Modeling and optimizing method for photothermal-photodynamic combined collaborative treatment

Abstract

The invention relates to the technical field of cancer treatment research, and discloses a photothermal-photodynamic combined collaborative treatment modeling and optimizing method which comprises the following specific steps: constructing a tumor growth model with time lag; on the basis of a tumor growth model, photo-thermal and photodynamic treatment intensity items and tumor killing items are introduced respectively, and a tumor treatment model is constructed. The problems that in the prior art, effective analysis of a photo-thermal therapy and photodynamic therapy synergistic therapy is lacked, and the photo-thermal and photodynamic synergistic therapy effect is difficult to predict are solved, and the method has the advantage of being capable of assisting in improving the cancer treatment effect.

Description

Technical Field

[0001] The present invention relates to the technical field of cancer treatment research, and more specifically, to a modeling and optimization method for photothermal-photodynamic combined synergistic therapy. Background Art

[0002] Cancer is one of the most serious threats to human life and health. In recent years, the incidence of cancer has continued to rise, and the incidence of cancer is becoming younger and younger, becoming the number one killer threatening human life and health. This is not only due to the high mortality rate of cancer, but also the difficulty and cost of cancer diagnosis and treatment. Traditional treatments (including radiotherapy, chemotherapy and surgery) have obvious side effects, such as decreased immunity, organ and normal tissue damage, etc. The society is also studying various new and effective tools to deal with tumors.

[0003] In the field of skin disease treatment, there are two new treatment methods, photothermal and photodynamic, which are easy to operate and low in cost, can target and accurately treat with few side effects. Researchers at home and abroad have applied their innovations to the diagnosis and treatment of cancer, and have developed the research directions of photothermal and photodynamic diagnosis and treatment methods for cancer cells, which have great application potential in the treatment of superficial skin cancers such as melanoma, nasopharyngeal carcinoma, breast cancer, esophageal cancer, etc.

[0004] Photothermal therapy (PTT) is a strategy in which nanoprobes convert absorbed light energy into heat energy under near-infrared light to kill tumor cells; photodynamic therapy (PDT) is a method that uses photosensitive molecules as photoactivators to promote oxygen source conversion under appropriate light excitation, generating cytotoxic singlet reactive oxygen free radicals to kill tumor cells. Both methods are excited by external light sources, so the treatment location and intensity can be precisely controlled, and the side effects are much smaller than radiotherapy and chemotherapy. Combining the two modes of photothermal and photodynamics and supplemented by resonant energy conversion and near-infrared upconversion technology can achieve indirect light excitation of photosensitizers to kill deep tumors.

[0005] In practice, photothermal therapy is a treatment method that injects nanoprobes with high photothermal conversion efficiency into the human body, uses the probe's targeting function to enrich it at the tumor site, converts light energy into heat energy under the irradiation of near-infrared light, and finally kills cancer cells with high temperature. Photodynamic therapy is a treatment method that injects photosensitive drugs into the human body, uses the drug's targeting function to enrich it at the tumor site, activates the photosensitive drugs under the irradiation of near-infrared light, triggers a photochemical reaction, and kills the tumor.

[0006] Since the treatment process of photothermal therapy is similar to that of photodynamic therapy, photothermal and photodynamic therapy are suitable for combined treatment: the photosensitizer used in photodynamic therapy can be used as a photothermal conversion agent for photothermal therapy, such as indocyanine green (ICG). Gold nanorods, as photothermal conversion agents, also have an enhancing effect on photodynamic therapy. Photosensitive molecules can obtain energy from the strong electromagnetic field generated by the surface plasmon resonance effect of gold nanorods and also become excited, thereby generating singlet oxygen.

[0007] When light shines on the gold nanorods, a surface plasmon resonance effect[4] is generated, and the free electrons oscillate collectively and couple with the electromagnetic waves to form a near-field electromagnetic wave that propagates along the metal surface. If the frequency of the incident light wave is consistent with the oscillation frequency of the electrons, the two will resonate. In the resonant state, the energy of the electromagnetic field is efficiently converted into the collective vibration energy of the free electrons on the metal surface. Therefore, the gold nanorods can effectively absorb light of a specific wavelength and convert it into heat.

[0008] The degree of electronic polarization of rod-shaped gold nanoparticles in each direction is different, resulting in two surface plasmon resonance modes, corresponding to the two characteristic dimensions of the long axis and the short axis. The transverse electron resonance produces a transverse absorption band, which is less dependent on the aspect ratio, located near 520nm, and has a weak intensity; the axial electron resonance produces a longitudinal absorption band, which is more dependent on the aspect ratio, and has a greater axial intensity, which plays a dominant role in the optical properties of the nanorods. Therefore, by adjusting the aspect ratio, the axial resonance absorption peak of the gold nanorod can be adjusted within the range of 520nm-1400nm. Therefore, the axial resonance absorption peak of the gold nanorod can be adjusted to the near-infrared region, and photothermal therapy of tumor cells in deep tissues can be performed under the irradiation of near-infrared lasers.

[0009] The local electric field enhanced by the nano-gold rod is mainly distributed at both ends of the gold rod. If the photosensitizer is hung on both sides of the gold rod with mesoporous silica as the medium to form a nano dumbbell-shaped structure and adsorb the photosensitizer, the performance of the photosensitizer can be significantly improved. Then, by using the photothermal effect of the gold rod itself, the effect of photothermal-photodynamic synergistic therapy can be achieved.

[0010] However, the existing technology lacks effective analysis of the synergistic treatment of photothermal therapy and photodynamic therapy, and there is a problem that it is difficult to predict the effects of the synergistic treatment of photothermal and photodynamic therapy. Therefore, how to invent a model that can predict the effects of photothermal-photodynamic combined treatment is a technical problem that urgently needs to be solved in this technical field. Summary of the invention

[0011] In order to solve the problem that it is difficult to predict the effects of photothermal and photodynamic synergistic therapy in the prior art, the present invention provides a modeling and optimization method for photothermal-photodynamic combined synergistic therapy, which has the characteristic of being able to assist in improving the effect of cancer treatment.

[0012] In order to achieve the above-mentioned purpose of the present invention, the technical scheme adopted is as follows:

[0013] The beneficial effects of the present invention are as follows:

[0014] A modeling method for photothermal-photodynamic combined synergistic therapy includes the following specific steps:

[0015] Construct tumor growth models with time lags;

[0016] On the basis of the tumor growth model, the photothermal and photodynamic treatment intensity terms and tumor killing terms were introduced respectively to construct a tumor treatment model.

[0017] Preferably, a tumor growth model with a time lag is constructed, specifically:

[0018] A tumor growth model with time lag is constructed based on either the Logistic growth model with time lag or the Allee model with time lag;

[0019] If the Logistic growth model with time lag is used, the tumor growth model with time lag is constructed as follows:

[0020]

[0021] If the Allee model with time lag is used, the tumor growth model with time lag is constructed as follows:

[0022]

[0023] Among them, x(t) represents the real-time tumor cell density, r0 represents the natural growth rate of tumor cells, K represents the maximum carrying capacity of the environment, τ represents the time lag caused by the cell cycle of tumor cells, and A represents the Allee coefficient.

[0024] Furthermore, on the basis of the tumor growth model, the treatment intensity terms of photothermal and photodynamic therapy and tumor killing terms were introduced to construct a tumor treatment model, specifically:

[0025] If the Logistic growth model with time lag is used, the constructed tumor treatment model is as follows:

[0026]

[0027] If the Allee growth model with time lag is used, the constructed tumor treatment model is as follows:

[0028]

[0029] Where H(t) is the real-time photothermal therapy intensity, is the intensity of time-delay photodynamic therapy; μH is the tumor cell killing rate of photothermal therapy, μ B is the killing rate of tumor cells by photodynamic therapy; It is the lag time of the photodynamic therapy process relative to the photothermal therapy process, that is, the phase difference between the effects of the two treatments.

[0030] Furthermore, the actual rate of change of photothermal therapy intensity is expressed as:

[0031]

[0032] The actual change rate of photodynamic therapy intensity is expressed as:

[0033]

[0034] Where Q is the heat source term, representing the constant heat generation of the photothermal converter as a heat source under constant laser light irradiation, α is the heat generation rate of the photothermal effect of the photosensitizer, C(t) is the photosensitizer concentration, β C is the active oxygen production rate of the photosensitizer without enhancement, β is the active oxygen production rate of the photosensitizer increased by surface plasmon resonance enhancement, and λ H is the non-therapeutic heat loss rate, λ B is the non-therapeutic loss rate of reactive oxygen species, γ H is the heat treatment process loss rate, γ B is the loss rate of active oxygen during treatment.

[0035] Furthermore, the change of C(t) is specifically expressed as:

[0036]

[0037] Furthermore, the initial conditions of the tumor treatment model are:

[0038] x(0)=K, H(0)=0, B(0)=0, C(0)=C0;

[0039] The model uses core-shell composite structure nanoparticles formed by shell-coated precious metal nanoparticles containing organic molecular photosensitizers as the treatment medium. All photosensitizers are enhanced by the metal surface plasmon resonance. The nanoparticles are evenly distributed in the tumor tissue, the external laser light source is constant and evenly irradiated, and the tumor is evenly distributed in space.

[0040] An optimization method for photothermal-photodynamic combined synergistic therapy, based on the modeling method, includes the following specific steps:

[0041] Substituting initial parameters into the model to initialize the tumor treatment model;

[0042] Modify the φ, β, and α parameters and solve the tumor treatment model separately, compare the solution results, and find the optimal parameter combination;

[0043] Based on the optimal parameter combination, the optimal synergistic treatment plan is designed.

[0044] Preferably, the parameters φ, β, and α are modified and the tumor treatment model is solved respectively, and the solution results are compared to find the main parameters that affect the tumor treatment effect. The specific steps are:

[0045] Modify the φ, β, and α parameters and solve the tumor treatment model respectively, and analyze the changes in tumor cell number density under different φ, β, and α parameters;

[0046] Analyze the effect of the changes of φ, β, and α parameters on the ratio of the number density of surviving cells N to the maximum environmental carrying capacity K (N / K);

[0047] A comprehensive analysis was conducted on the changes in tumor cell density under different φ, β, and α parameters, and the effects of φ, β, and α parameter changes on N / K to obtain the best parameter combination for killing tumor cells.

[0048] Furthermore, the effects of φ, β, and α parameters on the photothermal-photodynamic synergistic effect are analyzed. The specific steps are as follows:

[0049] Analyze the impact of changes in φ, β, and α parameters on Q;

[0050] Set photosensitivity C0 and Q as coordinate axes, fix the value of N / K, perform multiple simulations based on the tumor treatment model to obtain simulated isoelectric curves; compare the additive isoelectric curves and simulated isoelectric curves when the relationship between photothermal and photodynamic therapy is additive, and calculate the synergistic effect value;

[0051] Analyze the impact of changes in φ, β, and α parameters on the heat production parameter Q and the synergistic effect value, find the key parameters among φ, β, and α parameters, and regulate the photothermal and photodynamic combined synergistic therapy based on the key parameters.

[0052] Furthermore, the synergistic effect value R=S 阴影 / S Δ , where S 阴影 is the area bounded by the simulated iso-effect line and the summed iso-effect line, S Δ It is the area of ​​the triangle enclosed by the additive effect straight line and the horizontal and vertical axes. R is a proportional coefficient that reflects the synergistic effect of the two methods in the existing treatment plan. The larger the value of R, the better the synergistic effect of photothermal and photodynamic therapy.

[0053] The beneficial effects of the present invention are as follows:

[0054] The present invention discloses a modeling method for photothermal-photodynamic combined synergistic therapy. By simulating the spatiotemporal evolution of tumors during the treatment process, a perfect photothermal-photodynamic theoretical model is established. The model analysis provides guidance for the preparation of probes and the optimization of treatment plans. The problem that the prior art lacks effective analysis of the synergistic therapy of photothermal therapy and photodynamic therapy, and it is difficult to predict the effects of the synergistic therapy of photothermal therapy and photodynamic therapy is solved. The method has the characteristic of being able to assist in improving the effect of cancer treatment. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a flow chart of a modeling method for photothermal-photodynamic combined synergistic therapy of the present invention.

[0056] Figure 2 It is a schematic flow chart of an optimization method for photothermal-photodynamic combined synergistic therapy of the present invention.

[0057] Figure 3 Schematic diagram of the curve of cell number density changing with treatment time at different φ values ​​in Example 3.

[0058] Figure 4 Schematic diagram of the curve of cell number density changing with treatment time at different β values ​​in Example 3.

[0059] Figure 5 Schematic diagram of the curve of cell number density changing with treatment time at different α values ​​in Example 3.

[0060] Figure 6 This is a cross-sectional diagram of N / K with variables φ, β, and α in Example 3.

[0061] Figure 7 It is a schematic diagram of the influence curve of φ on N / K in Example 3.

[0062] Figure 8 It is a schematic diagram of the influence curve of β on N / K in Example 3.

[0063] Fig. 9 It is a schematic diagram of the influence curve of α on N / K in Example 3.

[0064] Fig.10 It is the isotropic curve diagram of the heat generation Q of the nano-gold rods and the initial concentration C0 of the photosensitizer when the N / K value is 0.5 in Example 3.

[0065] Fig.11 is the synergistic effect R=S based on the isobologram in Example 3 阴影 / S Δ Schematic diagram.

[0066] Fig.12 It is a schematic diagram of the isoeffect curve corresponding to the φ value in Example 3.

[0067] Fig.13 It is a schematic diagram of the iso-effect curve corresponding to the β value in Example 3.

[0068] Fig.14 It is a schematic diagram of the isoeffectiveness curve corresponding to the α value in Example 3.

[0069] Fig.15 This is a schematic diagram of the curve showing the influence of the φ value on the synergistic effect in Example 3.

[0070] Fig.16 This is a schematic diagram of the curve showing the influence of the β value on the synergistic effect in Example 3.

[0071] Fig.17 This is a schematic diagram of the curve showing the influence of the α value on the synergistic effect in Example 3.

[0072] Fig.18 It is an image of the numerical solution of the model in Example 4 where x varies with time t when the time lag τ=1, Q=1.5, and C0=10.

[0073] Fig.19 This is an image of the numerical solution of the model in Example 4 where τ=10, Q=3, and C0=20, showing how x changes with time t.

[0074] Fig. 20 This is an image of the numerical solution of the model in Example 4 where τ=1, Q=1.5, and C0=10, showing how H changes with time t.

[0075] Fig.21 This is an image of the numerical solution of the model in Example 4, where τ=1, Q=1.5, and C0=10, showing how B changes with time t.

[0076] Fig. 22 is x in Example 4 min The isotropic curve diagram when the value of is 4.91.

[0077] Fig.23 is x in Example 4 min The value of Value change graph.

[0078] Fig.24 is x in Example 4 min =4.91 corresponds to different Isophore plot of the values.

[0079] Fig.25 is x in Example 4 min =4.91 under different β values.

[0080] Fig.26 is x in Example 4 minβ-C0 curve when =4.91,Q=1.6. DETAILED DESCRIPTION

[0081] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0082] Example 1

[0083] like Figure 1 As shown, a modeling method for photothermal and photodynamic combined synergistic therapy includes the following specific steps:

[0084] Construct tumor growth models with time lags;

[0085] On the basis of the tumor growth model, the photothermal and photodynamic treatment intensity terms and tumor killing terms were introduced respectively to construct a tumor treatment model.

[0086] In a specific embodiment, a tumor growth model with a time lag is constructed, specifically: a Logistic growth model with a time lag is adopted, and the constructed tumor growth model with a time lag is specifically:

[0087]

[0088] Among them, x(t) represents the real-time tumor cell density, r0 represents the natural growth rate of tumor cells, K represents the maximum carrying capacity of the environment, and τ represents the time lag caused by the cell cycle of tumor cells.

[0089] In this embodiment, in the population dynamics modeling, the most commonly used model is the classic Logistic growth model. This model takes into account that the living space and environmental resources are limited and cannot provide the required space and energy basis for an infinite number of individuals, that is, each population has a corresponding maximum environmental carrying capacity in its living ecosystem. If the population density is too high, the average resources occupied by the individuals in the population will decrease, and the high population individual density will also cause the environment to deteriorate, thereby leading to an increase in diseases and other phenomena, the result of which is that the birth rate of the population decreases and the death rate increases, thereby reducing the population density.

[0090] In a specific embodiment, a Logistic growth model with a time lag is used, specifically:

[0091]

[0092] Where H(t) is the real-time photothermal therapy intensity, is the intensity of time-delay photodynamic therapy; μ H is the tumor cell killing rate of photothermal therapy, μ B is the killing rate of tumor cells by photodynamic therapy; It is the lag time of the photodynamic therapy process relative to the photothermal therapy process, that is, the phase difference between the effects of the two treatments.

[0093] In a specific embodiment, the actual change rate of photothermal therapy intensity is expressed as:

[0094]

[0095] The actual change rate of photodynamic therapy intensity is expressed as:

[0096]

[0097] Where Q is the heat source term, representing the constant heat generation of the photothermal converter as a heat source under constant laser light irradiation, α is the heat generation rate of the photothermal effect of the photosensitizer, C(t) is the photosensitizer concentration, β c is the active oxygen production rate of the photosensitizer without enhancement, β is the active oxygen production rate of the photosensitizer increased by surface plasmon resonance enhancement, and λ H is the non-therapeutic heat loss rate, λ B is the non-therapeutic loss rate of reactive oxygen species, γ H is the heat treatment process loss rate, γ B is the loss rate of active oxygen during treatment.

[0098] In this embodiment, since the photothermal effect process of the metal nanoparticles is directly related to the surface plasmon, βQ can actually be used to indirectly describe the increased active oxygen production rate of the photosensitizer under the surface plasmon enhancement.

[0099] In a specific embodiment, an unstable organic photosensitizer such as ICG actually decomposes continuously in a negative exponential relationship with time under light, and the change of C(t) is specifically expressed as:

[0100]

[0101] In a specific embodiment, the initial conditions of the tumor treatment model are:

[0102] x(0)=K, H(0)=0, B(0)=0, C(0)=C0.

[0103] Example 2

[0104] More specifically, in this embodiment, factors such as the uneven distribution of tumors in space and the differences between similar tumor cells are ignored, and a tumor growth model with time lag is constructed, specifically:

[0105] The tumor growth model with time lag constructed by using the Allee model with time lag is as follows:

[0106]

[0107] Among them, x(t) represents the real-time tumor cell density, r0 represents the natural growth rate of tumor cells, K represents the maximum carrying capacity of the environment, τ represents the time lag caused by the cell cycle of tumor cells, and A represents the Allee coefficient.

[0108] In this embodiment, the Allee model makes up for the shortcomings of the Logistic model. The population with the Allee effect takes into account the cooperative behavior between individuals in the population, that is, a minimum density sufficient to maintain survival is required to ensure that individuals between populations have sufficient conditions and opportunities to cooperate. If the density is lower than a certain threshold, the population density is too small, which will lead to a lack of cooperation between populations, a decrease in the fitness of individuals, and the population will go extinct.

[0109] In a specific embodiment, based on the tumor growth model, the treatment intensity terms of photothermal and photodynamic therapy and the tumor killing term are introduced respectively to construct a tumor treatment model, specifically:

[0110] Assuming that the dose-effect relationship curve is linear, the Allee growth model with time lag is adopted, and the tumor treatment model constructed is as follows:

[0111]

[0112] Where H(t) is the real-time photothermal therapy intensity, is the intensity of time-delay photodynamic therapy; μ H is the tumor cell killing rate of photothermal therapy, μ B is the killing rate of tumor cells by photodynamic therapy; It is the lag time of the photodynamic therapy process relative to the photothermal therapy process, that is, the phase difference between the effects of the two treatments.

[0113] In a specific embodiment, considering that the heat conduction equation and the diffusion equation respectively describe the transfer of heat and the diffusion of substances, their forms are actually the same, and the first-order pharmacokinetics is based on the result obtained by the diffusion equation, the actual rate of change of the photothermal therapy intensity is expressed as:

[0114]

[0115] The actual change rate of photodynamic therapy intensity is expressed as:

[0116]

[0117] Where Q is the heat source term, representing the constant heat generation of the photothermal converter as a heat source under constant laser light irradiation, α is the heat generation rate of the photothermal effect of the photosensitizer, C(t) is the photosensitizer concentration, β Cis the active oxygen production rate of the photosensitizer without enhancement, and β is the active oxygen production rate of the photosensitizer increased by surface plasmon resonance enhancement, λ H is the non-therapeutic heat loss rate, λ B is the non-therapeutic loss rate of reactive oxygen species, γ H is the heat treatment process loss rate, γ B is the loss rate of active oxygen during treatment.

[0118] In a specific embodiment, the change of C(t) is specifically expressed as:

[0119]

[0120] In a specific embodiment, the initial conditions of the tumor treatment model are:

[0121] x(0)=K, H(0)=0, B(0)=0, C(0)=C0;

[0122] In this embodiment, the model uses core-shell composite structure nanoparticles formed by precious metal nanoparticles coated with silica shells containing organic molecular photosensitizers as the treatment medium. All photosensitizers are enhanced by the metal surface plasmon resonance effect. The nanoparticles are evenly distributed in the tumor tissue, the external laser light source is constant and evenly irradiated, and the tumor is evenly distributed in space.

[0123] Example 3

[0124] like Figure 2 As shown, an optimization method for photothermal and photodynamic combined synergistic therapy, based on the modeling method, includes the following specific steps:

[0125] Substituting initial parameters into the model to initialize the tumor treatment model;

[0126] Modify the φ, β, and α parameters and solve the tumor treatment model separately, compare the solution results, and find the optimal parameter combination;

[0127] Based on the optimal parameter combination, the optimal synergistic treatment plan is designed.

[0128] In this embodiment, in order to explore the influence of factors represented by different parameters on the efficacy of photothermal and photodynamic therapy, as well as the synergy between metal nanoparticle photothermal therapy and molecular photosensitizer photodynamic therapy through simulation calculation, each parameter in the model needs to set a reference value. In this embodiment, the maximum capacity of the environment K is set to 10, the natural growth rate of the tumor r0 is set to 1, and the reasonable numerical range of other parameters is determined accordingly. The final parameter reference values ​​are shown in Table 2-2.

[0129] Table 2-2 Parameter names, meanings and reference values

[0130]

[0131] The natural growth rate of tumor cells r0, the maximum capacity of the environment K, and the Allee coefficient A are the parameters affecting the cells themselves. The heat generation rate of the photosensitizer's photothermal effect α and the photosensitizer's increased active oxygen generation rate β under surface plasmon enhancement are the performance parameters of the probe itself. The initial concentration of the photosensitizer C0 and the relative lag of photodynamic therapy It is a factor of human control during the treatment process using probe.

[0132] In a specific embodiment, the tumor treatment model is a nonlinear ordinary differential equation system. It is difficult to find an analytical solution to such an equation system. Therefore, this embodiment chooses to use the 4th-order Runge-Kutta method to find its numerical solution. The Runge-Kutta RK4 method is used to solve the tumor treatment model. There are o(h 5 ), the specific steps are:

[0133] Given the initial condition y ′ =f(x,y),y(x0)=y0

[0134] Among them, y represents all dependent variables, and x represents all independent variables;

[0135] Iteration using RK4 method:

[0136]

[0137] in

[0138] k1=f(x n ,y n )

[0139]

[0140]

[0141] k4=f(x n +h,y n +hk3)

[0142] Where h is the time interval.

[0143] In this embodiment, Mathematica software and Matlab are used as calculation tools. When solving, the time t range is selected as 0-5, the solution step is 0.1, and the accuracy is 10 -5 .

[0144] In a specific embodiment, the parameters φ, β, and α are modified and the tumor treatment model is solved respectively, and the solution results are compared to find the main parameters that affect the tumor treatment effect. The specific steps are:

[0145] Modify the φ, β, and α parameters and solve the tumor treatment model respectively, and analyze the changes in tumor cell number density under different φ, β, and α parameters;

[0146] In this embodiment, in order to measure the influence of different φ, β, α parameters on the treatment effect, the ratio (N / K) of the number density of surviving cells (N) after 1 unit time after the start of photothermal-photodynamic therapy to the maximum environmental carrying capacity K is taken as an indicator. The smaller the value of N / K, the more tumors are killed by the photothermal-photodynamic synergistic therapy, and the better the killing effect.

[0147] In this embodiment, the parameters φ, β, and α are changed to obtain a curve diagram of the change of cell number density with the photothermal-photodynamic therapy time. Figure 3 , 4 , 5. It can be seen that β has a greater impact on the treatment effect.

[0148] Analyze the effect of the changes of φ, β, and α parameters on the ratio of the number density of surviving cells N to the maximum environmental carrying capacity K (N / K);

[0149] In this embodiment, Figure 6 As shown in the figure, in order to analyze the influence of the changes in the parameters φ, β, and α on the ratio N / K of the number density of surviving cells N to the maximum environmental carrying capacity K, a cross-sectional diagram of N / K with φ, β, and α as variables was constructed. The cross-sectional diagram of the value of N / K obtained when the three parameters φ, β, and α are changed within a reasonable range is shown. It can be roughly seen from the figure that the value of N / K decreases with the increase of β and α, that is, the larger the values ​​of β and α, the better the killing effect on tumor cells. The influence of the treatment phase difference φ on the treatment effect is more complicated.

[0150] A comprehensive analysis was conducted on the changes in tumor cell density under different φ, β, and α parameters, and the effects of φ, β, and α parameter changes on N / K to obtain the best parameter combination for killing tumor cells.

[0151] In this embodiment, in order to comprehensively analyze the changes in tumor cell density under different φ, β, α parameters, such as Figure 7 , 8 As shown in Figures 9, based on the effects of changes in the φ, β, and α parameters on N / K, a schematic diagram of the influence curve of φ, β, and α on N / K was also constructed. When φ=0, that is, when there is no phase difference between photothermal and photodynamic, N / K has the best killing effect on tumor cells. N / K decreases sharply with the increase of β, and gradually decreases with the increase of α. However, it is obvious that the impact of changing parameter α on N / K is much smaller than the impact of changing parameter β on N / K.

[0152] In this embodiment, based on the above analysis, it is concluded that in actual treatment, the time delay φ should be reduced to close to 0, and β should be increased to at least 0.08.

[0153] In a specific embodiment, in order to verify that the model can describe the synergistic effect between photothermal therapy and photodynamic therapy, it is necessary to obtain the Loewe isoeffect line diagram for photothermal and photodynamic therapy. In the Loewe isoeffect line diagram, each curve represents a curve with the same therapeutic effect obtained by two drugs or treatment methods at different doses. Among them, the convex isoeffect line represents that the two drugs or treatment methods have an antagonistic effect, the concave represents that the two drugs or treatment methods have a synergistic effect, and the straight line represents that the two drugs or treatment methods have an additive effect.

[0154] In this embodiment, the influence of the parameters φ, β, and α on the photothermal-photodynamic synergistic effect is analyzed, and the specific steps are as follows:

[0155] Analyze the impact of changes in φ, β, and α parameters on Q;

[0156] Set photosensitivity C0 and Q as coordinate axes, fix the value of N / K, perform multiple simulations based on the tumor treatment model to obtain simulated isoelectric curves; compare the additive isoelectric curves and simulated isoelectric curves when the relationship between photothermal and photodynamic therapy is additive, and calculate the synergistic effect value;

[0157] In this embodiment, the values ​​of C0 and Q are set so that the value of N / K just reaches 0.5 under a series of C0 and Q values, thereby obtaining the same therapeutic effect. By the above method, within the reasonable range of C0 and Q, the values ​​of C0 and Q are traversed with a specific step length, and the N / K value corresponding to each pair of C0 and Q values ​​is calculated. Then, by selecting a series of C0 and Q values ​​corresponding to N / K=0.5, and finally using Q and C0 as the horizontal and vertical axes of the coordinate graph, respectively, a curve of C0 with respect to Q is drawn, that is, Fig.10 The simulated isoelectric curve diagram is shown. By connecting the intersection points of the synergistic effect curve and the horizontal and vertical axes, the corresponding additive isoelectric curve can be obtained.

[0158] In this embodiment, Fig.11 As shown, the synergistic effect value R = S 阴影 / S Δ , where S 阴影 is the area bounded by the simulated iso-effect line and the summed iso-effect line, S Δ It is the area of ​​the triangle enclosed by the additive effect straight line and the horizontal and vertical axes. R is a proportional coefficient that reflects the synergistic effect of the two methods in the existing treatment plan. The larger the value of R, the better the synergistic effect of photothermal and photodynamic therapy.

[0159] Analyze the impact of changes in φ, β, and α parameters on the heat production parameter Q and the synergistic effect value, find the key parameters among φ, β, and α parameters, and regulate the photothermal and photodynamic combined synergistic therapy based on the key parameters.

[0160] In this embodiment, in order to analyze the influence of the changes of φ, β, and α parameters on the heat generation parameter Q and the synergistic effect value, as shown in FIG. Fig.12 , 13 As shown in Figures 14, the iso-effect curves corresponding to the changes in the parameters φ, β, and α when the value of N / K is 0.5 are constructed through the tumor treatment model; from these iso-effect curves, it can be seen that in the model established by the present invention, in the process of nanoprobes killing tumor cells, there is an obvious synergistic effect between photothermal therapy and sensitizer photodynamic therapy. Therefore, the model proposed in the present invention verifies the ability to describe the synergistic effects of photothermal and photodynamic therapy. It can be seen that in different The isoeffective lines obtained under the parameters of β and α are The β and α parameters gradually move downward as they increase. However, the degree of downward movement of the three parameters is quite different, and the change of the β parameter has a greater impact on the iso-effect line.

[0161] In this embodiment, the synergistic effect is measured using the R value, such as Fig.15 , 16 As shown in Figure 17, further, a schematic diagram of the curve of the influence of changes in the φ, β, and α parameters on the synergistic effect was constructed. It can be seen that the change in the active oxygen yield β of the photosensitizer increased under surface plasmon enhancement has a dramatic effect on the synergistic effect R. As β gradually increases from 0.01 to 0.15, the synergistic effect R gradually increases from 0.25 to about 0.66, but the rate of increase gradually decreases, making the change in the synergistic effect gradually stabilized.

[0162] Obviously, the above embodiments of the present invention are merely examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included in the protection scope of the claims of the present invention. It can also be seen that the synergistic effect R decreases linearly with the increase of the photothermal heat production rate α of the photosensitizer, but the rate of decrease is slow. As α gradually increases from 0.01 to 0.15, the synergistic effect R gradually increases from 0.57 to about 0.51, that is, the synergistic effect R is not sensitive to changes in α.

[0163] In this embodiment, in summary, the increased photosensitizer reactive oxygen yield β under surface plasmon enhancement is a key factor affecting the synergistic effect of probe photothermal-photodynamic therapy. Therefore, the photosensitizer reactive oxygen yield parameter should be adjusted as high as possible during the probe preparation process to improve the synergistic effect and thus enhance the therapeutic effect.

[0164] The present invention simulates the combined photothermal and photodynamic therapy of probes, prepares nano dumbbell structure probes, characterizes the probe performance, and studies the photothermal and photodynamic synergistic behavior of the nanoprobes obtained under different preparation parameters.

[0165] Based on the analysis of the present invention, a large number of gold nanorods were prepared in this embodiment, and their absorption spectra were measured; then, the two ends of the nanogold rods with an absorption peak of about 800nm ​​were selected for SiO2 layer wrapping to prepare nano dumbbell-shaped probes. Then, the morphology of the probes was observed using a transmission electron microscope, and the more ideal probes were selected for indocyanine green ICG attachment operation to obtain the final sample.

[0166] The analysis of the present invention shows that the treatment effect is best when photothermal and photodynamic therapy start to work at the same time. The most important factor affecting the synergistic effect of photothermal and photodynamic therapy is the increased photosensitizer active oxygen yield β under surface plasmon enhancement. This result has guiding significance for parameter regulation in the probe preparation process and optimization of the treatment process. The experiment successfully regulated the aspect ratio of the nanogold rods by changing the experimental parameters, thereby regulating the resonance absorption peak of the nanogold rods. The experiment successfully prepared a nano dumbbell-shaped probe and determined the appropriate parameter range for preparation. It was also proved through preliminary biological experiments that after the nano dumbbell-shaped probe was attached to the photosensitizer ICG, photothermal and photodynamic therapy had a synergistic effect.

[0167] The dumbbell-shaped A@mSiO2-ICG nanocomposite material finally prepared by the present invention has more efficient photothermal-photodynamic synergistic performance than the fully encapsulated Au@mSiO2-ICG nanoprobe. After the technology matures, it will be more efficient than single photothermal or photodynamic therapy, and may help humans eliminate cancer cells more efficiently, more accurately, and with fewer side effects.

[0168] Example 4

[0169] In this embodiment, the Runge-Kutta method program written in Mathematica is used to calculate the numerical solution of the model equations, and directly provide an image of the change of tumor cell number density x with time t.

[0170] Let Q be 1.5, C0 be 10, and other parameters be reference values, and solve the model equations in the range of 0 to 5. The obtained image of the tumor cell number density x changing with time t is as follows: Fig.18 As shown in the figure, we can see that x reaches a minimum value and then rises again. This is because the equation The concentration of organic dye photosensitizer C decreases exponentially with time, which makes the actual photodynamic therapy intensity B as Fig.19At the same time, due to the decomposition of the photosensitizer, the heat generated by the photosensitizer photothermal effect decreases, and the actual photothermal therapy intensity H will also decrease over time until a certain value, such as Fig. 20 As shown, therefore, due to the decrease in treatment intensity, x will rise again to a certain equilibrium point less than 10.

[0171] However, in the actual treatment process, the situation where x rises again will not occur. This is because in actual treatment, the tumor will be treated more intensively within a time period shorter than the tumor cell cycle to ensure that all tumor cells are killed. In order to verify this situation, the τ value representing the tumor cell cycle is adjusted to 10 in this embodiment, and the obtained xt curve is as follows Fig.21 As shown, at this time, the tumor cells are almost completely killed at t=3. This is in line with the actual situation. However, in this embodiment, in order to facilitate the study of the influence of different parameters on the efficacy and synergistic effect, the time lag τ is still taken as the reference value 1 in the following chapters.

[0172] In this embodiment, when constructing the simulated isobologram, the minimum value of x in a single simulation is selected as the indicator of therapeutic effect. Using the baseline value of the parameter, and setting the value of C0 to 20 and the value of Q to 0, the minimum value of x at this time is calculated. min Then set the value of C0 to 0, and calculate Q = 3.51 to make x min The value of is the same. At this time, Fig. 22 As shown in the figure, the indicated dose values ​​required to achieve the same therapeutic effect by using metal nanoparticles alone for photothermal therapy and organic dye photosensitizers alone for photodynamic therapy are obtained. Q and C0 are used as the horizontal and vertical axes of the coordinate graph, respectively, and the two sets of values ​​obtained before are the two points located on the two coordinate axes respectively. Connecting these two points with a straight line will give the straight line corresponding to the additive effect in the isoelectric line diagram.

[0173] With a fixed step size of 0.4 for Q, calculate the C0 value corresponding to each Q value in the range of 0 to 3.51 so that each set of (Q, C0) data can make x min Using the obtained data points, plot x min The simulated isoelectric curve when the value of is 4.91.

[0174] It can be clearly seen that x min The isotropic line when the value of is 4.91 is below the straight line as the additive isotropic line. This indicates that there is an obvious synergistic effect between metal nanoparticle photothermal therapy and organic dye photosensitizer photodynamic therapy. The proposed model verifies the ability to describe the synergistic effect of photothermal and photodynamic therapy.

[0175] In this embodiment, when analyzing the influence of the changes of φ, β, and α parameters on the heat generation parameter Q and the synergistic effect value, four groups of parameters are selected: Q = 2, C0 = 7; Q = 2, C0 = 5; Q = 1, C0 = 5; Q = 1, C0 = 7. The parameters other than the reference value are taken. The obtained curve is as follows Fig.23 As shown in the figure, x min Value The increase in the value increases nearly linearly. This means that the smaller the delay between the photodynamic therapy phase and the photothermal therapy effect, the better the effect of the combined treatment. The slope of the straight line when Q=2, C0=7 is almost the same as the slope of the straight line when Q=1, C0=7, the slope of the straight line when Q=2, C0=5 is almost the same as the slope of the straight line when Q=1, C0=5, and the slope of the straight line when C0=7 is greater than the slope of the straight line when C0=5. This shows that the relative lag of photodynamic therapy has a more significant effect on the effect of photodynamic therapy.

[0176] When the three iso-effect lines from top to bottom correspond to x min =4.91 isoelectric curve Fig.24 As shown in the figure, it can be clearly seen that the smaller the relative lag of photodynamic therapy, the smaller the photosensitizer dose required to achieve the same therapeutic effect. The shapes of the three iso-effect lines remain basically unchanged, indicating that the relative lag of photodynamic therapy does not significantly affect the intensity of the synergistic effect.

[0177] β=0, β=0.05, β=0.1, under three parameter values, x min =4.91 when the iso-effect line is as follows Fig.25 As shown in the figure, other parameters are taken as the baseline value during calculation. It can be found that as the β value increases, the degree of downward bending of the curve increases. This means that under the stronger surface plasmon enhanced photodynamic effect, the synergy between photothermal and photodynamic is stronger, and the same therapeutic effect can be achieved with a smaller dose for combined treatment.

[0178] It should be noted that the iso-effect line when β = 0 is close to a straight line, that is, close to the iso-effect line of the additive effect. This shows that when β = 0, the synergy of photothermal and photodynamic therapy is so weak that it can be ignored. This shows that in the situation simulated by this model, the synergistic effect of photothermal and photodynamic therapy in combined therapy is dominated by the surface plasmon enhanced photodynamic effect, while the photothermal effect of the photosensitizer has a weak effect on the synergistic effect.

[0179] The dose used in combined therapy can be used as an indicator of the strength of the synergistic effect under different β conditions. For the convenience of selection, the Q value can be fixed at 1.6, and the x value under different β conditions can be calculated. min=4.91 as the indicator of synergistic effect. The C0 values ​​when β values ​​are 0, 0.025, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, and 0.35 are calculated respectively. The β-C0 is plotted as Fig.26 as shown in .

[0180] It can be seen that as the β value increases, the required C0 value continues to decrease, and the rate of decrease is getting slower and slower. This symbolizes that the photothermal and photodynamic synergistic effects are enhanced with the enhancement of the surface plasmon phenomenon. When the surface plasmon phenomenon promotes photodynamics weakly, its enhancement has a strong influence on the synergistic effect. However, as the surface plasmon phenomenon becomes more and more powerful in promoting photodynamics, the enhancement of the synergistic effect will become less and less obvious. This indicates that there may be an optimal cost-effectiveness ratio when the synergistic effect caused by enhancing the surface plasmon is used to increase the efficacy.

[0181] Obviously, the above embodiments of the present invention are only examples for clearly explaining the present invention, and are not intended to limit the implementation methods of the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the claims of the present invention.

Claims

1. A modeling method for photothermal-photodynamic combined synergistic therapy, characterized by: The method includes the following specific steps: constructing a tumor growth model with time lag; On the basis of the tumor growth model, the photothermal and photodynamic treatment intensity terms and tumor killing terms were introduced respectively to construct a tumor treatment model.

2. The modeling method of photothermal-photodynamic combined synergistic therapy according to claim 1, characterized in that: Construct a tumor growth model with time lag, specifically: A tumor growth model with time lag is constructed based on either the Logistic growth model with time lag or the Allee model with time lag; If the Logistic growth model with time lag is used, the tumor growth model with time lag is constructed as follows: If the Allee model with time lag is used, the tumor growth model with time lag is constructed as follows: Among them, x(t) represents the real-time tumor cell density, r0 represents the natural growth rate of tumor cells, K represents the maximum carrying capacity of the environment, τ represents the time lag caused by the cell cycle of tumor cells, and A represents the Allee coefficient.

3. The modeling method of photothermal-photodynamic combined synergistic therapy according to claim 2, characterized in that: On the basis of the tumor growth model, the treatment intensity terms of photothermal and photodynamic therapy and tumor killing terms were introduced to construct a tumor treatment model, specifically: If the Logistic growth model with time lag is used, the constructed tumor treatment model is as follows: If the Allee growth model with time lag is used, the constructed tumor treatment model is as follows: Where H(t) is the real-time photothermal therapy intensity, is the intensity of time-delay photodynamic therapy; μ H is the tumor cell killing rate of photothermal therapy, μ B is the killing rate of tumor cells by photodynamic therapy; It is the lag time of the photodynamic therapy process relative to the photothermal therapy process, that is, the phase difference between the effects of the two treatments.

4. The modeling method for photothermal-photodynamic combined synergistic therapy according to claim 3, characterized in that: The actual rate of change of photothermal therapy intensity is expressed as: The actual change rate of photodynamic therapy intensity is expressed as: Where Q is the heat source term, representing the constant heat generation of the photothermal converter as a heat source under constant laser light irradiation, α is the heat generation rate of the photothermal effect of the photosensitizer, C(t) is the photosensitizer concentration, β C is the active oxygen production rate of the photosensitizer without enhancement, β is the active oxygen production rate of the photosensitizer increased by surface plasmon resonance enhancement, and λ H is the non-therapeutic heat loss rate, λ B is the non-therapeutic loss rate of reactive oxygen species, γ H is the heat treatment process loss rate, γ B is the loss rate of active oxygen during treatment.

5. The modeling method for photothermal-photodynamic combined synergistic therapy according to claim 4, characterized in that: The change of C(t) is specifically expressed as:

6. The modeling method for photothermal-photodynamic combined synergistic therapy according to claim 5, characterized in that: The initial conditions of the tumor treatment model are: x(0)=K, H(0)=0, B(0)=0, C(0)=C0; The model uses core-shell composite structure nanoparticles formed by shell-coated precious metal nanoparticles containing organic molecular photosensitizers as the treatment medium. All photosensitizers are enhanced by the metal surface plasmon resonance. The nanoparticles are evenly distributed in the tumor tissue, the external laser light source is constant and evenly irradiated, and the tumor is evenly distributed in space.

7. A method for optimizing photothermal and photodynamic combined synergistic therapy, characterized in that: The tumor treatment modeling method according to any one of claims 4 to 6 comprises the following specific steps: Substituting initial parameters into the model to initialize the tumor treatment model; Modify the φ, β, and α parameters and solve the tumor treatment model separately, compare the solution results, and find the optimal parameter combination; Based on the optimal parameter combination, the optimal synergistic treatment plan is designed.

8. The optimization method of photothermal-photodynamic combined synergistic therapy according to claim 7, characterized in that: Modify the φ, β, and α parameters and solve the tumor treatment model respectively. Compare the solution results to find the main parameters that affect the tumor treatment effect. The specific steps are: Modify the φ, β, and α parameters and solve the tumor treatment model respectively, and analyze the changes in tumor cell density under different φ, β, and α parameters; Analyze the effect of the changes of φ, β, and α parameters on the ratio N / K of the number density of surviving cells to the maximum environmental carrying capacity K; A comprehensive analysis was conducted on the changes in tumor cell density under different φ, β, and α parameters, and the effects of φ, β, and α parameter changes on N / K to obtain the best parameter combination for killing tumor cells.

9. The optimization method of photothermal and photodynamic combined synergistic therapy according to claim 8, characterized in that: The effects of φ, β, and α parameters on the photothermal-photodynamic synergistic effect are further analyzed. The specific steps are as follows: Analyze the impact of changes in φ, β, and α parameters on Q; Set photosensitivity C0 and Q as coordinate axes, fix the value of N / K, perform multiple simulations based on the tumor treatment model to obtain simulated isoelectric curves; compare the additive isoelectric curves and simulated isoelectric curves when the relationship between photothermal and photodynamic therapy is additive, and calculate the synergistic effect value; Analyze the impact of changes in φ, β, and α parameters on the heat generation parameter Q and the synergistic effect value, find the key parameters among φ, β, and α parameters, and regulate the preparation plan of the probe used in photothermal-photodynamic therapy based on the key parameters.

10. The optimization method of photothermal and photodynamic combined synergistic therapy according to claim 9, characterized in that: The synergistic effect value R = S 阴影 / S Δ , where S 阴影 is the area bounded by the simulated iso-effect line and the summed iso-effect line, S Δ It is the area of ​​the triangle enclosed by the additive effect straight line and the horizontal and vertical axes. R is a proportional coefficient that reflects the synergistic effect of the two methods in the existing treatment plan. The larger the value of R, the better the synergistic effect of photothermal and photodynamic therapy.

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