Alpha nuclide drug in-vitro cellular response prediction method and system based on multi-module mathematical modeling and medium

Abstract

The invention discloses an alpha nuclide drug in-vitro cellular response prediction method and system based on multi-module mathematical modeling and a medium, and the method comprises the steps: constructing a basic parameter input module, a pharmacokinetic prediction module, a cell absorbed dose calculation module and a biological effect prediction module which are connected in sequence; a three-compartment dynamical model and a micro-dose learning point kernel convolution and DNA damage repair dynamical model are integrated, and full-chain and quantitative simulation from drug distribution, microscopic energy deposition to cell survival is achieved. The method overcomes the defects that an existing empirical model cannot accurately reflect the high LET characteristic of alpha particles, neglects the bystander effect and repair dynamics and the like, and the prediction precision is remarkably improved. According to the method, the curative effects of different drugs, cell lines and dosage schemes can be quickly simulated on a computer, the research and development cost and period are greatly reduced, and an efficient theoretical tool is provided for new drug screening and dosage optimization.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of radiobiology and mathematical modeling, and particularly relates to an alpha nuclide drug in vitro cell response prediction method and system based on multi-module mathematical modeling and a medium. BACKGROUND

[0002] Targeted alpha therapy (TAT) is a frontier direction in the field of radiotherapy. It utilizes the unique physical characteristics of high linear energy transfer and short range of alpha particles, which can efficiently kill tumor cells while minimizing radiation damage to surrounding normal tissues, and has great potential for clinical application, especially in the treatment of micrometastases and scattered tumors.

[0003] However, the current preclinical evaluation system for efficacy and safety of alpha nuclide drugs still relies heavily on traditional and relatively primitive in vitro cell experiments and animal models. These methods have significant and inherent limitations in terms of accuracy, efficiency and systematicity, which have become a key bottleneck restricting the rapid development of this new type of drug. The defects of the prior art are not single, but run through the entire chain from physical dose calculation to biological effect evaluation, which are embodied in the following aspects:

[0004] (1) Limitations of empirical dose response models: Currently, the prediction of in vitro cell survival rate relies mainly on empirical mathematical models based on average absorbed dose (Gy), such as the linear quadratic (L-Q) model. This type of model is derived from the study of low-LET radiation (such as X-rays and gamma rays), and its basic assumption is that energy deposition is uniform and biological effects are only related to total dose. However, the energy deposition of alpha particles is highly localized and random, and its microscopic dose distribution is extremely uneven. Direct application of L-Q model or similar empirical model cannot accurately reflect the unique biological effects of high-LET radiation, such as significantly higher relative biological effectiveness (RBE) and lower oxygen enhancement ratio (OER), resulting in systematic bias between predicted cell survival rate and experimental observation, and unable to provide reliable quantitative guidance for high-LET alpha nuclide therapy.

[0005] (2) Macrodosimetry misalignment at microscale: Traditional radiation dosimetry calculation is usually based on macroscopic average dose at organ or tissue level. When applied to cell or even subcellular scale, this average method seriously ignores the discrete distribution characteristics of alpha particle tracks, the geometric relationship between cell nucleus and radiation source (such as the localization of isotopes on cell membrane, cytoplasm or nucleus), and the dose heterogeneity within cell population. A cell may be hit by multiple alpha particles and die, while its neighboring cells may survive without being hit. This "all-or-nothing" dose distribution feature makes the average dose-based evaluation method unable to accurately correlate the final biological effect, thus making it difficult to guide individualized drug dose optimization and truly reflect the microscale efficacy of treatment.

[0006] (3) Lack of modeling of key biological processes or oversimplification: Most existing computational models are physically dose-driven, and the subsequent complex biological response processes are oversimplified or completely ignored. The dynamic uptake, internalization and metabolism of drugs between the culture medium and different compartments of cells (membrane, cytoplasm, nucleus) are not integrated, and the real scenario of the change of drug concentration over time cannot be simulated. Alpha particles mainly induce complex DNA double-strand breaks (DSB). Existing models generally lack modeling of the dynamic process of DSB induction and its subsequent repair through pathways such as non-homologous end joining (NHEJ) and homologous recombination (HR), and cannot reflect the influence of the difference in repair capacity of different cell lines on the final survival rate. In alpha nuclide therapy, the "bystander effect" of signal molecules released by irradiated cells inducing biological effects in adjacent unirradiated cells is significant, which can significantly expand the actual biological killing range. Most existing models do not take this key mechanism into account, resulting in a serious lack of prediction of cell population level effects.

[0007] (4) Cost and efficiency bottleneck in the development process: Due to the lack of a reliable theoretical tool to predict efficacy, the screening and dose optimization of new drugs rely heavily on a large number of, repeated and long-cycle in vitro clonogenic assays and animal experiments. This "trial-and-error" development model not only consumes high financial and time costs, but also limits the number of drug candidates and dose regimens that can be fully evaluated, becoming one of the key bottlenecks restricting the rapid development of alpha nuclide drugs. SUMMARY

[0008] In view of the shortcomings of the prior art, the present application provides an alpha nuclide drug in vitro cell response prediction method, system and medium based on multi-module mathematical modeling, which overcomes the shortcomings of the prior art and can accurately and efficiently simulate the in vitro cell response of alpha nuclide drugs on a computer before time-consuming and laborious experiments are performed, thereby providing strong theoretical support and guidance for early drug screening, dosimetry optimization and biological effect mechanism research.

[0009] To achieve the above object, the present application is realized by the following technical solutions:

[0010] A method for predicting in vitro cell response of alpha radionuclide drugs based on multi-module mathematical modeling, comprising the following steps:

[0011] Step S1: receiving and initializing parameters required for simulation, including experimental environment parameters, radionuclide parameters, drug and targeting information parameters, and cell line parameters;

[0012] Step S2: based on the parameters input in step S1, the time and space distribution of alpha radionuclide drugs in the culture medium, cell membrane and cytoplasm is dynamically simulated by using a multi-compartment kinetic model, and the data of the radioactivity of each compartment changing with time is output;

[0013] Step S3: based on the radioactivity distribution data output in step S2, the microdosimetry principle and dose point kernel convolution method are applied to calculate the absorbed dose rate of each cell nucleus;

[0014] Step S4: based on the absorbed dose rate of the cell nucleus output in step S3, the dynamic changes of the number of DNA double-strand breaks in the cell population are simulated by integrating DNA damage kinetics, repair kinetics and bystander effect, and finally the prediction results of the survival rate or the number of surviving cells changing with time are output.

[0015] Preferably, in step S2, the multi-compartment kinetic model is a three-compartment kinetic model, and the model simulates the dynamic distribution of radionuclide drugs in and out of cells by the following system of differential equations:

[0016] ;

[0017] ;

[0018] ;

[0019] wherein, is the chemical concentration of radionuclide drugs in the culture medium; is the chemical concentration of radionuclide drugs in the cytoplasm; is the number of bound targeting receptors on a single cell; is the total number of all targeting receptors on a single cell; is the volume of the culture medium; is the total number of cultured cells; is the volume of a single cell; is the association rate constant of the targeting carrier and the targeting receptor on the cell surface; is the dissociation rate constant of the targeting carrier and the targeting receptor on the cell surface; is the endocytosis rate constant of the cell surface targeting carrier-receptor complex. The degradation rate constant of the intracellular targeting vector-receptor complex in the cell.

[0020] Preferably, the step S2 further comprises a step of converting the chemical concentration into the radioactivity, in particular by the following formula:

[0021] ;

[0022] ;

[0023] ;

[0024] wherein, 、 、 are the radioactivity of the culture medium, the cytoplasm and the cell membrane, respectively; 、 are the initial radioactivity and the chemical concentration of the radionuclide drug in the culture medium; is the decay coefficient of the radionuclide.

[0025] Preferably, in the step S3, the absorbed dose rate of each nucleus is calculated by the following formula: which is calculated by the integral summation of the following parts:

[0026] the contribution of the radionuclide in the cytoplasm of the cell itself to the nucleus of the cell itself;

[0027] the contribution of the radionuclide on the cell membrane of the cell itself to the nucleus of the cell itself;

[0028] the contribution of the radionuclide in the cytoplasm and the cell membrane of the adjacent cells to the nucleus of the cell itself;

[0029] the contribution of the radionuclide in the culture medium to the nucleus of the cell itself.

[0030] Preferably, in the step S3, the absorbed dose rate of each nucleus is calculated by the following formula: which is calculated by the following formula:

[0031] ;

[0032] wherein, is the contribution of the radionuclide in the cytoplasm and the cell membrane of the cell itself to the nucleus of the cell itself; is the contribution of the radionuclide in the cytoplasm and the cell membrane of the adjacent cells to the nucleus of the cell itself; is the contribution of the radionuclide in the culture medium to the nucleus of the cell itself; is the dose point kernel function, wherein, represents the Euclidean distance between the source point and the target point; is the position of the radioactive source in space, is the center coordinate of the target position, i.e. the nucleus, is the mass of the nucleus.

[0033] Preferably, in the calculation of the absorbed dose rate of the nucleus, a piecewise variable step strategy is adopted for numerical integration, specifically:

[0034] In the near-field region at a distance of 0 to 2 microns from the nucleus, a fine grid step of 0.1 microns is used;

[0035] In the mid-field region at a distance of 2 to 20 microns from the nucleus, a medium grid step of 0.5 to 1.0 microns is used;

[0036] In the far-field region at a distance of 20 microns to the cutoff radius from the nucleus, a coarse grid step of 1 to 5 microns is used;

[0037] wherein the cutoff radius is determined by a preset dose energy accumulation contribution criterion:

[0038] ;

[0039] wherein, is 0.01 or 0.001.

[0040] Preferably, in the step S4, the change rate of the number of DNA double-strand breaks is described by the following equation:

[0041] ;

[0042] wherein, is the rate of DSB directly induced by radiation; is the DSB damage coefficient directly induced by radiation;

[0043] is the rate of DSB induced by bystander effect; is the DSB damage coefficient induced by bystander signal, is the concentration of bystander signal factor in the culture medium;

[0044] The change rate of the concentration of the bystander signal factor is described by the following equation:

[0045] ;

[0046] wherein, is the rate constant of bystander effect signal generation, is the rate constant of bystander effect signal decay;

[0047] , represent the rates of DSB repair through the fast and slow repair pathways; and the rates of change of the number of DSBs entering the fast and slow repair pathways are:

[0048] ;

[0049] ;

[0050] wherein, , are the number of DSBs entering the fast and slow repair pathways, respectively, , are the rate constants for the fast and slow repair pathways, respectively, , is the ratio of DSBs through the fast and slow repair pathways, and .

[0051] Preferably, before or during the step S1, there is further included a parameter fitting step for fitting unknown parameters in the model by an optimization algorithm, including:

[0052] fitting pharmacokinetic parameters based on time series data from cell uptake experiments;

[0053] fitting radiosensitivity parameters based on cell survival curves, conditioned medium experiments or gamma-H2AX focus kinetics data.

[0054] The present application also discloses an alpha radionuclide drug in vitro cell response prediction system for performing the above method, comprising:

[0055] a basic parameter input module for receiving and storing initial parameters; configured to:

[0056] provide a human-computer interaction interface or a data interface for receiving initial parameters input by a user or loading initial parameters from an external database; store and manage an internal database containing physical properties of radionuclides and biological properties of cell lines; integrate and initialize the received and called parameters to provide complete scene definition for subsequent simulation calculation;

[0057] a pharmacokinetic prediction module in communication connection with the basic parameter input module, for performing a multi-compartment kinetic simulation; configured to:

[0058] receive initial parameters from the basic parameter input module; run a multi-compartment pharmacokinetic mathematical model, which describes the dynamic transfer process of alpha radionuclide drugs in culture medium, cell membrane and cytoplasm through a set of coupled differential equations; perform a numerical integration algorithm to solve the differential equation set to obtain the spatiotemporal distribution of drug concentration and radioactivity in each compartment; output radioactivity distribution data to a cell absorbed dose calculation module;

[0059] a cell absorbed dose calculation module, communicatively connected with the pharmacokinetics prediction module, configured to calculate microdosimetry;

[0060] receive the spatiotemporal distribution of radioactivity from the pharmacokinetics prediction module; call pre-generated dose point kernel functions of radioactive particles stored in the database; perform microdosimetry calculation based on dose point kernel convolution integral, and adopt a piecewise variable step numerical integration strategy to balance the calculation efficiency and accuracy; calculate and output the absorbed dose rate data of each cell nucleus to the biological effect prediction module;

[0061] a biological effect prediction module, communicatively connected with the cell absorbed dose calculation module, configured to predict cell survival;

[0062] receive the absorbed dose rate data of the cell nucleus from the cell absorbed dose calculation module; run a biokinetics model integrating direct induction of DNA damage by radiation, bystander effect and DNA damage repair kinetics, which is described by a set of coupled differential equations; perform a numerical integration algorithm to solve the biokinetics differential equation set to dynamically simulate the changes of the number of DNA damage and the number of living cells in the cell population; output the final cell survival prediction result;

[0063] a parameter fitting module, communicatively connected with the basic parameter input module, configured to optimize model parameters based on experimental data.

[0064] receive user-provided experimental measurement data; call an optimization algorithm to iteratively optimize and estimate unknown parameters in the pharmacokinetics model or the biokinetics model with the experimental measurement data target; feed back and store the optimal parameter values fitted to the built-in database of the basic parameter input module for calling in prediction calculation.

[0065] The application further discloses a computer readable storage medium, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the method described above when executing the program.

[0066] This invention provides a method for predicting the in vitro cellular response of alpha nucleoside drugs based on multi-module mathematical modeling, which has the following advantages: By seamlessly connecting five modules—basic parameter input module, pharmacokinetics module, microdositology module, biological effect module, and parameter fitting module—a unified mathematical framework with end-to-end, multi-module coupling is constructed. This framework starts from drug binding to cells and gradually simulates its internalization distribution, microscale energy deposition, DNA damage initiation and repair, intercellular signal transduction, and finally cell survival. This allows the model to more realistically reflect the complete pathway and complex biological logic of alpha nucleoside drug action. Furthermore, by introducing microdositology and dose-point kernel convolution methods based on Monte Carlo simulation, the distorted average dose assumption is completely eliminated, enabling accurate reproduction of the discreteness, randomness, and high LET characteristics of alpha particle tracks. Moreover, by integrating DSB dual-pathway repair kinetics and a quantitative bystander effect model, the model can simulate the "shoulder" of the cell survival curve, hypersensitivity in the low-dose region, and the amplified swarm kill effect caused by the bystander effect. In addition, this invention can not only output the final cell survival rate, but also reveal the dynamic changes in the intermediate process. Attached Figure Description

[0067] To more clearly illustrate the technical solutions in this invention or the prior art, the accompanying drawings used in the description of this invention or the prior art will be briefly introduced below.

[0068] Fig. 1 A schematic diagram of the in vitro cellular response prediction system for α-nucleoside drugs of the present invention;

[0069] Fig. 2 A schematic diagram of the three-compartment model of pharmacokinetics in this invention. Detailed Implementation

[0070] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0071] Example 1, as Figs. 1-2 As shown, this invention provides a method for predicting the in vitro cellular response of α-nucleoside drugs based on multi-module mathematical modeling. This embodiment uses the prediction of radiopharmaceutical […]. 225 Taking the in vitro efficacy of Ac]PSMA-617 in the human prostate cancer cell line PC-3 as an example, the specific steps include:

[0072] Step S1: Receive and initialize the parameters required for the simulation, including experimental environment parameters, radionuclide parameters, drug and target information parameters, and cell line parameters; specifically including:

[0073] S1.1: Input experimental environment parameters:

[0074] Culture medium volume , set to 2 mL.

[0075] Total number of seeded cells , set to 1 x 10 5 cells.

[0076] Cell proliferation rate constant , calculated from PC-3 cell doubling time (e.g. 24 hours), set to 1.0 x 10 -5 S -1 .

[0077] Culture dish diameter, set to 35 mm.

[0078] Plating time , set to 24 hours.

[0079] Drug incubation time , set to 24 hours.

[0080] S1.2: Input radionuclide parameters:

[0081] User selects "Ac-225" from the system's built-in database. The system automatically calls its physical properties: half-life (9.92 days), complete decay chain information (including daughter nuclei such as Fr-221, At-217, and their branching ratios), and the energy spectrum (e.g. 5.83 MeV, 7.07 MeV, etc.) and emission probabilities of all alpha particles in the decay chain.

[0082] S1.3: Input drug and targeting information parameters:

[0083] Targeting vector: Select "PSMA-617".

[0084] Initial molarity : Set to 10 nM.

[0085] Initial radioactivity : Set to 50 kBq / mL.

[0086] S1.4: Input cell line parameters:

[0087] User selects "PC-3 (human prostate cancer cell line)" from the system's built-in cell library. The system automatically loads the pre-set parameters for this cell line:

[0088] Morphological parameters: Cell radius = 10 pm, Nucleus radius = 6 pm.

[0089] Radiosensitivity parameters (if known): e.g. coefficient of direct DSB induction by radiation = 20 DSB / Gy.

[0090] In this example, if the specific parameters of the interaction of PC-3 cells with 225 Ac]PSMA-617 are missing in the system's built-in database, the parameter fitting module is activated to guide the user to fit the unknown parameters by inputting experimental data. Specifically includes:

[0091] (1) Pharmacokinetic parameter fitting: if , , , , are unknown, the user inputs the uptake data of PC-3 cells for 225 Ac]PSMA-617 (or other radionuclide or fluorescent probe labeled PSMA-617) at different time points (such as 0, 0.5, 1, 3, 8, 24 hours) obtained by a gamma counter or a fluorescence microscope. Then, using the nonlinear least squares method, the optimal binding rate constant , dissociation rate constant , internalization rate constant , degradation rate constant and total number of cell surface receptors are automatically fitted by minimizing the residual error between the model predicted cell uptake curve and the experimental measured value.

[0092] (2) Radiosensitivity and repair parameter fitting: if , , , , are unknown, the user inputs three sets of experimental data: 1) PC-3 cell survival curves after different doses of alpha particle irradiation (using an alpha particle irradiation device or an alpha nuclide drug with known pharmacokinetics); 2) DSB focus formation and disappearance time kinetics data measured by γ-H2AX immunofluorescence staining after different doses of alpha particle irradiation of PC-3 cells; 3) Survival rate of unirradiated cells cultured in the medium (conditioned medium) of PC-3 cells irradiated with different doses and times of alpha particles or DSB focus formation and disappearance time kinetics data measured by γ-H2AX immunofluorescence staining. Then, using the Markov chain Monte Carlo method, the bystander signal production rate constant , bystander damage coefficient , fast repair rate constant , slow repair rate constant and repair pathway proportion , Equal parameters, so that the final prediction of cell survival rate and experimental measurement error is minimum.

[0093] Finally, the parameters obtained by fitting are stored in the system built-in database.

[0094] Step S2: Based on the parameters of step S1, the spatiotemporal distribution of alpha nuclide drugs in the culture medium, cell membrane and cytoplasm is dynamically simulated by using a multi-compartment kinetic model, and the data of radioactivity of each compartment changing with time are output; specifically including:

[0095] S2.1: Model initialization:

[0096] Set the initial conditions: , , .

[0097] Calculate the number of cells at the start of simulation (i.e. when the drug is added): .

[0098] S2.2: Numerical solution of kinetic equations:

[0099] The fourth-order Runge-Kutta method is used to numerically integrate the following three-compartment model differential equation group with a time step of , and the total simulation time is =24 hours.

[0100] ;

[0101] ;

[0102] ;

[0103] Wherein, is the chemical concentration of nuclide drugs in the culture medium; is the chemical concentration of nuclide drugs in the cytoplasm; is the number of targeted receptors that have been combined on a single cell; is the total number of all targeted receptors on a single cell; is the volume of the culture medium; is the total number of cultured cells; is the volume of a single cell; is the association rate constant of targeted carrier and cell surface targeted receptor; is the dissociation rate constant of targeted carrier and cell surface targeted receptor; is the endocytosis rate constant of cell surface targeted carrier-receptor complex; is the degradation rate constant of intracellular targeted carrier-receptor complex in the cell.

[0104] S2.3: Radioactivity conversion:

[0105] At each time step, convert the chemical concentration to radioactivity and account for nuclide decay:

[0106] ;

[0107] ;

[0108] ;

[0109] where, , , are the radioactivity of the medium, cytoplasm, and cell membrane, respectively; , are the initial radioactivity and chemical concentration of the nuclide drug in the medium; is the decay coefficient of the radionuclide.

[0110] S2.4: Output:

[0111] Final output , , Three time series curves accurately describe the spatial and temporal distribution of the radioactive source in the culture system, providing the "source term" for the next step of dose calculation.

[0112] This step realizes the prediction of the spatial and temporal distribution of the drug in the culture system, and can reflect the influence of different receptor binding characteristics on the accumulation of radioactivity in cells.

[0113] Step S3: Based on the radioactivity distribution data output by step S2, apply the principles of microdosimetry and dose point kernel convolution method to calculate the absorbed dose rate of each cell nucleus; specifically including:

[0114] S3.1: Dose point kernel preparation:

[0115] Use Monte Carlo tools (such as Geant4) to pre-calculate the dose point kernel function of different energy α particles and their secondary particles in water medium , and store it as a lookup table.

[0116] Call the pre-generated dose point kernel function of α particles of Ac-225 and all its daughter nuclei in water , and perform weighted summation on the energy deposition of particles at each level in the Ac-225 decay chain to calculate the dose point kernel function of the nuclide ;

[0117] S3.2: Dose rate calculation:

[0118] For each cell nucleus in the culture system, calculate its absorbed dose rate at time t ; absorbed dose rate of the cell nucleus is divided into three parts: self-cell endogenous dose, adjacent cell contribution and medium scattering, and weighted sum of energy deposition of each part is obtained by using the radionuclide pharmacokinetic module of the alpha radionuclide drug:

[0119] ;

[0120] wherein, is the contribution of the radionuclide in the cytoplasm and cell membrane of the self-cell to the cell nucleus of the self-cell; is the contribution of the radionuclide in the cytoplasm and cell membrane of the adjacent cell to the cell nucleus; is the contribution of the radionuclide in the medium to the cell nucleus; is the dose point kernel, wherein, , represents the Euclidean distance between the source point and the target point; is the position of the radiation source in space, is the target point position, i.e. the center coordinate of the cell nucleus, is the mass of the cell nucleus.

[0121] S3.3: Calculation optimization (piecewise variable step size integration):

[0122] In order to balance the calculation accuracy and efficiency, the convolution integral adopts a piecewise variable step size strategy:

[0123] Near field region (0-2 ): use fine grid, to accurately capture the high dose gradient of alpha particles within a very short range.

[0124] Medium field region (2-20 ): use medium grid, .

[0125] Far field region (20 - ): use coarse grid, . Wherein the cut-off radius is determined by the preset dose energy accumulation contribution criterion: ; to ensure that 99% of the dose contribution is included.

[0126] Step S4: DNA double-strand breaks (DSBs) can be induced in cells after receiving alpha particle irradiation, which is considered as the main initial event of the subsequent series of biological effects after alpha radionuclide irradiation. Its generation and removal are mainly affected by direct induction, bystander induction and DNA damage repair. Based on the absorbed dose rate of the nucleus output by step S3, this step simulates the dynamic changes of the number of DNA double-strand breaks in the cell population by integrating DNA damage kinetics, repair kinetics and bystander effect, and finally outputs the prediction results of cell survival rate or the number of surviving cells changing with time. Specifically, it includes:

[0127] S4.1 Kinetic equation construction and solution:

[0128] The nuclear dose rate is taken as input, together with the cell line-specific parameters defined in step S1, to construct a system of ordinary differential equations describing the kinetics of DSBs and cell survival.

[0129] Similarly, the fourth-order Runge-Kutta method is used for solution, and the simulation time covers the whole process from drug addition (t=0) to observation end (t=T).

[0130] S4.2 Core kinetic processes:

[0131] (1) DSB generation and repair:

[0132] Direct DSB generation: ; wherein, is the direct induction DSB damage coefficient of radiation.

[0133] Bystander effect DSB generation: irradiated cells can secrete bystander signal factors such as active nitrogen, active oxygen, exosomes, etc. into the culture medium. These secreted bystander signals can further induce DNA damage in cells. The present invention assumes that the cells in the culture dish are uniformly distributed, and the bystander signal factors generated after irradiation diffuse rapidly. The concentration of bystander signals in the culture medium is affected by the rate of cell secretion and degradation of bystander signal factors, and the rate of cell secretion of bystander signal factors is proportional to the induced DSB damage:

[0134] ;

[0135] wherein, is the bystander signal production rate constant, is the bystander signal decay rate constant.

[0136] By solving the equation of bystander signal concentration , calculate ; wherein, ​The DSB damage coefficient is induced by bystander signals.

[0137] DSB repair kinetics: The newly generated DSBs are proportionally allocated to fast (NHEJ) and slow (HR) repair pathways, and repaired with rate constants 、 respectively. The total repair rate is the sum of both. Specifically, 、 where ;

[0138] and 、 are the number of DSBs entering fast and slow repair pathways respectively, 、 are the repair rate constants for fast and slow repair pathways respectively;

[0139] ;

[0140] ;

[0141] where 、 are the proportions via fast and slow repair pathways, and .

[0142] The final DSB number change rate equation is: .

[0143] (2) Cell survival calculation:

[0144] The final cell number change is determined by both proliferation and DSB-dependent death:

[0145] ;

[0146] where is the cell proliferation rate constant, is the sensitivity constant for a specific cell line.

[0147] S5.3 Final output and result analysis:

[0148] After the module runs, the dynamic change curve of cell survival fraction in the entire simulation time and the final survival rate of experimental observation points (usually ) are output. At the same time, users can obtain dynamic data of all intermediate processes, such as drug distribution curve, cell nucleus dose rate history, DSB number change, bystander signal concentration, etc. These data have very high value for in-depth understanding of the mechanism of action of alpha nuclides and optimization of drug administration scheme.

[0149] The present application builds an end-to-end, multi-module coupled unified mathematical framework. The framework starts from the binding of drugs to cells, gradually simulates the internalization distribution, microscale energy deposition, DNA damage initiation and repair, intercellular signal transmission, and finally cell survival. Thus, the model can more truly reflect the complete path and complex biological logic of the action of alpha nuclide drugs, solve the fundamental problem of "model isolation" in the prior art, and provide an unprecedented overall perspective for understanding the action mechanism. In addition, by introducing a microdosimetry based on Monte Carlo simulation and a dose point kernel convolution method, the distorted average dose assumption is completely abandoned, and the discreteness, randomness and high LET characteristics of the alpha particle track can be accurately reproduced. And by integrating the DSB double-path (NHEJ / HR) repair kinetics and the quantitative bystander effect model, the model can simulate the "shoulder region" of the cell survival curve (reflecting the repair of sublethal damage), the hypersensitivity phenomenon in the low dose region, and the group killing expansion effect caused by the bystander effect. Compared with the traditional L-Q model, the prediction ability of the cell survival curve shape of the present model, especially the capture of the characteristics of high LET radiation, has achieved a qualitative leap. In addition, the present application not only outputs the final cell survival rate, but also reveals the dynamic changes of the intermediate processes, such as: the dynamic accumulation curve of the drug in different compartments of the cell. The history of the change of the nuclear dose rate with time. The real-time kinetics of DNA double-strand break generation and repair. The concentration change and contribution of bystander signaling molecules, etc. These intermediate data provide a unique, quantitative perspective for researchers to deeply understand the action mechanism of alpha nuclide (how the process is a key determinant of therapeutic effect). At the same time, the accurate description of the cell-scale dose-effect relationship by the model can provide important theoretical basis and pre-visualization platform for subsequent clinical microdosimetry calculation and optimization of individualized treatment planning, and strongly support the transformation from basic research to clinical application.

[0150] In the embodiment two, as shown in the figure, Fig. 1 the present application further discloses an alpha nuclide drug in vitro cell reaction prediction system for the method of the embodiment one, comprising:

[0151] a basic parameter input module, which is the front end and data cornerstone of the system, and is specifically realized as a graphical user interface or a standardized data configuration file interface. It is configured to perform the following operations:

[0152] 1) parameter receiving and verification: providing a form interface to guide the user to input or select the following four types of parameters:

[0153] experimental environment parameters: including culture medium volume , total number of planted cells , cell proliferation rate constant , culture dish diameter d, plating time Drug incubation time .

[0154] Radionuclide parameters: The user selects the nuclide name (e.g., Ac-225) from the drop-down menu. The system then automatically retrieves the nuclide's half-life, decay chain, decay branch ratios, and energy spectra of the emitted alpha and secondary particles from the built-in nuclide database.

[0155] Drug and target information parameters: including the name of the target carrier (e.g., PSMA-617) and the initial chemical concentration of the drug. (e.g., 1 nM) and initial radioactivity concentration (e.g., 1 kBq / mL).

[0156] Cell line parameters: The user selects the cell line name (e.g., human prostate cancer cells PC-3) from the drop-down menu. The system then retrieves the morphological parameters (e.g., cell radius) of that cell line from the built-in cell line database. Nuclear radius ) and initial radiation sensitivity parameters (such as radiation-induced DSB coefficient) ).

[0157] 2) Data Management: Integrates, formats, and temporarily stores user-input data and data retrieved from the built-in library, providing a unified and standardized initial condition for all subsequent computing modules.

[0158] The pharmacokinetic prediction module is communicatively connected to the basic parameter input module and receives all initialization parameters provided by the basic parameter input module. Its core is a numerical solver configured to perform the following operations:

[0159] 1) Model initialization: Based on the input parameters, set up the three-zone model (see attached diagram). Fig. 2 Initial conditions: , , And calculate the initial total number of cells. .

[0160] 2) Numerical solution: The fourth-order Runge-Kutta method is used, with a set time step (e.g., ...). Numerical solution of the following core dynamic differential equations.

[0161] ;

[0162] ;

[0163] ;

[0164] 3) Activity conversion and output: After the chemical concentration is obtained at each step, the chemical concentration is converted to radioactivity according to the following formula:

[0165] ;

[0166] ;

[0167] ;

[0168] The radioactivity distribution curve of each compartment can be obtained by numerical integration. Finally, the radioactivity time and space distribution data table of the entire simulation period is output to the next module.

[0169] The cell absorbed dose calculation module is in communication connection with the pharmacokinetics prediction module, and is configured to receive the radioactivity time and space distribution data output by the pharmacokinetics prediction module, and calculate the micro-dose distribution. The cell absorbed dose calculation module is configured to perform the following operations:

[0170] 1) Point kernel function call: according to the selected nuclide, the integrated dose point kernel function of the nuclide calculated in advance by a Monte Carlo tool (such as Geant4) is called from the built-in dose point kernel database ;

[0171] 2) Dose convolution calculation: for a single simulated cell in the culture system, the absorbed dose rate of its cell nucleus is calculated according to the following formula . The absorbed dose rate of the cell nucleus is divided into three parts: endogenous dose of itself, contribution of adjacent cells and medium scattering, and the energy deposition components of each part are weighted and summed with the nuclide drug time and space distribution curve obtained by the alpha nuclide drug pharmacokinetics module as the source term:

[0172] ;

[0173] 3) High efficiency integration implementation: when implementing convolution integration, a segmented variable step strategy and a truncated radius criterion are adopted to ensure high precision while optimizing calculation efficiency. Finally, the absorbed dose rate data of each cell nucleus at different time points are output.

[0174] The biological effect prediction module is in communication connection with the cell absorbed dose calculation module, and is configured to receive the absorbed dose rate data of the cell nucleus output by the cell absorbed dose calculation module, and predict the cell survival. The biological effect prediction module is configured to perform the following operations:

[0175] 1) Kinetic model solving: a coupled DSB kinetic and cell survival ordinary differential equation system is run, which takes the cell nucleus dose rate As input, the generation of dynamic simulation of DSB (directly with bystander effect), double-strand break repair and finally cell death / proliferation process. Details are described in Example 1.

[0176] 2) Numerical integration: Numerical integration method (e.g. 4th order Runge-Kutta method) is also used to solve the equation set, time step can be consistent with pharmacokinetic module or adjusted according to the speed of biological processes.

[0177] 3) Result generation and display: dynamically calculate and output key intermediate variables (e.g. , ) and the final results and the number of surviving cells curve over time. The system can visualize the predicted cell survival fraction and experimental data for comparison.

[0178] Parameter fitting module, as a supporting module, is bidirectionally connected with the basic parameter input module, and is used for optimizing model parameters based on experimental data. It is configured to perform the following operations:

[0179] 1) Data-driven fitting: when some parameters (e.g. certain new cell lines , , etc.) in the built-in database are missing, the module is activated. It guides the user to input the corresponding experimental data (e.g. time-uptake curve, cell survival curve, γ-H2AX focus dynamics data).

[0180] 2) Optimization algorithm execution: multiple optimization algorithms (e.g. nonlinear least squares method, particle swarm algorithm) are built-in, which automatically estimate the optimal set of unknown parameters by minimizing the error between the model prediction and the experimental observation.

[0181] 3) Database update: the reliable parameters obtained by fitting and verified are backfilled to the built-in database of the basic parameter input module, enriching the system knowledge base for subsequent prediction under the same conditions, realizing the self-learning and continuous optimization of the system.

[0182] The present application seamlessly connects the five modules of basic parameter input module, pharmacokinetics module, microdose module, biological effect module and parameter fitting module, and constructs an end-to-end quantitative simulation pipeline of "drug delivery-microscopic energy deposition-dynamic biological response". The present application completely changes the "model island" state of the prior art in which each process (such as drug distribution and dose calculation, dose and biological effect) is disconnected. The system can automatically use the output of the upstream module as the input of the downstream module, ensuring the coherence and consistency of the simulation process, so that the complex action mechanism of alpha nuclide drugs can be more truly reflected. The modular design of the system and the built-in database of the basic parameter input module make the system have strong versatility. Users only need to select or input new parameters (such as replacing nuclide Ac-225 with Bi-213, replacing targeted carriers, and selecting different cell lines) through the interface, and the system can automatically call the corresponding data and complete the simulation of the new scene without changing the core code. In addition, by introducing the parameter fitting module, the system is upgraded from a static prediction tool to a dynamic learning system. When facing prediction deviation caused by new cell lines or new drugs, the system can use a small amount of experimental data to automatically optimize and update the key unknown parameters in the model, so that the model can continuously adapt to the current research object.

[0183] In embodiment three, the present application further discloses a computer readable storage medium, comprising a memory, a processor and a computer program stored on the memory and executable on the processor, and the processor executes the program to implement the method of embodiment one. The computer readable storage medium is a non-transitory tangible medium, and its specific implementation forms include but are not limited to: electronic storage devices such as solid state disks, U disks, CF cards, SD cards, etc.; magnetic storage devices such as hard disks, magnetic disks, etc.; optical storage devices such as CD-ROM, DVD-ROM, Blu-ray discs, etc.; or other forms of storage media known to those skilled in the art. The computer program instruction sequence (i.e. code) for the processor to execute is stored in the medium in a physical way (such as magnetic domain orientation, optical reflection pit, floating gate transistor charge state, etc.).

[0184] When the storage medium is accessed or installed in a computing device (the computing device includes at least one processor, a memory coupled thereto, and necessary input / output interfaces), the computer program stored therein is loaded into the memory and executed by the processor, thereby instantiating and running the alpha nuclide drug in vitro cell response prediction system of embodiment one on the computing device. The execution of the program specifically implements the following processes:

[0185] Step one: system initialization;

[0186] After the program starts, it first creates and initializes an instance of the basic parameter input module in memory. This instance loads and manages the built-in nuclide database and cell line database, and waits for or receives user parameter input.

[0187] Step two: modularized collaborative prediction;

[0188] When the user completes parameter configuration through the graphical interface and starts the simulation, the program calls and executes the code of each functional module in a predetermined logical order:

[0189] Call pharmacokinetic prediction module code: this part of the code receives parameters, builds a three-compartment pharmacokinetic model, executes numerical solution algorithms, calculates the spatiotemporal distribution of radioactivity, and stores the result data in a designated area of memory.

[0190] Call cell absorbed dose calculation module code: this part of the code reads the output results of the pharmacokinetic module from memory, calls pre-stored dose point kernel function data, performs microdosimetric convolution calculation to obtain the absorbed dose rate of cell nuclei, and passes the results to the next module.

[0191] Call biological effect prediction module code: this part of the code reads dose data, runs biological kinetic models, solves differential equations of DNA damage and repair, bystander effect, and cell survival, and finally generates cell survival prediction results.

[0192] Step three: result output and interaction;

[0193] The program presents the final prediction results (such as cell survival curves, intermediate process kinetic graphs, and data tables) to the user through the graphical user interface.

[0194] When needed, the program can call parameter fitting module code, which guides the user to input experimental data, executes optimization algorithms, completes parameter estimation, and updates the built-in database.

[0195] Through the computer-readable storage medium of the embodiment, a complex multi-module prediction system can be solidified into a standardized software product, which can be easily copied, distributed, and installed on any compatible computing device, greatly improving the practicality and generalizability of the invention. The program instructions in the storage medium ensure that each execution follows exactly the same data processing logic and algorithm flow, eliminating errors that may be introduced by human operation, ensuring the consistency and repeatability of the prediction results, which is crucial for scientific research and new drug evaluation. Users do not need to be concerned about the underlying complex mathematical models and code implementation, but can obtain professional prediction results through the interactive interface. The medium and its program are independent of a specific biological laboratory, so that the computational simulation can be used as a standard service shared and used among different teams.

[0196] The above examples are only used to illustrate the technical solutions of the present application, but not to limit the present application; although the present application has been described in detail with reference to the foregoing examples, those ordinarily skilled in the art should understand: the technical solutions recorded in the foregoing examples can be modified, or some technical features can be replaced equivalently; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for predicting the in vitro cellular response of α-nucleoside drugs based on multi-module mathematical modeling, characterized in that: Includes the following steps: Step S1: Receive and initialize the parameters required for the simulation, including experimental environment parameters, radionuclide parameters, target vector parameters, and cell line parameters; Step S2: Based on the parameters input in Step S1, the spatiotemporal distribution of α-nucleoside drugs in the culture medium, cell membrane and cytoplasm is dynamically simulated by using a multi-compartment kinetic model, and the data of the change of radioactivity in each compartment over time are output. Step S3: Based on the radioactivity distribution data output in Step S2, the absorbed dose rate of a single cell nucleus is calculated using the principles of microdosimetry and the dose point kernel convolution method. Step S4: Based on the nuclear uptake dose rate output in Step S3, the dynamic changes in the number of DNA double-strand breaks in the cell population are simulated by integrating DNA damage kinetics, repair kinetics, and bystander effect, and finally the predicted results of cell survival rate or number of surviving cells over time are output.

2. The method for predicting in vitro cellular responses of α-nucleoside drugs based on multi-module mathematical modeling according to claim 1, characterized in that: In step S2, the multi-compartment kinetic model is a three-compartment kinetic model, which simulates the dynamic distribution of radionuclide drugs inside and outside the cell using the following set of differential equations: ； ； ； in, The concentration of radionuclide drugs in the culture medium; The concentration of nucleoside drugs in the cytoplasm; This represents the number of target receptors that have been bound on a single cell. The total number of all target receptors on a single cell; This refers to the volume of the culture medium. Total number of cultured cells; Volume of a single cell; This represents the binding rate constant between the targeting vector and the cell surface targeting receptor; This represents the dissociation rate constant between the targeting vector and the cell surface targeting receptor; is the endocytosis rate constant of the cell surface targeting carrier-receptor complex; This is the degradation rate constant of the intracellular targeting carrier-receptor complex within the cell.

3. The method for predicting in vitro cellular responses of α-nucleoside drugs based on multi-module mathematical modeling according to claim 2, characterized in that: Step S2 further includes the step of converting chemical concentration into radioactivity, which is specifically achieved through the following formula: ； ； ； in, , , These are the radioactivity levels of the culture medium, cytoplasm, and cell membrane, respectively. , The initial radioactivity and chemical concentration of the radiopharmaceutical in the culture medium; is the attenuation coefficient of the radioactive nuclide.

4. The method for predicting in vitro cellular responses of α-nucleoside drugs based on multi-module mathematical modeling according to claim 1, characterized in that: In step S3, the absorbed dose rate of each cell nucleus It is calculated by summing the integrals of the following parts: The contribution of intracellular radionuclides to their own nucleus; The contribution of radioactive isotopes on the cell membrane to the cell nucleus; The contribution of radionuclides in the cytoplasm and cell membrane of neighboring cells to the cell nucleus; The contribution of radionuclides in the culture medium to the cell nucleus.

5. The method for predicting in vitro cellular responses of α-nucleoside drugs based on multi-module mathematical modeling according to claim 4, characterized in that: In step S3, the absorbed dose rate of a single cell nucleus It is calculated using the following formula: ； in, The contribution of radionuclides in the cytoplasm and cell membrane of one's own cells to the cell nucleus; The contribution of radionuclides in the cytoplasm and cell membrane of neighboring cells to the cell nucleus; The contribution of radionuclides in the culture medium to the cell nucleus; Let be the dose point kernel function, where , representing the Euclidean distance between the source and the target; The location of the radioactive source in space. The target location is the coordinate of the center of the cell nucleus. For cell nucleus mass.

6. The method for predicting in vitro cellular responses of α-nucleoside drugs based on multi-module mathematical modeling according to claim 1, characterized in that: In calculating the absorbed dose rate in the cell nucleus, a piecewise variable step size strategy is used for numerical integration, specifically as follows: In the near-field region, which is 0 to 2 micrometers from the cell nucleus, a fine grid step size of 0.1 micrometers is used; In the mid-field region, 2 to 20 micrometers from the cell nucleus, a medium grid step size of 0.5 to 1.0 micrometers is used; Within 20 micrometers of the cell nucleus to the cutoff radius In the far field region, a coarse grid step size of 1 to 5 micrometers is used; Among them, the cutoff radius Determined by a preset dose-energy cumulative contribution criterion: ； in, Take 0.01 or 0.

001.

7. The method for predicting in vitro cellular responses of α-nucleoside drugs based on multi-module mathematical modeling according to claim 1, characterized in that: In step S4, the number of DNA double-strand breaks The rate of change is described by the following equation: ； in, , representing the rate of DSB generation directly induced by radiation; The direct radiation-induced DSB damage coefficient; , representing the DSB rate induced by the bystander effect; The damage coefficient of bystander signal-induced DSB. The concentration of bystander signaling factor in the culture medium; The concentration of the bystander signal factor The rate of change is described by the following equation: ； in, The rate constant is generated for the bystander effect signal. The bystander effect signal decay rate constant; , representing the DSB repair rate through the fast and slow repair pathways; the rate of change in the number of DSBs entering the fast and slow repair pathways are respectively: ； ； in, , These represent the number of DSBs entering the fast and slow repair pathways, respectively. , These are the rate constants for the fast and slow repair pathways, respectively. , The ratio of DSB repair pathways via fast and slow repair methods, and .

8. The method for predicting in vitro cellular responses of α-nucleoside drugs based on multi-module mathematical modeling according to claim 1, characterized in that: Before or during step S1, a parameter fitting step is also included, which is used to fit the unknown parameters in the model using an optimization algorithm, including: Pharmacokinetic parameters were fitted based on time-series data from cellular uptake experiments. Radiation sensitivity parameters were fitted based on cell survival curves, conditioned medium experiments, or γ-H2AX focal kinetic data.

9. An in vitro cellular response prediction system for α-nucleoside drugs used to perform the method according to any one of claims 1 to 8, characterized in that: include: The basic parameter input module, used to receive and store initialization parameters, is configured as follows: Provides a human-computer interaction interface or data interface for receiving initial parameters input by the user or loading initial parameters from an external database; stores and manages a built-in database containing the physical properties of radionuclides and the biological properties of cell lines; integrates and initializes the received and called parameters to provide a complete scene definition for subsequent simulation calculations; The pharmacokinetic prediction module, communicatively connected to the basic parameter input module, is used to perform multi-compartment kinetic simulations; it is configured as follows: Receive initial parameters from the basic parameter input module; run a multi-compartment pharmacokinetic mathematical model, which describes the dynamic transfer process of α-nucleoside drugs in the culture medium, cell membrane and cytoplasm through a set of coupled differential equations; The numerical integration algorithm is executed to solve the system of differential equations to obtain the spatiotemporal distribution of drug concentration and radioactivity in each compartment; the radioactivity distribution data is output to the cell uptake dose calculation module. A cell absorption dose calculation module, communicatively connected to the pharmacokinetics prediction module, is used to calculate the microscopic dose distribution; it is configured as follows: It receives spatiotemporal distribution data of radioactivity from the pharmacokinetics prediction module; calls the pre-generated radioactive particle dose point kernel function stored in the database; performs microdosimetry calculations based on dose point kernel convolution integrals, and adopts a piecewise variable step size numerical integration strategy to balance computational efficiency and accuracy. Calculate and output the absorbed dose rate data for each cell nucleus to the biological effect prediction module; A biological effect prediction module, communicatively connected to the cell uptake dose calculation module, is used to predict cell survival; it is configured as follows: Receives absorbed dose rate data of the cell nucleus from the cell absorbed dose calculation module; runs a biokinetic model that integrates radiation-induced DNA damage, bystander effect and DNA damage repair dynamics, which is described by a set of coupled differential equations; Numerical integration algorithms are executed to solve the biodynamic differential equations, dynamically simulating the changes in the number of DNA damage and the number of viable cells in the cell population; the final cell survival prediction results are output. The parameter fitting module, which is communicatively connected to the basic parameter input module, is used to optimize model parameters based on experimental data; it is configured as follows: Receive experimental measurement data provided by users; The optimization algorithm is invoked to iteratively optimize and estimate the unknown parameters in the pharmacokinetic or biokinetic model, using experimental measurement data as the target. The optimal parameter values ​​obtained by fitting are fed back and stored in the built-in database of the basic parameter input module for use in prediction calculations.

10. A computer-readable storage medium comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the method as described in any one of claims 1 to 8.

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