Optimization method of occlusal surface dental crown based on iconography and topology

Abstract

The invention discloses a method for optimizing an occlusal surface dental crown based on iconography and topology, which comprises the following steps of: firstly, carrying out digital modeling and feature point extraction and processing on the geometrical morphology of natural teeth by using a three-dimensional image or 3D (three-dimensional) scanning technology, and constructing a normal tooth standard feature library; secondly, determining geometric engineering laws and biological-functional laws of different types of working tooth surfaces, and constructing representative standard working tooth surface geometric features; and finally, constructing a topological-morphological characteristic parameter set and a functional logic relation graph of the biological characteristics, the geometrical morphological characteristics and the intrinsic rule relation between the geometrical morphological characteristics and the functional characteristics of the typical type of human teeth, and determining the relation between the morphological characteristics and the functional characteristics of the molar occlusal surface. A mathematical model is used for describing geometric features of an occlusal surface of a dental crown, reasonability of the model is verified through clinical cases and experience, and further optimization is carried out to obtain a geometric shape model of a false tooth.

Description

Technical Field

[0001] The invention relates to the technical field of denture modeling, and in particular to an optimization method for an occlusal crown based on imaging and topology. Background Art

[0002] Dentures are artificial teeth that replace missing natural teeth. They are restorations made after partial or complete tooth loss in the upper or lower jaws, and include abutments and crowns.

[0003] Both oral implants and tooth restoration require dentures. However, in current clinical practice, the denture production process mainly includes "biting tooth marks", making plaster molds, remolding dentures, trial fitting, grinding, and fitting / bonding dentures. Human factors affect the design, production, and restoration process of dentures, and the main problems they bring are: (1) The amount of grinding is large, which causes great damage to the real teeth; (2) The tooth restoration process is long and complicated, and it is difficult to effectively relieve the patient's pain; (3) It is difficult to form an ideal working tooth surface by making the denture working tooth surface based on "tooth marks", especially for the most complex molar occlusal surface, it is difficult to obtain an ideal functional tooth surface; (4) Human factors affect the various processes of tooth restoration mentioned above, and the actual working surface of the denture is accumulated, which further deviates from the ideal tooth surface of the real tooth, thereby causing a further decline in the chewing effect of the denture. Summary of the invention

[0004] In view of this, it is necessary to provide a high-simulation, high-performance optimization method for occlusal crowns based on imaging and topology.

[0005] A method for optimizing an occlusal crown based on radiology and topology, the method comprising the following steps: Step 1: Establish a standard feature library of normal teeth, digitally model the geometric shape of natural teeth, and construct a mathematical model of the geometric shape characteristics of the occlusal surface of natural teeth based on topology; Step 2: Determine the optimization objectives, constraints and decision variables of denture design; based on the standard characteristics of normal teeth, calculate the weights of each optimization objective through a multi-objective optimization comprehensive function, and calculate each decision variable of the denture through an optimization method; Step three, according to the various decision variables of the denture, the cusp point diagram, socket point diagram, protrusion point diagram and groove point diagram of the occlusal surface are defined and described respectively through the uniform 9-point point diagram method, and the cusp point diagram, socket point diagram, protrusion point diagram and groove point diagram are superimposed to obtain the comprehensive result of the occlusal surface.

[0006] Preferably, the step of establishing a standard feature library of normal teeth, digitally modeling the geometric morphology of natural teeth, and constructing a mathematical model of the geometric morphology characteristics of the occlusal surface of natural teeth based on topology in step 1 specifically includes: Step 1.1, use three-dimensional imaging or 3D scanning technology to scan normal teeth, perform statistical analysis on a large sample, and determine the geometric morphology of different types of working tooth surfaces; Step 1.2, establish a human permanent tooth feature parameter library and use a matrix to represent the geometric features of the crown; Step 1.3, construct the relationship and internal law model between the geometric morphological characteristics of the occlusal surface and the physiological function, determine the geometric morphological characteristics of the cusps and tooth sockets, and the quantitative parameters of the occlusal / masticatory functions of the corresponding teeth; The geometric features of the crown include the topological features of the body, the occlusal features of the corresponding teeth, and the adjacent surface features, which are represented by the matrix shown in formula (1): (1); in, T vw Indicates that the mark is vw The geometric features of the crown include 9 relatively independent elements, namely, the minimum wall thickness of the crown x1, the circumference of the crown x2, the height of the crown x3, the height of the crown tip x4, the ideal bevel angle x5, the depth of the tooth socket x6, the diameter of the tooth socket x7, the number of tooth tips x8 and the tooth tip orientation x9, wherein the height of the crown tip and the ideal bevel angle correspond to the tooth socket and tooth tip of the corresponding tooth.

[0007] Preferably, the step of determining the geometric features of the tooth cusps and tooth sockets and the quantitative parameters of the occlusal / masticatory functions of the corresponding teeth in step 1.3 specifically includes: Step 1.3.1, determine the quantitative parameters of the tooth cusp; The number of cusps on the occlusal surface of the molar is determined according to the human permanent tooth characteristic parameter library and the occlusal characteristics and adjacent surface characteristics of the corresponding teeth. The geometric features of each cusp include a reference point, a height, four inclined planes and a vertex, wherein the edges and vertices formed by the four inclined planes need to be rounded; Step 1.3.2, determine the quantitative parameters of the dental socket; Step 1.3.3, determine the angle difference between the tooth cusp and the tooth socket based on the relationship between the muscle closure path and the occlusal position, as shown in formula (2): (2); in, To determine the angle difference between the tooth cusp and the tooth socket, The value range of is 3~5°; α , β They are the angles between the bevel of the tooth cusp and the socket of the corresponding tooth; Step 1.3.4, determine the quantitative parameters of the groove; The model of the groove is a space segmented curve, which is projected on the XYO projection plane as L i, as shown in formula (3): (3); Among them, L i represents the i-th groove, k is the number of grooves, The values ​​are the coefficients of the polynomial; Step 1.3.5, determine the quantitative parameters of the spike; The protrusion is a small protrusion on the side of the crown, which is convex as a whole and plays a role in auxiliary positioning, support and diversion, as shown in formula (4): (4); in, p r Indicates a protrusion on the side of r; x i ,y i , z i h is the coordinate of the center of the circle between the protrusion and the tooth side, i , r i are the height and radius of the cone respectively.

[0008] Preferably, the tooth socket is represented by a portion of the inner surface of a spherical segment, and the geometric features of the socket include the radius of the spherical segment. a and the height of the ball notch h ; The inner surface of the spherical segment is shown in formula (5): (5); The height of the ball notch is the depth of the socket h , as shown in formula (6): (6); Among them, c1, c2, c3 are the coordinates of the center of the sphere, and r is the radius of the center of the sphere.

[0009] Preferably, the optimization objectives of the denture design in step 2 include the availability, energy saving and stability of the denture; the constraints include no physiological rejection reaction, no toxic side effects, the weight of a single crown, the matching degree with the paired molar, and the strength of the crown; the decision variables are 9 relatively independent elements describing the crown.

[0010] Preferably, the multi-objective optimization comprehensive function in step 2 is as shown in formula (7): (7); Where E is the weight vector, ， is the weight coefficient of the above objective and satisfies formula (8), (8); F is the objective function vector, , among which They are optimization goals for availability, energy saving and stability respectively.

[0011] Preferably, the specific steps of calculating the various decision variables of the denture by the optimization method in step 2 include: The multi-objective optimization comprehensive function is transformed into a single-objective unconstrained optimization method, as shown in formula (9): (9); In the formula, g k ( X ) is a constraint expression whose constraint part is quantifiable; Take the partial derivative of (9) for each decision variable (xi, i=1, 2, ..., 9) and set it to 0, and obtain the following 9 expressions: ; ; … (10); By solving the above formula, we can obtain the solutions of 9 independent elements of the geometric characteristics of the crown.

[0012] Preferably, the specific steps of defining and describing the cusp point diagram, the fossa point diagram, the protrusion point diagram and the groove point diagram of the occlusal surface respectively by the uniform 9-point diagram method in step 3, and superimposing the cusp point diagram, the fossa point diagram, the protrusion point diagram and the groove point diagram to obtain the comprehensive result of the occlusal surface include: Step 3.1, draw the occlusal projection in nine equal parts according to the scale; Step 3.2, accurately mark the position of the cusp point on the uniform 9-point diagram according to the cusp parameters to obtain the cusp point diagram; Step 3.3, accurately mark the position of the tooth socket on the uniform 9-point diagram according to the parameters of the tooth socket, and obtain the socket point diagram; Step 3.4, accurately mark the position of the groove on the uniform 9-point diagram according to the groove parameters to obtain the groove point diagram; Step 3.5, accurately mark the position of the bump on the uniform 9-point diagram according to the parameters of the bump, and obtain the bump point diagram; Step 3.6, superimpose the apex point diagram, fossa point diagram, protrusion point diagram and groove point diagram to obtain a uniform 9-point point diagram of the entire occlusal surface.

[0013] Preferably, the objective function vector The parameters in include: f 1——In order to meet the availability, it is necessary to select high-strength, low-density, non-toxic and non-rejection materials. The strength of the crown wall thickness x1 satisfies formula (11): (11); Among them, S represents the strength that the crown can provide. is the allowable compressive strength of the material, F1 is the occlusal force, A is the effective force-bearing area of ​​the crown = thickness × circumference, and the safety factor is 5; f 2——In order to save energy, the geometric parameters are optimized according to physiological functions to make crushing and grinding as labor-saving as possible; when crushing, the working surface inclination angle λ1=0; when grinding, the limited stroke is expected to be the largest. ; The inclination angle of the tooth cusp or tooth socket satisfies formula (12): (12); in, The inclination angle of the tip or the socket that matches the tip, and are the ideal values ​​of inclination angles for crushing and grinding respectively; f 3——In order to meet the requirements of stability, materials with high hardness and corrosion resistance should be selected. The fatigue strength of the crown should meet the formula (13): (13); Among them, S f Indicates the strength of the crown. is the fatigue strength; the safety factor is 5.

[0014] In the above-mentioned optimization method of the occlusal crown based on imaging and topology, first, three-dimensional imaging or 3D scanning technology is used to digitally model the geometric morphology of natural teeth, extract and process feature points, and construct a normal tooth standard feature library; then, the geometric engineering laws and biological-functional laws of different types of working tooth surfaces are determined, and representative standard working tooth surface geometric features are constructed; finally, the biological characteristics, geometric morphological characteristics of typical types of human teeth and their inherent relationship with functional characteristics are constructed. The topological-morphological feature parameter set and functional logic relationship map are constructed to determine the relationship between the morphological characteristics and functionality of the molar occlusal surface; the geometric characteristics of the occlusal surface of the crown are described by a mathematical model, and the rationality of the model is verified by clinical cases and experience, and further optimized to obtain the geometric morphological model of the denture. The method of the present invention is simple and can optimize abnormal geometric morphological models. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of an optimization method of an occlusal crown based on imaging and topology according to an embodiment of the present invention.

[0016] Figure 2 It is a 3D representation diagram of the occlusal surface of the occlusal crown optimization method based on imaging and topology according to an embodiment of the present invention.

[0017] Figure 3 It is a 3D representation diagram of a dental socket according to an optimization method of an occlusal crown based on imaging and topology according to an embodiment of the present invention.

[0018] Figure 4 It is a schematic diagram of a mathematical model of a tooth socket in an optimization method for an occlusal crown based on imaging and topology according to an embodiment of the present invention.

[0019] Figure 5 It is a schematic diagram of the relative movement of the temporomandibular mandible with respect to the temporomandibular mandible in the method for optimizing the occlusal crown based on imaging and topology according to an embodiment of the present invention.

[0020] Figure 6 It is a schematic diagram of the cycloidal motion of the temporomandibular joint in the method for optimizing the occlusal crown based on imaging and topology according to an embodiment of the present invention.

[0021] Figure 7 It is a schematic diagram of the force-motion logic relationship of molars based on imaging and topology (mesio-proximal view) according to an embodiment of the present invention.

[0022] Figure 8 It is a schematic diagram of the force-motion logic relationship of molars based on imaging and topology in an embodiment of the present invention (quasi-microscopic maxillofacial view).

[0023] Fig. 9 It is a schematic diagram of the logical relationship of the influence of the combination of cusps, pits and grooves on tooth function based on imaging and topology in an embodiment of the present invention.

[0024] Fig.10 It is a schematic diagram of the relationship between the muscle closure path and the occlusal position of the occlusal crown optimization method based on imaging and topology in an embodiment of the present invention.

[0025] Fig.11 It is a schematic diagram of the angle difference between the cusps and the sockets of the corresponding teeth in the method for optimizing the occlusal crown based on imaging and topology in an embodiment of the present invention.

[0026] Fig.12 It is a logical relationship diagram of the effect of the inclination of the common surface of the occlusal surfaces of a pair of occlusal teeth on chewing and liquid food according to an embodiment of the present invention based on imaging and topology.

[0027] Fig.13 It is a schematic diagram of constructing a system coordinate system and a local coordinate system of an optimization method for an occlusal crown based on imaging and topology according to an embodiment of the present invention.

[0028] Fig.14 It is a schematic diagram of a uniform 9-point diagram method of an optimization method for occlusal crowns based on imaging and topology according to an embodiment of the present invention. DETAILED DESCRIPTION

[0029] This embodiment takes the optimization method of the occlusal crown based on imaging and topology as an example, and the present invention will be described in detail below in conjunction with specific embodiments and drawings.

[0030] See also Figure 1 , showing an occlusal crown optimization method based on imaging and topology provided by an embodiment of the present invention, the method comprising the following steps: A standard feature library of normal teeth was established, the geometric morphology of natural teeth was digitally modeled, and a mathematical model of the geometric morphology characteristics of the occlusal surface of natural teeth based on topology was constructed; the optimization objectives, constraints and decision variables of denture design were determined; based on the standard characteristics of normal teeth, the weights of various optimization objectives were calculated through a multi-objective optimization comprehensive function, and the various decision variables of the denture were calculated through the optimization method; based on the various decision variables of the denture, the cusp point diagram, socket point diagram, protrusion point diagram and groove point diagram of the occlusal surface were defined and described respectively through the uniform 9-point point diagram method, and the cusp point diagram, socket point diagram, protrusion point diagram and groove point diagram were superimposed to obtain the comprehensive result of the occlusal surface.

[0031] Specifically, the geometric morphology of natural teeth is digitally modeled, a standard feature library of normal teeth is established, and a mathematical model of the geometric morphology of the occlusal surface of natural teeth based on topology is constructed. According to the movement and constraint relationship of the temporomandibular joint and its three ligaments, the movement relationship and kinematic mathematical model of the teeth driven by the temporal bone are determined. The connection and internal law model between the geometric morphology of the occlusal surface and physiological function are constructed, and the quantitative parameters of the occlusal and masticatory functions corresponding to the geometric morphology of the cusp and the fossa are determined. According to the quantitative parameters of the occlusal and masticatory functions of the occlusal surface, based on the standard characteristics of normal teeth and combined with constraint conditions, the quantitative parameters of the crown are multi-objective optimized. According to the various decision variables of the denture, the cusp, fossa, and protrusion of the occlusal surface are defined and described respectively by the uniform 9-point point diagram method, and the point diagrams for the cusp, the fossa, the protrusion, and the groove are superimposed to obtain the comprehensive results of the occlusal surface.

[0032] Specifically, in this embodiment, the real state of no less than 10,000 teeth of each type of tooth (preferably disease-free, original, and natural state) is taken for large-sample statistical analysis to determine the geometric engineering laws and biological-functional laws of different types of working tooth surfaces, and to construct a representative standard working tooth surface geometric feature library, including circumferential range, side smoothness (tentative name), topological features of the tooth top working surface (occlusal surface) (centered on the axis of symmetry, the number of protrusions, circumferential distribution, height value, and differences in geometric features with the corresponding teeth), etc.

[0033] The most complex biological characteristics of typical human teeth (anterior incisors, lateral incisors, monocuspids, bicuspids, molars) - geometric morphological characteristics and their inherent regular relationship with functional characteristics - topological-morphological characteristic parameter sets and functional logical relationship maps (spectrums) are proposed and constructed, with an emphasis on the relationship between the morphological characteristics of the occlusal surface of molars and functionality, mainly the topological spectrum of the occlusal surface.

[0034] Using 3D imaging or 3D scanning technology, we extract and process feature points and build a normal tooth standard feature library. We verify the rationality of the above models and geometric features with successful clinical cases and experience, and further optimize and obtain the denture geometry model.

[0035] 1.1 According to the definition of oral medicine, human teeth are composed of crowns and roots. The working surface of the crown is different for front teeth and back teeth: Anterior teeth: The working surface consists of labial, lingual, mesial and distal surfaces; Posterior teeth: The working surfaces consist of the buccal, lingual, mesial, distal and occlusal surfaces.

[0036] The object of the present invention is to determine and realize the ideal geometric parameters / topological features of the above-mentioned working tooth surfaces, especially the occlusal surfaces - the number, orientation and corresponding geometric shape of the protrusions - using non-uniform rational B-spline patches (surface functions).

[0037] 1.2 Statistical analysis of the topological characteristics of the occlusal surface of molars (posterior teeth). The tooth samples were collected from multiple dental clinical images. The statistical table of the topological characteristics of the occlusal surface of molars (posterior teeth) is shown in Table 1: Table 1. Statistics of topological characteristics of molar (posterior teeth) occlusal surface

[0038] Note: Only one orientation is given for each tooth cusp; it is expressed in local polar coordinates as radius and angle.

[0039] First to construct the morphological spectrum of natural human teeth - using a topological approach 1.3 Construction of reference system based on relatively independent teeth and considering the topology of dental arches, e.g. Fig.13 shown.

[0040] In the overall reference system X0Y0Z0-O0, considering the situation of each tooth, the spatial position of each tooth can be determined according to the FDI or position recording method of the clinical tooth position recording method. For a certain tooth, a local coordinate system can be used. Without loss of generality, the origin Z=0 of the local coordinates of any tooth is at the median position on a certain reference plane of the dental arch (artificially assumed), and the Z axis passes through the median of the dental arch and takes the geometrically symmetrical median of the tooth - the long axis of the tooth (assuming it exists), such as Fig.13The local reference system XYZ-O in .

[0041] For the occlusal surface of a tooth, a reference plane should be selected so that the cusp and its four inclined planes take non-negative values ​​and the dental fossa takes non-positive values, so that the definition and related terms of teeth in oral anatomy and physiology are as consistent as possible.

[0042] Construct a parameter library of human permanent teeth characteristics; provide a biomedical, functional and morphological basis for the high-precision design and production of dentures (including dental implants).

[0043] In order to accurately and concisely describe the geometric features of the occlusal surface, comprehensively express the cusp, pit, line angle, point angle, ridge (8 types), groove, etc., a matrix model is used: (1); In the formula, T vw Indicates a tooth mark vw The specific geometric features are represented by 9 relatively independent elements, and each element can be further characterized by matrix features. It is expressed by topological features to record orientation, quantity and geometric features, which is expandable.

[0044] The topological characteristics of teeth include the main body topological characteristics, the occlusal characteristics of the corresponding teeth and the adjacent surface characteristics, which describe the geometric morphological characteristics of the above-mentioned occlusal surfaces from different aspects such as topology and oral anatomy and physiology.

[0045] (a) Model of tooth cusp - regular tetrahedron, see Figure 2 . Feature description: datum, height, four obliques (a regular tetrahedron + chamfer / rounding), etc. The corresponding eigenvalues, geometric models, and mathematical models are as follows Coordinate reference point O10 (0,0,0) Spike P1p (0,0,zp1) The four inclined surfaces include: S1 (1st slope): n11 (plane normal vector - i11, j11, k11), P11(x111,y112,z113), P12(x121,y122,z123), P13 (x131, y132, z133) The constructible plane expression is: Ax+By+Cz+D=0 S2 (2nd slope): n12 (plane normal vector - i12, j12, k12), P21(x211,y212,z213), P22(x221,y222,z223), P23 (x231, y232, z233) S3 (3rd slope): n13 (plane normal vector - i13, j13, k13), P31 (x311, y312, z313), P32 (x321, y322, z323), P33 (x331, y332, z333) S4 (4th slope): n14 (plane normal vector - i14, j14, k14), P41 (x411, y412, z413), P42 (x421, y422, z423), P43 (x431, y432, z433) Among them, P11=P21+P31=P41 is the peak apex of the tooth cusp.

[0046] Among them, O10 is the coordinate reference point; P1p is the cusp point; n11 is the normal vector of the first inclined surface of the cusp (each cusp has 4 inclined surfaces); P11 is the first characteristic point of the first inclined surface; i11 is the i component of the normal vector of the first inclined surface.

[0047] The same applies to the expression of other cusps on the occlusal surface of the same tooth.

[0048] All edges and points must be rounded.

[0049] (b) Model of the tooth socket - ball-shaped socket, see Figure 3 and Figure 4 .

[0050] Assuming that the dimple is part of the inner surface of the spherical part, if the depth of the dimple is h; ; The height of the ball cavity - the depth of the socket h is determined by the following equation.

[0051] ; The 3D scanner performs a holographic scan inside the mouth and can directly obtain the 2a and h values.

[0052] (c) Line angle model - the intersection of two straight lines in space, the angle between two planes The intersection of two adjacent tooth surfaces forms a line, and the angle on the line is the line angle, which can be expressed by the intersection angle of two intersecting straight lines in space.

[0053] (d) Point angle: the intersection of three lines in space The intersection point formed by three adjacent tooth surfaces is a point angle, which can be represented by three intersecting planes in space.

[0054] (e) Ridge and groove The ridge is a raised edge on the enamel formed by two sets of spatial intersecting planes; the groove is a concave line on the occlusal surface.

[0055] The logical laws of the relationship between the morphology and function of the occlusal surface and its topological expression.

[0056] (f) Dental process The protrusion is a small protrusion on the side of the tooth crown, which can assist in positioning, support and diversion. The protrusion is generally very small, with a height of 0.2-0.8mm, and a bonding surface of 0.8-1.2mm2 with the side of the tooth. The whole is convex cone-shaped, which can be expressed by vector:

[0057] Among them, xi, yi, zi are the coordinates of the center of the protrusion and the side surface of the tooth, hi and ri are the height and radius of the protrusion cone respectively; pr represents the protrusion on the r side.

[0058] 2.1 Relative movement between maxilla and mandible: movement and constraint relationship of the temporomandibular joint and its three ligaments (temporomandibular ligament, sphenomandibular ligament and stylomandibular ligament) See also Figure 5 and Figure 6 The movement and function of the oral cavity, especially the realization of the tooth occlusion function, mainly rely on the relative movement of the temporomandibular joint and its ligament group relative to the temporomandibular maxilla (which can be regarded as static). The temporomandibular joint and its ligament group control the relative movement of the teeth, completing the functions of cutting (mainly incisors), crushing (mainly monocuspids, bicuspids and molars) and grinding (mainly molars).

[0059] Three ligaments: the temporomandibular ligament, the sphenomandibular ligament and the stylomandibular ligament cooperate with the temporomandibular joint to perform cycloidal movements, suspend the mandible, limit the movement of the mandible within the normal range, prevent dislocation, and ensure tooth function.

[0060] Studying the crushing and grinding of molars from a macroscopic and quasi-microscopic perspective is of decisive significance for dental implants and tooth restoration.

[0061] (11a); In the formula, c is the radius of the circle, c=8mm Pick , substitute into equation (11a) and take the derivative with respect to time, then: (11b); Formula (11b) is more accurate than formula (3). Of course, it should be unified into the xy-O coordinate system. , then: (11c).

[0062] θ is the relative rotation angle during the movement of the temporomandibular joint, and θ1 and θ2 are the relative rotation angle positions at the two extreme positions respectively; The relationship and law between geometric form and motion function 3.1 Occlusal movement On the surface, the movement of the teeth biting is the opening and closing of the mouth - the lower lip touches the upper lip - with only vertical relative movement. Figure 7 From a macroscopic perspective, the lower dental arch moves with the temporomandibular bone, and the movement of the temporomandibular joint is affected by the temporomandibular joint and three ligaments, forming a relative movement relative to the temporomandibular joint, and a vertical movement in the positive position; see Figure 8 From a quasi-microscopic perspective, the groups of cusps distributed at certain positions on the occlusal surface and the corresponding groups of pits on the occlusal surface are not completely consistent in convexity and concavity and completely coupled, but have a certain angle difference, and at the same time, guided by the inclined surface of the cusps, they form limited lateral and forward movements.

[0063] 3.2 Quasi-microscopic relative motion during occlusion and its corresponding function From the perspective of the specific relative movement of the occlusal surfaces - vertical movement, and the limited horizontal movement (in two directions) formed by the guidance of the sharp inclined surfaces, the occlusion process of the teeth is a combination of horizontal and vertical movements of the corresponding upper and lower teeth. The basic function of the vertical movement is crushing, the basic function of the horizontal movement is grinding, and the basic function of the combined movement is grinding based on crushing.

[0064] 3.3 Cusp and fossa See also Fig. 9 , showing the relationship between the combination of cusp, socket and groove on tooth function, first, positioning food, then, mashing - vertical relative movement; grinding - sliding along the inclined surface; tearing - lateral (transverse) movement.

[0065] See also Fig.10 and Fig.11 , the angle difference between the cusp and the fossa is determined based on the relationship between the muscle closing path and the occlusal position: ,in, To determine the angle difference between the tooth cusp and the tooth socket, The value range of is 3~5°; α , β They are the angles between the bevel of the tooth cusp and the socket of the corresponding tooth.

[0066] 3.4 Effect of overall occlusal tilt See also Fig.12 , relative to the overall physiological anatomy of the two dental arches that support and dentition, it is a spatial shape close to a plane, reflected in the overall occlusal surface. Under the condition of a normal sitting posture, for a pair of occlusal molars (such as the first molar), when it is observed on the vertical section along the direction of the dental arch, the inclination angle of the real occlusal plane (ROP) relative to the horizontal plane can be observed. , .

[0067] There are two functional functions: Food gains potential energy momentum toward the tongue and pharynx by its own weight; During the chewing process, with the help of oral fluid, tongue and cheeks, the chewed food flows into the pharynx and is swallowed.

[0068] 3.5 The function of “ditch” in determining food and diversion During the development and growth of deciduous and permanent teeth, with the formation of the cusps and pits of the main teeth (e.g. 46), as well as the guidance and stimulation of the corresponding occlusal teeth (16), the grooves that run along the cusp and pit side evolve. Food enters the space between the upper and lower teeth under the action of the lips, tongue, gums and cheeks, and undergoes multiple cycles of occlusion and chewing. In each cycle, the local part of the food is positioned at the initial contact moment of the cusp and pit, and as the occlusion proceeds, the food moves slightly in the occlusal area - vertically + along the inclined surface, and then partially fills the groove. In the next occlusal cycle, due to the combined action of the tongue, cheek, and oral fluid, the chewed part of the food mass moves toward the glossopharynx under the action of the inclined surface and groove.

[0069] Matrix expression of the relationship between geometric features and functional features:

[0070] In the formula, F vw , v =1,2,3; w =1,2,3, indicating the functional relationship of the occlusal surface according to the spatial geometric form. Specifically, the nine elements are: F11=x1; F12=x2; F13=x3; F21=x4; F22=x5; F23=x6; F31=x7; F32=x8; F33=x9. The above geometric elements corresponding to the optimal function are directly taken from the optimization decision variables.

[0071] Multi-objective optimization design The optimization of the geometric and topological characteristic parameters of the occlusal surface is an extremely complex engineering and technical problem. It is reasonable to conduct optimization analysis and design by comprehensively and systematically considering the oral working environment and conditions; on the other hand, in order to highlight the main issues, simplify the complex forms, and effectively reveal the essential laws, the effects of oral fluid, tongue, buccal surface, etc. are concentrated on the movement and power of the teeth; and the effects of organs such as oral muscles, ligaments, and temporomandibular joints are abstracted into motion constraints and dynamic parameters, thereby highlighting the relationship between the occlusal surface and movement / power.

[0072] In the optimization process, the core is to use multi-objective and multi-constraint optimization solutions. It is also very important to use imaging to obtain large samples, statistical analysis and comparison, obtain the characteristic parameters of the occlusal surface and verify them with mathematical model optimization, such as the optimization of the geometric parameters and topological characteristics of the cusps and sockets.

[0073] 4.1 Selection of multiple targets For dentures, the most important thing is its applicability and durability; for implant systems, the overall applicability and durability are required. This patent focuses on the occlusal surface of the crown, which is the core part that directly bears the physiology of the tooth and exerts the function of the tooth. The first and most important thing is to ensure the physiological function of the occlusal surface. For the lower molars (first molars 46), the optimization goals of this invention include O1: Usability (strength + wear resistance – maintains geometry) O2: Energy saving (energy saving for crushing + energy saving for grinding - the toughest and hardest materials of food) O3: Stability (fatigue strength + corrosion resistance - strong availability, effective long-term use) 4.2 Constraints No physiological rejection reaction occurs; No toxic side effects; The weight of a single crown is 15g-22g——x3×x2×x1≤22 Ensures optimal fit with paired upper molars (16)

[0074] Where x5 (1) is the angle of the tooth tip bevel. x5 (2) - the angle of the upper tooth (46) socket corresponding to molar 1.

[0075] Strength Constraints

[0076] That is, the teeth can provide 5 times the strength of natural teeth.

[0077] 4.3 Decision variables

[0078] Minimum crown wall thickness x1; Crown circumference x2; Crown height x3; The height of the crown tip (corresponding to the tooth socket) x4; Ideal bevel angle (corresponding to the tooth cusp condition) x5; Depth of tooth socket x6; Tooth socket diameter x7; The distribution of tooth cusps on the occlusal surface (number and orientation) is x8, x9.

[0079] 4.4 Analysis method and optimization results As far as the optimal design of teeth is concerned, the geometric form corresponding to the optimal function is the optimization goal. The influence of the function of the first right lower molar 46 from the occlusal corresponding tooth 16 is significant and must be considered in pairs; the influence from the adjacent teeth 45 and 47 is also partial, but for the occlusal surface, this influence is small and can be ignored; the physiological formation of the tooth itself should be the main basis.

[0080] In summary, the main factors to consider for any tooth (in this case, the first molar) are The geometry of the tooth itself is physiologically formed; The occlusion corresponds to the physiologically formed geometry of the teeth; Occlusal function of paired teeth.

[0081] 4.4.1 Multi-objective optimization comprehensive function

[0082] Where E is the weight vector

[0083] F——Objective function vector

[0084] ——Availability, energy saving and stability goals respectively ——The weight coefficient of the above objectives, and satisfy

[0085] You can take it.

[0086] Titanium is the first choice; crown thickness (wall thickness) is based on strength theory

[0087] Take a safety factor of 5. ——The geometric parameters should be optimized according to physiological functions to make crushing and grinding as labor-saving as possible: When crushing, the working surface inclination angle λ1=0; when grinding, the limited stroke is expected to be the largest.

[0088] Comprehensive optimization,

[0089] ——The design should be optimized according to the fatigue strength of the material, and materials with high hardness and corrosion resistance should be selected.

[0090]

[0091] In the formula, ——Fatigue resistance.

[0092] A safety factor of 5 is also taken.

[0093] 4.4.2 Analytical method - "unconstrained optimal solution", supplemented by large sample imaging + statistical methods.

[0094] (1) Change multiple targets to “single target” (2) Change from “constrained” to “unconstrained” (3) Using multiple variables to find partial derivatives and obtain limits (4) Assisted by imaging and large sample statistical analysis The unconstrained identity objective function is as follows:

[0095] Where gk(X) is the quantifiable constraint expression of the constraint part.

[0096] Take the partial derivative of equation (5-9) for each decision variable (xi, i=1, 2, ..., 9) and set it to 0, and obtain the following 9 expressions:

[0097] ......

[0099] By solving equation (5-10), we can get the preliminary optimization result.

[0100] Combining imaging and large sample statistics, the revised and determined decision parameters are as follows: 4.4.2 Tooth cusps By image and statistics: quantity, direction, height, slope angle {5, (4.0, 65°; 4.1, 135°; 3.9, 210°; 4.1, 280°; 4.0, 355°), (2.7, 2.9, 3.0, 2.8, 3.1), 22.5°} 4.4.3 Dental socket By image and statistics: quantity, location, depth, supplemented by experimental verification {4, (3.0, 28°; 4.5, 160°; 3.9, 250°; 4.5, 325°), (2.2, 2.5, 2.8)} 4.4.4 Tooth groove By Image and Statistics: Trends It is formed naturally by the cusp (including the subcusp) and the fossa. 4.5 Results The minimum wall thickness of the crown is x1=0.4; Crown circumference x2 = 37-44; Crown height x3 = 6.8-8.2; The height of the crown tip (highest; corresponding to the tooth socket) x4=3.1; The ideal bevel angle (corresponding to the tooth cusp condition) is x5=22.5°; The depth of the tooth socket is x6=1.9-2.8; Dental socket diameter x7 = 2.4-2.7; The distribution of cusps on the occlusal surface (number and orientation) x8=5, x9={4.0,65°} (one) Geometric characteristics and matching of cusps and sockets of upper and lower molars: The angle difference between the tooth tip and the tooth socket is 1.5-2.5 degrees; Same orientation.

[0101] According to the decision variables of the denture, the cusp point diagram, the fossa point diagram, the protrusion point diagram and the groove point diagram of the occlusal surface are defined and described respectively by the uniform 9-point diagram method. The comprehensive result of the occlusal surface is obtained by superimposing the cusp point diagram, the fossa point diagram, the protrusion point diagram and the groove point diagram, such as Fig.14 shown.

[0102] 5.1, draw the occlusal projection in nine equal parts according to the proportion; Fig.14 (a) shown.

[0103] 5.2, according to the parameters of the tooth cusp, accurately mark the position of the tooth cusp point on the uniform 9-point diagram to obtain the cusp point diagram; Fig.14 (b) shown.

[0104] 5.3, according to the parameters of the tooth socket, accurately mark the position of the tooth socket on the uniform 9-point diagram to obtain the socket point diagram; Fig.14 (c) shown.

[0105] 5.4, ​​accurately mark the position of the groove on the uniform 9-point diagram according to the groove parameters to obtain the groove point diagram; Fig.14 (d) shown.

[0106] 5.5, according to the parameters of the protrusion, accurately mark the position of the protrusion on the uniform 9-point diagram to obtain the protrusion point diagram; Fig.14 (e) shown.

[0107] 5.6, superimpose the cusp point diagram, the fossa point diagram, the protrusion point diagram and the groove point diagram to obtain a uniform 9-point point diagram of the entire occlusal surface; Fig.14 (f) shown.

[0108] In the above-mentioned optimization method of the occlusal crown based on imaging and topology, first, three-dimensional imaging or 3D scanning technology is used to digitally model the geometric morphology of natural teeth, extract and process feature points, and construct a normal tooth standard feature library; then, the geometric engineering laws and biological-functional laws of different types of working tooth surfaces are determined, and representative standard working tooth surface geometric features are constructed; finally, the biological characteristics, geometric morphological characteristics of typical types of human teeth and their inherent relationship with functional characteristics are constructed. The topological-morphological feature parameter set and functional logic relationship map are constructed to determine the relationship between the morphological characteristics and functionality of the molar occlusal surface; the geometric characteristics of the occlusal surface of the crown are described by a mathematical model, and the rationality of the model is verified by clinical cases and experience, and further optimized to obtain the geometric morphological model of the denture. The method of the present invention is simple and can optimize abnormal geometric morphological models.

[0109] It should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A method for optimizing occlusal crowns based on imaging and topology, characterized in that: The method comprises the following steps: Step 1: Establish a standard feature library of normal teeth, digitally model the geometric shape of natural teeth, and construct a mathematical model of the geometric shape characteristics of the occlusal surface of natural teeth based on topology; Step 2: Determine the optimization objectives, constraints and decision variables of denture design; based on the standard characteristics of normal teeth, calculate the weights of each optimization objective through a multi-objective optimization comprehensive function, and calculate each decision variable of the denture through an optimization method; Step three, according to the various decision variables of the denture, the cusp point diagram, socket point diagram, protrusion point diagram and groove point diagram of the occlusal surface are defined and described respectively through the uniform 9-point point diagram method, and the cusp point diagram, socket point diagram, protrusion point diagram and groove point diagram are superimposed to obtain the comprehensive result of the occlusal surface.

2. The method for optimizing occlusal crowns based on imaging and topology as claimed in claim 1, characterized in that: The steps of establishing a standard feature library of normal teeth, digitally modeling the geometric morphology of natural teeth, and constructing a mathematical model of the geometric morphology characteristics of the occlusal surface of natural teeth based on topology specifically include: Step 1.1, use three-dimensional imaging or 3D scanning technology to scan normal teeth, conduct statistical analysis on a large sample, and determine the geometric morphology of different types of working tooth surfaces; Step 1.2, establish a human permanent tooth feature parameter library and use a matrix to represent the geometric features of the crown; Step 1.3, construct the relationship and internal law model between the geometric morphological characteristics of the occlusal surface and the physiological function, determine the geometric morphological characteristics of the cusps and tooth sockets, and the quantitative parameters of the occlusal / masticatory functions of the corresponding teeth; The geometric features of the crown include the topological features of the body, the occlusal features of the corresponding teeth, and the adjacent surface features, which are represented by the matrix shown in formula (1): （1）； in, T vw Indicates that the mark is vw The geometric features of the crown include 9 relatively independent elements, namely, the minimum wall thickness of the crown x1, the circumference of the crown x2, the height of the crown x3, the height of the crown tip x4, the ideal bevel angle x5, the depth of the tooth socket x6, the diameter of the tooth socket x7, the number of tooth tips x8 and the tooth tip orientation x9, wherein the height of the crown tip and the ideal bevel angle correspond to the tooth socket and tooth tip of the corresponding tooth.

3. The method for optimizing occlusal crowns based on imaging and topology as claimed in claim 1, characterized in that: The steps of determining the geometric features of the cusps and tooth sockets and the quantitative parameters of the occlusal / masticatory functions of the corresponding teeth in step 1.3 specifically include: Step 1.3.1, determine the quantitative parameters of the tooth cusp; The number of cusps on the occlusal surface of the molar is determined according to the human permanent tooth characteristic parameter library and the occlusal characteristics and adjacent surface characteristics of the corresponding teeth. The geometric features of each cusp include a reference point, a height, four inclined planes and a vertex, wherein the edges and vertices formed by the four inclined planes need to be rounded; Step 1.3.2, determine the quantitative parameters of the dental socket; Step 1.3.3, determine the angle difference between the tooth cusp and the tooth socket based on the relationship between the muscle closure path and the occlusal position, as shown in formula (2): （2）； in, To determine the angle difference between the tooth cusp and the tooth socket, The value range of is 3~5°; α , β They are the angles between the bevel of the tooth cusp and the corresponding tooth socket; Step 1.3.4, determine the quantitative parameters of the groove; The model of the groove is a space segmented curve, which is projected on the XYO projection plane as L i , as shown in formula (3): （3）； Among them, L i represents the i-th groove, k is the number of grooves, The values ​​are the coefficients of the polynomial; Step 1.3.5, determine the quantitative parameters of the spike; The protrusion is a small protrusion on the side of the crown, which is convex as a whole and plays a role in auxiliary positioning, support and diversion, as shown in formula (4): （4）； in, p r Indicates a protrusion on the side of r; x i ,y i , z i h is the coordinate of the center of the circle between the protrusion and the tooth side, i , r i are the height and radius of the cone respectively.

4. The method for optimizing occlusal crowns based on imaging and topology as claimed in claim 3, characterized in that: The tooth socket is represented by a portion of the inner surface of a spherical segment, and the geometric features of the socket include the radius of the spherical segment. a and the height of the ball notch h ; The inner surface of the spherical segment is shown in formula (5): （5）； The height of the ball notch is the depth of the socket h , as shown in formula (6): （6）； Among them, c1, c2, c3 are the coordinates of the center of the sphere, and r is the radius of the center of the sphere.

5. The method for optimizing occlusal crowns based on imaging and topology as claimed in claim 2, characterized in that: The optimization objectives of the denture design in step 2 include the availability, energy saving and stability of the denture; the constraints include no physiological rejection reaction, no toxic side effects, the weight of a single crown, the matching degree with the paired molar, and the strength of the crown; the decision variables are 9 relatively independent elements describing the crown.

6. The method for optimizing occlusal crowns based on imaging and topology as claimed in claim 5, characterized in that: The multi-objective optimization comprehensive function in step 2 is shown in formula (7): （7）； Where E is the weight vector, ， is the weight coefficient of the above objective and satisfies formula (8), （8）； F is the objective function vector, , among which They are optimization goals for availability, energy saving and stability respectively.

7. The method for optimizing occlusal crowns based on imaging and topology as claimed in claim 6, characterized in that: The specific steps of calculating the various decision variables of the denture by the optimization method in step 2 include: The multi-objective optimization comprehensive function is transformed into a single-objective unconstrained optimization method, as shown in formula (9): （9）； In the formula, g k ( X ) is a constraint expression whose constraint part is quantifiable; Take the partial derivative of (9) for each decision variable (xi, i=1, 2, ..., 9) and set it to 0, and obtain the following 9 expressions: ； ； …… (10)； By solving the above formula, we can obtain the solutions of 9 independent elements of the geometric characteristics of the crown.

8. The method for optimizing occlusal crowns based on imaging and topology as claimed in claim 7, characterized in that: The specific steps of defining and describing the cusp point diagram, the fossa point diagram, the protrusion point diagram and the groove point diagram of the occlusal surface by the uniform 9-point diagram method in step 3, and superimposing the cusp point diagram, the fossa point diagram, the protrusion point diagram and the groove point diagram to obtain the comprehensive result of the occlusal surface include: Step 3.1, draw a 9-division diagram of the occlusal surface projection in proportion, accurately mark the position of the cusp point on the uniform 9-division diagram according to the parameters of the cusp, and obtain the cusp point diagram; Step 3.2, accurately mark the position of the tooth socket on the uniform 9-point diagram according to the parameters of the tooth socket, and obtain the socket point diagram; Step 3.3, accurately mark the position of the groove on the uniform 9-point diagram according to the groove parameters to obtain the groove point diagram; Step 3.4, accurately mark the position of the bump on the uniform 9-point diagram according to the parameters of the bump, and obtain the bump point diagram; Step 3.5, superimpose the apex point diagram, fossa point diagram, protrusion point diagram and groove point diagram to obtain a uniform 9-point point diagram of the entire occlusal surface.

9. The method for optimizing occlusal crowns based on imaging and topology as claimed in claim 6, characterized in that: The objective function vector The parameters in include: f 1——In order to meet the availability, it is necessary to select high-strength, low-density, non-toxic and non-rejection materials. The strength of the crown wall thickness x1 satisfies formula (11): （11）； Among them, S represents the strength that the crown can provide. is the allowable compressive strength of the material, F1 is the occlusal force, A is the effective force-bearing area of ​​the crown = thickness × circumference, and the safety factor is 5; f 2——In order to save energy, the geometric parameters are optimized according to physiological functions to make crushing and grinding as labor-saving as possible; when crushing, the working surface inclination angle λ1=0; when grinding, the limited stroke is expected to be the largest. ; The inclination angle of the tooth cusp or tooth socket satisfies formula (12): （12）； in, The inclination angle of the tip or the socket that matches the tip, and are the ideal values ​​of inclination angles for crushing and grinding respectively; f 3——In order to meet the requirements of stability, materials with high hardness and corrosion resistance should be selected. The fatigue strength of the crown should meet the formula (13): （13）； Among them, S f Indicates the strength of the crown. is the fatigue strength; the safety factor is 5.

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