CN117017533A - Personalized target dental arch curve model and modeling method - Google Patents
Personalized target dental arch curve model and modeling method Download PDFInfo
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- 210000002455 dental arch Anatomy 0.000 title claims abstract description 188
- 238000000034 method Methods 0.000 title claims abstract description 63
- 210000001847 jaw Anatomy 0.000 claims abstract description 123
- 238000005259 measurement Methods 0.000 claims abstract description 15
- 230000000875 corresponding effect Effects 0.000 claims description 24
- 230000008569 process Effects 0.000 claims description 13
- 230000002596 correlated effect Effects 0.000 claims description 6
- 210000004373 mandible Anatomy 0.000 claims description 5
- 238000011161 development Methods 0.000 abstract description 12
- 230000018109 developmental process Effects 0.000 abstract description 12
- 210000004513 dentition Anatomy 0.000 abstract description 7
- 230000036346 tooth eruption Effects 0.000 abstract description 7
- 238000004873 anchoring Methods 0.000 description 6
- 238000012937 correction Methods 0.000 description 5
- 238000010586 diagram Methods 0.000 description 4
- 210000004283 incisor Anatomy 0.000 description 4
- 210000003464 cuspid Anatomy 0.000 description 3
- 210000004763 bicuspid Anatomy 0.000 description 2
- 210000000988 bone and bone Anatomy 0.000 description 2
- 230000000694 effects Effects 0.000 description 2
- 230000014509 gene expression Effects 0.000 description 2
- 238000004458 analytical method Methods 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 238000007408 cone-beam computed tomography Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 210000001097 facial muscle Anatomy 0.000 description 1
- 238000002372 labelling Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000007619 statistical method Methods 0.000 description 1
- 238000002604 ultrasonography Methods 0.000 description 1
- 230000000007 visual effect Effects 0.000 description 1
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- A—HUMAN NECESSITIES
- A61—MEDICAL OR VETERINARY SCIENCE; HYGIENE
- A61C—DENTISTRY; APPARATUS OR METHODS FOR ORAL OR DENTAL HYGIENE
- A61C7/00—Orthodontics, i.e. obtaining or maintaining the desired position of teeth, e.g. by straightening, evening, regulating, separating, or by correcting malocclusions
- A61C7/002—Orthodontic computer assisted systems
Abstract
The application provides a personalized target dental arch curve model and a modeling method, wherein the modeling method comprises the following steps: determining the relation between a first characteristic parameter and a second characteristic parameter of any jaw when the jaw has an ideal bow according to the measured data of a plurality of reference jaws, wherein the dental bow curve of each reference jaw accords with the ideal bow standard; determining the relation between the personalized target dental arch curve corresponding to any dental jaw and the second characteristic parameter according to the measurement data; and determining the personalized target dental arch curve corresponding to any dental jaw with the first characteristic parameter according to the relation between the first characteristic parameter and the second characteristic parameter when any dental jaw has the ideal dental arch and the relation between the personalized target dental arch curve corresponding to any dental jaw and the second characteristic parameter. The personalized target dental arch curve model established by the modeling method can simultaneously meet the functional requirements of appearance aesthetics and dental development/dentition arrangement.
Description
Technical Field
The application belongs to the technical field of orthodontic treatment, particularly relates to an ideal dental arch curve generation technology, and particularly provides a personalized target dental arch curve model and a modeling method.
Background
In the orthodontic process of various oral deformities, especially in the orthodontic process of children/teenagers in the growth and development period, the arch shape and the size are important consideration factors, because the problems of arch shape, such as arch width, arch asymmetry and the like, cause and aggravate the sparse, crowded and uneven dentition and the comprehensive influence on the upper and lower jawbones and facial muscle forms, the operations of expanding, contracting or adjusting the asymmetric arch by taking the optimal arch shape as the target arch shape of any one of the jaws needing to be corrected are generally important links in the orthodontic process, and accordingly, the searching and determining of the ideal arch or the target arch (generally described by the target arch curve) which the arch shape should have is the premise and the key of successful arch adjustment operation.
Numerous attempts and studies have been made to find or determine the best way to describe the shape of an ideal arch, it is currently generally believed that the arch curve can be described using a form such as a beta function, spline function or polynomial function, for example, seba AlHarbi et al (Seba AlHarbia, eman a. Alkofib, abdulaziz AlMadic, mathematical Analyses of Dental Arch Curvature in Normal Occlusion, angle Orthodontist, vol 78, no. 2,2008, 281-287) consider that the shape of the arch curve can be smoothly and reasonably described by a fourth order polynomial, on the basis of which different methods of determining the target arch curve are proposed, such as those in the specification of patent CN11431989a, the actual arch curve before treatment can be fitted using the polynomial function form and the like, and the target arch curve is finally generated (i.e., the desired arch is achieved by the arch) by a practitioner or technician according to the treatment requirements.
Although the method can generate the personalized target dental arch curve according to the tooth arrangement situation of each patient, the process of adjusting the dental arch curve from the dental arch curve before correction to the target dental arch curve can only be manually carried out by virtue of the experience of doctors or technicians, and the adjustment process does not consider the anchoring effect of inherent characteristics irrelevant to dental arch states in dental jaws on constructing ideal dental arch curves, so that the generated personalized target dental arch curve is always comfortable only in visual sense, and the curve form of the personalized target dental arch curve cannot be ensured to meet the functional requirements of dental development and dentition arrangement.
Disclosure of Invention
The present application aims to solve the problems in the prior art, and provides a personalized target dental arch curve modeling method capable of simultaneously meeting the requirements of appearance aesthetics and dental development/dentition arrangement functions, and a personalized target dental arch curve model generated by using the method, starting from the inherent characteristics of any dental jaw.
A first aspect of the present application provides a method of modeling a personalized target dental arch model, the method comprising the steps of:
determining the relation between a first characteristic parameter and a second characteristic parameter of any jaw when the jaw is in an ideal arch according to the measurement data of a plurality of reference jaws, wherein the arch curve of each reference jaw accords with an ideal arch standard;
determining the relation between the personalized target dental arch curve corresponding to any dental jaw and the second characteristic parameter of the personalized target dental arch curve according to the measurement data;
and determining the personalized target dental arch curve corresponding to any dental jaw with the first characteristic parameter according to the relation between the first characteristic parameter and the second characteristic parameter when any dental jaw has the ideal dental arch and the relation between the personalized target dental arch curve corresponding to any dental jaw and the second characteristic parameter.
Further, the first characteristic parameter of any jaw remains unchanged during the course of its dental arch curve; the second characteristic parameter of any jaw is related to the ideal bow that it has; and, the second characteristic parameter of any jaw is statistically strongly correlated with the first characteristic parameter thereof.
Preferably, the first characteristic parameter of any jaw is determined by the geometric characteristics of a plurality of specific teeth of its upper or lower jaw.
Preferably, the second characteristic variable of any dental jaw is determined by the geometry of the arch curve when it is in the ideal arch.
Preferably, the personalized target arch curve is a polynomial function of degree 2N and only contains up to M even terms, wherein N, M is an integer and N.gtoreq.M.gtoreq.2.
Further, the coefficients of the M even terms may each be characterized by a second characteristic parameter.
Preferably, the relation between the personalized target arch curve of any jaw and the second characteristic parameter is determined according to the following steps:
obtaining an optimal dental arch curve of each reference dental jaw, wherein the optimal dental arch curve and the personalized target dental arch curve have the same function form, and the coefficients of M even terms of the optimal dental arch curve are determined based on the measurement data fitting of the reference dental jaw;
obtaining an intermediate dental arch curve of each reference dental arch, wherein the intermediate dental arch curve and the personalized target dental arch curve have the same function form, and M even-term coefficients of the intermediate dental arch curve comprise M-1 fixed coefficients and an intermediate coefficient, wherein the M-1 fixed coefficients are determined according to the statistical value of the corresponding even-term coefficients in each optimal dental arch curve, and the intermediate coefficient is determined based on the measurement data fitting of the reference dental arch;
according to the statistical relationship between the second characteristic parameters of each reference dental jaw and the intermediate coefficients and the statistical relationship between the intermediate coefficients of each reference dental jaw and M even-order terms of the optimal dental arch curve, M even-order term coefficients of the personalized target dental arch curve corresponding to any dental jaw represented by the second characteristic parameters are determined.
Preferably, the M-1 fixed coefficients are determined from the mean of the coefficients of the corresponding even terms in each optimal arch curve.
Preferably, the even term corresponding to the intermediate coefficient is the even term with the smallest frequency.
Preferably, the form of the polynomial function of degree 2N is:
Y＝AX 4 +BX 2 ，
wherein X, Y is the coordinates of each point on the function curve and X, Y is on the jaw plane, and A, B is the coefficients of the fourth and second terms of the function curve.
Preferably, the first characteristic parameter is the sum of 5-5 crown widths of the mandible.
Preferably, the second characteristic parameter is the 5/6 abutment dimension of the mandible.
A second aspect of the present application provides a personalized target dental arch model for characterizing an ideal dental arch that any dental jaw should have;
the personalized target dental arch curve model has a polynomial function form of 2N times and only comprises at most M even terms, wherein N, M is an integer, and N is more than or equal to M is more than or equal to 2;
the arbitrary dental jaw is provided with a first characteristic parameter, and the first characteristic parameter is kept unchanged in the dental arch curve changing process;
the coefficients of the M even terms may all be characterized by the first characteristic parameter.
Preferably, the arbitrary dental jaw further has a second characteristic parameter, and the second characteristic parameter is related to the shape of the personalized target dental arch curve corresponding to the arbitrary dental jaw; and the second characteristic parameter is statistically strongly correlated with the first characteristic parameter.
Preferably, the personalized target dental arch model is generated by the aforementioned personalized target dental arch modeling method.
According to the target dental arch curve modeling method and the target dental arch curve model established by the method, the target dental arch curve model which can be characterized by the invariable characteristic parameters of any dental jaw is finally obtained by searching the relation between the characteristic parameters which are invariable in the dental arch correcting process and the characteristic parameters which are relevant to the ideal arch and the relation between the characteristic parameters which are relevant to the ideal arch and the ideal arch curve function, and the personalized target dental arch curve model established by the method does not need to be adjusted by an operator according to personal experience, so that the defect that the target dental arch curve cannot be attractive and the physiological development characteristics and functional requirements of the dental jaw due to subjective factors is overcome, and the automatic generation of the personalized target dental arch curve is realized.
Drawings
FIG. 1 is a flow chart of a prior art personalized target dental arch curve generation method;
FIG. 2 is a flow chart of a prior art personalized target dental arch curve generation method;
FIG. 3 is a flow chart of a personalized target dental arch curve modeling method provided in accordance with an embodiment of the present application;
FIG. 4 is a schematic illustration of measuring crown width sum in some embodiments;
FIG. 5 is a schematic illustration of measurement of 5/6 contact dimensions in some embodiments;
FIG. 6 is a flow chart of determining a relationship between a personalized target arch curve of any dental jaw and a second characteristic parameter in some embodiments;
FIG. 7 is a schematic illustration of an implementation flow of some preferred embodiments;
FIG. 8 is a schematic illustration of the creation of a jaw plane from tooth feature points in some preferred embodiments;
FIG. 9 is a schematic diagram of feature points acquired on a reference dental jaw in some preferred embodiments;
FIG. 10 is a graph showing the result of coordinate adjustment of feature points of each reference dental jaw in some preferred embodiments;
FIG. 11 is a summary schematic of 5-6 abutment dimensions of each reference jaw in some preferred embodiments;
FIG. 12 is a diagram of statistics B in some preferred embodiments adjust And A is a best Schematic representation of the correlation;
FIG. 13 is a diagram of statistics A in some preferred embodiments best And B is connected with best Schematic representation of the correlation;
FIG. 14 is a graph of 5-6 adjacent spot size versus B in some preferred embodiments adjust Schematic diagram of the correlation.
Detailed Description
The present application will be further described below based on preferred embodiments with reference to the accompanying drawings.
In the description of the embodiments of the present application, it should be noted that, if the terms "upper," "lower," "inner," "outer," and the like indicate an azimuth or a positional relationship based on that shown in the drawings, or an azimuth or a positional relationship that a product of the embodiments of the present application conventionally put in use, it is merely for convenience of describing the present application and simplifying the description, and does not indicate or imply that the device or element to be referred to must have a specific azimuth, be configured and operated in a specific azimuth, and thus should not be construed as limiting the present application. Furthermore, in the description of the present application, terms first, second, etc. are used herein for distinguishing between different elements, but not limited to the order of manufacture, and should not be construed as indicating or implying any relative importance, as such may be different in terms of its detailed description and claims. Furthermore, various structures on the drawings are exaggerated or reduced for ease of understanding, but such is not intended to limit the scope of the present application.
Fig. 1 shows a flow chart of a prior art method of generating a personalized target arch curve, a specific embodiment of which is referred to in the prior art patent documents mentioned in the background. In the implementation of the method, as shown in fig. 1, firstly, characteristic points of teeth (such as the mid-incisor and side-incisor edge midpoint, cuspid, first premolars and second premolars, first molar and second molar near-mid-cheek cuspid and far-mid-cheek cuspid, etc.) are selected from a dental model to be corrected through step 110, and then curve fitting is performed by using the characteristic points to obtain maxillary and mandibular arch curves in the form of polynomial functions, etc., wherein coefficients of the polynomial can be determined in such a way that the sum of distances between the characteristic points and corresponding points on the function curve is minimized; the above-mentioned upper and lower jaw curves represent the dental arch shape before treatment (i.e. in a malformed state), the upper and lower jaw curves are further matched by step 120, finally, the width, length, depth, shape and matching degree of the upper and lower dental arch curves are individually adjusted by a doctor or technician according to the treatment requirement in step 130, and finally, the target dental arch curve is generated.
Although the method can generate the target dental arch curve individually aiming at different dental jaws to be corrected, on one hand, the method starts from the dental arch curve in a malformed state before treatment, and an experienced doctor or technician adjusts the dental arch curve manually and empirically to obtain a result, so that the effect is obviously dependent on the experience of an operator; on the other hand, the above adjustment results in the dental arch form which makes the subjective feeling of the operator (or both the operator and the patient) more ideal, and cannot ensure that the dental arch form meets the objective rules and functional requirements of dental development and dentition arrangement.
Fig. 2 shows a flow chart of another prior art method of generating a personalized target arch curve, a specific embodiment of which is also found in the prior art patent documents mentioned in the background. As shown in fig. 2, in step 210 of the method, some maxillary and mandibular arch curves are obtained from the big data dentition fitted arch curve (where the big data for fitting is derived from a population with normal arches); then selecting an appropriate arch curve form from a plurality of maxillary and mandibular arch curves in step 220, and determining the width, length and depth of the arch curve from the arch width, length and depth before treatment of the patient in step 230; finally, in step 240, this is also further adjusted by the physician or technician to obtain the target dental arch curve.
Although the method utilizes big data of normal arch crowd to generate ideal arches as reference, the selection of proper dental arch curve form from various ideal arches is still from experience, and after the proper dental arch curve is determined, the proper dental arch curve is adjusted based on the dental arch width, length and depth data before treatment, the basis of the adjustment is still the subjective feeling of an operator, and an 'anchoring' parameter which is not influenced by the subjective feeling of the operator and accords with objective rules of dental development and dentition arrangement is lacked as an adjustment basis, so that the target dental arch curve generated by the method is used as a treatment target, and the development and the function of dental arch with the target arch still cannot be ensured to be in an optimal state.
It can be seen that, for any jaw, if it is desired that the target dental arch curve not only meets the subjective aesthetic feeling, but also ensures that the function and development of the jaw is in an optimal state, the target dental arch curve should at least meet the following criteria:
(1) The target dental arch curve is used as an anchoring reference by the amount which is kept unchanged in the dental arch adjusting process, so that the dental arch curve with the same anchoring reference value can be adjusted to be consistent although in different dental arch deformity states, and obviously, the process can eliminate the influence of subjective factors caused by artificial adjustment;
(2) The target dental arch curve should also conform to subjective aesthetic feelings, and thus should take the form of a presently accepted polynomial function suitable for describing the dental arch curve morphology, for which reason the correspondence between the above-mentioned anchoring reference value and the polynomial function describing the ideal arch needs to be found.
Based on the above criteria, the application provides a personalized target dental arch curve modeling method independent of manual adjustment operation, as shown in fig. 3, the method comprises the following steps:
step 310, determining a relation between a first characteristic parameter and a second characteristic parameter of any jaw when the jaw is in an ideal arch according to the measured data of a plurality of reference jaws, wherein the arch curve of each reference jaw accords with the ideal arch standard;
step 320, determining the relation between the personalized target dental arch curve corresponding to any dental jaw and the second characteristic parameter thereof according to the measurement data;
and 330, determining the personalized target dental arch curve corresponding to the arbitrary dental jaw with the first characteristic parameter according to the relation between the first characteristic parameter and the second characteristic parameter when the arbitrary dental jaw has the ideal dental arch and the relation between the personalized target dental arch curve corresponding to the arbitrary dental jaw and the second characteristic parameter.
The method is described in detail below with reference to the accompanying drawings and specific examples.
In the method, firstly, the measurement data of a plurality of reference dental jaws meeting ideal arch standards are counted to acquire the relation between a first characteristic parameter serving as an anchoring reference and a second characteristic parameter representing ideal arch when any dental jaw is in ideal arch (namely, when the dental arch curve is provided with a target dental arch curve),
specifically, the reference dental jaw refers to a dental jaw which is evaluated by taking a pre-specified ideal arch standard (such as taking the overall shape of a dental arch curve or the geometric parameters of characteristic mark points and the like as the standard, and the establishment of the standard simultaneously considers aesthetic property and functionality), and the dental jaw meeting the standard represents a crowd with normal and ideal arrangement of dental arches and dental columns in the crowd. Various technical means known to those skilled in the art, such as CBCT, ultrasound, three-dimensional oral scanning, and the like, may be used to model, measure, and the like, the morphology of the plurality of reference dental jaws, and further obtain various measurement data thereof. Furthermore, the number of reference dental jaws should be sufficiently large to meet the criteria for performing correlation statistics. The above embodiments are known to those skilled in the art and will not be described in detail herein.
In particular, the first characteristic variable characterizes an intrinsic characteristic of any jaw, and this characteristic is independent of the arch state, i.e. the value of the first characteristic variable remains unchanged for any jaw, whether it is in an ideal arch state or in what phase of correction from a non-ideal arch to an ideal arch.
It should be noted that, the value of the first characteristic parameter remains unchanged, which means that in a treatment period, the jaw change caused by the development of the dental bone and the eruption of the teeth does not cause the need of reformulating the target for correction, for example, for an adult in a stable state of both the development of the dental bone and the eruption of the teeth, the value of the first characteristic parameter may remain unchanged in a longer period; however, for children/teenagers in the fast development of the jaw bone and the fast eruption phase of the teeth, the first characteristic parameter can only be considered to remain unchanged for a short period of time in months, in correspondence with which the target arch curve should also be generated for each short treatment cycle.
The first characteristic of any jaw may be determined by the geometry of a number of particular teeth of its upper or lower jaw, for example, in some preferred embodiments, the first characteristic may be a 5-5 crown width sum, or a 4-4 crown width sum, of the lower jaw. Referring to fig. 4, in the present application, the sum of n1-n2 crown widths refers to a result of measuring the crown width of each tooth from the left nth tooth 1 (left tooth numbering direction is the left molar direction from the left central incisor) to the right nth tooth 2 (right tooth numbering direction is the right molar direction from the right central incisor) of the upper jaw or lower jaw, and superimposing them.
The second characteristic parameter characterizes the characteristic of the dental arch which can be found on the ideal dental arch shape and is only related to the ideal dental arch curve, namely, if the specific value of the second characteristic parameter is determined, the shape of the target dental arch curve is also determined, and meanwhile, the second characteristic parameter is from the statistics of the reference dental arch of the crowd meeting the normal aesthetic and functional standards at the same time, and is an objective statistic excluding the influence of subjective factors, and is independent of the experience of doctors or technicians.
The second characteristic of any jaw may be determined by the geometry of its arcuate curve when in an ideal arcuate shape, for example, in some preferred embodiments, the second characteristic may be the 5/6 abutment dimension when the mandible is in an ideal arcuate shape. In the present application, the m1/m2 abutment dimension refers to the distance between the abutment points of the m1 st tooth and the m2 nd tooth on both sides of the upper jaw or lower jaw, and the ideal arcuate lower jaw shown in fig. 5 is taken as an example, and the 5/6 abutment dimension refers to the distance between the abutment points of the 5 th and 6 th teeth on the left side and the abutment points of the 5 th and 6 th teeth on the right side.
In the embodiment of the application, for any jaw, the second characteristic parameter is statistically strongly related to the first characteristic parameter, that is, in the process of adjusting the arch of any jaw, the first characteristic parameter is always kept unchanged and measurable, but the second characteristic parameter corresponds to the target state at the end of the correction period, and the second characteristic parameter is not actually realized until the arch state of the jaw reaches the ideal state, because the first characteristic parameter and the second characteristic parameter have strong correlation, a relation between a real-time measurable quantity and an objective target quantity excluding subjective influence factors can be established, that is, for any jaw, after the first characteristic parameter is measured, the objective correction target is determined by the second characteristic parameter, and then the relation between the second characteristic parameter of any jaw and the target arch curve to be realized by the step 200 is needed.
Generally, as described above, the dental arch curve may be expressed in the form of various curve functions, and thus the relationship of the second characteristic parameter to the target dental arch curve is the relationship between the second characteristic parameter and the coefficients of the appropriate curve function. For example, when describing an arch curve using a Beta function, it is necessary to determine both the relationship between the second characteristic parameter and the parameters of the Beta function; for another example, when describing the arch curve using a polynomial function, it is necessary to determine both the relationship between the second characteristic parameter and the coefficients of the respective polynomial degree.
It has been found that smooth ideal arch curves can be better described using a polynomial function, therefore, in a preferred embodiment of the present application, the personalized target arch curve is a polynomial function of degree 2N, and only up to M even terms are included in the polynomial function, wherein N, M is an integer and N.gtoreq.M.gtoreq.2.
For example, in one particular embodiment, the personalized target arch curve may be represented using the following fourth-order polynomial:
Y＝AX 4 +BX 2 ，
wherein X, Y is the coordinates of each point on the function curve and X, Y is located on the jaw plane, the X axis and the Y axis are orthogonal, the Y axis corresponds to the projection of the median sagittal plane on the jaw plane, A, B is the coefficients of the fourth term and the second term of the function curve, and the symmetry of the curve relative to the Y axis is ensured only by including the even term. The target dental arch curve of the above form is a curve on a two-dimensional plane, which includes two coefficients A, B that can adjust the shape of the curve, so that a specific expression of the relationship between the second characteristic parameter and A, B can be obtained by counting dental arches of a plurality of reference dental jaws.
It should be appreciated that the polynomial expression of the fourth order term described above is only one specific embodiment, and in some other embodiments, the target dental arch curve may also be a sixth order polynomial and include at least two multiple terms, such as a sixth order term and a quadratic term; in some other embodiments, the target dental arch curve may also be in the form of a three-dimensional curve.
By analysing the measured data of a plurality of reference dental arches it has been found that, since the dental arch curve comprises at least two polynomial coefficients which together influence the shape of the curve and whose influence is coupled to each other such that no significant correlation between the polynomial coefficients and the second characteristic parameters occurs, an intermediate dental arch curve has to be constructed by which the relation between the second characteristic parameters and the respective polynomial coefficients is established, for which purpose in some preferred embodiments the relation between the personalized target dental arch curve of any dental jaw and the second characteristic parameters is determined by the following steps, as shown in fig. 6:
step 410, obtaining an optimal dental arch curve of each reference dental jaw, wherein the optimal dental arch curve and the personalized target dental arch curve have the same function form, and coefficients of M even terms are determined based on the measurement data fitting of the reference dental jaw.
Specifically, the corresponding optimal arch curve can be fitted from the measured data of each reference dental jaw by methods known to those skilled in the art.
Step 420, obtaining an intermediate dental arch curve of each reference dental arch, wherein the intermediate dental arch curve and the personalized target dental arch curve have the same function form, and the coefficients of M even terms comprise M-1 fixed coefficients and an intermediate coefficient, wherein the M-1 fixed coefficients are determined according to the statistical value of the corresponding even term coefficients in each optimal dental arch curve, and the intermediate coefficient is determined based on the measurement data fitting of the reference dental arch.
Specifically, when m=2, statistics is firstly performed on one even term coefficient in multiple groups of optimal dental arch curves, a statistical value, such as a mean value, is obtained as a fixed coefficient of the even term, and then, under the condition that the fixed coefficient of the even term is unchanged, an intermediate dental arch curve of each reference dental jaw is obtained by fitting, and obviously, the other even term coefficient (i.e. the intermediate coefficient) of the intermediate dental arch curve is different for different reference dental jaws. In this way, an optimal dental arch error with each reference jaw can be obtained which is sufficiently small, but which contains only one intermediate dental arch of variable coefficients.
Through correlation statistics, the variable intermediate coefficient is found to be strongly correlated with the two polynomial coefficients and the second characteristic parameter of the optimal dental arch curve, so that the variable intermediate coefficient can be used as a bridge, and the relationship between the second characteristic parameter and the coefficients of each polynomial can be established, so that in step 430, M even term coefficients of the personalized target dental arch curve corresponding to any dental jaw represented by the second characteristic parameter can be determined according to the statistical relationship between the second characteristic parameter and the intermediate coefficient of each reference dental jaw and the statistical relationship between the intermediate coefficient of each reference dental jaw and M even terms of the optimal dental arch curve.
Through correlation statistics, it is found that, in the dental arch curve represented by the polynomial function, the coefficient of the higher order term is generally smaller by two orders of magnitude, that is, the coefficient of the lower order term varies significantly more than the coefficient of the higher order term, and the coefficient of the higher order term determines the basic shape of the curve, and the coefficient of the lower order term causes the difference in curve details, so that, in the preferred embodiment, the intermediate coefficient should be selected from the lower order terms (such as the smallest even order term) to improve the statistical correlation as much as possible.
In the above description, a polynomial function comprising two polynomials is taken as an example, and when M is greater than 2, the same procedure may be used, for example, to fix the coefficients of M-1 polynomials, obtain an intermediate dental arch curve with a variable intermediate coefficient, and calculate the correlation between the intermediate coefficient and the polynomial coefficients of each set of optimal dental arch curves.
After the statistical relationships between the second characteristic parameter and the first characteristic parameter and between the second characteristic parameter and each polynomial coefficient of the target dental arch curve are found in the steps 310 and 320, respectively, the relationship between the first characteristic parameter of any dental jaw and each polynomial coefficient of the target dental arch curve can be established in the step 330.
Example 1.
A specific embodiment 1 of the present application will be described below with reference to the accompanying drawings, and a specific flow of this embodiment is shown in fig. 7.
Step A, acquiring a three-dimensional digital model of a reference dental jaw:
in this embodiment, firstly, 55 sets of dental three-dimensional digital models meeting ideal dental arch state standards are obtained as reference dental, statistical analysis is performed, and statistical finding is performed, so that the target dental arch curve of the lower jaw is outwards shifted by 2.5mm, and the maxillary target dental arch curve meeting aesthetic and functional requirements can be obtained, so that in this embodiment, only the generation of the target dental arch curve of the lower jaw is performed.
After the three-dimensional digital model of the mandible is obtained, a plurality of characteristic points can be identified on the reference dental jaw in a manual or automatic labeling manner, wherein the characteristic points can be the dental cusp points on the dental crowns of specific teeth, the near-middle buccal cusp points or the far-middle buccal cusp points and other specific position points on each dental jaw known to the person skilled in the art.
And B, correcting a coordinate system:
for each reference dental jaw, coordinates are created with the midpoints of the left and right tooth feature points No. 1, and the left and right tooth feature points No. 6, as shown in fig. 8, the three-point composition plane is a jaw plane, and the jaw plane is an XY plane.
Step C, adjusting coordinates:
as shown in fig. 9, each reference jaw collects 18 feature points, which are the midpoint of the incisors of the left and right teeth No. 1, the midpoint of the incisors of the left and right teeth No. 2, the cusp of the left and right teeth No. 3, the cusp of the left and right teeth No. 4, the cusp of the left and right teeth No. 5, the mesial and distal cusps of the left and right teeth No. 6, and the mesial and distal cusps of the left and right teeth No. 7, respectively, and all feature points are on the jaw plane, the Z value of the coordinates thereof is 0, then the midpoint of the teeth No. 1-1 is set as the origin of coordinates (0, 0), and 55 sets of feature points are adjusted, and the final adjustment result is shown in fig. 10.
Step D, counting crown width data:
for each reference jaw, as shown in fig. 4, crown widths of the respective reference jaws are measured according to crown width measurement criteria, and crown width sums of 5-5, 4-4,3-3,2-2 are statistically summarized, wherein the manner of obtaining crown width sums has been described above.
Step E, counting the size data of the adjacent points:
for each reference jaw, the 5-6 abutment dimensions were measured and counted separately, as shown in fig. 5, wherein the manner of obtaining the abutment dimensions was described above, and the summary of the 5-6 abutment dimensions for each reference jaw is shown in fig. 11.
Step F, counting the correlation and corresponding relation between the crown width and the adjacent point size:
the 5-5 crown widths and (i.e., first characteristic parameters) and 5-6 abutment dimensions (i.e., second characteristic parameters) of the 55 sets of reference jaws are respectively counted, and the 5-5 crown widths and the 5-6 abutment dimensions of the portions of the 55 sets of reference jaws are listed in the following table 1, wherein the correlation between the 5-5 crown widths and the 5-6 abutment dimensions is found to be about 0.6 through statistics, and the correlation has a strong statistical correlation; the ratio of the two is further counted to obtain the average value of the ratio of the two.
Table 1 refers to the statistics of the dental jaw (part)
| 5-5 crown Width | 5-6 Adjacent Point size | Ratio of the two |
| 67.97 | 46.25 | 1.47 |
| 70.78 | 46.27 | 1.53 |
| 67.49 | 44.81 | 1.51 |
| 67.15 | 44.80 | 1.50 |
| 68.39 | 46.49 | 1.47 |
| 69.11 | 49.80 | 1.39 |
Step G, determining a functional form of a target dental arch curve:
fitting the different function types to find that the beta function has larger deviation in the use process; the fourth order polynomial function has better stability than the sixth order polynomial function, the sixth order function has larger fluctuation and the curve is not smooth, therefore, the fourth order polynomial function is selected as the dental arch curve function, the odd order terms are removed to ensure the symmetry of the curve relative to the Y axis, and the function form of the target dental arch curve is finally determined as Y=AX 4 +BX 2 。
Step H, fitting an optimal dental arch curve:
performing curve fitting on each reference dental jaw through the characteristic points to obtain the distance from the characteristic points to a fitted curve and the optimal dental arch with the minimum valueCurves with optimal coefficients of 4 th and 2 nd order terms respectively A best And B best 。
Table 2 below shows the A of the best arch curve obtained by partial fitting best And B best 。
TABLE 2 optimal coefficients (portions) of optimal dental arch curves
| A best | B best |
| -0.00003 | -0.02012 |
| -0.00007 | -0.00894 |
| -0.0001 | -0.00243 |
| -0.00009 | -0.00586 |
| -0.00006 | -0.01768 |
| -0.00005 | -0.01134 |
Step I, determining an intermediate dental arch curve:
it was found by statistics that although the 5-6 abutment size is closely related to the shape of the optimal arch curve, the 5-6 abutment size is related to A best And B best Does not exhibit a strong correlation, i.e., A best And B best The influence on the shape of the dental arch curve is coupled and cannot be characterized solely by its relation to the second characteristic parameter, for which purpose an intermediate dental arch curve needs to be established, which has a point size of abutment with 5-6, a, respectively best And B best Coefficients that all have a strong correlation.
Further, through statistical finding, the fourth term coefficient A best General quadratic term coefficient B best Two orders of magnitude smaller, which determines the basic shape of the curve, B best The variation is large, which forms different detail features of different curves, for which purpose a is first of all given by a best Is taken as the fixed coefficient A of each intermediate dental arch curve ave The fixed coefficients are kept unchanged, and curve fitting is further carried out by taking the sum of distances from the characteristic points to the curves as the minimum, so as to obtain an intermediate dental arch curve of each reference dental jaw, wherein the quadratic term coefficient of each dental arch curve is an intermediate coefficient B adjust 。
Step J, determining B adjust With 5-6 adjacent spot size, A best 、B best Is the relation of:
by B for each reference jaw adjust 5-6 Adjacent Point size, A best 、B best Statistics were performed, as shown in FIGS. 12 to 14, B adjust And A is a best Correlation is 0.765, A best And B is connected with best Correlation of-0.797,5-6 adjacent spot size to B adjust The correlation is: 0.799, i.e. using intermediate coefficient B adjust As a "bridge", the coupling correlation between the second characteristic parameter and the optimal dental arch curve coefficient may be split into a plurality of strongly correlated relations that may be transferred by linear expressions.
Step K, establishing the relation between the width of the crown of 5-5 and the optimal dental arch curve;
finally, using the relation between the width of the 5-5 dental crown obtained in the step F and the size of the 5-6 abutment point, and the size of the 5-6 abutment point obtained in the step J and A best 、B best The relationship between the two can be obtained by the sum of the widths of the crowns of 5-5 (i.e. in the followingThe first characteristic parameter which is kept unchanged in the process of adjusting the arch shape), obviously, for any tooth jaw needing arch shape correction, the corresponding personalized target arch curve can be obtained by measuring the width of the 5-5 crown and then utilizing the arch curve function in the representation form, the process does not contain interference of artificial adjustment, accords with aesthetic standards and the development characteristics of the tooth jaw, and can ensure that the requirements of the tooth jaw function are met.
It should be understood that the foregoing embodiments are merely illustrative of specific embodiments of the modeling method provided by the present application, and those skilled in the art may adjust parameters such as the selected reference jaw and various feature points thereof according to actual needs without departing from the scope of the present application, and may further perform several improvements and modifications to the present application, which also fall within the scope of the claims of the present application.
The application also provides a personalized target dental arch curve model, which is used for representing ideal dental arch of any dental jaw; the personalized target dental arch curve model has a polynomial function form of 2N times and only comprises at most M even terms, wherein N, M is an integer, and N is more than or equal to M is more than or equal to 2; the arbitrary dental jaw is provided with a first characteristic parameter, and the first characteristic parameter is kept unchanged in the dental arch curve changing process; the coefficients of the M even terms may all be characterized by the first characteristic parameter.
Preferably, the arbitrary dental jaw further has a second characteristic parameter, and the second characteristic parameter is related to the shape of the personalized target dental arch curve corresponding to the arbitrary dental jaw; and the second characteristic parameter is statistically strongly correlated with the first characteristic parameter.
The target dental arch curve model may be generated by the foregoing personalized target dental arch curve modeling method, and specific embodiments thereof have been described in detail above and will not be described herein.
Claims (15)
1. A method of modeling a personalized target dental arch curve, comprising the steps of:
determining the relation between a first characteristic parameter and a second characteristic parameter of any jaw when the jaw is in an ideal arch according to the measurement data of a plurality of reference jaws, wherein the arch curve of each reference jaw accords with an ideal arch standard;
determining the relation between the personalized target dental arch curve corresponding to any dental jaw and the second characteristic parameter of the personalized target dental arch curve according to the measurement data;
and determining the personalized target dental arch curve corresponding to any dental jaw with the first characteristic parameter according to the relation between the first characteristic parameter and the second characteristic parameter when any dental jaw has the ideal dental arch and the relation between the personalized target dental arch curve corresponding to any dental jaw and the second characteristic parameter.
2. The personalized targeted dental arch curve modeling method of claim 1, wherein:
the first characteristic parameter of any jaw is kept unchanged in the process of changing the dental arch curve;
the second characteristic parameter of any jaw is related to the ideal bow that it has; the method comprises the steps of,
the second characteristic of any jaw is statistically strongly correlated with its first characteristic.
3. The personalized targeted dental arch curve modeling method of claim 1, wherein:
the first characteristic parameter of any jaw is determined by the geometric characteristics of a plurality of specific teeth of its upper or lower jaw.
4. The personalized targeted dental arch curve modeling method of claim 1, wherein:
the second characteristic of any jaw is determined by the geometry of the arch curve when it is in the ideal arch.
5. The personalized targeted dental arch curve modeling method of claim 1,
the personalized target dental arch curve is a polynomial function of degree 2N and only comprises at most M even terms, wherein N, M is an integer and N is more than or equal to M is more than or equal to 2.
6. The personalized targeted dental arch curve modeling method of claim 5, wherein:
the coefficients of the M even terms may each be characterized by a second characteristic parameter.
7. The personalized target dental arch curve modeling method according to claim 5, wherein the relationship between the personalized target dental arch curve of any dental jaw and the second characteristic parameter is determined according to the steps of:
obtaining an optimal dental arch curve of each reference dental jaw, wherein the optimal dental arch curve and the personalized target dental arch curve have the same function form, and the coefficients of M even terms of the optimal dental arch curve are determined based on the measurement data fitting of the reference dental jaw;
obtaining an intermediate dental arch curve of each reference dental arch, wherein the intermediate dental arch curve and the personalized target dental arch curve have the same function form, and M even-term coefficients of the intermediate dental arch curve comprise M-1 fixed coefficients and an intermediate coefficient, wherein the M-1 fixed coefficients are determined according to the statistical value of the corresponding even-term coefficients in each optimal dental arch curve, and the intermediate coefficient is determined based on the measurement data fitting of the reference dental arch;
according to the statistical relationship between the second characteristic parameters of each reference dental jaw and the intermediate coefficients and the statistical relationship between the intermediate coefficients of each reference dental jaw and M even-order terms of the optimal dental arch curve, M even-order term coefficients of the personalized target dental arch curve corresponding to any dental jaw represented by the second characteristic parameters are determined.
8. The personalized targeted dental arch curve modeling method of claim 7, wherein:
and the M-1 fixed coefficients are determined according to the average value of the coefficients of corresponding even terms in each optimal dental arch curve.
9. The personalized targeted dental arch curve modeling method of claim 7, wherein:
and the even number item corresponding to the intermediate coefficient is the even number item with the minimum times.
10. The personalized targeted dental arch curve modeling method of claim 5, wherein the polynomial function of degree 2N is in the form of:
Y＝AX 4 +BX 2 ，
wherein X, Y is the coordinates of each point on the function curve and X, Y is on the jaw plane, and A, B is the coefficients of the fourth and second terms of the function curve.
11. The personalized targeted dental arch curve modeling method of claim 1, wherein:
the first characteristic parameter is the sum of the widths of the 5-5 crowns of the mandible.
12. The personalized targeted dental arch curve modeling method of claim 1, wherein:
the second characteristic parameter is the 5/6 adjacent point size of the lower jaw.
13. A personalized target dental arch curve model for characterizing an ideal dental arch that any dental jaw should have, characterized by:
the personalized target dental arch curve model has a polynomial function form of 2N times and only comprises at most M even terms, wherein N, M is an integer, and N is more than or equal to M is more than or equal to 2;
the arbitrary dental jaw is provided with a first characteristic parameter, and the first characteristic parameter is kept unchanged in the dental arch curve changing process;
the coefficients of the M even terms may all be characterized by the first characteristic parameter.
14. The personalized target dental arch model of claim 13, wherein:
the arbitrary dental jaw is also provided with a second characteristic parameter, and the second characteristic parameter is related to the shape of the personalized target dental arch curve corresponding to the arbitrary dental jaw; the method comprises the steps of,
the second characteristic parameter is statistically strongly correlated with the first characteristic parameter.
15. The personalized target dental arch model of claim 14, wherein the personalized target dental arch model is generated by the personalized target dental arch modeling method of claim 1.
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