Method for constructing HBV-related HCC risk model by using ESPL1 serum marker

Abstract

The invention relates to a method for constructing an HBV (Hepatitis B Virus) related HCC (Hepatitis C Chromatography) risk model by using an ESPL1 serum marker. The method comprises the following steps: firstly, identifying and extracting key oscillation characteristic indexes in an ESPL1 concentration curve through an improved time domain-frequency domain hybrid analysis system (TF-HySys) according to the fluctuation characteristic of the serum marker concentration on a time sequence; then, a dynamic probability coupling matrix (PCM) is constructed by utilizing the obtained oscillation characteristic indexes, preset auxiliary marker concentration / characteristics and clinical characteristic data; thirdly, constructing a differential equation inversion integration model (InDiMod) based on the PCM to carry out HCC risk modeling, and outputting a comprehensive dynamic risk integral (iDRS); secondly, establishing a'risk layering-threshold dynamic linkage system '(RT-DynLink) to carry out risk layering; and finally, integrating the above steps to develop an individual HCC risk trajectory generation and visual engine (TrajGen-Vis), and providing support for clinical intervention decision.

Description

Technical Field

[0001] The present invention belongs to the field of HBV-related HCC risk prediction, and more specifically relates to a method for constructing an HBV-related HCC risk model using the ESPL1 serum marker. Background Art

[0002] Hepatitis B virus (HBV) infection is a major risk factor for hepatocellular carcinoma (HCC). However, early prediction and identification of patients at high risk of developing HCC in HBV-infected patients for timely intervention and treatment has been a clinical challenge.

[0003] Currently, serological markers such as alpha-fetoprotein (AFP) are commonly used to diagnose HCC. However, due to limitations in sensitivity and specificity, the diagnostic efficacy of these markers alone is suboptimal. The cell cycle regulator ESPL1 has also been found to play an important role in the pathogenesis of HCC, but further research is needed to determine how to effectively utilize it to predict HCC risk. Furthermore, most HCC risk prediction models used in clinical practice are based on classic statistical models such as the Cox model or logistic regression. These models often only consider some of the patient's pathophysiological characteristics, while ignoring the dynamic changes in biomarker concentrations and the complex interactions that may exist between multiple markers. Therefore, there is room for improvement in predictive accuracy and stability.

[0004] Therefore, it is necessary to develop new prediction models that can accurately quantify the changing characteristics of biomarkers such as ESPL1, while comprehensively considering the complex interrelationships between multiple clinical characteristics and markers, so as to improve the prediction accuracy and early warning ability of HBV-related HCC risk. Summary of the Invention

[0005] The present invention mainly solves the technical problem of how to establish a dynamic prediction model that can effectively warn of the risk of hepatitis B virus (HBV)-related hepatocellular carcinoma (HCC) by accurately quantifying the oscillatory characteristics of ESPL1 and other biomarkers, combining clinical characteristics, and fully considering the complex interactions between these factors.

[0006] In order to achieve the above object, the present invention is implemented by adopting the following technical solutions: the method comprises:

[0007] Longitudinal serum samples collected from HBV-infected patients are accurately and quantitatively tested for the concentration of ESPL1 and other pre-set auxiliary serum markers. Clinical characteristics and endpoint events of the patients are simultaneously recorded. An oscillation feature quantification algorithm is used to identify and extract non-periodic key oscillation feature indicators in the ESPL1 concentration curve within a pre-set biomolecular oscillation window through a time-domain-frequency domain hybrid analysis system. These indicators include, but are not limited to, phase offset, amplitude decay rate, and approximate chaotic attractor dimension. These features serve as the original feature input for modeling.

[0008] A dynamic probabilistic coupling matrix is ​​constructed using the resulting oscillatory characteristic indicators, auxiliary marker concentrations, and clinical characteristic data. Using a coupling analysis method based on the Kumaraswamy distribution function, the coupling probability strength between each marker or characteristic in its current state is calculated. The coupling pattern is dynamically analyzed as clinical risk factors change, along with the location of coupling relationship transition events. This allows for the identification of personalized early warning intervals, and the annotation of time probability windows indicating qualitative changes in HCC risk at specific critical inflection points.

[0009] Based on the probabilistic coupling matrix, assuming that the coupling relationship is driven by a low-dimensional stochastic differential equation, a variational Bayesian-nonlinear dynamics manifold learning inversion algorithm is used to inversely reconstruct the differential equation and its parameter distribution that best fits the observed coupling evolution, output a comprehensive dynamic risk integral, and achieve dynamic prediction of the probability of occurrence of individual future key coupling transitions;

[0010] Based on the fractal entropy threshold adaptive mechanism, combined with clinical staging and biochemical background, patients are divided into subgroups with similar pathophysiology. For each subgroup, multi-scale fractal entropy analysis of the integrated dynamic risk integral sequence is performed to dynamically determine the group-adaptive critical entropy value and warning risk interval. The threshold is updated in real time based on new data and coupled transition events.

[0011] A curvature synapse labeling algorithm is used to locate high-value inflection points in the risk integral-time trajectory based on differential geometry methods. The inflection points are then linked to the probabilistic coupling matrix and key coupling transition events predicted by the dynamic model to generate a risk trajectory surface diagram. This enables visualization of the risk trajectory and intuitive labeling of key events, providing dynamic and explainable decision support for clinical intervention and individualized follow-up.

[0012] In one approach, the oscillation feature quantification algorithm not only analyzes ESPL1 serum concentrations, but also simultaneously performs the same oscillation feature extraction on time series concentration data of auxiliary serum markers including AFP, DCP, and GP73, thereby enriching the model input features and improving the ability to capture instability signals of multi-molecular systems before HCC occurs. The size and parameters of the oscillation analysis window can be flexibly adjusted based on clinical data on the natural history of hepatitis B and the incubation period of HCC to adapt to the differences in biological rhythms among different patient groups.

[0013] In one approach, during the construction of the probabilistic coupling matrix, the flexible shape parameters of the Kumaraswamy distribution function are used to model the asymmetric and nonlinear relationships between markers and clinical characteristics. This can dynamically reflect different coupling modes such as synergy, antagonism, or irrelevance, and identify coupling relationship conversion events that occur with the progression of clinical risk factors such as liver fibrosis. These events can serve as key time nodes for subsequent risk prediction and intervention.

[0014] In one approach, the differential equation model inversely reconstructed through the variational Bayesian-nonlinear dynamic manifold learning inversion algorithm can perform high-dimensional dimensionality reduction and parameter optimization on the dynamic relationship between the various features in the probabilistic coupling matrix, thereby obtaining a comprehensive dynamic risk integral. This integral can not only reflect the current individual's HCC risk level, but also dynamically predict the probability and time window of future key coupling transition events, providing a scientific basis for individualized risk assessment.

[0015] In one solution, the fractal entropy threshold adaptive mechanism can dynamically adjust the critical threshold of risk stratification based on the fluctuation characteristics of the risk score sequence within the patient group, avoiding the risk of misjudgment caused by a fixed cut-off point, and improving the model's sensitivity to early system abnormalities and the accuracy of risk stratification through real-time updated group adaptive critical entropy values ​​and warning risk intervals.

[0016] In one scheme, a curvature synaptic labeling algorithm is used to perform curvature analysis on the risk integral-time trajectory through differential geometry methods. This can accurately locate high-value inflection points in the risk evolution process, and "synaptically" link these inflection points with the probability coupling matrix and key coupling transition events predicted by the dynamic model. The generated risk trajectory surface diagram not only visualizes the dynamic evolution of the risk integral, but also intuitively marks high-risk conversion events and warning intervals, providing clinicians with interpretable decision support information.

[0017] In one scenario, the method is suitable for early screening and risk stratification of HCC in people at high risk of HBV infection, and can also be expanded to dynamic risk modeling scenarios of other chronic diseases turning into cancer. The method is individualized, dynamic, and interpretable, and is easy to integrate with clinical information systems or intelligent decision support systems to achieve risk prediction and stratified management in the context of precision medicine.

[0018] In one scenario, the model can be combined with newly collected longitudinal serum samples and the latest clinical data during actual application to dynamically update core parameters such as oscillation characteristics, probability coupling matrix and risk integral in real time, ensuring that the model's predictive ability is continuously optimized with patient status and data accumulation, thereby improving the risk warning sensitivity and timeliness of clinical intervention in long-term follow-up.

[0019] Beneficial effects of the present invention:

[0020] By precisely quantifying the oscillatory characteristics of the biomarker ESPL1 and considering its complex interactions with other factors, this paper constructs a dynamic, highly sensitive, and robust HBV-related HCC risk prediction model. This model can effectively warn of disease risk and provide an intuitive and detailed basis for clinical decision-making, thereby facilitating early intervention, reducing disease progression, and improving patients' quality of life. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 Flow chart of the method of the present invention. DETAILED DESCRIPTION

[0022] To facilitate understanding of the present invention, the present invention will be described more fully below with reference to the accompanying drawings. The drawings illustrate exemplary embodiments of the present invention. However, the present invention may be implemented in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and comprehensive understanding of the present invention.

[0023] Unless otherwise defined, all technical and scientific terms used herein have the same meanings as those understood by those skilled in the art to which the present invention pertains. The terms used in the present specification are for the purpose of describing specific embodiments only and are not intended to limit the present invention. To facilitate understanding of the present invention, a more comprehensive description of the present invention will be provided below with reference to the accompanying drawings. Typical embodiments of the present invention are shown in the drawings. However, the present invention may be embodied in many different forms and is not limited to the embodiments described herein. Rather, these embodiments are provided to provide a more thorough and comprehensive understanding of the present invention.

[0024] like Figure 1 As shown, a method for constructing an HBV-related HCC risk model using the ESPL1 serum marker includes the following steps:

[0025] Step 1. First, longitudinal serum samples collected from HBV-infected patients were precisely quantitatively measured for ESPL1 and other pre-defined auxiliary serum markers (such as AFP, DCP, and GP73). Patient clinical characteristics (such as age, gender, HBV DNA load, liver function indicators, and degree of liver fibrosis / cirrhosis) and endpoint events (presence and timing of HCC) were simultaneously recorded. The key to this approach lies in the innovative introduction of an "Oscillatory Feature Quantification" (OFQ) algorithm. This algorithm, which targets the time series fluctuations of serum marker concentrations, does not simply calculate the mean and standard deviation. Instead, it uses an improved time-domain-frequency hybrid analysis system (TF-HySys) to identify and extract key non-periodic oscillation characteristics (such as phase offset, amplitude decay rate, and approximate chaotic attractor dimension) in the ESPL1 concentration curve within a pre-defined biomolecular oscillation window (the window size is determined based on clinical data on the natural history of hepatitis B and the incubation period of HCC) that reflects abnormal perturbations in underlying molecular pathways. These unique indicators serve as the original feature input for modeling, aiming to capture early system instability signals overlooked by conventional concentration gradient analysis, specifically targeting the characteristic "pre-cancerous oscillation" pattern of ESPL1 that may exist before the development of HCC.

[0026] The implementation of the OFQ algorithm begins with the preprocessing and dynamic window division of the ESPL1 serum concentration time series. First, for each HBV-infected patient's longitudinal serum sample (time point sequence T = {t1, t2, ..., t n}, corresponding concentration sequence C={c1,c2,...,c n}, based on the natural history of hepatitis B and clinical data on HCC latency, a dynamic biomolecular oscillation window is defined. The window length W is not fixed, but is obtained by a nonlinear piecewise function W = f(P b ,D h ,δF) adaptive adjustment: where P b The quantitative code for the patient's current clinical stage of hepatitis B (such as chronic hepatitis CHB, cirrhosis LC), D h is the acceleration factor based on the patient's liver fibrosis degree (such as FIB-4 index, liver stiffness value LSM), δF is the coefficient of variation between adjacent time points in the window. k (The central time point is t k , the actual window range is The improved time-frequency hybrid analysis system (TF-HySys) is used to extract oscillation features. TF-HySys first performs time-domain analysis and calculates the normalized weighted phase deviation (NWPD) of the sequence. This indicator uses the local extreme point detection algorithm to identify all concentration peaks and valleys within the window (P max ,P min ), then construct the time offset vector ΔT=[Δt1,Δt2,...,Δt m ](in Expected peak time The NWPD is calculated by extrapolating the oscillation frequency of the preceding window.

[0027]

[0028] where σ T is the standard deviation of sampling time within the window, κ=∑w j is the normalization constant, the weight factor The concentration value c of the extreme point j Average concentration of the window The deviation of (σ C The tanh function compresses large offsets and amplifies the importance of small perturbations, particularly focusing on subtle asynchronous changes in the preclinical stage.

[0029] The frequency domain analysis part uses wavelet packet decomposition and entropy joint modulation technology. Perform three-layer adaptive wavelet packet decomposition (using Morlet wavelet basis) to generate 8 frequency band components B = {B1, B2, ..., B8}. The key is to use the Spectral Entropy Threshold Gating (SETG) algorithm instead of the traditional power spectrum analysis. Calculate each frequency band B i The energy entropy H e (B i ):

[0030]

[0031] Where WT is the wavelet coefficient, Ω i Indicates frequency band B i A set of coefficients. A dynamic entropy threshold H optimized by a genetic algorithm is preset thresh =g(LC_Status,δAFP), the threshold is determined by the patient's liver cirrhosis status code (LC_Status) and the AFP concentration change rate within the window (δAFP). Only those with entropy values ​​lower than H threshThe "ordered" frequency band is calculated and its integrated amplitude damping ratio (IADR) is calculated as follows:

[0032]

[0033] In the formula is the selected band index set, and Band B i The average amplitude in the first and second halves of the window, weighted by ρ i =exp(-λH e (B i IADR quantifies the overall attenuation of ordered oscillation patterns within a window, corresponding to the inactivation of abnormal signaling pathways associated with liver cancer.

[0034] Finally, the dynamic instability characteristics are captured by an improved chaotic attractor dimension approximation. The phase space is reconstructed using the concentration sequence in the window, and the optimal embedding dimension \(m\) and time delay τ are selected (based on the improved minimum mutual information false neighbor point joint criterion). For the reconstructed phase space point set X = {x1, x2, ..., x N}, calculate the weighted correlation dimension integral (WCDI) as an approximate value of the chaotic attractor dimension:

[0035]

[0036] in is the correlation integral (Θ is the Heaviside step function), is the Gaussian density weighting function (μ ∈ is the average concentration difference scale within the window, σ ∈ The weighted integral highlights the intermediate scale ∈ with the greatest clinical predictive value and suppresses noise interference. Finally, the four core oscillation features (NWPD, IADR, WCDI and transient impulse strength coefficient (TISC) calculated by the high-frequency band energy ratio of the wavelet packet) are integrated to form the feature vector F K , serving as the raw input for subsequent risk modeling. The OFQ algorithm innovatively captures the pro-tumor kinetic instability signal associated with HCC development in the ESPL1 concentration series through time-frequency synergy, entropy-gated screening, and weighted correlation dimension integration.

[0037] Step 2: Using the oscillatory characteristic indicators obtained in step 1 and the auxiliary marker concentrations / features and clinical characteristic data, a dynamic "probabilistic coupling matrix" (PCM) is constructed. This step abandons traditional correlation analysis (such as Pearson or Spearman) or feature selection algorithms (such as LASSO). The core of PCM is to use an improved Kumaraswamy distribution-based coupling analysis (KD-CA), which is particularly suitable for asymmetric and nonlinear relationship modeling due to its flexible shape. KD-CA not only calculates the coupling probability strength between two markers / features in the current state, but more importantly, it dynamically analyzes the transition probability and transfer entropy change characteristics of their coupling mode (such as synergy, antagonism, and irrelevance) as clinical risk factors (such as liver fibrosis progression) change. In particular, we focused on atypical transition events (such as mutations from weak correlation to strong synergy / antagonism) in the coupling patterns between the ESPL1 oscillation characteristics and other key factors (such as AFP concentration and liver fibrosis score). These transition events are regarded as potential markers of high-risk "molecular synergy conversion" for HCC. From them, we screened out the coupling relationship change pathways with the most predictive value and clinical interpretability, forming a structured relationship subgraph with high information density in the PCM, rather than just an independent feature list.

[0038] The implementation process begins with the dynamic alignment and coupling strength quantification of multimodal feature data within the longitudinal time window. For each patient, the oscillation window ω divided in step 1 k On the other hand, the ESPL1 oscillation eigenvector F is integrated within the window k =[f NWPD ,f IADR ,f WCDI ,f TISC ] k , the concentration change rate of auxiliary serum markers (such as AFP, DCP) (calculated as the L2 norm of the first-order derivative within the window) and the clinical characteristic state vector C k (including age-standardized liver fibrosis score, HBV DNA logarithmic change, etc.) The core of PCM, Kumaraswamy distribution function coupling analysis (KD-CA), first for each pair of target features (i, j), use its observation value x in the window i,k ,x j,k , fitting a modified, risk factor-conditioned bivariate Kumaraswamy distribution. The probability density function (PDF) of this distribution is reparameterized as:

[0039]

[0040] where u = Φ -1 (x i,k ), v = Ψ -1 (x j,k ) are the values ​​of features i and j after being transformed by marginal distribution functions Φ(·) and Ψ(·) (making them obey the uniform distribution [0,1] to adapt to the Kumaraswamy distribution), and the parameters (a, b, c, d) are estimated by combining maximum likelihood estimation with clinical risk factors (such as liver fibrosis score Fib k The correction term of the driver is jointly optimized: Specifically, a=a0+α·Fib k , c=c0+γ·log 10 (HBV DNA k ) etc., in order to dynamically adjust the distribution pattern so that it evolves with the disease process. Key innovations Then an asymmetric coupling phase modulation factor is introduced, where λ k Controls the strength of asymmetry, The coupling probability strength CP under this PDF definition is the potential inter-feature phase difference offset (which establishes an implicit mapping with the oscillation phase offset extracted in step 1). i,j,k Defined as the probability that the joint value of a feature falls in the high-density area of ​​its distribution:

[0041]

[0042] where Ω H (ξ k ) is based on the distribution kurtosis and the current risk state threshold ξ k Dynamically defined high probability region boundaries (such as 95% probability intervals surrounded by isodensity lines).

[0043] The coupled mode dynamic transfer analysis is achieved through the state transfer entropy tracking technology. Define the three-element coupled mode state S i,j,k :

[0044] Synergy (S+): When

[0045] Antagonism (S-): When

[0046] Independent (I): Otherwise CP i,j,k ≤θ +

[0047] Threshold θ + It is adaptively determined by the 80% quantile of the coupling strength distribution of the feature pair in the entire queue. For each feature pair (i, j), its coupling state sequence {S i,j,k Si,j,k+1 ,...,S i,j,k+T The core innovation lies in calculating the atypical transition entropy (ATE) to quantify the abnormality of state transitions:

[0048]

[0049] where p obs (m→n) is the observed transition frequency from state m to state n, p ref (m→n) is the baseline value of the transition probability based on the entire cohort (within the same liver fibrosis stage). Entropy gain factor Capturing the sensitivity of coupling strength to liver fibrosis progression at the time of metastasis development. Specifically, we defined HCC high-risk-associated transition events as metastases that met one of the following criteria:

[0050] 1. Transitions involving ESPL1 characteristics: m∈{I,S-}→n=S+ and ATE>η1

[0051] 2. With dramatic changes: |CP i,j,k -CP i,j,k+1 |>Δ threshold ∧ATE>η2 (η1,η2 are critical values ​​optimized by C-index of survival analysis).

[0052] The final PCM construction integrates the above dynamic coupling and transition information into a structural subgraph. k For slicing, create a directed graph G of all feature nodes k (V,E). Node v i Representative features, key edge weights w i→j Designed as a three-part composite:

[0053]

[0054] in is the set of all transitions occurring between windows, Ω(HR i,j )=1+log(Hazard Ratio from Cox model) to integrate the prognostic strength of the feature's association with the transition event and HCC. In particular, we focus on high-weight edges containing the ESPL1 feature. If its weight exceeds 3 standard deviations of the global edge weight distribution in the same window, it is anchored as a "Molecular Synergy Switch Hub (MSSH)." Dynamic PCM P k Essentially represented as these hub edges and their associated subgraphs (by edge filtering function Generated) adjacency tensor, where τk The matrix was adaptively determined by maximizing the intertemporal mutual information between the subgraph structure and the future HCC risk score. This matrix asymmetrically condenses the key coupled pathways driven by ESPL1 that evolve with disease stage and their high-risk transition events, providing structured input for subsequent kinetic inversion models.

[0055] Step 3: Based on the highly informative structural relationship subgraphs and their dynamic characteristics contained in the PCM constructed in Step 2, the "Inverted Differential Equation Integration Model" (InDiMod) was innovatively applied to HCC risk modeling. This approach abandons standard logistic regression, Cox model, or tree / neural network-based models. The core of InDiMod is the assumption that these complex coupling relationships (such as the synergistic enhancement of ESPL1 oscillations and AFP concentrations) are driven by a set of low-dimensional, biophysically meaningful stochastic differential equations (SDEs). Instead of conventional SDE modeling, this step employs an inversion strategy: utilizing the observed time series of coupling pattern evolution (derived from longitudinal data), an improved joint inversion algorithm combining variational Bayesian inference and nonlinear dynamic manifold learning (VB-NLDML) is used to inversely reconstruct the potential core driving SDE forms and their parameter distributions that best fit the evolution of these coupled dynamics. The reconstructed SDEs not only predict the probability of a "critical transition" (i.e., cross-domain prediction conversion point) in the coupling relationship structure of an individual in the future unit time, but also integrate this transition probability into the clinical endpoint event data, and directly output the "Integrated Dynamic Risk Score" (iDRS) representing the possibility of the current system state deviating from the steady state and tending towards the occurrence of HCC. This integral naturally has time dynamic properties and can reflect the rate of risk evolution.

[0056] The dynamic probability coupling matrix (PCM) constructed in step 2 is used to reconstruct the high-dimensional coupling dynamic trajectory. For the target patient, the historical time window sequence {ω1,ω2,...,ω K} on the PCM subgraph set {P1,P2,...,P K Each P k Contains nodes connected by high-weight edges (such as ESPL1 oscillation feature f NWPD , AFP concentration change rate, liver fibrosis score, etc.) and its dynamic coupling weight matrix W (k) The core innovation lies in treating the PCM structure at each time point \(k\) as an observation snapshot of the underlying dynamical system and assuming that its evolution is governed by a set of low-dimensional stochastic differential equations (SDEs):

[0057] dZ(t)=μ(Z(t),t;θ)dt+σ(Z(t),t;θ)dB t

[0058] where Z(t)∈ d (d number of nodes) is the unobserved dynamical eigenstate vector, μ(·) is the drift function, σ(·) is the diffusion matrix, and θ is a biophysical parameter (such as pathway activation threshold and intermolecular interaction strength coefficient). The key inversion strategy of InDiMod is implemented by the joint variational Bayesian-nonlinear manifold learning (VB-NLDML) algorithm: First, each PCM subgraph P is transformed into k Mapped to the latent space manifold coordinates. The encoder is designed as follows:

[0059]

[0060] where φ(·) is an adaptive edge message function based on Lie algebra representation (maintaining the symmetry of the graph structure), ψ(·) encodes the window time interval Δt k =t k -t k-1 The mechanical effect of Γ is the graph pooling operator with attention gating. Output h k As Z(t k ) is estimated from noisy observations.

[0061] The joint optimization phase of VB-NLDML uses a two-channel variational inference: on the one hand, the variational posterior distribution q is established φ (θ,Z 1:K |P 1:K ) approximates the true posterior p(θ,Z 1:K |P 1:K ). Parameterize the posterior via asymmetric KL divergence constraints:

[0062]

[0063] The observation likelihood term p(P k |Z k ) is generated inversely by the EGCDE encoder (i.e. from Z k Reconstructing the graph structure), the KL term constrains the biophysical parameters θ to obey a clinically interpretable prior distribution (such as activation parameters constrained by the Hill function), and the maximum mean difference term MMD(·) forces the hidden state Z to align with the intrinsic coordinates extracted by the nonlinear dynamics manifold learning (NLDML) module. The NLDML module is constructed based on nonparametric phase space reconstruction: trajectories sampled from the variational posterior Compute the generalized Jacobian spectral density in the extended phase space:

[0064]

[0065] here is a differentiable mapping function from latent variables to PCM graph space, K meta is a kernel function modulated based on clinical metadata (e.g., HBeAg status). The spectral peak of SD-GJD at the characteristic frequency \(f\) reveals the dominant dynamic mode, based on which the optimal SDE prototype is derived: for example, when a double-peak spectrum is detected (frequency ratio of about 1:3), it is inferred that the system has a bistable switching behavior (e.g., μ(Z) = θ1Z - θ2Z 3 Duffing-type drift term); or when the spectral distribution has a long tail, it corresponds to the Levy noise driven diffusion (e.g., σ(Z)dL t ).

[0066] VB and NLDML are jointly optimized through Entropy-Regularized Interaction Learning (ERIL): the Z trajectory generated by the variational posterior guides the SD-GJD calculation, and the SDE structure identified by NLDML (such as the damped oscillation mode at a specific frequency) is further optimized through the regularization term Constrained variational parameter distribution (where is the SDE prototype parameter mapped from the spectral feature). After this joint inversion, the personalized SDE system parameter posterior distribution q is finally obtained. * (θ) and state trajectory

[0067] Critical transition prediction and iDRS integral generation based on inversion of SDE system. Define the critical transition index: when the dynamic state crosses the bifurcation manifold formed by the drift function zero point When , the system undergoes a drastic state change. The probability of such a critical transition occurring within the next ΔT is calculated as:

[0068]

[0069] in The integral captures the time that the state point stays in the neighborhood of the bifurcation manifold (reflecting the degree of system instability). The integrated dynamic risk score (iDRS) combines the transition probability with clinical prognostic information:

[0070]

[0071] The first term Ψ(·) is the transition probability normalized by the hyperbolic tangent function, and the survival gradient term is the survival function generated by the inverted SDE The decline rate within the window is calculated (reflecting the rate of prognosis deterioration under the current kinetic state), and the third item focuses on enhancing the transition events corresponding to the MSSH (molecular cooperative conversion hub) pathway marked by PCM (HR mss is the hazard ratio adjusted by Cox model), the denominator The iDRS score integrates implicit kinetic instability signals, explicit survival deterioration rates, and synergistic mutation events in key molecular pathways into a unified risk scale, directly driving downstream risk stratification decisions.

[0072] Step 4: Establish an optimized "Risk Stratification-Threshold Dynamic Linkage System" (RT-DynLink). This approach abandons the common practice of using fixed cutoff values ​​or receiver operating characteristic (ROC) curves to optimize thresholds. This step introduces an improved "Fractal Entropic Threshold Adaptation" (FETA) mechanism based on the individual iDRS score sequence output from Step 3 and its corresponding coupling relationship structure evolution path. FETA first divides the patient population into subgroups with similar pathophysiological backgrounds based on clinical liver disease stage (e.g., chronic hepatitis B, compensated / decompensated cirrhosis) and basic biochemical markers. For each subgroup, FETA calculates the multiscale fractal entropy of the iDRS score sequence (reflecting the complexity and regularity of risk evolution) and utilizes entropy-clinical outcome association analysis based on the maximum information coefficient to dynamically determine the dynamic critical entropy value (D-CET) required to trigger an early warning for each individual risk within that subgroup, as well as the corresponding early warning risk range (EWS-Range). D-CET and EWS-Range are not globally constant, but are adaptively updated using the fractal entropy change rate as new data are added to the subgroup and new coupling transition events occur, ensuring that the early warning system is highly sensitive to ESPL1-dominated microenvironmental instability signals in specific clinical states (such as cirrhosis) while maintaining robustness.

[0073] Based on the complete technical chain of steps 1-3, the implementation of the InDiMod model in step 3 begins with the implicit dynamical system reconstruction of the dynamic PCM subgraph sequence. Assuming that the observed PCM structural evolution (such as the synergistic weight transition between the ESPL1 NWPD characteristics and the AFP change rate) is driven by an underlying low-dimensional stochastic differential equation (SDE), the core inversion algorithm VB-NLDML is implemented through the following mechanism:

[0074] First, the equivariant graph convolutional dynamics encoder (EGCDE) is used to map the temporal PCM into a continuous manifold trajectory. t PCM subgraph Gt (node ​​v i ∈V represents the oscillatory feature / marker / clinical variable, and the edge weight Encoding coupling strength and mode), designing a graph convolution operator with Lie group equivariance:

[0075]

[0076] Where ⊕ represents the splicing operation, is the set of neighbor nodes, Δt is the time interval between the current and previous windows, and the function κ(·) is the hyperbolic tangent activation after affine transformation, so that it satisfies the translation invariance under group action.

[0077] The variational Bayesian-nonlinear manifold learning (VB-NLDML) joint optimization inverts the SDE in three steps:

[0078] 1. Variational Inference Framework: Defining Parameterized Posterior Approximating the true posterior p(θ,Z{1:T}|G{1:T}), the variational lower bound is:

[0079]

[0080] Likelihood term p(G t |Z t ,θ) is modeled by the inverse decoder of EGCDE (i.e., reconstructing the adjacency matrix of Gt from Zt), and the KL divergence constrains the biophysical parameters θ (such as pathway feedback strength and noise attenuation coefficient) to obey the clinical knowledge-driven prior (e.g., θ follows the Gamma distribution to ensure positivity).

[0081] 2. Nonlinear manifold regularization: Based on phase space reconstruction theory, from the latent trajectory Z t Compute the eigenspectrum of the generalized Jacobian matrix:

[0082]

[0083] where λ(ω) is J(Z t ) at the frequency ω, P(ω|Θ meta ) is composed of metadata Θ meta This regularization term forces the latent dynamics to match the behavior of typical biological systems (such as the saddle point bifurcation spectrum of a bistable system).

[0084] 3. Automatic derivation of SDE prototype: When the spectral energy is at the critical frequency ω c Significant clustering (satisfying Triggering the rule engine to parse the corresponding SDE format:

[0085] If a supercritical Hopf bifurcation spectrum is detected (e.g. Re[λ]>0 and Im[λ]≠0), an oscillatory system with noise is generated:

[0086]

[0087] If a saddle-node bifurcation feature appears (e.g., λ1≈0 and λ2<0), it is derived as a threshold switching system:

[0088] AFP norm is the normalized marker concentration, dWt is the Wiener process, and dLt is the Levy noise (simulating sudden pathological disturbances).

[0089] Generation mechanism of critical transition probability and iDRS integral:

[0090] Based on the inversion of the SDE system, the bifurcation manifold is defined (μ is the drift term). The probability of the system undergoing a critical transition at time t is decoupled through the Fokker-Planck equation:

[0091] The final integrated kinetic risk score (iDRS) coupled transition probability and clinical prognostic information:

[0092]

[0093] in is the survival function derived from SDE, The MSSH set represents the rate of decline in survival probability at time t. The MSSH set includes high-risk coupling pathways labeled by PCM as "molecular synergistic conversion hubs" (e.g., the synergistic effect of ESPL1 oscillation and a sudden increase in liver fibrosis score). An iDRS value > 0.82 (approximately the optimal Youden index) triggers a high-risk warning, and its dynamic slope reflects the time sensitivity of HCC development.

[0094] Step 5: Integrate the dynamic risk prediction core formed in the previous steps to develop the "Personalized HCC Risk Trajectory Generation and Visualization Engine" (TrajGen-Vis). Abandon the standard Kaplan-Meier curve or static risk score chart. The core of this engine uses an innovative "Curvature Synapse Tagging" (CvS) algorithm to process the individual's iDRS integral sequence, coupled transition event probability, and PCM structural feature changes on the time axis. The CvS algorithm first locates the geometric "inflection points" (curvature sudden change points) with high predictive value on the individual risk trajectory on the iDRS-time plane through a trajectory feature extraction method based on differential geometry. These inflection points are "synaptically" linked to the occurrence time of key coupling relationship transitions predicted by PCM and InDiMod. The engine ultimately dynamically generates and visualizes a risk trajectory surface plot (Risk Trajectory Surface Plot) for an individual's future time window. This plot integrates the predicted iDRS evolution path, the locations of high-probability coupling relationship transition events (which serve as "landmarks" on the trajectory), the current personalized warning interval determined by FETA, and annotates the time-to-event probability window (TEPW) indicating a qualitative change in HCC risk at specific critical inflection points. This plot provides an intuitive, dynamic, and spatiotemporal map of HBV-HCC risk based on the underlying molecular coupling dynamics, providing strong support for clinical intervention decisions.

[0095] Those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing related hardware through a computer program. The program can be stored in a computer-readable storage medium, and when executed, the program can include the processes in the above-described method embodiments. The storage medium can be a magnetic disk, an optical disk, a read-only memory (ROM), or a random access memory (RAM).

[0096] It should be understood that the detailed description of the technical solutions of the present invention using the preferred embodiments above is illustrative and not restrictive. A person skilled in the art, after reading the present specification, may modify the technical solutions described in the embodiments or replace some of the technical features therein with equivalents; such modifications or replacements do not deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for constructing an HBV-related HCC risk model using the ESPL1 serum marker, characterized by: The method includes: Longitudinal serum samples collected from HBV-infected patients are accurately and quantitatively tested for the concentration of ESPL1 and other pre-set auxiliary serum markers. Clinical characteristics and endpoint events of the patients are simultaneously recorded. An oscillation feature quantification algorithm is used to identify and extract non-periodic key oscillation feature indicators in the ESPL1 concentration curve within a pre-set biomolecular oscillation window through a time-domain-frequency domain hybrid analysis system. These indicators include, but are not limited to, phase offset, amplitude decay rate, and approximate chaotic attractor dimension. These features serve as the original feature input for modeling. A dynamic probabilistic coupling matrix is ​​constructed using the resulting oscillatory characteristic indicators, auxiliary marker concentrations, and clinical characteristic data. Using a coupling analysis method based on the Kumaraswamy distribution function, the coupling probability strength between each marker or characteristic in its current state is calculated. The coupling pattern is dynamically analyzed as clinical risk factors change, along with the location of coupling relationship transition events. This allows for the identification of personalized early warning intervals, and the annotation of time probability windows indicating qualitative changes in HCC risk at specific critical inflection points. Based on the probabilistic coupling matrix, assuming that the coupling relationship is driven by a low-dimensional stochastic differential equation, a variational Bayesian-nonlinear dynamics manifold learning inversion algorithm is used to inversely reconstruct the differential equation and its parameter distribution that best fits the observed coupling evolution, output a comprehensive dynamic risk integral, and achieve dynamic prediction of the probability of occurrence of individual future key coupling transitions; Based on the fractal entropy threshold adaptive mechanism, combined with clinical staging and biochemical background, patients are divided into subgroups with similar pathophysiology. For each subgroup, multi-scale fractal entropy analysis of the integrated dynamic risk integral sequence is performed to dynamically determine the group-adaptive critical entropy value and warning risk interval. The threshold is updated in real time based on new data and coupled transition events. A curvature synapse labeling algorithm is used to locate high-value inflection points in the risk integral-time trajectory based on differential geometry methods. The inflection points are then linked to the probabilistic coupling matrix and key coupling transition events predicted by the dynamic model to generate a risk trajectory surface diagram. This enables visualization of the risk trajectory and intuitive labeling of key events, providing dynamic and explainable decision support for clinical intervention and individualized follow-up.

2. The method for constructing an HBV-related HCC risk model using the ESPL1 serum marker according to claim 1, characterized in that: The oscillation feature quantification algorithm not only analyzes ESPL1 serum concentrations, but also simultaneously performs the same oscillation feature extraction on time series concentration data of auxiliary serum markers including AFP, DCP, and GP73, thereby enriching the model input features and improving the ability to capture destabilization signals of multi-molecular systems before HCC occurs. The size and parameters of the oscillation analysis window can also be flexibly adjusted based on clinical data on the natural history of hepatitis B and the incubation period of HCC to adapt to the differences in biological rhythms among different patient groups.

3. The method for constructing an HBV-related HCC risk model using the ESPL1 serum marker according to claim 1, characterized in that: During the construction of the probabilistic coupling matrix, the flexible shape parameters of the Kumaraswamy distribution function are used to model the asymmetric and nonlinear relationships between markers and clinical characteristics. This can dynamically reflect different coupling modes such as synergy, antagonism, or irrelevance, and identify coupling relationship conversion events that occur with the progression of clinical risk factors for liver fibrosis. These events can serve as key time nodes for subsequent risk prediction and intervention.

4. The method of claim 1, wherein: The differential equation model inversely reconstructed through the variational Bayesian-nonlinear dynamic manifold learning inversion algorithm can perform high-dimensional dimensionality reduction and parameter optimization on the dynamic relationship between each feature in the probabilistic coupling matrix, thereby obtaining a comprehensive dynamic risk integral. This integral can not only reflect the current individual's HCC risk level, but also dynamically predict the probability and time window of future key coupling transition events, providing a scientific basis for individualized risk assessment.

5. The method of claim 1, wherein: The fractal entropy threshold adaptive mechanism can dynamically adjust the critical threshold of risk stratification according to the fluctuation characteristics of the risk score sequence within the patient group, avoiding the risk of misjudgment caused by a fixed cut-off point, and improving the model's sensitivity to early system abnormalities and the accuracy of risk stratification through real-time updated group adaptive critical entropy values ​​and warning risk intervals.

6. The method of claim 1, wherein: By adopting the curvature synaptic labeling algorithm and performing curvature analysis on the risk integral-time trajectory through differential geometry methods, high-value inflection points in the risk evolution process can be accurately located. These inflection points can be "synaptically" linked with the probability coupling matrix and key coupling transition events predicted by the dynamic model. The generated risk trajectory surface diagram not only visualizes the dynamic evolution of the risk integral, but also intuitively marks high-risk conversion events and warning intervals, providing clinicians with interpretable decision support information.

7. The method of claim 1, wherein: The method is suitable for early screening and risk stratification of HCC in people at high risk of HBV infection, and can also be expanded to dynamic risk modeling scenarios of other chronic diseases progressing to cancer. The method is individualized, dynamic, and interpretable, and is easy to integrate with clinical information systems or intelligent decision support systems to achieve risk prediction and stratified management in the context of precision medicine.

8. The method of claim 1, wherein: In actual application, the model can combine newly collected longitudinal serum samples and the latest clinical data to dynamically update the oscillation characteristics, probability coupling matrix and risk integral core parameters in real time, ensuring that the model's predictive ability is continuously optimized with patient status and data accumulation, thereby improving the risk warning sensitivity and timeliness of clinical intervention in long-term follow-up.

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