A combined personalized target dental arch curve modeling method and model

Abstract

The application provides a combined personalized target dental arch curve modeling method and model, the modeling method comprising: determining the relationship between the first characteristic parameter and the second characteristic parameter of a specific dental arch and an ideal arch shape according to the measurement data of a plurality of reference dental arches, wherein the dental arch curve of each reference dental arch conforms to the ideal arch shape standard, and the first characteristic parameter and the second characteristic parameter remain unchanged within one dental arch adjustment period of the specific dental arch; generating a first curve and a second curve according to the relationship between the first characteristic parameter and the second characteristic parameter and the ideal arch shape respectively; splicing the part of the first curve in the first dentition interval and the part of the second curve in the second dentition interval to obtain the personalized target dental arch curve corresponding to at least one dental arch adjustment period of the specific dental arch. The technical scheme provided by the application can establish a target dental arch curve that is more in line with the function and development stage of different positions of the dental arch.

Description

Technical Field

[0001] This application belongs to the field of orthodontic technology and relates to target dental arch curve generation technology, specifically providing a combined personalized target dental arch curve model and modeling method. Background Technology

[0002] Orthodontic arch correction refers to the use of various orthodontic instruments to expand, shrink, and adjust the shape of the dental arch. By adjusting the arch shape towards the ideal shape, it provides the necessary foundation for the ideal alignment of the teeth. For individuals with oral malocclusion problems, especially children / adolescents in their growth and development period, if the dental arch is too wide, too narrow, or asymmetrical, it will lead to or worsen sparse, crowded, or malocclusion, and have a comprehensive impact on the morphology of the upper and lower jaws and facial muscles. Furthermore, since the dental arch shape of children and adolescents is constantly changing with age, if this problem is not addressed in a timely manner, simple orthodontic treatment will be ineffective or even fail. Therefore, determining the ideal or target arch shape (usually described by a target dental arch curve) that a tooth or jaw to be corrected should have is an important step in orthodontic procedures.

[0003] Currently, there are various methods for generating or determining the ideal dental arch shape. For example, curve fitting of the real dental arch curve before treatment (corresponding to the tooth arrangement state before treatment) can be used in the form of polynomial functions, beta functions, spline functions, etc. Then, a curve that fits well with the selected ideal dental arch curve can be selected from several established ideal dental arch curves (corresponding to several typical normal dental arch shapes). Then, the doctor or technician can make personalized adjustments to the width, length, etc. of the selected ideal dental arch curve according to the treatment needs, and finally generate the target dental arch curve (i.e., the dental arch shape expected to be achieved through treatment).

[0004] While the above methods can generate personalized target arch curves for each patient's tooth alignment, the process of adjusting the arch curve from the pre-treatment state to the target arch curve relies solely on the experience of the dentist or technician and cannot be considered. Furthermore, these adjustments do not take into account the "anchoring" effect of inherent features in the jaw unrelated to the arch shape in constructing the ideal arch curve. Therefore, the generated personalized target arch curves are often only visually comfortable and cannot guarantee that their shape meets the functional requirements of jaw development and tooth alignment. In addition, analysis of numerous normal arch shapes reveals that different locations of the jaw exhibit different arch shapes, and for children / adolescents, the degree and rate of jaw development vary significantly across different regions. Therefore, it is necessary to establish target arch curves that better reflect the function and developmental stage of different jaw locations. Summary of the Invention

[0005] The purpose of this application is to solve the problems existing in the prior art and provide a combined personalized target dental arch curve modeling method and a dental arch curve model established therefrom.

[0006] The first aspect of this application provides a method for modeling a combined personalized target dental arch curve model, the method comprising the following steps:

[0007] The relationship between the first characteristic parameter, the second characteristic parameter and the ideal arch shape of a specific tooth are determined based on the measurement data of multiple reference tooth jaws. The arch curves of each reference tooth jaw conform to the ideal arch shape standard, and the first characteristic parameter and the second characteristic parameter remain unchanged within one arch adjustment cycle of the specific tooth jaw.

[0008] The first curve and the second curve are generated based on the relationship between the first characteristic parameter, the second characteristic parameter and the ideal arc shape, respectively;

[0009] The portion of the first curve located in the first dentition interval and the portion of the second curve located in the second dentition interval are spliced ​​together to obtain a personalized target dental arch curve for a specific dentition corresponding to at least one dental arch adjustment cycle.

[0010] Preferably, the first feature parameter is determined by the geometric features of the first set of teeth, wherein the first set of teeth includes multiple specific teeth of the maxilla or mandible of a specific jaw.

[0011] Preferably, the second feature parameter is determined by the geometric features of the second set of teeth, wherein the second set of teeth is a proper subset of the first set of teeth.

[0012] Preferably, the first characteristic parameter and the second characteristic parameter are determined by different sets of teeth at different developmental stages of a specific jaw.

[0013] Preferably, the first feature parameter is the crown width of mandibular teeth 5-5; and the second feature parameter is the crown width of mandibular teeth 2-2, 3-3, or 4-4.

[0014] Preferably, the first feature parameter is the crown width of the 4-4 teeth of the mandible; and the second feature parameter is the crown width of the 2-2 teeth of the mandible or the crown width of the 3-3 teeth.

[0015] Preferably, the first dentition interval is the left and right posterior tooth region; and the second dentition interval is the anterior tooth region.

[0016] Preferably, the junction between the first and second dentition intervals is located within the projection area of ​​the canines on the occlusal plane.

[0017] Further, the first curve for a specific jaw is generated through the following steps:

[0018] The relationship between the first characteristic parameter of a specific jaw and its ideal dental arch characteristic parameter is determined based on the measurement data.

[0019] Based on the measurement data, determine the relationship between the first curve of a specific dentition and its ideal dental arch characteristic parameters;

[0020] Based on the relationship between the first characteristic parameter of a specific jaw and the characteristic parameter of its ideal dental arch, and the relationship between the first curve of a specific jaw and the characteristic parameter of its ideal dental arch, a first curve represented by the first characteristic parameter of the specific jaw is determined.

[0021] Preferably, the ideal dental arch feature parameter of a particular dentition is only related to its ideal arch shape; and the ideal dental arch feature parameter of a particular dentition is statistically strongly correlated with its first feature parameter.

[0022] Preferably, the ideal dental arch characteristic parameters of a particular dentition are determined by the geometric characteristics of the arch curve when it is in the ideal arch shape.

[0023] Preferably, the ideal dental arch characteristic parameter is the size of the 5 / 6 contact point of the mandible when a specific jaw is in the ideal arch shape.

[0024] Preferably, the first curve is a polynomial function of degree 2N and contains at most M even-degree terms, where N and M are integers and N≥M≥2.

[0025] Preferably, the coefficients of the M even-order terms are all statistically strongly correlated with the characteristic parameters of the ideal dental arch.

[0026] Furthermore, the relationship between the first curve of a specific dentition and its ideal dental arch characteristic parameters is determined according to the following steps:

[0027] Obtain the optimal dental arch curve for each reference dentition, wherein the optimal dental arch curve has the same functional form as the first curve of a specific dentition, and the coefficients of its M even-degree terms are determined by fitting the measurement data of the reference dentition.

[0028] Obtain the intermediate dental arch curve for each reference dentition, wherein the intermediate dental arch curve has the same functional form as the first curve of a specific dentition, and its coefficients of M even-order terms include M-1 fixed coefficients and one intermediate coefficient, wherein the M-1 fixed coefficients are determined based on the statistical values ​​of the coefficients of the corresponding even-order terms in each optimal dental arch curve, and the intermediate coefficient is determined based on the fitting of the measurement data of the reference dentition.

[0029] Based on the statistical relationship between the ideal dental arch characteristic parameters and intermediate coefficients of each reference dentition, and the statistical relationship between the intermediate coefficients of each reference dentition and the M even-order terms of the optimal dental arch curve, the relationship between the first curve of a specific dentition and its ideal dental arch characteristic parameters is determined, wherein the coefficients of the M even-order terms of the first curve are represented by the ideal dental arch characteristic parameters of the specific dentition.

[0030] Preferably, the M-1 fixed coefficients are determined based on the average of the coefficients of the corresponding even-order terms in each optimal dental arch curve.

[0031] Preferably, the even-order term corresponding to the intermediate coefficient is the even-order term with the smallest degree.

[0032] Preferably, the polynomial function of degree 2N is in the form of:

[0033] Y = AX 4 +BX 2 ,

[0034] Where X and Y are the coordinates of each point on the function curve, and both X and Y are located on the jaw plane, and A and B are the coefficients of the fourth and second terms of the function curve, respectively.

[0035] Preferably, the second curve is a perfect circle, and the diameter of the perfect circle is statistically strongly correlated with the second feature parameter.

[0036] Preferably, the second curve is a beta function, and the integral parameter of the beta function is statistically strongly correlated with the second feature parameter.

[0037] Preferably, the combined personalized target dental arch curve further includes a transition curve, wherein the first curve and the second curve are spliced ​​together by the transition curve.

[0038] Further, the transition curve is generated through the following steps:

[0039] The portion of the first curve in the first dentition section is truncated to a specific length in the posterior dentition area;

[0040] A transition curve is generated by fitting the remaining part of the first curve with the portion of the second curve located in the second dental arch interval.

[0041] The second aspect of this application provides a combined personalized target dental arch curve model for characterizing the ideal dental arch shape that a specific jaw should have;

[0042] The curve model is obtained by splicing the portion of the first curve located in the first dentition section of a specific dentition and the portion of the second curve located in the second dentition section of a specific dentition.

[0043] The first curve has a polynomial function of degree 2N and contains at most M even-degree terms, where N and M are integers and N≥M≥2. The coefficients of the M even-degree terms are characterized by the first characteristic parameter of a specific dentition.

[0044] The second curve is a perfect circle, and its diameter is characterized by a second characteristic parameter of a specific dentition.

[0045] The first and second characteristic parameters remain unchanged within a dental arch adjustment cycle for a specific dentition.

[0046] Preferably, the specific jaw also has an ideal arch feature parameter, which is related to the shape of a first curve of the specific jaw; and the ideal arch feature parameter is statistically strongly correlated with the first feature parameter.

[0047] Preferably, the curve model is generated using the aforementioned combined personalized target dental arch curve modeling method.

[0048] The combined personalized target dental arch curve modeling method and the combined personalized target dental arch curve model established by the embodiments of this application comprehensively consider the aesthetic and functional requirements of the dental arch shape, and combine the differences in the development of different positions of the jaw during the development process. Different positions are characterized by different function forms to represent their ideal shape, so that the generation of the target dental arch curve eliminates the influence of subjective factors, and is more in line with the physiological development characteristics of the jaw while taking into account aesthetics and functionality. Attached Figure Description

[0049] Figure 1 A flowchart of an existing method for generating personalized target dental arch curves;

[0050] Figure 2 This is a flowchart of a combined personalized target dental arch curve modeling method provided according to an embodiment of this application;

[0051] Figure 3 The result is the fit of a real dental arch to an ideal dental arch morphology standard using a quartic function;

[0052] Figure 4 A diagram of the teeth in the lower jaw;

[0053] Figure 5 A flowchart for generating a first curve according to some preferred embodiments of this application;

[0054] Figure 6 A flowchart illustrating the relationship between a first curve of a particular dentition and its ideal dental arch characteristic parameters in some embodiments;

[0055] Figure 7The results are a summary of the first curves of multiple reference dental arches with ideal dental arch morphology;

[0056] Figure 8 This is a flowchart illustrating a specific implementation of an embodiment of this application;

[0057] Figure 9 This is a schematic diagram illustrating the establishment of the jaw plane according to an embodiment of this application;

[0058] Figure 10 This is the result of adjusting the coordinates of feature points of each reference jaw according to the embodiments of this application;

[0059] Figure 11 This is a schematic diagram illustrating the measurement of the crown width of a reference tooth according to an embodiment of this application;

[0060] Figure 12 This is a schematic diagram illustrating the measurement of the dimensions of 5-6 adjacent points of a reference tooth according to an embodiment of this application;

[0061] Figure 13 This is a summary diagram of the dimensions of the 5-6 adjacent points of each reference jaw according to the embodiments of this application;

[0062] Figure 14 B is the statistical value based on the embodiments of this application. adjust With A best A diagram illustrating the correlation;

[0063] Figure 15 For the statistics of A according to the embodiments of this application best With B best A diagram illustrating the correlation;

[0064] Figure 16 Based on the statistics of 5-6 adjacent point dimensions according to the embodiments of this application, and B adjust A diagram illustrating the correlation;

[0065] Figure 17 This is a schematic diagram of circular fitting of the anterior tooth region of a reference dentition according to an embodiment of this application;

[0066] Figure 18 This is a schematic diagram showing the first curve and the second curve as described in the embodiments of this application;

[0067] Figure 19 This is a schematic diagram of a combined personalized target dental arch curve generated according to an embodiment of this application. Detailed Implementation

[0068] The present application will now be further described based on preferred embodiments and with reference to the accompanying drawings.

[0069] In the description of the embodiments of this application, it should be noted that the terms "upper," "lower," "inner," and "outer," etc., indicating orientation or positional relationships based on the orientation or positional relationships shown in the accompanying drawings, or the orientation or positional relationships commonly used when the product of this application is in use, are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this application. Furthermore, in the description of this application, the terms "first," "second," etc., are used to distinguish different units, but these are not limited by the manufacturing order, nor should they be construed as indicating or implying relative importance; their names may differ in the detailed description and claims of this application. In addition, various structures in the accompanying drawings have been enlarged or reduced for ease of understanding, but this is not intended to limit the scope of protection of this application.

[0070] Figure 1 A flowchart of an existing method for generating personalized target dental arch curves is shown, such as... Figure 1 As shown, in implementing this method, firstly, in step 110, characteristic points of the teeth are selected from the dental model to be treated (such as the midpoint of the incisal edge of the central incisor and lateral incisor, the cusp of the canine, the buccal cusp of the first and second premolars, the mesiobuccal cusp and distobuccal cusp of the first and second molars, etc.). Then, in step 120, curve fitting is performed using the above characteristic points to obtain the real dental arch curves of the maxilla and mandible in the form of polynomial functions, which represent the dental arch morphology before treatment (i.e., in a malformed state). Further, in step 130, a standard dental arch curve that matches the real dental arch curve is found using a pre-established standard dental arch curve library as the basis for generating the target dental arch curve. Finally, in step 140, the dentist or technician adjusts the standard dental arch curve according to their own experience and treatment needs to finally generate the target dental arch curve.

[0071] While the above methods can generate personalized target arch curves for different dentitions requiring orthodontic treatment, they are based on several factors. First, they start from the pre-treatment, deformed arch curve and are adjusted manually by experienced dentists or technicians. Therefore, the effectiveness is highly dependent on the operator's experience. Second, although the generation of the actual arch curve utilizes landmarks on the dentition, the subsequent approach to determining the target arch curve is to approximate the arch shape of the dentition towards one of several pre-determined ideal arch shapes, rather than generating a truly personalized target arch based on the inherent characteristics of the dentition itself. It reflects more the operator's (or the operator's and patient's) subjective perception of an ideal arch shape, and cannot guarantee that it necessarily conforms to the objective laws of dentition development and tooth alignment and functional requirements.

[0072] In particular, through statistical analysis of a large population with normal oral conditions, the applicant discovered that although common quartic function curves can be used to fit a dental arch that meets both aesthetic and functional standards, this curve is largely achieved by minimizing mathematical errors. However, the actual dentition may exhibit different developmental and change trends in different regions (e.g., anterior and posterior regions) at different stages of growth and development, resulting in a complex overall shape of the dental arch curve. This makes it difficult to characterize with a single type of curve function. Instead, different types of curves should be used to describe the dental arch in different regions. Furthermore, the ideal dental arch shape in different regions is strongly correlated with certain inherent morphological features of the dentition. Thus, starting from these inherent features, a truly personalized target dental arch curve corresponding to each specific dentition can be obtained.

[0073] Based on the above considerations, embodiments of this application provide a combined personalized target dental arch curve modeling method. This method is used to establish a target dental arch curve for any specific dentition in at least one dental arch adjustment cycle. The specific dentition can be any dentition that requires dental arch adjustment operations due to oral malformation problems, such as arch expansion, arch reduction, or dental arch asymmetry correction operations.

[0074] Furthermore, dental arch adjustments may involve multiple adjustment cycles. For example, for children and adolescents whose jawbones are still developing, the jawbones themselves are constantly growing during the process of adjusting their dental arches. Therefore, the dental arch adjustment process may involve multiple adjustment cycles. Within each dental arch adjustment cycle, the development of the jawbones itself remains basically consistent, and a target dental arch curve can be used as the adjustment target for that stage.

[0075] In some preferred embodiments, such as Figure 2 As shown, the method includes the following steps:

[0076] Step 210: Determine the relationship between the first characteristic parameter, the second characteristic parameter and the ideal arch shape of a specific tooth based on the measurement data of multiple reference tooth jaws. The arch curves of each reference tooth jaw conform to the ideal arch shape standard, and the first characteristic parameter and the second characteristic parameter remain unchanged within one arch adjustment cycle of the specific tooth jaw.

[0077] Step 220: Generate the first curve and the second curve based on the relationship between the first characteristic parameter, the second characteristic parameter and the ideal arc shape, respectively;

[0078] Step 230: The portion of the first curve located in the first dentition interval and the portion of the second curve located in the second dentition interval are spliced ​​together to obtain a personalized target dental arch curve for a specific dentition corresponding to at least one dental arch adjustment cycle.

[0079] The core of this method is to establish the relationship between the inherent first and second characteristic parameters of any specific dentition and the ideal dental arch shape. For a specific dentition that needs dental arch adjustment, since its first and second characteristic parameters characterize the morphological characteristics of the dentition itself and do not change due to changes in the dental arch shape within a dental arch adjustment cycle, they can be used as "anchoring" standards to determine its relationship with the ideal dental arch shape. Using this relationship to establish a personalized target dental arch curve that corresponds one-to-one with the specific dentition, it can obviously eliminate the influence of subjective factors in the process of manually adjusting and generating the target dental arch curve, and is more in line with the functional and developmental laws of the dentition.

[0080] In the embodiments of this application, a reference dentition refers to a dentition that meets a pre-specified ideal arch shape standard (such as the overall shape of the dental arch curve or the geometric parameters of characteristic landmarks, with both aesthetics and functionality considered in its formulation). It represents a population whose dentition arch shape and tooth arrangement are relatively normal and ideal. Various techniques known to those skilled in the art, such as CBCT, ultrasound, and 3D oral scanning, can be used to model and measure the morphology of multiple reference dentitions to obtain various measurement data. Furthermore, the number of reference dentitions should be sufficient to meet the criteria for correlation statistics. The above embodiments are known to those skilled in the art and will not be elaborated further here.

[0081] In the embodiments of this application, a first curve is generated based on the relationship between a first feature parameter and an ideal arch shape, and a second curve is generated based on the relationship between a second feature parameter and an ideal arch shape. Then, the portions of the first curve in the first dentition interval and the portions of the second curve in the second dentition interval are spliced ​​together. By splicing the portions of different curves in different dentition intervals, a combined dental arch curve is obtained, mainly based on the following considerations:

[0082] 1) Using a curve of a single function form, such as a beta function curve or a quartic curve, to describe the dental arch morphology can mathematically find fitting parameters that minimize the overall cost function. However, in some dentition regions, such as the anterior region, the morphology may differ from the optimal morphology that conforms to functional and developmental characteristics. Figure 3 The results of fitting a real dentition to an ideal dental arch morphology standard using a quartic function are shown, such as... Figure 3As shown, although the fitted dental arch curve can satisfy the requirement of minimizing the overall cost function of each landmark point on the dentition, the curve shape in its anterior region is closer to a rounded trapezoid. However, based on the analysis of the geometric characteristics of each anterior tooth of this jaw (e.g., the crown width of its left No. 3 to right No. 3 teeth), it is found that the arrangement of its anterior teeth should be closer to a circle. Obviously, by using curves with different function forms to describe different dentition regions, although it may be possible to obtain a dental arch curve with a non-minimized cost function mathematically, it is more in line with the functional requirements of the dental arch shape.

[0083] 2) For individuals in the dentofacial development stage, the dentofacial region not only exhibits different dental arch morphologies in different areas, but also shows significant differences in the development speed and status of each area during the dentofacial development process. The relationship between the ideal dental arch morphologies of each area is constantly changing, forming the characteristic of the ideal dental arch curve changing in stages and regions as a whole. Therefore, it is necessary to establish a combination of personalized target dental arch curves for specific dentofacial regions in stages and dentitions to better fit the developmental characteristics of the dentofacial region.

[0084] Specifically, the first characteristic parameter and the second characteristic parameter both characterize the inherent characteristics of an arbitrary specific tooth in a dental arch adjustment cycle. These characteristics are independent of the dental arch morphology in the adjustment cycle. That is, regardless of whether it is in the ideal arch shape state of the dental arch adjustment cycle, the values ​​of its first characteristic parameter and the second characteristic parameter remain unchanged in the dental arch adjustment cycle.

[0085] Correspondingly, the eruption time and speed of different teeth vary at different stages of dental development. For example, the mixed dentition period generally begins at 5 to 6 years of age and ends at around 12 years of age. During this period, the shedding of deciduous teeth and the eruption and growth of permanent teeth do not occur simultaneously or synchronously. Therefore, in some specific embodiments, the values ​​of the first characteristic parameter and the second characteristic parameter need to take into account the situation of the erupted teeth in different dental arch adjustment cycles and be determined according to the characteristics of different sets of teeth.

[0086] In some preferred embodiments, the first feature parameter is determined by the geometric features of a first set of teeth, wherein the first set of teeth includes multiple specific teeth of the maxilla or mandible of a particular jaw. The second feature parameter is determined by the geometric features of a second set of teeth, wherein the second set of teeth is a proper subset of the first set of teeth, i.e., the first set of teeth contains and exceeds all teeth in the second set of teeth. The specific implementation methods for determining the first and second feature parameters are described below with reference to the accompanying drawings.

[0087] Figure 4 A specific mandibular tooth position diagram is shown, and the plane in which the diagram is located is the jaw plane, as shown below. Figure 4As shown, in some preferred embodiments, the first set of teeth may include 10 teeth, numbered L5 to R5. Correspondingly, the first characteristic parameter is the sum of the crown widths of teeth 5-5 in the mandible, i.e. Figure 4 The sum of the crown widths of teeth L5 to R5 in the middle jaw (it should be noted that, in this application, the sum of the crown widths of n1-n2 refers to the sum of the crown widths of each tooth measured from the leftmost tooth Ln1 to the rightmost tooth Rn2 in the maxilla or mandible), the second set of teeth is a proper subset of the first set of teeth, and may contain four teeth from L2 to R2. Correspondingly, the second feature parameter is the sum of the crown widths of teeth 2-2 in the mandible, i.e. Figure 4 The sum of the crown widths of teeth L2 to R2 in the middle; in addition, the second set of teeth may also include 6 teeth from L3 to R3, or 8 teeth from L4 to R4. Accordingly, the second characteristic parameter is the sum of the crown widths of teeth 3-3 or 4-4 in the mandible.

[0088] In other embodiments, when teeth L5 and R5 have not yet erupted or reached a stable state, they cannot be used as stable references and are therefore excluded when generating the target dental arch curve. Thus, the first set of teeth is determined to be 8 teeth from L4 to R4 in the mandible, and the second set of teeth is determined to be 6 teeth from L3 to R3 in the mandible, or 4 teeth from L2 to R2. Accordingly, the first feature parameter is the sum of the crown widths of teeth 4-4 in the mandible, and the second feature parameter is the sum of the crown widths of teeth 3-3 or 2-2 in the mandible.

[0089] As mentioned above, the basis for determining the first and second characteristic parameters is that the first and second characteristic parameters reflect the inherent characteristics of a specific dentition at a certain stage of dentition development. That is, at this stage of dentition development, the inherent characteristics do not change regardless of whether the dental arch is in an ideal arch shape. At the same time, the first and second characteristic parameters are determined by different sets of teeth at different stages of dentition development.

[0090] Furthermore, such as Figure 4 As shown, in a preferred embodiment of this application, the first dentition interval is the left and right posterior tooth region, and the second dentition interval is the anterior tooth region. Preferably, the junction of the first and second dentition intervals is located at the canines (i.e., Figure 4 The projection area of ​​teeth L3 and R3 in the occlusal plane.

[0091] The steps for generating the first and second curves are explained in detail below with reference to the accompanying drawings.

[0092] (1) Generate the first curve.

[0093] Figure 5A flowchart illustrating the generation of the first curve in some embodiments of this application is shown, such as... Figure 5 As shown, the first curve is generated through the following steps:

[0094] Step 310: Determine the relationship between the first characteristic parameter of a specific dentition and its ideal dental arch characteristic parameter based on the measurement data;

[0095] Step 320: Determine the relationship between the first curve of a specific dentition and its ideal dental arch characteristic parameters based on the measurement data;

[0096] Step 330: Based on the relationship between the first characteristic parameter of a specific jaw and its ideal dental arch characteristic parameter, and the relationship between the first curve of a specific jaw and its ideal dental arch characteristic parameter, determine the first curve represented by the first characteristic parameter of the specific jaw.

[0097] Ideal dental arch feature parameters characterize the features that can be found on a specific dentition when it is in the ideal dental arch morphology, which are only related to the ideal dental arch curve. That is, if the specific value of the ideal dental arch feature parameter is determined, the dental arch curve used to describe the target dental arch morphology can also be determined at the same time. At the same time, since the ideal dental arch feature parameter comes from the statistics of reference dentitions of people who meet both normal aesthetic and functional standards, it does not depend on the experience of doctors or technicians and is an objective statistical quantity that excludes the influence of subjective factors.

[0098] For a specific dentition, the ideal dental arch characteristic parameters can be determined by the geometric features of the arch curve when it is in the ideal arch shape. For example, in some preferred embodiments, the ideal dental arch characteristic parameters are the 5 / 6 interproximal contact points when the mandible is in the ideal arch shape. In this application, the m1 / m2 interproximal contact point dimensions refer to the distance between the interproximal points of the m1 and m2 teeth on both sides of the maxilla or mandible. Figure 4 For example, the 5 / 6 adjacency point size refers to the distance between the adjacency points of teeth L5 and L6 on the left and the adjacency points of teeth R5 and R6 on the right.

[0099] In the embodiments of this application, for any specific dentition, its ideal dental arch characteristic parameter is statistically strongly correlated with its first characteristic parameter. That is, when a specific dentition undergoes arch shape adjustment, its first characteristic parameter remains unchanged during one of the dental arch adjustment cycles and can be measured before the start of the dental arch adjustment cycle. Its ideal dental arch characteristic parameter corresponds to the target state at the end of the orthodontic cycle. The ideal dental arch characteristic parameter is only actually realized when the dental arch shape of the specific dentition reaches the ideal state of the dental arch adjustment cycle.

[0100] Since the first characteristic parameter is strongly correlated with the ideal dental arch characteristic parameter, a relationship can be established between a real-time measurable quantity and an objective target quantity that excludes subjective influencing factors. That is, for any specific dentition, once its first characteristic parameter is measured, its objective orthodontic target is determined by the ideal dental arch characteristic parameter, thereby also determining the first curve.

[0101] In the embodiments of this application, the first curve represents the main morphology of the ideal dental arch and tooth arrangement, and can be described using various curve functions. Therefore, the relationship between the characteristic parameters of the ideal dental arch and the first curve is the same as the relationship between the second characteristic parameters and the coefficients of a suitable curve function. Studies have found that using a polynomial function curve can better describe a smooth ideal dental arch curve compared to a Beta function curve. Therefore, in the preferred embodiment of this application, the first curve is a polynomial function of degree 2N, and the polynomial function contains at most M even-degree terms, where N and M are integers and N≥M≥2.

[0102] For example, in one specific embodiment, the first curve can be represented using the following fourth-degree polynomial:

[0103] Y = AX 4 +BX 2 ,

[0104] In this curve, X and Y represent the coordinates of various points on the curve, both located on the occlusal plane. Their X and Y axes are orthogonal, with the Y axis corresponding to the projection of the midsagittal plane onto the occlusal plane. A and B are the coefficients of the fourth and second degree terms of the curve, respectively. Including only even-degree terms ensures the curve's symmetry relative to the Y-axis. This first curve, in its above form, is a two-dimensional plane curve containing two coefficients, A and B, that can adjust the curve's shape. Therefore, by statistically analyzing the dental arch curves of multiple reference dentitions, a specific expression relating the ideal dental arch characteristic parameters to A and B can be obtained.

[0105] It should be understood that the polynomial expression of the above-mentioned fourth-degree term is only one specific embodiment. In some other embodiments, the first curve may also be a sixth-degree polynomial, and include at least two multiple terms, such as a sixth-degree term and a second-degree term; in some other embodiments, the first curve may also be in the form of a three-dimensional curve.

[0106] Analysis of measurement data from multiple reference dentitions revealed that, because the first curve includes at least two polynomial coefficients, these two coefficients jointly influence the curve shape, and their influences are mutually coupled. This results in no significant correlation between the polynomial coefficients and the characteristic parameters of the ideal dental arch. Therefore, it is necessary to construct an intermediate dental arch curve to establish the relationship between the characteristic parameters of the ideal dental arch and the various polynomial coefficients. To this end, in some preferred embodiments, such as... Figure 6 As shown, the relationship between the first curve of any specific dentition and its ideal dental arch characteristic parameters can be determined through the following steps:

[0107] Step 321: Obtain the optimal dental arch curve for each reference dentition, wherein the optimal dental arch curve has the same functional form as the first curve, and the coefficients of its M even-degree terms are determined by fitting the measurement data of the reference dentition.

[0108] Specifically, the optimal dental arch curve can be fitted based on the measurement data of each reference jaw using methods known to those skilled in the art.

[0109] Step 322: Obtain the intermediate dental arch curve for each reference dentition. The intermediate dental arch curve has the same functional form as the first curve. Its M even-order terms include M-1 fixed coefficients and one intermediate coefficient. The M-1 fixed coefficients are determined based on the statistical values ​​of the coefficients of the corresponding even-order terms in each optimal dental arch curve, and the intermediate coefficient is determined based on the measurement data of the reference dentition.

[0110] Specifically, when M=2, firstly, the coefficient of one even-order term in multiple sets of optimal dental arch curves is statistically analyzed to obtain its statistical value, such as the mean, which is used as the fixed coefficient of that even-order term. Then, with the fixed coefficient of that even-order term unchanged, the intermediate dental arch curve for each reference dentition is fitted. Obviously, the other even-order term coefficient of this intermediate dental arch curve (i.e., the intermediate coefficient) is different for different reference dentitions. In this way, an intermediate dental arch curve with a sufficiently small error compared to the optimal dental arch curve of each reference dentition, but containing only one variable coefficient, can be obtained.

[0111] Correlation statistics revealed that the variable intermediate coefficients are strongly correlated with the two polynomial coefficients of the optimal dental arch curve and the ideal dental arch characteristic parameters. Therefore, these intermediate coefficients can be used as a "bridge" to establish the relationship between the ideal dental arch characteristic parameters and the coefficients of each polynomial. Thus, in step 330, the coefficients of the M even-degree terms of the first curve of a specific dental arch characterized by the ideal dental arch characteristic parameters can be determined based on the statistical relationship between the ideal dental arch characteristic parameters and the intermediate coefficients of each reference dental arch, as well as the statistical relationship between the intermediate coefficients of each reference dental arch and the M even-degree terms of the optimal dental arch curve.

[0112] Correlation statistics reveal that, for dental arch curves represented by polynomial functions, the coefficients of higher-order terms are generally two orders of magnitude smaller than those of lower-order terms. This means that the variation in the coefficients of lower-order terms is much greater than that of higher-order terms. Furthermore, the coefficients of higher-order terms determine the basic shape of the curve, while the coefficients of lower-order terms cause the differences in curve details. Therefore, in a preferred embodiment, the intermediate coefficients should be selected from lower-order terms (such as the smallest even-order terms) to maximize the statistical correlation.

[0113] The above example uses a polynomial function containing two multiple terms. When M is greater than 2, the same method can be used. For example, fix the coefficients of M-1 polynomials to obtain an intermediate dental arch curve with a variable intermediate coefficient, and statistically analyze the correlation between the intermediate coefficient and the polynomial coefficients of each group of optimal dental arch curves.

[0114] After finding the statistical relationships between the ideal dental arch characteristic parameters and the first characteristic parameter, as well as between the ideal dental arch characteristic parameters and the polynomial coefficients of the first curve, in steps 321 and 322 above, the relationship between the first characteristic parameter of a specific jaw and the polynomial coefficients of the first curve can be established in step 323. Since the first characteristic parameter is a quantity that remains unchanged in a dental arch adjustment cycle for a specific jaw, this method can automatically generate the first curve using measurable data of the jaw before the dental arch adjustment cycle.

[0115] (2) Generate the second curve.

[0116] Figure 7 The results show the summation of first curves for multiple reference dentitions with ideal dental arch morphology, where each first curve is aligned with the anterior proximal point as the origin.

[0117] Figure 7 The three black circles represent the intersections of the first curves. The two intersections on the left and right are located within the projection areas of teeth L3 and R3 on the jaw plane, respectively. These intersections indicate that the first curves in the anterior region tend to extend to the left and right front, thus giving the anterior region a rounded trapezoidal shape. However, clinical studies on the function and developmental characteristics of the dental arch morphology show that the arrangement of the teeth in the anterior region is closer to a perfect circle under ideal conditions. Therefore, in the preferred embodiment of this application, the target dental arch curve is described by a circular second curve in the anterior region and by a first curve in the form of a polynomial function in the posterior region.

[0118] Specifically, in the embodiments of this application, the diameter of the perfect circle of the second curve is statistically strongly correlated with the second feature parameter. Therefore, after obtaining the measured value of the second feature parameter, the second curve characterized by the second feature parameter can be obtained.

[0119] In addition, in some alternative embodiments, a beta function can be used as the second curve, and the integral parameter of the beta function is statistically strongly correlated with the second characteristic parameter.

[0120] (3) The splicing of the first curve and the second curve.

[0121] After obtaining the first curve and the second curve through the above steps, in step 230, the portion of the first curve in the first dentition interval and the portion of the second curve in the second dentition interval are spliced ​​together to obtain a personalized target dental arch curve for a specific dentition corresponding to at least one dental arch adjustment cycle.

[0122] Since the first curve and the second curve may be misaligned at the junction of the first and second dental arch intervals, in some preferred embodiments, a transition curve is used to connect the truncated first curve and the second curve. This transition curve can be generated through the following steps:

[0123] The portion of the first curve in the first dentition section is truncated to a specific length in the posterior dentition area;

[0124] A transition curve is generated by fitting the remaining part of the first curve with the portion of the second curve located in the second dental arch interval.

[0125] Special attention should be paid to the specific length of the cut. It should not be too small to avoid a sharp turn when the first curve and the second curve are spliced ​​together, nor should it be too large to avoid excessive deviation in the shape of the target curve after fitting. In some preferred embodiments, the specific length of the cut is greater than or equal to the crown length of the first premolar and less than or equal to 10 mm.

[0126] A specific embodiment of this application will be described below with reference to the accompanying drawings. Figure 8 The specific process of this embodiment is shown, such as Figure 8 As shown, this embodiment includes the following steps:

[0127] Step A: Obtain a 3D digital model of the reference jaw and annotate feature points:

[0128] In this embodiment, 55 sets of three-dimensional digital models of teeth and jaws that meet the ideal dental arch morphology standard are first obtained as reference teeth and jaws, and data statistical analysis is performed. The statistics show that the target dental arch curve of the mandible can be obtained by shifting the target dental arch curve of the mandible outward by 2.5mm, which meets the aesthetic and functional requirements. Therefore, in this embodiment, only the target dental arch curve of the mandible is generated.

[0129] After obtaining the three-dimensional digital model of the mandible, multiple feature points can be identified on the reference jaw by manual or automatic annotation. Feature points can be specific locations on each jaw known to those skilled in the art, such as the cusp, mesobalvular cusp, or distobuccal cusp on the crown of a specific tooth. For example, 18 feature points can be marked on the reference jaw: the midpoint of the incisal edge of the left and right No. 1 teeth, the midpoint of the incisal edge of the left and right No. 2 teeth, the cusp of the left and right No. 3 teeth, the buccal cusp of the left and right No. 4 teeth, the buccal cusp of the left and right No. 5 teeth, the mesobalvular and distobuccal cusps of the left and right No. 6 teeth, and the mesobalvular and distobuccal cusps of the left and right No. 7 teeth.

[0130] Step B, coordinate system alignment:

[0131] For each reference jaw, coordinates are created using the midpoint of the left and right tooth feature points (number 1) and the left and right tooth feature points (number 6), as follows: Figure 9 As shown, the plane formed by the three points is the jaw plane, and the jaw plane is the XY plane.

[0132] Step C, adjust the coordinates:

[0133] Set the midpoint of tooth 1-1 as the origin (0, 0, 0), and adjust 55 sets of feature points. The final adjustment result is as follows. Figure 10 As shown.

[0134] Step D: Collect data on crown width.

[0135] For each reference jaw, such as Figure 11 As shown, the crown width of each reference tooth jaw was measured according to the crown width measurement standard, and the crown widths of teeth 5-5, 4-4, 3-3, and 2-2 were statistically summarized. The method for obtaining the crown width sum has been explained above.

[0136] Step E: Calculate the adjacent point size data:

[0137] For each reference jaw, such as Figure 12 As shown, the dimensions of the 5th and 6th adjacent points were measured and statistically analyzed. The method for obtaining the adjacent point dimensions has been explained above. The summary results of the 5th and 6th adjacent point dimensions of each reference tooth are shown in the appendix. Figure 13 .

[0138] Step F: Analyze the correlation and correspondence between crown width and adjacent point dimensions.

[0139] The crown width of tooth 5-5 (i.e., the first characteristic parameter) and the proximal point size of tooth 5-6 (i.e., the ideal dental arch characteristic parameter) of 55 reference dentitions were statistically analyzed. Table 1 below lists the crown width of tooth 5-5 and the proximal point size of tooth 5-6 in some of the 55 reference dentitions. Statistical analysis showed that the correlation between the crown width of tooth 5-5 and the proximal point size of tooth 5-6 exceeded 0.55. Further analysis of the ratio between the two yielded the mean value of the ratio.

[0140] Table 1. Statistical data for the reference dentition (partial).

[0141]

[0142]

[0143] Step G: Determine the functional form of the first curve:

[0144] Fitting different function types revealed that the beta function exhibited significant deviations during use. Compared to the sixth-degree polynomial, the quartic polynomial showed better stability, while the sixth-degree polynomial exhibited greater fluctuations and a less smooth curve. Therefore, the quartic polynomial was chosen as the arch curve function, with odd-degree terms removed to ensure the curve's symmetry relative to the Y-axis. The final function form for the first curve was determined to be Y = AX. 4 +BX 2 .

[0145] Step H, optimal dental arch curve fitting:

[0146] For a reference dentition, curve fitting is performed using its feature points to obtain the optimal dental arch curve where the sum of the distances from the feature points to the fitted curve is minimized. The optimal coefficients of the fourth and second degree terms are A, respectively. best and B best .

[0147] Table 2 below shows the A values ​​of the optimal dental arch curve obtained from partial fitting. best and B best .

[0148] Table 2. Optimal coefficients (partial) of the optimal dental arch curve.

[0149] -0.00003 -0.02012 -0.00007 -0.00894 -0.0001 -0.00243 -0.00009 -0.00586 -0.00006 -0.01768 -0.00005 -0.01134

[0150] Step 1, Determine the intermediate dental arch curve:

[0151] Statistical analysis revealed that although the size of the 5-6 adjacent points is closely related to the shape of the optimal dental arch curve, the size of the 5-6 adjacent points is not directly related to A. best and B best The correlation between A and B is not strong, i.e., A does not show a strong correlation. best and B bestThe influence on the shape of the dental arch curve is coupled and cannot be characterized solely by its relationship with the characteristic parameters of the ideal dental arch. Therefore, it is necessary to establish an intermediate dental arch curve, which has dimensions related to the 5-6 adjacent points and A. best and B best All coefficients have a strong correlation.

[0152] Furthermore, statistical analysis revealed that the coefficient A of the fourth term... best The coefficient of the quadratic term B is generally higher. best Two orders of magnitude smaller, which determines the basic shape of the curve, B best The changes are significant, resulting in different detailed features in different curves. Therefore, we will first take A... best The mean value is used as a fixed coefficient A for each intermediate dental arch curve. ave For the intermediate dental arch curve of each reference dentition, this fixed coefficient remains unchanged. Then, curve fitting is performed by minimizing the sum of the distances from feature points to the curve to obtain the intermediate dental arch curve for each reference dentition. The quadratic coefficient of each dental arch curve is the intermediate coefficient B. adjust .

[0153] Step J, determine B adjust Dimensions of adjacent points 5-6, A best B best Relationship:

[0154] By analyzing the B-type of each reference dentition adjust 5-6 Adjacent point dimensions, A best B best To conduct statistics, such as Figures 14 to 16 As shown, B adjust With A best The correlation is 0.765, A best With B best The correlation is -0.797, and the size of the 5-6 adjacent nodes is related to B. adjust The correlation is 0.799, meaning that using the intermediate coefficient B... adjust As a "bridge", the coupling correlation between the ideal dental arch feature parameters and the optimal dental arch curve coefficients can be decomposed into multiple strongly correlated relationships that can be passed through linear expressions.

[0155] Step K: Establish the relationship between the crown width of tooth 5-5 and the first curve;

[0156] Finally, using the relationship between the crown width of tooth 5-5 obtained in step F and the contact point dimensions of tooth 5-6, and the relationship between the contact point dimensions of tooth 5-6 obtained in step J and A... best B bestThe relationship between these parameters allows us to obtain the optimal dental arch curve function characterized by the 5-5 crown width (i.e., the first characteristic parameter that remains constant throughout a dental arch adjustment cycle). Obviously, for any dentition that requires dental arch shape correction, after measuring its 5-5 crown width, the corresponding first curve can be obtained using the dental arch curve function expressed above. This process does not involve interference from artificial adjustments, conforms to aesthetic standards and dental development characteristics, and ensures that the functional needs of the dentition are met.

[0157] Step L: Fit the arch shape of the reference anterior tooth region using a perfect circle:

[0158] The anterior teeth regions of 55 reference dentitions were fitted using circular fitting methods, and the fitting results are as follows: Figure 17 As shown.

[0159] Step M, establish the relationship between the crown width of tooth 2-2 and the second curve:

[0160] The correlation between the 2-2 crown width and the corresponding circular shape in the anterior region of each reference tooth was statistically analyzed. The correlation was 0.95, thus obtaining a second curve characterized by the 2-2 crown width.

[0161] Step N, Curve splicing:

[0162] like Figure 18 As shown, each first curve is shortened by 8.5 mm towards the inward direction from the edge of the first dentition interval. Then, a transition curve is used to bridge the remaining part of the first curve and the part of the second curve in the first dentition interval, ultimately obtaining a combined personalized target dental arch curve, as shown in the figure. Figure 19 As shown.

[0163] It should be understood that the above embodiments are only for illustrating specific implementation methods of the modeling method provided in this application. Those skilled in the art can adjust the selected reference jaw and its various feature points and other parameters according to actual needs without departing from the implementation concept of this application. They can also make several improvements and modifications to this application, and these improvements and modifications also fall within the protection scope of the claims of this application.

[0164] This application also provides a combined personalized target dental arch curve model through embodiments, used to characterize the ideal dental arch shape that a specific jaw should have;

[0165] The curve model is obtained by splicing the portion of the first curve located in the first dentition section of a specific jaw and the portion of the second curve located in the second dentition section of a specific jaw.

[0166] The first curve has the form of a polynomial function of degree 2N and contains at most M even-degree terms, where N and M are integers and N≥M≥2. The coefficients of the M even-degree terms are all characterized by the first characteristic parameter of a specific dentition. The second curve is a circle, and its diameter is characterized by the second characteristic parameter of a specific dentition. The first and second characteristic parameters remain unchanged within one dental arch adjustment cycle of a specific dentition.

[0167] In some preferred embodiments, the particular jaw also has an ideal arch feature parameter, which is related to the shape of a first curve of the particular jaw; and the ideal arch feature parameter is statistically strongly correlated with the first feature parameter.

[0168] In some preferred embodiments, the curve model is generated by the aforementioned combined personalized target dental arch curve modeling method, the specific implementation of which has been described in detail above and will not be repeated here.

Claims

1. A combined personalized target dental arch curve modeling method, characterized in that, include: The relationship between the first characteristic parameter, the second characteristic parameter, and the ideal arch shape of a specific tooth are determined based on the measurement data of multiple reference tooth jaws. The arch curves of each reference tooth jaw conform to the ideal arch shape standard, and the first characteristic parameter and the second characteristic parameter remain unchanged within one arch adjustment cycle of the specific tooth jaw. The first characteristic parameter is the sum of the crown widths of teeth 5-5 in the mandible, and the second characteristic parameter is the sum of the crown widths of teeth 2-2 in the mandible. The first curve and the second curve are generated based on the relationship between the first characteristic parameter, the second characteristic parameter and the ideal arc shape, respectively; A transition curve is used to bridge the portion of the first curve in the first dentition section and the portion of the second curve in the second dentition section to obtain a personalized target arch curve for a specific dentition in one arch adjustment cycle. The first curve is a polynomial function of degree 2N containing only M even-degree terms, where N and M are integers and N=M=2. Its specific form is as follows: , X , Y The coordinates of each point on the function curve are respectively, and X , Y All are located on the jaw plane. A , B These are the coefficients of the fourth and second terms of the function curve, respectively. The first curve is generated through the following steps: The relationship between the first characteristic parameter of a specific jaw and its ideal dental arch characteristic parameter is determined based on the measurement data. The ideal dental arch characteristic parameter is the distance between the adjacent points of teeth L5 and L6 on the left side of the mandible and teeth R5 and R6 on the right side when the specific jaw is in the ideal arch shape. Based on the measurement data, determine the relationship between the first curve of a specific dentition and its ideal dental arch characteristic parameters; Based on the relationship between the first characteristic parameter of a specific dentition and its ideal dental arch characteristic parameter, and the relationship between the first curve of a specific dentition and its ideal dental arch characteristic parameter, a first curve represented by the first characteristic parameter of the specific dentition is determined, wherein the relationship between the first curve of the specific dentition and its ideal dental arch characteristic parameter is determined according to the following steps: Obtain the optimal dental arch curve for each reference dentition, wherein the optimal dental arch curve has the same functional form as the first curve of a specific dentition, and the coefficients of its M even-degree terms are determined by fitting the measurement data of the reference dentition. Obtain the intermediate dental arch curve for each reference dentition, wherein the intermediate dental arch curve has the same functional form as the first curve of a specific dentition, and its coefficients of M even-order terms include M-1 fixed coefficients and one intermediate coefficient, wherein the M-1 fixed coefficients are determined based on the statistical values ​​of the coefficients of the corresponding even-order terms in each optimal dental arch curve, and the intermediate coefficient is determined based on the fitting of the measurement data of the reference dentition. Based on the statistical relationship between the ideal dental arch characteristic parameters and intermediate coefficients of each reference jaw, and the statistical relationship between the intermediate coefficients of each reference jaw and the M even-order terms of the optimal dental arch curve, the relationship between the first curve of a specific jaw and its ideal dental arch characteristic parameters is determined, wherein the coefficients of the M even-order terms of the first curve are represented by the ideal dental arch characteristic parameters of the specific jaw. The second curve is a perfect circle, and its diameter is characterized by a second characteristic parameter of a specific dentition.

2. The combined personalized target dental arch curve modeling method according to claim 1, characterized in that: The first dentition interval is the left and right posterior tooth region; and, The second dental arch interval is the anterior tooth region.

3. The combined personalized target dental arch curve modeling method according to claim 1, characterized in that: The intersection of the first dentition interval and the second dentition interval is located within the projection area of ​​the canine in the occlusal plane.

4. The combined personalized target dental arch curve modeling method according to claim 1, characterized in that: The M-1 fixed coefficients are determined based on the average of the coefficients of the corresponding even-order terms in each optimal dental arch curve.

5. The combined personalized target dental arch curve modeling method according to claim 1, characterized in that: The even-order term corresponding to the intermediate coefficient is the even-order term with the smallest degree.

6. The combined personalized target dental arch curve modeling method according to claim 1, characterized in that, The transition curve is generated using the following steps: The portion of the first curve in the first dentition section is cut off to the posterior dentition section by a specific length, wherein the specific length cut off is greater than or equal to the crown length of the first premolar and less than or equal to 10 mm; A transition curve is generated by fitting the remaining part of the first curve with the portion of the second curve located in the second dental arch interval.

7. A combined personalized target dental arch curve model, used to characterize the ideal dental arch shape that a specific jaw should possess, characterized in that, Generated using the combined personalized target dental arch curve modeling method as described in claim 1.

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