[00100] In many embodiments, the polymeric shell appliance is shaped to engage the first crown at a first location to generate the first force and to engage the second crown at a second location to generate the second force.

[00101] In many embodiments, the polymeric shell appliance is configured to couple the first force to the first crown at a first location and the second force to the second crown at a second location, wherein the polymeric shell appliance is configured to couple the first counter force to the first crown at a third location and the second counter force to the second crown at a fourth location, the first location closer to the gingiva than the third location and the second location closer to the gingiva than the second location.

[00102] In many embodiments, the polymeric shell appliance is configured to generate a first counter moment with the first counter force and a second counter moment with the second counter force with the first counter moment less than the second counter moment in order to encourage the first tooth to move toward the second tooth.

[00103] In many embodiments, the first tooth comprises an anterior tooth and the second tooth comprises a posterior tooth.

[00104] In many embodiments, the first tooth comprises a posterior tooth and the second tooth comprises an anterior tooth.

[00105] In many embodiments, the posterior tooth comprises one or more posterior teeth comprising one or more of a molar, a premolar, or a canine, and the anterior tooth comprises one or more anterior teeth comprising one or more of a central incisor, a lateral incisor, a cuspid, a first bicuspid, or a second bicuspid.

[00106] In many embodiments, one or more of the one or more anterior teeth or the one or more of the posterior teeth are moved together with en masse separation along an arch.

[00107] In many embodiments, the method further comprises providing an appliance as in any one of the preceding claims.

[00108] In another aspect, a method of moving a first tooth toward a second tooth is provided. The method comprises applying a first force to the first tooth directed away from the second tooth and a second force to the second tooth directed away from first tooth in order to inhibit rotation of the first and the second tooth as one or more of the first tooth or the second tooth are urged toward the other tooth.

[00109] In another aspect, an appliance for moving one or more teeth is provided. The appliance comprises: a plurality of tooth receiving cavities to engage a plurality of teeth comprising a first tooth and a second tooth, the plurality of tooth receiving cavities comprising a first cavity shaped to receive the first tooth and a second cavity shaped to receive the second tooth, the first cavity and the second cavity arranged to urge the first tooth in a first direction and the second tooth in a second direction; a first engagement structure to engage a first tooth of the plurality of teeth; and a second engagement structure to engage a second tooth of the plurality of teeth; wherein the first engagement structure and the second engagement structure are arranged to urge the first tooth in a third direction opposite the first direction and the second tooth in a fourth direction opposite the second direction.

[00110] In many embodiments, first tooth comprises a first attachment and the first engagement structure comprises a first attachment engaging structure, and the second tooth comprises a second attachment and the second engagement structure comprises a second attachment engaging structure. The first engagement structure, the second engagement structure, the first tooth receiving cavity and the second tooth receiving cavity can be arranged to provide a first counter moment to the first tooth to decrease rotation of the first tooth and a second counter moment to decrease rotation of the second tooth. The first engagement structure can comprise one or more of a first attachment engaging structure, a first power ridge, or a first shape profile corresponding to a surface of the first tooth and the second engagement structure can comprise one or more of a second attachment engaging structure, a second power ridge, or a second shape profile corresponding to the surface of the first tooth.

[00111] In many embodiments, the appliance comprises the appliance of any one of the embodiments provided herein.

[00112] In another aspect, a system to generate a plurality of appliances for moving a plurality of teeth of a subject is provided. The system comprises: an input; a display; and a processor coupled to the display and the input. The processor comprises instructions embodied on a tangible medium to: display the plurality of teeth of the subject at a plurality of stages of a treatment, each stage corresponding to an appliance of the plurality of appliances; adjust each of the plurality of teeth on the display in response to user input to position the teeth at each stage of the treatment; and determine a shape profile of a polymeric shell appliance shaped for placement on the plurality of teeth, the polymeric shell appliance comprising a plurality of tooth receiving cavities shaped to receive each of the plurality of teeth and provide a differential moments to each of the plurality of teeth in order to move the teeth.

[00113] In many embodiments, the processor comprises instructions to determine the shape profile of the appliance with a plurality of attachment engaging structures shaped to engage a plurality of attachments with the plurality of attachments and the plurality of attachment engaging structures shaped and arranged to engage each other and provide the plurality of differential moments to said each of the plurality of teeth.

[00114] In many embodiments, the processor comprises instructions to generate an appliance as in any one of the embodiments herein.

[00115] In many embodiments, the processor comprises instructions to directly fabricate the polymeric shell appliance with one or more of 3D printing, fused deposition modeling, or stereo lithography.

[00116] Although reference is made to an appliance comprising a polymeric shell appliance, the embodiments disclosed herein are well suited for use with many appliances that receive teeth, for example appliances without one or more of polymers or shells. The appliance can be fabricated with one or more of many materials such as metal, glass, reinforced fibers, carbon fiber, composites, reinforced composites, aluminum, biological materials, and combinations thereof for example. The appliance can be shaped in many ways, such as with thermoforming or direct fabrication as described herein, for example. Alternatively or in combination, the appliance can be fabricated with machining such as an appliance fabricated from a block of material with computer numeric control machining.

[00117] Orthodontic systems of the present disclosure can include tooth attachments and one or more orthodontic appliances that engage the attachments when worn by a patient. Appliances having teeth receiving cavities that receive and reposition teeth, e.g., via application of force due to appliance resiliency, are generally illustrated with regard to FIG. 1 A. As illustrated, FIG. 1A shows one exemplary adjustment polymeric shell appliance 1 1 which is worn by the patient in order to achieve an incremental repositioning of each of a plurality of teeth 10 in the jaw. The appliance can include a shell (e.g., polymeric shell) having teeth-receiving cavities that receive and resiliently reposition the teeth. Similar appliances, including those utilized in the Invisalign(TM) System, are described in numerous patents and patent applications assigned to Align Technology, Inc. including, for example in U.S. Pat. Nos. 6,450,807, and 5,975,893, as well as on the company's website, which is accessible on the World Wide Web (see, e.g., the url "align.com"). Appliances according to the present disclosure can be designed to engage one or more

attachments positioned on a tooth of the patient, as further described below. As further described herein, tooth attachments can be designed, oriented, and/or located on a patient's tooth to precisely control the moments produced on a patient's tooth as the appliance is worn by the patient. Customized design and use in orthodontic treatment as described herein can advantageously improve effectiveness of treatment and clinical results by more precisely applying force vectors of necessary magnitude and direction for desired movement. Orthodontic systems of the present disclosure including appliances and tooth attachments as described further provide an efficient force distribution mechanism that can more effectively reduce unwanted force and moment.

[00118] The plurality of teeth 10 may comprise one or more attachments 102. The polymeric shell appliance 11 comprises a plurality of tooth receiving cavities 101 shaped to receive each of the plurality of teeth. Each of the plurality of tooth receiving cavities comprises an inner surface profile shaped to correspond to the exterior surface of the received tooth. In many embodiments, the interior surface of the polymeric shell appliance matches at least a portion of the surface of the received tooth, such as opposing surfaces of the profile of the received tooth. The polymeric shell appliance 11 may comprise one or more engagement structures 104 to engage the one or more attachments. In many embodiments, the one or more engagement structures are configured to provide force to the tooth when the appliance engages the one or more attachments. The one or more engagement structures 104 can be configured in many ways to provide force in a predetermined direction to the one or more attachments 102. For example, the one or more engagement structures may comprise a structure configured to receive with the one or more attachments 102 with at least some deflection and/or distortion of the engagement structure 104 in order to apply force to the attachment and tooth. The engagement structure 104 may comprise one or more protrusions 105, for example, configured to engage the attachment. In many embodiments, the engagement structure 104 comprises a cavity 106 shaped to receive the attachment. The one or more protrusions 105 protrudes from the polymeric shell inside the cavity 106 with a shape to engage a flat surface of the attachment and apply force in a direction substantially normal to the flat surface of the attachment.

[00119] One or more tooth attachments 102 for delivering a movement force or system of forces is further illustrated with reference to FIG. IB. The tooth movement can be described with reference to a center of resistance 103. Tooth attachment devices for delivering forces similar to the attachment of FIG. IB and suitable for incorporation in accordance with embodiments as disclosed herein are described in U.S. App. Ser. No. 12/623,340, filed on November 20, 2009, published as U.S.

2010/0138025 on June 3, 2010, entitled "Orthodontic systems and methods including parametric attachments," the entire disclosure of which is incorporated herein by reference. Methods and systems for determining dental aligner geometries suitable for incorporation in accordance with embodiments disclosed herein are described in U.S. App. Ser. No. 13/865,091, filed on April 17, 2013, published as U.S.

2013/0230818, entitled "Method and system for optimizing dental aligner geometry", the entire disclosure of which is incorporated herein by reference.

[00120] The attachment is coupled to a surface of the tooth on the tooth crown and can couple with or engage a dental appliance or aligner as illustrated in FIG. 1 A when the appliance is worn by the patient. When worn by the patient, the appliance engages the tooth crown and attachment, with interaction/contact between an activator, e.g., one or more surfaces or portions of the internal cavity of the appliance, and corresponding surfaces/portions of the tooth attachment and/or tooth crown to apply a system of forces for eliciting tooth movement. Various tooth movements can be accomplished, as further noted below.

[00121] As set forth in the prior applications, an appliance can be designed and/or provided as part of a set or plurality of appliances and treatment can be administered according to a treatment plan. In such an embodiment, each appliance may be configured so that one or more tooth-receiving cavities have a geometry corresponding to an intermediate or final tooth arrangement intended for the appliance. Appliance geometries can be further designed or modified (e.g., modified to accommodate or operate in conjunction with tooth attachments) so as to apply a desired force or system of forces to the patient's teeth and elicit a desired tooth movement and gradually reposition teeth to an intended arrangement. The patient's teeth are progressively repositioned from their initial tooth arrangement toward a final tooth arrangement by placing a series of incremental position adjustment appliances over the patient's teeth. The adjustment appliances can be generated all at the same stage or in sets or batches, e.g., at the beginning of a stage of the treatment, and the patient wears each appliance until the pressure of each appliance on the teeth can no longer be felt. A plurality of different appliances (e.g., set) can be designed and even fabricated prior to the patient wearing any appliance of the plurality. At that point, the patient replaces the current adjustment appliance with the next adjustment appliance in the series until no more appliances remain. 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 over-correction may be desirable in order to offset potential relapse after the repositioning method has been terminated, e.g., to permit movement of individual teeth back toward their pre- corrected positions. Over-correction may also be beneficial to speed the rate of correction, e.g., 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.

[00122] Orthodontic appliances, such as the appliance illustrated in FIG. 1A, impart forces to the crown of a tooth and/or an attachment positioned on the tooth at each point of contact between a tooth receiving cavity of the appliance and received tooth and/or attachment. The magnitude of each of these forces and their distribution on the surface of the tooth determines the type of orthodontic tooth movement which results. Types of tooth movements are conventionally delineated as extrusion, intrusion, rotation, tipping, translation and root movement. Tooth movement of the crown greater than the movement of the root is referred to as tipping. Equivalent movement of the crown and root is referred to as translation. Movement of the root greater than the crown is referred to as root movement. Tooth movements may be in any direction in any plane of space, and may comprise one or more of rotation or translation along one or more axes.

[00123] In many embodiments, the appliances herein are used to reposition one or more of the patient's teeth in order to treat an orthodontic condition and/or achieve a desired tooth arrangement. For example, an orthodontic appliance as described herein can be used to reposition teeth in order to reduce the size of a space between teeth, also known as "space closure." A space may be present in a patient's arch due to extraction of one or more teeth, such as a first bicuspid extraction or a second bicuspid extraction. Space closure may be performed by repositioning one or more teeth near the extraction site, e.g., by moving one or more teeth anterior to the extraction site in a posterior direction, by moving one or more teeth posterior to the extraction site in an anterior direction, or a combination thereof. In many

embodiments, space closure involves moving one or more anterior teeth towards the space while maintaining the posterior teeth in their current locations. Alternatively, space closure can involve moving one or more posterior teeth towards the space while maintaining the anterior teeth in their current locations. Optionally, one or more anterior teeth and one or more posterior teeth are moved towards each other in order to close a space. In such embodiments, the anterior teeth may be moved prior to, concurrently with, or after moving the posterior teeth, and the distance over which the anterior teeth are moved can be greater than, less than, or equal to the distance over which the posterior teeth are moved.

[00124] FIG. 2 shows components of an alignment apparatus 100 and corresponding forces. The alignment apparatus 100 may comprise one or more of the attachments and polymeric shell appliances configured and arranged to provide teeth moving forces as described herein. Each tooth of the plurality of teeth 10 comprises a root 12 and a crown 14, and the polymeric appliance (omitted for clarity) can apply forces to the crown and/or attachments on the crown in order to move each tooth. Each tooth of the plurality of teeth can move with respect to a center of resistance.

[00125] The plurality of teeth 10 may comprise two or more of any teeth of the mouth. The plurality of teeth 10 may comprise one or more of a plurality of posterior teeth 20 such as a plurality of molars or bicuspids and combinations thereof. The plurality of posterior teeth 20 may comprise one or more of a bicuspid 26, a first molar 24 or a second molar 22, for example. The plurality of posterior teeth may comprise a third molar comprising a wisdom tooth, for example. Alternatively or in combination, the plurality of teeth 10 may comprise one or more of a plurality of anterior teeth 30. The plurality of anterior teeth may comprise one or more of a bicuspid, a cuspid (canine), or incisor, for example. In many embodiments, the plurality of anterior teeth 30 comprises a cuspid 32 (canine), and one or more adjacent incisors, such as incisor 34 and incisor 36.

[00126] In many embodiments, each of the plurality of attachments (e.g., attachments 1 10, 1 12, 1 14, and 130, and 140) comprises a flat surface to engage a corresponding respective engagement structure of the aligner (not shown). The engagement structure of the aligner may comprise a protrusion that engages the flat surface in order to impart force from the polymeric shell appliance to the attachment and tooth with the attachment. The protrusion of the engagement structure can be configured in many ways, and may comprise a protrusion on an inner surface of an attachment receiving cavity of the appliance or a ball shaped structure that engages the flat surface, for example. In many embodiments, the attachment engaging structure of the appliance engages the attachment so as to exert force in a direction substantially normal to the flat surface of the attachment.

[00127] Many embodiments as disclosed herein are particularly well suited for closing extraction sites, such as an extraction site between the posterior teeth 20 and the anterior teeth 30. In many embodiments one or more teeth are moved to fill an extraction site with a movement in a target direction 105. Although the target direction 105 can extend in any direction, in many embodiments the target direction 105 extends along a sagittal direction (e.g., along a mesial-distal direction). The amount of tipping and/or counter rotation of the teeth can be controlled with the size and shape of the appliance, engagement structures of the appliance, and/or attachments, in order to direct movement of one or more teeth with appropriate amounts of force.

[00128] In many embodiments, when moving a tooth in order to perform space closure or other orthodontic treatments, it is desirable to move the tooth root concurrently with the tooth crown, such that the tooth translates along the target direction with little or no tipping, also known as a "bodily movement" of the tooth. For instance, when repositioning one or more anterior teeth in order to perform space closure, it may be desirable to retract the anterior teeth without tipping the crowns towards the tongue so as to avoid loss of inclination and/or change in vertical height of the tooth.

[00129] Tipping of a tooth may occur when the appliance applies force primarily to the tooth crown and/or when the amount of force on the tooth crown exceeds a certain threshold value. In many embodiments, each tooth comprises a center of resistance to forces applied to the tooth, and the tooth may rotate about the center of resistance, or approximately rotate in three dimensions about the center of resistance. The center of resistance of the tooth may be located away from the tooth crown such that application of force onto the crown results in a moment to the tooth about the center of resistance that elicits tooth rotation.

[00130] For example, referring again to the embodiment of FIG. 2, the first molar 24 may comprise a center of resistance 25 located near the trifurcation of the roots. The second molar 22 may comprise a center of resistance 23 located near the trifurcation of the roots. The bicuspid 26 may comprise a center of resistance 27, for example. The cuspid 32 may comprise a center of resistance 33. Each of the incisor 34 and the incisor 36 may comprise a center of resistance. The location of each of the centers of resistance of the plurality of teeth as described herein may correspond to a center of resistance known to a person of ordinary skill the art.

[00131] The application of force to a tooth in order to move the tooth can result in a moment to the tooth about the center of resistance. In many embodiments, a target tooth to be moved such as cuspid 32 receives a force from the polymeric shell appliance, which can be a direct force from the surface of the interior of the shell or indirect force through an attachment, or combinations thereof. For instance, attachment 140 can be optionally placed on the tooth 32 in order to direct the tooth 32 with a planned movement. Engagement of attachment 140 with polymeric shell appliance 1 1 (e.g., via an engagement structure located on polymeric shell appliance 1 1) can result in a force vector to the attachment 140 and tooth as indicated with arrow 141. As tooth 32 resists forces with a center of resistance 33, a moment 146 about the center of resistance can result. The moment 146 can result in rotation of tooth 32, e.g., tipping.

[00132] In many embodiments, the appliances herein are shaped to modify the force system applied to the tooth so as to elicit translational tooth movement with little or no tipping movement. For instance, the appliances herein can be shaped to reduce the amount of force applied to the crown, e.g., to within a range from about 0.5 N to about 3 N. Modification of the force system can be achieved by modifying the shape of a tooth receiving cavity, use of attachments and attachment engagement structures, use of external force producing mechanisms such as elastics, or combinations thereof, as discussed above and herein.

[00133] Alternatively or in combination, the appliances herein can be shaped to modify the energy distribution on the tooth so as to elicit translational tooth movement with little or no tipping movement. For example, the appliances herein can be shaped to distribute energy onto the tooth roots as well as onto the tooth crown. Modification of the energy distribution can be achieved by modifying the shape of a tooth receiving cavity, use of attachments and attachment engagement structures, use of external force producing mechanisms such as elastics, or combinations thereof, as discussed above and herein.

[00134] Various methods can be used to alter the force system and/or energy distribution on a tooth in order to elicit bodily movement of the tooth. For instance, in many embodiments, the appliances herein are shaped to apply a counter moment onto the tooth that opposes the moment that would otherwise produce tooth rotation, such that the movement of a tooth is provided with a differential moment between the moment and the counter moment. The counter moment can be produced by modifying a position and/or orientation of the tooth receiving cavity relative to the position and/or orientation of the corresponding received tooth such that when the appliance is worn by the patient, the tooth receiving cavity applies the counter moment onto the tooth. Alternatively or in combination, in many embodiments, an attachment on a tooth is provided to generate a counter moment, such that the movement of a tooth is provided with a differential moment between the moment and the counter moment. The counter moment can be generated by interaction between the attachment and an engagement structure located on the appliance when the appliance is worn. In many embodiments, the attachment provided to generate the counter moment is located farther away from the center of resistance than the locus of engagement of the attachment or crown surface that urges the target tooth in the target direction, such that the force vector in the target direction is greater than the counter force in the opposite direction in order to generate the differential moment and urge the target tooth in the target direction.

[00135] Referring again to the exemplary embodiment of FIG. 2, a counter moment 136 can be provided with an attachment 130 or directed engagement of the tooth with the polymeric shell appliance 11 or combinations thereof, which generates a force vector as shown with arrow 131, opposite the force vector of attachment 140 shown with arrow 141. In many embodiments, the attachment 140 that urges the tooth 32 in target direction 105 is located closer to the center of resistance 33 and gingiva than the counter attachment 130, such that counter moment 136 can approximate moment 146 in order to control rotation of tooth 32 as the tooth moves along target direction 105. For example, counter moment 136 can be less than moment 146 to allow the tooth to tip with rotation in the target direction 105, greater than moment 146 in order to rotate the crown away from target direction 105, or similar to moment 146 in order to maintain an orientation of tooth 32 when the tooth moves along target direction 105. In many embodiments, the appliance 1 1 comprising the polymeric shell comprises engagement structures to engage the attachments, and the locations and shapes of the engagement structures can be arranged to provide suitable amounts of counter forces in order to provide counter moments to direct tooth movement along a target path.

[00136] In many embodiments, a posterior most tooth comprises a substantial exposed surface 16 suitable for engagement with the polymeric appliance. The polymeric shell appliance 1 1 can generate force along the posterior surface of the crown at a locus of engagement as indicated with arrows 122. The anteriorly directed force indicated with arrows 122 generates a moment 126 about the center of resistance 23 of second molar 22, for example. In many embodiments, the force of the appliance indicated with arrows 122 generates a moment 127 around the center of resistance 25 of first molar 24, and a moment 128 about the center of resistance 27 of the bicuspid 26, for example. One or more of the plurality of posterior teeth may have an attachment placed thereon to generate a counter moment.

[00137] Attachment 110 can generate a counter force as indicated with arrow 1 11 opposite the force indicated with arrows 122 in order to generate a counter moment 116. The counter moment 116 can be greater than moment 126, such that the crown of second molar 22 is rotated away from first molar 24, for example with the differential moment resulting from the sum of moment 126 with counter moment 116. Alternatively, counter moment 1 16 can be less than moment 126 and also inhibit rotation of second molar 22 toward first molar 24.

[00138] The moment and counter moment of each tooth can be determined based on the amount of force applied to the tooth and the distance from the center of resistance to the location of the force along the elongate axis of the tooth. The force shown with arrows 122 is applied at distance 160 along the elongate axis of the tooth from the center of resistance 23. The counter force shown with arrows 1 1 1 is applied at a distance 162 from the center of resistance 23. In many embodiments, the moment 126 approximately equals the product of the distance 160 and the force represented by arrows 122. The counter moment 112 approximately equals the product of distance 162 and the counter force on attachment 1 10 represented by arrow 1 11. A person of ordinary skill in the art will recognize may ways to determine the moments as described herein, for example with finite element modeling and integrating the moments at a plurality of positions relative to the center of resistance along the tooth.

[00139] Attachment 1 12 can generate a counter force as indicated with arrow 1 13 opposite the force indicated with arrows 122 in order to generate a counter moment 1 17. The counter moment 117 can be greater than moment 127, such that the _H crown of first molar 24 is rotated away from bicuspid 26, for example with the differential moment resulting from the sum of moment 127 with counter moment 1 17. Alternatively, counter moment 117 can be less than moment 127 and also inhibit rotation of first molar 24 toward bicuspid 26.

[00140] Attachment 1 14 can generate a counter force as indicated with arrow

115 opposite the force indicated with arrows 122 in order to generate a counter moment 1 18. The counter moment 1 18 can be greater than moment 128, such that the crown of bicuspid 26 is rotated away from the target tooth comprising cuspid 32, for example with the differential moment resulting from the sum of moment 128 with counter moment 1 18. Alternatively, counter moment 118 can be less than moment 128 and also inhibit rotation of bicuspid 26 toward the target tooth comprising cuspid

32.

[00141] In many embodiments, a ratio is defined between the magnitude of the total moment applied to the tooth and the amount of force applied to the tooth along the targeted movement direction, referred to herein as the "moment-force ratio." For instance, in the embodiment of FIG. 2, the moment-force ratio for tooth 32 is defined as the ratio between the sum of moment 146 and counter moment 136, and force 141. The value of the moment-force ratio may determine the resultant movement of the tooth, e.g., whether the tooth translates, rotates, or both. In many embodiments, the appropriate moment-force ratio to be applied to a tooth in order to produce translation while reducing rotation varies based on the characteristics of the particular tooth, e.g., tooth size, complexity of the root structure, and/or location of the center of resistance. For example, for a posterior tooth, the moment-force ratio to produce translation with little or no rotation can be within a range from about 4 mm to about 10 mm. As another example, for an anterior tooth, the moment-force ratio to produce translation with little or no rotation can be within a range from about 6 mm to about 15 mm.

[00142] In many embodiments, it is desirable to move a first group of one or more teeth while maintaining a second group of one or more teeth ("anchoring teeth") in their current arrangement. For instance, space closure may be performed by retracting one or more anterior teeth while anchoring one or more posterior teeth, or by advancing one or more posterior teeth while anchoring one or more anterior teeth. In the embodiment of FIG. 2, one or more of the plurality of posterior teeth 20 can be configured with differential moments in order to control orientation of the one or more teeth. In many embodiments, counter moments of posterior teeth are arranged to inhibit movement of the posterior teeth. Work in relation to embodiments suggests that rotating the crown of the tooth away from a force to move a neighboring tooth can inhibit movement of the tooth, and rotation of a crown of a tooth toward a force from a neighboring tooth can facilitate movement of the tooth toward the neighboring tooth. In many embodiments, the plurality of posterior teeth 20 comprises a block of adjacent teeth configured to anchor the appliance and move the target tooth with little or no movement of the plurality of adjacent anchor teeth. Alternatively or in combination, one or more of the plurality of posterior teeth 20 can be configured to move toward the target tooth, for example. Although certain embodiments herein are described in the context of repositioning anterior teeth while anchoring posterior teeth, it shall be appreciated that the present disclosure is equally applicable to repositioning posterior teeth while anchoring anterior teeth.

[00143] The systems, methods, and devices of the present disclosure can be used to apply differential moments to a patient's teeth in order to reduce or inhibit movement of one or more anchoring teeth, also referred to herein as "increasing anchorage." In many embodiments, an orthodontic appliance is shaped to apply a moment to a first group of one or more teeth to be moved (e.g., to close a space) and apply a counter moment to a second group of one or more anchoring teeth, thereby producing a differential moment between the first and second groups of teeth. A differential moment can be produced by modifying the shape of one or more tooth receiving cavities, use of attachments and attachment engagement structures, use of external force producing mechanisms such as elastics, or combinations thereof, as discussed above and herein. [00144] In many embodiments, differential moments are provided between groups of teeth as described herein in order to provide tooth movement with improved control. In many embodiments, a first group of teeth comprises a first moment and a second group of teeth comprises a second moment, and a differential moment between a first moment of the first group of teeth and a second moment of the second group of teeth allows selective movement of the teeth, e.g., anterior and/or posterior teeth. For example, in many embodiments, a large differential moment is provided between a group of one or more posterior teeth and a group of one or more anterior teeth in order to anchor the posterior teeth. The counter moment of the posterior teeth can be greater than the moment of the anterior teeth in order to anchor the posterior teeth, for example, to provide maximum anchorage to the posterior teeth. In alternative embodiments, a large differential moment is provided between a group of one or more posterior teeth and a group of one or more anterior teeth in order to anchor the anterior teeth. The counter moment of the anterior teeth can be greater than the moment of the posterior teeth in order to anchor the anterior teeth, for example, to provide maximum anchorage to the anterior teeth.

[00145] In many embodiments, a plurality of teeth are coupled together such that they collectively behave as a single unit, e.g., in order to increase anchorage of the teeth. Teeth that are coupled together in this manner may exhibit greater resistance to repositioning. The shell appliances described herein may provide a greater capacity for creating anchorage compared to other types of appliances (e.g., wire and bracket appliances) due to the increased degree of contact between the appliance surface and the surfaces of the received teeth (e.g., occlusal, lingual, and/or buccal surfaces). A polymeric shell appliance can be configured to couple groups of one or more teeth to each other in many ways. For example, a first group of one or more teeth can be coupled to a second group of one or more teeth. In many embodiments, the first group of one or more teeth comprises a first plurality of teeth, and the polymeric shell appliance comprises a shape to generate the first counter moment with each of the first plurality of adjacent teeth, in which the first counter moment comprises a combination of similarly oriented moments from said each of the first plurality of adjacent teeth as shown and described herein, for example with reference to FIG. 2. The second group of one or more teeth may comprise a second plurality of teeth and the polymeric shell appliance may comprise a shape to generate the second counter moment with each of the second plurality of adjacent teeth, in which the second counter moment comprises a combination of similarly oriented moments from said each of the second plurality of adjacent teeth.

[00146] In many embodiments, a tooth comprising a moment comprises a tooth with a force applied from an appliance to generate a moment or counter moment about the center of resistance. A group of teeth comprising a moment or a counter moment may comprise an appliance engaging one or more of the teeth to provide the moment or counter moment about the center of resistance.

[00147] In many embodiments, the plurality of tooth receiving cavities is shaped and arranged to balance the differential moment between the first one or more teeth and the second one or more teeth with the polymeric appliance extending between the first group of one or more teeth and the second group of one or more teeth. Alternatively or in combination, the plurality of tooth receiving cavities can be shaped and arranged to balance the first counter moment and the second counter moment between the first one or more teeth and the second one or more teeth

[00148] In many embodiments, a counter moment is provided with a group of one or more teeth, for example with a plurality of posterior teeth. The counter moment may comprise a sum of the counter moments of each tooth of the group of teeth. The combined counter moment may comprise a counter moment about a combined center of resistance away from the center of resistance of each of the teeth of the group. A person of ordinary skill in the art can determine a center of resistance for a group of teeth with one or more known ways and in accordance with the embodiments disclosed herein.

[00149] Referring again to the embodiment of FIG. 2, in many embodiments, moment 136 opposes moment 116, moment 1 17 and moment 118, for example.

Moments 116, 1 17 and 118 are similarly oriented as shown. With a right handed triple coordinate system, moment 136 will be oriented toward one side of the plurality of teeth (outward from the page toward the view) and moment 116, moment 1 17, and moment 1 18 will be similarly oriented (inwardly from the page away from the viewer) toward an opposite side of the teeth from moment 136. For example moment 136 can be oriented toward a buccal side of the group of teeth, and moment 116, moment 117, and moment 118 can be similarly oriented toward a lingual side of the group of teeth. The sum of moment 1 16, moment 1 17, and moment 1 18 can be considered as a counter moment on the posterior teeth 20 that opposes the moment 136 on the one or more anterior teeth 20. In many embodiments, the counter moment on the posterior teeth 20 increases anchorage of the posterior teeth 20 while the moment 136 on the anterior teeth 20 induces movement of the anterior teeth.

[00150] Although reference is made to a plurality of posterior teeth as an anchoring block with counter moments, in many embodiments, the plurality of posterior teeth can be configured as an anchoring block without counter rotation and counter moments and without attachments in order to move one or more target teeth with the polymeric shell coupled to the plurality of posterior teeth and the one or more target teeth.

[00151] In many embodiments, movement of one or more teeth along a target vector can result in movement of one or more adjacent teeth. For example, as depicted in FIG. 2, movement of cuspid 32 toward the extraction site can result in extrusion of one or more adjacent incisors, for example incisor 34 and incisor 36. In many embodiments, polymeric shell appliance 1 1 is configured to provide one or more activation forces to one or more teeth. The polymeric shell appliance 1 1 can be configured with activation of the polymeric shell to apply an activation force 150 to incisor 34. In many embodiments, the activation force 150 is not sufficient to intrude incisor 34 with incisor 34 in the target position, and activation force 150 is sufficient to inhibit extrusion of incisor 34. Extrusion of incisor 34 with movement of cuspid 32 can result in an increased deflection of appliance 1 1 and increased activation force 150 in order to inhibit further extrusion of incisor 34. Similarly, the polymeric shell appliance can be configured to apply an activation force 152 to incisor 36, and the activation force 152 may be insufficient to intrude incisor 36 while inhibiting extrusion of incisor 36. Additionally, as discussed above and herein, the polymeric shell appliance can be configured to apply a counter moment 154 (e.g., lingual root torque) to incisors 32, 34, and 36 to prevent tipping while the incisors are being retracted.

[00152] Optionally, the appliances herein can include one or more external force producing mechanisms. The external force producing mechanism can be any device capable of being coupled to the teeth in order to exert force onto the teeth, such as an elastic (e.g., class I elastic, class II elastic, class III elastic), spring, wire, or the like. The external force producing mechanism can be separate from an orthodontic appliance worn over the teeth. The external force producing mechanism can be coupled directly to one or more teeth (e.g., via bonding or adhesives), or may be indirectly coupled to one or more teeth (e.g., via an attachment or button mounted on a surface of a tooth, a hook or other fastening feature located on an aligner, a temporary anchorage device (TAD) implanted into bone of the upper jaw or lower jaw, or combinations thereof). In embodiments where the external force producing mechanism is coupled to a tooth-mounted attachment or button, the shell appliance can include a hole or cut-out accommodating the attachment or button. In many embodiments, the external force producing mechanism includes a first end coupled directly or indirectly to a tooth in the patient's upper jaw and a second end coupled directly or indirectly to a tooth in the patient's lower jaw. Alternatively, the ends of the external force producing mechanism can be directly or indirectly coupled to different teeth on the same jaw (e.g., upper jaw or lower jaw).

[00153] Ari external force producing mechanism can be used to refine the delivery of a force, moment, and/or counter moment on teeth in order to provide increased control over movement or anchorage of the teeth. In many embodiments, an external force producing mechanism is coupled to one or more teeth in order to increase anchorage of one or more anchoring teeth. For example, the external force producing mechanism can apply a force to a group of one or more anchoring teeth along a direction that reduces or inhibits movement of the group of anchoring teeth, also known as "backing up anchorage." An external force producing mechanism can be referred to herein as an "external anchorage producing mechanism." Alternatively or in combination, an external force producing mechanism can be coupled to one or more teeth in order to increase movement of one or more teeth, e.g., for space closure.

[00154] FIG. 6A illustrates an alignment apparatus 600 including an external force producing mechanism 602. The alignment apparatus 600 includes a shell appliance (omitted for clarity) worn over a plurality of upper teeth 604. Optionally, the alignment apparatus 600 includes a plurality of attachments 606 attached to the upper teeth 604 and arranged to interact with the shell appliance in order to exert forces onto the teeth 604. In many embodiments, the teeth 604 include a group of one or more anterior teeth 608 and a group of one or more posterior teeth 610, and the alignment apparatus produces one or more moments 612 on the anterior teeth 608 and one or more counter moments 614 on the posterior teeth 610. The moment(s) 612 and counter moment(s) 614 can elicit retraction of the anterior teeth 608 while

maintaining anchorage of the posterior teeth 610 as described above and herein, e.g., to close a space between the anterior teeth 608 and posterior teeth 610.

[00155] In the depicted embodiment, the external force producing mechanism 602 is a class II elastic with a first end 616 coupled to one or more upper teeth 604 (e.g., an upper canine) and a second end 618 coupled to one or more lower teeth 620 (e.g., a lower molar). The first end 616 can be coupled directly to the crown of an upper tooth 604 or indirectly (e.g., via a tooth-mounted attachment or the shell appliance). The second end 618 can be coupled directly to the crown of a lower tooth 620 or indirectly (e.g., via a tooth-mounted attachment or a shell appliance worn over the lower teeth 620). The first end 616 can be positioned anteriorly relative to the second end 618 so as to produce a tension within the external force producing mechanism 602 that pulls the upper arch in a posterior direction. This tension can be considered as being made up of a distal force component 622 and an extrusive force component 624 that are exerted on the upper arch. It shall be appreciated that the tension can also be considered as being made up of a mesial force component and an extrusive force component that are exerted on the lower arch (not shown). In many embodiments, the distal force component 622 is transmitted to the posterior teeth 610 of the upper arch so as to enhance anchorage and maintain their position within the upper arch (e.g., inhibit anterior movement). Optionally, the distal force component 622 is transmitted to the anterior teeth 608 of the upper arch in order to enhance posterior movement, e.g., for space closure.

[00156] FIG. 6B illustrates an alignment apparatus 650 including an external force producing mechanism 652. The alignment apparatus 650 includes a shell appliance (omitted for clarity) worn over a plurality of lower teeth 654. Optionally, the alignment apparatus 650 includes a plurality of attachments 656 attached to the lower teeth 654 and arranged to interact with the shell appliance in order to exert forces onto the teeth 654. In many embodiments, the teeth 654 include a group of one or more anterior teeth 658 and a group of one or more posterior teeth 660, and the alignment apparatus produces one or more moments 662 on the anterior teeth 658 and one or more counter moments 664 on the posterior teeth 660. The moment(s) 662 and counter moment(s) 664 can elicit retraction of the anterior teeth 658 while maintaining anchorage of the posterior teeth 660 as described above and herein, e.g., to close a space between the anterior teeth 658 and posterior teeth 660.

[00157] In the depicted embodiment, the external force producing mechanism 652 is a class III elastic with a first end 666 coupled to one or more lower teeth 654 (e.g., a lower canine) and a second end 668 coupled to one or more upper teeth 670 (e.g., an upper molar). The first end 666 can be coupled directly to the crown of a lower tooth 654 or indirectly (e.g., via a tooth-mounted attachment or the shell appliance). The second end 668 can be coupled directly to the crown of a upper tooth 670 or indirectly (e.g., via a tooth-mounted attachment or a shell appliance worn over the upper teeth 670). The first end 666 can be positioned anteriorly relative to the second end 668 so as to produce a tension within the external force producing mechanism 652 that pulls the lower arch in a posterior direction. This tension can be considered as being made up of a distal force component 672 and an extrusive force component 674. It shall be appreciated that the tension can also be considered as being made up of a mesial force component and an extrusive force component that are exerted on the upper arch (not shown). In many embodiments, the distal force component 672 is transmitted to the posterior teeth 660 of the lower arch so as to enhance anchorage and maintain their position within the lower arch (e.g., inhibit anterior movement). Optionally, the distal force component 672 is transmitted to the anterior teeth 658 of the lower arch in order to enhance posterior movement, e.g., for space closure.

[00158] FIG. 7 illustrates an alignment apparatus 700 including an external force producing mechanism 702. The alignment apparatus 700 includes a shell appliance (omitted for clarity) worn over a plurality of upper teeth 704. Optionally, the alignment apparatus 700 includes a plurality of attachments 706 attached to the upper teeth 704 and arranged to interact with the shell appliance in order to exert forces onto the teeth 704. In many embodiments, the teeth 704 include a group of one or more anterior teeth 708 and a group of one or more posterior teeth 710, and the alignment apparatus produces one or more moments 712 on the anterior teeth 708 and one or more counter moments 714 on the posterior teeth 710. The moment 712 and counter moment(s) 714 can elicit retraction of the anterior teeth 708 while

maintaining anchorage of the posterior teeth 710 as described above and herein, e.g., to close a space between the anterior teeth 708 and posterior teeth 710. [00159] In the depicted embodiment, the external force producing mechanism 702 has a first end 716 coupled to one or more upper teeth 704 (e.g., an upper canine) and a second end 718 coupled to a temporary anchorage device (TAD) 720 implanted in the bone of the patient's upper jaw. The first end 716 can be coupled directly to the crown of an upper tooth 704 or indirectly (e.g., via a tooth-mounted attachment or the shell appliance). The first end 716 can be positioned anteriorly relative to the second end 718 so as to produce a tension within the external force producing mechanism 702 that pulls the upper arch in a posterior direction. This tension can be considered as being made up of a distal force component 722 and an extrusive force component 724. In many embodiments, the distal force component 722 is transmitted to the posterior teeth 710 so as to enhance anchorage and maintain their position within the upper arch (e.g., inhibit anterior movement). Optionally, the distal force component 722 is transmitted to the anterior teeth 708 in order to enhance posterior movement, e.g., for space closure.

[00160] In alternative embodiments, an external force producing mechanism can be coupled between a lower tooth and a TAD in the patient's lower jaw so as to apply a distal force component to the teeth of the lower jaw. Other configurations and combinations are also possible (e.g., an external force producing mechanism coupled between a TAD in the upper jaw and a lower tooth, or an external force producing mechanism coupled between a TAD in the lower jaw and an upper tooth) and fall within the scope of the present disclosure. Additionally, it shall be appreciated that the embodiments of external force producing mechanisms described herein can be modified in order to increase anchorage of one or more anterior teeth while inducing movement of one or more posterior teeth, or vice- versa. For example, a class III elastic can be used to support anchorage of one or more posterior teeth in the lower arch, e.g., with one end of the class III elastic coupled to a TAD in the posterior region of the upper arch so as to facilitate retraction of one or more anterior teeth in the lower arch. As another example, a class II elastic can be used to support anchorage of one or more posterior teeth in the upper arch, e.g., with one end of the class II elastic coupled to a TAD in the posterior region of the lower arch so as to facilitate retraction of one or more anterior teeth in upper arch.

[00161] The orthodontic shell appliances of the present disclosure can include teeth receiving cavities shaped to produce the forces, moments, and/or counter moments described herein. In many embodiments, a tooth receiving cavity comprises a position and/or orientation that is away from (e.g., different from) the current position and/or orientation of a corresponding received tooth, and the deflection and/or deformation of the tooth-receiving cavity due to the mismatch between the positions and/or orientations results in application of force to the tooth. The position and/or orientation of the tooth receiving cavity can be configured to apply a force system to the tooth in order to elicit repositioning of the tooth to a targeted position and/or orientation. The position and/or orientation of the tooth receiving cavity may be substantially similar to the targeted position and/or orientation of the received tooth. Alternatively, the position and/or orientation of the tooth receiving cavity may be away from (e.g., different from) a targeted position and/or orientation of the received tooth.

[00162] FIG. 3A shows a tooth position prior to completion of a stage of treatment, a target position upon completion of the stage and a position and orientation of a tooth receiving cavity to complete the stage of treatment. A received tooth of the plurality of teeth 10 comprises a position and orientation prior to placement of the appliance 1 1. A target position and orientation 200 of the tooth upon completion of the treatment stage can be determined with user input. Each of the plurality of tooth receiving cavities 101 of the polymeric shell appliance 1 1 comprises one or more of a position or orientation away from the target position and orientation along the targeted direction of movement 105. The targeted movement may comprise a movement vector, with the position and orientation of the tooth receiving cavity position away from the targeted position and orientation, for example. The received tooth may comprise one or more attachments and the polymeric shell may comprise one or more engagement structures to provide a differential moment as described herein.

[00163] FIG. 3B shows a polymeric shell appliance configured with one or more activation sites to store energy with a tooth at a target position and orientation comprising a non-extruded position and orientation of the tooth . In the depicted embodiment, the force is oriented in an intrusive direction and insufficient to intrude the tooth and sufficient to inhibit extrusion of the tooth. The tooth receiving cavity of the polymeric shell appliance comprises a shape profile 50 in a free standing unloaded configuration. When the polymeric shell appliance receives the tooth, the activation site of the polymeric shell appliance deflects to deflected shape profile 55 in order to store energy and conforms to the shape profile 60 of the received tooth. The stored energy provides a force 70 oriented in an intrusive direction that is insufficient to intrude the tooth.

[00164] Alternatively, the target position and orientation comprises a non- intruded position and orientation of the tooth, and the force is oriented in an extrusive direction and insufficient to extrude the tooth and sufficient to inhibit intrusion of the tooth.

[00165] FIG. 4 shows a method 400 of determining tooth receiving cavities of an appliance away from the target locations in accordance with embodiments. Some or all of the steps of the method 400 can be performed by one or more processors. In many embodiments, some or all of the steps of the method 400 are performed automatically without requiring user input. Alternatively or in addition, some or all of the steps of the method 400 may involve user input, e.g., received via a user input interface or device.

[00166] In step 410, an initial data set of initial locations of one or more teeth is received. The initial data set can represent an initial arrangement of the patient's teeth, for example. The initial data set can comprise one or more three-dimensional digital models of the teeth in an initial arrangement, e.g., obtained via scanning techniques known to one of skill in the art.

[00167] In a step 415, the initial data set is manipulated by the user to determine target locations of one or more teeth for each of a plurality of stages of treatment. In many embodiments, the user (e.g., an orthodontic practitioner or technician) inputs commands via a user interface (e.g., a user interface implemented as part of treatment planning software and presented to the user on a display) in order to specify the target locations for the teeth. For example, the teeth of the initial data set can be segmented from each other so as to be individually manipulable, and the user can move each tooth from the initial location to the target location. The user can view and teeth and determine that the locations of the teeth are suitable for each of a plurality of treatment stages.

[00168] In step 420, a target data set of target locations of the one or more teeth is received. The target data set can represent a target arrangement of the patient's teeth that is desired to be achieved through treatment with the appliances described herein.

[00169] The processor system may comprise instructions to include an attachment on one or more of the plurality of teeth. In many embodiments, the processor system comprises instructions to determine a shape of an attachment and an attachment engaging structure of the appliances.

[00170] Alternatively or in combination, the processor system may comprise instructions to include an external force producing mechanism coupled to one or more of the plurality of teeth. In many embodiments, the processor system comprises instructions to determine a shape and location of an external force producing mechanism in order to exert a targeted force onto one or more teeth, e.g., to back up anchorage of posterior teeth as described herein.

[00171] In step 430, one or more intermediate data sets representing one or more intermediate locations of the one or more teeth are generated. Each intermediate data set can correspond to a treatment stage comprising an intermediate arrangement of the teeth between the initial arrangement and the target arrangement. In many embodiments, the intermediate data sets represent a sequence of successive tooth arrangements traversed by the one or more teeth as they move from their initial locations to their target locations. Optionally, the intermediate data sets can be displayed to the user (e.g., as manipulable three-dimensional digital tooth models on a display) to allow the user to directly view and/or modify the intermediate

arrangements as desired. In alternative embodiments, the intermediate data sets are not displayed to the user, such that treatment staging of step 430 is performed automatically without involving any user input.

[00172] In step 440, one or more appliance geometries for moving the one or more teeth from the initial locations to the target locations are generated. The geometries can comprise geometries (e.g., positions, orientations, inner surface profiles, attachment engagement structures) for tooth receiving cavities of the appliances described herein. Various techniques can be used to determine appropriate appliance geometries for moving the teeth. For instance, each appliance can be designed to move one or more teeth from a previous arrangement to a subsequent arrangement in the sequence of initial, intermediate, and target arrangements.

Optionally, the appliance can be designed to retain one or more teeth when the locations of the teeth in the previous and subsequent arrangements do not change (e.g., anchor teeth). In many embodiments, the geometry of each appliance is shaped to impart a force system on each tooth (e.g., directly on the tooth surface or indirectly via tooth-mounted attachments) in order to elicit the desired tooth movement (or retention). The force system can comprise any suitable combination of forces, counter forces, moments, or counter moments, as provided herein. For example, the appliance geometry can be designed to elicit a paired moment and counter moment on a tooth (or a plurality of teeth) when worn by the patient in order to generate a differential moment for controlling tooth movement, as described herein. The processor may comprise instructions to include an attachment in response to a target differential moment to a tooth in order to move a tooth in a target direction. The processor may comprise instructions to include an external force producing mechanism in order to modify a force system applied to one or more teeth.

[00173] In many embodiments, the processor system comprises instructions to determine one or more forces as described herein. The processor system may comprise instructions to determine one or more of a first force about a first center of resistance of a first tooth, the first center of resistance of the first tooth, a first counter force of the first tooth, a first moment about the first tooth, a first counter force of the first tooth, a first counter moment of the first tooth, the first force opposite the second force, the first moment opposite the second moment, a sum of the first force and the second force, the sum of the first force along a targeted direction of tooth movement, and iterations thereof for the first tooth to move the first tooth in a targeted direction. The processor system can be configured to determine each of these forces for a second tooth, and similar forces for each of a plurality of teeth.

[00174] In many embodiments, the tooth arrangement of an appliance is away from (offset from or different from) the corresponding tooth arrangement desired to be achieved by wearing the appliance. For example, at least one tooth receiving cavity of the appliance can comprise a position and/or orientation away from the desired position and/or orientation of the corresponding received tooth. This offset between the appliance geometry and the corresponding desired tooth arrangement can allow for more precise control and application of force systems for moving (or retaining) teeth (e.g., via the application of differential moments). This approach can be advantageous compared to alternative approaches where the appliance geometry is shaped to match the desired tooth arrangement (e.g., the positions and/or orientations of tooth receiving cavities match the desired positions and/or orientations of the teeth). Tooth response data for achieved movements in response to a movement goal and related forces suitable for incorporation in accordance with embodiments disclosed herein are described in described in U.S. App. Ser. No. 12/623,340, filed on November 20, 2009, published as U.S. 2010/0138025 on June 3, 2010, entitled "Orthodontic systems and methods including parametric attachments" and U.S. App. Ser. No. 13/865,091, filed on April 17, 2013, published as U.S. 2013/0230818, entitled "Method and system for optimizing dental aligner geometry," the entire disclosures of which have been previously incorporated herein by reference. The appliance can be designed with tooth receiving cavities positioned and/or oriented in response to tooth movement data and the target tooth position for each of a plurality of teeth for each of a plurality of stages of the treatment. In many embodiments, the use of appliance geometries that do not match the corresponding tooth arrangements as described herein can improve the performance of orthodontic appliances for achieving planned tooth movements.

[00175] In many embodiments, the generated appliance geometries are not displayed to the user, such that the user only sees the sequence of successive tooth arrangements for moving the teeth, without seeing the corresponding appliance geometries used to achieve such arrangements. This can be beneficial for simplifying and streamlining the information that is presented to the user, particularly when the appliance geometries comprising the positions and orientations of the shape profiles of the tooth receiving cavities are offset from the desired tooth arrangements for each of a plurality of stages of treatment.

[00176] Optionally, following step 440, the generated appliance geometries can be output, e.g., as instructions for controlling a fabrication machine for manufacturing orthodontic appliances having the specified geometries, and optionally tooth attachments and/or external force producing mechanisms to be used in conjunction with the appliances.

[00177] Although the above steps show method 400 of determining appliance geometries in accordance with embodiments, a person of ordinary skill in the art will recognize many variations based on the teaching described herein. Some of the steps may comprise sub-steps. Many of the steps may be repeated as often as is beneficial. Some of the steps can be removed, and additional steps provided. One or more steps of the method 400 may be performed with any data processing system, such as the embodiments described herein. Some of the steps may be optional, such as step 430. The order of the steps can be varied. For example, steps 410, 415, 420, and 430 may be performed in any suitable order.

[00178] FIG. 5 is a simplified block diagram of a data processing system 500 that may be used in executing methods and processes described herein in accordance with embodiments. The data processing system 500 typically includes at least one processor 502 that communicates with one or more peripheral devices via bus subsystem 504. These peripheral devices typically include a storage subsystem 506 (memory subsystem 508 and file storage subsystem 514), a set of user interface input and output devices 518, and an interface to outside networks 516. This interface is shown schematically as "Network Interface" block 516, and is coupled to

corresponding interface devices in other data processing systems via communication network interface 524. Data processing system 500 can include, for example, one or more computers, such as a personal computer, workstation, mainframe, laptop, and the like.

[00179] The user interface input devices 518 are not limited to any particular device, and can typically include, for example, a keyboard, pointing device, mouse, scanner, interactive displays, touchpad, joysticks, etc. Similarly, various user interface output devices can be employed in a system of the invention, and can include, for example, one or more of a printer, display (e.g., visual, non-visual) system/subsystem, controller, projection device, audio output, and the like.

[00180] Storage subsystem 506 maintains the basic required programming, including computer readable media having instructions (e.g., operating instructions, etc.), and data constructs. The program modules discussed herein are typically stored in storage subsystem 506. Storage subsystem 506 typically includes memory subsystem 508 and file storage subsystem 514. Memory subsystem 508 typically includes a number of memories (e.g., RAM 510, ROM 512, etc.) including computer readable memory for storage of fixed instructions, instructions and data during program execution, basic input/output system, etc. File storage subsystem 514 provides persistent (non-volatile) storage for program and data files, and can include one or more removable or fixed drives or media, hard disk, floppy disk, CD-ROM, DVD, optical drives, and the like. One or more of the storage systems, drives, etc may be located at a remote location, such coupled via a server on a network or via the internet/World Wide Web. In this context, the term "bus subsystem" is used generically so as to include any mechanism for letting the various components and subsystems communicate with each other as intended and can include a variety of suitable components/systems that would be known or recognized as suitable for use therein. It will be recognized that various components of the system can be, but need not necessarily be at the same physical location, but could be connected via various local-area or wide-area network media, transmission systems, etc.

[00181] Scanner 520 includes any means for obtaining a digital representation (e.g., images, surface topography data, etc.) of a patient's teeth (e.g., by scanning physical models of the teeth such as casts 521 , by scanning impressions taken of the teeth, or by directly scanning the intraoral cavity), which can be obtained either from the patient or from treating professional, such as an orthodontist, and includes means of providing the digital representation to data processing system 500 for further processing. Scanner 520 may be located at a location remote with respect to other components of the system and can communicate image data and/or information to data processing system 500, for example, via a network interface 524. Fabrication system 522 fabricates appliances 523 based on a treatment plan, including data set information received from data processing system 500. Fabrication machine 522 can, for example, be located at a remote location and receive data set information from data processing system 500 via network interface 524.

[00182] While preferred embodiments of the present disclosure have been shown and described herein, it will be obvious to those skilled in the art that such embodiments are provided by way of example only. Numerous variations, changes, and substitutions will now occur to those skilled in the art without departing from the invention. It should be understood that various alternatives to the embodiments of the invention described herein may be employed in practicing the invention. It is intended that the following claims define the scope of the invention and that methods and structures within the scope of these claims and their equivalents be covered thereby.