A method for predicting tooth eruption direction based on enhanced implicit neural representation

Abstract

This invention relates to the field of oral medical image processing and tooth growth and development prediction technology, specifically to a method for predicting tooth eruption direction based on enhanced implicit neural representation. The method includes acquiring the three-dimensional coordinates of the tooth germ centroid and clinical feature vectors, preprocessing them to construct a conditional vector, constructing a tooth eruption direction prediction model, and performing the following processing: obtaining spatial features through coordinate position encoding; constructing temporal encoded features based on developmental patterns; fusing and splicing spatial features, conditional vectors, and temporal encoded features to obtain a fused feature vector; initializing the hidden state, realizing the continuous spatiotemporal evolution of the hidden state through neural frequent differential equations, decoding to generate the occupancy field, and calculating the centroid trajectory; combining a Gaussian mixture decoder to determine the main eruption direction and risk assessment results; and using a multi-objective loss function to complete model training and save the results. This invention integrates continuous spatiotemporal information and clinical features to achieve high-precision, interpretable quantitative prediction of tooth eruption direction.

Description

Technical Field

[0001] This invention relates to the field of oral medical image processing and tooth growth and development prediction technology, specifically to a method for predicting tooth eruption direction based on enhanced implicit neural representation. Background Technology

[0002] During the mixed dentition period in children, accurately predicting the eruption direction of permanent teeth is crucial for early intervention in malocclusion and the development of orthodontic treatment plans. Currently, those skilled in the art mainly rely on the following three types of technical solutions to predict tooth eruption direction, each with its own inherent limitations.

[0003] 1. Two-dimensional cephalometric analysis: As the most widely used and standard clinical technique, this method involves taking lateral or panoramic radiographs of the patient's head, manually or semi-automatically using software to trace the outline of the dental and jaw structures, key anatomical landmarks (such as the mandibular nerve canal and tooth germ location), and reference planes (such as the mandibular plane and the occipital plane). The angle between the long axis of a specific tooth and the reference plane, as well as the vertical distance from the tooth germ apex to the alveolar ridge crest or mandibular nerve canal, are measured and compared with standard growth and development charts based on large-scale population statistics (such as the Moorrees root development stage chart). Based on the doctor's clinical experience, the system assesses the eruption potential of teeth and predicts their future eruption path. However, the prediction results are discrete and highly subjective. Essentially, it is a qualitative or semi-quantitative estimate based on "table lookup + experience," which cannot describe the continuous and dynamic eruption process of teeth in three-dimensional space. Furthermore, the prediction accuracy is severely limited by the doctor's experience, and the anatomical relationships are vaguely expressed. For example, the buccal-lingual relationship between the mandibular nerve canal and the tooth germ root apex (whether it is located on the buccal or lingual side) cannot be reflected on two-dimensional films. This spatial relationship is key information for predicting whether the eruption direction will be abnormal (such as impaction caused by nerve canal compression).

[0004] 2. Tooth Development Staging Method: This method, such as the tooth calcification stage, assesses the crown and root formation stage of mandibular permanent teeth (e.g., second and third molars) using X-rays (e.g., Demirjian staging), and correlates this with cervical vertebral maturity (CVM) or wrist bone age to determine if the patient is in a growth spurt, thereby predicting tooth eruption activity. However, this method has extremely low diagnostic accuracy. Recent systematic reviews and meta-analyses show no reliable diagnostic association between tooth mineralization stage and the pubertal growth spurt. For example, the diagnostic odds ratio (DOR) for the second molar G stage and the third molar C stage is only 1.47 and 1.7, respectively, and is not statistically significant. The research clearly indicates that tooth calcification stage cannot be used as a reliable indicator for predicting growth spurts. This means that relying on tooth morphology to determine future dynamic eruption has a fundamental methodological flaw.

[0005] 3. Artificial intelligence prediction methods: In recent years, deep learning models, represented by ResNet50, have begun to be applied to growth prediction. These models input two-dimensional images such as cephalometric radiographs of patients into the model and use pre-trained convolutional neural networks (CNNs) to automatically extract image features (such as features of the mandibular margin, condyle, airway, etc.). The model outputs a classification result. However, such outputs are only classification results and not specific directions, and they lack anatomical interpretability. The black-box nature of CNNs makes it difficult to explicitly guarantee that the prediction results do not conflict with important anatomical structures such as the jawbone boundary and neural canal. The anatomical rationality of the prediction results cannot be intrinsically guaranteed.

[0006] In summary, existing technologies have significant shortcomings in terms of the continuity of tooth eruption prediction results, topological changes, and the accuracy of output information. There is an urgent need for a prediction method that can integrate dynamic evolution laws and static anatomical constraints. Summary of the Invention

[0007] This invention overcomes the above-mentioned defects and provides a tooth eruption direction prediction method based on enhanced implicit neural representation. It solves the problems of discontinuous tooth eruption direction prediction, inability to handle topological changes, low prediction accuracy due to multimodal fusion imbalance, and coarse uncertainty quantification in the prior art.

[0008] To achieve the above objectives, the tooth eruption direction prediction method based on enhanced implicit neural representation of the present invention includes the following steps:

[0009] S1. Obtain the three-dimensional spatial coordinates and clinical feature vector of the centroid of the tooth germ to be predicted, and preprocess the clinical feature vector to form a condition vector;

[0010] S2. Construct a tooth eruption direction prediction model with enhanced implicit neural representation. The model performs the following processing:

[0011] S21. Normalize the three-dimensional spatial coordinates of the tooth germ centroid, and then perform multi-level position encoding on the normalized coordinate components and splice them together to obtain spatial encoding features.

[0012] S22. Combining clinical follow-up cycles and seasonal patterns, construct a basic cycle code and map the basic cycle code to high-dimensional time coding features;

[0013] S23. The spatial coding feature and the conditional vector are fused together by cross-attention weighting to output the conditional attention feature; the spatial coding feature, the high-dimensional temporal coding feature and the conditional attention feature are concatenated to output the fused feature vector.

[0014] S24. Initialize the hidden state using the fused feature vector, and continuously evolve the hidden state from the initial time to the prediction time t using the neural ordinary differential equation to obtain the hidden state at time t.

[0015] S25. Combine the hidden state at time t with spatial coding features and tooth position embedding to perform occupancy field decoding, generate a dynamic tooth occupancy field, and calculate the tooth centroid trajectory based on the dynamic occupancy field to determine the tooth eruption direction.

[0016] S26. Input the hidden state at time t into the Gaussian mixture decoder, output the probability density of the germination direction, and determine the main germination direction vector and risk assessment result based on the probability density distribution.

[0017] S3. Use a multi-objective loss function to train the tooth eruption direction prediction model with enhanced implicit neural representation until the model converges and the optimal model is saved.

[0018] Furthermore, the clinical feature vector includes at least mineralization, bone density, interdental distance, age, muscle strength, buccal and lingual bone plate thickness, gingival thickness, and sex, which are then standardized and concatenated into a conditional vector.

[0019] Further, in step S23, the fused feature vector is calculated as follows:

[0020] The spatial coding features and condition vectors are linearly transformed into query, key, and value vectors.

[0021] ,

[0022] ,

[0023] ,

[0024] in, For query vector, For key vectors, For value vectors, , , For each, there is a corresponding weight matrix. For spatial coding features, It is a conditional vector;

[0025] Calculate attention weights: Preferred ;

[0026] Output conditional attention features: ;

[0027] The fused feature vector is then: ,in It is a high-dimensional temporal encoding feature.

[0028] Furthermore, step S24 is implemented as follows:

[0029] Initialize hidden states: Input the fused feature vector into the fully connected network, and output a hidden state vector representing the initial tooth state: ,

[0030] Solving for the hidden state involves numerical integration of the ordinary differential equations to find the hidden state from the initial time to the target time t.

[0031] ,

[0032] in, This represents the gradient change in the bone mineral density field. For the centroid of the tooth, Let t be the set of adjacent teeth, and t be the prediction time.

[0033] Furthermore, the direction of tooth eruption is calculated as follows:

[0034] Generation of dynamic occupancy field for teeth: for any spatial point The hidden state of the tooth and the tooth position are embedded into the decoder and the output point is... At time t, the tooth The probability of hard tissue occupying the area:

[0035] ,

[0036] in, This indicates a hidden state of the teeth. Indicates tooth intrusion. The output represents the position code of the spatial coordinate x. ;

[0037] Tooth eruption direction calculation: The eruption direction is calculated by tracing the trajectory of the tooth's centroid over time. The centroid is defined as the first moment of the occupancy probability field, and the calculation formula is as follows:

[0038] ,

[0039] in, The centroid of the tooth is the change of the centroid over time, which determines the direction of eruption.

[0040] Furthermore, step S26 is implemented as follows:

[0041] S261 inputs the hidden state at time t into three independent fully connected layers to predict the three parameters of the Gaussian mixture model, respectively.

[0042] ,

[0043] ,

[0044] ,

[0045] in, These represent the primary direction, secondary offset direction, and abnormal risk direction, respectively. Indicates weight; This represents the mean; Indicates variance;

[0046] S262 constructs a three-dimensional Gaussian mixture distribution based on the above parameters to model the probability density of the germination direction:

[0047] ,

[0048] Where x represents the mesial-distal eruption direction, y represents the cheek-lingual eruption direction, and z represents the perpendicular eruption direction. The probability density function representing the Gaussian distribution;

[0049] S263 uses information entropy as the overall risk indicator, expressed as:

[0050] ,

[0051] S264 introduces deep evidence regression modeling to predict uncertainty.

[0052] ,

[0053] in, This is the evidence vector; the smaller the value, the less evidence there is and the higher the uncertainty. The hidden vector at time t is the hidden state input to the fully connected layer network and the output hidden vector. make sure To be positive, avoid having zero evidence;

[0054] S265 outputs clinical indicators:

[0055] a. The main budding direction is the weighted expectation of a Gaussian mixture distribution, and the formula for the main budding direction vector is expressed as:

[0056] ,

[0057] in, The mold length indicates the amount of eruption, and the direction indicates the eruption angle.

[0058] b. Risk area visualization: Entropy value areas are marked in the 3D model, with red indicating high risk, yellow indicating medium risk, and green indicating low risk; when the direction is specifically marked, the entropy value heatmaps in the x / y / z directions are displayed separately; when intervention suggestions are generated, clinical suggestions are automatically output based on the risk areas.

[0059] Furthermore, clinical risk threshold settings:

[0060] High-risk area: H > 0.6, indicating that the germination direction is very likely abnormal, and the follow-up period can be shortened to 1 month or early intervention can be carried out;

[0061] Medium-risk area: 0.3 < H ≤ 0.6, indicating potential risk, follow-up every 2 months is recommended;

[0062] Low-risk area: H≤0.3, indicating a stable germination path, and can be followed up for 3 months as usual.

[0063] Furthermore, the multi-level position encoding adopts a sine-cosine hybrid encoding.

[0064] ,

[0065] in, The position code represents the x-axis direction, where x represents the coordinate component and L represents the coding level. Similarly, the position code for the y-axis direction can be obtained. Position encoding in the z-axis direction .

[0066] Furthermore, the basic periodic coding ensures consistency of follow-up period data and fits seasonal patterns, as shown in the following formula:

[0067] ,

[0068] Where t represents the prediction time. Indicates the clinical follow-up period. Representing the seasonal growth cycle; then the high-dimensional temporal encoding feature is represented as:

[0069] ,

[0070] in, Represents high-dimensional temporal coding features. This represents a multilayer perceptron. and Represents the weight matrix. This represents the activation function. , Indicates bias.

[0071] Furthermore, in step S3, the multi-objective loss function is used to balance prediction accuracy, physical plausibility, and model smoothness, and is expressed as:

[0072] ,

[0073] in, This represents the negative log-likelihood loss. Indicates physical prior loss. Indicates smoothing loss. This represents the regularization loss.

[0074] Compared with the prior art, the advantages of the present invention are as follows:

[0075] This invention employs a dual-layer temporal coding system, fusing basic periodic coding with high-dimensional feature mapping and incorporating a bone age lag adaptive adaptation strategy. This effectively fits the nonlinear temporal patterns of tooth growth and development, achieving refined and continuous modeling of the dynamic developmental trends of tooth germ eruption. A cross-attention fusion mechanism is introduced, dynamically weighting and fusing spatial, clinical, and temporal coding features. Feature weights are adaptively allocated based on key clinical indicators such as mineralization and bone density, addressing the issues of multimodal fusion imbalance and lack of clinical prior knowledge in existing technologies, significantly improving the anatomical rationality of prediction results. A spatiotemporal coupling evolution mechanism is proposed, relying on neural frequent differential equations to complete the continuous spatiotemporal evolution of the latent state and decoding to generate a dynamic occupancy field. This reconstructs the dynamic evolution of tooth eruption from a physiological mechanism perspective, addressing the pain points of traditional schemes such as ambiguous three-dimensional spatial relationship representation and difficulty in modeling topological changes. Simultaneously, a Gaussian mixture model is introduced to decompose the eruption path into independent Gaussian components in three orthogonal directions: mesiodistal, buccal-lingual, and vertical. The weights, mean, and variance parameters corresponding to each direction are output synchronously, achieving multi-directional and refined uncertainty quantification assessment. This invention can be adapted to different scenarios to assist doctors in making diagnoses, and provides objective, continuous, and quantifiable three-dimensional predictive evidence for early intervention of malocclusion and the formulation of orthodontic plans, significantly improving its clinical applicability and practical value. Attached Figure Description

[0076] Figure 1 This is a schematic diagram of the tooth eruption direction prediction method based on enhanced implicit neural representation of the present invention; Detailed Implementation

[0077] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0078] like Figure 1As shown, this invention proposes a method for predicting tooth eruption direction based on enhanced implicit neural representation.

[0079] 1. Obtain the data and clinical characteristics of the teeth to be predicted and perform data preprocessing;

[0080] The dental data in this embodiment of the invention is based on high-quality intraoral scan-CBCT fusion data, and the CBCT data must meet the following standards:

[0081] 1) Fusion accuracy: Registration was completed using the ICP (Iterative Closest Point) algorithm, with a root mean square error (RMSE) of <0.1mm and a statistical RMSE of 0.08±0.02mm on a 500-example validation set;

[0082] 2) Image parameters:

[0083] CBCT: Layer thickness ≤ 0.3 mm, ensuring that mineralized cores (< 0.1 mm) are clearly identifiable;

[0084] Oral scan: resolution ≤0.05mm, scanning range covers the entire dentition and alveolar bone margin, no motion artifacts (displacement >0.1mm);

[0085] 3) Structural segmentation: U-Net++ network was used to separate unerupted tooth germs, deciduous teeth, mandibular nerve canal, maxillary sinus, buccal and lingual bone plates and soft tissues. The segmentation Dice coefficients were: tooth germ 0.95±0.03, bone 0.94±0.02, and soft tissue 0.92±0.04.

[0086] 4) Feature annotation: The feature annotation was jointly performed by three attending physicians with more than 5 years of experience in pediatric orthodontics. The annotation consistency Kappa=0.89 (P<0.01), and the annotation result was a binary segmentation mask. During the training of the dynamic occupancy field, this binary mask was used as a hard label. The binary cross-entropy loss function was used to constrain the network output, enabling the network to generalize to a smooth probability boundary during the inference stage.

[0087] The clinical features in this invention include eight categories: mineralization, bone density, interdental distance, age, muscle strength, buccal and lingual bone plate thickness, gingival thickness, and sex. After standardization, these features are concatenated into a conditional vector for subsequent feature fusion.

[0088] II. Construct a tooth eruption direction prediction model with enhanced implicit neural representation. The model includes a spatial encoding module, a temporal encoding module, a multimodal feature fusion module, a spatiotemporal evolution module, and a probabilistic decoding module. The model performs the following processing:

[0089] 1. Spatial Coding Module: Extract the three-dimensional spatial coordinates of the centroid of the tooth germ, normalize them, and then perform multi-level positional coding on the coordinate components. The coordinate components are then spliced ​​together to obtain spatial coding features, so as to achieve global-local spatial information fusion.

[0090] Specifically, the spatial features of tooth germ development exhibit significant scale heterogeneity, requiring simultaneous characterization of the global spatial location of the tooth germ and jawbone (millimeter-level) as well as the local details of the mineralized core morphology (sub-millimeter-level). This invention employs multi-frequency sine-cosine hybrid encoding to map low-dimensional spatial coordinates to high-dimensional features, achieving native "global-local" fusion. The encoding formula is as follows:

[0091] ,

[0092] in, This represents the position code along the x-axis, where x represents the coordinate component and L represents the coding level. Similarly, we can obtain... , In this embodiment of the invention, L=10, then each coordinate component generates 20-dimensional features (10 pairs of sine-cosine functions), and the three-dimensional coordinates generate a total of 60-dimensional spatial features;

[0093] Among them, the low-frequency component corresponds to the long-wavelength signal, and the global relationship is modeled, such as through... The relative distance between the coded tooth germ and the mandibular nerve canal (error < 0.5 mm) is determined by... Distinguish whether the tooth germ is located in the maxilla or mandible;

[0094] High-frequency components: correspond to short-wavelength signals, focusing on local details, such as... Capture the morphology of the mineralized core's edge. Identify minute deviations in the tip of the tooth germ;

[0095] Furthermore, coordinate normalization is based on the three-dimensional centroid of the tooth germ. Using 12.8 mm as the origin, normalize with a radius of 12.8 mm to eliminate individual size differences and ensure cross-sample comparability of encoded features;

[0096] The three coordinate components are concatenated to obtain the spatial coding features:

[0097] ,

[0098] in, This is spatial coding feature.

[0099] 2. Time coding module: Combining clinical follow-up cycles and seasonal patterns, a basic cycle coding is constructed. The basic cycle coding features are mapped to high-dimensional time coding features through a 2-layer MLP to adapt to individual development.

[0100] Specifically, targeting the nonlinear characteristics of tooth germ development, a two-layer structure of basic periodic coding and learned feature mapping is designed to achieve accurate coding of continuous time variables while adapting to individual differences (such as bone age lag).

[0101] Basic cycle coding: Combining clinical follow-up cycles with seasonal patterns, a dual-cycle coding system was designed to ensure consistency between the clinical follow-up cycle (3 months) and the seasonal pattern (12 months). The formula is as follows:

[0102] ,

[0103] Where t represents the prediction time. Indicates the clinical follow-up period. This indicates the seasonal growth cycle; the routine follow-up period for children during the mixed dentition period is 3 months. This ensures that the final model output is consistent with the clinical follow-up time point, facilitating the verification of prediction results. Based on longitudinal follow-up data, the tooth germ mineralization rate in summer (June-August) is 4.8%±1.2% higher than in winter (December-February) (positively correlated with vitamin D levels and outdoor activity time). This pattern can be fitted over a 12-month period, reducing the prediction error caused by seasonal factors by 9%.

[0104] High-dimensional temporal encoded feature generation:

[0105] The 4-dimensional basic features are mapped to 128-dimensional temporal features using a 2-layer MLP (including Swish activation). The system automatically learns nonlinear development trends (such as S-shaped mineralization curves), using the following formula:

[0106] ,

[0107] in, This represents a multilayer perceptron. , These are trainable weights; , The bias is used; Swish is the activation function, which can better fit non-linear trends. This represents the set of parameters for the time encoding module.

[0108] The dual-layer time coding structure designed in this invention integrates basic periodic coding and high-dimensional feature mapping, combined with a bone age adaptive adaptation strategy, to effectively fit the nonlinear temporal pattern of tooth growth and development.

[0109] 3. Multimodal feature fusion module: Fuses clinical features with the spatial and temporal features of the tooth germ to obtain a fused feature vector for enrichment;

[0110] Specifically, the goal of the multimodal feature fusion module is to dynamically integrate heterogeneous clinical factors. In this embodiment of the invention, the conditional vector concatenated from eight types of clinical features is combined with the aforementioned spatial coding features, and then weighted and fused using a cross-attention mechanism to output conditional attention features, as follows:

[0111] (1) The spatial coding features and condition vectors are linearly transformed into query, key, and value vectors.

[0112] ,

[0113] ,

[0114] ,

[0115] in, For query vector, For key vectors, For value vectors, , , For each, there is a corresponding weight matrix. For spatial coding features, It is a conditional vector;

[0116] (2) Calculate attention weights: Preferred This avoids the gradient vanishing problem during training caused by excessively high dimensionality.

[0117] (3) Output conditional attention characteristics: ;

[0118] (4) The fused feature vector is: ,in It is a high-dimensional temporal encoding feature.

[0119] Furthermore, this invention also introduces a Bayesian gating mechanism to estimate the variance of noise for each feature. Calculate the gating weights , This represents the sensitivity adjustment factor, which determines the decay rate of noise variance on the gating weights. If the data quality is high, the noise variance is small, and the gating weights are closer to 1, allowing high-quality features to enter the next layer of the network for computation. If the data quality is poor, the noise variance is large, and the gating weights are close to 0, automatically suppressing interference from low-quality data (such as CBCT artifacts).

[0120] This invention solves the problems of multimodal fusion imbalance and lack of clinical prior by weighted fusion of spatial coding features, temporal coding features and clinical features, and greatly improves the anatomical rationality of prediction results.

[0121] 4. Spatiotemporal Evolution Module (E-INR): The tooth germ state evolution is realized through Neural ODE. Combined with bone density, centroid trajectory and adjacent tooth state, the dynamic occupancy field of tooth eruption is decoded and generated, realizing the end-to-end mapping from tooth features to eruption trajectory.

[0122] This invention uses a dynamic occupancy field to represent the dental anatomy. For tooth i, the occupancy probability is... , representing the probability that spatial point x is occupied by the hard tissue of tooth i at time t. This representation naturally supports topological changes. During the resorption of deciduous teeth, the occupancy probability gradually decreases from 1 to 0, while during the eruption of permanent teeth, it gradually increases from 0 to 1. The specific evolution process is as follows:

[0123] (1) Initialize hidden state: Input the fused feature vector generated in step 3 into a 4-layer fully connected network, and output the hidden state vector to represent the tooth state at the initial time: ,in, This indicates that the fused feature vector z is mapped to the initial hidden state. The parameter set of a fully connected network;

[0124] (2) Solve for the hidden state by numerically integrating the constant differential equation of God to find the hidden state from the initial time to the target time t:

[0125] ,

[0126] in, This represents the gradient change in the bone mineral density field. For the centroid of the tooth, For adjacent teeth assembly, The state of adjacent teeth is represented by GNN aggregation, and t is the prediction time.

[0127] (3) Generation of dynamic tooth occupancy field: for any spatial point The hidden state of the tooth and the tooth position are embedded into the decoder and the output point is... At time t, the tooth The probability of hard tissue occupying the area:

[0128] ,

[0129] in, This indicates a hidden state of the teeth. Indicates tooth intrusion. The output represents the position code of the spatial coordinate x. ;

[0130] (4) Calculation of tooth eruption direction: The eruption direction is calculated by tracing the trajectory of the tooth centroid over time. The centroid is defined as the first moment of the occupied probability field. The calculation formula is as follows:

[0131] ,

[0132] in, The centroid of the tooth is the change of the centroid over time, which determines the direction of eruption.

[0133] This invention introduces the occupation field into tooth germ development prediction for the first time through a spatiotemporal evolution module, naturally adapting to the topological changes caused by deciduous tooth resorption and permanent tooth eruption. It breaks through the fundamental limitation of traditional symbolic distance functions in handling topological changes, eliminates the interpolation error of traditional methods, and unifies and integrates multi-source physical constraints to ensure the anatomical rationality of the eruption path.

[0134] 5. Probability Decoding Module: By combining Gaussian mixture models with deep evidence regression, it provides quantification of the main emergence direction and uncertainty, and offers decision support for the main path and risk stratification.

[0135] Specifically, this embodiment of the invention employs a Gaussian mixture model (GMM) with three Gaussian components, corresponding to the "primary germination direction," "secondary offset direction," and anomaly risk direction, as detailed below:

[0136] (1) Input the hidden state at time t into three independent fully connected layers to predict the three parameters of the Gaussian mixture model respectively.

[0137] ,

[0138] ,

[0139] ,

[0140] in, These represent the primary direction, secondary offset direction, and abnormal risk direction, respectively. Represents the normalized activation function. Let exp represent the hyperbolic tangent activation function, and let exponential function represent the exponential function. This represents the weight, used to quantify the contribution ratio of each direction; This represents the mean, used to predict the principal components in each direction; Variance is used to quantify the uncertainty of predictions in various directions; This corresponds to the bias value;

[0141] in, ,satisfy Quantify the contribution ratio of each direction:

[0142] (Main direction weight): In normal cases , representing the probability of the main germination direction occurring;

[0143] (Secondary offset weight): In normal cases This corresponds to a slight directional shift (such as ±2° tilt).

[0144] (Abnormal risk weight): Normal cases Cases of obstruction This is directly related to the priority of clinical interventions.

[0145] Assuming the mean, the principal components in each direction are predicted and can be decomposed into three-dimensional components: near-distal (x), cheek-tongue (y), and vertical (z). For example... =(0.3,0.2,0.93) means:

[0146] x-direction: 0.3 mm of budding distally each month;

[0147] Y-direction: 0.2mm eruption towards the cheek each month;

[0148] z-direction: 0.93 mm per month towards the occlusal direction (dominant direction).

[0149] Variance quantifies the prediction uncertainty in each direction. This indicates that the main direction is stable. This indicates large fluctuations in the abnormal direction;

[0150] (2) Based on the above parameters, a three-dimensional Gaussian mixture distribution is constructed to model the probability density of the germination direction:

[0151]

[0152] Where x represents the mesial-distal eruption direction, y represents the cheek-lingual eruption direction, and z represents the perpendicular eruption direction. The probability density function representing the Gaussian distribution;

[0153] (3) Information entropy is used as the overall risk indicator and decomposed into x, y, and z-direction-specific entropy values ​​to support targeted risk assessment. The higher the entropy value, the more uncertain the prediction (the higher the risk). The expression is:

[0154] ,

[0155] Clinical risk threshold setting:

[0156] High-risk area: H > 0.6, indicating that the germination direction is very likely abnormal, and the follow-up period can be shortened to 1 month or early intervention can be carried out;

[0157] Medium-risk area: 0.3 < H ≤ 0.6, indicating potential risk, follow-up every 2 months is recommended;

[0158] Low-risk area: H≤0.3, indicating a stable germination path, and can be followed up for 3 months as usual.

[0159] (4) Simultaneously, when calculating the information entropy H, Deep Evidence Regression (DER) is introduced to treat the GMM parameters as evidence. Uncertainty is predicted by modeling the Dirichlet distribution. For out-of-distribution data (such as rare impacted teeth and supernumerary teeth), the evidence value is automatically reduced, thereby increasing the entropy value and avoiding "overconfidence". The formula is as follows:

[0160] ,

[0161] in, Indicates in Under the given conditions, the probability distribution of the predicted result y, This is the evidence vector; the smaller the value, the less evidence there is and the higher the uncertainty. Hidden state at time t The 128-dimensional hidden vector input to the output of the fully connected layer network is processed through... make sure To be positive, avoid having zero evidence;

[0162] If the evidence vector α is large, it indicates that the evidence is sufficient, the Dirichlet distribution is concentrated in a certain category, and the output entropy value H is low, indicating that the prediction is reliable and should be handled according to the conventional follow-up plan.

[0163] If the evidence vector α is very small, it indicates insufficient evidence. The Dirichlet distribution tends to be uniform, causing the entropy H to increase significantly, exceeding the high-risk threshold of 0.6, thus automatically triggering a "high-risk" alarm.

[0164] (5) Output clinical indicators that doctors can understand:

[0165] 1) The main germination direction is extracted by weighted summation using the GMM (Gross Model), which includes direction (angle) and germination amount (magnitude) information. The formula for the main germination direction vector is as follows:

[0166] ,

[0167] in, The vector magnitude represents the germination rate. , This indicates the amount of germination from near to far (positive for far, negative for near). Indicates the cheek-tongue orientation (positive for cheek, negative for tongue). Indicates vertical direction (positive for occlusal direction, negative for apical direction); modulus length This indicates the total germination rate (mm / month), such as... The month indicates that the buds sprout 0.2mm each month.

[0168] 2) Risk area visualization, in which entropy value areas are marked in the 3D model, with red indicating high risk, yellow indicating medium risk, and green indicating low risk; when the direction is specifically marked, the entropy value heat map in the x / y / z direction is displayed separately; when the intervention suggestion is generated, clinical suggestions are automatically output based on the risk area.

[0169] This invention combines continuous spatiotemporal coordinates, multimodal clinical features, and implicit neural representations through a probabilistic decoding module, achieving high-precision and interpretable quantitative prediction of tooth eruption direction.

[0170] 3. Design a multi-objective loss function to train the tooth eruption direction prediction model with enhanced implicit neural representation until the model converges and the optimal model is saved.

[0171] Specifically, to balance prediction accuracy, physical plausibility, and model smoothness, the multi-objective loss function designed in this embodiment of the invention is as follows:

[0172] ,

[0173] in, This represents negative log-likelihood loss, which constrains the consistency between the predicted tooth eruption direction probability and the actual developmental trajectory, increases the probability weight of the main eruption direction, and makes the prediction results more focused on the reasonable path. This represents the loss of physical prior knowledge, which significantly suppresses abrupt predictions that violate physical common sense, making the spatial continuity and temporal smoothness of the tooth eruption path conform to biological laws. This indicates smooth loss, ensures the spatial continuity of the risk area, and conforms to clinical anatomical logic (e.g., the impacted growth risk area is usually distributed along the germination path). This represents the regularization loss, which limits the size of network parameters, effectively suppresses model overfitting, and improves generalization ability.

[0174] Once the model training is complete, the optimal model is automatically saved for subsequent tooth eruption direction prediction.

[0175] Furthermore, during training, this embodiment of the invention uses weighted random sampling based on tooth germ mineralization, assigning higher sampling probabilities to regions with higher mineralization and richer structural information, focusing on key information regions, and improving training efficiency. At the same time, during inference, it supports resolution adaptation, with low resolution used for rapid screening and high resolution used for detailed anatomical evaluation, to meet the efficiency and accuracy requirements of different scenarios.

[0176] To further verify the effectiveness of the method of this invention, the fusion data of oral scanning and CBCT of the maxillary lateral incisors of an 8-year-old male were used as an example for model inference verification: After standardization of 8 clinical features, mineralization m=0.50; bone density b=0.50, interroot distance d=0.45, age a=0.33, muscle strength f=0.10, buccal and lingual bone plate thickness l=0.40, gingival thickness g=0.45, and gender s=0 (male), which were concatenated into a 10-dimensional conditional vector: The last two dimensions are kept as 0 for expansion;

[0177] Coordinate encoding: The three-dimensional coordinates of the tooth germ centroid are: After normalization, spatial features are generated through sine-cosine hybrid encoding, and the high-frequency components capture no significant offset at the tooth germ tip (<0.05mm).

[0178] Time coding: The follow-up period is predicted to be t=6 months. A basic period coding is constructed and mapped to 128-dimensional time features through a 2-layer MLP. The S-shaped growth trend of mineralization rate over time is fitted.

[0179] Multimodal fusion: The fused features are finally generated through cross-attention, and the gating mechanism determines that the noise variance of all features is <0.1 (good data quality).

[0180] Spatiotemporal evolution: After initializing the hidden state of the fused features through a 4-layer fully connected network, the hidden state is continuously evolved to finally generate the centroid trajectory and determine the germination direction;

[0181] Probability Decoding: GMM Prediction , , The mean of the main direction Entropy (Low risk), all three directional entropy values ​​are <0.3 (no directional risk).

[0182] The final output of the model is as follows:

[0183] Main eruption direction: mesiodistal to distal 0.25mm / month, buccal to lingual 0.18mm / month, vertical to occlusal direction 0.90mm / month (vertical direction is the dominant direction);

[0184] Risk assessment: Low risk, no risk of impaction or deviation;

[0185] Intervention recommendation: Regular follow-up every 3 months, no special intervention required.

[0186] Follow-up verification: CBCT examination after 6 months showed that the actual eruption direction was consistent with the prediction, the vertical eruption rate was 0.88 mm / month (error 0.02 mm / month), and there was no shift in the position of the tooth germ, verifying the accuracy of the model prediction.

[0187] The foregoing has provided a detailed description of one embodiment of the present invention, but this description is merely a preferred embodiment and should not be construed as limiting the scope of the invention. All equivalent variations and modifications made within the scope of the claims of this invention should still fall within the patent coverage of this invention.

Claims

1. A method for tooth eruption direction prediction based on enhanced implicit neural representation, characterized in that, The method includes: S1. Obtain the three-dimensional spatial coordinates and clinical feature vector of the centroid of the tooth germ to be predicted, and preprocess the clinical feature vector to form a condition vector; S2. Construct a tooth eruption direction prediction model with enhanced implicit neural representation. The model performs the following processing: S21. Normalize the three-dimensional spatial coordinates of the tooth germ centroid, and then perform multi-level position encoding on the normalized coordinate components and splice them together to obtain spatial encoding features. S22. Combining clinical follow-up cycles and seasonal patterns, construct a basic cycle code and map the basic cycle code to high-dimensional time coding features; S23. After cross-attention weighted fusion of the spatial coding features and the conditional vector, output the conditional attention features; concatenate the spatial coding features, high-dimensional temporal coding features and conditional attention features to output the fused feature vector. S24. Initialize the hidden state using the fused feature vector, and continuously evolve the hidden state from the initial time to the prediction time t using the neural ordinary differential equation to obtain the hidden state at time t. S25. Combine the hidden state at time t with spatial coding features and tooth position embedding to perform occupancy field decoding, generate a dynamic tooth occupancy field, and calculate the tooth centroid trajectory based on the dynamic occupancy field to determine the tooth eruption direction. S26. Input the hidden state at time t into the Gaussian mixture decoder, output the probability density of the germination direction, and determine the main germination direction vector and risk assessment result based on the probability density distribution. S3. Use a multi-objective loss function to train the tooth eruption direction prediction model with enhanced implicit neural representation until the model converges and the optimal model is saved.

2. The tooth eruption direction prediction method based on enhanced implicit neural representation according to claim 1, wherein, The clinical feature vector includes at least mineralization, bone density, interdental distance, age, muscle strength, buccal and lingual bone plate thickness, gingival thickness, and sex, which are then standardized and concatenated into a conditional vector.

3. The tooth eruption direction prediction method based on enhanced implicit neural representation according to claim 2, characterized in that, In step S23, the fused feature vector is calculated as follows: The spatial coding features and condition vectors are linearly transformed into query, key, and value vectors. ， ， ， wherein, is a query vector, is a key vector, is a value vector, , , is a respective corresponding weight matrix, is a spatial encoding feature, is a condition vector; Computing attention weights: , preferably ; Output condition attention feature: ; The fusion feature vector is: wherein is a high-dimensional time coding feature.

4. The method for predicting tooth eruption direction based on enhanced implicit neural representation according to claim 3, characterized in that, The implementation process of step S24 is as follows: Initialize hidden states: Input the fused feature vector into the fully connected network, and output a hidden state vector representing the initial tooth state: , Solving for the hidden state involves numerical integration of the ordinary differential equations to find the hidden state from the initial time to the target time t. ， wherein, denotes a gradient change of the bone density field, is a tooth centroid, is a neighboring tooth set, and t is a prediction time.

5. The tooth eruption direction prediction method based on enhanced implicit neural representation according to claim 4, wherein, The direction of tooth eruption is calculated as follows: Generation of dynamic occupancy field for teeth: for any spatial point The hidden state of the tooth and the tooth position are embedded into the decoder and the output point is... At time t, the tooth The probability of hard tissue occupying the area: ， in, This indicates a hidden state of the teeth. Indicates tooth intrusion. The output represents the position code of the spatial coordinate x. ; Tooth eruption direction calculation: The eruption direction is calculated by tracing the trajectory of the tooth's centroid over time. The centroid is defined as the first moment of the occupancy probability field, and the calculation formula is as follows: ， wherein, is the tooth centroid, i.e. the change in time of the tooth centroid, i.e. the eruption direction.

6. The method for predicting tooth eruption direction based on enhanced implicit neural representation according to claim 4, characterized in that, Step S26 is implemented as follows: S261 inputs the hidden state at time t into three independent fully connected layers to predict the three parameters of the Gaussian mixture model. ， ， ， in, These represent the primary direction, secondary offset direction, and abnormal risk direction, respectively. Indicates weight; This represents the mean; Indicates variance; S262 constructs a three-dimensional Gaussian mixture distribution based on the above parameters to model the probability density of the germination direction: ， wherein x represents the mesial-distal direction of eruption, y represents the buccal-lingual direction of eruption, and z represents the vertical direction of eruption, denotes a probability density function of a Gaussian distribution; S263 uses information entropy as the overall risk indicator, expressed as: ， S264 introduces deep evidence regression modeling to predict uncertainty. ， wherein, is the evidence vector, the smaller the value, the less evidence, the higher the uncertainty, is the hidden vector output by the hidden state input fully connected layer network at time t, through ensure is positive, avoid evidence is 0; S265 outputs clinical indicators: a. The main budding direction is the weighted expectation of a Gaussian mixture distribution, and the formula for the main budding direction vector is expressed as: ， wherein, The module length represents the eruption amount, and the direction represents the eruption angle. b. Risk area visualization: Entropy value areas are marked in the 3D model, with red indicating high risk, yellow indicating medium risk, and green indicating low risk; when the direction is specifically marked, the entropy value heatmaps in the x / y / z directions are displayed separately; when intervention suggestions are generated, clinical suggestions are automatically output based on the risk areas.

7. The method for predicting tooth eruption direction based on enhanced implicit neural representation according to claim 5, characterized in that, Clinical risk threshold setting: High-risk area: H > 0.6, indicating that the germination direction is very likely abnormal, and the follow-up period can be shortened to 1 month or early intervention can be carried out; Medium-risk area: 0.3 < H ≤ 0.6, indicating potential risk, follow-up every 2 months is recommended; Low-risk area: H≤0.3, indicating a stable germination path, and can be followed up for 3 months as usual.

8. The tooth eruption direction prediction method based on enhanced implicit neural representation according to claim 1, wherein, The multi-level positional coding adopts a sine-cosine hybrid coding method. ， wherein represents a position encoding in the x-axis direction, x represents a coordinate component, L represents an encoding level, and a position encoding in the y-axis direction and a position encoding in the z-axis direction can be similarly obtained .​ 9. The tooth eruption direction prediction method based on enhanced implicit neural representation according to claim 1, wherein, The basic periodic coding ensures consistency of follow-up period data and fits seasonal patterns, as shown in the following formula: ， where t denotes the prediction time, denotes the clinical follow-up period, denotes the seasonal growth period; then the high-dimensional time coding feature is represented as: ， in, Represents high-dimensional temporal coding features. This represents a multilayer perceptron. and Represents the weight matrix. This represents the activation function. , Indicates bias.

10. The method for predicting tooth eruption direction based on enhanced implicit neural representation according to claim 1, characterized in that, In step S3, the multi-objective loss function is used to balance prediction accuracy, physical plausibility, and model smoothness, and is expressed as: ， wherein, represents a negative log-likelihood loss, represents a physical prior loss, represents a smoothing loss, represents a regularization loss.

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