CN115312153B - Intelligent monitoring and optimized drug delivery system for cancer chemotherapy based on multi-stage Gaussian pseudospectral method - Google Patents
Intelligent monitoring and optimized drug delivery system for cancer chemotherapy based on multi-stage Gaussian pseudospectral methodInfo
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Abstract
本发明公开了一种基于多阶段高斯伪谱法的癌症化疗智能监测与优化给药系统，包括，肿瘤大小监测模块和肿瘤部位药物浓度检测模块一端与数据指标显示模块电连接，另一端与药物作用下肿瘤生长模型拟合模块电连接，药物作用下肿瘤生长模型拟合模块再与癌症化疗优化给药模型与性能参数设定模块连接；耐药细胞数检测模块和心脏毒性检测模块一端与数据指标显示模块电连接，另一端与癌症化疗优化给药模型与性能参数设定模块连接；癌症化疗优化给药模型与性能参数设定模块与数据处理模块连接，数据处理模块再与抗癌药物给定模块连接，抗癌药物给定模块与数据指标显示模块连接。使用本系统医生可实时查看化疗进程中相应的指标值，系统计算出抗癌药物给定值。
The present invention discloses an intelligent monitoring and optimized drug delivery system for cancer chemotherapy based on a multi-stage Gaussian pseudospectral method, comprising: a tumor size monitoring module and a tumor site drug concentration detection module, one end of which is electrically connected to a data indicator display module, and the other end is electrically connected to a tumor growth model fitting module under drug action, which is further connected to a cancer chemotherapy optimized drug delivery model and performance parameter setting module; a drug-resistant cell number detection module and a cardiotoxicity detection module, one end of which is electrically connected to a data indicator display module, and the other end is connected to a cancer chemotherapy optimized drug delivery model and performance parameter setting module; the cancer chemotherapy optimized drug delivery model and performance parameter setting module is connected to a data processing module, which is further connected to an anticancer drug setting module, which is further connected to a data indicator display module. Using this system, doctors can view the corresponding indicator values during chemotherapy in real time, and the system calculates the given values of anticancer drugs.
Description
Technical Field
The invention belongs to the field of chemotherapy administration optimization control, and relates to an intelligent monitoring and optimizing administration system for cancer chemotherapy based on a multi-stage Gaussian pseudo-spectrum method.
Background
As the incidence of cancer increases year by year, how to treat cancer more effectively is attracting attention. Chemotherapy is one of the most effective means of treating cancer, and related studies have been underway by workers in various fields. A system that can monitor the course of chemotherapy in real time and perform optimal dosing is of great importance in improving the effectiveness of chemotherapy and in reducing the cost of chemotherapy.
Therefore, the research on the high-efficiency control algorithm realizes the optimal scheduling of the anticancer drugs and the monitoring of the related indexes of the chemotherapy process, and has great theoretical value and effective application value for improving the survival time and the life quality of cancer patients.
Disclosure of Invention
In view of the above, the invention relates to an intelligent monitoring and optimizing drug delivery system for cancer chemotherapy based on a multi-stage Gaussian pseudo-spectrum method, when the system is in the cancer chemotherapy process, a doctor can check corresponding index values in the chemotherapy process in real time, and the system optimizes drug delivery according to given anticancer drugs calculated by corresponding data, so that the labor amount and the treatment cost are greatly reduced, and the doctor can be better assisted in mastering the treatment process and mastering the treatment effect.
The invention adopts the following technical scheme that the intelligent monitoring and optimizing drug delivery system for cancer chemotherapy based on the multi-stage Gaussian pseudo-spectrum method comprises a tumor size monitoring module, a tumor part drug concentration detecting module, a drug effect tumor growth model fitting module, a drug resistant cell number detecting module, a heart toxicity detecting module, a cancer chemotherapy optimizing drug delivery module, a performance parameter setting module, a data processing module, an anticancer drug giving module and a data index display module, wherein one end of the tumor size monitoring module and one end of the tumor part drug concentration detecting module are electrically connected with the data index display module, the other end of the tumor size monitoring module and one end of the tumor part drug concentration detecting module are electrically connected with the drug effect tumor growth model fitting module, one end of the drug effect tumor growth model fitting module is electrically connected with the cancer chemotherapy optimizing drug delivery module and the performance parameter setting module, the other end of the drug resistant cell number detecting module and the heart toxicity detecting module are electrically connected with the cancer chemotherapy optimizing drug delivery module, the cancer chemotherapy optimizing drug delivery module is connected with the performance parameter setting module and the data processing module, the data processing module is connected with the anticancer drug giving module, the anticancer drug giving module is connected with the data index display module,
The tumor size monitoring module is used for detecting the number of tumor cells in real time and inputting a tumor growth model fitting module under the action of a drug;
The tumor part drug concentration detection module is used for detecting the concentration of the tumor part anticancer drug and inputting the tumor growth model fitting module under the action of the drug;
the tumor growth model fitting module is used for fitting a tumor growth model according to the number of tumor cells and the concentration of the anticancer drugs at the tumor part;
The drug-resistant cell number detection module is used for detecting the number of tumor drug-resistant cells in the chemotherapy process and inputting a cancer chemotherapy optimized drug-delivery model and a performance parameter setting module;
the heart toxicity detection module is used for detecting heart toxicity in the chemotherapy process and inputting a cancer chemotherapy optimized administration model and a performance parameter setting module;
The cancer chemotherapy optimizing administration model and performance parameter setting module is used for establishing a cancer chemotherapy optimizing administration model, setting initial parameters of the chemotherapy optimizing administration model and adjusting parameters in a chemotherapy process;
The data processing module is used for converting cancer chemotherapy time into discrete point sequences with Gaussian distribution according to a multi-stage Gaussian pseudo-spectrum method, performing discrete approximation on corresponding variables on time segments, solving to obtain an anticancer drug control quantity, and inputting the anticancer drug control quantity into the anticancer drug giving module;
the anticancer drug giving module is used for determining the input time and the input dosage of the anticancer drug.
The invention has the beneficial effects that:
Firstly, a tumor growth model fitted by the tumor cell number and the tumor part anticancer drug concentration detected in real time through a tumor size monitoring module and a tumor part drug concentration detecting module is used for establishing a cancer chemotherapy optimized drug administration model with the tumor drug resistant cell number and the heart toxicity detected in real time through a drug resistant cell number detecting module and a heart toxicity detecting module, and an optimized drug scheduling scheme is obtained and the chemotherapy progress is displayed and monitored in real time under the solving of Gaussian pseudo-spectrum method, so that the cancer chemotherapy is more convenient and intelligent.
The drug administration model established by the invention considers the inhibition effect of drug-resistant cells on the cancer chemotherapy process, so that the constraint condition for reducing the drug-resistant cells is added in the model, thereby guaranteeing the curative effect of the anti-cancer drug as much as possible, and the constraint condition for heart toxicity is added in the model, so that the side effect on the heart of a patient can be reduced as much as possible in the chemotherapy process, thereby prolonging the survival time of the patient and guaranteeing the life quality of the patient.
Finally, because the model solving related to the invention needs to be performed in real time and efficiently, the method has higher requirements on the selection of a solving algorithm, and the Gaussian pseudo-spectrum method has the advantages of high solving precision and high solving speed, so that in the invention, the accurate giving of anticancer drugs and the real-time monitoring of a drug delivery system can be better realized by adopting the Gaussian pseudo-spectrum method to solve the drug delivery model.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objects and other advantages of the invention may be realized and obtained by means of the instrumentalities and combinations particularly pointed out in the specification.
Drawings
FIG. 1 is a schematic diagram of the structure of the present invention;
FIG. 2 is a schematic diagram of a data processing module and a module connected thereto according to the present invention;
FIG. 3 is a graph of a given anticancer drug obtained after pseudo-spectral point control parameterization optimization;
FIG. 4 is a graph showing the change of tumor cell number, the concentration of drug in vivo and the cumulative toxicity of drug obtained after the pseudo-spectrum point control parameterization optimization.
Detailed Description
Other advantages and effects of the present invention will become apparent to those skilled in the art from the following disclosure, which describes the embodiments of the present invention with reference to specific examples. The invention may be practiced or carried out in other embodiments that depart from the specific details, and the details of the present description may be modified or varied from the spirit and scope of the present invention. It should be noted that the illustrations provided in the following embodiments merely illustrate the basic idea of the present invention by way of illustration, and the following embodiments and features in the embodiments may be combined with each other without conflict.
In which the drawings are for illustrative purposes only and are not intended to be construed as limiting the invention, and in which certain elements of the drawings may be omitted, enlarged or reduced in order to better illustrate embodiments of the invention, and not to represent actual product dimensions, it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
Example 1
The invention provides a cancer chemotherapy intelligent monitoring and optimizing drug delivery system based on a multi-stage Gaussian pseudo-spectrum method, which comprises a tumor size monitoring module 1, a tumor part drug concentration detecting module 2, a tumor growth model fitting module 3 under the action of drugs, a drug resistant cell number detecting module 4, a cardiac toxicity detecting module 5, a cancer chemotherapy optimizing drug delivery model, a performance parameter setting module 6, a data processing module 7, an anticancer drug giving module 8 and a data index display module 9, wherein one end of the tumor size monitoring module 1 and one end of the tumor part drug concentration detecting module 2 are electrically connected with the data index display module 9, the other end of the tumor part drug concentration detecting module 2 is electrically connected with the tumor growth model fitting module 3 under the action of drugs, the tumor growth model fitting module 3 under the action of drugs is electrically connected with the cancer chemotherapy optimizing drug delivery model and the performance parameter setting module 6, one end of the drug resistant cell number detecting module 4 and the cardiac toxicity detecting module 5 are electrically connected with the data index display module 9, the other end of the cancer chemotherapy optimizing drug delivery model is connected with the performance parameter setting module 6, the cancer optimizing drug delivery model is connected with the performance parameter setting module 6, the data processing module 7 is connected with the data giving module 8, and the anticancer drug giving module 8 is connected with the anticancer drug giving module 8.
The tumor size monitoring module 1 is used for detecting the number of tumor cells in real time and inputting the tumor cell number into the tumor growth model fitting module 3 under the action of the drug.
The tumor part drug concentration detection module 2 is used for detecting the concentration of the tumor part anticancer drug and inputting the tumor growth model fitting module 3 under the action of the drug.
And the tumor growth model fitting module 3 is used for fitting a tumor growth model according to the number of tumor cells and the concentration of the anticancer drug at the tumor part.
The drug-resistant cell number detection module 4 is used for detecting the number of tumor drug-resistant cells in the chemotherapy process and inputting the tumor drug-resistant cells into the cancer chemotherapy optimized drug-administration model and performance parameter setting module 6.
The cardiotoxicity detection module 5 is used for detecting cardiotoxicity in the chemotherapy process and inputting a cancer chemotherapy optimized administration model and performance parameter setting module 6.
The cancer chemotherapy optimizing administration model and performance parameter setting module 6 is used for establishing a cancer chemotherapy optimizing administration model, setting initial parameters of the chemotherapy optimizing administration model and adjusting parameters in a chemotherapy process;
The data processing module 7 is configured to convert the cancer chemotherapy time into a discrete point array with gaussian distribution according to a multi-stage gaussian pseudo-spectrum method, perform discrete approximation on the corresponding variable on the time segment, solve to obtain an anticancer drug control amount, and input the anticancer drug control amount into the anticancer drug giving module 8.
The anticancer drug giving module 8 is used for determining the input time and the input dosage of the anticancer drug.
The data index display module 9 is used for displaying information such as tumor cell number, anticancer drug concentration at tumor part, tumor drug resistant cell number, cardiotoxicity, anticancer drug input time and input dosage in chemotherapy process.
The process of fitting the tumor growth model under the action of the drug according to the number of tumor cells and the concentration of the anticancer drug at the tumor part is carried out in a nonlinear fitting module in 1st Opt software according to a tumor growth kinetic equation and a corresponding pharmacokinetics equation, so that a needed parameter value is obtained to generate a mathematical model of tumor growth under the given action of the corresponding anticancer drug. The generated tumor growth model and the whole cancer chemotherapy administration model complement each other, and can dynamically manage the inhibition of tumor growth, thereby realizing the real-time monitoring of the growth process of the tumor and the real-time adjustment of the given dosage and time of the anticancer drugs.
As shown in fig. 2, the data processing module includes a gaussian pseudo-spectral point matching control parameterization module and a nonlinear programming problem solving module, and the following description is made on the processing of each module of the system according to fig. 2;
the information collection module is used for respectively collecting the number of tumor cells, the concentration of the anti-cancer drugs at the tumor part, the number of the drug-resistant cells and the cardiotoxicity in the beginning and the progress of chemotherapy through the tumor size monitoring module, the drug concentration detection module at the tumor part, the drug-resistant cell number detection module and the cardiotoxicity detection module, and inputting the collected information into the initialization module;
The initialization module (i.e. the aforementioned performance parameter setting module) is used for setting an initial drug control quantity u (0) (t), setting an optimization accuracy tol, and setting the iteration number D to zero;
the Gaussian pseudo-spectrum matching point control parameterization module is used for converting cancer chemotherapy time [ t 0,tf ] into discrete point rows with Gaussian distribution, and performing discrete approximation on variables corresponding to time segments;
The nonlinear programming problem solving module is used for obtaining a drug control quantity u (D) (t) meeting the convergence requirement through calculation and outputting the drug control quantity u (D) (t) to the control signal output module;
The control signal output module transmits the drug control quantity u (D) (t) to the anticancer drug giving module and the data index display module.
The working steps of the Gaussian pseudo-spectrum point matching control parameterization module are as follows:
Step 1, equally dividing a time interval of a chemotherapy cycle, dividing the whole interval into I+1 sections by setting an initial time t 0, an end time t f and I internal time nodes t 1,t2,…,tI, respectively marking the length of each section as a 1,a2,…,aI+1, and introducing a new time variable ζ to perform time-scale transformation on a control time domain in a j-th section corresponding time interval of [ t j-1,tj ]:
The transformation of each subinterval is the same, and the LG setpoint needs to be subjected to the following inverse transformation at the moment corresponding to the time domain t E [ t j-1,tj ]:
By transforming equation (13), the state vector differential term in the generic form OCP (with respect to time domain t E [ t 0,tf ]) Then the conversion is in a form based on the time domain ζ ε ζ 0,ζf:
Step 2, recording the number of matched points adopted by the vector of the j-th section as K j, and respectively representing the state vector x j (ζ) and the control vector u j (ζ) of the section as:
At this time, X represents a state vector, U represents a control vector, and X j (ζ) is a state vector based on the j-th segment in the time domain ζ∈ [ ζ 0,ζf ], and U j (ζ) is a state vector based on the j-th segment in the time domain ζ∈ [ ζ 0,ζf ]. Meanwhile, X j,m＝Xj(ζj,m) is the value of the state vector at the initial instant of the j-th segment (m=0) or at the LG configuration point (m=1, K j),Uj,m＝Uj(ζj,m) is the value of the control vector at LG setpoint, Z j,m (ζ) and A basis function for a lagrangian interpolation polynomial:
ζ j,m(m＝1,…,Kj) is the mth point of the jth segment, ζ j,0 is the initial time of the jth segment, ζ j,0＝ζ0 = -1, (j=1,... Both sides of the formula (16) can simultaneously derive ζ:
The simultaneous (3) and (7) are available:
Wherein, the For the derivative of the basis function of the lagrangian interpolation polynomial, X j,m is the value of the state vector at the initial instant of the j-th segment (m=0) or at the LG configuration point (m=1,..,For the value of the derivative of the basis function of the lagrangian interpolation polynomial at the initial instant of the j-th segment (m=0), X j,0 is the value of the state vector at the initial instant of the j-th segment (m=0),Differentiating terms for state vectors
Step3, bringing K j LG coordination points into a formula (20) to obtain a discretized nonlinear equation system:
Wherein, the Is a vector formed by the first column of the state differential matrix P j,Is a matrix formed by the rest columns of P j, namely:
Wherein, the Is the value of the discretized n x -dimensional state vector at K j points,Is a discrete control parameter;
Step 4, determining the value of X j,0, when j=1, X 1,0＝x0 is a given initial value, and when 1< j < i+1, X j,0 is calculated by the following formula:
Xj,0＝Xj-1(ζf),j=2,...,I+1 (11)
And X j-1(ζf) is calculated by a numerical integration formula:
As a differential term of the state vector, the state vector X j-1(ζf),aj-1 which is integrated to find the corresponding time zone of the j-1 th segment represents the corresponding time zone of the j-1 th segment.
And 5, after multi-stage Gaussian distribution point discretization treatment, the original optimal administration problem of cancer chemotherapy based on the time domain t E [ t 0,tf ] is converted into a nonlinear programming problem based on the time domain ζE [ ζ 0,ζf ].
And step 6, the nonlinear programming problem solving module calls GPOPS a solver to solve.
Example 2:
the example obtains a basic cancer chemotherapy optimized administration model through tumor cell growth kinetics and related theory:
wherein J and x 1 are the number of tumor cells, u 1 is the concentration of anticancer drug, x 2 is the concentration of in vivo drug, x 3 is the accumulated drug concentration, Is the derivative of the number of tumor cells,As a derivative of the concentration of the drug in the body,
For accumulating the derivative of drug toxicity, T is time, T is treatment period, lambda is tumor growth factor, ρ is the maximum value of natural growth of tumor under Gompertz growth model, k is the killing fraction of anticancer drug, alpha is the drug effective concentration, beta is the half-life factor of anticancer drug, N 0 is the initial tumor cell number, v 0 is the initial in vivo drug concentration,For initial cumulative drug toxicity, η 1,η2,η3 is the concentration constraint, v max,U max is the upper limit value of the in-vivo drug concentration, the constraint value of the accumulated drug toxicity upper limit and the upper limit value of the drug administration rate, H (x 2 (t) -alpha) is a step function, when the in-vivo drug concentration is greater than the drug onset concentration, the value is 1, and when the in-vivo drug concentration is less than the drug onset concentration, the value is 0.
The intelligent monitoring and optimizing medicine feeding system for cancer chemotherapy runs an internal pseudo-spectrum distribution point control parameterization algorithm, and comprises the following specific steps:
e1, in the cancer chemotherapy proceeding stage, an information acquisition module is started, and a cancer chemotherapy optimized administration model is input;
E2, starting operation of an initialization module, setting an initial anticancer drug given amount mu (0) (t) =0 in a chemotherapy process, setting the precision to tol=10 -6, and setting the iteration times D to zero;
E3, operating a Gaussian pseudo-spectrum point matching control parameterization module, converting cancer chemotherapy time [ t 0,tf ] into a discrete point array with Gaussian distribution by adopting a Gaussian pseudo-spectrum point matching control parameterization algorithm, and performing discrete approximation on a variable corresponding to a time segment to convert a problem into a new nonlinear programming problem;
E4, operating a nonlinear programming problem solving module, calculating to obtain an anticancer drug control quantity mu (D) (t) meeting the requirement through a nonlinear programming problem solving algorithm, and outputting the anticancer drug control quantity mu (D) (t) to a control signal output module;
And E5, controlling the signal output module to operate, and transmitting the anticancer drug control quantity mu (D) (t) to the anticancer drug given module through the control signal output module.
Fig. 3 and 4 show given curves, tumor cell number change curves, in-vivo drug concentration curves and drug accumulated toxicity curves of the anticancer drugs obtained after pseudo-spectrometry point control parameterization optimization. Corresponding data at any time point in the treatment process can be obtained from the curves, so that a doctor can monitor the chemotherapy process in real time for reference by the doctor.
Finally, it is noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that modifications and equivalents may be made thereto without departing from the spirit and scope of the present invention, which is intended to be covered by the claims of the present invention.
Claims (4)
1. The intelligent monitoring and optimizing drug delivery system for cancer chemotherapy based on the multistage Gaussian pseudo-spectrum method is characterized by comprising a tumor size monitoring module (1), a tumor part drug concentration detecting module (2), a tumor growth model fitting module (3) under the action of drugs, a drug resistant cell number detecting module (4), a cardiotoxicity detecting module (5), a cancer chemotherapy optimizing drug delivery module and performance parameter setting module (6), a data processing module (7), an anticancer drug giving module (8) and a data index display module (9), wherein one end of the tumor size monitoring module (1) and one end of the tumor part drug concentration detecting module (2) are electrically connected with the data index display module (9), the other end of the tumor part drug concentration detecting module (2) is electrically connected with the tumor growth model fitting module (3) under the action of drugs, the tumor growth model fitting module (3) under the action of drugs is electrically connected with the cancer chemotherapy optimizing drug delivery module (6), one end of the drug resistant cell number detecting module (4) and the cardiotoxicity detecting module (5) are electrically connected with the data index display module (9), the other end of the drug resistant cell number detecting module is electrically connected with the cancer chemotherapy optimizing drug delivery module (6), the cancer chemotherapy optimizing drug delivery module is connected with the performance parameter setting module (7) and the anticancer drug giving module (7) is electrically connected with the anticancer drug giving module (7), the anticancer drug giving module (8) is connected with the data index display module (9), wherein,
The tumor size monitoring module (1) is used for detecting the number of tumor cells in real time and inputting a tumor growth model fitting module (3) under the action of a drug;
the tumor part drug concentration detection module (2) is used for detecting the concentration of the tumor part anticancer drug and inputting the tumor growth model fitting module (3) under the action of the drug;
the tumor growth model fitting module (3) is used for fitting a tumor growth model according to the number of tumor cells and the concentration of the anticancer drugs at the tumor part;
The drug-resistant cell number detection module (4) is used for detecting the number of tumor drug-resistant cells in the chemotherapy process and inputting a cancer chemotherapy optimized drug-delivery model and performance parameter setting module (6);
the heart toxicity detection module (5) is used for detecting heart toxicity in the chemotherapy process and inputting a cancer chemotherapy optimized administration model and performance parameter setting module (6);
the cancer chemotherapy optimized administration model and performance parameter setting module (6) is used for establishing the cancer chemotherapy optimized administration model, setting initial parameters of the chemotherapy optimized administration model and adjusting parameters in a chemotherapy process;
The data processing module (7) is used for converting cancer chemotherapy time into discrete point sequences with Gaussian distribution according to a multi-stage Gaussian pseudo-spectrum method, performing discrete approximation on corresponding variables on time segments, solving to obtain anticancer drug control quantity, and inputting the anticancer drug control quantity into the anticancer drug giving module (8);
the anticancer drug giving module (8) is used for determining the input time and the input dosage of the anticancer drug.
2. The intelligent monitoring and optimizing administration system for cancer chemotherapy based on multistage Gaussian pseudo-spectrum method of claim 1, wherein the optimal administration model for cancer chemotherapy is as follows
min J(u1(t))＝x1(T)
x1(0)＝N0,x2(0)＝v0,
x1(t1)≤η1,x1(t2)≤η2,x1(t3)≤η3
0≤x2(t)≤vmax,for all t∈[0,T]
0≤u1(t)≤umax for all t∈[0,T]
Wherein J and x 1 are the number of tumor cells, u 1 is the concentration of anticancer drug, x 2 is the concentration of in vivo drug, x 3 is the accumulated drug concentration,Is the derivative of the number of tumor cells,As a derivative of the concentration of the drug in the body,For accumulating the derivative of drug toxicity, T is time, T is treatment period, lambda is tumor growth factor, ρ is the maximum value of natural growth of tumor under Gompertz growth model, k is the killing fraction of anticancer drug, alpha is the drug effective concentration, beta is the half-life factor of anticancer drug, N 0 is the initial tumor cell number, v 0 is the initial in vivo drug concentration,For initial cumulative drug toxicity, η 1,η2,η3 is the concentration constraint, v max,U max is the upper limit value of the in-vivo drug concentration, the constraint value of the accumulated drug toxicity upper limit and the upper limit value of the drug administration rate, H (x 2 (t) -alpha) is a step function, when the in-vivo drug concentration is greater than the drug onset concentration, the value is 1, and when the in-vivo drug concentration is less than the drug onset concentration, the value is 0.
3. The intelligent monitoring and optimizing drug delivery system for cancer chemotherapy based on multi-stage Gaussian pseudo-spectrometry according to claim 1, wherein the processing steps of the multi-stage Gaussian pseudo-spectrometry are as follows:
Step 1, equally dividing a time interval of a chemotherapy cycle, dividing the whole interval into I+1 sections by setting an initial time t 0, an end time t f and I internal time nodes t 1,t2,…,tI, respectively marking the length of each section as a 1,a2,…,aI+1, and introducing a new time variable ζ to perform time-scale transformation on a control time domain in a j-th section corresponding time interval of [ t j-1,tj ]:
The transformation of each subinterval is the same, and the LG setpoint needs to be subjected to the following inverse transformation at the moment corresponding to the time domain t E [ t j-1,tj ]:
By transforming equation (1), the state vector differential term in the generic form OCP (with respect to the time domain t E [ t 0,tf ]) Then the conversion is in a form based on the time domain ζ ε ζ 0,ζf:
Step 2, recording the number of matched points adopted by the vector of the j-th section as K j, and respectively representing the state vector x j (ζ) and the control vector u j (ζ) of the section as:
At this time, X represents a state vector, U represents a control vector, X j (ζ) is a state vector based on the j-th segment in the time domain ζ∈ [ ζ 0,ζf ], U j (ζ) is a state vector based on the j-th segment in the time domain ζ∈ [ ζ 0,ζf ], and at the same time, X j,m＝Xj(ζj,m) is a value (m=0) of the state vector at the initial time of the j-th segment or a value (m=1) at the LG configuration point, K j),Uj,m＝Uj(ζj,m) is a value of the control vector at the LG configuration point, Z j,m (ζ) and A basis function for a lagrangian interpolation polynomial:
ζ j,m(m＝1,…,Kj) is the mth matching point of the jth segment, ζ j,0 is the initial time of the jth segment, ζ j,0＝ζ0 = -1, (j=1, i+1), and the two sides of the formula (3) can obtain the derivative of ζ at the same time:
where X j,m is the value of the state vector at the initial instant of the j-th segment (m=0) or at the LG configuration point (m=1, K j);
The simultaneous (3) and (7) are available:
Wherein, the For the derivative of the basis function of the lagrangian interpolation polynomial, X j,m is the value of the state vector at the initial instant of the j-th segment (m=0) or at the LG configuration point (m=1,..,For the value of the derivative of the basis function of the lagrangian interpolation polynomial at the initial instant of the j-th segment (m=0), X j,0 is the value of the state vector at the initial instant of the j-th segment (m=0),Differentiating terms for state vectors
Step 3, bringing K j LG coordination points into a formula (8) to obtain a discretized nonlinear equation system:
Wherein, the Is a vector formed by the first column of the state differential matrix P j,Is a matrix formed by the rest columns of P j, namely:
Wherein, the Is the value of the discretized n x -dimensional state vector at K j points,Is a discrete control parameter;
Step 4, determining the value of X j,0, when j=1, X 1,0＝x0 is a given initial value, and when 1< j < i+1, X j,0 is calculated by the following formula:
Xj,0＝Xj-1(ζf),j=2,...,I+1 (11)
And X j-1(ζf) is calculated by a numerical integration formula:
As a differential term of the state vector, the state vector X j-1(ζf),aj-1 which is integrated to find the corresponding time zone of the j-1 th segment represents the corresponding time zone of the j-1 th segment.
4. The intelligent monitoring and optimizing drug delivery system for cancer chemotherapy based on the multistage Gaussian pseudo-spectrum method of claim 3, wherein the intelligent monitoring and optimizing drug delivery system comprises the steps of calling GPOPS a solver to solve the nonlinear programming problem obtained in the step 4, and obtaining the anticancer drug control quantity meeting the requirement.
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