Non-small cell lung cancer fractionated radiotherapy progress prediction method based on mathematical mechanism model

Abstract

The application discloses a non-small cell lung cancer fractionated radiotherapy progress prediction method based on a mathematical mechanism model, which is based on in-depth research on tumor proliferation mechanism and radiotherapy killing effect, and simultaneously carries out segmented integral analysis on the fractionated radiotherapy process, constructs a mathematical mechanism model considering dynamic growth change of tumor volume in the fractionated radiotherapy process, and realizes non-small cell lung cancer fractionated radiotherapy progress prediction by using the mathematical mechanism model. The application can use low-cost python software to realize one-key personalized simulation of NSCLC fractionated radiotherapy progress, provides a new visual angle of numerical simulation for doctors, accurately predicts the volume change of the tumor of a patient after fractionated radiotherapy, and provides a recommended scheme, potential opportunity, reference dose and interval frequency and the like for intervention and intervention of radiotherapy planning.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of computer networks, and particularly relates to a non-small cell lung cancer fractionated radiotherapy progress prediction method based on a mathematical mechanism model. BACKGROUND

[0002] Lung cancer (LC) is one of the most invasive cancer types, and it has always shown its characteristics of high incidence and high mortality in the global range, among which non-small cell lung cancer (NSCLC) accounts for about 80-85% of the total number of lung cancer.

[0003] Radiotherapy, together with chemotherapy, surgery, targeted therapy and immunotherapy, is known as the "five horse-drawn carriages" of lung cancer treatment, and is the main force in cancer treatment, playing an irreplaceable role in the comprehensive treatment of lung cancer. More than 60% of cancer patients have radiotherapy intervention in the treatment process, and 40% of cancer cures are attributed to the role of radiotherapy. Among them, stereotactic body radiotherapy (SBRT) has become the best treatment plan for inoperable NSCLC, and the PACIFIC research mode of immunological consolidation treatment after concurrent radiotherapy and chemotherapy is the standard treatment for inoperable locally advanced NSCLC. Therefore, radiotherapy plays a crucial role in the treatment of lung cancer at all stages and throughout the entire process of lung cancer treatment.

[0004] Simulation prediction systems have gradually been used in clinical lung cancer radiotherapy progress, and the operation core depends on the built-in mathematical mechanism model logic. The mathematical model adjusts the parameters for numerical simulation, intuitively presents the prediction changes of lung cancer radiotherapy progress, provides a reference basis for the development of different individual plans, helps physical personnel to quickly and efficiently compare and screen out possible best plan intervals, and saves a lot of cost, playing an important role in radiotherapy planning and design. The model research for lung cancer radiotherapy progress prediction is still in its infancy, among which the mechanism model based on ordinary differential equations can effectively combine the theory of radiation biology and be applied most widely. At present, in the research of new fractionated radiotherapy prediction models for non-small cell lung cancer (NSCLC), different researchers have further explored and applied the Gompertz formula, three-component hypothesis and other contents, and proposed a tumor fractionated radiotherapy model based on Gompertz, a tumor fractionated radiotherapy model based on three components, a multi-component model based on the Logistic model, a TCP model based on tumor heterogeneity and regeneration, a TCP model incorporating "4R" and delayed regeneration effect, a fractionated radiotherapy model combining micro-dose kinetics, a mathematical model based on tumor volume dynamics, etc.

[0005] Some of the above models help to understand the invasion and growth of lung cancer cells, so that researchers can accurately and efficiently infer the development changes in lung cancer radiotherapy in vivo / in vitro environment, and also provide recommended programs, potential opportunities, reference doses and interval frequencies for the intervention and intervention of radiotherapy planning.

[0006] However, differential equation mechanism models are widely used in tumor radiotherapy progress prediction. The classical model form is simple and easy to understand, but it is difficult to fully explain the development and changes of complex tumors, so the analysis of specific problems needs to be reasonably expanded by researchers based on the principles of radiation biology. The mechanism model in the future is more closely combined with the theoretical mechanism. The current mathematical model is still in the initial stage. Considering the heterogeneity of tumors and other factors, there is no model that can summarize most of the tumors in the site, and the related research gap needs to be further explored by researchers. At the same time, how to incorporate more relevant parameters related to clinical and molecular pathology, imageomics, make the model more accurate, and more in line with real data needs researchers to further explore; In addition, complex mathematical formulas are often not conducive to the learning and understanding of clinicians, so attention should also be paid to the refinement of cancer types and the simplification of models in future mathematical model prediction. Therefore, "personalization", "precision" and "simplification" will become the research trend of future tumor models. SUMMARY

[0007] The purpose of the present application is to overcome the shortcomings of the prior art and provide a non-small cell lung cancer fractionated radiotherapy progress prediction method based on a mathematical mechanism model.

[0008] The purpose of the present application is achieved by the following technical solution: a non-small cell lung cancer fractionated radiotherapy progress prediction method based on a mathematical mechanism model, comprising the following steps:

[0009] 1) Construct a mathematical mechanism model considering the dynamic growth change of tumor volume during fractionated radiotherapy; wherein the mathematical mechanism model comprises a tumor volume dynamic growth change model, a tumor single radiotherapy model, a single radiotherapy period tumor volume change model considering that the tumor still has volume proliferation change during radiotherapy irradiation, and a radiotherapy interval tumor volume change model considering tumor proliferation during radiotherapy interval; the type of tumor is non-small cell lung cancer (NSCLC);

[0010] 2) input the fractionated radiotherapy input parameters to be predicted into the mathematical mechanism model, the input parameters comprising tumor initial volume, fractionated radiotherapy dose, fractionated radiotherapy duration, and radiotherapy interval time;

[0011] 3) The mathematical mechanism model calculates according to the preprocessed input parameters, and outputs the predicted volume of the tumor at different radiotherapy stages.

[0012] According to a preferred scheme of the present application, the tumor volume dynamic growth change model is used to represent the dynamic growth change of the tumor volume in the course of fractionated radiotherapy, which is a main formula of the mathematical mechanism model, and has a form of:

[0013] ;

[0014] In the formula, V is the final tumor volume after N times of radiotherapy, V0 is the initial tumor volume, Vg is the change of the tumor volume during the i-th radiotherapy, Vgi is the change of the tumor volume during the interval between the i-th radiotherapy and the (i+1)-th radiotherapy, and N is the total number of radiotherapies.

[0015] In the formula, the tumor volume change model during single radiotherapy is used to obtain the change of the tumor volume during the i-th radiotherapy, and the tumor volume change model during single radiotherapy considers that the tumor still has a volume proliferation change during the radiotherapy process, and has a form of:

[0016] ;

[0017] In the formula, t0 is the start time of the i-th radiotherapy, and is set to 0, t1 is the end time of the i-th radiotherapy; a is the intrinsic growth rate of tumor cells; α and β are coefficients corresponding to the items; d is the dose of the i-th radiotherapy; V i is the size of the tumor volume before the i-th radiotherapy, is a change function of the tumor volume with time during the i-th radiotherapy.

[0018] In the formula, the change of the tumor volume with time during the i-th radiotherapy is obtained through a tumor single radiotherapy model, and the tumor single radiotherapy model has a form of:

[0019] .

[0020] In the formula, the tumor volume change model during radiotherapy interval is used to obtain the change Vgi of the tumor volume during the interval between the i-th radiotherapy and the (i+1)-th radiotherapy, i and considers the tumor proliferation during the radiotherapy interval, and the tumor volume change model during radiotherapy interval has a form of:

[0021] ;

[0022] In the formula, b is the ratio of the intrinsic growth rate a to the tumor cell growth capacity k, i.e., b=a / k, is a set coefficient used to represent the "5Rs" proliferation of the tumor, and t2 is the start time of the (i+1)-th radiotherapy.

[0023] ​According to a preferred scheme of the present application, the step 3) is specifically: according to the time sequence of radiotherapy, the calculation is performed in cycles with a set time interval as a step; in each calculation, the number of tumor cell death is calculated according to the radiotherapy dose and time, considering the killing effect of radiotherapy on tumor cells; at the same time, the number of tumor cell proliferation is calculated, fully considering the tumor cell proliferation phenomenon in the process of radiotherapy and the tumor cell repair process after radiotherapy, and then the tumor volume is updated;

[0024] The tumor volume obtained in each calculation step is sorted and arranged according to the radiotherapy time sequence to form a complete radiotherapy process data sequence.

[0025] According to a preferred scheme of the present application, the coefficients a and b in the mathematical mechanism model are coefficients to be fitted, which are related to the user (patient) and different for different patients. In order to ensure the accuracy of tumor progression prediction, a fitting method is used to obtain the coefficients based on the radiotherapy data of the user that has been completed, wherein the radiotherapy data of the user that has been completed refers to the radiotherapy history data (including the initial tumor volume, the radiotherapy dose, and the actual tumor volume on the i-th day) that has been completed before the progression prediction is performed by using the progression prediction method of the present application. These data are usually the radiotherapy data of the user in the early stage of radiotherapy, which are used to reflect the influence of radiotherapy means on the tumor of the user. These data are collected and recorded in the current clinical radiotherapy treatment and are used as important reference data for subsequent specific radiotherapy scheme making. Therefore, when the method of the present application is used, these data already exist, and the present application does not limit the specific acquisition method of these data.

[0026] The fitting method is:

[0027] The radiotherapy data of the user that has been completed, including the initial tumor volume, the radiotherapy dose, and the actual tumor volume on the i-th day , i represents the number of days of graded radiotherapy, j represents the state before and after radiotherapy, j=1 represents before radiotherapy, and j=2 represents after radiotherapy;

[0028] Based on the radiotherapy data of the user that has been completed, the actual non-small cell lung cancer volume on the i-th day predicted by the mathematical mechanism model ; the objective function of the planning model is fitted by using the least square method as follows:

[0029] ;

[0030] The coefficients a and b are obtained by fitting.

[0031] The beneficial effects of the present application are that the present application establishes a new lung cancer radiotherapy prediction method based on radiobiology theory, further taking into account the dynamic proliferation of tumors during radiotherapy; at the same time, the present application first reveals the linear inhibition effect of cell proliferation before and after radiotherapy, greatly simplifying the modeling work for radiobiological effects in tumor proliferation, and obviously optimizing the simulation prediction effect.

[0032] The present application focuses on assisting fractionated radiotherapy clinical planning, the implementation method is simple, has broad clinical application prospects, and conforms to the clinical goal of killing and protecting in radiotherapy. The present application can effectively reduce social and medical costs, improve clinical work efficiency, and meet the needs of clinical practical application. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 Flow chart for non-small cell lung cancer fractionated radiotherapy progress prediction method;

[0034] Figure 2 Schematic diagram of data acquisition method for in vitro, in vivo and clinical model verification;

[0035] Figure 3 A549 cell line change and simulation result graph; wherein A549-2Gy, A549-4Gy, A549-6Gy, A549-8Gy are the actual OD value changes of A549 cell lines under the corresponding radiation amount; A549-2Gy-simulation, A549-4Gy-simulation, A549-6Gy-simulation, A549-8Gy-simulation are the simulation results under the corresponding radiation amount;

[0036] Figure 4 Linear relationship diagram of proliferation inhibition after radiotherapy;

[0037] Figure 5 A549 tumor proliferation effect-radiotherapy dose relationship scatter plot;

[0038] Figure 6 Nude mouse tumor volume change, tumor mass change, and simulated tumor volume comparison result graph; wherein 2Gy-simulation, 6Gy-simulation are the simulation results under the corresponding radiation amount;

[0039] Figure 7 Clinical patient tumor volume change and simulation prediction result schematic diagram. In the figure, '-week-simulation' represents the simulation result in weeks, '-day-simulation' represents the simulation result in days. DETAILED DESCRIPTION

[0040] Preferred embodiments of the present application will be described in more detail below. Although the following describes preferred embodiments of the present application, it is to be understood that the present application can be carried out in various forms and should not be limited by the embodiments set forth herein. Rather, these embodiments are provided so that this application will be thorough and complete, and fully convey the scope of the present application to those skilled in the art.

[0041] The present application will be described in detail below with reference to the accompanying drawings.

[0042] As Figure 1 shown, the present application is based on a mathematical mechanism model-based fractionated radiotherapy progression prediction method for non-small cell lung cancer, comprising the following steps:

[0043] 1) Constructing a mathematical mechanism model considering the dynamic growth change of tumor volume during fractionated radiotherapy; wherein the mathematical mechanism model comprises a tumor volume dynamic growth change model, a tumor single radiotherapy model, a single radiotherapy period tumor volume change model considering that the tumor still exists volume proliferation change during radiotherapy irradiation process, and a radiotherapy interval tumor volume change model considering tumor proliferation during radiotherapy interval; the tumor type is non-small cell lung cancer (NSCLC);

[0044] 2) Inputting the input parameters of the fractionated radiotherapy to be predicted into the mathematical mechanism model, the input parameters comprising tumor initial volume, fractionated radiotherapy dose, fractionated radiotherapy duration, and radiotherapy interval time;

[0045] 3) The mathematical mechanism model calculates according to the preprocessed input parameters, and outputs the predicted volume of the tumor at different radiotherapy stages.

[0046] Among them, step 1) is the core key of the present application, and the mathematical mechanism model considering the dynamic growth change of tumor volume during fractionated radiotherapy is theoretically established in the following sub-steps:

[0047] ①Establishing a tumor growth model

[0048] There are rich mathematical models to describe the normal proliferation pattern of tumors, among which the Logistic model (LM) and the Gompertz model (GM) are widely used. In this study, the LM model is used to better simulate the proliferation relationship of tumor volume:

[0049]

[0050] In the formula, p is the initial volume of the tumor, K is the growth capacity of the tumor, and a is the innate growth rate.

[0051] ②Establishing a tumor single radiotherapy model

[0052] Among the numerous models of the effect of radiation dose on tumor population, the most mature and widely used is the linear-quadratic model (L-Q model):

[0053]

[0054]

[0055] wherein, α, β are the first and second term coefficients, respectively, d is the radiation dose, V is the tumor volume size, and p is the initial volume.

[0056] Considering that the tumor still exists volume proliferation during radiotherapy, the above model is further modified to the construction of a single radiotherapy model based on dynamic tumor volume change:

[0057]

[0058]

[0059] wherein, V is the tumor volume size, and C is an arbitrary constant in the analytical solution.

[0060] ③Establishment of tumor fraction radiotherapy model

[0061] The difference from single radiotherapy is that the tumor proliferation during the interval of radiotherapy must be considered, as well as the influence of the "5Rs" radiation response existing in the surviving tumor cells during the fraction radiotherapy. Therefore, the tumor volume after a fraction radiotherapy is the sum of the tumor volume remaining after a radiotherapy and the tumor volume proliferated during the rest period after radiotherapy. Therefore, for the fraction integration of the LQ model and the tumor growth model, considering N times of fraction radiotherapy, the tumor volume dynamic growth change model is established:

[0062]

[0063] wherein, is the final tumor volume after N times of radiotherapy, is the initial tumor volume, is the change of tumor volume during the i-th radiotherapy, is the change of tumor volume during the interval of the i-th radiotherapy, and N is the total number of radiotherapy.

[0064] Change of tumor volume during the i-th radiotherapy Obtained from the tumor volume change model during single radiotherapy:

[0065]

[0066] Wherein, t0 is the start time of the i th radiotherapy, set to 0, t1 is the end time of the i th radiotherapy; a is the intrinsic growth rate of tumor cells, alpha and beta are the coefficients of the corresponding items, d is the i th radiotherapy dose, V i is the size of the tumor volume before the i th radiotherapy, is the function of the change of the tumor volume with time during the i th radiotherapy.

[0067] The tumor proliferation during the interval of the fractionated radiotherapy is different from the normal growth, researches show that the response of tumor cells to radiation is "repair", "redistribution", "re-oxygenation", "repopulation", "radiosensitivity" and other complex biological effects ("5Rs"). The mathematical model of independent simulation and analysis is undoubtedly complex and challenging, and the final result of the overall "5rs" effect is worthy of the goal, and the proliferation mode of the total number of tumor cells still surviving after radiotherapy has a certain functional relationship, which is replaced by mu, and this linear relationship will be applicable to the total number of tumor cells after radiotherapy.

[0068] Therefore, the tumor proliferation volume during the interval of the i th radiotherapy is is the integral of the logical model containing the "5Rs" effect:

[0069]

[0070] Wherein, b is the ratio of the intrinsic growth rate a and the tumor cell growth capacity k, that is, b=a / k, is a set coefficient for representing the "5Rs" proliferation of the tumor, t2 is the start time of the i+1 th radiotherapy.

[0071] The mathematical mechanism model considering the dynamic growth change of the tumor volume during the fractionated radiotherapy is as follows:

[0072]

[0073] In the process of applying the model, the application needs to obtain the coefficients alpha and beta based on the radiotherapy data of the user who has completed the current radiotherapy by using a fitting method.

[0074] The fitting method is:

[0075] The radiotherapy data of the user who has completed the current radiotherapy is obtained, and the radiotherapy data includes the initial tumor volume, the radiotherapy dose, the actual tumor volume of the i th day , i represents the number of days of the fractionated radiotherapy, j represents the state before and after radiotherapy, j=1 represents before radiotherapy, and j=2 represents after radiotherapy;

[0076] Based on the radiotherapy data of the user who has completed the current radiotherapy, the actual volume of non-small cell lung cancer of the i th day is predicted by using the mathematical mechanism model The objective function of the planning model is fitted by using the least square method as follows:

[0077]

[0078] The constraint conditions are as follows:

[0079] The coefficients α and β are obtained by solving the objective function fitting.

[0080] The model of the application is calculated in a time sequence according to the radiotherapy, and the calculation is performed in a certain time interval as a step. In each calculation, the number of tumor cell deaths is calculated according to the radiotherapy dose and time, considering the killing effect of radiotherapy on tumor cells; at the same time, the number of tumor cell proliferation is calculated according to the proliferation mechanism and repair ability of tumor cells, and the tumor volume is updated. In the calculation process, the re-proliferation of tumor cells during radiotherapy and the repair process of tumor cells after radiotherapy are fully considered, so as to simulate the real radiotherapy progress.

[0081] The tumor volume data obtained in each calculation step is arranged, arranged in the order of radiotherapy time, and a complete radiotherapy process data sequence is formed. Through data integration, the dynamic change data of tumor volume in the whole radiotherapy cycle is obtained, which provides comprehensive data support for subsequent analysis.

[0082] After the calculation and analysis are completed, the system will generate detailed numerical results. These conclusions include radiotherapy time, corresponding tumor predicted volume and other information.

[0083] In an optional scheme of the application, the system generates an interactive function image on a new Web page according to the calculation results. Taking a 2D image as an example, the horizontal coordinate represents the radiotherapy time, and the vertical coordinate represents the tumor volume. The user can view the function data such as tumor volume at the corresponding time point by moving the mouse to the image. In the upper right corner of the Web page, the user can see the operation toolbar. By clicking the “Picture Download” button, the current image can be saved to the local in png format; by clicking the “Zoom” button, the selected area on the image can be zoomed in; by clicking the “Pan” button, the content of other areas of the image in the coordinate system can be viewed by dragging the mouse; by clicking the “Zoom In” or “Zoom Out” button, all function images can be uniformly zoomed in or out; by clicking the “Auto Scale” button, the image will be automatically adjusted in size and position to make it perfectly aligned with the coordinate axis; by clicking the “Reset Axis” button, the image will be restored to the default display state. At the same time, the system will automatically download a new Excel table on the Web page, which records the data on which the generated image is based, including input parameters, intermediate data in the calculation process and final prediction results, so as to facilitate the user to back up and deeply analyze the data.

[0084] This study obtained simulated progression data of NSCLC tumor volume in various dimensions by nonlinear fitting of a fractionated radiotherapy planning model, and understood the simulated growth changes of NSCLC under fractionated radiotherapy. Through numerical simulation of the tumor growth model, theoretical proliferation data of tumor cells under normal growth mode under fractionated radiotherapy were obtained, and the actual reproliferation of tumor cells during fractionated radiotherapy of NSCLC was compared with the proliferation difference under normal growth mode.

[0085] To further illustrate the effectiveness of the method of the present invention, the following experimental results further illustrate the invention, wherein the data acquisition methods in in vitro, in vivo, and clinical model validation are as follows: Figure 2 As shown in A, B, and C.

[0086] Example 1: In Vitro Culture Experiment of NSCLC

[0087] ①Cell culture

[0088] In the study of NSCLC adenocarcinoma, the human A549 cell line was cultured in RPMI-1640 / DMEM medium containing 10% FBS at 37°C and 5% CO2.

[0089] ② Cell dilution and plating

[0090] Cells in the logarithmic growth phase were digested into a suspension using 0.25% trypsin solution, diluted tenfold with culture medium, and the cell concentration was calculated using a modified Boehringer's involucre. Based on the original solution concentration, the cell solution was diluted from 30*10... 4 The concentration of each sample was sequentially diluted 2, 4, 6, 8, 16, 32, and 64 times, and 100 μl of each solution was inoculated into 96-well plates and incubated at 37°C in a 5% CO2 environment.

[0091] ③ Cell concentration gradient measurement

[0092] After culturing for 2 hours to allow complete cell adhesion, the cells were aspirated and 110 μl of detection buffer (DMEM:CCK-8 at a ratio of 10:1) was added. Cells were then cultured for another 3 hours, and OD values ​​were read at 450 nm. Analysis and graphing were performed using Origin, and an appropriate cell suspension concentration was selected.

[0093] ④ Growth curve plotting

[0094] Take one dish of passaged NSCLC cells, ensuring the cells are in good condition and in the logarithmic growth phase. Wash and digest the cells, prepare a cell suspension, and count them. Then dilute the cell suspension to 1*102 4 / mL, assembled in 96-well plates, and placed in a 37°C, 5% CO2 environment for culture. Cell growth was observed every other day, and OD values were measured by group, and recorded for 5 days, and finally a growth curve was plotted.

[0095] 5. Fractionated radiotherapy curve plotting

[0096] Similarly, the cells were digested, counted, diluted to 10*10 4 / ml, and then plated for culture. One day after plating, the cells were irradiated at 0, 2, 4, 6, and 8 Gy under simulated clinical normal radiotherapy treatment procedures (SIMENS PM type linear accelerator, 6 MV X-ray, gantry 1800, field 10 cm x 10 cm, vertical source skin distance 100 cm, dose rate 200 cGy / min, room temperature). OD values were measured by group before and after daily radiotherapy, recorded for 4 days, and finally a fractionated radiotherapy growth curve was plotted.

[0097] Example Two NSCLC animal culture experiment

[0098] 1. Tumor formation in nude mice

[0099] The cells were recovered and cultured in a 37°C, 5% CO2 incubator, and after digestion and passaging, the cell suspension was collected and uniformly blown. The average number of cells per nude mouse was controlled to be about 5*10 6 cells / 200 μl. The tumor cell suspension with a cell number of 5*10 6 cells / 200 ul was subcutaneously injected into the selected BALB / c-nu nude mice, which were male, 4 weeks old, and weighed 18-20 g.

[0100] 2. Growth curve plotting of nude mice

[0101] The nude mice were bred in the animal center, and the growth environment temperature of the nude mice was controlled to be 20-26°C, and the humidity was 40%-70%. SPF level breeding feed and sterilized drinking water were used for breeding for 16 days. From the 10th day, the maximum length and short diameter of the tumor were observed and recorded every 3 days using a vernier caliper, and the body weight of the nude mice was measured using an electronic balance. The tumor volume estimation formula was: tumor volume (mm 3 ) = 0.5ab 2 (a is the long diameter of the tumor, and b is the short diameter of the tumor, in mm). The change of the tumor volume of the nude mice with time was calculated, and a tumor volume growth curve was plotted.

[0102] 3. Fractionated radiotherapy curve plotting of nude mice

[0103] The nude mice were randomly divided and anesthetized and fixed by 1.5% isoflurane, and the injection amount was 0.2 ml / 20 g. After anesthesia, the tumor was irradiated in the center of the radiotherapy center, and the irradiation method was the same as above. The nude mice were placed on the table, and the tumor position was adjusted to the center of the irradiation field, and each group was irradiated at 0, 2, 6 y doses. After irradiation, the nude mice were quickly taken out and placed in a sterile feeding cage for continuous feeding, and the body weight of the nude mice before and after radiotherapy and the tumor volume size after each radiotherapy were recorded for 3 days.

[0104] Example Three: Clinical retrospective analysis of NSCLC

[0105] Based on literature review, pre-experimental analysis of 4 patients with histologically confirmed stage III NSCLC who received simple adaptive radiotherapy at Heidelberg University Hospital in Germany from September 2018 to May 2019 was performed. This analysis was approved by the Ethics Committee of Heidelberg University Hospital (S278 / 2019).

[0106] Example Four: Numerical simulation and statistical analysis

[0107] The data of Examples One to Three were collected, and the actual tumor volume change data under fractionated radiotherapy of NSCLC at the cell, animal, and clinical levels were obtained by CCK8 counting, nude mouse weight and tumor diameter measurement, and clinical tumor target data collection (cell level OD value change reflects the effect of radiotherapy). At the same time, the progress of the NSCLC fractionated radiotherapy of Examples One to Three was predicted using the method of the present application, and the numerical simulation results were obtained, i.e. the predicted tumor volume change data of the simulation method of the present application (cell level experiment can obtain the predicted change of OD value of cell strain according to the prediction result). The simulation results at the cell experiment level are shown in Figure 3 , Figure 3 A, B, C, and D in Figure 6 , Figure 6 A, B, and C are the tumor volume change, tumor mass change, and simulated tumor volume comparison results of nude mice, respectively; the simulation results at the clinical level are shown in Figure 7 , Figure 7 A, B, C, and D are the tumor volume change (GTV1, GTV2, GTV3, and GTV4) and simulation prediction results of the four clinical patients, respectively. Understand the dynamic growth change of NSCLC under fractionated radiotherapy. Among them, in the cell experiment, the linear relationship between the actual re-proliferation amount of NSCLC during fractionated radiotherapy and the proliferation difference under normal growth pattern was obtained by linear regression analysis, and the proliferation rule pattern under the influence of "5Rs" radiobiological effect during fractionated radiotherapy was simplified, and the results are as followsFigure 4 As shown, Figure 4 In the diagram, A, B, C, and D correspond to the linear relationships between actual and simulated reproliferation rates at radiation doses of 2 Gy, 4 Gy, 6 Gy, and 8 Gy, respectively. Based on these relationships, further linear regression analysis revealed a linear dependence between the linear proliferation difference and the radiation dose, as shown in the following figures. Figure 5 As shown.

[0108] The statistical analysis in this study was performed using SPSS AU23.0. Statistical methods such as the Wilcoxon signed-rank test and paired-samples t-test were used to compare the actual progression of NSCLC under fractionated radiotherapy with the simulated progression using the method of this invention, verifying the applicability of the numerical simulation efficacy of the research model. Statistical results at the cellular level are shown in Table 1, at the animal level in Table 2, and at the clinical level in Table 3. All continuous variables are expressed as mean ± SD; P < 0.05 was considered statistically significant.

[0109] Table 1: Paired-sample Wilcoxon analysis of research models in cell-level experiments

[0110]

[0111] Table 2: Paired t-test analysis of research models in animal-level experiments

[0112]

[0113] Table 3: Paired t-test analysis of research models in clinical-level experiments

[0114]

[0115] The various embodiments of the present invention have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments.

Claims

1. A method for predicting the progress of fractionated radiotherapy for non-small cell lung cancer based on a mathematical mechanism model, characterized in that, The method comprises the following steps: 1) constructing a mathematical mechanism model considering dynamic growth changes of tumor volume during fractionated radiotherapy; wherein the mathematical mechanism model comprises a tumor volume dynamic growth change model, a tumor single radiotherapy model, a single radiotherapy period tumor volume change model considering that tumor still exists volume proliferation change during radiotherapy irradiation process, and a radiotherapy interval tumor volume change model considering tumor proliferation during radiotherapy interval; the type of tumor is non-small cell lung cancer; The tumor volume dynamic growth change model is in the form of: ； wherein Vf is the final tumor volume after N fractions of radiotherapy, Vo is the initial tumor volume, Vi is the change in tumor volume during the i-th fraction of radiotherapy, Vi is the change in tumor volume during the i-th fraction of radiotherapy, N is the total number of fractions of radiotherapy; The single radiotherapy period tumor volume change model is used to obtain the change of tumor volume during the i-th radiotherapy period The single radiotherapy period tumor volume change model takes into account the volume proliferation change of the tumor during the radiotherapy irradiation process, and has the form: ； where t0 is the start time of the i-th radiotherapy, set as 0, t1 is the end time of the i-th radiotherapy; a is the intrinsic growth rate of tumor cells; a, b are coefficients corresponding to items, d is the i-th radiotherapy dose, V i is the size of the tumor volume before the i-th radiotherapy, is the change function of the tumor volume with time during the i-th radiotherapy; The radiotherapy interval tumor volume change model is used to obtain a change Vgin the volume of the tumor during the i-th radiotherapy interval i , taking into account tumor proliferation during the radiotherapy interval, the radiotherapy interval tumor volume change model has the form: ； wherein b is the ratio of the intrinsic growth rate a to the tumor cell growth capacity k, i.e. b = a / k, is a set coefficient for expressing the "5Rs" proliferation of the tumor, and t2 is the start time of the i+1th radiotherapy; 2) inputting the input parameters of the fractionated radiotherapy to be predicted into the mathematical mechanism model, wherein the input parameters comprise tumor initial volume, fractionated radiotherapy dose, fractionated radiotherapy duration, and radiotherapy interval time; 3) the mathematical mechanism model calculates according to the preprocessed input parameters, and outputs the predicted volume of tumor at different radiotherapy stages.

2. The method of claim 1, wherein, the change in tumor volume over time during the ith radiation treatment is obtained from a tumor single radiation treatment model, which is: 。 3. The method of claim 1, wherein, The step 3) is specifically: according to the time sequence of radiotherapy, the calculation is performed in cycles with a set time interval as a step; in each calculation, the killing effect of radiotherapy on tumor cells is considered, the number of tumor cell deaths is calculated according to the radiotherapy dose and time; at the same time, the tumor cell repopulation phenomenon during radiotherapy and the tumor cell repair process after radiotherapy are fully considered, the number of tumor cell proliferation is calculated, and the tumor volume is updated.

4. The method of claim 3, wherein, In the step 3), the tumor volume obtained in each calculation step is arranged, arranged according to the radiotherapy time sequence, and a complete radiotherapy process data sequence is formed.

5. The method of claim 1, wherein, The coefficients α and β in the mathematical mechanism model are obtained by a fitting method based on the radiotherapy data that the user has completed.

6. The method of claim 5, wherein, The fitting method is: Obtaining the radiotherapy data that the user has completed at present, the radiotherapy data including the initial tumor volume, the radiotherapy dose, the actual tumor volume on the i-th day , i represents the number of days of fractionated radiotherapy, j represents the state before and after radiotherapy, j=1 represents before radiotherapy, and j=2 represents after radiotherapy; Based on the current user has completed the radiotherapy data, the actual volume of non-small cell lung cancer on the i day is predicted by using a mathematical mechanism model The objective function of the planning model is fitted by using the least square method as follows: ； The coefficients α and β are obtained by fitting.

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