WO2022268073A1 - 产生壳状牙齿矫治器的设计方案的方法 - Google Patents

产生壳状牙齿矫治器的设计方案的方法 Download PDF

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Publication number
WO2022268073A1
WO2022268073A1 PCT/CN2022/100124 CN2022100124W WO2022268073A1 WO 2022268073 A1 WO2022268073 A1 WO 2022268073A1 CN 2022100124 W CN2022100124 W CN 2022100124W WO 2022268073 A1 WO2022268073 A1 WO 2022268073A1
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Prior art keywords
shell
design
shaped dental
tooth
dental appliance
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PCT/CN2022/100124
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English (en)
French (fr)
Inventor
周可拓
郑轶刊
黄雷
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无锡时代天使医疗器械科技有限公司
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Priority claimed from CN202110716622.4A external-priority patent/CN115517790A/zh
Priority claimed from CN202110717119.0A external-priority patent/CN115517791A/zh
Priority claimed from CN202111218778.6A external-priority patent/CN115990066A/zh
Application filed by 无锡时代天使医疗器械科技有限公司 filed Critical 无锡时代天使医疗器械科技有限公司
Publication of WO2022268073A1 publication Critical patent/WO2022268073A1/zh

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    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
    • A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
    • A—HUMAN NECESSITIES
    • A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
    • A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
    • A61C7/08—Mouthpiece-type retainers or positioners, e.g. for both the lower and upper arch
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G06F30/23—Design optimisation, verification or simulation using finite element methods [FEM] or finite difference methods [FDM]

Definitions

  • the present application generally relates to a method of generating a design for a shell-shaped dental appliance.
  • Shell-shaped dental appliances made of polymer materials are becoming more and more popular due to the advantages of beauty, convenience and cleaning.
  • a design and manufacturing method of a shell-shaped dental appliance is to press a heated and softened polymer membrane material on a tooth model that matches the target tooth layout of a certain treatment step to form a shell-shaped tooth for the treatment step.
  • a dental appliance which is a one-piece shell that forms a cavity to accommodate the teeth.
  • the shell-shaped dental appliance When the shell-shaped dental appliance is worn on the patient's teeth, due to the difference between the patient's current tooth layout and the target tooth layout, the shell-shaped dental appliance will be elastically deformed, and accordingly, the The shell-like appliances apply elastic forces on the corresponding teeth to move the patient's teeth to the target tooth arrangement.
  • FIG. 1 schematically shows a shell-shaped dental appliance 11 and a corresponding dentition 13 .
  • One aspect of the present application provides a computer-executed method for generating a shell-shaped dental appliance design plan, which includes: obtaining a dental orthodontic treatment plan, which includes a series of successive orthodontic steps, and their orthodontic goals are sequentially A first intermediate tooth layout ...
  • a last intermediate tooth layout and a target tooth layout obtaining a reference design for a series of successive shell-shaped dental appliances corresponding to the series of successive orthodontic steps; calculating the series of successive tooth aligners Whether the reference design of the shell-shaped orthodontic appliance can achieve the corresponding orthodontic goal; and if the reference design of the shell-shaped orthodontic appliance of an orthodontic step cannot achieve the orthodontic goal of the orthodontic step, modify the shell-shaped orthodontic of the orthodontic step.
  • the geometry of the corresponding part of the reference design of the appliance is used to improve its force application, and the optimal design of the shell-shaped appliance for this orthodontic step is obtained.
  • the reference designs of the series of successive shell-shaped dental appliances are directly generated based only on the geometry of the orthodontic target of the series of successive orthodontic steps.
  • the geometry of the reference design of the series of successive shell-shaped dental appliances is respectively consistent with the treatment goals of the series of successive treatment steps.
  • the optimized design of the shell-shaped dental appliance differs from the corresponding reference design only in geometry.
  • the shell-shaped appliance forms a cavity for accommodating multiple teeth, and the portion of the appliance that accommodates a single tooth is called the tooth cavity of the tooth.
  • the optimal design of the shell-shaped appliance allows two adjacent teeth to Dental cavities of adjacent teeth partially overlap.
  • the optimal design of the shell-shaped dental appliance allows a partial overlap of tooth cavities in the range of 0.3-0.5 mm.
  • a shell-shaped dental appliance forms a cavity for accommodating multiple teeth and attachments fixed to the surface of the teeth.
  • the cavity is called the accessory cavity of the accessory, and the optimal design of the shell-shaped dental appliance allows the tooth cavity to partially overlap with the accessory cavity.
  • the computer-executed method for generating a shell-shaped dental appliance design scheme further includes: for each of the series of successive orthodontic steps, based on its initial tooth layout and target tooth layout, calculate and obtain The ideal force system required to reposition the teeth from the initial tooth layout to the target tooth layout; based on its initial tooth layout and the reference design of the shell-shaped dental appliance, the calculation of the reference design of the shell-shaped dental appliance worn in the A reference force system applied to the teeth of the initial tooth layout; and modifying the reference design based on the ideal force system and the reference force system to obtain the optimal design.
  • the computer-executed method for generating a shell-shaped dental appliance design scheme further includes: taking the ideal force system as the target, and based on given conditions, calculating and obtaining an optimal force system; and based on the The difference between the reference force system and the optimized force system is modified to obtain the optimal design by modifying the reference design.
  • the computer-executed method for producing a shell-shaped dental appliance design scheme is characterized in that it also includes: displaying one of the following selected orthodontic steps on the user interface according to user instructions: compensation force system, compensation design quantity, equivalent compensation design quantity and any combination thereof, wherein the compensation force system is the difference between the reference force system and the optimized force system, and the compensation design quantity is the reference design and The difference between the design quantities of the optimal design, the equivalent compensation design quantity is the compensation design quantity calculated based on the compensation force system.
  • the computer-executed method for generating a shell-shaped dental appliance design scheme further includes: displaying the patient's dental image on the user interface, wherein the dental dental image has a tooth with a compensation force system Marked to indicate one of the following: compensating force system, compensating design quantity, and equivalent compensating design quantity.
  • the given condition includes: the force limit of the shell-shaped dental appliance based on the given material and thickness.
  • the force system is the sum of static forces and moments.
  • the computer-executed method for generating a shell-shaped dental appliance design scheme further includes: obtaining a three-dimensional digital model representing the patient's initial tooth layout and a diagnostic conclusion provided by a dentist; The three-dimensional digital model of the layout and the diagnosis conclusion, generate the orthodontic treatment plan; and after obtaining the confirmation of the orthodontic treatment plan by the dentist, generate the series of successive shell-shaped dental treatment device reference design.
  • modifying the geometry of the corresponding part of the reference design of the shell-shaped dental appliance in the orthodontic step includes one of the following: changing the relative positional relationship of the tooth cavity, changing the geometry of the tooth cavity, and increasing the local pressure Points, adding local reinforcement structures, and any combination of the above, wherein the shell-shaped dental appliance forms a cavity to accommodate multiple teeth, and the part that accommodates a single tooth is called the tooth cavity of the tooth.
  • Yet another aspect of the present application provides a shell-like appliance system comprising a series of successive shell-like appliances, each for gradually repositioning teeth from an initial tooth layout to a first intermediate tooth layout.. . Finally the intermediate tooth layout up to the target tooth layout, wherein said series of successive shell-shaped dental appliances is obtained based on a reference design modification of a corresponding series of successive shell-shaped dental appliances, said modification is based on said one
  • the difference between the actual orthodontic effect and the expected orthodontic effect of the reference design of a series of successive shell-shaped dental appliances, the geometry of at least one of the series of successive shell-shaped dental appliances is different from the corresponding reference design, wherein,
  • the series of successive reference designs of shell-shaped dental appliances are directly generated based on the first intermediate tooth layout...the last intermediate tooth layout and the target tooth layout respectively.
  • the geometry of the reference design of the series of successive shell-shaped dental appliances coincides with the first intermediate tooth layout . . . the last intermediate tooth layout and the target tooth layout, respectively.
  • the actual treatment effect and the expected treatment effect are expressed in a static force system.
  • Yet another aspect of the present application provides a computer-executed method for generating a shell-shaped dental appliance design, which includes: acquiring the initial tooth layout and the target tooth layout of the first orthodontic step; acquiring the shell of the first orthodontic step The reference design of the shell-shaped dental appliance; the force system applied when the shell-shaped dental appliance of the reference design is worn on the patient's teeth in the initial tooth layout is recorded as the reference force system; based on the initial tooth layout and The target tooth layout is calculated to obtain an ideal force system for repositioning the teeth from the initial tooth layout to the target tooth layout when the shell-shaped dental appliance is required to be worn on the teeth in the initial tooth layout an applied force system; and based on the reference force system and the ideal force system, modifying the reference design to obtain an optimized design.
  • the reference design is generated directly based on the target tooth layout.
  • the geometry of the tooth-accommodating cavities of the reference design matches the target tooth layout.
  • the computer-executed method for generating the design of the shell-shaped dental appliance further includes: obtaining the initial tooth layout of the second treatment step and the optimal design of the shell-shaped dental appliance, wherein the second The orthodontic step is a previous orthodontic step of the first orthodontic step; and the initial tooth layout of the first orthodontic step is calculated based on the initial tooth layout of the second orthodontic step and the optimal design of the shell-shaped dental appliance.
  • the computer-executed method for generating the design of the shell-shaped dental appliance further includes: taking the ideal force system as the target, and calculating an optimal force system based on given conditions; and according to the The difference between the reference force system and the optimized force system is modified to obtain the optimal design by modifying the reference design.
  • the force system is the sum of static forces and moments.
  • the given condition includes: under the condition of given material and thickness, the limit value of orthodontic force that can be realized by the shell-shaped dental appliance.
  • the given condition further includes one of the following: the force limit of the anchorage teeth, root control requirements, vertical control requirements, and any combination of the above.
  • the modification includes one of the following: changing the relative positional relationship of tooth cavities, adding artificially designed structures, and a combination of the above, wherein the shell-shaped dental appliance forms a cavity for accommodating multiple teeth, which The part that houses a single tooth is called the dental cavity of that tooth.
  • the artificially designed structure includes one of the following: local modification, point force application structure, local reinforcement structure, and any combination of the above.
  • Figure 1 schematically shows a shell-shaped appliance and the corresponding dentition
  • Fig. 2 is a schematic flow chart of a manufacturing method of a shell-shaped dental appliance in an embodiment of the present application
  • Figure 3A schematically shows the optimized design of the shell-shaped dental appliance in one embodiment of the present application
  • Figure 3B schematically shows the additional force applied to the teeth when the shell-shaped dental appliance shown in Figure 3A is worn on the teeth;
  • Fig. 4 schematically shows the optimized design of the shell-shaped dental appliance in one embodiment of the present application
  • Fig. 5 is the operation interface of the computer program used to generate the design scheme of the shell-shaped dental appliance in an example of the present application
  • Fig. 6 is the operation interface of the computer program used to generate the design scheme of the shell-shaped dental appliance in another example of the present application.
  • FIG. 7 is a schematic block diagram of a design and manufacture system 200 for a shell-shaped dental appliance in an embodiment of the present application.
  • Orthodontic treatment using shell-shaped appliances is to wear multiple successive shell-shaped appliances in order to reposition the patient's teeth from the original layout to the first intermediate layout, the second intermediate layout... and finally Intermediate layouts to target layouts.
  • one aspect of the present application provides a new design and manufacturing method of shell-shaped dental appliances. Take for example shell appliances in two consecutive steps, namely a first shell appliance for repositioning teeth from a first tooth layout to a second tooth layout, and a shell appliance for repositioning said teeth from a A second shell-shaped appliance repositioning the second tooth layout to a third tooth layout, wherein the first tooth layout, the second tooth layout, and the third tooth layout are sequential tooth layouts.
  • the following method can be used to generate the design scheme of the shell-shaped dental appliance for the two consecutive orthodontic steps.
  • an original design of the first shell-shaped dental appliance is generated based on the first tooth layout and the second tooth layout.
  • the first ideal force system required from the first tooth layout to the second tooth layout is calculated, and the original design scheme (also referred to as the reference design scheme) of the first shell-shaped dental appliance can The achieved first reference force system, and the first optimized force system (calculated based on given conditions with the first ideal force system as the target).
  • an optimal design solution of the first shell-shaped dental appliance is generated.
  • the fourth layout may be different from the second layout. Then, based on the fourth tooth layout and the third tooth layout, the above operations are repeated to obtain the optimized design of the second shell-shaped dental appliance. Finally, the first and second shell-shaped dental aligners are manufactured using the optimal design plan control equipment of the first and second shell-shaped dental aligners.
  • the simplest example of an original design for a shell-shaped appliance is that the geometry of the tooth-accommodating cavities matches the target tooth layout for the corresponding orthodontic step.
  • the sequential first to third tooth layouts can be located at any stage of the treatment plan, for example, the first tooth layout can be the original tooth layout of the patient, or the shell-shaped teeth of a certain treatment step The tooth layout that can be achieved by the optimal design of the appliance.
  • each tooth in the original orthodontic plan is likely to be different from the tooth layout that can be achieved by the shell-shaped dental appliance manufactured by the method of the present application. Therefore, in this application, there are two groups of tooth layouts, one is a series of sequential tooth layouts of the orthodontic plan (that is, the tooth layout designed by dental professionals), and the other is the tooth layout that can be achieved by shell-shaped dental appliances. A series of successive tooth layouts.
  • FIG. 2 is a schematic flowchart of a manufacturing method 100 of a shell-shaped dental appliance in an embodiment of the present application.
  • first and second shell-shaped dental appliances are designed with the goal of repositioning the patient's teeth from a first configuration to a second configuration and then to a third configuration.
  • a first design solution of a first shell-shaped dental appliance is acquired.
  • the first design scheme is a design scheme of a single shell-shaped dental appliance, and is a reference design scheme with the design goal of repositioning the patient's teeth from the first layout to the second layout.
  • the geometry of the tooth-accommodating cavity of the shell-shaped dental appliance in the first design of the first shell-shaped dental appliance is the same as that of the patient's teeth in the second layout. match.
  • the first design scheme as a reference design scheme is not limited to this design, it can also be any other suitable design, for example, the design scheme of the shell-shaped dental appliance that only increases the design amount based on experience, the increase The design quantities of are not obtained through computational verification.
  • the first design of the first shell-shaped dental appliance may include the thickness and material properties of the membrane material used to make the shell-shaped dental appliance.
  • an ideal force system is calculated based on the first layout and the second layout.
  • the inventors of the present application believe that the static force system (including the static force and moment applied to each tooth) applied to the teeth when the shell-shaped dental appliance is worn on the teeth (assuming that the entire dentition is rigid) ) has a relatively definite relationship with the amount of tooth movement it can achieve. Therefore, in the case of known tooth movement, an ideal force system can be calculated inversely, if a shell-shaped dental appliance can exert the ideal force when worn on the patient's teeth in the first configuration , then the shell-like appliance can be considered capable of repositioning the patient's teeth from the first configuration to the second configuration.
  • the ideal force system can be calculated based on a simplified mathematical model.
  • the appliance-tooth-periodontal ligament system is a linear system, and the load has a linear relationship with the tooth movement; (2) the movement of the same tooth in all directions The load corresponding to the amount, and the load corresponding to the amount of tooth movement, satisfy the principle of linear superposition.
  • a matrix calculation tool can be used to perform simulation based on this simplified mathematical model to calculate the ideal force system.
  • a rigid constraint can be established between the outer boundary of the periodontal ligament and the origin of each tooth (that is, the origin of the local coordinate system of each tooth) (the relative motion of the two is the relative motion of two rigid bodies ), and impose corresponding displacement constraints on the origin of each tooth.
  • a rigid fixed boundary condition can be applied to its origin
  • the following displacement constraints can be imposed on its origin: the displacement in the design displacement direction is the design value multiplied by -1, and 0 in other directions.
  • k (i, j) is the item in the i-th row and the j-th column in the matrix K, which represents the local stiffness matrix between the origin of the i-th tooth and the six degrees of freedom of the j-th tooth,
  • the K matrix is a 84*84 matrix.
  • each value on the diagonal of the matrix K t can be obtained through simulation calculation of a single tooth forced displacement constraint. For example, corresponding to the single-step maximum movement u of each tooth in each given direction, the load L of the tooth in this direction can be obtained through simulation calculation, then the corresponding on the diagonal of the matrix K t Values are L/u.
  • u (i) is the item in the i-th row of the matrix U, representing the movement of the i-th tooth
  • u (i)1 ⁇ u (i)6 respectively represent the movement amount of the origin of the i-th tooth in the directions of three translational degrees of freedom and three rotational degrees of freedom (that is, the translational amounts along the x, y, and z axes and rotation amount),
  • f (i) is the item in the i-th row of the matrix F, representing the reverse force of the i-th tooth
  • corresponding to u (i)1 ⁇ u (i)6 , f (i)1 ⁇ f (i)6 respectively represent the force of the i-th tooth in the direction of three translation degrees of freedom and three rotation degrees of freedom and moment.
  • i and j represent tooth numbers.
  • a single jaw for example, upper jaw or lower jaw
  • the maximum value of i and j is 14.
  • the design and manufacture of the first shell-shaped dental appliance will be described below with an example in which only a single canine is displaced by 0.2 mm.
  • the One fang of the second layout was displaced 0.2 mm.
  • u (3)1 -0.2
  • other items in the matrix U are all 0, and the matrix U is substituted into the equation (1), and the determinant of 84*1 is calculated, and each item corresponds to 14 teeth Loads in six degrees of freedom.
  • the calculated ideal force system is that the load of the canine in the distal direction is 2N.
  • the force system that can be generated by the first design proposal of the first shell-shaped dental appliance is calculated.
  • the tooth-accommodating cavities of the first design of the first shell-shaped appliance coincide with the patient's teeth in the second configuration.
  • the force and the reaction force are mutual, in the example where the canines move 0.2mm away, there must be teeth other than the canines that are stressed when wearing the appliance of the first design, for example, the premolars are affected by the mesial directional force.
  • the canines when the appliance is worn, non-design forces other than the distal displacement of the canines will occur, for example, the canines may be subject to a moment of distal tilt.
  • the simplified mathematical model can be used to calculate the force system generated when the appliance of the first design is worn on the patient's teeth in the first layout, as the first reference force Tie.
  • each item of the K matrix used is jointly unique to the appliance material and the shape of the teeth (including the initial arrangement state of the teeth, the shape of the crown, and the shape of the root). Determined, denoted as K a matrix.
  • each item in the Ka matrix can be obtained by performing finite element simulation calculation on the wearing of the appliance, each simulation is for the maximum design quantity of a single tooth in one direction, and each simulation obtains 84 values, A column of the matrix K a is formed, and a total of 84 simulations are performed to form a complete matrix K a .
  • the appliance of the first design scheme cannot achieve the orthodontic goal (that is, the canines are moved away by 0.2 mm) on the one hand, and on the other hand, it may cause an unexpected amount of tooth movement.
  • the first design scheme is unqualified, therefore, a new design scheme of the appliance needs to be produced.
  • an optimized force system can be generated without changing the original correction path (that is, the second layout is still taken as the design target), and then based on the difference between the reference force system and the optimized force system, A second design solution is generated based on the first design solution.
  • the first optimal force system is generated based on the given constraint conditions with the first ideal force system as the target.
  • the following factors may be considered: the limit value of the orthodontic force that the orthodontic appliance can achieve, the orthodontic requirements (for example, root control requirements and vertical control requirements, etc.), And anchorage tooth force and so on.
  • the optimal force system can be set
  • the maximum deformation that the appliance can achieve in this direction ( That is, the maximum deformation that can be achieved before the appliance yields) is used as the movement amount in this direction, and the item on the main diagonal (that is, the load related to the corresponding tooth in the corresponding direction) is divided in the matrix K a Parameters) other items are cleared, based on the amount of movement and the modified matrix K a , the limit value of the orthodontic force that the appliance can achieve in the direction can be calculated according to equation (1) .
  • limits can be set on the moment loads of the teeth in the optimized force system based on the root control requirements of the tooth movement. For example, the ratio of force and moment loads on the same tooth in an optimized force system can be kept the same as in an ideal force system.
  • the limitation of torque based on root control requirements in addition to the above example of limiting the ratio of force and torque, can also simply limit the torque itself, making it smaller than a predetermined value , or limit the ratio of force and moment to a predetermined range, as long as the limitation of moment meets the control root requirement.
  • the load less than a certain critical value will not cause bone remodeling of the alveolar bone, that is to say, in this case, the teeth will not really move. Therefore, if the load on a tooth is less than said critical value, it can be regarded as an anchored tooth.
  • different teeth may have different critical values in different degrees of freedom directions.
  • the critical value of canine distal displacement can be 0.4N
  • the critical value of premolar proximal inclination can be 5Nmm.
  • the computer can automatically generate the first optimized force system based on the first reference force system and given constraints, with the first ideal force system as the target.
  • a second design solution is generated based on the first design solution and the difference between the first optimized force system and the first reference force system.
  • the first optimized force system is what the appliance of the second design scheme needs to achieve. Therefore, in one embodiment, the first optimized force system can be adjusted according to the difference between the first optimized force system and the first reference force system.
  • the design scheme is modified to obtain the second design scheme.
  • the difference between the first reference force system and the first optimization force system can be called the first compensation force system.
  • the first reference force system is denoted as S'
  • the first optimization force system is denoted as S target
  • the second A compensation force is denoted as S_d.
  • the process of generating the second design scheme is a process of iteratively finding an optimal solution.
  • the first design scheme may be modified by adjusting design quantities to obtain the second design scheme.
  • the adjustment of the design amount may be to adjust the pose of the corresponding teeth in the second layout as the basis of the appliance design, so that the adjusted second layout is relative to the first layout, and the position of the corresponding teeth The amount of displacement is adjusted accordingly.
  • the initial value of the compensation design quantity can be given according to the first compensation force system as the starting point of iterative optimization.
  • the initial value of the compensation design quantity can be as follows:
  • Canine distal displacement 0.02mm (the design amount of canine distal displacement of 0.2mm corresponds to the distal canine force of 0.9N, in order to obtain the canine distal force of 0.1N in the compensation force system, it is necessary to On the basis of the first design plan, increase the design amount by about 0.02mm);
  • Canine proximal inclination 1.5 degrees (in order to obtain an approximate inclination moment of 10Nmm in the compensation force system, it is necessary to increase the design of canine proximal inclination by 1.5 degrees on the basis of the first design scheme);
  • Premolar distal inclination 0.3 degrees (in order to obtain the -2Nmm premolar proximal inclination moment in the compensation force system, it is necessary to add 0.3 degrees of premolar distal inclination design on the basis of the first design scheme).
  • the introduction of these compensation design quantities may cause stress in other directions.
  • the compensation design quantity of canine proximal inclination will cause the incisor lingual inclination moment again, and its influence should be minimized in subsequent iterations.
  • a boundary constraint for each degree of freedom of each tooth may be given, for example, the tilt compensation amount of a single tooth may be limited to no more than 2 degrees.
  • a global constraint may also be given, for example, limiting the sum of the absolute values of the tilt compensation amounts of all teeth to not exceed 5 degrees.
  • an objective optimization function can be used to iteratively find the optimal solution to compensate the design quantity.
  • an objective optimization function may be defined to minimize the sum of squares of the compensation loads of all teeth (calculations may be given different weights for forces and moments).
  • the minimum solution of the nonlinear problem with constraints can be performed.
  • the sequential least squares programming method can be used to solve the problem.
  • the specific implementation can refer to Kraft D (1988) published in Tech.Rep.DFVLR-FB 88-28, DLR German Aerospace Center-Institute for Flight Mechanics, Koln, Germany "A Software Package for Sequential Quadratic Programming".
  • the final compensation design quantity can be obtained.
  • the canines are displaced by 0.2 mm
  • the following final compensation design values are calculated using the above method: the canines are proximally inclined 1.2 degrees and elongated by 0.05 mm, the incisor labial is inclined 0.4 degrees and depressed by 0.05 mm, and the first molar is depressed by 0.03 mm.
  • the final compensation design quantity is combined with the design quantity of the first design scheme to obtain the design quantity of the second design scheme.
  • the design quantities of the second design plan are as follows: the canines are displaced by 0.2 mm, proximally inclined by 1.2 degrees, and elongated by 0.05 mm, and the labial incisors are inclined by 0.4 degrees and depressed by 0.05 mm, the first molar depression was 0.03mm.
  • the shell-shaped dental appliance forms a cavity to accommodate multiple teeth, and the part corresponding to a tooth can be called the tooth cavity of the tooth.
  • the positional relationship of these tooth cavities determines the shell-shaped dental appliance to a certain extent.
  • the adjustment of the design amount refers to changing the applied force of the shell-shaped dental appliance by changing the positional relationship of these tooth cavities.
  • FIG. 3A schematically shows an optimal design 20 of a shell-shaped dental appliance in one embodiment of the present application, wherein the geometry of the cavity 23 of the tooth 21 (shown in dotted line) does not conform to the tooth 21 , compared with the geometry of the tooth 21, the geometry of the tooth cavity 23 is slightly narrowed at the upper right and slightly concave at the upper left.
  • FIG. 3B schematically shows the case where the shell-shaped dental appliance shown in FIG. 3A is worn on the teeth and undergoes deformation. It will generate additional force on the teeth 21 in the direction of the two arrows in the figure.
  • the local modification may be to modify the local geometry of the appliance design, so as to change the force system exerted by the appliance on the teeth. Different from adjusting the design volume, the geometric form of the partially modified part of the appliance is different from the corresponding crown, and the two no longer match.
  • increasing the local point force application structure is to form a convex point in the tooth cavity of the appliance.
  • the convex point abuts against the surface of the tooth to form a new force application point.
  • the local thickening may be to increase the thickness of a part of the appliance through an additive process, so as to change the mechanical properties of the part of the appliance.
  • the local modification may be to modify the local material of the appliance through a material modification process, so as to change the mechanical properties of the part of the appliance.
  • arranging a reinforcing rib is arranging a reinforcing rib at a predetermined position of the appliance, so as to change the mechanical properties of the corresponding part.
  • the operator and its corresponding effect can be preset in the computer program, so that the computer can The difference automatically selects the corresponding operator to modify the first design.
  • the operator can be set with a step size of 0.02mm, and the corresponding effect is a force of 0.1N.
  • an operator selection strategy can be set in the computer program, so that the computer can automatically select the operator in the iteration according to the strategy.
  • the second design proposal is designed to achieve the second layout
  • the actually achievable tooth layout may not match the second layout.
  • the design scheme of the orthodontic appliance needs to calculate the fourth layout that can be achieved by the second design scheme.
  • the second layout is the tooth layout in the original treatment plan.
  • the following method may be used to calculate the fourth layout that can be achieved by the second design scheme.
  • the amount D of orthodontic treatment can be defined by the following equation (9):
  • the load that the appliance applies to the tooth changes as the tooth moves.
  • the load x in order to simplify the calculation, when calculating the achieved amount of correction according to equation (9), the load x can be set constant, and its influence on the result can be balanced by other parameters.
  • f ij may be defined by the following equation (10):
  • a, T i,j , Y i,j , and Bi,j are all parameters, which can be preset based on experience, big data, and experimental tests. It should be noted that for different teeth and different treatment directions of the same case, each parameter may have different values.
  • N groups of parameters can be obtained (N is a natural number greater than or equal to 1). Therefore, N can be calculated accordingly. results D 1 , D 2 . . . D N . Then, its probability or weight can be calculated for each of the N results, and finally, based on the N results and their probabilities, the amount D of treatment achievement can be calculated.
  • the probability of each result can be calculated using the following method.
  • the probability of each outcome can be calculated according to the following equation (11):
  • the distal inclination moment of the canine is 3Nmm. Calculated according to the shape of the tooth, every 1° of inclination corresponds to a displacement of 0.1mm. If there are 3 groups of parameters as shown in Table 1 below, the achievement and probability of the corresponding 3 groups of canine distal tilt can be calculated:
  • the final far reaching amount is:
  • the correction amount of each tooth in each direction that can be achieved by the second design scheme can be calculated, and then the fourth layout can be calculated based on these correction amounts and the first layout.
  • the finite element analysis method can be used to wear the finite element model of the shell-shaped dental appliance on the jaw ( On the finite element model including teeth and periodontal tissue), the amount of orthodontic treatment can be obtained through simulation.
  • an orthodontic plan can include an accessory design plan, which includes the type of accessory, the location where the accessory is added (the tooth that needs to be added and the position where the accessory is added on the surface of the tooth), and the timing of adding the accessory (at which orthodontic step). add attachments), etc.
  • a complete set of shell-shaped dental appliance optimization design scheme (including a series of successive shell-shaped dental appliance designs) for realizing a dental treatment plan (including a series of successive orthodontic steps)
  • the difference between the optimal design of each shell-shaped dental appliance and the corresponding reference design is only in the geometry, that is to say, it does not change the design of the original orthodontic plan about the position and timing of adding accessories.
  • the orthodontic plan does not allow the tooth collision to exceed 0.2mm.
  • the optimally designed tooth collision of the shell-shaped dental appliance is allowed to exceed this threshold, for example, the threshold is increased to 0.3-0.5mm. This is because the shell-shaped appliance forms a cavity to accommodate each tooth, and the positional relationship of each tooth cavity determines the force applied to the teeth by the shell-shaped appliance to a certain extent, and the positions of the cavities of two adjacent teeth overlap. Overlap can provide additional compensating force, and under reasonable design, this will not make the two adjacent teeth collide during the orthodontic process.
  • the optimal design allows the partial overlapping depth range of the tooth cavities of two adjacent teeth to be greater than the design ideas of traditional shell-shaped dental appliances, and this is also applicable to the partial overlap of tooth cavities and accessory cavities (accessory cavities are Refers to the cavity of the shell-shaped dental appliance to accommodate the accessories fixed on the surface of the teeth).
  • FIG. 4 schematically shows an optimized design 30 of a shell-shaped dental appliance in an embodiment of the present application, which includes a tooth cavity 31 for accommodating teeth 33, and a tooth cavity 35 for accommodating teeth 37 , wherein the teeth 33 and 37 are two adjacent teeth, wherein the dotted line part shows the position of the tooth cavity 31 in the optimized design, and the tooth cavities 31 and 35 partially overlap.
  • the first and second shell-shaped dental appliances are manufactured by using the second and fourth design solution control devices.
  • the first and second shell-shaped dental appliances can be produced by using their control devices respectively.
  • the second and fourth designs may respectively include three-dimensional digital models representing the corresponding male molds, so they can be used to control equipment (for example , stereolithography molding equipment) to make these positive molds, and then press a film on the positive molds with hot pressing film forming technology to obtain the first and second shell-shaped dental appliances.
  • control equipment for example , stereolithography molding equipment
  • the second and fourth designs may respectively include three-dimensional digital models representing the first and second shell-shaped dental appliance, therefore, They can be used to control the 3D printing equipment to directly manufacture the first and second shell-shaped tooth aligners.
  • the simplified mathematical model is used to calculate the force system
  • the force system can also be calculated by using finite element analysis.
  • the finite element model of the shell-shaped dental appliance is worn on the rigid finite element model of the dentition, and the force system exerted by the shell-shaped dental appliance on each tooth is calculated by the finite element analysis method.
  • the method for producing the design scheme of the shell-shaped dental appliance of the present application is executed by a computer.
  • the user can interact with the computer through the user interface of the computer program, so that the computer can be based on a series of successive A series of calculations are performed on the tooth layout and a corresponding series of reference design schemes of the shell-shaped aligners to generate a series of optimized design schemes of the shell-shaped aligners.
  • the computer program can intuitively show the compensation force to the user in a visual way (for example, image or text or a combination of both) according to the instruction input by the user. system or compensation design volume.
  • FIG. 5 shows a user interface of the computer program in an embodiment of the present application.
  • the user interface displays the maxillary and mandibular teeth, and the compensation design amount is represented by color shade (ie, color purity).
  • the tooth with no compensation design amount is white, and the filling color of the tooth becomes darker with the increase of the compensation design amount.
  • the tooth with a small compensation design amount is filled with light red, and the tooth with a large compensation design amount is filled with dark red.
  • the purity change of any other color can also be used to represent the size of the compensation force system or compensation design quantity.
  • changes in hue or lightness can also be used to represent the compensation force system or the size of the compensation design.
  • the change of pattern density can also be used to represent the size of the compensation force system or compensation design.
  • any suitable graphical way can be used to represent the magnitude of the compensation force system or the compensation design quantity.
  • the total compensation force system or compensation design quantity can be displayed according to the user's choice, or only the compensation force system or compensation design quantity in the selected direction can be displayed, for example, axial inclination (including near inclination and far inclination), Torque (including anterior crown lingual inclination, anterior crown labial inclination, posterior crown inclination, and posterior crown buccal inclination), torsion, vertical (including elevation and depression), and combined (including compensation in all directions).
  • axial inclination including near inclination and far inclination
  • Torque including anterior crown lingual inclination, anterior crown labial inclination, posterior crown inclination, and posterior crown buccal inclination
  • torsion vertical (including elevation and depression), and combined (including compensation in all directions).
  • the compensation force system or compensation design quantity of the selected correction step can be displayed, and the compensation force system or compensation design quantity of each correction step can also be dynamically displayed one by one.
  • the maxillary teeth and mandibular teeth displayed on the user interface are in the actual tooth layout that can be achieved by the optimal design scheme of the corresponding orthodontic step.
  • the user interface can simultaneously display the upper and lower jaw dentition according to the user's selection, and can also display only one of the upper and lower jaw dentition according to the user's selection.
  • FIG. 6 shows a user interface of the computer program in another embodiment of the present application.
  • the user interface displays the upper and lower teeth, and places graphical markers, such as circular icons, on the teeth with compensation forces/amounts.
  • the computer program displays the compensation force system/compensation amount corresponding to the tooth in text form according to the icon selected by the user (for example, the user selects by clicking on the mouse).
  • any other suitable way to display the compensation force system/compensation amount can also be used, for example, the dental model of the original design can also be compared with the dental model of the final design. Overlay, fill in the difference with a color or pattern to indicate the teeth where there is a compensating force/amount.
  • the force system can also be optimized through artificially designed structures, for example, artificially designed structures such as local modification, local point force structure, local thickening, and reinforcing ribs. Artificially designed structures are different. Artificially designed structures based on the natural geometry of teeth. In the case of using these modification methods, if only the compensation design amount is displayed, the change of the tooth movement amount cannot be fully reflected.
  • artificially designed structures such as local modification, local point force structure, local thickening, and reinforcing ribs.
  • Artificially designed structures are different. Artificially designed structures based on the natural geometry of teeth. In the case of using these modification methods, if only the compensation design amount is displayed, the change of the tooth movement amount cannot be fully reflected.
  • the compensation force system can be transformed into an equivalent compensation design amount (that is, assuming that the compensation force system is realized only by adjusting the design amount,
  • the corresponding compensation design quantity is calculated based on the compensation force system, which is regarded as the equivalent compensation design quantity), and the compensation design quantity or equivalent compensation design quantity can be displayed according to the user's choice.
  • Yet another aspect of the present application provides a shell-shaped dental appliance design and manufacturing system. Dentists, shell-shaped dental appliance designers, and production managers exchange data through the system, and use the system to complete shell-shaped teeth based on relevant data. Device design and production.
  • FIG. 7 is a schematic block diagram of a design and manufacture system 200 for a shell-shaped dental appliance in an embodiment of the present application.
  • the design and manufacture system 200 of the shell-shaped dental appliance includes a client 201, a customer management system 203, a medical design order management system 205, a medical design system 207, a mechanical calculation system 209, a production order management system 211, a production design system 213 and a production control system 215.
  • the client 201 is a computer terminal of a dentist, and in one embodiment, it may be a computer installed with a client computer program. Dentists can propose design requirements for orthodontic solutions through the client 201 .
  • client 201 Although only one client 201 is shown in FIG. 7 , it can be understood that multiple clients 201 can be provided for use by different dentists.
  • the customer management system 203 stores and manages the authority of the dentist and the data of the patient, and acts as an interface between various subsystems.
  • the dentist After the dentist completes the diagnosis of a patient who needs orthodontic treatment, he can send information such as a three-dimensional digital model representing the patient's current tooth layout and diagnostic conclusions (for example, requirements for orthodontic treatment) through the client 201.
  • information such as a three-dimensional digital model representing the patient's current tooth layout and diagnostic conclusions (for example, requirements for orthodontic treatment) through the client 201.
  • diagnostic conclusions for example, requirements for orthodontic treatment
  • the customer management system 203 After the customer management system 203 receives the order from the dentist, it sends it to the medical design order management system 205, which distributes the design order to the corresponding medical design personnel.
  • the medical design system 207 can be used to generate an orthodontic treatment plan (from the current tooth layout to the target tooth layout) based on the three-dimensional digital model representing the patient's current tooth layout and diagnostic conclusions. All tooth layouts) and the corresponding shell-shaped aligner reference design scheme.
  • the shell-shaped appliance reference design may be a series of successive shell-shaped appliances matching the series of sequential tooth layouts.
  • the medical design system 207 may be a computer installed with a computer program for generating orthodontic treatment plans and reference designs for shell-shaped dental appliances. Although only one medical design system 207 is shown in FIG. 7 , it can be understood that multiple medical design systems can be provided for use by multiple medical designers respectively.
  • the customer management system 203 will send a notification to the client 201 after receiving the orthodontic treatment plan, and the dentist can check the orthodontic treatment plan on the client 201 . If the dentist thinks that the orthodontic treatment plan is unreasonable, he can propose a modification suggestion through the client 201, and the customer management system 203 sends the modification suggestion to the medical design order management system 205, and the medical design personnel based on the The above revisions suggest a redesign of the orthodontic treatment plan until it meets the stated dentist's requirements.
  • the customer management system 203 After the dentist confirms the orthodontic treatment plan, the customer management system 203 will send a notification to the medical design order management system 205, and the orthodontic treatment plan and its corresponding shell-shaped dental appliance reference design plan will be It is sent to the mechanical calculation system 209, which generates the final shell-shaped dental appliance design scheme according to the method of the present application, and sends it to the customer management system 203.
  • the customer management system 203 will send the final design of the shell-shaped dental appliance to the production order management system 211, which will be sent to the production design system 213 to generate A series of corresponding three-dimensional digital models of the positive molds required for production are then sent to the corresponding production control system 215, which controls the production equipment to manufacture a corresponding series of shell-shaped dental appliances.
  • the production order management system 211 and the production design system 213 can run on the same computing device, and for example, the medical order management system 205 , customer management system 203 and production order management system 211 can run on the same computing device.
  • some subsystems may be located in different locations, and these subsystems may be connected through a network.
  • the mechanical calculation system 209 will not change the orthodontic treatment scheme confirmed by the dentist , based on factors such as the mechanical properties of the material, modify the reference design scheme of the shell-shaped dental appliance, and obtain the optimized design scheme of the shell-shaped dental appliance that can realize the orthodontic treatment plan.
  • initial tooth layout that is, the patient's tooth layout before orthodontic treatment
  • target tooth layout that is, the tooth layout expected to be achieved by the orthodontic treatment plan
  • initial tooth layout that is, the initial tooth layout of this orthodontic step
  • target tooth layout that is, the desired tooth layout of this orthodontic step

Abstract

一种计算机执行的产生壳状牙齿矫治器设计方案的方法，其包括：获取牙齿正畸治疗方案，它包括一系列逐次的矫治步骤，它们的矫治目标依次为逐次的第一中间牙齿布局……最后中间牙齿布局以及目标牙齿布局；获取与一系列逐次的矫治步骤相对应的一系列逐次的壳状牙齿矫治器的参考设计；计算一系列逐次的壳状牙齿矫治器的参考设计是否能够达成对应的矫治目标；以及若一个矫治步骤的壳状牙齿矫治器的参考设计无法达成该矫治步骤的矫治目标，则修改该矫治步骤的壳状牙齿矫治器的参考设计相应部分的几何形态，以改善其施力，得到该矫治步骤的壳状牙齿矫治器的优化设计。

Description

产生壳状牙齿矫治器的设计方案的方法 技术领域
本申请总体上涉及一种产生壳状牙齿矫治器的设计方案的方法。
背景技术
由于美观、便捷以及利于清洁等优点，以高分子材料制成的壳状牙齿矫治器越来越受欢迎。
壳状牙齿矫治器的一种设计和制作方法是，在与某一矫治步的目标牙齿布局相吻合的牙齿模型上，将经加热软化的高分子膜片材料压膜形成该矫治步的壳状牙齿矫治器，其为一体的壳状，形成容纳牙齿的空腔。当该壳状牙齿矫治器佩戴于患者牙齿上时，由于患者当前牙齿布局与所述目标牙齿布局之间存在差异，将导致所述壳状牙齿矫治器发生弹性变形，相应地，发生弹性变形的壳状牙齿矫治器在对应的牙齿上施加弹性力，以将患者牙齿移动到所述目标牙齿布局。图1示意性地展示了壳状牙齿矫治器11和对应的牙列13。
本申请的发明人认为，这种壳状牙齿矫治器的设计仍停留在几何设计阶段，缺乏对牙齿在矫治过程中受力情况的分析，尤其缺乏对受力状态下牙齿移动的验证。因此，这种方案可能导致以下问题：(1)单步矫治后牙齿的真实移动位置与设计的位置不一致。目前的一种方案是，将上一矫治步牙齿的设计位姿(即目标位姿)作为下一矫治步排牙设计的输入(即初始位姿)，造成每一矫治步产生的设计位移量与真实位移量的偏差逐步累积。当该偏差累积到一定程度后，会严重影响壳状牙齿矫治器矫治能力的表达。(2)由于排牙设计不考虑壳状牙齿矫治器的力学性能，设计过程中缺乏对牙齿施力的验证，因此，无法完全规避诸如矫治施力过大及施力无法实现等风险。
为了克服以上问题，出现了一种将牙齿矫治力系纳入考虑的壳状牙齿矫治器 的设计方法，其通过改变牙齿移动路径使牙齿受力达到预期。为了满足力学性能，医生在考虑分步时不得不在咬合关系、过程控制等方面进行妥协，这使得临床治疗方案受到限制。
因此，有必要提供一种新的壳状牙齿矫治器的设计和制作方法，以解决上述问题。
发明内容
本申请的一方面提供了一种计算机执行的产生壳状牙齿矫治器设计方案的方法，其包括：获取牙齿正畸治疗方案，它包括一系列逐次的矫治步，它们的矫治目标依次为逐次的第一中间牙齿布局...最后中间牙齿布局以及目标牙齿布局；获取与所述一系列逐次的矫治步相对应的一系列逐次的壳状牙齿矫治器的参考设计；计算所述一系列逐次的壳状牙齿矫治器的参考设计是否能够达成的对应的矫治目标；以及若一个矫治步的壳状牙齿矫治器的参考设计无法达成该矫治步的矫治目标，则修改该矫治步的壳状牙齿矫治器的参考设计相应部分的几何形态，以改善其施力，得到该矫治步的壳状牙齿矫治器的优化设计。
在一些实施方式中，所述一系列逐次的壳状牙齿矫治器的参考设计是分别仅基于所述一系列逐次的矫治步的矫治目标的几何形态直接产生。
在一些实施方式中，所述一系列逐次的壳状牙齿矫治器的参考设计的几何形体分别与所述一系列逐次的矫治步的矫治目标相吻合。
在一些实施方式中，所述壳状牙齿矫治器的优化设计与对应的参考设计的区别仅在于几何形态。
在一些实施方式中，壳状牙齿矫治器形成容纳多颗牙齿的空腔，其容纳单颗牙齿的部分称为该牙齿的牙齿空腔，所述壳状牙齿矫治器的优化设计允许两颗相邻牙齿的牙齿空腔局部重叠。
在一些实施方式中，所述壳状牙齿矫治器的优化设计允许的牙齿空腔的局部重叠的范围为0.3～0.5mm。
在一些实施方式中，壳状牙齿矫治器形成容纳多颗牙齿以及固定于牙齿表面的附件的空腔，其容纳单颗牙齿的部分称为该牙齿的牙齿空腔，其容纳某一附件的空腔称为该附件的附件空腔，所述壳状牙齿矫治器的优化设计允许牙齿空腔与附件空腔局部重叠。
在一些实施方式中，所述的计算机执行的产生壳状牙齿矫治器设计方案的方法还包括：对于所述一系列逐次的矫治步的每一个，基于其初始牙齿布局和目标牙齿布局，计算获得将牙齿从该初始牙齿布局重新定位到该目标牙齿布局所需的理想力系；基于其初始牙齿布局以及壳状牙齿矫治器的参考设计，计算获得该参考设计的壳状牙齿矫治器佩戴于处于该初始牙齿布局的牙齿上时施加于牙齿的参考力系；以及基于所述理想力系和参考力系修改所述参考设计得到所述优化设计。
在一些实施方式中，所述的计算机执行的产生壳状牙齿矫治器设计方案的方法还包括：以所述理想力系为目标，基于给定的条件，计算获得优化力系；以及基于所述参考力系和所述优化力系之差，修改所述参考设计，得到所述优化设计。
在一些实施方式中，所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，它还包括：根据用户指令，在用户界面展示选中的矫治步的以下之一：补偿力系、补偿设计量、等效补偿设计量以及它们的任意组合，其中，所述补偿力系是所述参考力系和所述优化力系之差，所述补偿设计量是所述参考设计和所述优化设计的设计量之差，所述等效补偿设计量是基于所述补偿力系计算得到的补偿设计量。
在一些实施方式中，所述的计算机执行的产生壳状牙齿矫治器设计方案的方法还包括：在用户界面展示所述患者的牙颌图像，其中，该牙颌图像中具有补偿力系的牙齿上带有标记，以指示以下之一：补偿力系、补偿设计量以及等效补偿设计量。
在一些实施方式中，所述给定条件包括：基于给定材料和厚度，壳状牙齿矫治器的受力极限。
在一些实施方式中，所述力系是静态的力和力矩的总和。
在一些实施方式中，所述的计算机执行的产生壳状牙齿矫治器设计方案的方法还包括：获取牙科医生提供的表示患者初始牙齿布局的三维数字模型以及诊断结论；基于所述表示患者初始牙齿布局的三维数字模型以及所述诊断结论，产生所述牙齿正畸治疗方案；以及在获取所述牙科医生对所述牙齿正畸治疗方案的确认后，产生所述一系列逐次的壳状牙齿矫治器的参考设计。
在一些实施方式中，修改所述矫治步的壳状牙齿矫治器的参考设计相应部分的几何形态包括以下之一：改变牙齿空腔的相对位置关系，改变牙齿空腔的几何形态，增加局部压力点，增加局部加强结构，以及以上的任意组合，其中，壳状牙齿矫治器形成容纳多颗牙齿的空腔，其容纳单颗牙齿的部分称为该牙齿的牙齿空腔。
本申请的又一方面提供了一种壳状牙齿矫治器系统，它包括一系列逐次的壳状牙齿矫治器，分别用于将牙齿逐渐地从初始牙齿布局重新定位到第一中间牙齿布局...最后中间牙齿布局直至目标牙齿布局，其中，所述一系列逐次的壳状牙齿矫治器是基于对应的一系列逐次的壳状牙齿矫治器的参考设计修改获得，所述修改是基于所述一系列逐次的壳状牙齿矫治器的参考设计的实际矫治效果与期望的矫治效果之差，所述一系列逐次的壳状牙齿矫治器的至少一个的几何形态不同于对应的参考设计，其中，所述一系列逐次的壳状牙齿矫治器的参考设计是分别基于所述第一中间牙齿布局...最后中间牙齿布局以及目标牙齿布局直接产生。
在一些实施方式中，所述一系列逐次的壳状牙齿矫治器的参考设计的几何形态分别与所述第一中间牙齿布局...最后中间牙齿布局以及目标牙齿布局相吻合。
在一些实施方式中，所述实际矫治效果和期望的矫治效果是以静态力系表达。
本申请的又一方面提供了一种计算机执行的产生壳状牙齿矫治器设计方案 的方法，其包括：获取第一矫治步的初始牙齿布局和目标牙齿布局；获取所述第一矫治步的壳状牙齿矫治器的参考设计；计算所述参考设计的壳状牙齿矫治器佩戴于处于所述初始牙齿布局的患者牙齿上时施加的力系，记为参考力系；基于所述初始牙齿布局和目标牙齿布局计算得到理想力系，所述理想力系是将牙齿从所述初始牙齿布局重新定位到所述目标牙齿布局，要求壳状牙齿矫治器佩戴于处于所述初始牙齿布局的牙齿上时施加的力系；以及基于所述参考力系和理想力系，修改所述参考设计，得到优化设计。
在一些实施方式中，所述参考设计是基于所述目标牙齿布局直接产生。
在一些实施方式中，所述参考设计的容纳牙齿的空腔的几何形态与所述目标牙齿布局相吻合。
在一些实施方式中，所述的计算机执行的产生壳状牙齿矫治器设计方案的方法还包括：获取第二矫治步的初始牙齿布局和壳状牙齿矫治器的优化设计，其中，所述第二矫治步是所述第一矫治步的前一矫治步；以及基于所述第二矫治步的初始牙齿布局和壳状牙齿矫治器的优化设计，计算得到所述第一矫治步的初始牙齿布局。
在一些实施方式中，所述的计算机执行的产生壳状牙齿矫治器设计方案的方法还包括：以所述理想力系为目标，基于给定的条件，计算得到优化力系；以及根据所述参考力系和所述优化力系之差修改所述参考设计，得到所述优化设计。
在一些实施方式中，所述力系是静态的力和力矩的总和。
在一些实施方式中，所述给定的条件包括：在给定材料和厚度的情况下，壳状牙齿矫治器所能实现的矫治力极限值。
在一些实施方式中，所述给定的条件还包括以下之一：支抗牙受力极限、控根要求、垂直向控制要求以及以上的任意组合。
在一些实施方式中，所述修改包括以下之一：改变牙齿空腔的相对位置关系，，添加人工设计结构以及以上的组合，其中，壳状牙齿矫治器形成容纳多颗牙齿的 空腔，其容纳单颗牙齿的部分称为该牙齿的牙齿空腔。
在一些实施方式中，所述人工设计结构包括以下之一：局部修形、点施力结构、局部加强结构以及以上的任意组合。
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以下将结合附图及其详细描述对本申请的上述及其他特征作进一步说明。应当理解的是，这些附图仅示出了根据本申请的若干示例性的实施方式，因此不应被视为是对本申请保护范围的限制。除非特别指出，附图不必是成比例的，并且其中类似的标号表示类似的部件。
图1示意性地展示了壳状牙齿矫治器和对应的牙列；
图2为本申请一个实施例中的壳状牙齿矫治器的制作方法的示意性流程图；
图3A示意性地展示了本申请一个实施例中壳状牙齿矫治器的优化设计；
图3B示意性地展示了图3A所示壳状牙齿矫治器的佩戴于牙齿上时对牙齿额外施加的力；
图4示意性地展示了本申请一个实施例中壳状牙齿矫治器的优化设计；
图5为本申请一个例子中用于产生壳状牙齿矫治器设计方案的计算机程序的操作界面；
图6为本申请又一例子中用于产生壳状牙齿矫治器设计方案的计算机程序的操作界面；以及
图7为本申请一个实施例中的壳状牙齿矫治器设计制造系统200的示意性模块图。
具体实施方式
以下的详细描述中引用了构成本说明书一部分的附图。说明书和附图所提及的示意性实施方式仅仅出于是说明性之目的，并非意图限制本申请的保护范围。在本申请的启示下，本领域技术人员能够理解，可以采用许多其他实施方式，并且可以对所描述实施方式做出各种改变，而不背离本申请的主旨和保护范围。应当理解的是，在此说明并图示的本申请的各个方面可以按照很多不同的配置来布置、替换、组合、分离和设计，这些不同配置都在本申请的保护范围之内。
利用壳状牙齿矫治器的牙科正畸治疗，是按秩序佩戴多个逐次的壳状牙齿矫治器，以将患者牙齿从原始布局逐次地重新定位到第一中间布局、第二中间布局……最后中间布局直至目标布局。
为了克服现有的壳状牙齿矫治器的设计方法所存在的不足之处，本申请的一方面提供了一种新的壳状牙齿矫治器的设计和制作方法。以两个连续的矫治步的壳状牙齿矫治器为例，即用于将牙齿从第一牙齿布局重新定位到第二牙齿布局的第一壳状牙齿矫治器，以及用于将所述牙齿从所述第二牙齿布局重新定位到第三牙齿布局的第二壳状牙齿矫治器，其中，所述第一牙齿布局、第二牙齿布局及第三牙齿布局为逐次的牙齿布局。在一个实施例中，可以利用以下方法产生所述两个连续的矫治步的壳状牙齿矫治器的设计方案。
首先，基于所述第一牙齿布局和第二牙齿布局产生所述第一壳状牙齿矫治器的原始设计方案。接着，计算得到从所述第一牙齿布局到所述第二牙齿布局所需的第一理想力系，所述第一壳状牙齿矫治器的原始设计方案(也称为参考设计方案)所能达成的第一参考力系，以及第一优化力系(以所述第一理想力系为目标，基于给定条件计算得到)。然后，根据所述第一优化力系与第一参考力系之差，基于所述第一壳状牙齿矫治器的原始设计方案，产生所述第一壳状牙齿矫治器的优化设计方案。接着，计算所述第一壳状牙齿矫治器的优化设计方案所能达成的第四牙齿布局，其中，该第四布局可能与所述第二布局不同。然后，基于所述第 四牙齿布局和第三牙齿布局重复以上操作，获得所述第二壳状牙齿矫治器的优化设计方案。最后，利用所述第一和第二壳状牙齿矫治器的优化设计方案控制设备制作所述第一和第二壳状牙齿矫治器。
在一个实施例中，一个壳状牙齿矫治器的原始设计方案的一个最简单的例子是其容纳牙齿的空腔的几何形态与对应矫治步的目标牙齿布局吻合。
可以理解，所述逐次的第一至第三牙齿布局可以是位于矫治方案的任何阶段，例如，所述第一牙齿布局可以是患者的原始牙齿布局，也可以是某一矫治步的壳状牙齿矫治器的优化设计方案所能达成的牙齿布局。
需要说明的是，原始矫治方案中的各牙齿布局很可能与利用本申请的方法制作获得的壳状牙齿矫治器所能达成的牙齿布局有差异。因此，在本申请中，存在两组牙齿布局，一组是矫治方案的一系列逐次的牙齿布局(即由牙科专业人员设计的牙齿布局)，另一组是壳状牙齿矫治器所能够达成的一系列逐次的牙齿布局。
请参图2，为本申请一个实施例中的壳状牙齿矫治器的制作方法100的示意性流程图，在下面的例子中，仅对两个连续矫治步的壳状牙齿矫治器的制作进行了说明，分别记为第一和第二壳状牙齿矫治器，它们是以将患者牙齿从第一布局重新定位到第二布局再重新定位到第三布局为目标进行设计。
在101中，获取第一壳状牙齿矫治器的第一设计方案。
所述第一设计方案是单个壳状牙齿矫治器的设计方案，是以把患者牙齿从第一布局重新定位到第二布局为设计目标的参考设计方案。
在一个实施例中，所述第一壳状牙齿矫治器的第一设计方案中的壳状牙齿矫治器的容纳牙齿的空腔的几何形态与处于所述第二布局的所述患者的牙齿相吻合。可以理解，作为参考设计方案的所述第一设计方案并不限于该设计，它也可以是任意其他合适的设计，例如，仅基于经验增加了设计量的壳状牙齿矫治器设计方案，该增加的设计量不是通过计算验证获得。
在一个实施例中，所述第一壳状牙齿矫治器的第一设计方案可以包括用于制 作壳状牙齿矫治器的膜片材料的厚度及其材料性能。
在103中，基于所述第一布局和第二布局计算理想力系。
基于大量的研究和实验，本申请的发明人认为壳状牙齿矫治器佩戴于牙齿上时(假设整个牙列是刚性的)施加于牙齿的静态力系(包括施加于各牙齿的静态力和力矩)与它所能达成的牙齿移动量之间存在比较确定的关系。因此，在已知牙齿移动量的情况下，可以反向计算出一个理想力系，若一壳状牙齿矫治器在佩戴于处于所述第一布局的所述患者牙齿上时能够施加该理想力系，那么，可以认为该壳状牙齿矫治器能够把所述患者牙齿从所述第一布局重新定位到所述第二布局。
在一个实施例中，可以基于简化数学模型计算所述理想力系。
利用简化数学模型计算力系时，可以基于以下假设：(1)矫治器-牙齿-牙周膜系统为线性系统，载荷与牙齿移动量呈线性关系；(2)同一颗牙齿在各方向的移动量所对应的载荷，以及各牙齿移动量所对应的载荷，满足线性叠加原则。
在一个实施例中，可以利用矩阵计算工具基于这个简化的数学模型进行仿真，以计算所述理想力系。在一个实施例中，在仿真中，可以在牙周膜外边界与各牙原点(即各牙齿的局部坐标系的原点)之间建立刚性约束(两者的相对运动为两个刚体的相对运动)，并对各牙的原点施加相应的位移约束。其中，对于支抗牙，可以对其原点施加刚性固定边界条件，对于移动牙，可以对其原点施加以下位移约束：在设计位移方向上的位移为设计量乘-1，其余方向为0。
在全局坐标系下，可以建立各牙原点沿各方向的位移和该点的约束反力之间的刚度关系，由以下等式(1)表达：
KU＝F       等式(1)
其中，
Figure PCTCN2022100124-appb-000001
其中，k (i，j)为矩阵K中第i行第j列的项，代表第i颗牙齿的原点和第j颗牙齿的六个自由度之间的局部刚度矩阵，
Figure PCTCN2022100124-appb-000002
单颌共有14颗牙，每颗牙有6个自由度，因此，K矩阵是一个84*84的矩阵。
在一个实施例中，计算理想力系时，由于不存在矫治器，所采用的K矩阵中仅主对角线上的项为非零项，其余均为零项，将该矩阵记为K t。在一个实施例中，所述矩阵K t的所述对角线上的每一个数值，可以通过单牙强制位移约束的仿真计算获取。例如，对应每一颗牙齿在每一给定方向的单步最大移动量u，通过仿真计算可以获得该牙齿在该方向的载荷L，则所述矩阵K t的所述对角线上的对应数值为L/u。
其中，
Figure PCTCN2022100124-appb-000003
其中，u (i)为矩阵U中第i行的项，代表第i颗牙齿的移动量，
Figure PCTCN2022100124-appb-000004
其中，u (i)1～u (i)6分别代表第i颗牙齿的原点在三个平移自由度和三个旋转自由度方向上的移动量(即沿x、y、z轴的平移量和旋转量)，
Figure PCTCN2022100124-appb-000005
其中，f (i)为矩阵F中第i行的项，代表第i颗牙齿的反向力，
Figure PCTCN2022100124-appb-000006
其中，与u (i)1～u (i)6相对应，f (i)1～f (i)6分别代表第i颗牙齿在三个平移自由度和三个旋转自由度方向上的力和力矩。
其中，i和j代表牙齿编号，在该实施例中，只针对单颌(例如，上颌或下颌)进行仿真，因此，i和j的最大值为14。
若存在缺牙的情况，可以将上述矩阵中对应的项赋值为0。
为了便于说明，下面以仅单颗尖牙远移0.2mm的例子对所述第一壳状牙齿矫治器的设计和制作进行说明，在该例子中，与所述第一布局相比，所述第二布局的一颗尖牙远移了0.2mm。
在上述例子中，u (3)1＝-0.2，矩阵U中的其他项均为0，将矩阵U代入方程式(1)，计算得到84*1的行列式，其各项分别对应14颗牙齿在六个自由度方向上的载荷。计算得到理想力系为所述尖牙在远中方向上的载荷为2N。
在105中，计算所述第一壳状牙齿矫治器的第一设计方案所能够产生的力系。
在一个实施例中，所述第一壳状牙齿矫治器的第一设计方案的容纳牙齿的空腔与处于所述第二布局的所述患者的牙齿相吻合。
由于力与反作用力是相互的，在所述尖牙远移0.2mm的例子中，佩戴所述第一设计方案的矫治器时必然有尖牙以外的牙齿受力，例如，前磨牙受到近中方向的力。另外，佩戴所述矫治器时将产生尖牙远移之外的非设计受力，例如，尖牙可能受到远倾的力矩。
在一个实施例中，可以利用所述简化数学模型计算得到所述第一设计方案的 矫治器佩戴于处于所述第一布局的所述患者牙齿上时所产生的力系，作为第一参考力系。
利用所述简化数学模型计算矫治器所能产生的力系时，所采用的K矩阵的每一个项是由矫治器材料、牙齿形态(包括牙齿初始排列状态、牙冠形态、牙根形态)共同唯一决定的，记为K a矩阵。在一个实施例中，K a矩阵中的每一项可以通过对矫治器的佩戴进行有限元仿真计算获得，每次仿真是针对单牙单方向的最大设计量，每次仿真获得84个数值，构成矩阵K a的一个列，共进行84次仿真，构成完整的矩阵K a。
对于上述尖牙远移0.2mm的例子，在给定用于制作矫治器的膜片材料的性能和厚度的情况下，计算得到如下参考力系：
尖牙远中方向受力f (3)1’＝0.9N(在理想力系中，尖牙远中方向受力f (3)1＝2N)；
尖牙远中力矩f (3)4’＝10Nmm(在理想力系中，尖牙远中力矩f (3)4＝0Nmm)；
前磨牙近中力矩f (4)4’＝7Nmm(在理想力系中，前磨牙近中力矩f (4)4＝0Nmm)。
基于所述第一参考力系可知，所述第一设计方案的矫治器一方面无法实现矫治目标(即将尖牙远移0.2mm)，另一方面，其可能造成不期望的牙齿移动量。显然，所述第一设计方案不合格，因此，需要产生一个新的矫治器设计方案。
在一个实施例中，可以在不改变原矫治路径(即依然将所述第二布局作为设计目标)的前提下，产生一个优化力系，再基于所述参考力系和优化力系之差，基于所述第一设计方案产生第二设计方案。
在107中，以所述第一理想力系为目标，基于给定的限制条件，产生第一优化力系。
在一个实施例中，在产生第一优化力系时，可以考虑以下几方面的因素：矫治器所能达成的矫治力极限值，矫治要求(例如，控根要求以及垂直向控制要求等)，以及支抗牙受力等。
对于所述尖牙远移0.2mm的例子，可以基于矫治器的结构和材料性能，计算得到其能够在尖牙上施加的远中方向力的极限值。若矫治器在弹性范围内该极限值能够达到f (3)1(即完美力系中的尖牙远中方向受力，2N)，那么，可以设优化力系的对应力值的目标f (3)1_target＝f (3)1。若矫治器在弹性范围内该极限值f (3)1”无法达到f (3)1(必然地，f (3)1”≥f (3)1’)，那么，可以设优化力系的对应力值的目标f (3)1_target＝f (3)1”。
在一个实施例中，利用所述简化数学模型计算矫治器对某一牙齿在某一方向上所能达成的矫治力极限值时，可以将该矫治器在该方向上所能实现的最大变形量(即该矫治器发生屈服之前所能实现的最大变形量)作为该方向的移动量，将所述矩阵K a中除主对角线上的项(即与对应牙齿在对应方向上的载荷相关的参数)之外的其他项清零，基于该移动量和修改后的矩阵K a，根据等式(1)即可计算获得所述矫治器在所述方向上的所能达成的矫治力极限值。
在一个例子中，基于给定的矫治器结构和材料性能，计算得到f (3)1”＝1N，相应地，f (3)1_target＝1N。
另一方面，可以基于牙齿移动的控根需求，对优化力系中牙齿的力矩载荷设置限制。例如，可以使优化力系中同一牙齿上的力和力矩载荷之比与理想力系保持一致。
f (3)4_target/f (3)1_target＝f (3)4/f (3)1             方程式(8)
对于所述尖牙远移0.2mm的例子，由于理想力系中f (3)4＝0Nmm，因此，优化力系中f (3)4_target＝0Nmm。
在本申请的启示下，可以理解，基于控根需求对力矩的限制，除了以上对力和力矩的比值进行限制的例子之外，也可以是单纯对力矩本身的限制，使之小于预定的值，或者限制力和力矩的比值，使之位于一个预定的范围，只要使对力矩的限制满足控根需求即可。
临床大量实验发现，小于某一临界值的载荷不会使牙槽骨发生骨改建，也就 是说，在这种情况下，牙齿不会真正移动。因此，一颗牙齿上的载荷小于所述临界值，它就可以被当作支抗牙。可以理解，不同牙齿在不同自由度方向的临界值可能不同。例如，尖牙远移的临界值可以取0.4N，前磨牙近倾的临界值可以取5Nmm。
基于以上，产生以下第一优化力系：
尖牙远中方向载荷：
f (3)1_target＝1N
尖牙远中力矩：
f (3)4_target＝0Nmm
前磨牙近倾力矩：
f (4)4target＝5Nmm
在一个实施例中，计算机可以以所述第一理想力系为目标，基于所述第一参考力系和给定的限制条件，自动产生所述第一优化力系。
在109中，基于所述第一设计方案以及所述第一优化力系与第一参考力系之差产生第二设计方案。
所述第一优化力系是第二设计方案的矫治器需要达成的，因此，在一个实施例中，可以根据所述第一优化力系与第一参考力系之差，对所述第一设计方案进行修改，以得到所述第二设计方案。
对于上述尖牙远移0.2mm的例子，基于以上计算得到的第一参考力系和第一优化力系，两者之差如下：
尖牙远中方向载荷之差：
f (3)1_d＝f (3)1_target-f (3)1’＝1-0.9＝0.1N
尖牙近倾力矩之差：
f (3)4_d＝f (3)4_target-f (3)4’＝0-(-10)＝10Nmm
前磨牙近倾力矩之差：
f (4)4_d＝f (4)4_target-f (4)4’＝5-7＝-2Nmm
可以将所述第一参考力系和第一优化力系之差称为第一补偿力系，以下将第一参考力系记作S’，将第一优化力系记作S target，将第一补偿力系记作S_d。
需要注意的是，通过改变矫治器设计方案改变力系时，可能会造成不期望的力系改变。因此，产生所述第二设计方案的过程(即产生基于所述第一设计方案的补偿设计量的过程)是一个迭代寻找最优解的过程。
以下仍然用上述尖牙远移0.2mm的例子对产生补偿设计量的过程进行详细说明。
在一个实施例中，可以通过调整设计量的方式修改所述第一设计方案以获得所述第二设计方案。在一个实施例中，调整设计量可以是调整作为矫治器设计基础的所述第二布局中对应牙齿的位姿，使调整之后的所述第二布局相对于所述第一布局，相应牙齿的位移量得到相应调整。
首先，可以根据第一补偿力系给出补偿设计量的初始数值，作为迭代优化的起始点。
在所述例子中，补偿设计量的初始数值可以如下：
尖牙远移：0.02mm(尖牙远移0.2mm的设计量所对应的尖牙远中受力为0.9N，为了获得补偿力系中0.1N的尖牙远中受力，需要在所述第一设计方案的基础上增加大约0.02mm的设计量)；
尖牙近倾：1.5度(为了获得补偿力系中10Nmm的近倾力矩，需要在所述第一设计方案的基础上增加1.5度尖牙近倾设计量)；
前磨牙远倾：0.3度(为了获得补偿力系中-2Nmm前磨牙近倾力矩，需要在所述第一设计方案的基础上增加0.3度前磨牙远倾设计量)。
需要说明的是，这些补偿设计量的引入可能引起其他方向的受力，例如，尖牙近倾补偿设计量会再次引起切牙舌倾力矩，在后续迭代的过程中需要尽量降低其影响。
在一个实施例中，对于所述迭代，可以给定每一颗牙在每一个自由度的边界约束，例如，可以限定单牙倾斜补偿量不超过2度。
在一个实施例中，对于所述迭代，还可以给定全局约束，例如，限定所有牙的倾斜补偿量绝对值之和不超过5度。
接着，就可以利用目标优化函数进行迭代寻找补偿设计量的最优解。在一个实施例中，可以将目标优化函数定义为使所有牙齿的补偿载荷的平方和最小(对于力和力矩可以给定不同的权重进行计算)。
然后，可以基于所述目标优化函数，进行有约束条件的非线性问题最小值求解。例如，可以采用顺序最小二乘编程方法进行求解，具体实现可参由Kraft D(1988)发表于Tech.Rep.DFVLR-FB 88-28，DLR German Aerospace Center-Institute for Flight Mechanics，Koln，Germany的《A Software Package for Sequential Quadratic Programming》。
利用以上方法，即可求解得到最终的补偿设计量。
对于上述尖牙远移0.2mm的例子，利用上述方法计算得到以下最终补偿设计量：尖牙近倾1.2度并伸长0.05mm，切牙唇倾0.4度并压低0.05mm，第一磨牙压低0.03mm。
最后，把所述最终的补偿设计量与所述第一设计方案的设计量合并，得到所述第二设计方案的设计量。
对于上述尖牙远移0.2mm的例子，得到的第二设计方案的设计量如下：尖 牙远移0.2mm，近倾1.2度，并伸长0.05mm，切牙唇倾0.4度，并压低0.05mm，第一磨牙压低0.03mm。
壳状牙齿矫治器形成容纳多颗牙齿的空腔，可以把对应一颗牙齿的部分称为该牙齿的牙齿空腔，这些牙齿空腔的位置关系在一定程度上决定了该壳状牙齿矫治器对各牙齿的施力。在一个实施例中，所述设计量调整是指通过改变这些牙齿空腔的位置关系来改变壳状牙齿矫治器的施力。
在本申请的启示下，可以理解，修改矫治器设计方案的手段有多种，除了以上所述的调整设计量之外，还包括：局部修形(通过改变收容一颗牙齿的空腔的几何形态以改变对该牙齿的施力，可以通过该手段调整对该牙齿施加的矫治力或支抗力)、增加局部压力点以及局部加强结构等。
请参图3A，示意性地展示了本申请一个实施例中的壳状牙齿矫治器的优化设计20，其中，其容纳牙齿21(以虚线表示)的牙齿空腔23的几何形态与牙齿21不符，与牙齿21的几何形态相比，牙齿空腔23的几何形态在右上方稍收窄，在左上方稍内凹。
请参图3B，示意性地展示了图3A所示壳状牙齿矫治器佩戴于牙齿上发生形变后的情况，它将对牙齿21产生额外的沿图中两个箭头方向的力。
在一个实施例中，局部修形可以是对矫治器设计的局部几何形态进行修改，以改变矫治器施加于牙齿的力系。与调整设计量不同的是，矫治器经局部修形的部分的几何形态与对应牙冠存在差异，两者不再吻合。
在一个实施例中，增加局部点施力结构是在矫治器容纳牙齿的空腔内形成凸点，矫治器佩戴于牙齿上时，该凸点与牙齿表面相抵靠，形成新的施力点。
在一个实施例中，局部增厚可以是通过增材工艺增加矫治器局部的厚度，以改变矫治器该局部的机械性能。
在一个实施例中，局部改性可以是通过材料改性工艺对矫治器局部材料进行改性，以改变矫治器该局部的机械性能。
在一个实施例中，设置加强筋是在矫治器预定部位设置加强筋，以改变对应部分的机械性能。
在一个实施例中，对于相应的矫治器修改手段，可以在计算机程序中预先设定操作符及其对应的效果(即造成的力系差异)，使得计算机能够根据优化力系与参考力系的差值自动选择相应的操作符，以对所述第一设计方案进行修改。例如，对于设计量调整中的尖牙远移，可以以0.02mm为步长设置操作符，而其对应的效果是0.1N的力。
在一个实施例中，可以在计算机程序中设定操作符选择策略，使得计算机能够根据该策略，在所述迭代中自动选择操作符。
在111中，计算所述第二设计方案所能达成的第四布局。
虽然，所述第二设计方案是以达成所述第二布局为设计目标，但其实际能够达成的牙齿布局很可能与所述第二布局不吻合，为了产生比较理想的所述第二壳状牙齿矫治器的设计方案，需要计算所述第二设计方案所能达成的第四布局。其中，所述第二布局是原矫治方案中的牙齿布局。
在一个实施例中，可以采用以下方法计算所述第二设计方案所能达成的第四布局。
设在时间节点t，编号为i的牙齿在j方向上受到的载荷为x，持续时间为t 0，可以用以下等式(9)定义矫治达成量D：
Figure PCTCN2022100124-appb-000007
在实际情况下，矫治器施加于牙齿的载荷随牙齿的移动而变化。在一个实施例中，为简化计算，根据等式(9)计算矫治达成量时，可以设载荷x为固定不变，通过其他参数平衡它对结果造成的影响。在一个实施例中，可以用以下等式(10)定义f ij：
Figure PCTCN2022100124-appb-000008
其中，a、T i，j、Y i，j、B i，j均为参数，可以基于经验、大数据、实验测试等进行预设。需要说明的是，对于同一病例的不同牙齿和不同矫治方向，每一参数可能有不同的值，排列组合后可以得到N组参数(N为大于等于1的自然数)，因此，可以相应计算得到N个结果D 1、D 2......D N。然后，可以针对该N个结果的每一个计算其概率或权重，最后，基于该N个结果及其概率，可以计算得到矫治达成量D。
在一个实施例中，将与邻牙的位置关系纳入考虑，可以采用以下方法计算每一结果的概率。
设两颗邻牙坐标原点之间的原始距离为d ini，达成单步设计量时的距离为d des，最短距离为d min(距离过短，所述两邻牙将发生碰撞)，对应所述N个结果的原点距离分别为d 1、d 2......d N。在一个实施例中，可以根据以下等式(11)计算每一结果的概率：
Figure PCTCN2022100124-appb-000009
那么，可以根据以下等式(12)计算矫治达成量D：
Figure PCTCN2022100124-appb-000010
下面基于上述第二设计方案，以所述尖牙远倾的达成量为例，对矫治达成量的计算进行说明。
基于所述第二设计方案计算得到所述尖牙的远倾力矩为3Nmm。根据牙齿形态折算，每1°远倾量折合对应0.1mm移动量。若存在如下表1所示的3组参数，则可以计算得到相应的3组尖牙远倾的达成量及其概率：
参数设置 达成量 概率
a＝1，T＝2，Y＝10，B＝30 D 1＝(3-2)*1＝1° P＝e^(-0.1/0.2)＝0.61
a＝2，T＝4，Y＝15，B＝30 D 2＝0 P＝e^(-0/0.2)＝1
a＝2，T＝1，Y＝10，B＝30 D 3＝(3-1)*2＝4° P＝e^(-0.4/0.2)＝0.13
表1
最终的远倾达成量为：
D＝(1*0.61+0*1+4*0.13)/(0.61+1+0.13)＝0.65°
根据以上的方法可以计算出所述第二设计方案所能达成的每一颗牙齿在每一方向上的矫治量，进而基于这些矫治量和所述第一布局即可以计算得到第四布局。
在本申请的启示下，可以理解，除了以上方法，还可以采用其他合适的方法计算矫治达成量，例如，可以采用有限元分析方法，将壳状牙齿矫治器的有限元模型佩戴于牙颌(包括牙齿和牙周组织)的有限元模型上，通过仿真得到矫治达成量。
以所述第四布局替代所述第一布局，以所述第三布局替代所述第二布局，基于所述第三布局产生第二壳状牙齿矫治器的第三设计方案作为参考设计方案，重复101至109的操作即可得到优化的第二壳状牙齿矫治器的第四设计方案。
可以理解，一个牙齿矫治方案可以包括附件设计方案，它包括附件的种类，附件的添加位置(需要添加附件的牙齿以及在该牙齿表面添加附件的位置)，以及附件的添加时机(在哪个矫治步添加附件)等。
在一个实施例中，用于实现一个牙齿矫治方案(包括一系列逐次的矫治步)的一套完整的壳状牙齿矫治器的优化设计方案(包括一系列逐次的壳状牙齿矫治器的设计)，其每一壳状牙齿矫治器的优化设计与对应的参考设计的区别仅在于几何形态，也就是说它不改变原牙齿矫治方案关于附件添加位置和时机的设计。
通常，牙齿矫治方案不允许牙齿碰撞超过0.2mm，在一个实施例中，允许 壳状牙齿矫治器的优化设计的牙齿碰撞超过这个阈值，例如，将该阈值提高至0.3～0.5mm。这是因为壳状牙齿矫治器形成容纳各牙齿的空腔，各牙齿空腔的位置关系在一定程度上决定了壳状牙齿矫治器对牙齿的施力，两颗邻牙的空腔的位置交叠能够提供额外的补偿力，在合理的设计下，这并不会使这两颗邻牙在矫治过程中真正发生碰撞。换言之，优化设计允许两颗邻牙的牙齿空腔局部重叠的深度范围大于传统的壳状牙齿矫治器的设计思路，这也同样适用于牙齿空腔与附件空腔的局部重叠(附件空腔是指壳状牙齿矫治器收容固定于牙齿表面的附件的空腔)。
请参图4，示意性地展示了本申请一个实施例中壳状牙齿矫治器的优化设计30，它包括牙齿空腔31，用于收容牙齿33，以及牙齿空腔35，用于收容牙齿37，其中，牙齿33和37是两颗相邻的牙齿，其中，虚线部分展示了牙齿空腔31在该优化设计中的位置，牙齿空腔31和35局部重叠。
虽然，以上实施例只对如何产生两个连续的矫治步的壳状牙齿矫治器的设计方案进行了说明，但可以理解，对于更多连续的矫治步，只要基于对应的牙齿布局，重复相应的操作即可得到对应的壳状牙齿矫治器的设计方案。
在113中，利用所述第二和第四设计方案控制设备制作所述第一和第二壳状牙齿矫治器。
获得所述第二和第四设计方案之后，可以分别利用它们控制设备制作所述第一和第二壳状牙齿矫治器。
在一个实施例中，若采用热压膜成型工艺制作壳状牙齿矫治器，所述第二和第四设计方案可以分别包括表示对应阳模的三维数字模型，因此，可以利用它们控制设备(例如，立体光固化成型设备)制作这些阳模，然后，以热压膜成型技术在所述阳模上压膜获得所述第一和第二壳状牙齿矫治器。
在一个实施例中，若采用3D打印技术制作壳状牙齿矫治器，所述第二和第四设计方案可以分别包括表示所述第一和第二壳状牙齿矫治器的三维数字模型，因此，可以利用它们控制3D打印设备直接制作所述第一和第二壳状牙齿矫治器。
虽然在以上的例子中均是利用简化的数学模型计算力系，但可以理解，除了简化的数学模型，也可以利用有限元分析计算力系。例如，将壳状牙齿矫治器的有限元模型佩戴于刚性的牙列的有限元模型上，以有限元分析方法计算所述壳状牙齿矫治器施加于各牙齿的力系。
本申请的产生壳状牙齿矫治器的设计方案的方法是由计算机执行的，在一个实施例中，用户能够通过计算机程序的用户界面与所述计算机进行交互，使得所述计算机基于一系列逐次的牙齿布局以及对应的一系列逐次的壳状矫治器的参考设计方案，进行一系列计算，以产生一系列逐次的壳状矫治器的优化设计方案。
在一个实施例中，通过所述计算机程序的其中一个用户界面，所述计算机程序能够根据用户输入的指令，以可视化的方式(例如，图像或文字或两者组合)直观地向用户展示补偿力系或补偿设计量。
请参图5，展示了本申请一个实施例中所述计算机程序的一个用户界面。在该例子中，该用户界面展示上颌与下颌牙齿，并以颜色深浅(即颜色纯度)表示补偿设计量。其中，无补偿设计量的牙齿为白色，牙齿的填充颜色随补偿设计量的增加而变深，例如，补偿设计量小的牙齿以浅红色填充，补偿设计量大的牙齿以深红色填充。
在本申请的启示下，可以理解，除了红色之外，还可以用任何其他颜色的纯度变化来表示补偿力系或补偿设计量的大小。除了颜色纯度之外，还可以用色相或明度的变化来表示补偿力系或补偿设计量的大小。除了颜色之外，还可以用花纹密度的变化来表示补偿力系或补偿设计量的大小。总之，可以采用任何合适的图形化的方式来表示补偿力系或补偿设计量的大小。
在一个实施例中，可以根据用户的选择，展示总的补偿力系或补偿设计量，或仅展示选中方向的补偿力系或补偿设计量，例如，轴倾(包括近倾和远倾)、转矩(包括前牙冠舌倾、前牙冠唇倾、后牙冠内倾及后牙冠颊倾)、扭转、垂直向(包括升高和压低)以及综合(包括所有方向的补偿)。
在一个实施例中，可以根据用户的选择，展示选中矫治步的补偿力系或补偿 设计量，还可以动态地逐一展示各矫治步的补偿力系或补偿设计量。
在一个实施例中，所述用户界面所展示的上颌牙齿与下颌牙齿处于对应矫治步的优化设计方案所能实际达成的牙齿布局。
在一个实施例中，所述用户界面能够根据用户的选择同时展示上、下颌牙列，也能够根据用户的选择仅展示上、下颌牙列之一。
请参图6，展示了本申请又一实施例中所述计算机程序的一个用户界面。在该例子中，该用户界面展示上颌与下颌牙齿，并且在有补偿力系/补偿量的牙齿上设置图形标记，例如，圆形图标。所述计算机程序根据用户选中的图标(例如，用户通过鼠标点击进行选择)以文字形式展示对应牙齿的补偿力系/补偿量。
在本申请的启示下，可以理解，除了以上实施例之外，还可以采用任何其他合适的方式展示补偿力系/补偿量，例如，还可以把原始设计的牙模与最终设计的牙模进行叠加，用颜色或花纹填充两者存在差别之处，以指示存在补偿力系/补偿量的牙齿。
由以上可知，除了调整设计量之外，还可以通过人工设计结构实现优化力系，例如，局部修形、局部点施力结构、局部增厚以及加强筋等人工设计结构，人工设计结构是不同于牙齿的自然几何形态的人工设计的结构。在采用了这些修改手段的情况下，若仅展示补偿设计量，就无法完整体现牙齿移动量的变化。因此，为了完整展示修改后设计方案所带来的牙齿移动量变化，在一个实施例中，可以把补偿力系转化为等效补偿设计量(即假设仅通过调整设计量实现该补偿力系，基于该补偿力系计算出相应的补偿设计量，将其作为等效补偿设计量)，并可以根据用户选择，展示补偿设计量或等效补偿设计量。
本申请的又一方面提供一种壳状牙齿矫治器设计制造系统，牙科医生、壳状牙齿矫治器设计人员以及生产管理人员通过该系统进行数据交换，并利用该系统基于相关数据完成壳状牙齿器械的设计与生产。
请参图7，为本申请一个实施例中的壳状牙齿矫治器设计制造系统200的示 意性模块图。
壳状牙齿矫治器设计制造系统200包括客户端201、客户管理系统203、医学设计订单管理系统205、医学设计系统207、力学计算系统209、生产订单管理系统211、生产设计系统213以及生产控制系统215。
客户端201是牙科医生的计算机终端，在一个实施例中，它可以是安装了客户端计算机程序的计算机。牙科医生能够通过客户端201提出牙齿矫治方案设计需求等。
虽然图7中仅展示了一个客户端201，但可以理解，可以提供多个客户端201以供不同的牙科医生使用。
客户管理系统203存储和管理牙科医生的权限以及患者的数据，并充当各子系统之间的接口。
牙科医生在完成对一个需要牙齿正畸治疗的患者的诊断后，可以把表示该患者当前牙齿布局的三维数字模型以及诊断结论(例如，对牙齿正畸治疗的要求)等信息通过客户端201发送给客户管理系统203。
客户管理系统203在收到牙科医生的订单后，将其发送至医学设计订单管理系统205，由它把设计订单分配给相应的医学设计人员。当一个医学设计人员接收到一个医学设计订单，可以利用医学设计系统207，基于所述表示患者当前牙齿布局的三维数字模型和诊断结论，产生牙齿正畸治疗方案(自当前牙齿布局至目标牙齿布局的所有牙齿布局)以及对应的壳状牙齿矫治器参考设计方案。在一个实施例中，所述壳状牙齿矫治器参考设计方案可以是与所述一系列逐次的牙齿布局相吻合的一系列逐次的壳状牙齿矫治器。
在一个实施例中，医学设计系统207可以是安装了用于产生牙齿正畸治疗方案以及壳状牙齿矫治器的参考设计方案的计算机程序的计算机。虽然图7中仅展示了一个医学设计系统207，但可以理解，可以提供多个医学设计系统以分别供多个医学设计人员使用。
客户管理系统203在收到所述牙齿正畸治疗方案之后将发送通知至客户端201，所述牙科医生能够在客户端201上检查所述牙齿正畸治疗方案。若所述牙科医生认为所述牙齿正畸治疗方案不合理，可以通过客户端201提出修改建议，客户管理系统203将该修改建议发送至医学设计订单管理系统205，由所述医学设计人员基于所述修改建议重新设计牙齿正畸治疗方案，直至满足所述牙科医生的要求。
当所述牙科医生确认所述牙齿正畸治疗方案后，客户管理系统203将发送通知至医学设计订单管理系统205，所述牙齿正畸治疗方案及其对应的壳状牙齿矫治器参考设计方案将被发送至力学计算系统209，由它根据本申请的方法产生最终的壳状牙齿矫治器设计方案，并发送至客户管理系统203。
当所述牙科医生通过客户端201确认生产订单后，客户管理系统203将把所述最终的壳状牙齿矫治器设计方案发送至生产订单管理系统211，由其发送至生产设计系统213，以产生生产所需的对应的一系列逐次的阳模的三维数字模型，接着，其被发送至相应的生产控制系统215，由其控制生产设备制作对应的一系列的壳状牙齿矫治器。
可以理解，只要具备充足的处理能力，以上一些子系统可以在同一计算设备上运行，例如，生产订单管理系统211和生产设计系统213可以在同一计算设备上运行，又例如，医学订单管理系统205、客户管理系统203和生产订单管理系统211可以在同一计算设备上运行。
在一个实施例中，一些子系统可以位于不同地点，这些子系统可以通过网络连接。
在传统的方案中，在基于经牙科医生确认的牙齿正畸治疗方案设计壳状牙齿矫治器的过程中，若医学设计人员发现壳状牙齿矫治器的参考设计方案无法实现对应的牙齿正畸治疗方案，就会对原牙齿正畸治疗方案进行修改，每次修改后都需要牙科医生再次思考和确认，这将占用牙科医生的大量时间。在本申请的方案中，若发现壳状牙齿矫治器的参考设计方案无法实现经确认的牙齿正畸治疗方案， 力学计算系统209将在不改变经牙科医生确认的牙齿正畸治疗方案的前提下，基于材料的力学特性等因素，修改壳状牙齿矫治器的参考设计方案，得到能够实现所述牙齿正畸治疗方案的壳状牙齿矫治器的优化设计方案。一方面，这节省了牙科医生的时间；另一方面，它充分利用了材料和结构的特性，将壳状牙齿矫治器的性能发挥到了极致；又一方面，牙科医生只需参与牙齿正畸治疗方案的设计，而无需参与壳状牙齿矫治器的设计，通常，牙科医生在医学专业上具有优势，而并不一定充分理解壳状牙齿矫治器的材料以及各种结构的特性，因此，这种模式使得各方能够充分发挥各自的专业优势。
需要说明的是，在本申请中，第一、第二、第三等用语并无特指，需要根据上下文确定它们所指的内容。
还需要说明的是，在本申请中，“布局”和“牙齿布局”含义相同。
可以理解，对于整体的牙齿矫治方案，有初始牙齿布局(即牙齿正畸治疗之前患者的牙齿布局)和目标牙齿布局(即牙齿正畸治疗方案期望达到的牙齿布局)，对于每一矫治步，也有初始牙齿布局(即该矫治步的起始牙齿布局)和目标牙齿布局(即该矫治步期望达到的牙齿布局)。
尽管在此公开了本申请的多个方面和实施例，但在本申请的启发下，本申请的其他方面和实施例对于本领域技术人员而言也是显而易见的。在此公开的各个方面和实施例仅用于说明目的，而非限制目的。本申请的保护范围和主旨仅通过后附的权利要求书来确定。
同样，各个图表可以示出所公开的方法和系统的示例性架构或其他配置，其有助于理解可包含在所公开的方法和系统中的特征和功能。要求保护的内容并不限于所示的示例性架构或配置，而所希望的特征可以用各种替代架构和配置来实现。除此之外，对于流程图、功能性描述和方法权利要求，这里所给出的方框顺序不应限于以同样的顺序实施以执行所述功能的各种实施例，除非在上下文中明确指出。
除非另外明确指出，本文中所使用的术语和短语及其变体均应解释为开放式 的，而不是限制性的。在一些实例中，诸如“一个或多个”、“至少”、“但不限于”这样的扩展性词汇和短语或者其他类似用语的出现不应理解为在可能没有这种扩展性用语的示例中意图或者需要表示缩窄的情况。

Claims (28)

  1. 一种计算机执行的产生壳状牙齿矫治器设计方案的方法，其包括：
    获取牙齿正畸治疗方案，它包括一系列逐次的矫治步，它们的矫治目标依次为逐次的第一中间牙齿布局...最后中间牙齿布局以及目标牙齿布局；
    获取与所述一系列逐次的矫治步相对应的一系列逐次的壳状牙齿矫治器的参考设计；
    计算所述一系列逐次的壳状牙齿矫治器的参考设计是否能够达成的对应的矫治目标；以及
    若一个矫治步的壳状牙齿矫治器的参考设计无法达成该矫治步的矫治目标，则修改该矫治步的壳状牙齿矫治器的参考设计相应部分的几何形态，以改善其施力，得到该矫治步的壳状牙齿矫治器的优化设计。
  2. 如权利要求1所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，所述一系列逐次的壳状牙齿矫治器的参考设计是分别仅基于所述一系列逐次的矫治步的矫治目标的几何形态直接产生。
  3. 如权利要求2所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，所述一系列逐次的壳状牙齿矫治器的参考设计的几何形体分别与所述一系列逐次的矫治步的矫治目标相吻合。
  4. 如权利要求1所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，所述壳状牙齿矫治器的优化设计与对应的参考设计的区别仅在于几何形态。
  5. 如权利要求1所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，壳状牙齿矫治器形成容纳多颗牙齿的空腔，其容纳单颗牙齿的部分称为该牙齿的牙齿空腔，所述壳状牙齿矫治器的优化设计允许两颗相邻牙齿对应的牙齿空腔局部重叠。
  6. 如权利要求5所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，所述壳状牙齿矫治器的优化设计允许的牙齿空腔的局部重叠的深度范围为0.3～0.5mm。
  7. 如权利要求1所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，壳状牙齿矫治器形成容纳多颗牙齿以及容纳固定于牙齿表面的附件的空腔，其容纳单颗牙齿的部分称为该牙齿的牙齿空腔，其容纳某一附件的空腔称为该附件的附件空腔，所述壳状牙齿矫治器的优化设计允许牙齿空腔与附件空腔局部重叠。
  8. 如权利要求1所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，它还包括：
    对于所述一系列逐次的矫治步的每一个，基于其初始牙齿布局和目标牙齿布局，计算获得将牙齿从该初始牙齿布局重新定位到该目标牙齿布局所需的理想力系；
    基于其初始牙齿布局以及壳状牙齿矫治器的参考设计，计算获得该参考设计的壳状牙齿矫治器佩戴于处于该初始牙齿布局的牙齿上时施加于牙齿的参考力系；以及
    基于所述理想力系和参考力系修改所述参考设计得到所述优化设计。
  9. 如权利要求8所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，它还包括：
    以所述理想力系为目标，基于给定的条件，计算获得优化力系；以及
    基于所述参考力系和所述优化力系之差，修改所述参考设计，得到所述优化设计。
  10. 如权利要求9所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，它还包括：根据用户指令，在用户界面展示选中的矫治步的以下之一：补偿力系、补偿设计量、等效补偿设计量以及它们的任意组合，其中，所述补偿力系是所述参考力系和所述优化力系之差，所述补偿设计量是所述参考设计和所述优化设计的设计量之差，所述等效补偿设计量是基于所述补偿力系计算得到的补偿设计量。
  11. 如权利要求10所述的计算机执行的产生壳状牙齿矫治器设计方案的方 法，其特征在于，它还包括：在用户界面展示所述患者的牙颌图像，其中，该牙颌图像中具有补偿力系的牙齿上带有标记，以指示以下之一：补偿力系、补偿设计量以及等效补偿设计量。
  12. 如权利要求9所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，所述给定条件包括：基于给定材料和厚度，壳状牙齿矫治器的受力极限。
  13. 如权利要求8所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，所述力系是静态的力和力矩的总和。
  14. 如权利要求1所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，它还包括：
    获取牙科医生提供的表示患者初始牙齿布局的三维数字模型以及诊断结论；
    基于所述表示患者初始牙齿布局的三维数字模型以及所述诊断结论，产生所述牙齿正畸治疗方案；以及
    在获取所述牙科医生对所述牙齿正畸治疗方案的确认后，产生所述一系列逐次的壳状牙齿矫治器的参考设计。
  15. 如权利要求1所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，修改所述矫治步的壳状牙齿矫治器的参考设计相应部分的几何形态包括以下之一：改变牙齿空腔的相对位置关系，改变牙齿空腔的几何形态，增加局部压力点，增加局部加强结构，以及以上的任意组合，其中，壳状牙齿矫治器形成容纳多颗牙齿的空腔，其容纳单颗牙齿的部分称为该牙齿的牙齿空腔。
  16. 一种壳状牙齿矫治器系统，它包括一系列逐次的壳状牙齿矫治器，分别用于将牙齿逐渐地从初始牙齿布局重新定位到第一中间牙齿布局...最后中间牙齿布局直至目标牙齿布局，其中，所述一系列逐次的壳状牙齿矫治器是基于对应的一系列逐次的壳状牙齿矫治器的参考设计修改获得，所述修改是基于所述一系列逐次的壳状牙齿矫治器的参考设计的实际矫治效果与期望的矫治效果之差，所述一系列逐次的壳状牙齿矫治器的至少一个的几何形态不同于对应的参考设计， 其中，所述一系列逐次的壳状牙齿矫治器的参考设计是分别基于所述第一中间牙齿布局...最后中间牙齿布局以及目标牙齿布局直接产生。
  17. 如权利要求16所述的壳状牙齿矫治器系统，其特征在于，所述一系列逐次的壳状牙齿矫治器的参考设计的几何形态分别与所述第一中间牙齿布局...最后中间牙齿布局以及目标牙齿布局相吻合。
  18. 如权利要求16所述的壳状牙齿矫治器系统，其特征在于，所述实际矫治效果和期望的矫治效果是以静态力系表达。
  19. 一种计算机执行的产生壳状牙齿矫治器设计方案的方法，其包括：
    获取第一矫治步的初始牙齿布局和目标牙齿布局；
    获取所述第一矫治步的壳状牙齿矫治器的参考设计；
    计算所述参考设计的壳状牙齿矫治器佩戴于处于所述初始牙齿布局的患者牙齿上时施加的力系，记为参考力系；
    基于所述初始牙齿布局和目标牙齿布局计算得到理想力系，所述理想力系是将牙齿从所述初始牙齿布局重新定位到所述目标牙齿布局，要求壳状牙齿矫治器佩戴于处于所述初始牙齿布局的牙齿上时施加的力系；以及
    基于所述参考力系和理想力系，修改所述参考设计，得到优化设计。
  20. 如权利要求19所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，所述参考设计是基于所述目标牙齿布局直接产生。
  21. 如权利要求20所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，所述参考设计的容纳牙齿的空腔的几何形态与所述目标牙齿布局相吻合。
  22. 如权利要求19所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，它还包括：
    获取第二矫治步的初始牙齿布局和壳状牙齿矫治器的优化设计，其中，所述第二矫治步是所述第一矫治步的前一矫治步；以及
    基于所述第二矫治步的初始牙齿布局和壳状牙齿矫治器的优化设计，计算得到所述第一矫治步的初始牙齿布局。
  23. 如权利要求19所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，它还包括：
    以所述理想力系为目标，基于给定的条件，计算得到优化力系；以及
    根据所述参考力系和所述优化力系之差修改所述参考设计，得到所述优化设计。
  24. 如权利要求23所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，所述力系是静态的力和力矩的总和。
  25. 如权利要求23所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，所述给定的条件包括：在给定材料和厚度的情况下，壳状牙齿矫治器所能实现的矫治力极限值。
  26. 如权利要求25所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，所述给定的条件还包括以下之一：支抗牙受力极限、控根要求、垂直向控制要求以及以上的任意组合。
  27. 如权利要求19所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，所述修改包括以下之一：改变牙齿空腔的相对位置关系，，添加人工设计结构以及以上的组合，其中，壳状牙齿矫治器形成容纳多颗牙齿的空腔，其容纳单颗牙齿的部分称为该牙齿的牙齿空腔。
  28. 如权利要求27所述的计算机执行的产生壳状牙齿矫治器设计方案的方法，其特征在于，所述人工设计结构包括以下之一：局部修形、点施力结构、局部加强结构以及以上的任意组合。
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Citations (3)

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CN101977564A (zh) * 2008-01-29 2011-02-16 矫正技术公司 用于优化牙科矫正器几何形状的方法和系统
US20180168776A1 (en) * 2016-12-19 2018-06-21 Align Technology, Inc. Aligners with enhanced gable bends
CN111437047A (zh) * 2020-04-01 2020-07-24 上海正雅齿科科技股份有限公司 旋转中心设计检验方法、壳状牙科器械设计及制备方法

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Publication number Priority date Publication date Assignee Title
CN101977564A (zh) * 2008-01-29 2011-02-16 矫正技术公司 用于优化牙科矫正器几何形状的方法和系统
US20180168776A1 (en) * 2016-12-19 2018-06-21 Align Technology, Inc. Aligners with enhanced gable bends
CN111437047A (zh) * 2020-04-01 2020-07-24 上海正雅齿科科技股份有限公司 旋转中心设计检验方法、壳状牙科器械设计及制备方法

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