Orthodontic tooth movement measurement method based on circular coordinate system

Abstract

The invention discloses an orthodontic tooth movement measurement method based on a circular coordinate system, which comprises the following steps of: acquiring cone beam CT (Computed Tomography) images of upper and lower jaw dentitions and alveolar bones before and after orthodontics, selecting the maximum section of the tooth in the lip-tongue direction along a tooth long axis, and intercepting a relative position map of the teeth and the alveolar bones before and after orthodontics; extracting outer contour diagrams of relative positions of the teeth and the alveolar bone before and after orthodontics from the relative position diagrams of the teeth and the alveolar bone before and after orthodontics, and overlapping the outer contour diagrams; matching the outer contour of the tooth before orthodontic treatment with the outer contour of the tooth after orthodontic treatment; the orthodontic tooth movement is measured based on the circular coordinate system, if the rotation radius is larger than or equal to 10 times of the root length, the orthodontic tooth movement mode in the lip-tongue direction is parallel movement, and if the rotation radius is smaller than 10 times of the root length, the orthodontic tooth movement mode in the lip-tongue direction is inclined movement. According to the method, the orthodontic movement mode is defined from the mathematical theory for the first time, the mathematical theory boundary value is given, and the orthodontic movement modes of teeth in the lip-tongue direction and the vertical direction are quantitatively analyzed.

Description

Technical Field

[0001] The invention belongs to the technical field of orthodontic tooth movement measurement, and in particular relates to an orthodontic tooth movement measurement method based on a circular coordinate system. Background Art

[0002] wrong Deformity is one of the most common oral diseases in humans, with an incidence rate of up to 70%. This disease not only has an adverse effect on the patient's oral health and function, but also has a negative impact on the aesthetic morphology of the oral and maxillofacial area, thereby affecting the patient's mental health and quality of life. With the continuous development of society and the improvement of living standards, people's requirements for oral health and aesthetics are increasing. Therefore, more and more adults choose to receive orthodontic treatment, aiming to restore oral function while pursuing higher aesthetic standards. However, a considerable number of patients have alveolar bone defects such as "bone fenestration" and / or "bone cracking" on the labial alveolar bone of the anterior teeth, and are often accompanied by insufficient soft tissue such as thin gums and narrow keratinized gingival width. If no intervention is taken, the labial movement of the upper and lower anterior teeth during the orthodontic process may aggravate or promote the absorption of the labial and buccal alveolar bone, thereby causing gingival recession and even loose teeth falling off, greatly increasing the risk of orthodontic treatment.

[0003] Periodontists have proposed a method that combines traditional fixed orthodontics, corticotomy, bone grafting, and guided tissue regeneration, namely Periodontally Corticotomy and Regenerative Surgery (PCRS), in order to correct alveolar bone defects before orthodontic lip movement of teeth, and to prevent and avoid the risk of loss of periodontal supporting tissues and even tooth loss after orthodontics. A large number of studies have shown that compared with traditional fixed corrections alone, the PCRS method can increase alveolar bone volume, keratinized gingival width, and gingival thickness, improve gingival recession and periodontal biotype, and effectively shorten the orthodontic treatment course to 1 / 4-1 / 3 of the traditional course.

[0004] During orthodontic treatment, patients with certain characteristics of periodontal soft and hard tissues face a higher risk of alveolar bone resorption and gingival recession, and need periodontal tissue regeneration combined with corticotomy intervention during orthodontic treatment. Regarding these two issues, previous studies and analyses based on cephalometrics, CBCT, and three-dimensional oral scans have shown that the prediction model of periodontal soft tissue after orthodontic-orthodontic patients showed that in univariate analysis, orthodontic movement-related indicators (SNA, SNB) were significant, which is consistent with the clinical experience of orthodontists and periodontists; however, in multivariate regression, orthodontic movement-related indicators were not significant. This shows that cephalometrics has great limitations in explaining periodontal tissue remodeling, and its validity is low and insensitive. Cephalometric measurement is a method of quantitatively analyzing the bones, teeth and soft tissues of the head through lateral skull X-rays. It helps orthodontists and orthodontists evaluate the growth and development of the face and craniofacial region, diagnose jaw and tooth deformities and develop treatment plans. Because it mainly evaluates the relative position of the maxillary and mandibular bones and the skull base, it is less effective in evaluating the relative position of the alveolar bone and teeth. In addition to cephalometric measurement, orthodontists have also used a variety of methods to explore the relationship between orthodontic movement and alveolar bone remodeling. The measurement methods, measurement items and alveolar bone conditions included are not exactly the same, but they are all based on qualitative analysis of incisal displacement, apex displacement and inclination angle, and the conclusions of different studies are also inconsistent. At present, there is no measurement method that can systematically analyze and describe orthodontic movement quantitatively without being limited to orthodontic malocclusion classification. Therefore, there is an urgent need for an orthodontic tooth movement measurement method that can quantitatively analyze the impact of orthodontic movement on periodontal soft and hard tissue remodeling.

[0005] At present, the screening criteria for surgical patients and the determination of the amount of bone grafting during surgery still rely on the doctor's experience and judgment, and lack a strong theoretical basis for clinical research. If patients who are at risk of loss of periodontal soft and hard tissues during orthodontic treatment cannot be accurately screened, doctors will face the problem of over-medicalization when giving patients PCRS surgical intervention. If the amount of bone grafting required during surgery cannot be accurately judged, the surgeon can only try to avoid the risk of reduction of periodontal soft and hard tissues during orthodontic treatment by more bone grafting, which will lead to excessive local bone grafting, and it will be difficult to fully reconstruct the bone powder near the soft tissue flap, resulting in excessive thickness of the labial and lingual bones after surgery. Although it can ensure the safety of orthodontic tooth movement, it may make tooth movement difficult, and even bring aesthetic and functional problems such as narrowing of the vestibule groove, changes in facial soft tissue contours, and facial discomfort; if the amount of bone grafting is insufficient, it will lead to insufficient increase in the thickness of the labial and lingual bones after surgery, making it difficult to fully avoid the risk of loss of periodontal supporting tissues and loose and falling teeth during orthodontic treatment for patients with insufficient periodontal soft and hard tissues.

[0006] The invention patent with application publication number CN110811653A discloses a method for measuring the three-dimensional movement of teeth during orthodontic treatment, which includes the following steps: superimposing the CBCT tooth model at the beginning of treatment and the intraoral scan model to construct a complete tooth model; matching and superimposing the intraoral scan model after a period of treatment with the model at the initial moment for comparison; isolating a single tooth for analysis to construct a local three-dimensional coordinate system of the target tooth; marking three reference points at the crown and bracket positions on the front and back intraoral models respectively, calculating the spatial transformation matrix based on the coordinates of the reference points, and then calculating the three-dimensional translation and rotation movement of the tooth to obtain the three-dimensional tooth movement. This technical solution has the following problems: (1) This method overlaps the maxillary tooth model as a whole, rather than overlapping a single tooth, so the overlap of a single tooth is inaccurate, which in turn affects the subsequent measurement results; and this technology can only overlap the maxillary dentition, and lacks the ability to overlap and subsequently measure the mandibular dentition. (2) This method can only measure the absolute movement position of the tooth, but cannot reflect the relative position relationship between the tooth and the alveolar bone. In many clinical cases, observing the movement of the root through the movement of the crown has great limitations, because the movement of the root may only be reflected in the crown. Moreover, the reference point is selected on the bracket that is artificially bonded to the crown. The bracket is small in size and the distance between the reference points is very close. The selection error is large, and the movement of the root will be reflected in the bracket more subtle, resulting in inaccurate subsequent measurement results. (3) This method relies on oral scanning and CBCT data. The application of oral scanning equipment is not yet widespread, so its application is limited. (4) The local three-dimensional coordinate system of the target tooth constructed by this method takes the impedance center as the origin, but the position of the impedance center cannot be determined theoretically, and the repeatability is very poor. It cannot be used as a reference system for measuring the alveolar bone. (5) The construction rules for the XYZ axes of the local three-dimensional coordinate system of the tooth in this method are not accurate enough and the repeatability is poor. Summary of the invention

[0007] In order to solve the problems existing in the prior art, the present invention provides an orthodontic tooth movement measurement method based on a circular coordinate system, and the measurement method comprises the following steps in order:

[0008] Step 1: Obtain cone beam CT images of the upper and lower jaw dentition and alveolar bone of the orthodontic patient before and after orthodontics, and adjust the cone beam CT image planes before and after orthodontics to be consistent with the long axis direction of the orthodontic teeth;

[0009] Step 2: Select the maximum cross-section of the tooth in the labial / buccal-lingual / palatal direction along the long axis of the tooth, intercept the relative position diagrams of the orthodontic tooth and the alveolar bone before and after orthodontics, and then extract the relative position outer contour diagrams of the teeth and the alveolar bone before and after orthodontics from the relative position diagrams of the teeth and the alveolar bone before and after orthodontics, and overlap the relative position outer contours of the teeth and the alveolar bone before and after orthodontics;

[0010] Step 3: After the outer contours of the relative positions of the teeth and the alveolar bone before and after orthodontics are overlapped, the outer contour of the teeth before orthodontics is matched with the outer contour of the teeth after orthodontics, that is, the outer contour of the teeth before orthodontics is used to replace the outer contour of the teeth in the outer contour diagram of the relative positions of the teeth and the alveolar bone after orthodontics; after the outer contour of the teeth before orthodontics is matched with the outer contour of the teeth after orthodontics, an overlapping diagram of the outer contours of the teeth before and after orthodontics can be formed;

[0011] Step 4: Based on the formed overlapping diagram of the outer contours of the teeth before and after orthodontics, the enamel-cementum junction on the labial side of the tooth and the enamel-cementum junction on the lingual side of the tooth are marked on the outer contour of the tooth before orthodontics, and the midpoint of the line connecting the labial and lingual enamel-cementum junctions is marked; at the same time, the enamel-cementum junction on the labial side of the tooth and the lingual side of the tooth are marked on the outer contour of the tooth after orthodontics, and the midpoint of the line connecting the labial and lingual enamel-cementum junctions is marked;

[0012] Step 5: draw a straight line through the root apex of the orthodontic front tooth and the midpoint of the line connecting the labial and lingual enamel-cementum junction, which is the long axis of the orthodontic front tooth; draw a straight line through the root apex of the orthodontic back tooth and the midpoint of the line connecting the labial and lingual enamel-cementum junction, which is the long axis of the orthodontic back tooth; intersect the long axis of the orthodontic front tooth and the long axis of the orthodontic back tooth at one point, and use the intersection as the rotation center of the labial and lingual movement of the orthodontic tooth, use the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic front tooth and the rotation center as the rotation radius, and use the angle between the long axis of the orthodontic front tooth and the long axis of the orthodontic back tooth as the rotation angle;

[0013] Step 6: Make a circle with the rotation center as the point and the rotation radius as the radius. The circle intersects with the long axis of the orthodontic tooth at one point. The distance between the intersection and the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic tooth is taken as the movement distance of the orthodontic tooth in the long axis direction. The distance between the intersection and the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic tooth before orthodontics is taken as the labial and lingual movement distance of the orthodontic tooth at the midpoint of the enamel-cementum junction. At the same time, make a circle with the rotation center as the center and the distance between the root apex of the orthodontic tooth before orthodontics and the rotation center as the radius. The circle intersects with the long axis of the orthodontic tooth at one point. The distance between the intersection and the root apex of the orthodontic tooth before orthodontics is taken as the labial and lingual movement distance of the orthodontic tooth at the root apex.

[0014] Step 7: If the rotation radius is greater than or equal to 10 times the root length, the orthodontic tooth will move in the labiolingual direction in parallel; if the rotation radius is less than 10 times the root length, the orthodontic tooth will move in the labiolingual direction in tilted movement.

[0015] Preferably, in step 2, for the maxillary teeth, the relative position diagram of the teeth and the alveolar bone before and after orthodontics includes the complete hard palate and nasal floor contour; for the mandibular teeth, the relative position diagram of the teeth and the alveolar bone before and after orthodontics includes the complete mandibular bone contour.

[0016] In any of the above schemes, preferably, in step 2, for maxillary teeth, the outlines of the hard palate and the nasal floor are overlapped; for mandibular teeth, the outline of the mandibular base bone is overlapped.

[0017] In any of the above schemes, preferably, in step 2, the outer contours of the relative positions of the teeth and the alveolar bone before and after orthodontics are overlapped, and the overlap is suitable for teeth whose torsion angle does not exceed 15 degrees before orthodontics.

[0018] In any of the above schemes, preferably, in step three, the outer contour of the tooth before orthodontics is matched with the outer contour of the tooth after orthodontics, and the matching standard is to match the contour of the crown, the contour of the root neck, and the contour of the middle part of the root.

[0019] In any of the above schemes, it is preferred that in step five, the long axis of the teeth before orthodontics and the long axis of the teeth after orthodontics intersect at a point, and the intersection point is located inside or outside the overlapping diagram of the outer contours of the teeth before and after orthodontics, that is, the rotation center of the labiolingual movement of the orthodontic teeth is located inside or outside the overlapping diagram of the outer contours of the teeth before and after orthodontics.

[0020] In any of the above schemes, preferably, in step 7, if the rotation radius is greater than or equal to 10 times the root length, the movement mode of the orthodontic tooth in the labiolingual direction is parallel movement, and the judgment model is Wherein, OM1 is the rotation radius, which is the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior teeth and the rotation center, mm;

[0021] M1Ap1 - root length, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior tooth and the root apex of the orthodontic anterior tooth, mm.

[0022] In any of the above schemes, it is preferred that in step seven, in actual application, if the movement of the orthodontic teeth in the labiolingual direction is small, it is necessary to adjust the rotation radius boundary for determining whether the movement of the orthodontic teeth in the labiolingual direction is parallel movement.

[0023] In any of the above schemes, preferably, in step 7, if the difference between the labial-lingual movement distance of the orthodontic tooth at the midpoint of the cementoenamel junction and the labial-lingual movement distance of the orthodontic tooth at the root apex is kept within the commonly used cone beam CT voxel, then the difference is negligible, the labial-lingual movement mode of the orthodontic tooth is parallel movement, and the judgment model is adjusted to In the formula,

[0024] L1——Labiolingual movement distance of orthodontic teeth at the midpoint of the cementoenamel junction, mm;

[0025] OM1——rotation radius, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior teeth and the rotation center, mm;

[0026] M1Ap1 - root length, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior tooth and the root apex of the orthodontic anterior tooth, mm.

[0027] In the present invention, image processing software such as Photoshop and Procreate can be used to extract the outer contour of the relative position of teeth and alveolar bones from the outer contour images of the relative positions of teeth and alveolar bones before and after orthodontics; GeoGebra image processing software can be used to measure the overlapping images of the outer contours of teeth before and after orthodontics, or measurement tools such as rulers, triangles, and compasses can be directly used for measurement.

[0028] Steps 1 to 7 are the process of measuring the movement of one orthodontic tooth. Steps 1 to 7 can be repeated for the movement measurement of other orthodontic teeth.

[0029] In step three, since there is often external root resorption in teeth after orthodontics, in order to eliminate and offset the influence of root resorption on the measurement, after the outer contours of the relative positions of the teeth and the alveolar bone before and after orthodontics overlap, it is necessary to match the outer contours of the teeth before orthodontics with the outer contours of the teeth after orthodontics, that is, use the outer contours of the teeth before orthodontics to replace the outer contours of the teeth in the outer contour diagram of the relative position of the teeth and the alveolar bone after orthodontics.

[0030] In step 7, determine the model The deduction process is as follows: When orthodontic teeth move in the labiolingual direction, they move in parallel.

[0031] L1=2OM1Sinα

[0032] L2=2OAp1Sinα

[0033]

[0034] Where:

[0035] L1——Labiolingual movement distance of orthodontic teeth at the midpoint of the cementoenamel junction, mm;

[0036] L2——the labial-lingual movement distance of the orthodontic tooth at the root apex, mm;

[0037] OM1——rotation radius, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior teeth and the rotation center, mm;

[0038] OAp1 – the distance between the apex and the rotation center of the orthodontic front tooth, mm;

[0039] α——Rotation angle, that is, the angle between the long axis of the teeth before orthodontics and the long axis of the teeth after orthodontics, degrees;

[0040] M1Ap1 - root length, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior tooth and the root apex of the orthodontic anterior tooth, mm.

[0041] When the rotation radius is greater than or equal to 10 times the root length, OM1-M1Ap1≈OM1, The movement of orthodontic teeth in the labiolingual direction can be considered as parallel movement.

[0042] The orthodontic tooth movement measurement method based on the circular coordinate system of the present invention has the following beneficial effects:

[0043] (1) The present invention is the first to create an orthodontic tooth movement measurement method based on a circular coordinate system. This method is a mathematical analysis method used to quantitatively analyze the sagittal (labio-lingual) and vertical orthodontic tooth movement patterns.

[0044] (2) The present invention obtains overlapping views of the labial-lingual teeth and alveolar bone contours by overlapping the CBCT images of the teeth before and after orthodontics, and decomposes the complex labial-lingual tooth movement during orthodontics into four parameters: rotation radius, rotation angle, rotation chord length, and vertical (long axis direction) displacement for accurate quantitative description. The rotation center is the intersection of the long axes of the front and back teeth during orthodontic tooth movement; the rotation radius is the distance from the midpoint of the cementoenamel junction of the labial and lingual sides of the front teeth to the rotation center.

[0045] (3) The measurement method of the present invention mathematically defines the classic orthodontic movement mode for the first time and provides a mathematical theoretical boundary value, taking an important step towards the scientific measurement of orthodontic movement. This measurement method breaks through the constraints of the original measurement system, focuses on the relative position relationship between the alveolar bone and the teeth, and scientifically and comprehensively quantitatively analyzes the orthodontic movement patterns of single-rooted teeth in the labial-lingual and vertical directions.

[0046] (4) This invention provides a solid scientific basis for further advancing the study of the effects of orthodontic movement on periodontal soft and hard tissue reconstruction. Subsequent research based on this invention is expected to provide a further scientific basis for the accurate screening of orthodontic patient groups with a high risk of periodontal soft and hard tissue defects, and to provide a scientific basis for the combined periodontal-orthodontic treatment of bone defects. Provide diagnosis and treatment routines and technical procedures for patients with deformities, clarify the amount of bone grafting required during surgery, and provide a basis for multidisciplinary clinical cooperation and healthy correction. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 A flowchart of a preferred embodiment of an orthodontic tooth movement measurement method based on a circular coordinate system according to the present invention;

[0048] Figure 2 for Figure 1 The cone beam CT image of the orthodontic tooth before orthodontic treatment obtained in the illustrated embodiment (the cone beam CT image is consistent with the long axis direction of the target tooth);

[0049] Figure 3 for Figure 1 Cone beam CT images of orthodontic teeth after orthodontic treatment obtained in the illustrated embodiment (the cone beam CT images are consistent with the long axis direction of the target teeth);

[0050] Figure 4 for Figure 1 Overlapping diagram of the outer contours of the relative positions of the orthodontic teeth and the alveolar bone before and after orthodontic treatment in the illustrated embodiment;

[0051] Figure 5 for Figure 1 Overlapping diagram of the outer contours of orthodontic teeth before and after orthodontic treatment in the illustrated embodiment;

[0052] Figure 6 for Figure 1 The illustrated embodiment is a process diagram for measuring orthodontic tooth movement based on a circular coordinate system, wherein: (a) the enamel-cementum junction on the labial side of the tooth and the enamel-cementum junction on the lingual side of the tooth are marked on the outer contour of the tooth before and after orthodontics, and the midpoint of the enamel-cementum junction on the labial side of the tooth and the enamel-cementum junction on the lingual side of the tooth before and after orthodontics is marked; (b) a straight line is drawn through the root apex points of the teeth before and after orthodontics and the midpoint of the line connecting the labial and lingual enamel-cementum junctions, and the straight line is the long axis of the teeth before and after orthodontics; (c) the long axes of the teeth before and after orthodontics intersect at one point, and the intersection is the rotation center of the labial and lingual movement of the orthodontic teeth; (d) the rotation center is used as the center of the circle, and the midpoint of the line connecting the labial and lingual enamel-cementum junctions of the front teeth before orthodontics and the right tooth are drawn. The distance between the rotation centers, and the distance between the root apex of the tooth before orthodontics and the rotation center as the radius to draw a circle, and intersect with the long axis of the tooth after orthodontics; (e) the circle intersects with the long axis of the tooth after orthodontics at two points, and the distance between one intersection point and the midpoint of the line connecting the labial and lingual enamel-cementum junction of the tooth after orthodontics is the movement distance of the orthodontic tooth in the long axis direction; (f) the circle intersects with the long axis of the tooth after orthodontics at two points, and the distance between one intersection point and the midpoint of the line connecting the labial and lingual enamel-cementum junction of the tooth before orthodontics is the labial and lingual movement distance of the orthodontic tooth at the midpoint of the enamel-cementum junction, and the distance between the other intersection point and the root apex of the tooth before orthodontics is the labial and lingual movement distance of the orthodontic tooth at the root apex. DETAILED DESCRIPTION

[0053] In order to further understand the content of the present invention, the present invention will be described in detail below in conjunction with specific embodiments.

[0054] like Figure 1 As shown, according to a preferred embodiment of the orthodontic tooth movement measurement method based on a circular coordinate system of the present invention, the measurement method comprises the following steps in chronological order:

[0055] Step 1: Obtain cone beam CT images of the upper and lower jaw dentition and alveolar bone of the orthodontic patient before and after orthodontics, and adjust the cone beam CT image planes before and after orthodontics to be consistent with the long axis direction of the orthodontic teeth;

[0056] Step 2: Select the maximum cross-section of the tooth in the labial / buccal-lingual / palatal direction along the long axis of the tooth, intercept the relative position diagrams of the orthodontic tooth and the alveolar bone before and after orthodontics, and then extract the relative position outer contour diagrams of the teeth and the alveolar bone before and after orthodontics from the relative position diagrams of the teeth and the alveolar bone before and after orthodontics, and overlap the relative position outer contours of the teeth and the alveolar bone before and after orthodontics;

[0057] Step 3: After the outer contours of the relative positions of the teeth and the alveolar bone before and after orthodontics are overlapped, the outer contour of the teeth before orthodontics is matched with the outer contour of the teeth after orthodontics, that is, the outer contour of the teeth before orthodontics is used to replace the outer contour of the teeth in the outer contour diagram of the relative positions of the teeth and the alveolar bone after orthodontics; after the outer contour of the teeth before orthodontics is matched with the outer contour of the teeth after orthodontics, an overlapping diagram of the outer contours of the teeth before and after orthodontics can be formed;

[0058] Step 4: Based on the formed overlapping diagram of the outer contours of the teeth before and after orthodontics, the enamel-cementum junction on the labial side of the tooth and the enamel-cementum junction on the lingual side of the tooth are marked on the outer contour of the tooth before orthodontics, and the midpoint of the line connecting the labial and lingual enamel-cementum junctions is marked; at the same time, the enamel-cementum junction on the labial side of the tooth and the lingual side of the tooth are marked on the outer contour of the tooth after orthodontics, and the midpoint of the line connecting the labial and lingual enamel-cementum junctions is marked;

[0059] Step 5: draw a straight line through the root apex of the orthodontic front tooth and the midpoint of the line connecting the labial and lingual enamel-cementum junction, which is the long axis of the orthodontic front tooth; draw a straight line through the root apex of the orthodontic back tooth and the midpoint of the line connecting the labial and lingual enamel-cementum junction, which is the long axis of the orthodontic back tooth; intersect the long axis of the orthodontic front tooth and the long axis of the orthodontic back tooth at one point, and use the intersection as the rotation center of the labial and lingual movement of the orthodontic tooth, use the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic front tooth and the rotation center as the rotation radius, and use the angle between the long axis of the orthodontic front tooth and the long axis of the orthodontic back tooth as the rotation angle;

[0060] Step 6: Make a circle with the rotation center as the point and the rotation radius as the radius. The circle intersects with the long axis of the orthodontic tooth at one point. The distance between the intersection and the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic tooth is taken as the movement distance of the orthodontic tooth in the long axis direction. The distance between the intersection and the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic tooth before orthodontics is taken as the labial and lingual movement distance of the orthodontic tooth at the midpoint of the enamel-cementum junction. At the same time, make a circle with the rotation center as the center and the distance between the root apex of the orthodontic tooth before orthodontics and the rotation center as the radius. The circle intersects with the long axis of the orthodontic tooth at one point. The distance between the intersection and the root apex of the orthodontic tooth before orthodontics is taken as the labial and lingual movement distance of the orthodontic tooth at the root apex.

[0061] Step 7: If the rotation radius is greater than or equal to 10 times the root length, the orthodontic tooth will move in the labiolingual direction in parallel; if the rotation radius is less than 10 times the root length, the orthodontic tooth will move in the labiolingual direction in tilted movement.

[0062] In step 2, for maxillary teeth, the relative position diagram of teeth and alveolar bones before and after orthodontics includes the complete hard palate and nasal floor contours; for mandibular teeth, the relative position diagram of teeth and alveolar bones before and after orthodontics includes the complete mandibular bone contour. For maxillary teeth, the contours of the hard palate and nasal floor are overlapped; for mandibular teeth, the contours of the mandibular base bone are overlapped. The outer contours of the relative positions of teeth and alveolar bones before and after orthodontics are overlapped, and this overlap is applicable to teeth whose twist angle before orthodontics does not exceed 15 degrees.

[0063] In step three, the outer contour of the tooth before orthodontics is matched with the outer contour of the tooth after orthodontics, and the matching standard is to match the contour of the crown, the contour of the root neck, and the contour of the middle part of the root.

[0064] In step five, the long axis of the teeth before orthodontics and the long axis of the teeth after orthodontics are intersected at one point, and the intersection point is located inside or outside the overlapping diagram of the outer contours of the teeth before and after orthodontics, that is, the rotation center of the labiolingual movement of the orthodontic teeth is located inside or outside the overlapping diagram of the outer contours of the teeth before and after orthodontics.

[0065] In step 7, if the rotation radius is greater than or equal to 10 times the root length, the orthodontic tooth moves in the labiolingual direction in parallel, and the model is determined to be In the formula,

[0066] OM1——rotation radius, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior teeth and the rotation center, mm;

[0067] M1Ap1 - root length, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior tooth and the root apex of the orthodontic anterior tooth, mm.

[0068] In practical applications, if the labiolingual movement of the orthodontic tooth is small, it is necessary to adjust the radius of rotation for judging whether the labiolingual movement of the orthodontic tooth is parallel movement. If the difference between the labiolingual movement distance of the orthodontic tooth at the midpoint of the cementoenamel junction and the labiolingual movement distance of the orthodontic tooth at the root apex is kept within the commonly used cone beam CT voxel, the difference is negligible, and the labiolingual movement of the orthodontic tooth is parallel movement, and the judgment model is adjusted to In the formula,

[0069] L1——Labiolingual movement distance of orthodontic teeth at the midpoint of the cementoenamel junction, mm;

[0070] OM1——rotation radius, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior teeth and the rotation center, mm;

[0071] M1Ap1 - root length, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior tooth and the root apex of the orthodontic anterior tooth, mm.

[0072] In this embodiment, the cone beam CT image of the orthodontic tooth before orthodontic treatment (the cone beam CT image is consistent with the long axis direction of the target tooth) is obtained as follows: Figure 2 As shown in FIG. 1 , the cone beam CT image of the orthodontic tooth after orthodontic treatment (the cone beam CT image is consistent with the long axis direction of the target tooth) is shown in FIG. Figure 3 As shown in the figure, the relative position of the teeth and alveolar bone before and after orthodontic treatment overlaps as shown in the figure. Figure 4 As shown, the overlapping diagram of the outer contours of orthodontic teeth before and after orthodontic treatment is shown in Figure 5 shown.

[0073] In this embodiment, the process of measuring orthodontic tooth movement based on the circular coordinate system is as follows: Figure 6As shown in the figure, among which: (a) the enamel-cementum junction on the labial side of the tooth and the enamel-cementum junction on the lingual side of the tooth are marked on the outer contour of the tooth before and after orthodontics, and the midpoint of the enamel-cementum junction on the labial side of the tooth and the enamel-cementum junction on the lingual side of the tooth before and after orthodontics is marked; (b) a straight line is drawn through the root apex of the teeth before and after orthodontics and the midpoint of the line connecting the labial and lingual enamel-cementum junctions, and the straight line is the long axis of the teeth before and after orthodontics; (c) the long axes of the teeth before and after orthodontics intersect at one point, and the intersection is the rotation center of the labial and lingual movement of the orthodontic teeth; (d) the rotation center is taken as the center of the circle, and the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junctions of the teeth before orthodontics and the rotation center ... are drawn as the center of the circle. A circle is made with the distance between the root apex point of the tooth before orthodontics and the rotation center as the radius, and the circle intersects with the long axis of the tooth after orthodontics; (e) The circle intersects with the long axis of the tooth after orthodontics at two points, and the distance between one intersection point and the midpoint of the line connecting the labial and lingual enamel-cementum junction of the tooth after orthodontics is the movement distance of the orthodontic tooth in the long axis direction; (f) The circle intersects with the long axis of the tooth after orthodontics at two points, and the distance between one intersection point and the midpoint of the line connecting the labial and lingual enamel-cementum junction of the tooth before orthodontics is the labial and lingual movement distance of the orthodontic tooth at the midpoint of the enamel-cementum junction, and the distance between the other intersection point and the root apex point of the tooth before orthodontics is the labial and lingual movement distance of the orthodontic tooth at the root apex. Figure 6 The descriptions of each marked point are as follows:

[0074] A1 – cementoenamel junction on the labial side of the orthodontic anterior teeth;

[0075] B1 – cementoenamel junction on the lingual side of orthodontic anterior teeth;

[0076] M1 is the midpoint of the line connecting the labial cementoenamel junction of the pre-orthodontic tooth and the lingual cementoenamel junction of the tooth;

[0077] A2 – cementoenamel junction on the labial side of the tooth after orthodontics;

[0078] B2 – cementoenamel junction on the lingual side of the orthodontic tooth;

[0079] M2 is the midpoint of the line connecting the cementoenamel junction on the labial side of the tooth and the cementoenamel junction on the lingual side of the tooth after orthodontics;

[0080] Ap1 – the apex of the orthodontic front tooth;

[0081] Ap2 – the apex of the tooth after orthodontic treatment;

[0082] O——The intersection of the long axis of the teeth before orthodontics and the long axis of the teeth after orthodontics, that is, the center of rotation;

[0083] M1′——the intersection of a circle with the rotation center as the point and the rotation radius as the radius and the long axis of the tooth after orthodontics; Ap1′——the intersection of a circle with the rotation center as the center and the distance between the apex point of the tooth before orthodontics and the rotation center as the radius and the long axis of the tooth after orthodontics;

[0084] L1 is the distance between the intersection of the circle with the rotation center as the point and the rotation radius as the radius and the long axis of the orthodontic tooth, and the midpoint of the line connecting the enamel-cementum junction on the labial and lingual sides of the orthodontic tooth before orthodontics, that is, the labial and lingual movement distance of the orthodontic tooth at the midpoint of the enamel-cementum junction;

[0085] L2 - the distance between the intersection of the long axis of the tooth after orthodontics and the apex of the tooth before orthodontics, that is, the labial-lingual movement distance of the orthodontic tooth at the apex, which is the center of the circle and the distance between the apex of the tooth before orthodontics and the center of rotation as the radius.

[0086] In this embodiment, the orthodontic tooth movement measurement results based on the circular coordinate system are shown in Table 1.

[0087] Table 1 Orthodontic tooth movement measurement results based on circular coordinate system

[0088] Tooth position 41 (right mandibular central incisor) Root length (OM1Ap1) 11.82mm Radius of rotation (OM1) 49.71mm Rotation angle (α) 3.19° Rotation chord length (L1) 2.77mm Rotation chord length (L2) 2.17mm Vertical displacement (OM1OM1′) 0.61mm Lip and tongue movement Tilt movement

[0089] In this embodiment, image processing software such as Photoshop and Procreate can be used to extract the outer contour of the relative position of the teeth and the alveolar bone from the outer contour diagram of the relative position of the teeth and the alveolar bone before and after orthodontics; GeoGebra image processing software can be used to measure the overlapping diagram of the outer contour of the teeth before and after orthodontics, or directly use measuring tools such as rulers, triangles, and compasses for measurement. Steps 1 to 7 are the movement measurement process for one orthodontic tooth, and steps 1 to 7 can be repeated for the movement measurement of other orthodontic teeth.

[0090] In step three, since there is often external root resorption in teeth after orthodontics, in order to eliminate and offset the influence of root resorption on the measurement, after the outer contours of the relative positions of the teeth and the alveolar bone before and after orthodontics overlap, it is necessary to match the outer contours of the teeth before orthodontics with the outer contours of the teeth after orthodontics, that is, use the outer contours of the teeth before orthodontics to replace the outer contours of the teeth in the outer contour diagram of the relative position of the teeth and the alveolar bone after orthodontics.

[0091] In step 7, determine the model The deduction process is as follows: When orthodontic teeth move in the labiolingual direction, they move in parallel.

[0092] L1=2OM1Sinα

[0093] L2=2OAp2Sinα

[0094]

[0095] Where:

[0096] L1——Labiolingual movement distance of orthodontic teeth at the midpoint of the cementoenamel junction, mm;

[0097] L2——the labial-lingual movement distance of the orthodontic tooth at the root apex, mm;

[0098] OM1——rotation radius, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior teeth and the rotation center, mm;

[0099] OAp1 – the distance between the apex and the rotation center of the orthodontic front tooth, mm;

[0100] α——Rotation angle, that is, the angle between the long axis of the teeth before orthodontics and the long axis of the teeth after orthodontics, degrees;

[0101] M1Ap1 - root length, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior tooth and the root apex of the orthodontic anterior tooth, mm.

[0102] When the rotation radius is greater than or equal to 10 times the root length, OM1-M1Ap1≈OM1, The movement of orthodontic teeth in the labiolingual direction can be considered as parallel movement.

[0103] The orthodontic tooth movement measurement method based on the circular coordinate system of this embodiment has the following beneficial effects: (1) For the first time, a method for measuring orthodontic tooth movement based on the circular coordinate system was created. The method is a mathematical analysis method used to quantitatively analyze the sagittal (labio-lingual) and vertical orthodontic tooth movement patterns. (2) By overlapping the CBCT images of the teeth before and after orthodontics, overlapping views of the labio-lingual teeth and alveolar bone contours are obtained, and the complex labio-lingual tooth movement during the orthodontic process is decomposed into four parameters: rotation radius, rotation angle, rotation chord length, and vertical (long axis direction) displacement for accurate quantitative description. (3) This measurement method mathematically defines the classic orthodontic movement mode for the first time and gives the mathematical theoretical boundary value, which is an important step in the scientific measurement of orthodontic movement; this measurement method breaks through the shackles of the original measurement system, focuses on the relative position relationship between the alveolar bone and the teeth, and scientifically and comprehensively quantitatively analyzes the labio-lingual and vertical orthodontic movement patterns of single-rooted teeth. (4) This measurement method provides a solid scientific basis for further advancing research on the effects of orthodontic movement on periodontal soft and hard tissue remodeling. Subsequent research based on this measurement method is expected to provide a further scientific basis for the accurate screening of orthodontic patients at high risk of periodontal soft and hard tissue defects, and to provide a scientific basis for the combined periodontal-orthodontic treatment of bone defects. Provide diagnosis and treatment routines and technical procedures for patients with deformities, clarify the amount of bone grafting required during surgery, and provide a basis for multidisciplinary clinical cooperation and healthy correction.

[0104] Special note: The technical solution of the present invention involves many parameters, and the synergistic effects between the various parameters need to be comprehensively considered to obtain the beneficial effects and significant progress of the present invention. Moreover, the value ranges of the various parameters in the technical solution are obtained after a large number of experiments. For each parameter and the combination of each parameter, the inventor has recorded a large amount of experimental data. Due to space limitations, the specific experimental data will not be disclosed here.

[0105] It is not difficult for those skilled in the art to understand that the orthodontic tooth movement measurement method based on the circular coordinate system of the present invention includes any combination of the invention content and the specific implementation method of the above-mentioned invention specification and the various parts shown in the drawings. Due to the limited space and to make the specification concise, the various schemes composed of these combinations are not described one by one. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for measuring orthodontic tooth movement based on a circular coordinate system, characterized in that: The measuring method comprises the following steps in chronological order: Step 1: Obtain cone beam CT images of the upper and lower jaw dentition and alveolar bone of the orthodontic patient before and after orthodontics, and adjust the cone beam CT image planes before and after orthodontics to be consistent with the long axis direction of the orthodontic teeth; Step 2: Select the maximum cross-section of the tooth in the labial / buccal-lingual / palatal direction along the long axis of the tooth, intercept the relative position diagrams of the orthodontic tooth and the alveolar bone before and after orthodontics, and then extract the relative position outer contour diagrams of the teeth and the alveolar bone before and after orthodontics from the relative position diagrams of the teeth and the alveolar bone before and after orthodontics, and overlap the relative position outer contours of the teeth and the alveolar bone before and after orthodontics; Step 3: After the outer contours of the relative positions of the teeth and the alveolar bone before and after orthodontics are overlapped, the outer contour of the teeth before orthodontics is matched with the outer contour of the teeth after orthodontics, that is, the outer contour of the teeth before orthodontics is used to replace the outer contour of the teeth in the outer contour diagram of the relative positions of the teeth and the alveolar bone after orthodontics; after the outer contour of the teeth before orthodontics is matched with the outer contour of the teeth after orthodontics, an overlapping diagram of the outer contours of the teeth before and after orthodontics can be formed; Step 4: Based on the formed overlapping diagram of the outer contours of the teeth before and after orthodontics, the enamel-cementum junction on the labial side of the tooth and the enamel-cementum junction on the lingual side of the tooth are marked on the outer contour of the tooth before orthodontics, and the midpoint of the line connecting the labial and lingual enamel-cementum junctions is marked; at the same time, the enamel-cementum junction on the labial side of the tooth and the lingual side of the tooth are marked on the outer contour of the tooth after orthodontics, and the midpoint of the line connecting the labial and lingual enamel-cementum junctions is marked; Step 5: draw a straight line through the root apex of the orthodontic front tooth and the midpoint of the line connecting the labial and lingual enamel-cementum junction, which is the long axis of the orthodontic front tooth; draw a straight line through the root apex of the orthodontic back tooth and the midpoint of the line connecting the labial and lingual enamel-cementum junction, which is the long axis of the orthodontic back tooth; intersect the long axis of the orthodontic front tooth and the long axis of the orthodontic back tooth at one point, and use the intersection as the rotation center of the labial and lingual movement of the orthodontic tooth, use the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic front tooth and the rotation center as the rotation radius, and use the angle between the long axis of the orthodontic front tooth and the long axis of the orthodontic back tooth as the rotation angle; Step 6: Make a circle with the rotation center as the point and the rotation radius as the radius. The circle intersects with the long axis of the orthodontic tooth at one point. The distance between the intersection and the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic tooth is taken as the movement distance of the orthodontic tooth in the long axis direction. The distance between the intersection and the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic tooth before orthodontics is taken as the labial and lingual movement distance of the orthodontic tooth at the midpoint of the enamel-cementum junction. At the same time, make a circle with the rotation center as the center and the distance between the root apex of the orthodontic tooth before orthodontics and the rotation center as the radius. The circle intersects with the long axis of the orthodontic tooth at one point. The distance between the intersection and the root apex of the orthodontic tooth before orthodontics is taken as the labial and lingual movement distance of the orthodontic tooth at the root apex. Step 7: If the rotation radius is greater than or equal to 10 times the root length, the orthodontic tooth will move in the labiolingual direction in parallel; if the rotation radius is less than 10 times the root length, the orthodontic tooth will move in the labiolingual direction in tilted movement.

2. The orthodontic tooth movement measurement method based on a circular coordinate system according to claim 1, characterized in that: In step 2, for maxillary teeth, the relative position diagram of teeth and alveolar bones before and after orthodontics includes the complete hard palate and nasal floor contours; for mandibular teeth, the relative position diagram of teeth and alveolar bones before and after orthodontics includes the complete mandibular bone contour.

3. The orthodontic tooth movement measurement method based on a circular coordinate system according to claim 2, characterized in that: In step 2, for maxillary teeth, the hard palate and the nasal floor are overlapped; for mandibular teeth, the mandibular base bone is overlapped.

4. The orthodontic tooth movement measurement method based on a circular coordinate system according to claim 3, characterized in that: In step 2, the outer contours of the relative positions of the teeth and the alveolar bone before and after orthodontics are overlapped. This overlap is applicable to teeth whose twisting angle does not exceed 15 degrees before orthodontics.

5. The orthodontic tooth movement measurement method based on a circular coordinate system according to claim 4, characterized in that: In step three, the outer contour of the tooth before orthodontics is matched with the outer contour of the tooth after orthodontics, and the matching standard is to match the contour of the crown, the contour of the root neck, and the contour of the middle part of the root.

6. The orthodontic tooth movement measurement method based on a circular coordinate system according to claim 5, characterized in that: In step five, the long axis of the teeth before orthodontics and the long axis of the teeth after orthodontics are intersected at one point, and the intersection point is located inside or outside the overlapping diagram of the outer contours of the teeth before and after orthodontics, that is, the rotation center of the labiolingual movement of the orthodontic teeth is located inside or outside the overlapping diagram of the outer contours of the teeth before and after orthodontics.

7. The orthodontic tooth movement measurement method based on a circular coordinate system according to claim 6, characterized in that: In step 7, if the rotation radius is greater than or equal to 10 times the root length, the orthodontic tooth moves in the labiolingual direction in parallel, and the model is determined to be In the formula, OM1——rotation radius, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior teeth and the rotation center, mm; M1Ap1 - root length, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior tooth and the root apex of the orthodontic anterior tooth, mm.

8. The orthodontic tooth movement measurement method based on a circular coordinate system according to claim 7, characterized in that: In step seven, in actual application, if the movement of the orthodontic teeth in the labiolingual direction is small, it is necessary to adjust the rotation radius boundary value for determining whether the movement of the orthodontic teeth in the labiolingual direction is parallel movement.

9. The orthodontic tooth movement measurement method based on a circular coordinate system according to claim 8, characterized in that: In step 7, if the difference between the labial-lingual movement distance of the orthodontic tooth at the midpoint of the cementoenamel junction and the labial-lingual movement distance of the orthodontic tooth at the root apex is kept within the commonly used cone-beam CT voxel, the difference is negligible, and the labial-lingual movement mode of the orthodontic tooth is parallel movement. The judgment model is adjusted to In the formula, L1——Labiolingual movement distance of orthodontic teeth at the midpoint of the cementoenamel junction, mm; OM1——rotation radius, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior teeth and the rotation center, mm; M1Ap1 - root length, that is, the distance between the midpoint of the line connecting the labial and lingual enamel-cementum junction of the orthodontic anterior tooth and the root apex of the orthodontic anterior tooth, mm.

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