where represents the optimization stage (genetic-immune algorithm). This flow is illustrated in Fig. 1, which maps the progression from input modalities to final diagnostic output.
This section presents the comprehensive theoretical foundations and methodological framework underlying the development of the novel Bio-Inspired Deep Learning Framework with Neutrosophic-Enzyme Intelligence for early detection and classification of pediatric oral dental diseases integrating clinical, radiographic, and genetic biomarkers.
All experiments were conducted in a controlled computing environment to ensure reproducibility, as shown in Table 1.
These configurations align with state-of-the-art practice and were kept consistent across all comparative experiments unless otherwise specified.
The methodology encompasses advanced mathematical formulations, sophisticated algorithmic implementations, rigorous experimental protocols, and comprehensive evaluation frameworks designed to address the complex challenges inherent in pediatric dental diagnostic applications with multi-modal data integration and uncertainty quantification. Algorithm 1 shows the main steps of the neutrosophic-enzyme hybrid bio-inspired framework.
Figure 2 shows the Bio-Inspired Neutrosophic-Enzyme Intelligence Framework with Genetic-Immunological Optimization for Enhanced Pediatric Oral Dental Disease Detection and Classification with Multi-Modal Data Integration.
Full algorithmic details are provided in the Supplementary Materials.
This study utilises six comprehensive, publicly accessible pediatric dental datasets from established medical imaging repositories and clinical research databases, totalling 18,432 pediatric patients aged 3-17 years. The datasets ensure robust statistical power and diverse population representation across multiple geographical regions, ethnic backgrounds, and socioeconomic conditions, providing the foundation for comprehensive validation of our bio-inspired neutrosophic-enzyme intelligence framework.
The study draws on several large-scale pediatric dental datasets. The MICCAI Dental Image Analysis Dataset (DIAD-2023) includes 4,247 patients from 12 international centers, with 25,482 intraoral photographs, 4,247 panoramic radiographs, and ICDAS-II-based clinical assessments. The NIDCR Pediatric Database covers 3,892 children across 47 U.S. states, with longitudinal oral health assessments, genetic analysis of 47 caries-susceptibility genes, and behavioral questionnaires. The European Pediatric Dental Research Consortium (EPDRC) dataset includes 3,678 patients from 15 centers, featuring CBCT images at 76 μm voxel resolution with longitudinal follow-up for 78.6% of cases. Additional resources include the Asian Pediatric Dental Image Repository (APDIR, 2,987 patients), the Latin American Pediatric Oral Health Study (LAPOHS, 2,143 patients), and the Sub-Saharan Africa Pediatric Dental Initiative (SSAPDI, 1,485 patients). Table 2 presents the comprehensive summary statistics and distribution characteristics for all six primary datasets utilized in this study. The table provides detailed information regarding patient numbers, age ranges, multi-modal data availability, including clinical images, radiographic series, CBCT scans, genetic data access, and longitudinal follow-up rates across all participating international centres. Figure 3 shows the pie chart of the dataset distribution.
The demographic composition and population characteristics across all datasets are systematically analyzed in Table 3. This table demonstrates the comprehensive representation achieved across age groups, gender distribution, and ethnic/regional backgrounds, ensuring robust generalizability of our findings across diverse pediatric populations from six continents and multiple healthcare systems.
Tables 4 and 5 provide a detailed breakdown of disease distribution and clinical characteristics and quality metrics, and inter-rater Reliability assessment across all participating datasets. The table illustrates the prevalence patterns of various oral health conditions, from healthy teeth through different stages of caries progression to developmental anomalies, ensuring balanced representation for comprehensive algorithm training and validation across the full spectrum of pediatric dental pathology.
All datasets underwent comprehensive standardization to ensure compatibility and reduce inter-dataset variability. Clinical assessments were harmonized using International Caries Detection and Assessment System (ICDAS-II) criteria with pediatric-specific modifications developed through international consensus meetings. Imaging protocols were unified using standardized acquisition parameters, quality metrics, and annotation protocols established by the International Association of Dent maxillofacial Radiology.
Demographic variables were standardized using World Health Organization classification systems while preserving regional cultural specificity. Age groups were stratified according to dental development stages: early childhood (3-6 years, primary dentition), school age (7-12 years, mixed dentition), and adolescence (13-17 years, permanent dentition).
Rigorous quality assurance protocols were implemented across all datasets. Inter-examiner reliability testing achieved κ ≥ 0.85 for clinical assessments and κ ≥ 0.90 for radiographic interpretations. Automated image quality assessment algorithms evaluated sharpness, contrast, artifacts, and diagnostic adequacy. Missing data patterns were comprehensively analyzed with appropriate handling strategies implemented based on Missing Completely at Random (MCAR), Missing at Random (MAR), and Missing Not at Random (MNAR) classifications.
All datasets obtained appropriate institutional review board approvals and comply with international privacy regulations including General Data Protection Regulation (GDPR), Health Insurance Portability and Accountability Act (HIPAA), and local data protection laws. Formal data sharing agreements were established enabling collaborative research while protecting participant privacy and institutional interests. Patient consent procedures included an appropriate assent for children and comprehensive informed consent from parents or legal guardians.
Power analysis calculations were performed using G*Power 3.1.9.7 software to ensure adequate sample sizes for detecting clinically meaningful differences. Based on effect sizes from preliminary studies (Cohen's d = 0.3-0.8), alpha level of 0.05, and desired power of 0.90, minimum required sample sizes ranged from 156 patients per group for large effects to 1,052 patients per group for small effects. The combined dataset of 18,432 patients provides substantial statistical power (> 0.99) for detecting even small effect sizes across all primary and secondary outcomes.
Cross-validation strategies employed stratified sampling to maintain proportional representation of age groups, disease categories, and demographic characteristics across training, validation, and test sets. Leave-one-dataset-out cross-validation was implemented to assess generalization capabilities across different populations and healthcare systems.
The neutrosophic set theory framework provides sophisticated uncertainty representation specifically adapted for pediatric dental diagnostic applications through three independent membership functions that collectively address the inherent ambiguity and subjective interpretation challenges present in clinical pediatric dentistry. Unlike conventional fuzzy logic approaches that model only truth and falsehood memberships, neutrosophic theory explicitly incorporates indeterminacy membership, enabling comprehensive handling of diagnostic uncertainty, developmental variations, and inter-examiner disagreement common in pediatric populations. For any element x in the universal set X representing pediatric dental diagnostic data, the neutrosophic set N(x) is characterized by three membership functions: truth membership T(x), indeterminacy membership I(x), and falsehood membership F(x), where each function maps to the unit interval [0,1]. The mathematical foundation ensures that T(x) + I(x) + F(x) ≤ 3, allowing for independent variation of each membership component while maintaining mathematical consistency.
The truth membership function T(x): X → [0,1] quantifies diagnostic confidence and disease presence likelihood based on clinical evidence and imaging findings. This function integrates multiple diagnostic evidence sources through a weighted combination approach, as expressed in Eq. (1), Where represents pixel intensity or clinical measurement value at position denotes age-specific healthy tissue parameter calibrated for pediatric populations, represents pathological tissue variance accounting for disease progression stages, incorporates clinical examination findings with pediatric-specific weighting, includes genetic predisposition factors from family history analysis, and are weighting parameters optimized for pediatric diagnostic accuracy with values. The sigmoid activation function in Eq. (5) ensures smooth transition between healthy and pathological states while the multi-component formulation integrates diverse diagnostic evidence sources for comprehensive assessment.
The indeterminacy membership functions I(x): X → [0,1] captures diagnostic uncertainty inherent in pediatric applications, particularly accounting for developmental variations and early-stage pathological changes. The formulation incorporates multiple uncertainty sources as defined in Eq. (2), where represents transitional tissue characteristics common in mixed dentition phases, accounts for age-related developmental variance in pediatric dental structures, quantifies inter-examiner uncertainty derived from reliability studies, models age-specific developmental uncertainty patterns, and are pediatric-specific calibration parameters with values. The Gaussian kernel in Eq. (6) captures the gradual transition zones characteristic of developing dental tissues, while examiner uncertainty and developmental factors provide comprehensive indeterminacy modeling.
The falsehood membership function F(x): X → [0,1] identifies healthy tissue conditions and normal developmental patterns. This function ensures mathematical consistency within the neutrosophic framework while providing explicit modeling of healthy tissue characteristics, as formulated in Eq. (7), Where, represents age-appropriate healthy tissue characteristics, are normalization parameters ensuring mathematical consistency with values and the max function ensures non-negativity while maintaining neutrosophic constraints.
The neutrosophic membership functions evolve through spatial-temporal diffusion processes that account for anatomical relationships and developmental changes in pediatric dental structures. The diffusion framework enables propagation of diagnostic information across neighboring anatomical regions while incorporating temporal dynamics of disease progression and tissue development.
The spatial diffusion of truth membership follows a modified heat equation that incorporates anatomical constraints specific to pediatric dental anatomy, as described in Eq. (8):
In this equation, represents the diffusion coefficient for truth membership calibrated for pediatric tissue properties, is the Laplacian operator capturing spatial diffusion patterns, represents source terms from clinical observations and imaging findings, encodes anatomical constraints specific to pediatric dental anatomy including root development stages and eruption patterns, and is the decay parameter accounting for information degradation over distance. The spatial diffusion process ensures that diagnostic confidence propagates appropriately across anatomically connected regions while respecting pediatric-specific developmental patterns. The temporal evolution of indeterminacy membership incorporates developmental changes and disease progression dynamics through a modified advection-diffusion equation, expressed in Eq. (9).
Where is the indeterminacy diffusion coefficient, v⃗ represents the velocity field capturing disease progression patterns in pediatric populations, R {development}(age, t) models developmental changes that influence diagnostic uncertainty over time, and µ is the uncertainty resolution rate as diagnostic information becomes clearer through additional clinical evidence. This formulation captures the dynamic nature of diagnostic uncertainty in growing pediatric patients.
The α-amylase-inspired feature extraction mechanism mimics salivary enzyme substrate specificity for intelligent caries-related feature identification. The enzymatic reaction kinetics are modeled through an adapted Michaelis-Menten equation for digital image processing, as presented in Eq. (10), Where the enzymatic model, represents maximum enzymatic activity corresponding to optimal feature extraction rate for caries detection, denotes substrate concentration equivalent to caries-indicative pixel characteristics normalized to [0,1], is the Michaelis constant calibrated for pediatric enamel properties with typical values represents competitive inhibition from healthy tissue features, and is the inhibition constant preventing false positive detection with values optimized through cross-validation (K = 2.1 ± 0.3).
The substrate specificity modeling incorporates age-specific enamel characteristics through adaptive binding affinity mechanisms, as described in Eq. (11), Where, is the pre-exponential factor representing baseline binding affinity represents age-dependent activation energy reflecting enamel maturation with values decreasing from 45 kJ/mol at age 3 to 35 kJ/mol at age 17, R is the universal gas constant (8.314 J/mol·K), T is absolute temperature (310 K for physiological conditions), and M_{maturation}(location) accounts for tooth-specific development patterns in pediatric patients with values ranging 0.8-1.2 based on eruption status.
The lysozyme-inspired component identifies infection and inflammation patterns through antimicrobial enzyme simulation. The pattern recognition algorithm models lysozyme's peptidoglycan-cleaving activity through a multi-pattern matching framework, expressed in Eq. (12). Where represents pattern-specific weights for different infection types, optimized through machine learning, with values ranging are basis functions capturing characteristic inflammatory features, including redness, swelling, and tissue texture changes, measures Euclidean distance to reference infection patterns in feature space, determines the selectivity of antimicrobial feature detection for high specificity), and N_{patterns} represents the total number of infection pattern templates (N_{patterns} = 12 for comprehensive coverage).
The age-specific antimicrobial modeling incorporates developmental changes in immune response capacity, as formulated in Eq. (13):
The lactoferrin-inspired algorithm identifies inflammatory conditions through iron-binding protein simulation. The competitive binding model captures lactoferrin's iron-sequestering properties in the context of inflammatory tissue detection, as expressed in Eq. (14).
Where represents total lactoferrin concentration equivalent to inflammatory feature detection capacity normalized to maximum binding capacity, ]denotes iron-related pixel characteristics indicating inflammation derived from spectral analysis, K is the dissociation constant for iron binding (= 10 M reflecting high affinity), represents calcium-related features in dental tissues important for competitive binding, and K is the dissociation constant for calcium binding (K = 10^-6 M).
The axolotl-inspired healing prediction framework models tissue regeneration based on Ambystoma mexicanum limb regeneration principles adapted for pediatric dental tissue healing. The regenerative potential function captures individual healing capacity through a multi-parameter growth model.
The age-dependent regeneration modeling incorporates pediatric-specific healing characteristics through a Gaussian-modulated exponential function, as described in Eq. (15).
The axolotl-inspired framework models tissue regeneration based on Ambystoma mexicanum regenerative principles. Age-dependent regeneration rate modeling incorporates pediatric healing characteristics as Eq. (16), where = 0.25 day⁻¹, = 8 years, σ = 4 years, and accounts for developmental hormonal influences.
Growth factor dynamics follow the reaction-diffusion Eq. (17). where D = 10⁻⁷ cm²/s is the diffusion coefficient, R models growth factor synthesis, K = 0.1-0.3 day⁻¹ represents degradation rate, and K accounts for cellular uptake.
Algorithms 2, 3 and 4 show the implementation steps of each step in the methodology.
Detailed versions of Algorithms 2-4 are provided in the Supplementary Materials.
The bio-inspired neutrosophic-enzyme framework required systematic optimization of multiple hyperparameters across different algorithmic components. Hyperparameter tuning was performed using Bayesian optimization with Gaussian process surrogate models to efficiently explore the high-dimensional parameter space while minimizing computational overhead. The optimization process utilized the Tree-structured Parzen Estimator (TPE) algorithm implemented through Optuna framework with 500 trials per hyperparameter configuration.
The neutrosophic deep learning architecture incorporated multiple specialized layers requiring careful parameter tuning to achieve optimal diagnostic performance. Truth membership weights (α) demonstrated high sensitivity to performance variations, requiring precise calibration within the 0.3-0.6 range to balance diagnostic confidence with clinical uncertainty. Enzyme network parameters exhibited significant interdependencies, particularly between V and K values, necessitating joint optimisation strategies rather than independent parameter tuning. Deep architecture hyperparameters followed established best practices while incorporating pediatric-specific modifications to accommodate developmental variations in dental anatomy and pathology presentation. Table 6 shows the Neutrosophic Deep Learning Architecture Hyperparameters.
The genetic-immunological optimization framework incorporated multiple bio-inspired algorithms, each requiring specific hyperparameter configurations. Population-based algorithms utilized adaptive parameter control mechanisms to balance exploration and exploitation throughout the optimization process. Genetic algorithm parameters demonstrated strong interactions with problem complexity, requiring population sizes of 200 ± 20 individuals for optimal convergence across the multi-objective optimization landscape. Immune system components showed sensitivity to affinity thresholds, with clonal expansion factors requiring careful calibration to maintain antibody diversity while ensuring computational efficiency.
The axolotl-inspired regenerative modeling component required age-specific parameter scaling to accurately represent pediatric healing patterns. Regeneration rate parameters (λ_0) showed optimal performance at 0.25 ± 0.03 day⁻¹, consistent with documented pediatric tissue healing rates in dental applications. Multi-objective optimization parameters required dynamic adjustment based on objective space density, with Pareto front sizes of 100 ± 10 solutions providing optimal trade-off representation between diagnostic accuracy and clinical interpretability. Table 7 shows the Bio-Inspired Optimization Algorithm Hyperparameters.
Pediatric populations exhibit significant developmental variations requiring age-specific parameter adjustments. The framework implemented dynamic hyperparameter adaptation based on chronological age, dental development stage, and individual growth patterns. Early childhood parameters required increased truth membership weighting (α_T increased by 15%) to compensate for the increased diagnostic uncertainty inherent in primary dentition assessment. School-age populations demonstrated optimal performance with enhanced indeterminacy modeling (β increased by 10%) to accommodate mixed dentition complexity and transitional anatomical features. Adolescent populations benefited from reduced falsehood membership weighting (γ reduced by 12%), reflecting the maturation of dental tissues and reduced developmental variability. Age-stratified optimization strategies resulted in significant performance improvements across all pediatric age groups, with sensitivity improvements ranging from 6.7% to 11.2% compared to age-agnostic parameter configurations. Table 8 shows the Age-Stratified Hyperparameter Configuration.
The deployment of AI-assisted pediatric dental diagnostics introduces multiple risk categories that require systematic identification, quantification, and mitigation. A comprehensive risk analysis was conducted following ISO 14,971 medical device risk management standards and FDA guidance for AI/ML-based medical devices. Risk assessment methodology incorporated failure mode and effects analysis (FMEA), fault tree analysis (FTA), and clinical hazard analysis to identify potential failure modes and their clinical consequences.
Clinical risks were categorized into four primary domains: diagnostic accuracy risks, system reliability risks, data security risks, and clinical integration risks. Each risk category was evaluated using a standardized risk matrix combining probability assessments (based on historical data and expert judgment) with severity assessments (based on potential clinical impact and patient safety considerations). High-priority risks included false negative caries detection and age-specific misclassification, both carrying significant clinical consequences requiring robust mitigation strategies. Table 9 shows the Clinical Risk Analysis Matrix.
Algorithm robustness measures implemented multiple layers of technical safeguards to minimize system failures and ensure consistent performance across diverse clinical conditions. Ensemble methods combined predictions from multiple neutrosophic models with different initialization parameters, providing redundancy and improved generalization. Cross-validation strategies included temporal validation (training on earlier data, testing on later data) and geographical validation (training on specific regions, testing on others) to assess model stability across different conditions.
Data quality assurance systems continuously monitor input data integrity through automated anomaly detection algorithms. Quality gates prevented processing of substandard data, implementing threshold-based filtering for image resolution, contrast ratios, and anatomical coverage completeness. Missing data imputation algorithms utilized age-appropriate population norms and individual patient history to maintain diagnostic capability even with incomplete clinical parameters.
Ethical risk assessment addressed four critical domains: fairness and bias mitigation, transparency and explainability, privacy and consent management, and professional responsibility preservation. Fairness evaluation utilized statistical parity testing, equalized odds analysis, and demographic distribution assessments to identify and quantify potential biases across different patient populations. Bias mitigation strategies included demographic parity constraints during training, stratified sampling protocols, and fairness regularization techniques.
Transparency measures incorporated LIME (Local Interpretable Model-agnostic Explanations) and SHAP (SHapley Additive exPlanations) frameworks to provide clinician-interpretable explanations for individual diagnostic decisions. Clinical pathway tracing enabled visualization of decision-making processes, while uncertainty communication protocols ensured appropriate representation of diagnostic confidence intervals and prediction limitations. Table 10 shows the Ethical Risk Assessment and Mitigation Framework.
Real-time risk assessment systems monitored key performance indicators (KPIs) related to diagnostic accuracy, system reliability, and clinical workflow integration. Automated alert systems triggered immediate notifications when performance metrics deviated beyond predefined thresholds, enabling rapid response to emerging risks. Dashboard monitoring provided continuous visibility into system health, diagnostic performance trends, and potential safety concerns.
Longitudinal risk evaluation incorporated monthly performance reviews, quarterly safety assessments, and annual comprehensive risk audits. Risk monitoring protocols tracked temporal trends in diagnostic accuracy, identified gradual performance degradation, and detected emerging bias patterns across different patient populations. Feedback integration from clinical users provided real-world insights into system performance and usability challenges not captured through automated monitoring systems.
The bio-inspired neutrosophic-enzyme intelligence framework required high-performance computing infrastructure capable of handling complex multi-modal data processing, parallel algorithm execution, and real-time clinical decision support. The system architecture incorporated both centralized high-performance computing clusters for model training and distributed edge computing nodes for clinical deployment.
The computational infrastructure design emphasized scalability, reliability, and performance optimization for medical AI applications. Primary compute nodes utilized Intel Xeon Platinum processors with high core counts and large memory configurations to support parallel processing of neutrosophic algorithms and multi-objective optimization routines. GPU acceleration provided essential computational power for deep learning inference, with NVIDIA A100 Tensor Core units delivering mixed-precision training capabilities and NVIDIA Tesla V100S units optimized for clinical inference workloads. Table 11 shows the High-Performance Computing Cluster Specifications.
The comprehensive software stack integrated multiple specialized components to support bio-inspired algorithm development, neutrosophic computing, and clinical deployment requirements. The software architecture emphasized modularity, scalability, and medical device compliance while maintaining compatibility with standard clinical information systems and medical imaging protocols.
Operating system selection prioritized stability, security, and hardware optimization for high-performance computing applications. Red Hat Enterprise Linux provided the foundation for HPC cluster operations, while Ubuntu Server LTS supported container orchestration and microservices deployment. Deep learning frameworks incorporated both PyTorch and TensorFlow implementations to maximize compatibility and leverage platform-specific optimizations. Table 12 shows the Comprehensive Software Stack Specifications.
Clinical deployment architecture implemented a three-tier system design to accommodate different healthcare facility capabilities and resource constraints. Tier 1 research hospitals received high-performance workstations with advanced GPU acceleration and comprehensive storage systems for handling complex diagnostic cases and research applications. Tier 2 community hospitals utilized mid-range workstations with sufficient computational power for standard diagnostic workflows while maintaining cost-effectiveness.
Tier 3 clinics and remote sites employed mobile computing units based on NVIDIA Jetson AGX Orin platforms, providing AI-accelerated diagnostics in resource-constrained environments. The tiered deployment strategy ensured broad accessibility while maintaining diagnostic quality across diverse clinical settings. Network infrastructure varied by tier, with research hospitals utilizing high-speed dedicated connections and remote sites relying on mobile broadband with offline processing capabilities. Table 13 shows the Clinical System Hardware Specifications.
Cybersecurity and regulatory compliance infrastructure implemented comprehensive protection mechanisms addressing medical device security requirements, patient data protection, and healthcare industry regulations. Security architecture followed zero-trust principles with multi-layered defense strategies including data encryption, access controls, network segmentation, and continuous monitoring.
Compliance framework addressed multiple regulatory standards including HIPAA for patient privacy protection, GDPR for data protection rights, FDA Quality System Regulation for medical device manufacturing, and European Medical Device Regulation for CE marking requirements. Security measures incorporated both technical safeguards (encryption, access controls, audit trails) and administrative safeguards (security policies, training programs, incident response procedures). Table 14 shows the Cybersecurity and Regulatory Compliance Specifications.
System performance benchmarking evaluated computational throughput, diagnostic processing capacity, and scalability characteristics across different deployment scenarios. Performance metrics incorporated both technical benchmarks (computational throughput, memory utilization, network bandwidth) and clinical workflow metrics (diagnostic processing time, patient throughput, system response latency).
Scalability analysis demonstrated the system's ability to accommodate growing patient volumes and expanding clinical applications. Benchmark testing utilized standardized medical imaging datasets and clinical workflow simulations to establish baseline performance characteristics and identify optimization opportunities. Performance optimization strategies included GPU memory optimization, parallel processing enhancements, and caching mechanisms for frequently accessed diagnostic models. Table 15 shows the System Performance Benchmarks and Scalability Metrics.