CN114431989A - Target arch curve-based coordinate system establishing method, automatic tooth arrangement method and tooth movement evaluation method - Google Patents

Target arch curve-based coordinate system establishing method, automatic tooth arrangement method and tooth movement evaluation method Download PDF

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CN114431989A
CN114431989A CN202210014853.5A CN202210014853A CN114431989A CN 114431989 A CN114431989 A CN 114431989A CN 202210014853 A CN202210014853 A CN 202210014853A CN 114431989 A CN114431989 A CN 114431989A
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tooth
curve
dental arch
coordinate system
axis
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CN114431989B (en
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舒广
戴帆帆
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Clear Medical Technology Changzhou Co ltd
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    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61CDENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
    • A61C9/00Impression cups, i.e. impression trays; Impression methods
    • A61C9/0033Gingival retraction appliances
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61CDENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
    • A61C11/00Dental articulators, i.e. for simulating movement of the temporo-mandibular joints; Articulation forms or mouldings
    • AHUMAN NECESSITIES
    • A61MEDICAL OR VETERINARY SCIENCE; HYGIENE
    • A61CDENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
    • A61C7/00Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
    • A61C7/002Orthodontic computer assisted systems

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Abstract

The invention relates to a method for establishing a coordinate system based on a target dental arch curve, and an automatic tooth arrangement method and a tooth movement evaluation method based on the dental arch curve coordinate system. The arch curve coordinate system has different local coordinate systems formed by tangent axes, main normal axes and secondary normal axes at different points of the curve, is adaptive to the three-dimensional positions of teeth, can guide more efficient and accurate automatic tooth arrangement and more accord with clinical tooth movement evaluation, and is beneficial to more scientific, more reasonable and more accurate tooth movement scheme design and curative effect evaluation.

Description

Target arch curve-based coordinate system establishing method, automatic tooth arrangement method and tooth movement evaluation method
Technical Field
The invention belongs to the technical field of dental orthodontics, and particularly relates to a method for establishing a coordinate system based on a target dental arch curve, an automatic tooth arrangement method based on the dental arch curve coordinate system and a tooth movement evaluation method.
Technical Field
The existing orthodontic treatment enters a digital era, and no matter the technology is digital fixed correction or digital bracket-free invisible correction, digital tooth arrangement is required to be carried out on the basis of a digital tooth jaw model before treatment, a target position tooth jaw model is arranged, and tooth movement evaluation from an initial position to a target position is carried out. The efficient and accurate automatic tooth arrangement and the scientific and accurate establishment of the tooth movement evaluation method have very important significance on treatment target design, treatment mechanical system construction and curative effect evaluation.
At present, the mainstream orthodontic tooth arrangement software still depends on manual tooth arrangement of technicians, and the tooth arrangement efficiency is low. In recent years, a method of automatic tooth arrangement has been proposed (for example, see patent documents 1 and 2 described below). In the automatic tooth arrangement method, it is necessary to establish an arch curve, a global coordinate system and a local coordinate system of teeth, and then arrange the teeth by calculation of the coordinate system, however, in the above automatic tooth arrangement method, the established coordinate system is still a conventional cartesian coordinate system (rectangular coordinate system), and calculation of each angle during tooth arrangement depends on a specific empirical value.
For the evaluation of tooth movement, a simplified mathematical model is usually adopted, and a common method is to establish a global rectangular coordinate system in a three-dimensional position space with a jawbone as a reference, and determine the movement amount and the movement direction of each tooth in the sagittal direction, the coronal direction and the vertical direction before and after treatment. This method gives the same sagittal, coronal and vertical orientation to all teeth, however, this does not correspond to the feature that the teeth are arranged on a circular arch and possess individualized positions, angles and directions of movement. Another common method is to establish a local reference coordinate system for a single tooth before treatment, and evaluate the amount and direction of movement of the single tooth along its own long axis (or a tangent to its own long axis) (see, for example, patent document 3 below). The method has personalized tooth moving direction, but the teeth are wrong before treatment
Figure RE-GDA0003569721200000011
The state is greatly influenced
Figure RE-GDA0003569721200000012
Coincidence of tooth moving direction pointed by local coordinate system established by position along self long axis and tooth pointed direction in normal arrangementThe clinically actual direction of movement is not the same. Therefore, the two methods for evaluating tooth movement do not fit clinical practice, only have mathematical significance, and cannot evaluate tooth movement scientifically and accurately. Considering that the nature of orthodontic tooth movement is the reconstruction of alveolar bone under mechanical force guidance, a tooth movement evaluation method based on a curved natural coordinate system of alveolar bone morphology has been proposed (for example, refer to patent document 4 below), which gives a tooth personalized biomechanical movement evaluation but requires personalized or large data mean CBCT alveolar bone data.
It should be noted that although the prior art (see, for example, patent documents 5 and 6 below) refers to a tooth movement measuring method, the emphasis is on obtaining an overlap of tooth models with intact crowns before and after treatment by using CBCT images and/or three-dimensional surface interdigitation, and then calculating the movement amount of the teeth before and after treatment, and the mathematical calculation of the tooth movement amount itself is still established on the conventional rectangular coordinate system.
Prior Art
Patent document 1: CN107374758A
Patent document 2: CN108403234A
Patent document 3: CN108245264A
Patent document 4: CN113827362A
Patent document 5: CN110811653A
Patent document 6: CN111388125A
Disclosure of Invention
Problems to be solved by the invention
According to the techniques described in patent documents 1 and 2, the teeth are automatically aligned on the dental arch curve by calculation between the local rectangular coordinate system and the global rectangular coordinate system, the calculated value of each dimension angle refers to a fixed empirical value or a theoretical value, the tooth angle cannot adapt to the personalized dental arch curve form, or the tooth long axis direction is simply pointed to the vertical axis direction of the global coordinate system, the teeth after automatic alignment are still insufficient in accuracy, and more manual fine adjustment may be required in the later period.
According to the technique described in patent document 4, a curved natural coordinate system based on the dental arch curve is established, and the amount of tooth movement is measured in the curved natural coordinate system, which can more scientifically and accurately reflect the biomechanical movement of teeth, but requires CBCT data of a patient, and has no universality for medical units without CBCT equipment in the base layer, and although large-data-mean CBCT data can be used for substitution, the accuracy is lower than that of individual real CBCT data. In addition, for automated tooth alignment, the coordinate system based on the alveolar arch curve is inferior to the coordinate system based on the arch curve because the arch curve can guide the alignment of the crowns more accurately based on the crown feature point fitting.
In response to the problems of the prior art, the inventors of the present application have recognized that a better coordinate system is needed to enable more efficient and accurate automated tooth placement, to more reasonably and accurately evaluate tooth movement, and to provide greater versatility. Through research, a method for establishing a natural curve coordinate system based on a target dental arch curve is found, and automatic tooth arrangement and tooth movement evaluation are carried out by a computer based on the dental arch curve coordinate system.
A first aspect of the present application provides a method for establishing a coordinate system based on a target dental arch curve, which sequentially comprises the following steps:
obtaining a target arch curve based on the pre-treatment tooth arrangement or the big data arch curve;
and establishing a curve natural coordinate system based on the target dental arch curve.
In some embodiments, the specific method for obtaining the target arch curve based on the pre-treatment tooth arrangement or the big data arch curve is:
(1) acquiring a digital dental model before treatment, selecting tooth characteristic points on the upper jaw model and the lower jaw model respectively, fitting an upper jaw dental arch curve and a lower jaw dental arch curve respectively by using a mathematical method,
wherein the characteristic points of the tooth are incisal edge middle points of middle incisors and side incisors, cusp teeth cusp points, buccal cusp points of first premolars and second premolars, mesial buccal cusp points and distal buccal cusp points of first molars and second molars, and can also be coronal axis points, geometric center points of crowns, adjacent contact points or functional cuspate points;
the fitted dental arch curve has different forms in the three-dimensional direction, on the horizontal plane, the dental arch curve is roughly divided into a pointed circle, an oval circle, a square circle and a personalized arch, on the sagittal plane, the dental arch curve is in a Spee curve form, and on the coronal plane, the dental arch curve is in a Wilson curve form; alternatively, the first and second electrodes may be,
obtaining an upper jaw dental arch curve and a lower jaw dental arch curve according to a dental arch curve fitted by the big data dentition, selecting a proper dental arch curve form in the big data, and determining the width, the length and the depth of the dental arch curve according to the width, the length and the depth of the dental arch before treatment;
(2) automatically matching the upper jaw dental arch curve and the lower jaw dental arch curve to ensure that the upper jaw dental arch curve and the lower jaw dental arch curve have uniform normal coverage on a horizontal plane;
(3) the doctor or the technician can adjust the width, the length, the depth and the shape of the dental arch curve and the matching degree of the upper dental arch curve and the lower dental arch curve according to the treatment requirement in an individualized way, and finally generates the target dental arch curve.
In some embodiments, the step of establishing a natural coordinate system of the curve based on the target dental arch curve is:
(1) selecting a middle point on a target dental arch curve as an origin of a coordinate system, and sequentially determining reference points and intervals corresponding to tooth positions on the dental arch curve according to the width of teeth of a patient from the origin of the coordinate system;
(2) regarding any point on the dental arch curve, taking the tangent line of the curve at the point as the tangent axis of the local coordinate system, and taking the plane vertical to the tangent axis as a normal plane;
(3) determining a secondary normal axis of a local coordinate system on a normal plane where a reference point corresponding to each tooth position is located, wherein the method comprises the following steps: make the teeth opposite
Figure RE-GDA0003569721200000031
Converting the standard reference values of crown axis inclination and crown inclination of the plane into angle data of the tooth long axis relative to the dental arch curve or according to the normal after treatment
Figure RE-GDA0003569721200000032
Model or untreated normality
Figure RE-GDA0003569721200000033
Obtaining angle data of a tooth long axis of each tooth position relative to a dental arch curve by using big data of the dental model, and determining a projection line of the tooth long axis on a normal plane as a secondary normal axis;
the practitioner can individually adjust the minor normal axis of each dental site reference point according to the requirements of the patient treatment scheme;
for points between every two tooth position reference points on the dental arch curve, obtaining a minor normal axis corresponding to each point by using an interpolation method or other mathematical methods;
(4) the tangent axis and the secondary normal axis of each point form a secondary tangent plane of a local coordinate system of the dental arch curve, the perpendicular line of the secondary tangent plane is a main normal axis, the tangent axis and the main normal axis form a close plane, and the main normal axis and the secondary normal axis form a normal plane;
finally, a natural dental arch curve coordinate system with different local coordinate systems consisting of tangent axes, secondary normal axes, primary normal axes, osculating planes, secondary tangent planes and normal planes at different positions of the three-dimensional dental arch curve is established.
A second aspect of the present application provides an automatic tooth alignment method using the above-described method for establishing a coordinate system based on a target arch curve to automatically align teeth.
In some embodiments, the specific method for automatic alignment of teeth based on the target arch curve coordinate system is as follows:
obtaining a target arch curve and establishing a natural coordinate system of the curve according to the method of the first aspect of the application;
selecting tooth characteristic points consistent with the tooth characteristic points of the fitted dental arch curve;
determining a long tooth axis and a transverse tooth axis of the tooth;
the middle points of the incisor feature points on the two sides are coincided with the middle point of the dental arch curve, and the teeth are moved in sequence to make the feature points of the teeth coincide on the dental arch curve;
checking the abutment collision, moving the teeth along the dental arch curve to make the abutment contact with the teeth, without gap or collision, or reserving a small amount of collision of adjacent surfaces or a small amount of distance between adjacent surfaces according to the requirement of stripping of adjacent surfaces or reserving gaps in a medical scheme;
rotating the teeth around a minor normal axis of a local curve coordinate system of the teeth to enable an included angle between a transverse axis of the teeth and a tangent axis of the curve coordinate system on a close plane of the curve coordinate system to be 0, so that the crown torsion of the teeth is positioned;
rotating the tooth around the tangent axis of the tooth local curve coordinate system to make the included angle between the tooth long axis and the minor normal axis of the curve coordinate system on the normal plane of the curve coordinate system be 0, thereby positioning the crown inclination of the tooth, namely the crown torque;
rotating the tooth around the main normal axis of the tooth local curve coordinate system to make the tooth long axis and the minor normal axis reach certain standard value in the tangent plane of the curve coordinate system and to locate the crown axis inclination of the tooth
Figure RE-GDA0003569721200000041
Converting the standard value of the plane crown axis inclination into a crown axis inclination value of a relative curve coordinate system measured by big data;
checking the coverage between the upper and lower dentitions, and making each tooth move buccally and lingually along the main normal axis of the local coordinate system to achieve standard coverage between the upper and lower dentitions or personalized coverage according to the requirements of medical schemes;
checking the collision of the opposite jaws, and moving each tooth up and down along a secondary normal axis of a local coordinate system to ensure that the upper jaw and the lower jaw are in light contact or non-contact, or partially keep heavy contact according to the requirement of a medical scheme;
to obtain better occlusion and abutment, the angles of the teeth can be adjusted appropriately;
checking abutting collision again, if the teeth need to move along the arch curve, repositioning crown torsion, crown axis inclination and crown inclination of the teeth after moving, checking coverage, checking jaw collision, and sequentially iterating to move and rotate the teeth until reasonable tooth arrangement is achieved to finish automatic tooth arrangement;
the ideal bite relation parameters can generate a new coordinate system template.
A third aspect of the present application provides a tooth movement evaluation method for performing tooth movement evaluation using the above-described method for establishing a coordinate system based on a target arch curve.
In some embodiments, the specific method for tooth movement evaluation based on the target arch curve coordinate system is as follows:
obtaining a target arch curve and establishing a natural coordinate system of the curve according to the method of the first aspect of the application;
according to the method of the second aspect of the application, the teeth are automatically aligned, and a technician or a doctor can manually adjust the teeth according to treatment requirements on the basis of the automatic alignment result of the teeth to obtain the final target position tooth arrangement;
calculating tooth coordinates;
calculating tooth movement changes;
outputting tooth coordinates and tooth movement changes.
In some embodiments, the step of calculating the tooth coordinates is:
(1) defining the orientation of the coordinate system:
in the natural coordinate system of the dental arch curve, the tangent axis of the curve is the mesial-distal direction of the teeth, the primary normal axis is the labial (buccal) lingual (palatal) direction of the teeth, and the secondary normal axis is the vertical direction of the teeth;
in the natural coordinate system of the dental arch curve, the normal plane of the curve is the labial (buccal) lingual (palatal) plane of the tooth, the slave incisal plane of the curve is the mesial-distal plane of the tooth, and the osculating plane of the curve is the horizontal plane of the tooth;
(2) calculating coordinates of the tooth, including three-dimensional position and three-dimensional angle:
positioning corresponding points of the tooth measuring points on the dental arch curve, wherein the corresponding points are vertical points of the tooth measuring points on the dental arch curve, and a local coordinate system established on the corresponding points of the dental arch curve is the local coordinate system of the teeth;
the near-far middle coordinate refers to the tooth position on the tangent axis, namely the curve distance between the corresponding point of the tooth measuring point on the alveolar arch curve and the origin of the curve coordinate system;
the labial (buccal) lingual (palatal) coordinate refers to the tooth position on the principal normal axis, namely the linear distance between the perpendicular point of the tooth measuring point on the principal normal axis and the corresponding point on the alveolar arch curve;
the vertical coordinate refers to the tooth position on a secondary normal axis, namely the linear distance between the perpendicular point of the tooth measuring point on the secondary normal axis and the corresponding point on the alveolar arch curve;
the torsion angle is the included angle between the tooth transverse axis and the curve tangent axis on the close plane;
the axial inclination angle refers to an included angle between a tooth long axis and a curve minor normal axis on a secondary tangent plane;
the inclination angle is an included angle between a tooth long axis and a curve minor normal axis on a normal plane;
the initial position tooth coordinates and the target position tooth coordinates are calculated, and the intermediate stage tooth coordinates can also be calculated.
In some embodiments, the step of calculating the change in tooth movement is:
the tooth movement change is equal to the difference value of the tooth coordinate of the initial position and the tooth coordinate of the target position, and comprises three-dimensional displacement and three-dimensional angle change;
the difference value between the initial position tooth coordinate and the tooth coordinate at any stage can be calculated, and the tooth movement change at the stage is evaluated;
the mesial-distal movement refers to the movement of teeth along a tangent axis, namely the change of the coordinates of the mesial-distal positions of the teeth, wherein the movement close to the middle point of the curve is mesial movement, and the movement far from the middle point of the curve is distal movement;
labial (buccal) lingual (palatal) movement refers to movement of a tooth along a primary normal axis, i.e., change of labial (buccal) lingual (palatal) coordinates of the tooth, wherein labial (buccal) movement refers to outward movement and lingual (palatal) movement refers to inward movement;
the stretching and the depressing refer to the movement of the teeth along a minor normal axis, namely the change of the vertical coordinate of the teeth, wherein the upper jaw moves downwards to be stretched and the upper jaw moves upwards to be depressed, and the lower jaw moves reversely;
twist refers to the change in twist angle in the osculating plane;
axis refers to the change in the angle of inclination of the shaft in the plane of tangency;
tilt refers to the change in angle of inclination in the normal plane.
In some embodiments, the measurement points for evaluating the amount of tooth movement include a cusp point or incisal edge midpoint, a crown center point, a root center point, a tooth impedance center point, and a cusp point.
The invention has the beneficial effects that: the curve natural coordinate system based on the target dental arch curve can be used for automatic tooth arrangement and tooth movement evaluation at the same time, and the coordinate system is more efficient and accurate than the existing automatic tooth arrangement method at least in the aspect of tooth torsion arrangement, is superior to the coordinate system established based on the initial teeth in the prior art in the aspect of clinical significance of tooth movement evaluation, and is superior to the coordinate system based on the alveolar arch curve in the aspect of universality, so that the tooth movement scheme design and the curative effect evaluation which are more scientific, more reasonable and more accurate are facilitated.
Drawings
FIG. 1 is a three-dimensional view of an arch curve based on cusp and incisal edge points fitting in one embodiment of the present invention.
FIG. 2 is a side view of a dental arch curve based on a dental crown axis point fit in one embodiment of the present invention.
FIG. 3 is a top view of an arch curve based on dental abutment point fitting in one embodiment of the present invention.
Fig. 4 is a three-dimensional view of a dental arch curve coordinate system in one embodiment of the invention.
Fig. 5 is a top view of an automatic tooth arrangement based on an arch curve coordinate system in an embodiment of the present invention.
Fig. 6 is a side view of an automatic tooth arrangement based on an arch curve coordinate system in an embodiment of the present invention.
Fig. 7 is a schematic view of tooth measurement points in one embodiment of the present invention.
FIG. 8 is a schematic representation of the evaluation of tooth torsion angle change in an arch curve coordinate system in an embodiment of the present invention.
FIG. 9 is a schematic representation of the evaluation of changes in inclination of the tooth axes in the arch curve coordinate system in accordance with an embodiment of the present invention.
FIG. 10 is a schematic representation of the evaluation of the change in the angle of inclination of a tooth in the curvilinear arch coordinate system in accordance with an embodiment of the present invention.
Label 1: the midpoint of the incisal margin of the tooth; marker 2: a cusp point; marker 3: arch curve of the teeth; marker 4: a tooth coronal plane axis point; marker 5: a dental abutment; marker 6: tangent axis of curve natural coordinate system; marker 7: a principal normal axis of a curvilinear natural coordinate system; marker 8: a minor normal axis of a curved natural coordinate system; mark 9: a dental transverse axis; mark 10: a long axis of the tooth; mark 11: a crown center point; marker 12: a tooth impedance center point; marker 13: a root center point; marker 14: a root tip point; marker 15: the tooth moves from the point A to the point B in the mesial-distal displacement, which is the curve arc length between the points A 'and B'; marker 16: the bucco-lingual displacement of the tooth from point A to point B is the difference between the line distance of point A 'and the line distance of point B' on the main normal axis; marker 17: the torsion angle is an included angle between a transverse axis of the tooth and a tangent axis on the osculating plane, and the torsion change of the tooth from the point A to the point B is the difference between the torsion angles of the point A and the point B; mark 18: the vertical displacement of the tooth from the point A to the point B is the difference between the line distance of the point A 'on the secondary normal axis and the line distance of the point B' on the point A; marker 19: the axial inclination angle is an included angle between the long axis of the tooth and the minor normal axis on the tangent plane, and the axial inclination of the tooth from the point A to the point B is changed into the difference between the axial inclination angles of the point A and the point B; 20, marking: the inclination angle is the included angle between the major axis of the tooth and the minor normal axis on the normal plane, and the inclination of the tooth from the point A to the point B is changed into the difference between the inclination angles of the point A and the point B
Detailed Description
The following description of the embodiments of the present invention will be made with reference to the accompanying drawings in order to better illustrate the contents of the present invention, but the illustrated embodiments are only examples and do not limit the scope of the invention.
The invention provides a method for establishing a coordinate system based on a target dental arch curve, which specifically comprises the following steps:
1. obtaining a digital model of the teeth:
obtaining a digitized three-dimensional tooth model by performing intraoral or extraoral scanning of the upper and lower teeth of a patient, the model having high-precision dental crown information;
2. obtaining a target arch curve based on the pre-treatment tooth arrangement or big data arch curve:
(a) selecting tooth characteristic points on the upper jaw model and the lower jaw model respectively, wherein the tooth characteristic points comprise incisal marginal middle points (1) of middle incisors and lateral incisors, cusp tooth cusps, buccal cusps of first premolars and second premolars, mesial buccal cusps and distal buccal cusps (2) of first molars and second molars as shown in figure 1, and the characteristic points of the first molars and the second molars can also be the middle points of the mesial buccal cusps and the distal buccal cusps so as to avoid the influence of tooth torsion;
(b) respectively fitting an upper jaw dental arch curve and a lower jaw dental arch curve (3) by using a mathematical method, wherein the fitted mathematical method comprises a polynomial equation, a Beta function, a spline function and the like;
(c) the characteristic point of the tooth can be a coronal axis point (4) as shown in fig. 2, a geometric central point of a crown, a functional cusp point, or an adjacent contact point (5) as shown in fig. 3, wherein if a gap exists between two adjacent teeth but the two adjacent teeth are not in contact, the adjacent contact point is the midpoint of the closest point of the two teeth;
(d) if the individual tooth is missing, arrested or significantly ectopic
Figure RE-GDA0003569721200000071
The lack of the local tooth characteristic points or the dislocation caused by the reasons further causes the asymmetry of the fitted dental arch curve, the missing tooth characteristic points can be supplemented with reference to the bone morphology on the dental model or the characteristic points of obvious dislocation can be adjusted, then the fitting of the target dental arch curve is carried out, or the characteristic points of teeth at two sides are mirror-symmetrical before the fitting, then the fitting of the target dental arch curve is carried out, for slight asymmetry, the symmetry of the dental arch curve can be directly restrained in a mathematical equation, and a doctor can select the asymmetric dental arch curve according to the treatment requirements of a patient;
(e) as shown in fig. 1, the fitted dental arch curve has different forms in three dimensions, and in the horizontal plane, the dental arch curve is roughly divided into a cuspate circle, an oval circle, a square circle and a personalized arch, and in the sagittal plane, the dental arch curve is in a Spee curve form, and in the coronal plane, the dental arch curve is in a Wilson curve form;
(f) the width, length and depth of the dental arch curve can be determined according to the width, length and depth of the dental arch curve before the patient is treated, the dental arch width is the distance between two first molar teeth, the dental arch length is the vertical distance from the middle incisor middle point to the far middle of the two first molar teeth, the dental arch depth is the vertical distance from the lowest part of the dental cusp (generally the buccal cusp of the first premolar or the second premolar or between the buccal cusp) to the connecting line between the incisor margin and the far middle buccal cusp of the second molar tooth, in some embodiments, the width and length of the dental arch curve can also be determined by taking the second molar tooth as a reference, and the large data dental arch curve can be derived from the normal dental arch curve without orthodontic treatment
Figure RE-GDA0003569721200000081
The population can also be derived from a population after orthodontic treatment for obtaining normal occlusion;
(g) automatically matching the upper jaw dental arch curve and the lower jaw dental arch curve to ensure that the upper jaw dental arch curve and the lower jaw dental arch curve have uniform normal coverage on a horizontal plane, namely the upper jaw dental arch curve and the lower jaw dental arch curve are uniformly separated from each other by a certain distance which can be set by software and the range of the distance is not more than 3 mm;
(h) the doctor or the technician can adjust the width, the length, the depth and the shape of the dental arch curve and the matching degree of the upper dental arch curve and the lower dental arch curve according to the treatment requirement in an individualized way, and finally generates the target dental arch curve.
3. Establishing a curve natural coordinate system based on the target dental arch curve, and specifically comprising the following steps of:
(a) selecting a middle point on a target dental arch curve as an origin of a coordinate system, regarding any point on the dental arch curve, taking a tangent line of the curve at the point as a tangent axis (6) of a local coordinate system, and taking a plane vertical to the tangent axis as a normal plane;
(b) sequentially determining reference points corresponding to all tooth positions on the dental arch curve from the origin of the coordinate system according to the width of the teeth of the patient;
(c) a secondary normal axis (8) of a local coordinate system is determined on a normal plane where the reference point corresponding to each tooth position is located, and the method comprises the following steps: make the teeth opposite
Figure RE-GDA0003569721200000082
Converting the standard reference values of crown axis inclination and crown inclination of the plane into angle data of the tooth long axis relative to the dental arch curve or according to the normal after treatment
Figure RE-GDA0003569721200000083
Model or untreated normality
Figure RE-GDA0003569721200000084
Obtaining angle data of a tooth long axis of each tooth position relative to a dental arch curve by using big data of the dental model, and determining a projection line of the tooth long axis on a normal plane as a secondary normal axis;
(d) the physician can individually adjust the minor normal axis of each tooth reference point in the software according to the requirements of the treatment scheme of the patient;
(e) for points between every two tooth position reference points on the dental arch curve, obtaining a minor normal axis corresponding to each point by using an interpolation method or other mathematical methods;
(f) the tangent axis and the secondary normal axis of each point form a secondary tangent plane of a local coordinate system of the dental arch curve, the perpendicular line of the secondary tangent plane is a main normal axis (7), the tangent axis and the main normal axis form a close plane, and the main normal axis and the secondary normal axis form a normal plane;
(g) finally, a natural coordinate system of the dental arch curve is established as shown in fig. 4, and the coordinate system has different local coordinate systems consisting of tangent axes, secondary normal axes, primary normal axes, osculating planes, slave tangent planes and normal planes at different point positions of the three-dimensional dental arch curve.
The invention provides a method for automatically aligning teeth based on a coordinate system of a target dental arch curve, which comprises the following steps:
1. obtaining a target dental arch curve according to the method provided by the invention and establishing a curve natural coordinate system;
2. carrying out automatic alignment of three-dimensional positions of teeth:
(a) selecting tooth characteristic points consistent with the tooth characteristic points of the fitted dental arch curve;
(b) the middle points of the incisor feature points on the two sides are coincided with the middle point of the dental arch curve, and the teeth are moved in sequence to make the feature points of the teeth coincide on the dental arch curve;
(c) checking the adjacent collision, moving the teeth along the dental arch curve to ensure that the adjacent surfaces of the teeth are just contacted, or reserving a small amount of adjacent surface collision or a small amount of distance between the adjacent surfaces according to the requirement of stripping the adjacent surfaces or reserving gaps of a medical scheme;
3. carrying out automatic alignment of three-dimensional angles of teeth:
(a) determining a transverse tooth axis (9) and a long tooth axis (10) of the tooth, wherein the long tooth axis can be a main component axis of mathematical calculation, and can also be a connecting line from a crown central point (11) to a root central point (13), a connecting line from the crown central point to a cusp point (14), a connecting line from the cusp point to the cusp point and the like, when only a crown model is used, the cusp point or the root central point is generated virtually, and the transverse tooth axis is along the back tooth and is generated virtually for the big data
Figure RE-GDA0003569721200000091
The line connecting the mesial edge ridge point and the distal edge ridge point in the face median sulcus direction, the line connecting the mesial edge ridge point and the distal edge ridge point in the anterior tooth along the cusp or incisal edge direction, or other methods may be used to define the transverse axis of the tooth in the mesial-distal direction, such as the line connecting the mesial adjacent point and the distal adjacent point, or
Figure RE-GDA0003569721200000092
The perpendicular line of the connecting line of the buccal cusp and the lingual cusp on the face, and the like;
(b) rotating the teeth around the minor normal axis of the local curvilinear coordinate system of the teeth to make the included angle between the transverse axis of the teeth and the tangent axis of the curvilinear coordinate system on the intimate plane of the curvilinear coordinate system be 0, thereby positioning the crown torsion of the teeth, as shown in fig. 5, the incisor crowns are twisted and aligned;
(c) rotating the tooth around the main normal axis of the tooth local curve coordinate system to make the tooth long axis and the minor normal axis reach certain standard value in the tangent plane of the curve coordinate system, so as to obtain the tooth with proper tooth thicknessPositioning crown axis inclination of teeth, the standard value is relative to the existing value
Figure RE-GDA0003569721200000093
Converting the standard value of the plane crown axis inclination into a crown axis inclination value of a relative curve coordinate system measured by big data;
(d) rotating the teeth around the tangent axis of the local curvilinear coordinate system of the teeth to make the included angle between the long axis of the teeth and the minor normal axis of the curvilinear coordinate system on the normal plane of the curvilinear coordinate system be 0, thereby positioning the crown inclination (crown torque) of the teeth, and aligning the incisor crowns in an inclined manner as shown in fig. 6;
4. self-checking and personalized adjustment of occlusion relation:
(a) checking the coverage between the upper and lower dentitions, and making each tooth move buccally and lingually along the main normal axis of the local coordinate system to achieve standard coverage between the upper and lower dentitions, or setting personalized coverage according to the requirements of medical schemes;
(b) checking the collision of the opposite jaws, and moving each tooth up and down along a secondary normal axis of a local coordinate system to ensure that the upper jaw and the lower jaw are in light contact or non-contact, or setting local heavy contact according to the requirements of a medical scheme;
(c) other angles of the teeth can be adjusted properly to obtain better occlusion;
(d) checking again for abutment collisions, repositioning the teeth after movement for crown twist, crown axis tilt and crown tilt if the teeth need to be moved along the desired arch curve,
(e) checking coverage, checking jaw collision, checking adjacent collision, and sequentially iterating to move and rotate the teeth until reaching reasonable or personalized tooth arrangement to complete automatic tooth arrangement;
(f) the ideal bite relation parameters can generate a new coordinate system template.
The invention provides a tooth movement evaluation method based on a coordinate system of a target dental arch curve, which specifically comprises the following steps:
1. obtaining a target dental arch curve according to the method provided by the invention and establishing a curve natural coordinate system;
2. according to the method provided by the invention, the teeth are automatically aligned based on the dental arch curve coordinate system, and a technician or a doctor can manually adjust the teeth based on the automatic alignment result of the teeth according to the treatment requirement to obtain the final target position tooth arrangement;
3. calculating tooth coordinates:
(a) defining the orientation of the coordinate system: in the natural coordinate system of the dental arch curve, the tangent axis of the curve is the mesial-distal direction of the teeth, the primary normal axis is the labial (buccal) lingual (palatal) direction of the teeth, and the secondary normal axis is the vertical direction of the teeth;
in the natural coordinate system of the dental arch curve, the normal plane of the curve is the labial (buccal) lingual (palatal) plane of the tooth, the slave incisal plane of the curve is the mesial-distal plane of the tooth, and the osculating plane of the curve is the horizontal plane of the tooth;
(b) selecting tooth measuring points: as shown in fig. 7, the tooth measurement point may be a incisal edge midpoint or a cusp point (1), or may be a crown central point (11), a tooth impedance central point (12), a root central point (13) or a cusp point (14);
(c) positioning a tooth local coordinate system: positioning corresponding points of tooth measurement points on an arch curve, namely perpendicular points of the tooth measurement points on the arch curve, wherein A ' points and B ' points shown in figures 8-10 are respectively corresponding points of measurement points A and B on the arch curve when teeth are at A positions and B positions, if the B positions are automatic tooth arrangement results of the teeth based on an arch curve coordinate system, the B points and the B ' points are probably overlapped, and a local coordinate system established on the corresponding points of the arch curve is a local coordinate system of the teeth;
(d) calculating the three-dimensional position of the tooth:
the near-far center coordinate refers to the tooth position on the tangent axis, i.e. the curve distance between the corresponding point of the tooth measuring point on the alveolar arch curve and the origin of the curve coordinate system, such as the curve a' O in fig. 8 and 9;
labial (buccal) lingual (palatal) coordinates refer to tooth positions on the principal normal axis, i.e., the linear distance between the perpendicular point of the tooth measurement point on the principal normal axis and the corresponding point on the alveolar arch curve, as shown by line AA' (16) in fig. 8;
the vertical coordinate refers to the tooth position on the minor normal axis, i.e., the linear distance between the perpendicular point of the tooth measurement point on the minor normal axis and the corresponding point on the alveolar arch curve, such as line AA' (18) in fig. 9;
(e) calculating the three-dimensional angle of the tooth:
the torsion angle is an included angle (17) between the tooth transverse axis and a curve tangent axis in the osculating plane;
the axial inclination angle refers to an included angle (19) between the tooth major axis and a curve minor normal axis on a secondary tangent plane;
the inclination angle is an included angle (20) between the tooth major axis and a curve minor normal axis on a normal plane;
(f) and calculating the initial position tooth coordinates and the target position tooth coordinates, and calculating the tooth coordinates in any intermediate stage.
4. Calculating tooth movement changes: the tooth movement change is equal to the difference value between the tooth coordinate of the initial position and the tooth coordinate of the target position, including three-dimensional displacement and three-dimensional angle change, and the tooth movement change of the evaluation stage can also be calculated by calculating the difference value between the tooth coordinate of the initial position and the tooth coordinate of any stage;
the mesial-distal movement refers to the movement of the tooth along the tangent axis, i.e. the change of the coordinates of the tooth's mesial-distal, such as the curve arc length a ' B ' (15) in fig. 8 and 9, wherein the movement close to the middle point of the curve is mesial movement and the movement far from the middle point of the curve is distal movement;
labial (buccal) lingual (palatal) movement refers to movement of the teeth along the primary normal axis, i.e., change in labial (buccal) lingual (palatal) coordinates of the teeth, as shown by the difference (16) in line spacing between AA 'and BB' in fig. 8, wherein labial (buccal) movement refers to outward movement and lingual (palatal) movement refers to inward movement;
elongation, depression refers to movement of the tooth along the minor normal axis, i.e., change in the tooth's vertical coordinate, as shown by the difference between the line distances AA ' and B B ' in fig. 9 (18); wherein, the upper jaw moves downwards to be elongated and the lower jaw moves upwards to be depressed, and vice versa;
twist refers to the change in twist angle in the osculating plane, as shown by the difference between the twist angle at position a and the twist angle at position B in fig. 8;
the inclination of the shaft refers to the change of the inclination of the shaft in a tangent plane, such as the difference between the inclination of the shaft at the position A and the inclination of the shaft at the position B in FIG. 9;
tilt refers to the change in tilt angle in the normal plane, as shown by the difference between the tilt angle at the A position and the tilt angle at the B position in FIG. 10.
5. Outputting tooth coordinates and tooth movement changes: if tooth coordinates and tooth movement changes are calculated for a plurality of measurement points of the tooth, a plurality of sets of tooth coordinates and tooth movement change scales are output.
For juvenile patients, there are growth variations in the three dimensions of length, width, and depth of the dental arch during orthodontic treatment. The doctor can perform personalized adjustment of the length, width and bending depth of the dental arch curve according to the prediction of the growth and development amount of the jaw bone of the patient. For the dental arch curve coordinate system, doctors can properly adjust according to the characteristics of patients and treatment needs, and set coordinate angles of personalized treatment concepts, such as adjusting a minor-normal axis and a tangent axis, so that a better automatic tooth arrangement result and a better tooth movement evaluation result are obtained.
The figures are only by way of example and the invention is not limited to the embodiments shown in the figures. Any equivalent modifications and substitutions to those skilled in the art are also within the scope of the present invention. Accordingly, equivalent changes and modifications made without departing from the spirit and scope of the present invention should be covered by the present invention.

Claims (10)

1. A method for establishing a coordinate system based on a target dental arch curve sequentially comprises the following steps:
obtaining a target arch curve based on the pre-treatment tooth arrangement or the big data arch curve;
and establishing a curve natural coordinate system based on the target dental arch curve.
2. The method for establishing a coordinate system based on a target dental arch curve according to claim 1, wherein the specific method for obtaining the target dental arch curve based on the pre-treatment tooth arrangement or the big data dental arch curve is as follows:
(1) acquiring a digital dental model before treatment, selecting tooth characteristic points on the upper jaw model and the lower jaw model respectively, fitting an upper jaw dental arch curve and a lower jaw dental arch curve respectively by using a mathematical method,
wherein the characteristic points of the tooth are incisal edge midpoint of incisor, canine of canine, premolar and molar, and can also be coronal axis point, dental crown geometric center point, adjacent contact point or functional cuspate point,
the fitted dental arch curve has different forms in the three-dimensional direction, on the horizontal plane, the dental arch curve is roughly divided into a pointed circle, an oval circle, a square circle and a personalized arch, on the sagittal plane, the dental arch curve is in a Spee curve form, and on the coronal plane, the dental arch curve is in a Wilson curve form; alternatively, the first and second electrodes may be,
obtaining an upper jaw dental arch curve and a lower jaw dental arch curve according to a dental arch curve fitted by the big data dentition, selecting a proper dental arch curve form in the big data, and determining the width, the length and the depth of the dental arch curve according to the width, the length and the depth of the dental arch before treatment;
(2) automatically matching the upper jaw dental arch curve and the lower jaw dental arch curve to ensure that the upper jaw dental arch curve and the lower jaw dental arch curve have uniform normal coverage on a horizontal plane;
(3) the doctor or the technician can adjust the width, the length, the depth and the shape of the dental arch curve and the matching degree of the upper dental arch curve and the lower dental arch curve according to the treatment requirement in an individualized way, and finally generates the target dental arch curve.
3. The method for establishing a coordinate system based on a target dental arch curve according to claim 1, wherein the curve natural coordinate system is established according to the following steps:
(1) selecting a middle point on a target dental arch curve as an origin of a coordinate system, and sequentially determining reference points and intervals corresponding to tooth positions on the dental arch curve according to the width of teeth of a patient from the origin of the coordinate system;
(2) regarding any point on the dental arch curve, taking the tangent line of the curve at the point as the tangent axis of the local coordinate system, and taking the plane vertical to the tangent axis as a normal plane;
(3) determining a secondary normal axis of a local coordinate system on a normal plane where a reference point corresponding to each tooth position is located, wherein the method comprises the following steps: make the teeth opposite
Figure RE-FDA0003569721190000011
Converting the standard reference values of crown axis inclination and crown inclination of the plane into angle data of the tooth long axis relative to the dental arch curve or according to the normal after treatment
Figure RE-FDA0003569721190000012
Model or untreated normality
Figure RE-FDA0003569721190000013
Obtaining angle data of a tooth long axis of each tooth position relative to a dental arch curve by using big data of the dental model, and determining a projection line of the tooth long axis on a normal plane as a secondary normal axis;
the physician can individually adjust the minor normal axis of each tooth position reference point according to the requirement of the treatment scheme of the patient;
for points between every two tooth position reference points on the dental arch curve, obtaining a minor normal axis corresponding to each point by using an interpolation method or other mathematical methods;
(4) the tangent axis and the secondary normal axis of each point form a secondary tangent plane of a local coordinate system of the dental arch curve, the perpendicular line of the secondary tangent plane is a main normal axis, the tangent axis and the main normal axis form a close plane, and the main normal axis and the secondary normal axis form a normal plane;
finally, a natural dental arch curve coordinate system with different local coordinate systems consisting of tangent axes, secondary normal axes, primary normal axes, osculating planes, secondary tangent planes and normal planes at different positions of the three-dimensional dental arch curve is established.
4. An automatic tooth arrangement method using the method for establishing a coordinate system based on a target arch curve according to any one of claims 1 to 3 for automatic tooth arrangement.
5. The automatic tooth arrangement method according to claim 4, wherein the specific method for automatic tooth arrangement based on the target arch curve coordinate system is as follows:
obtaining a target arch curve and establishing a curve natural coordinate system according to the method of any one of claims 1-3;
selecting tooth characteristic points consistent with the tooth characteristic points of the fitted dental arch curve;
determining a long tooth axis and a transverse tooth axis of the tooth;
the middle points of the characteristic points of the incisors on the two sides are coincided with the middle point of the dental arch curve, and the characteristic points of all teeth are coincided on the dental arch curve in sequence;
software checks for abutment collisions and moves the teeth along the arch curve to bring the teeth into point contact without gaps or collisions or to retain a small amount of abutment collisions or small amount of inter-abutment distance according to medical protocol requirements;
rotating the teeth around a minor normal axis of a local curve coordinate system of the teeth to enable an included angle between a transverse axis of the teeth and a tangent axis of the curve coordinate system on a close plane of the curve coordinate system to be 0, so that the crown torsion of the teeth is positioned;
rotating the tooth around the tangent axis of the tooth local curve coordinate system to make the included angle between the tooth long axis and the minor normal axis of the curve coordinate system on the normal plane of the curve coordinate system be 0, thereby positioning the crown inclination of the tooth, namely the crown torque;
rotating the tooth around the main normal axis of the tooth local curve coordinate system to make the tooth long axis and the minor normal axis reach certain standard value in the tangent plane of the curve coordinate system so as to position the crown axis inclination of the tooth
Figure RE-FDA0003569721190000021
Converting the standard value of the plane crown axis inclination into a crown axis inclination value of a relative curve coordinate system measured by big data;
checking the coverage between the upper and lower dentitions, and making each tooth move buccally and lingually along the main normal axis of the local coordinate system to achieve standard coverage between the upper and lower dentitions or personalized coverage according to the requirements of medical schemes;
checking the collision of the opposite jaws, and moving each tooth up and down along a secondary normal axis of a local coordinate system to ensure that the upper jaw and the lower jaw are in light contact or non-contact, or partially keep heavy contact according to the requirement of a medical scheme;
to obtain better occlusion and abutment, the angles of the teeth can be adjusted appropriately;
and (4) checking abutting collision again, if the teeth need to move along the dental arch curve, repositioning crown torsion, crown axis inclination and crown inclination of the teeth after moving, checking coverage, checking jaw collision, and sequentially iterating to move and rotate the teeth until reasonable tooth arrangement is achieved to finish automatic tooth arrangement.
The ideal bite relation parameters can generate a new coordinate system template.
6. A tooth movement evaluation method using the method of establishing a coordinate system based on a target arch curve according to any one of claims 1 to 3.
7. The tooth movement evaluation method according to claim 6, wherein the tooth movement evaluation is performed according to the following steps:
the method according to claim 4 or 5, wherein the teeth are automatically aligned, and the technician or physician can manually adjust the teeth based on the automatic alignment result according to the treatment requirement to obtain the final target position tooth arrangement;
calculating tooth coordinates;
calculating tooth movement changes;
outputting tooth coordinates and tooth movement changes.
8. The tooth movement evaluation method according to claim 6 or 7, wherein the step of calculating the tooth coordinates comprises:
(1) defining the orientation of the coordinate system:
in the natural coordinate system of the dental arch curve, the tangent axis of the curve is the mesial-distal direction of the teeth, the primary normal axis is the labial (buccal) lingual (palatal) direction of the teeth, and the secondary normal axis is the vertical direction of the teeth;
in the natural coordinate system of the dental arch curve, the normal plane of the curve is the labial (buccal) lingual (palatal) plane of the tooth, the slave incisal plane of the curve is the mesial-distal plane of the tooth, and the osculating plane of the curve is the horizontal plane of the tooth;
(2) calculating coordinates of the tooth, including three-dimensional position and three-dimensional angle:
positioning corresponding points of the tooth measuring points on the dental arch curve, wherein the corresponding points are vertical points of the tooth measuring points on the dental arch curve, and a local coordinate system established on the corresponding points of the dental arch curve is the local coordinate system of the teeth;
the near-far middle coordinate refers to the tooth position on the tangent axis, namely the curve distance between the corresponding point of the tooth measuring point on the alveolar arch curve and the origin of the curve coordinate system;
the labial (buccal) lingual (palatal) coordinate refers to the tooth position on the principal normal axis, namely the linear distance between the perpendicular point of the tooth measuring point on the principal normal axis and the corresponding point on the alveolar arch curve;
the vertical coordinate refers to the tooth position on a secondary normal axis, namely the linear distance between the perpendicular point of the tooth measuring point on the secondary normal axis and the corresponding point on the alveolar arch curve;
the torsion angle is the included angle between the tooth transverse axis and the curve tangent axis on the close plane;
the axial inclination angle refers to an included angle between a tooth long axis and a curve minor normal axis on a secondary tangent plane;
the inclination angle is an included angle between a tooth long axis and a curve minor normal axis on a normal plane;
the initial position tooth coordinates and the target position tooth coordinates are calculated, and the intermediate stage tooth coordinates can also be calculated.
9. A tooth movement evaluation method according to any one of claims 6 to 8, wherein the step of calculating the change in tooth movement is:
the tooth movement change is equal to the difference value of the tooth coordinate of the initial position and the tooth coordinate of the target position, and comprises three-dimensional displacement and three-dimensional angle change;
the difference value between the initial tooth coordinate and the tooth coordinate at any stage can be calculated, and the tooth movement change at the stage is evaluated;
the mesial-distal movement refers to the movement of teeth along a tangent axis, namely the change of the coordinates of the mesial-distal positions of the teeth, wherein the movement close to the middle point of the curve is mesial movement, and the movement far from the middle point of the curve is distal movement;
labial (buccal) lingual (palatal) movement refers to movement of a tooth along a primary normal axis, i.e., change of labial (buccal) lingual (palatal) coordinates of the tooth, wherein labial (buccal) movement refers to outward movement and lingual (palatal) movement refers to inward movement;
the stretching and the depressing refer to the movement of the teeth along a minor normal axis, namely the change of the vertical coordinate of the teeth, wherein the upper jaw moves downwards to be stretched and the upper jaw moves upwards to be depressed, and the lower jaw moves reversely;
twist refers to the change in twist angle in the osculating plane;
axis refers to the change in the angle of inclination of the shaft in the plane of tangency;
tilt refers to the change in angle of inclination in the normal plane.
10. The tooth movement evaluation method according to any one of claims 6 to 9, wherein the tooth measurement points for evaluating the amount of movement of the tooth include a cusp point or a midpoint of an incisal edge, a center point of a crown, a center point of a root, a center point of tooth impedance, and a cusp point.
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