Tumor treatment strategy decision-making method based on threshold guidance and related device

Abstract

The invention discloses a tumor treatment strategy decision-making method based on threshold guidance and a related device, and aims to solve the problems of drug resistance, lack of adaptability, difficulty in clinical implementation and the like of an existing tumor treatment strategy, and the method comprises the following steps: defining a threshold-guided treatment period and a threshold-guided non-treatment period, and constructing a threshold-guided dynamic system model, carrying out theoretical analysis and numerical simulation on dynamic behaviors, carrying out comparative analysis with other treatment strategies, carrying out theoretical parameter sensitivity analysis, and optimizing an adaptive treatment strategy by utilizing reinforcement learning. According to the method, treatment decisions are dynamically adjusted through a single-threshold strategy, high individuation and precise treatment are achieved, heterogeneity of tumor dynamics among patients can be effectively handled, tumor development time is remarkably prolonged, the dosage is reduced, toxic and side effects are reduced, and the living quality and treatment compliance of the patients are improved; and a novel effective method is provided for tumor treatment.

Description

Technical Field

[0001] This application belongs to the field of strategy analysis technology and relates to a threshold-guided tumor treatment strategy decision-making method and related device. Background Technology

[0002] Cancer has long been a leading cause of morbidity and mortality worldwide. Traditional cancer treatment strategies, such as continuous aggressive therapy, while capable of significantly reducing tumor burden in the short term, are prone to drug resistance, leading to treatment failure and even recurrence and metastasis. This phenomenon indicates that simply increasing drug dosage or extending treatment duration cannot fundamentally solve the problem of drug resistance.

[0003] As a promising alternative, adaptive therapy has been proposed and explored in several cancer types, such as prostate cancer. Its core idea is to move beyond simply pursuing maximum tumor burden elimination. Instead, it actively utilizes the ecological competition between drug-sensitive and drug-resistant tumor cells through intermittent drug administration, inhibiting the expansion of drug-resistant cells. By appropriately reducing or discontinuing medication, a certain number of drug-sensitive cells are preserved to continue suppressing drug-resistant cells in subsequent treatment cycles, thereby prolonging the treatment's effectiveness. Clinical trials and mathematical modeling studies have shown that adaptive therapy holds promise for significantly extending progression-free survival and overall survival by delaying the onset of treatment resistance.

[0004] To quantitatively analyze and optimize adaptive treatment regimens, various mathematical models have been proposed to describe the evolutionary dynamics of tumors under treatment and the mechanisms of treatment switching. Typical examples include: 1) Periodic Switching System: This system uses a pre-set fixed treatment period and non-treatment period for periodic switching (e.g., two weeks of medication followed by three weeks of no medication). Its advantages are its simple structure, ease of analysis and implementation. However, the switching rules are entirely based on the preset time and do not depend on the patient's actual condition (e.g., tumor size or biomarker levels), lacking adaptability. For patients with slow-growing tumors or significant individual differences, a fixed cycle can easily lead to overtreatment or undertreatment, failing to meet the "personalized, on-demand dosing" principle emphasized in adaptive therapy.

[0005] 2) State-dependent switching systems (e.g., the Filippov system): To avoid unnecessary treatment burden, some studies employ a state-dependent switching framework, introducing thresholds to describe intermittent treatment strategies based on tumor burden. A typical approach of these models is to switch treatment states based on the current tumor size; that is, once the tumor size or other relevant indicators reach a preset threshold, the system immediately switches between "dosing / discontinuing" states. While this method achieves a formal "threshold-guided" approach, it requires frequent or near-continuous monitoring of the patient's state, which is not easily achieved in clinical practice. Furthermore, overly frequent state switching can cause "on / off jitter," which is detrimental to the stable implementation of the treatment plan and patient adherence.

[0006] Current cancer treatment strategies suffer from numerous problems. While traditional continuous aggressive therapies can significantly reduce tumor burden in the short term, they easily lead to drug resistance, resulting in treatment failure and even relapse and metastasis. Existing adaptive therapy modeling frameworks are either based on fixed-cycle switching systems, lacking adaptability and prone to overtreatment or undertreatment; or based on state-dependent switching systems, requiring frequent monitoring of patient status, which is difficult to implement in clinical practice and may cause "on / off jitter." These model frameworks fail to organically combine the standard "periodic monitoring" process in clinical practice with "threshold-guided" decision-making logic, making it difficult to directly guide real-world dosing decisions. Therefore, there is an urgent need in the field for a universal modeling and analysis framework that conforms to actual clinical procedures and incorporates threshold-guided strategies for both periodic and intermittent treatment. Summary of the Invention

[0007] The purpose of this application is to address the problems in the prior art and provide a threshold-guided tumor treatment strategy decision-making method and related device.

[0008] To achieve the above objectives, this application adopts the following technical solution: In the first aspect, this application proposes a threshold-guided tumor treatment strategy decision-making method, which includes the following steps; Collect biomarker level data for dynamic monitoring of patients; By inputting biomarker level data and corresponding detection time information into a pre-constructed and optimized tumor treatment strategy decision model, corresponding tumor adaptive treatment strategies can be obtained. The pre-constructed and optimized tumor treatment strategy decision-making model is a threshold-guided dynamic system model optimized through reinforcement learning.

[0009] Furthermore, the threshold-guided dynamic system model is as follows:

[0010] in, and These represent drug-sensitive tumor cells and drug-resistant tumor cells, respectively. and The intrinsic growth rates of the two types of cells; and This represents the competition coefficient, used to quantify the competitive inhibition strength between two cell types. This indicates the corresponding reduction rate of drug-sensitive cell survival under treatment; parameter k represents environmental carrying capacity, with the first subscript representing the system and the second subscript representing the cell. and This indicates that under treatment, drug-sensitive tumor cells and drug-resistant tumor cells The maximum number that can be achieved; and This indicates the maximum number of the two cell types that can be achieved without treatment; Indicates the current time; Indicates the time period for treatment. Indicates the period during which no treatment will be administered; Indicates the initial number of tumor cells; This indicates that the number of cells is a positive real number.

[0011] Furthermore, the tumor treatment strategy decision-making model includes a free system and a control system, as detailed below:

[0012] in, The differential equation representing the treatment state; The differential equation representing the non-treatment state; The system of differential equations governing the dynamic behavior of the free system is as follows:

[0013] The differential equations for the dynamic behavior of the control system are as follows: .

[0014] Furthermore, the tumor treatment strategy includes: Within a preset fixed time interval, determine whether the tumor size data exceeds a preset threshold. When the tumor size exceeds a preset threshold At this time, the period is defined as the treatment period, during which the control system is activated. When the tumor size does not exceed This period is defined as a non-treatment period, during which the free system is activated. Treatment time period Non-treatment time period The details are as follows:

[0015] in, Indicates the prior treatment period; This indicates the prior non-treatment period.

[0016] Furthermore, the tumor treatment strategy decision model is optimized, including: Construct a Markov decision process and define its core elements: state, action, reward, and state transition probability; Construct a minimal decision framework to compare different reinforcement learning strategies; The algorithm employs a near-end strategy optimization, leveraging the dual-head output structure and the time-series modeling capabilities of LSTM to extract key time-series features from dynamic changes, thereby achieving adaptive adjustment. Furthermore, the proposed near-end strategy optimization algorithm, leveraging the dual-head output structure and the temporal modeling capabilities of the Long Short-Term Memory (LSTM) network, extracts key temporal features from dynamic changes to achieve adaptive adjustment, as detailed below: Input layer receives environmental state And the dimensions are mapped to 32 dimensions through a linear transformation layer; Long Short-Term Memory (LSTM) network is introduced to process time-series data on tumor size. Its input layer has a dimension of 32 and its output layer has a dimension of 64. The output of LSTM is then connected to a shared deep feature processing network with the following hierarchical structure: 64-dimensional → 128-dimensional → 64-dimensional → 32-dimensional → 16-dimensional → 10-dimensional. This allows for the extraction of core information relevant to decision-making from high-level features. Advantage estimation is performed using a proximal policy optimization algorithm, which uses the advantage function to estimate the relative merits of a certain action under the current policy and guides the agent to choose a better action. The 10-dimensional features output from the shared network are input into the policy network and mapped to 31 dimensions through a linear layer. The action probability distribution is then output after passing through a Softmax activation function. .

[0017] Secondly, this application proposes a threshold-guided tumor treatment strategy decision-making system, comprising: The data acquisition module is used to collect biomarker level data for dynamic monitoring of patients; The strategy guidance module is used to input biomarker level data and corresponding detection time information into a pre-built and optimized tumor treatment strategy decision model to obtain the corresponding tumor adaptive treatment strategy. The pre-constructed and optimized tumor treatment strategy decision-making model is a threshold-guided dynamic system model optimized through reinforcement learning.

[0018] Thirdly, this application proposes an electronic device including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the steps of the above-described method.

[0019] Fourthly, this application provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the above-described method.

[0020] Fifthly, this application proposes a computer program product, which includes computer instructions, wherein a processor of a computer device reads the computer instructions and executes the computer instructions to implement the steps of the above-described method.

[0021] Compared with the prior art, this application has the following beneficial effects: This application achieves highly personalized and precise treatment by dynamically adjusting treatment decisions through a single-threshold strategy. It effectively addresses the heterogeneity of tumor dynamics among patients, avoiding the limitations of a "one-size-fits-all" approach. It significantly prolongs time to tumor progression (TTP) and reduces drug dosage. Compared to the maximum tolerated dose (MTD), intermittent treatment (IT), and dual-threshold (AT50) strategies, the TTP increase reaches a maximum of 86.5%, while substantially reducing cumulative drug dosage, minimizing toxic side effects (such as myelosuppression, nausea, and fatigue), improving patient quality of life and treatment adherence, and lowering medical costs. By integrating a proximal strategy optimization (PPO) algorithm with a pruning mechanism, it effectively prevents drastic changes in treatment strategies during training, reducing clinical decision-making risks. Leveraging a dual-head output structure and LSTM temporal modeling capabilities, the agent can extract key temporal features from the dynamic changes in tumor burden, enabling adaptive adjustment of treatment duration. Rigorous mathematical modeling, existence and stability analysis of periodic solutions (including boundary periodic solutions and positive periodic solutions), and large-scale numerical simulations provide a solid theoretical foundation and empirical evidence.

[0022] Furthermore, this application dynamically adjusts treatment decisions through a single threshold strategy, triggering or stopping treatment based on whether the real-time tumor burden exceeds a preset threshold, thereby achieving true individualized adaptation. Compared to traditional fixed-cycle therapies, this method effectively addresses the heterogeneity of tumor dynamics among patients, avoiding the limitations of a "one-size-fits-all" approach. Combined with a reinforcement learning optimization framework, the system can further learn patient-specific responses, dynamically adjusting treatment parameters (such as treatment duration) to improve the accuracy and adaptability of treatment.

[0023] Furthermore, through numerical simulation and clinical data validation, the AT-PSC strategy proposed in this application significantly prolongs TTP (with a maximum increase of 86.5%) compared to the maximum tolerated dose (MTD), intermittent treatment (IT), and dual threshold (AT50) strategies, while substantially reducing the cumulative drug dose. This directly translates to a reduction in toxic side effects (such as bone marrow suppression, nausea, and fatigue), improved patient quality of life and treatment adherence, and lower medical costs.

[0024] Furthermore, this application effectively prevents drastic changes in treatment strategies during training by integrating a pruning mechanism from the proximal policy optimization (PPO) algorithm, thereby reducing the risk of clinical decision-making. Simultaneously, leveraging the dual-head output structure and LSTM temporal modeling capabilities, the agent can extract key temporal features from the dynamic changes in tumor burden, enabling adaptive adjustment of treatment duration and thus extending time to tumor progression (TTP). In addition, the multi-objective reward function designed in this application, which integrates survival rewards, treatment-saving rewards, and tumor progression penalties, can guide the strategy to minimize treatment intensity while effectively inhibiting tumor growth, simplifying clinical procedures and improving the feasibility of treatment strategies while ensuring efficacy.

[0025] Furthermore, through rigorous mathematical modeling, existence and stability analysis of periodic solutions (including boundary periodic solutions and positive periodic solutions), and large-scale numerical simulations, this application provides a solid theoretical foundation and empirical evidence. Attached Figure Description

[0026] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0027] Figure 1 This is a flowchart of the method described in this application.

[0028] Figure 2 This is a schematic diagram of the system in this application.

[0029] Figure 3 This is a flowchart of the application.

[0030] Figure 4 This is a schematic diagram of the model.

[0031] Figure 5 for and Schematic diagram of boundary periodic solution.

[0032] Figure 6 for and Schematic diagram of boundary periodic solution.

[0033] Figure 7 This is a schematic diagram of TTP for different thresholds and durations of treatment.

[0034] Figure 8 This diagram illustrates the dynamic outcomes for patients under different strategies.

[0035] Figure 9 shows the thermodynamic diagram of TTP improvement under different parameters.

[0036] Figure 10 This is a distribution map of TTP improvement under different treatment durations.

[0037] Figure 11 Optimize the architecture diagram to enhance learning.

[0038] Figure 12 A schematic diagram of Kaplan-Meier survival curves under different reinforcement learning strategies. Detailed Implementation

[0039] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0040] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0041] It should be noted that similar labels and letters in the following figures indicate similar items. Therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures.

[0042] In the description of the embodiments of this application, it should be noted that if terms such as "upper," "lower," "horizontal," or "inner" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings, or the orientation or positional relationship commonly used when the product of the invention is in use, they are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation on this application. In addition, terms such as "first" and "second" are only used to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0043] Furthermore, the use of the term "horizontal" does not imply that the component must be absolutely horizontal, but rather that it can be slightly tilted. For example, "horizontal" simply means that its direction is more horizontal than "vertical," and does not mean that the structure must be completely horizontal, but can be slightly tilted.

[0044] In the description of the embodiments of this application, it should also be noted that, unless otherwise explicitly specified and limited, the terms "set," "install," "connect," and "link" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0045] The present application will now be described in further detail with reference to the accompanying drawings: See Figure 1 This application discloses a threshold-guided tumor treatment strategy decision-making method, including the following steps; S101 collects biomarker level data for dynamic monitoring of patients; S102 inputs the biomarker level data and corresponding detection time information into the pre-constructed and optimized tumor treatment strategy decision model to obtain the corresponding tumor adaptive treatment strategy; Among them, the pre-constructed and optimized tumor treatment strategy decision model is a threshold-guided dynamic system model optimized through reinforcement learning.

[0046] In practical applications, the decision-making model for tumor treatment strategies is as follows:

[0047] in, and These represent drug-sensitive tumor cells and drug-resistant tumor cells, respectively. and The intrinsic growth rates of the two types of cells; and This represents the competition coefficient, used to quantify the competitive inhibition strength between two cell types. This indicates the corresponding reduction rate in the survival rate of drug-sensitive cells under treatment; the parameter k represents the environmental carrying capacity, with the first subscript representing the system and the second subscript representing the cell. Therefore... and This indicates that under treatment, drug-sensitive tumor cells and drug-resistant tumor cells The maximum number that can be achieved; and This indicates the maximum number of the two cell types that can be achieved without treatment; Indicates the current time; Indicates the time period for treatment. Indicates the period during which no treatment will be administered; Indicates the initial number of tumor cells; The number of cells must be a positive real number.

[0048] It should be noted that the tumor treatment strategy decision-making model includes both a free system and a control system, as detailed below:

[0049] in, The differential equation representing the treatment state; The differential equation representing the non-treatment state; The differential equations for the dynamic behavior of a free system are as follows:

[0050] The differential equations for the dynamic behavior of the control system are as follows:

[0051] In practical applications, adaptive cancer treatment strategies include: Within a preset fixed time interval, determine whether the tumor size data exceeds a preset threshold. When the tumor size exceeds a preset threshold During this time period, the control system is activated. When the tumor size does not exceed During this period, the system is designated as a non-treatment period, and the free system is activated during this period. Treatment time period Non-treatment time period The details are as follows:

[0052] in, Indicates the prior treatment period; This indicates the prior non-treatment period.

[0053] It should be noted that the optimized tumor treatment strategy decision-making model includes: Construct a Markov decision process and define its core elements: state, action, reward, and state transition probability; Construct a minimal decision framework to compare different reinforcement learning strategies; The algorithm employs a near-end strategy optimization, leveraging the dual-head output structure and the time-series modeling capabilities of LSTM to extract key time-series features from dynamic changes, thereby achieving adaptive adjustment. In practical applications, a proximal strategy optimization algorithm is adopted, leveraging the dual-head output structure and the temporal modeling capabilities of the Long Short-Term Memory (LSTM) network to extract key temporal features from dynamic changes and achieve adaptive adjustment, as detailed below: Input layer receives environmental state And the dimensions are mapped to 32 dimensions through a linear transformation layer; Long Short-Term Memory (LSTM) network is introduced to process time-series data on tumor size. Its input layer has a dimension of 32 and its output layer has a dimension of 64. The output of LSTM is then connected to a shared deep feature processing network with the following hierarchical structure: 64-dimensional → 128-dimensional → 64-dimensional → 32-dimensional → 16-dimensional → 10-dimensional. This allows for the extraction of core information relevant to decision-making from high-level features. Advantage estimation is performed using a proximal policy optimization algorithm, which uses the advantage function to estimate the relative merits of a certain action under the current policy and guides the agent to choose a better action. The 10-dimensional features output from the shared network are input into the policy network and mapped to 31 dimensions through a linear layer. The action probability distribution is then output after passing through a Softmax activation function. .

[0054] like Figure 2 As shown in the figure, this application discloses a threshold-guided tumor treatment strategy decision-making system, including: The data acquisition module is used to collect data from dynamic monitoring of patients; The strategy decision module is used to input tumor size biomarker level data and corresponding detection time information into a pre-constructed and optimized tumor treatment strategy-guided decision model to obtain the corresponding tumor adaptive treatment strategy. Among them, the pre-constructed and optimized tumor treatment strategy decision model is a threshold-guided dynamic system model optimized through reinforcement learning.

[0055] Example: To make adaptive cancer therapy more aligned with clinical practice and avoid overtreatment and unrealistically frequent monitoring, this application provides an adaptive cancer therapy method based on a single-threshold treatment strategy. This method combines fixed, periodic monitoring with a threshold-guided strategy to construct a general modeling framework for periodic and intermittent therapy. Specifically, it includes the following steps: S1: Define the threshold-guided treatment and non-treatment periods.

[0056] In this application, the key to the single-threshold treatment strategy is defining the treatment period and the non-treatment period. Traditional modeling frameworks often use a periodic switching system, which consists of a control system ( ) and free systems ( It consists of two subsystems. Among them, Describe the growth of tumor cells in the untreated state and their interactions with other cell types; This describes the growth dynamics of tumor cells under therapeutic conditions. Specifically, it can be described as follows:

[0057] in, and Each is composed of a specific set of differential equations. The corresponding time period for treatment has been specified. The corresponding time period during which no treatment will be performed has been specified.

[0058] like Figure 4 As shown, in a traditional cycle-switching system, and With fixed and Alternate switching ( , These are the a priori treatment period and the a priori non-treatment period, respectively. , (For the monitoring period), this periodic switching system is suitable for modeling non-adaptive treatments, but ignoring the patient's condition may lead to overtreatment, thus violating the principles of adaptive treatment.

[0059] To address this issue, this application proposes a threshold-guided treatment plan: within a preset fixed time interval... During the (preliminary treatment period), the decision to proceed with treatment is dynamically made based on whether the tumor size exceeds a preset threshold. The specific steps are as follows: 1) When the tumor size exceeds a preset threshold This period is defined as the treatment period, and the control system is activated during this period. ); 2) When the tumor size does not exceed This period is defined as the non-treatment period, during which the free system is activated. ).

[0060] In addition, time period This refers to the a priori non-treatment period, i.e., the "treatment holiday" for intermittent tumor treatment without a threshold strategy.

[0061] Therefore, based on the above description, this application will and Defined as:

[0062] The above formula shows that at the detection time point After measuring the size of the patient's tumor, if the value is less than a preset threshold... If the patient does not receive treatment during this period, then no treatment will be given; otherwise, the patient will be given treatment for a specified duration. Treatment.

[0063] S2: Construct a threshold-guided dynamic system model.

[0064] Based on the treatment periods defined in S1, this application further constructs a dynamic system model, including a free system ( ) and control system ( Its dynamic behavior is defined by the following set of differential equations: 1) Free system ( : Used to describe the growth and competitive dynamics of tumor cells in the absence of treatment. Various mathematical models, including the exponential growth model, the logistic growth model, and the Gompertz growth model, have been widely used to simulate tumor growth; they can all be considered as free systems ( Potential candidate models for this study are as follows. This section investigates how threshold-guided cyclical therapy affects the dynamics of tumor growth based on the Logistic growth model, specifically in the following form:

[0065] in, and These represent drug-sensitive tumor cells and drug-resistant tumor cells, respectively. and This represents the intrinsic growth rate of the two types of cells; a larger value indicates a faster cell growth rate. and The competition coefficient represents the intensity of competitive inhibition between two cell types. A higher value indicates a greater competitive advantage for drug-resistant cells; correspondingly, A higher value indicates a greater competitive advantage for drug-sensitive cells; and This indicates environmental carrying capacity; the first subscript represents the system, and the second subscript represents the cell. Therefore... and These represent the state without treatment ( Drug-sensitive cells and drug-resistant cells The maximum number that can be achieved.

[0066] 2) Control system: Used to describe the dynamic changes of tumor cells under treatment conditions, its differential equation is as follows:

[0067] Compared to a free system, this system introduces parameters. (Representing the corresponding reduction rate in the survival rate of drug-sensitive cells under treatment) Simulates the inhibitory effect of treatment on cell growth. Specifically, set... , That is, the maximum number of both types of cells that can be reached after treatment is reduced. This indicates that the treatment had no effect on drug-resistant cells.

[0068] Therefore, based on the S1 general modeling framework, the specific model of adaptive therapy can be represented as follows:

[0069] Through the above construction method, this dynamic system can describe the growth and changes of tumors in both treated and untreated states, and capture changes in tumor burden under different treatment rhythms.

[0070] S3: Theoretical analysis and numerical simulation of dynamic behavior.

[0071] In dynamical systems, a periodic solution is a function of time, describing the trajectory of all system variables over time. For tumor growth models, a periodic solution implies that the tumor size fluctuates regularly within a certain range, and the tumor does not grow indefinitely or disappear. The existence and stability of periodic solutions can theoretically verify the feasibility of treatment strategies or plans, thereby helping to optimize treatment plans and providing quantitative tools for personalized medicine. Therefore, the existence and stability of periodic solutions in several specific cases are analyzed and demonstrated below, and their effectiveness is verified through numerical simulations.

[0072] 1) Dynamical systems under threshold-free strategies Without a threshold policy, the model is called a periodic switching system. This system operates in a fixed mode within a free system ( ) and control system ( The model alternates between treatment and non-treatment periods. In this case, the model's treatment and non-treatment periods are fixed and independent of tumor status:

[0073] When the number of drug-resistant cells is zero ( Under the boundary conditions of ), the dynamic equations of the subsystem corresponding to the periodically switching system can be expressed as:

[0074] It can be proven that when the parameters satisfy the following assumptions (denoted as...) The model has a stable boundary periodic solution. ):

[0075] in, , The definition is as follows:

[0076] Theoretical analysis shows that, under this fixed-period pattern, the system may also produce stable periodic solutions, but this requires a high treatment intensity ( ), tumor growth rate ( ) and cell competition intensity ( Factors such as treatment intensity and tumor growth rate must meet relatively stringent conditions. This means that the stability of its therapeutic effect is highly dependent on a complex set of parameters (such as treatment intensity and tumor growth rate), severely lacking robustness and difficult to adapt to individual differences among different patients. This also theoretically explains why it is difficult to achieve the expected therapeutic effect using a fixed cycle switching mode.

[0077] 2) Threshold-guided dynamical systems Based on a threshold-guided dynamics system framework, this application proposes... A periodic solution indicates that there is One treatment period and The periodic solution of a non-treatment period system model. More generally, for a system with a vanishing component (i.e., or A system that is equal to 0, its The periodic solution is the boundary periodic solution, denoted as . In particular, The periodic solution corresponds to the case where the patient is treated in all prior treatment periods, which is the same as the periodic solution of the periodic switching system.

[0078] i) Consider In the case where the system contains only one treatment period, analysis of the fixed point and the linearized periodic mapping yields the following results. There exists if and only if the preset threshold is satisfied. ( It depends on a specific threshold of the model parameters), and if the parameters satisfy the following assumptions (denoted as ). If the periodic solution is asymptotically stable, then the solution is locally asymptotically stable.

[0079] in, , The definition is as follows:

[0080] Therefore, the above results demonstrate that by introducing a threshold strategy, system stability no longer depends solely on fixed parameters. Instead, even with parameter uncertainties, stability can be improved by adjusting the threshold. and monitoring cycle The system adapts to changes, thus ensuring that treatment remains effective despite parameter fluctuations and that tumor size remains stable.

[0081] Figure 5 The threshold-guided control method of this application presents various stable boundary periodic solutions. The numerical simulation results show that the solid lines in the figure represent the dynamic changes of drug-sensitive cells, and the meanings of the long stripes are as follows: Blue area: Indicates cases where the tumor size exceeded the threshold during the prior treatment period. During the actual treatment period, the system dynamics are controlled by the control system ( )describe.

[0082] Gray area: Indicates that during the prior treatment period, the tumor burden did not exceed the threshold. During periods when treatment is not administered, the system dynamics remain governed by the free system ( )describe.

[0083] Blank area: Represents a fixed "treatment holiday," i.e., a priori non-treatment period, during which the system dynamics are determined by the free system ( )describe.

[0084] It can be seen that under various treatment modes, All exhibited stable periodic oscillations, indicating that the control method provided in this application can induce tumors into multiple controllable dynamic equilibrium states. Most importantly, compared to regimens requiring continuous drug administration, the intermittent treatment guided by the threshold strategy in this application significantly reduces the actual number of treatment triggers while ensuring effective tumor size suppression (achieving the same therapeutic effect), thereby potentially reducing cumulative drug dosage and toxic side effects.

[0085] ii) For In cases where the system contains at least two prior treatment periods with treatment, the existence and stability of periodic solutions can also be proven by constructing more complex periodic mappings. This means that the framework of this application can simulate complex clinical scenarios, which is something that traditional periodic switching systems cannot achieve.

[0086] Figure 6 Numerical simulation results of higher-order boundary periodic solutions under the threshold-guided control method of this application are presented. Subgraphs A, C, and E are... Boundary periodic solutions, subgraphs B, D, and F correspond to Boundary periodic solutions. Simulation results show that the method in this application can generate rich and stable higher-order periodic oscillation modes. This characteristic contrasts sharply with traditional fixed-cycle therapies, which can only generate simple oscillation modes, demonstrating the significant advantage of this application in simulating complex clinical dynamic behaviors. Furthermore, for the same type of higher-order periodic solutions (such as...), The system may exhibit different stable oscillation patterns, which is consistent with the common phenomenon in clinical practice that the same treatment plan will produce different treatment effects for different patients, indirectly demonstrating the personalized adaptability of the method.

[0087] iii) In the foregoing, only the boundary periodic solution was considered, i.e., the case containing only drug-sensitive cells. The existence and stability of the positive periodic solution (PPS) will be further discussed below. PPS refers to the condition where, under a threshold-guided treatment strategy, drug-sensitive cells (…) ) and drug-resistant cells ( The coexistence and stable oscillation of periodic solutions are used to characterize the state of periodic fluctuations in tumor burden under treatment in clinical practice, but which are not completely eliminated.

[0088] In a preferred embodiment, the special case of exponential growth of tumor cells in the untreated phase is considered, that is, the untreated phase... At this point, the system model is represented by the following equation:

[0089] Theoretical analysis based on periodic mapping can prove that when the competition coefficient and satisfy At most one That is, it either does not exist or exists uniquely; furthermore, when When the initial state of the tumor is near this periodic solution, the system trajectory will continue to converge to this oscillation mode, achieving long-term coexistence and controlled fluctuations of sensitive and resistant cells under periodic treatment; conversely, when... If a positive periodic solution exists, then the periodic solution is unstable. In this case, the system is highly sensitive to small perturbations and it is difficult to form predictable stable oscillations in clinical practice.

[0090] In actual clinical practice, This can be understood as a relatively mild competition between drug-sensitive and drug-resistant cells: they both inhibit each other and can coexist and oscillate under treatment pressure. This aligns with the goal of adaptive therapy—to retain a certain proportion of drug-sensitive cells through intermittent treatment, allowing them to suppress the expansion of drug-resistant cells in competition, thereby delaying the onset of drug resistance dominance and uncontrolled tumor growth. Therefore, theoretically, by estimating the competition coefficient of patient tumor samples and testing whether the above criteria are met, doctors can be informed to determine whether a treatment strategy guided by a certain threshold is effective and adjust the treatment plan accordingly.

[0091] Furthermore, mathematically, the existence problem of PPS can be equivalent to the solvability problem of a system of linear algebraic equations. Specifically, for a given... Periodic solution, in a dosing phase The time integrals of the two cell densities are defined above:

[0092] make It can be proven that if If it exists, then the linear algebraic system There exists a correct solution ( and (Uniquely determined by each system parameter). Therefore, the existence of the positive solution of the linear system under given model parameters can serve as a priori criterion for determining whether the corresponding positive periodic solution is possible. This provides a simple analytical tool for designing treatment parameters (such as threshold, treatment duration, monitoring frequency, etc.).

[0093] More generally, this application also considers more complex higher-order... ( In one embodiment, take That is, each treatment cycle and monitoring cycle are of the same length. Under this setting, two typical cycle patterns are considered: one is... Periodic solutions, i.e., each Each monitoring cycle contains One treatment period and one non-treatment period; the second is... The periodic solution means that every 5 monitoring cycles include 2 treatment periods and 3 non-treatment periods.

[0094] Similar to the results obtained from the aforementioned theoretical analysis, if or If a linear system exists, then its corresponding positive solution must also exist. This means that even in more complex higher-order cases, the existence of a clean linear system determined by the system parameters can still serve as a priori criterion for judging whether its corresponding positive periodic solution is possible.

[0095] S4: Comparison and analysis with other treatment strategies.

[0096] To verify the superiority of the method proposed in this application, the adaptive treatment strategy proposed in this application is further compared with other relevant strategies, and the time to tumor progression (TTP) based on different strategies is compared, that is, the time from the start of treatment to the occurrence of objective tumor progression (beyond baseline). (20% of the time length).

[0097] It is important to note that, for ease of comparison and analysis, the system is no longer built based on the Logistic growth model, but rather a two-population Lotka-Volterra model is used:

[0098] Within this framework, drug-sensitive cells and drug-resistant cells are respectively... and Proliferate at a rate and with and Both die naturally at a certain rate, and share a limited environmental carrying capacity. This leads to competition for resources. The administration of treatment interferes with the ability of drug-sensitive cells to utilize remaining resources. The drug's utilization inhibits the cell proliferation efficiency, and the therapeutic effect is expressed as the rate at which sensitive cells are killed, which is related to the growth rate of the sensitive cell population and the drug concentration. Proportional This is a proportionality constant. In addition, tumor size... It is represented by the sum of the number of the two types of cells.

[0099] Consider a binary dosing strategy, where the drug concentration is fixed at 1 during treatment and 0 during non-treatment. Therefore, Defined as a treatment function with a value range of 0 or 1, different treatment strategies correspond to different forms of treatment functions, as follows: Continuous treatment strategy, also known as maximum tolerated dose (MTD) strategy: This strategy involves the patient continuously receiving drug treatment at the highest dose they can tolerate. It is always equal to 1; Intermittent treatment strategy (IT): This involves alternating treatments within a pre-set fixed time cycle, with each treatment period... After that, it became the length. Treatment vacation, under this strategy If and only if ; Dual-threshold guided adaptive therapy strategy (AT50): based on tumor size relative to baseline The percentage is set with upper and lower thresholds, and the lower threshold... Upper threshold Treatment is paused when the tumor size falls below the lower threshold and resumed only when the tumor size rises back above the upper threshold. Under this strategy, Dynamically switches between 0 and 1; Single-threshold guided adaptive treatment strategy: This is the treatment strategy proposed in this application. However, based on the relationship between the treatment time and the detection cycle, this strategy can be further subdivided into: A single-threshold treatment strategy (AT-FSC) that covers the entire monitoring period, i.e. Under this strategy, If and only if and (The tumor size at the monitoring point exceeds the threshold); The single-threshold treatment strategy (AT-PSC) covers a portion of the detection cycle within the treatment window. Under this strategy, If and only if and .

[0100] Within the AT-PSC treatment framework proposed in this application, clinicians monitor tumor burden and update treatment strategies every 30 days. Unlike the fixed threshold (AT-FSC) algorithm used by Zhang et al., the innovation of this application lies in the fact that the treatment window only covers a portion of each monitoring cycle, and treatment decisions are made based on the optimal threshold obtained through search. and optimal treatment duration To be determined jointly.

[0101] Referring to Figure 9(A), compared to the original dual-threshold adaptive treatment strategy (AT50), the threshold-designed AT50 strategy shows that: time to tumor progression (TTP) decreases with the preset threshold. The increase in TTP exhibits an approximately monotonically rising trend, peaking near higher thresholds. The single-threshold treatment strategy (AT-FSC), with a treatment window covering the entire monitoring period, is also highly dependent on the choice of threshold parameters. In the optimal case, TTP increases by 13.2% relative to AT50 and by 66.7% relative to the maximum tolerated dose (MTD), further highlighting the crucial role of personalized threshold optimization in delaying tumor progression. The single-threshold treatment strategy (AT-PSC), with a treatment window covering a portion of the monitoring period, achieves the best overall TTP within a similar threshold range and is significantly superior to the AT-PSC strategy. However, it should be noted that when the threshold... Setting too high (close to or exceeding) When TTP drops sharply, it exhibits a "cliff effect".

[0102] Figure 9(B) further illustrates that when the preset threshold is fixed, and the treatment duration is... When optimized, the AT-PSC strategy achieved a 27.6% increase in TTP compared to the AT50 strategy and an 86.5% increase compared to the MTD strategy. It is worth noting that when treatment duration... When the treatment duration is set to 10-20 days, TTP can reach high levels, indicating that a full 30-day treatment cycle is not necessary. This finding has significant clinical implications: shortening the treatment duration can directly reduce the cumulative drug dosage, thereby helping to reduce treatment-related toxicities (such as bone marrow suppression, nausea, and fatigue), improve patient adherence and quality of life, and reduce healthcare costs.

[0103] To systematically validate the therapeutic advantages of the AT-PSC strategy, this application analyzed data from seven real prostate cancer patients, simulating five treatment strategies for each patient, with a maximum simulation time range of 5000 days. For determining the parameters of the AT-PSC strategy, a global search method was employed to systematically evaluate the performance of different combinations of preset thresholds and treatment durations, thereby determining the optimal treatment strategy based on time to tumor progression (TTP). Table 1 shows the optimal TTP for each patient under different treatment strategies, indicating that the AT-PSC treatment strategy proposed in this application is superior to all other treatment strategies.

[0104] Table 1. TTP under different treatment strategies

[0105] Figure 8 As shown in the representative results of one patient, the AT-PSC treatment strategy achieves more durable tumor control with fewer drugs, demonstrating a significant advantage over other strategies. This is mainly due to the dual optimization mechanism of the AT-PSC strategy: threshold... Ensure the precise timing of treatment initiation, and parameters The duration of treatment can be individually adjusted. The synergistic effect of both treatments effectively slows the proliferation of drug-resistant cell populations while maximizing the preservation of drug-sensitive cell populations. Therefore, equivalent or even better therapeutic efficacy can be achieved with fewer treatment days, significantly reducing the patient's overall drug burden.

[0106] S5: Sensitivity Analysis of Theoretical Parameters To evaluate the effectiveness of the AT-PSC strategy under different tumor biological parameters, the growth rate of drug-sensitive cells was simulated. Drug-resistant cell growth rate and duration of treatment The impact on extending TTP.

[0107] As shown in Figure 9, subfigure (a) illustrates the fixation of the growth rate of drug-resistant cells. At that time, how does TTP affect the growth rate of sensitive cells? and duration of treatment The variations occur in different combinations, while subgraph (b) shows the fixed... The results from both figures show that optimal improvement in TTP depends on the growth kinetics of the tumor cell population. In particular, in patients with rapid proliferation of drug-sensitive cells and slow growth of drug-resistant cells, fine-tuning the duration of treatment can significantly delay tumor progression. This further illustrates the importance of incorporating individualized growth parameters into treatment strategy design.

[0108] Figure 10 This study presents the distribution of the improvement in time to tumor progression (TTP) by the AT-PSC strategy compared to the AT-FSC strategy across different treatment durations. Overall, TTP improvement does not monotonically increase with treatment duration; instead, it reaches its optimum near the intermediate duration. The median TTP improvement is highest when the treatment duration is 12–16 days, indicating that in most cases, a “moderate” treatment duration provides the greatest survival benefit. With further extension of treatment duration (≥18 days), TTP improvement steadily declines, becoming more pronounced after 20 days, and the median TTP improvement approaches zero at 30 days. This demonstrates that excessively long continuous treatment not only fails to provide additional benefit but may even completely negate the strategy's advantages.

[0109] Extreme value analysis showed that some patients may gain significant benefits at almost any treatment duration, which further supports the previous conclusion that treatment strategies should be parameterized and optimized according to individual growth characteristics, and that a uniform fixed-cycle protocol is unlikely to be applicable to all tumor types. Individualized adjustment of treatment duration is crucial to achieving optimal efficacy.

[0110] Based on the above results, a 14-day treatment duration yielded the best overall TTP improvement (median gain of 208 days) and exhibited relatively high stability. Therefore, it is recommended to use a 14-day treatment course as the baseline treatment period in clinical practice, combined with real-time monitoring and dynamic adjustments to optimize the treatment regimen.

[0111] S6: Utilizing reinforcement learning to optimize adaptive treatment strategies As previously discussed, thresholding strategies based on dynamic system models (such as the Lotka-Volterra competition model) have been shown to significantly prolong time to tumor progression (TTP) and reduce cumulative drug dosage. However, existing strategies rely on fixed parameters (such as treatment duration). Optimization still requires experience-based adjustments and lacks real-time adaptive capabilities for individual patient dynamic responses. This limits the maximum effectiveness of the strategy in heterogeneous tumor populations and may lead to treatment failure or increased toxicity due to inappropriate parameter settings.

[0112] Reinforcement learning (RL) interacts with the environment through a trial-and-error mechanism, enabling it to learn optimal decision-making strategies in real time, making it highly suitable for simulating the dynamic process of tumor treatment. Therefore, to overcome the aforementioned limitations, this application employs reinforcement learning as an optimization framework to optimize the proposed adaptive treatment strategy. The specific steps are as follows: (1) Construction of reinforcement learning framework In reinforcement learning frameworks, problems are typically modeled as Markov decision processes (MDPs), which include states, actions, rewards, and state transition probabilities. These describe the probability that an agent will transition to a new state after taking an action in a given state, and the immediate reward received. The agent's goal is to learn a policy through interaction with the environment, i.e., to choose the appropriate action in a given state to maximize the expected cumulative reward.

[0113] In adaptive cancer therapy, the goal of the agent is to learn a treatment strategy and select the optimal treatment action (treatment duration) based on the patient's current condition. This maximizes the time to tumor progression. Therefore, the state space is defined as the normalized tumor size; the action space is the treatment duration selected at each decision point (selecting 0 means no treatment).

[0114] The reward function guides the model's optimization strategy and plays a crucial role in the algorithm's selection of actions under a given state. To achieve the goals of prolonging survival, reducing treatment burden, and delaying tumor progression, a multi-objective balancing scheme is adopted, with the specific reward function defined as follows:

[0115] in, The survival bonus is +0.1 for each day of survival. A treatment-saving bonus is awarded, which is +0.05 for each additional non-treatment day; Progress penalty (-0.1).

[0116] (2) Optimization of fixed continuous treatment time To initially verify the effectiveness of the reinforcement learning method, this application first constructs a minimal decision framework, in which the action space is restricted to two discrete options. This means that at the beginning of each decision cycle, a decision is made based on the patient's current tumor status: whether to proceed with treatment or continue treatment for 30 days. This strategy is denoted as... This is equivalent to an adaptive treatment strategy (AT-FSC) that covers the entire treatment window. However, preliminary results suggest that a fixed 30-day treatment duration may not be optimal, as overtreatment could accelerate the development of resistance.

[0117] Based on this, the action space is redefined as To design The strategy, as demonstrated by the experimental results, is... In comparison, this strategy achieved further improvement in TTP in most patients (an average increase of 18.5 months).

[0118] To determine the theoretically supported optimal treatment duration, a mathematical model based on tumor progression was used to formulate the following guidelines regarding treatment duration. Optimization issues:

[0119] By training using the dataset of a third patient, we obtained... The theoretical optimal duration of treatment was determined. This result indicates that a 19-day treatment window achieves the optimal balance between tumor suppression and minimizing side effects. Based on this theoretical finding, implementation... The strategy was tested and verified experimentally, showing that its median TTP was relatively high. It was further improved by about 7 months.

[0120] (3) Adaptive continuous treatment time To achieve truly personalized adaptive therapy, the limitation of fixed duration is removed, and the action space is expanded to a set of discrete choices. A total of 31 actions (referred to as Within this framework, The agent not only decides whether to treat, but also how long the treatment will last.

[0121] Specifically, this application uses the Proximal Policy Optimization (PPO) algorithm as the core of the reinforcement learning framework (see details for the architecture). Figure 11 To achieve autonomous learning and optimization of adaptive cancer treatment strategies, the steps are as follows: a) Environmental Status Input Input layer receives environmental state That is, the normalized tumor size, and the dimension is mapped to 32 dimensions through a linear transformation layer; b) Temporal Feature Extraction A Long Short-Term Memory (LSTM) network is introduced to process time-series data on tumor size. Its input layer has a dimension of 32 and its output layer has a dimension of 64. The output of the LSTM is then fed into a shared deep feature processing network with the following hierarchical structure: 64-dimensional → 128-dimensional (extended features) → 64-dimensional → 32-dimensional → 16-dimensional → 10-dimensional. This allows for the extraction of core information relevant to decision-making from the high-level features. c) Advantage estimation PPO utilizes the advantage function to estimate the relative merits of a given action under the current policy, thereby guiding the agent to choose a better action. To achieve more stable estimation of the advantage function, this application employs an integration of Generalized Advantage Estimation (GAE), which relies on the output of the value network. To calculate the advantage value.

[0122] In this framework, the input to the value network is the 10-dimensional features of the shared network output, followed by an independent linear layer that maps the 10-dimensional features to a 1-dimensional state value estimate.

[0123] d) Strategy Update The policy network also takes the 10-dimensional features from the shared network output as input and maps them to 31 dimensions (corresponding to the action space: treatment duration 0-30 days) through a linear layer. Finally, it outputs the action probability distribution through a Softmax activation function. .

[0124] During training, the probability ratio between the new and old policies is first calculated, and then the objective function is pruned. This is done through comparison. and The differences between them are used to control the scope of policy updates. Specifically, if If the value exceeds this range, the objective function will select the pruned value to avoid excessive policy updates. Finally, after 100,000 training iterations, the policy update is completed.

[0125] The specific objective function can be expressed as:

[0126] in, This is for advantage estimation; clip is a cutoff function, which means that when the independent variable exceeds the set upper / lower limit, the function will return the corresponding upper / lower limit. This is used to limit the magnitude of each update (usually set to 0.1 or 0.2).

[0127] e) Strategy Evaluation The system will continuously track the best TTP strategy and record the complete trajectory for subsequent analysis to ensure the convergence and reproducibility of the strategy.

[0128] Figure 12 Kaplan-Meier survival curves were presented comparing the same patient under four different strategies. The results showed that RL(0-30) achieved the maximum extension of TTP among all considered treatment options.

[0129] In addition, based on real data from 7 prostate cancer patients, this reinforcement learning strategy was compared with the AT-PSC strategy, and the results are shown in Table 2.

[0130] Table 2 Comparison of TTP between Reinforcement Learning and AAT-PSC strategies

[0131] The results showed that the RL strategy further improved the TTP of all patients, with an average increase of 60 days, representing a relative improvement of 3%. Notably, the RL strategy extended the TTP of patient 3 from 2,967 days to 3,180 days, equivalent to an increase of 8.19%, which further demonstrates the excellent ability of reinforcement learning methods to optimize treatment timing.

[0132] The core advantage of reinforcement learning (RL) strategies lies in their ability to generate highly personalized treatment plans based on each patient's unique tumor dynamics. Unlike the AT-PSC strategy, which relies on a fixed threshold, RL strategies can monitor tumor status in real time and evaluate future returns through a value function, thereby dynamically adjusting the treatment strategy during treatment for more refined treatment control. Therefore, compared to fixed strategies, RL strategies are more flexible and personalized, while also possessing strong interpretability.

[0133] This application provides a computer device according to an embodiment. The computer device of this embodiment includes: a processor, a memory, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the steps in the various method embodiments described above. Alternatively, when the processor executes the computer program, it implements the functions of each module / unit in the various device embodiments described above.

[0134] A computer program can be divided into one or more modules / units, one or more modules / units are stored in memory and executed by a processor to complete this application.

[0135] Computer equipment can be desktop computers, laptops, handheld computers, and cloud servers, among other computing devices. Computer equipment may include, but is not limited to, processors and memory.

[0136] The processor can be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc.

[0137] Memory can be used to store computer programs and / or modules. The processor performs various functions of the computer device by running or executing the computer programs and / or modules stored in the memory, and by calling the data stored in the memory.

[0138] When modules / units integrated into a computer device are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, the computer-readable medium does not include electrical carrier signals and telecommunication signals.

[0139] This application also provides a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform... Figure 3 The methods provided are among the various optional methods available in the code, so they will not be elaborated upon here.

[0140] The terms "first," "second," etc., in the specification, claims, and drawings of this application are used to distinguish different objects, not to describe a specific order. Furthermore, the term "comprising," and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, apparatus, product, or device that includes a series of steps or units is not limited to the listed steps or modules, but may optionally include steps or modules not listed, or may optionally include other step units inherent to these processes, methods, apparatuses, products, or devices.

[0141] In the embodiments of this application, the terms "module" or "unit" refer to a computer program or part of a computer program that has a predetermined function and works with other related parts to achieve a predetermined goal, and can be implemented wholly or partially using software, hardware (such as processing circuitry or memory), or a combination thereof. Similarly, a processor (or multiple processors or memory) can be used to implement one or more modules or units. Furthermore, each module or unit can be part of an overall module or unit that includes the functionality of that module or unit.

[0142] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, computer software, or a combination of both. To clearly illustrate the interchangeability of hardware and software, the components and steps of each example have been generally described in terms of functionality. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this application.

[0143] The methods and related apparatus provided in this application are described with reference to the method flowcharts and / or structural diagrams provided in this application. Specifically, each block of the method flowchart and / or structural diagram, as well as combinations of blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable device to create a machine, such that the instructions, which execute via the processor of the computer or other programmable device, generate instructions for implementing the process. Figure 1 A schematic diagram of one or more processes and / or structures. Figure 1 The computer program instructions may be stored in a computer-readable storage medium that can direct a computer or other programmable device to function in a particular manner, causing the instructions stored in the computer-readable storage medium to produce an article of manufacture including the instruction means, or to be transmitted via a computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.). The instruction means is implemented in the process. Figure 1 A schematic diagram of one or more processes and / or structures. Figure 1 The functions specified in one or more boxes. These computer program instructions may also be loaded onto a computer or other programmable device to cause a series of operational steps to be performed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable device for implementing the process. Figure 1 A process or multiple processes and / or structures illustrate the steps of the functions specified in one or more boxes.

[0144] The steps in the method of this application embodiment can be adjusted, combined, or deleted according to actual needs.

[0145] The modules in the device of this application embodiment can be merged, divided, and deleted according to actual needs.

[0146] The above-disclosed embodiments are merely preferred embodiments of this application and should not be construed as limiting the scope of this application. Therefore, any equivalent variations made in accordance with the claims of this application shall still fall within the scope of this application.

Claims

1. A threshold-guided tumor treatment strategy decision-making method, characterized in that, Includes the following steps; Collect biomarker level data for dynamic monitoring of patients; By inputting biomarker level data and corresponding detection time information into a pre-constructed and optimized tumor treatment strategy decision model, corresponding tumor adaptive treatment strategies can be obtained. The pre-constructed and optimized tumor treatment strategy decision-making model is a threshold-guided dynamic system model optimized through reinforcement learning.

2. The threshold-guided tumor treatment strategy decision-making method according to claim 1, characterized in that, The threshold-guided dynamic system model is as follows: in, and These represent drug-sensitive tumor cells and drug-resistant tumor cells, respectively. and The intrinsic growth rates of the two types of cells; and This represents the competition coefficient, used to quantify the competitive inhibition strength between two cell types. This indicates the corresponding reduction rate of drug-sensitive cell survival under treatment; parameter k represents environmental carrying capacity, with the first subscript representing the system and the second subscript representing the cell. and This indicates that under treatment, drug-sensitive tumor cells and drug-resistant tumor cells The maximum number that can be achieved; and This indicates the maximum number of the two cell types that can be achieved without treatment; Indicates the current time; Indicates the time period for treatment. Indicates the period during which no treatment will be administered; Indicates the initial number of tumor cells; This indicates that the number of cells is a positive real number.

3. The threshold-guided tumor treatment strategy decision-making method according to claim 2, characterized in that, The tumor treatment strategy decision-making model includes a free system and a control system, as detailed below: in, The differential equation representing the treatment state; The differential equation representing the non-treatment state; The system of differential equations governing the dynamic behavior of the free system is as follows: The differential equations for the dynamic behavior of the control system are as follows: 。 4. The threshold-guided tumor treatment strategy decision-making method according to claim 1, characterized in that, The tumor treatment strategy includes: Within a preset fixed time interval, determine whether the tumor size data exceeds a preset threshold. When the tumor size exceeds a preset threshold At this time, the period is defined as the treatment period, during which the control system is activated. When the tumor size does not exceed This period is defined as a non-treatment period, during which the free system is activated. Treatment time period Non-treatment time period The details are as follows: in, Indicates the prior treatment period; This indicates the prior non-treatment period.

5. The threshold-guided tumor treatment strategy decision-making method according to claim 1, characterized in that, Optimizing the tumor treatment strategy decision model includes: Construct a Markov decision process and define its core elements: state, action, reward, and state transition probability; Construct a minimal decision framework to compare different reinforcement learning strategies; By employing a near-end strategy optimization algorithm and leveraging the dual-head output structure and LSTM's time series modeling capabilities, key time series features are extracted from dynamic changes to achieve adaptive adjustment.

6. The threshold-guided tumor treatment strategy decision-making method according to claim 5, characterized in that, The proposed near-end strategy optimization algorithm, leveraging the dual-head output structure and the temporal modeling capabilities of the Long Short-Term Memory (LSTM) network, extracts key temporal features from dynamic changes to achieve adaptive adjustment, as detailed below: Input layer receives environmental state And the dimensions are mapped to 32 dimensions through a linear transformation layer; Long Short-Term Memory (LSTM) network is introduced to process time-series data on tumor size. Its input layer has a dimension of 32 and its output layer has a dimension of 64. The output of LSTM is then connected to a shared deep feature processing network with the following hierarchical structure: 64-dimensional → 128-dimensional → 64-dimensional → 32-dimensional → 16-dimensional → 10-dimensional. This allows for the extraction of core information relevant to decision-making from high-level features. Advantage estimation is performed using a proximal policy optimization algorithm, which uses the advantage function to estimate the relative merits of a certain action under the current policy and guides the agent to choose a better action. The 10-dimensional features output from the shared network are input into the policy network and mapped to 31 dimensions through a linear layer. The action probability distribution is then output after passing through a Softmax activation function. .

7. A threshold-guided tumor treatment strategy decision-making system, characterized in that, include: The data acquisition module is used to collect biomarker level data for dynamic monitoring of patients; The strategy guidance module is used to input biomarker level data and corresponding detection time information into a pre-built and optimized tumor treatment strategy decision model to obtain the corresponding tumor adaptive treatment strategy. The pre-constructed and optimized tumor treatment strategy decision-making model is a threshold-guided dynamic system model optimized through reinforcement learning.

8. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the steps of the method as described in any one of claims 1-6.

9. A computer-readable storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-6.

10. A computer program product, characterized in that, The computer program product includes computer instructions, a processor of a computer device reads the computer instructions, and the processor of the computer device executes the computer instructions to implement the steps of the method as described in any one of claims 1 to 6.

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