Magnetic nanoparticle heat production simulation method based on Monte Carlo algorithm

Abstract

The invention relates to a Monte Carlo algorithm-based magnetic nanoparticle heat production simulation method. The method comprises the following steps of S1, initializing boundary and internal magnetic nanoparticle related parameters; s2, setting initial positions of the magnetic nanoparticles, and assuming that the magnetic nanoparticles are randomly and disorderly distributed in a limited space in an initial state; s3, after the magnetic field is added, the magnetic nanoparticles are distributed in a chain shape in the direction of the magnetic field under the influence of the external magnetic field; monte Carlo is used for simulating movement of the magnetic nanoparticles after being influenced by a magnetic field; s4, importing the moved geometric model of the magnetic nanoparticles into a biological heat transfer model; and S5, setting the magnetic nanoparticles as a heat source, setting parameters of the biological heat transfer model, and performing temperature simulation. The method is beneficial to accurately simulating the temperature distribution of the magnetic nanoparticles after heat production in the biological tissue.

Description

Technical Field

[0001] The present invention relates to the field of the thermal effect of magnetic nanoparticles, and particularly relates to a method for simulating the heat generation of magnetic nanoparticles based on the Monte Carlo algorithm. Background Art

[0002] Magnetic nanoparticles exhibit superparamagnetism when their size is reduced to a certain extent and generate heat under an alternating magnetic field. The core principle is that magnetic nanoparticles exhibit hysteresis loss and relaxation loss in an alternating magnetic field, that is, the electromagnetic energy they lose is converted into heat energy. Generally, abnormal biological tissue cells will undergo apoptosis when the temperature reaches 42°C, while the heat resistance of healthy tissue cells can generally reach 46°C. Therefore, controlling the heat generation effect of magnetic nanoparticles and keeping the temperature of biological tissue within a suitable range can destroy abnormal tissue without damaging healthy tissue. In the process of studying the heat generation effect of magnetic nanoparticles, how to simulate the random distribution of magnetic nanoparticles in biological tissue and their heat generation effect is a problem to be studied. Summary of the Invention

[0003] The purpose of the present invention is to provide a method for simulating the heat generation of magnetic nanoparticles based on the Monte Carlo algorithm, which is conducive to accurately simulating the temperature distribution after heat generation of magnetic nanoparticles in biological tissue.

[0004] In order to achieve the above purpose, the technical solution adopted by the present invention is: a method for simulating the heat generation of magnetic nanoparticles based on the Monte Carlo algorithm, including the following steps:

[0005] Step S1: Initialize the parameters related to the boundary and internal magnetic nanoparticles;

[0006] Step S2: Set the initial positions of the magnetic nanoparticles. Assume that in the initial state, the magnetic nanoparticles are randomly and disorderly distributed in a limited space;

[0007] Step S3: After applying the magnetic field, the magnetic nanoparticles are affected by the external magnetic field and are distributed in a chain along the magnetic field direction; use Monte Carlo to simulate the movement of the magnetic nanoparticles after being affected by the magnetic field;

[0008] Step S4: Import the geometric model of the magnetic nanoparticles after movement into the bioheat transfer model;

[0009] Step S5: Set the magnetic nanoparticles as heat sources, set the parameters of the bioheat transfer model, and perform temperature simulation.

[0010] Further, in step S1, the boundary is set as an ellipse, and its parameters include the major axis length a and the minor axis length b. The magnetic nanoparticles are set as circles, and their parameters include the particle diameter d and the number of magnetic nanoparticles num.

[0011] Further, step S2 specifically includes the following steps:

[0012] Step S21: Take the coordinates of magnetic nanoparticles with a uniform probability distribution within a given finite space range;

[0013] Step S22: Determine whether the magnetic nanoparticles exceed the boundary. If they exceed, return to step S21 to re-take the coordinates of the magnetic nanoparticles. If not, proceed to the next step;

[0014] Step S23: Determine whether the currently taken magnetic nanoparticles coincide with the previously taken magnetic nanoparticles. If they coincide, return to S21 to re-take the coordinates of the magnetic nanoparticles. If not, proceed to the next step;

[0015] Step S24: Determine whether the number of currently taken magnetic nanoparticles has reached the set number num of magnetic nanoparticles. If not, continue to take until the set number num of magnetic nanoparticles is reached.

[0016] Further, step S3 specifically includes the following steps:

[0017] Step S31: Set the magnetic field strength, magnetic field direction, and the number of Monte Carlo simulation iterations N; Initialize the parameters i = 1, j = 1, where i represents the i-th magnetic nanoparticle and j represents the j-th iteration;

[0018] Step S32: Move the i-th magnetic nanoparticle and determine whether the magnetic nanoparticle exceeds the boundary or coincides with other magnetic nanoparticles after moving. If it exceeds the boundary or coincides with other magnetic nanoparticles, re-move the magnetic nanoparticle until the magnetic nanoparticle is within the boundary and there is no coincidence;

[0019] Step S33: Calculate the overall potential energy of the magnetic nanoparticle after moving and before moving, represented by E new and E old respectively; If E old is less than E new , then save the coordinates of the magnetic nanoparticle after displacement as the new coordinates. Otherwise, retain the new coordinates after this displacement with a set probability;

[0020] Step S34: Determine whether the iteration number j has reached N. If it has reached, end the iteration and the Monte Carlo simulation is completed. If not, let:

[0021]

[0022] j = j + 1

[0023] where num represents the number of magnetic nanoparticles; Then repeat steps S32 - S34 to continue the loop iteration.

[0024] Furthermore, the overall potential energy mainly includes magnetic potential energy, steric energy, magnetic interaction energy, and van der Waals potential energy.

[0025] Furthermore, step S4 specifically includes the following steps:

[0026] Step S41: Construct a geometric model of the organ contour outside the boundary, where the boundary is inside the organ contour;

[0027] Step S42: Import the geometric model including the organ contour, the boundary, and the magnetically modified nanoparticles moved inside it into the bioheat transfer model;

[0028] Step S43: Set the outside of the boundary as healthy tissue and the inside of the boundary as local abnormal tissue.

[0029] Furthermore, in step S5, set the magnetically modified nanoparticles inside the boundary as heat sources, set the heat transfer time as 300 s, and use the finite element analysis method to analyze and obtain the model temperature distribution results.

[0030] Compared with the prior art, the present invention has the following beneficial effects: The present invention provides a method for simulating heat generation of magnetically modified nanoparticles based on the Monte Carlo algorithm. When simulating the heat generation of magnetically modified nanoparticles, this method considers the case where magnetically modified nanoparticles agglomerate into chains in the presence of an external magnetic field. On this basis, the simulation of the temperature distribution after heat generation of magnetically modified nanoparticles in biological tissues is realized, improving the accuracy of the simulation, and thus providing technical support for subsequent research on controlling the heat generation effect of magnetically modified nanoparticles. Description of the Drawings

[0031] Figure 1 is the flowchart of the method implementation of the embodiment of the present invention;

[0032] Figure 2 is the initial state diagram of the magnetically modified nanoparticles in the embodiment of the present invention;

[0033] Figure 3 is the Monte Carlo simulation result diagram in the embodiment of the present invention;

[0034] Figure 4 is the overall model diagram in the embodiment of the present invention;

[0035] Figure 5 is the model temperature distribution simulation diagram in the embodiment of the present invention. Detailed Embodiments

[0036] The present invention will be further described below in conjunction with the drawings and embodiments.

[0037] It should be noted that the following detailed description is exemplary and is intended to provide further illustration of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present application belongs.

[0038] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular forms are also intended to include the plural forms. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they specify the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0039] As Figure 1 shown, this embodiment provides a method for simulating the heat generation of magnetic nanoparticles based on the Monte Carlo algorithm, including the following steps:

[0040] Step S1: Initialize the parameters related to the boundary and internal magnetic nanoparticles.

[0041] Step S2: Set the initial positions of the magnetic nanoparticles. Assume that in the initial state, the magnetic nanoparticles are randomly and disorderly distributed in a finite space.

[0042] Step S3: After applying a magnetic field, the magnetic nanoparticles are affected by the external magnetic field and are distributed in a chain along the magnetic field direction; use Monte Carlo simulation to simulate the movement of the magnetic nanoparticles after being affected by the magnetic field.

[0043] Step S4: Import the geometric model of the moved magnetic nanoparticles into the bioheat transfer model.

[0044] Step S5: Set the magnetic nanoparticles as heat sources, set the parameters of the bioheat transfer model, and perform temperature simulation.

[0045] In step S1, an elliptical boundary is constructed, and its parameters include the major axis length a and the minor axis length b. The magnetic nanoparticles are set as circular, and its parameters include the particle diameter d and the number of magnetic nanoparticles num. In this embodiment, the major axis of the given elliptical boundary is 0.7 um, the minor axis is 0.4 um, the particle diameter d is set to 16 nm, and the number of magnetic nanoparticles num is set to 100.

[0046] The specific implementation steps of step S2 are as follows.

[0047] Step S21: Take the coordinates of the magnetic nanoparticles with a uniform probability distribution within the given finite space range.

[0048] Step S22: Determine whether the magnetic nanoparticles exceed the boundary. If they exceed, return to step S21 to re-take the coordinates of the magnetic nanoparticles. If they do not exceed, proceed to the next step.

[0049] Step S23: Determine whether the currently picked magnetic nanoparticles coincide with the previously picked magnetic nanoparticles. If they coincide, return to S21 to pick the coordinates of the magnetic nanoparticles again. If they do not coincide at all, proceed to the next step.

[0050] Step S24: Determine whether the number of currently picked magnetic nanoparticles has reached the set number num of magnetic nanoparticles. If not, continue to pick until the number of particles set in Step S1, which is 100, is reached.

[0051] Figure 2 It is the initial state diagram of the magnetic nanoparticles obtained by initialization in this embodiment.

[0052] In this embodiment, as Figure 3 shown, after being affected by the magnetic field according to Step S3, the particles agglomerate into a chain-like structure. The specific implementation steps of Step S3 are as follows.

[0053] Step S31: Set the magnetic field strength, set the magnetic field direction to be along the x-axis direction, and set the number of Monte Carlo simulation iterations N to 400000. Initialize the parameters i = 1, j = 1, where i represents the i-th magnetic nanoparticle and j represents the j-th iteration.

[0054] Step S32: Move the i-th magnetic nanoparticle, and determine whether the magnetic nanoparticle exceeds the boundary or coincides with other magnetic nanoparticles after the movement. If it exceeds the boundary or coincides with other magnetic nanoparticles, move the magnetic nanoparticle again until the magnetic nanoparticle is within the boundary and there is no coincidence.

[0055] Step S33: Calculate the overall potential energy of the magnetic nanoparticle after and before the movement, and represent them with E new and E old respectively.

[0056] The overall potential energy mainly includes magnetic potential energy, steric energy, magnetic interaction energy, and van der Waals potential energy, and can be expressed as:

[0057] E total = E R + E D - E H - E V

[0058]

[0059]

[0060] Among them, E total represents the overall potential energy, E R represents the magnetic potential energy, E D represents the steric energy, E Hrepresents the magnetic interaction energy, E V represents the van der Waals potential energy; ζ is the number of surfactant molecules adsorbed on the surface of a unit particle, α is the thickness of the surfactant on the particle surface, S is the surface distance between particles, μ0 is the magnetic permeability of vacuum, taking 4π×10 -7 H / m, R is the distance between particles, is the distance vector from particle i to particle j, is the magnetic moment of the particle, is the applied magnetic field, A is the Hamaker constant, taking 10 -19 , L = 2S / d.

[0061] Record the particle coordinates before and after each displacement and calculate the potential energy E old and E new . If E old is less than E new , then save the coordinates of the particle after displacement as the new coordinates, otherwise retain the new coordinates after this displacement with a set transfer probability; specifically: generate a random number r uniformly distributed in [0,1] after each displacement, and the transfer probability is expressed as:

[0062]

[0063] where k is the Boltzmann constant, generally taking 1.38×10 -23 ; T is the temperature, taking 310.15K; when P>r, retain the new coordinates after displacement, otherwise retain the original coordinates.

[0064] Step S34: Determine whether the iteration number j reaches N. If it reaches N, end the iteration and the Monte Carlo simulation is completed. If it does not reach, then let:

[0065]

[0066] j = j + 1

[0067] where num represents the number of magnetic nanoparticles, num = 100; then repeat steps S32 - S34 to continue the loop iteration. That is, if i exceeds the number of magnetic nanoparticles, start the loop iteration from i = 1, but the j count continues to accumulate until it reaches N.

[0068] The specific implementation steps of step S4 are as follows.

[0069] Step S41: Construct a geometric model of the organ contour outside the boundary, and the boundary is inside the organ contour.

[0070] Step S42: Import the geometric model including the organ contour, the boundary and the magnetic nanoparticles moved inside it into the bioheat transfer model.

[0071] Step S43: Set the area outside the boundary as healthy tissue and the area inside the boundary as locally abnormal tissue.

[0072] In this embodiment, as Figure 4 shown, in order to more clearly observe the influence of the internal particle distribution of magnetic hyperthermia on temperature, Figure 3 is magnified and imported into the biological tissue model. At this time, the long axis of the internal ellipse is 7 mm, the short axis is 4 mm, the particle size is 0.16 mm, and the external tissue contour adopts a mouse liver model.

[0073] In step S5, set the magnetic nanoparticles inside the boundary as heat sources, set the heat transfer time to 300 s, and use the finite element analysis method to analyze and obtain the model temperature distribution result. As Figure 5 shown, high temperature occurs locally where the particles aggregate, and the temperature distribution is slightly uneven.

[0074] Those skilled in the art should understand that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) containing computer-usable program codes.

[0075] The present application is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to the embodiments of the present application. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for implementing the functions specified in Figure 1 one or more flows and / or Figure 1 blocks or multiple blocks.

[0076] These computer program instructions can also be stored in a computer-readable memory capable of guiding a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that implement the functions specified in Figure 1 one or more flows and / or Figure 1 blocks or multiple blocks.

[0077] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus, so that a series of operation steps are performed on the computer or other programmable apparatus to produce a computer-implemented process, thereby the instructions executed on the computer or other programmable apparatus provide steps for implementing the functions specified in one process Figure 1 one process or multiple processes and / or blocks Figure 1 steps of the functions specified in one block or multiple blocks.

[0078] As mentioned above, it is only the preferred embodiment of the present invention, and is not a limitation of the present invention in other forms. Any person skilled in the art may use the disclosed technical content to make changes or modifications into equivalent embodiments with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiments based on the technical essence of the present invention without departing from the technical solution content of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A method for simulating the heat generation of magnetic nanoparticles based on the Monte Carlo algorithm, characterized in that, It includes the following steps: Step S1: Initialize the parameters related to the boundary and internal magnetic nanoparticles; Step S2: Set the initial positions of the magnetic nanoparticles. Assume that in the initial state, the magnetic nanoparticles are randomly and disorderly distributed within a finite space; Step S3: After applying a magnetic field, the magnetic nanoparticles are affected by the external magnetic field and are distributed in a chain along the magnetic field direction; Use Monte Carlo simulation to simulate the movement of the magnetic nanoparticles after being affected by the magnetic field; Step S4: Import the geometric model of the moved magnetic nanoparticles into the bioheat transfer model; Step S5: Set the magnetic nanoparticles as heat sources, set the parameters of the bioheat transfer model, and conduct temperature simulation.

2. The method for simulating the heat generation of magnetic nanoparticles based on the Monte Carlo algorithm according to claim 1, wherein, In Step S1, the boundary is set as an ellipse, and its parameters include the major axis length a and the minor axis length b. The magnetic nanoparticles are set as circles, and their parameters include the particle size d and the number of magnetic nanoparticles num.

3. The method for simulating heat generation of magnetic nanoparticles based on the Monte Carlo algorithm according to claim 1, wherein Step S2 specifically includes the following steps: Step S21: Take the coordinates of the magnetic nanoparticles with a uniform probability distribution within a given finite space range; Step S22: Determine whether the magnetic nanoparticles exceed the boundary. If they exceed, return to Step S21 to re-take the coordinates of the magnetic nanoparticles. If they do not exceed, proceed to the next step; Step S23: Determine whether the currently taken magnetic nanoparticles coincide with the previously taken magnetic nanoparticles. If they coincide, return to S21 to re-take the coordinates of the magnetic nanoparticles. If they do not coincide at all, proceed to the next step; Step S24: Determine whether the number of currently taken magnetic nanoparticles has reached the set number of magnetic nanoparticles num. If it has not reached, continue to take until the set number of magnetic nanoparticles num is reached.

4. The method for simulating the heat generation of magnetic nanoparticles based on the Monte Carlo algorithm according to claim 1, characterized in that Step S3 specifically includes the following steps: Step S31: Set the magnetic field strength, magnetic field direction, and the number of iterations N of the Monte Carlo simulation; Initialize the parameters i = 1, j = 1, where i represents the i-th magnetic nanoparticle and j represents the j-th iteration; Step S32: Move the i-th magnetic nanoparticle, and determine whether the magnetic nanoparticle exceeds the boundary or coincides with other magnetic nanoparticles after moving. If it exceeds the boundary or coincides with other magnetic nanoparticles, re-move the magnetic nanoparticle until the magnetic nanoparticle is within the boundary and there is no coincidence; Step S33: Calculate the overall potential energy of the magnetic nanoparticles after and before movement, denoted by E new and E old respectively; if E old is less than E new , then save the coordinates of the magnetic nanoparticles after displacement as the new coordinates, otherwise retain the new coordinates after this displacement with a set probability; Step S34: Determine whether the number of iterations j has reached N. If it has reached, end the iteration and the Monte Carlo simulation is completed. If it has not reached, then let: j = j + 1 where num represents the number of magnetic nanoparticles; Then repeat Steps S32 - S34 to continue the loop iteration.

5. The method for simulating heat generation of magnetic nanoparticles based on the Monte Carlo algorithm according to claim 4, characterized in that, The overall potential energy mainly includes magnetic potential energy, steric energy, magnetic interaction energy, and van der Waals potential energy.

6. The method for simulating the heat generation of magnetic nanoparticles based on the Monte Carlo algorithm according to claim 5, wherein The overall potential energy is expressed as: E total = E R + E D - E H - E V Among them, E represents total the overall potential energy, E R represents the magnetic potential energy, E D represents the steric energy, E H represents the magnetic interaction energy, E V represents the van der Waals potential energy; ζ is the number of surfactant molecules adsorbed on the surface of a unit particle, α is the thickness of the surfactant on the particle surface, S is the surface distance between particles, μ0 is the magnetic permeability of vacuum, R is the distance between particles, is the distance vector from particle i to particle j, is the magnetic moment of the particle, is the applied magnetic field, A is the Hamaker constant, L = 2S / d.

7. The method for simulating heat generation of magnetic nanoparticles based on the Monte Carlo algorithm according to claim 4, characterized in that, Record the particle coordinates before and after each displacement and calculate the potential energy E old and E new ; If E old is less than E new , then save the coordinates of the particle after displacement as the new coordinates, otherwise retain the new coordinates after this displacement with a set transition probability. Specifically: Generate a random number r uniformly distributed in [0, 1] after each displacement, and the transition probability is expressed as: where k is the Boltzmann constant, T is the temperature. When P > r, retain the new coordinates after displacement, otherwise retain the original coordinates.

8. The method for simulating heat generation of magnetic nanoparticles based on the Monte Carlo algorithm according to claim 1, wherein Step S4 specifically includes the following steps: Step S41: Construct a geometric model of the organ contour outside the boundary, and the boundary is inside the organ contour; Step S42: Import the geometric model including the organ contour, boundary, and the moved magnetic nanoparticles inside it into the bioheat transfer model; Step S43: Set the outside of the boundary as healthy tissue and the inside of the boundary as local abnormal tissue.

9. The method for simulating heat generation of magnetic nanoparticles based on the Monte Carlo algorithm according to claim 1, characterized in that In step S5, the magnetic nanoparticles inside the boundary are set as the heat source, the heat transfer time is set to 300 s, and the finite element analysis method is used to analyze and obtain the model temperature distribution result.

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