阅读说明：本技术 基于牙槽骨形态的曲线自然坐标系下的牙齿移动评价方法 (Tooth movement evaluation method based on alveolar bone morphology under curve natural coordinate system ) 是由 陈文杰 范祎 于 2021-08-10 设计创作，主要内容包括：本发明涉及一种基于牙槽骨形态的曲线自然坐标系下的牙齿移动评价方法,属于牙科正畸技术领域,其基于牙槽骨形态来构建牙槽弓曲线,并基于该牙槽弓曲线和牙槽骨形态来构建曲线自然坐标系,进而基于该曲线自然坐标系来计算牙齿的坐标、移动量和移动方向。本发明提供反映牙齿相对于牙槽骨的、具有生理意义的移动的评价方法,有助于更科学、更合理、更准确的牙齿移动方案设计和疗效评价。(The invention relates to a tooth movement evaluation method under a curve natural coordinate system based on alveolar bone morphology, belonging to the technical field of dental orthodontics. The invention provides an evaluation method for reflecting the movement of teeth relative to alveolar bones and having physiological significance, and is beneficial to more scientific, more reasonable and more accurate tooth movement scheme design and curative effect evaluation.)

1. A tooth movement evaluation method based on a curve natural coordinate system of alveolar bone morphology sequentially comprises the following steps:

obtaining an alveolar arch curve based on the alveolar bone morphology;

obtaining a curvilinear natural coordinate system based on the alveolar arch curve and alveolar bone morphology; and the combination of (a) and (b),

tooth coordinates are obtained based on the curved natural coordinate system and the amount and direction of movement of the tooth are calculated.

2. The tooth movement evaluation method under the curve natural coordinate system based on the alveolar bone morphology according to claim 1, wherein the alveolar bone morphology is obtained from individual CBCT data of the jaw or from a mean value of CBCT big data of the jaw; the doctor can carry out personalized adjustment to the alveolar bone shape according to the treatment requirement or based on the growth rule.

3. The tooth movement evaluation method in a curved natural coordinate system based on an alveolar bone morphology according to claim 1 or 2, wherein the alveolar arch curve and the curved natural coordinate system are obtained according to the following steps:

determining the positions of the middle points of alveolar ridges at two sides according to the forms of the alveolar ridge tops at the labial side and the lingual side of the tooth, and fitting the middle points of all the alveolar ridges by using a least square method to obtain an alveolar arch curve positioned at the center of the alveolar ridge tops, wherein an individual CBCT (cone-beam computed tomography) data is used for generating an individualized alveolar arch curve or a CBCT (cone-beam computed tomography) big data is used for generating a standardized alveolar arch curve, and the individualized or standardized alveolar arch curve can be changed according to the individualized adjustment of a doctor on the form of an alveolar bone; and the combination of (a) and (b),

and establishing a curve natural coordinate system, wherein a certain point on the alveolar arch curve is selected as an origin of the coordinate system, for any point on the alveolar arch curve, a tangent line, a main normal line and a secondary normal line of the curve at the point are taken as three axes of the coordinate system, and a normal plane, a secondary tangent plane and an osculating plane of the curve at the point are taken as three coordinate surfaces of the coordinate system.

4. The method for evaluating tooth movement according to any one of claims 1 to 3, wherein in the natural coordinate system of the curve, a tangential axis of the curve is a mesial-distal direction of the tooth, a primary normal axis is a labial (buccal) lingual (palatal) direction of the tooth, and a secondary normal axis is a vertical direction of the tooth;

in the curvilinear natural coordinate system, the normal plane of the curve is the labial (buccal) lingual (palatal) plane of the tooth, the sagittal 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.

5. The method for evaluating tooth movement according to any of claims 1 to 4, wherein the coordinates, the amount of movement, and the direction of movement of the tooth are defined based on the curved natural coordinate system,

the near-far center coordinate refers to the tooth position on the tangent axis, namely the curve distance between the perpendicular point of the tooth on the alveolar arch curve and the origin of the curve coordinate system;

labial (buccal) lingual (palatal) coordinates refer to the tooth position on the principal normal axis, i.e. the linear distance between the tooth's perpendicular point on the principal normal axis and the tooth's perpendicular point on the alveolar arch curve;

the vertical coordinate refers to the tooth position on a minor normal axis, namely the linear distance between a vertical point of the tooth on the minor normal axis and a vertical point of the tooth 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 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.

6. The tooth movement evaluation method according to any one of claims 1 to 5, wherein the amount of movement of the tooth is evaluated at four measurement points, which are a crown center point, a cusp point, a tooth impedance center point and a crest center point, respectively.

7. The method for evaluating tooth movement in a curved natural coordinate system based on an alveolar bone morphology according to any one of claims 1 to 6, wherein the change in tooth angle is evaluated in two measurement axes, which are a long tooth axis and a horizontal tooth axis, respectively.

8. The method for evaluating tooth movement according to any one of claims 1 to 7, wherein the output value includes tooth coordinates and tooth coordinate changes in a curved natural coordinate system based on the alveolar bone morphology.

Technical Field

The invention belongs to the technical field of dental orthodontics, and particularly relates to a tooth movement evaluation method based on alveolar bone morphology under a curve natural coordinate system.

Technical Field

Orthodontic treatment is usually realized by adopting fixed or invisible correction technology, namely wearing a correctorAnd (4) treating deformity. Brackets or braces apply various types of corrective forces to the teeth to control movement of the teeth within the alveolar bone. The establishment of a scientific and accurate tooth movement evaluation system has very important significance on treatment target design, treatment mechanics system construction and curative effect evaluation.

Conventional methods for evaluating tooth movement generally use simplified mathematical models, and one common method is to establish a global rectangular coordinate system (also called cartesian coordinate system) in a three-dimensional position space with reference to a jaw bone, and determine the amount and direction of movement of each tooth in the sagittal, coronal, and vertical directions before and after treatment. The method is applied to all teethThe same sagittal, coronal and vertical orientations are given, however, this does not correspond to the feature of teeth arranged in a circular arch and possessing personalized 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 patent document 1). The method, while having a personalized direction of tooth movement, ignores the clinical significance of tooth movement because the pre-treatment tooth is in errorState in errorThe tooth moving direction pointed by the local coordinate system established by the position along the long axis of the tooth is different from the clinically practical moving direction pointed by the normally arranged teeth, the difference exists between the tooth moving direction and the clinically practical moving direction, and the difference is larger when the teeth are not uniform before treatment. 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.

In orthodontics, teeth move within the physiological anatomical range of the alveolar bone, rather than along artificially defined spatial coordinates. The orthodontic force is generally applied to the crown of the tooth and transmitted to the periodontal ligament around the root of the tooth through the tooth body, acts on the alveolar bone after being buffered and absorbed by the periodontal ligament, and further causes reconstruction of the alveolar bone. The bone cells on the compression side are continuously absorbed, the bone cells on the tension side are continuously divided and precipitated into new bones, and the malpositioned teeth finally and gradually move to the ideal position of the alveolar bone under the action of the correcting force. It can be seen that the essence of tooth movement is the reconstruction of periodontal tissues (including alveolar bone), and the definition of spatial displacement change can only reflect the relative displacement of tooth relative to alveolar tissues, so as to provide accurate and scientific diagnostic design basis for doctors. However, the related art has not recognized the above point and is basically limited to the above two methods, and there has not been a method of constructing a curved natural coordinate system based on the morphology of the alveolar bone and evaluating the movement of the tooth based on the curved natural coordinate system.

It should be noted that although the prior art (see patent document 2) refers to a complete orthodontic model based on geometric and constitutive models including teeth, alveolar bone and periodontal ligament, it is only used to simulate and calculate the force distribution and tooth movement of teeth after wearing an appliance by using finite element method, rather than the method provided by us to construct a mathematical coordinate system conforming to clinical practice to scientifically evaluate the three-dimensional movement of teeth, which belongs to completely different concepts for those skilled in the art.

Prior Art

Patent document 1: CN108245264A

Patent document 2: CN111265316A

Disclosure of Invention

In view of the problems in the prior art, the inventors of the present application have conducted extensive studies while recognizing the deep nature of tooth movement, and as a result, have found a tooth movement evaluation method based on the alveolar bone morphology in a curved natural coordinate system. The present invention constructs an alveolar arch curve based on the alveolar bone morphology, constructs a curved natural coordinate system based on the alveolar arch curve, and calculates the amount and direction of movement of teeth based on the curved natural coordinate system. The invention provides an evaluation coordinate system reflecting tooth movement relative to alveolar bones and having physiological significance, wherein the tooth movement evaluation system indirectly reflects the reconstruction amount and the reconstruction direction of the alveolar bones and reflects the real biomechanics mechanism of tooth movement in orthodontic treatment.

According to the invention, the tooth movement evaluation method based on the alveolar bone shape under the curve natural coordinate system is provided. The method comprises the following steps:

obtaining an alveolar arch curve based on the alveolar bone morphology;

obtained based on the alveolar arch curve and alveolar bone morphology (also known as curvilinear movable frame); and the combination of (a) and (b),

tooth coordinates are obtained based on the curved natural coordinate system and the amount and direction of movement of the teeth are calculated.

In one embodiment, the alveolar bone morphology is obtained from individual CBCT data of the jaw, or from a mean of CBCT big data of the jaw; the doctor can carry out personalized adjustment to the alveolar bone shape according to the treatment requirement or based on the growth rule.

In a particular embodiment, the method of obtaining an alveolar arch curve based on alveolar bone morphology comprises the steps of:

aiming at each tooth, determining the midpoint position of alveolar ridges on two sides according to the shapes of the labial and lingual alveolar ridge crests of the tooth; and the combination of (a) and (b),

and fitting the middle points of all alveolar ridges by using a least square method to obtain an alveolar arch curve positioned at the center of the top of the alveolar ridge, wherein an upper alveolar arch curve is obtained based on the form of the upper jaw alveolar bone, a lower alveolar arch curve is obtained based on the form of the lower jaw alveolar bone, in addition, a personalized alveolar arch curve is obtained from the form of the alveolar bone generated based on individual CBCT data, a standardized alveolar arch curve is obtained from the form of the mean alveolar bone generated based on CBCT big data, and the personalized or standardized alveolar arch curve can be changed according to the personalized adjustment of the form of the alveolar bone by a doctor.

The applicant has found that the alveolar arch curve obtained by the above-specified method is advantageous for more accurately evaluating tooth movement and is superior in effect.

In one embodiment, the method of establishing a curvilinear natural coordinate system based on an alveolar arch curve and an alveolar bone morphology comprises the steps of:

selecting a certain point on the alveolar arch curve as the origin of a coordinate system, such as the middle point of the alveolar arch curve;

for any point on the alveolar arch curve, a tangent, a main normal and a secondary normal of the curve at the point are taken as three axes of a coordinate system, and a normal plane, a secondary tangent plane and an osculating plane of the curve at the point are taken as three coordinate surfaces of the coordinate system, so that a curve natural coordinate system is established.

In a curve natural coordinate system, a tangent axis of a curve is in the mesial-distal direction of a tooth, a main normal axis of the curve is in the labial (buccal) lingual (palatal) direction of the tooth, and a secondary normal axis of the curve is directed to the center of an alveolar bone at the labial (buccal) lingual (palatal) side and is in the vertical direction of the tooth;

in the curvilinear natural coordinate system, the normal plane of the curve is the labial (buccal) lingual (palatal) plane of the tooth, the sagittal 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.

In one embodiment, the coordinates, amount of movement, and direction of movement of the tooth are defined based on a curvilinear natural coordinate system as follows:

the near-far middle coordinate refers to the tooth position on the tangent axis, namely the curve arc length between the perpendicular point of the tooth on the alveolar arch curve and the origin of the curve coordinate system;

labial (buccal) lingual (palatal) coordinates refer to tooth positions on a principal normal axis, i.e., the linear distance between a perpendicular point of a tooth on the principal normal axis and a perpendicular point of the tooth on the alveolar arch curve;

the vertical coordinate refers to the tooth position on a minor normal axis, namely the linear distance between a vertical point of the tooth on the minor normal axis and a vertical point of the tooth 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 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 one embodiment, the amount of tooth movement is evaluated at four measurement points, the crown center point, the apex point, the tooth impedance center point, and the crest top tooth center point. The applicants have found that the selection of these four specific measurement points for evaluation more accurately reflects the particular pattern and amount of movement of different parts of the tooth.

In one embodiment, the tooth angle change is evaluated in two measurement axes, which are the long tooth axis and the transverse tooth axis, respectively.

The tooth coordinate and the tooth coordinate change value can be output by a curve natural coordinate system established based on the alveolar bone form.

The invention has the beneficial effects that: tooth movement is no longer represented only in a three-dimensional movement direction and movement amount in a mathematical sense, but in a three-dimensional movement direction and movement amount of a tooth in an alveolar bone that is in accordance with clinical biomechanics practice. In addition, the natural coordinate system of the curve established based on the alveolar bone shape keeps the characteristic that the teeth arranged at different positions of the dental arch have personalized local coordinate systems and is not affected by the errors of tooth inclination, torsion, dislocation and the like before treatmentThe effect of the state. The tooth movement evaluation method is more beneficial to understanding of the clinical actual movement change of the teeth by a doctor, thereby being beneficial to more scientific, more reasonable and more accurate tooth movement scheme design and curative effect evaluation.

Drawings

Fig. 1 is a top view of a natural coordinate system of a curve created based on the morphology of an alveolar bone according to an embodiment of the present invention.

Fig. 2 is a side view of a curvilinear natural coordinate system established based on alveolar bone morphology in accordance with an embodiment of the present invention.

Fig. 3 is a front view of a curvilinear natural coordinate system established based on alveolar bone morphology in an embodiment of the present invention.

FIG. 4 is a schematic view of measurement points and measurement axes for evaluating tooth movement in one embodiment of the present invention.

Fig. 5 is a schematic view for evaluating the mesial-distal displacement, the bucco-lingual displacement and the change in torsion angle of a tooth in a curved natural coordinate system according to an embodiment of the present invention.

FIG. 6 is a graphical representation of the evaluation of tooth vertical displacement, mesial displacement, and change in shaft inclination in a curvilinear natural coordinate system in accordance with an embodiment of the present invention.

FIG. 7 is a schematic representation of evaluating changes in tooth inclination angle in a curvilinear natural coordinate system in accordance with an embodiment of the present invention.

Label 1: alveolar ridge crest contour lines; marker 2: labial and lingual alveolar ridge midpoints; marker 3: alveolar arch curve; marker 4: tangent axis of curve natural coordinate system; marker 5: a principal normal axis of a curvilinear natural coordinate system; marker 6: a minor normal axis of a curved natural coordinate system; marker 7: a crown center point; marker 8: a root tip point; mark 9: a tooth impedance center point; mark 10: a central point of a tooth at the crest of a ridge; mark 11: a tooth length axis; marker 12: a dental transverse axis; marker 13: the tooth moves from the point A to the point B, and the mesial-distal displacement is the curve arc length between the points A 'and B', namely, the integration is carried out on the tangent length along the tangent axis; marker 14: the lingual (buccal) lingual (palatal) coordinate is the line distance between the perpendicular point of the tooth measuring point on the main normal axis and the curve perpendicular point, and the buccal-lingual displacement of the tooth moving from the point A to the point B is the difference between the line distance of the point A 'on the main normal axis and the line distance of the point B' on the main normal axis; marker 15: the parallel line of the tooth transverse axis intersects with the tangent axis of the coordinate system to form an angle; marker 16: 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; marker 17: the vertical coordinate is the line distance between the vertical point of the tooth measuring point on the minor normal axis and the curve vertical point, and the vertical displacement of the tooth moving from the point A to the point B is the difference between the line distance of the point A 'on the minor normal axis and the line distance of the point B' on the minor normal axis; marker 18: 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; marker 19: the inclination angle is the angle between the major axis and the minor normal axis of the tooth on the normal plane, and the inclination of the tooth from point A to point B is changed to the difference between the inclination angles of point A and 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 tooth movement evaluation method based on the alveolar bone morphology under the curve natural coordinate system specifically comprises the following steps:

1. obtaining a digital model of the teeth and jaw:

(a) 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;

(b) obtaining teeth and jaw bone images of a patient through CBCT scanning, and reconstructing a tooth model and a jaw bone model by utilizing three-dimensional software segmentation, wherein the tooth model simultaneously comprises information of a tooth crown and a tooth root, and the jaw bone model comprises information of an alveolar bone;

(c) registering the tooth model from the oral scan with the tooth and jaw model from the CBCT in a crown surface area to obtain a three-dimensional dental model with high-precision crown, root and jaw information;

(d) if the patient does not shoot the CBCT, obtaining a standardized tooth root and jaw bone model corresponding to the oral-scanning dental crown model by using the mean value of the large database;

(e) after obtaining the three-dimensional dental model, the practitioner can individually adjust the alveolar bone morphology in the model according to the treatment requirements of the practitioner or based on the patient's growth assessment.

2. Obtaining an alveolar arch curve based on alveolar bone morphology:

(a) for each tooth, determining the midpoint position (2) of alveolar ridges on two sides according to the labial and lingual alveolar ridge crest forms (1) of the tooth;

(b) fitting the midpoints of all alveolar ridges by using a least square method to obtain a curve, wherein the curve is positioned at the center of the crest of the alveolar ridge, namely an alveolar arch curve (3);

(c) if the distance between the corresponding midpoint of the alveolar ridge and the fitted curve is too large (for example, exceeds 1mm) due to the tooth dislocation, deleting the corresponding midpoint, re-fitting to obtain a new alveolar arch curve, and repeating the steps to check the midpoint of each alveolar ridge.

Wherein, an upper alveolar arch curve is obtained based on the form of the maxillary alveolar bone, and a lower alveolar arch curve is obtained based on the form of the mandibular alveolar bone; obtaining an individualized alveolar arch curve from an alveolar bone morphology generated based on individual CBCT data, and obtaining a standardized alveolar arch curve from an alveolar bone morphology generated based on CBCT big data; the individualized or standardized alveolar arch curve can be changed correspondingly according to the individualized adjustment of the alveolar bone shape by a doctor.

The alveolar arch curve is a three-dimensional curve, similar to the arch curve in FIG. 1, and has a spee curve (horizontal cross section) in FIG. 2Curve), in fig. 3, a wilson curve (cross)Curve) of the profile.

3. Establishing a curve natural coordinate system based on the alveolar bone morphology and the alveolar arch curve:

(a) selecting a point on the alveolar arch curve as the origin of a natural coordinate system of the curve, wherein the point can be any point on the curve, such as the middle point of the alveolar arch curve;

(b) for any point on the alveolar arch curve, the tangent line, the major normal line and the minor normal line of the curve at the point are taken as three axes of a coordinate system, for example, a tangent axis (4), a major normal axis (5) and a minor normal axis (6), as shown in fig. 3, the minor normal axis (6) points to the center of the alveolar bone on the lingual (palatal) side of the lip (cheek), and the major normal axis (5) is perpendicular to both the tangent axis and the minor normal axis;

(c) the normal plane, the tangent plane and the osculating plane of the curve at this point are taken as the three coordinate planes of the coordinate system. The normal plane is composed of a main normal axis and a secondary normal axis and is vertical to the tangent line; the secondary tangent plane consists of a tangent axis and a secondary normal axis and is vertical to the main normal axis; the osculating plane is formed by the tangent axis and the primary normal axis, perpendicular to the secondary normal axis.

In the natural coordinate system of the curve, the tangent axis of the curve is the mesial-distal direction of the tooth, the primary normal axis is the labial (buccal) lingual (palatal) direction of the tooth, and the secondary normal axis is the vertical direction of the tooth.

In the curvilinear natural coordinate system, the normal plane of the curve is the labial (buccal) lingual (palatal) plane of the tooth, the sagittal 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.

4. Establishing measuring points and measuring axes for evaluating tooth movement:

(a) evaluating the tooth displacement change at four measuring points, wherein the four measuring points are respectively a dental crown central point (7), a cusp point (8), a tooth impedance central point (9) and a ridge top tooth central point (10), and respectively reflect the specific movement form and movement amount of different parts of the tooth;

(b) evaluating the change of the tooth angle in two measuring axes, namely a tooth long axis (11) and a tooth transverse axis (12); the tooth long axis and the tooth transverse axis are determined according to the tooth geometric shapes at different positions; the tooth long axis can be the main component axis of the tooth, can be the connecting line of the geometric center point of the tooth crown and the geometric center point of the tooth root, can be the connecting line of the midpoint of the incisor margin and the cusp point for incisors, can be the connecting line of the cusp point and the cusp point for cuspids, can be the connecting line of the midpoint of the bucco-lingual cusp and the cusp point for bicuspids, and can be the connecting line of the cusp point and the cusp point for molarsA line connecting the center point of the surface and the root bifurcation point; the transverse axis of the tooth can be a connecting line of a mesial adjacent point and a distal adjacent point, and can be perpendicular to the long axis of the tooth and can be the incisor margin, the mesial-distal marginal ridge of the cuspid, the bicuspid and the molarStraight lines parallel to the central groove of the surface.

5. The coordinates, the amount of movement, and the direction of movement of the tooth are defined based on a curved natural coordinate system as follows:

(a) near-far center coordinates: the tooth position on the tangent axis, namely the curve arc length between the perpendicular point of the tooth on the alveolar arch curve and the origin of the curve coordinate system;

(b) labial (buccal) lingual (palatal) coordinates: tooth position on the principal normal axis, i.e., the linear distance (14) between the tooth's vertical point on the principal normal axis and the tooth's vertical point on the alveolar arch curve;

(c) vertical coordinate: tooth position on the minor normal axis, i.e. the linear distance (17) between the tooth's vertical point on the minor normal axis and the tooth's vertical point on the alveolar arch curve;

(d) torsion angle: an angle (16) between the transverse axis of the tooth and the tangent axis of the curve on the osculating plane;

(e) shaft inclination angle: an angle (18) between the major axis of the tooth and the minor axis of the curve on the sagittal plane;

(f) inclination angle: an included angle (19) between the tooth major axis and the minor curve normal axis on the normal plane;

(g) moving in the near-far direction: the tooth moves along the tangent axis, namely the change of the tooth near-far center coordinates, namely the arc length (13) of a curve between two points, wherein the movement close to the middle point of the curve is near-center movement, and the movement far from the middle point of the curve is far-center movement; if a tooth moves from position A to position B along the outside of the curve, or from position A to position B along the inside of the curve, the definition of mesial-distal movement of the tooth may be converted from an arc length along the curve to an outer arc length along the outside of the curve or an inner arc length along the inside of the curve, respectively, according to the clinical preference of the practitioner.

(h) Labial (buccal) lingual (palatal) movement: the tooth moves along the main normal axis, namely the change of the tooth lip (cheek) tongue (palate) to the coordinate, wherein, outwards moves for the lip (cheek) and inwards moves for the tongue (palate), and the lip and tongue from the position A to the position B moves towards the position B, namely the difference (14) between the line distance AA 'and the line distance BB' on the main normal axis;

(i) elongation and depression: movement of the tooth along the minor normal axis, i.e. change of vertical coordinates of the tooth, wherein the upper teeth move down or the lower teeth move up to be elongated, the upper teeth move up or the lower teeth move down to be depressed, and the vertical movement of position a to position B, i.e. the difference between the line distance AA 'and the line distance BB' on the minor normal axis (17);

(j) twisting: a change in twist angle in the osculating plane, a twist change (16) being the difference in twist angle from position A to position B;

(k) shaft inclination: a change (18) in the inclination of the shaft from the tangent plane, the inclination of the shaft being the difference between the inclination of the shaft from the position A to the position B;

(l) Inclination: a change in the tilt angle on the normal plane, a tilt change (19) being the difference in tilt angle from position A to position B;

(m) on the three-dimensional alveolar arch curve, the coordinate axes and the coordinate planes of any two points are not parallel, and fig. 5, 6 and 7 are only used for illustrating the definition of three-dimensional displacement and three-dimensional angle change of the tooth, and the coordinate planes of the point A and the point B are respectively unified on a common osculating plane, a common tangential plane and a common normal plane.

6. According to the tooth movement evaluation method in the curve natural coordinate system, the tooth coordinate (near-far middle coordinate, labial-lingual coordinate, vertical coordinate, torsion angle, shaft inclination angle and inclination angle) of a certain position can be output, and the coordinate change (near-far middle displacement, labial-lingual displacement, vertical displacement, torsion, shaft inclination and inclination) of the tooth moving from the position A to the position B can also be output.

In addition, the natural coordinate system of the curve established based on the alveolar bone morphology can be dynamically changed along with the growth and development of the jaw bone. For juvenile patients, there is a growth variation of the jaw bone in three dimensions, length, width and height, during orthodontics treatment. The doctor can perform personalized adjustment of the length, width and height of the alveolar arch curve according to the prediction of the growth and development amount of the jaw bone of the patient. The standardized adjustment of the length, width and height of the alveolar arch curve can be carried out according to the statistical mean value of the growth and development amount of male and female in a certain age group.

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 considered within the scope of the present invention.