Method for predicting temperature in biological tissue based on polydispersity of magnetic nanoparticles

Abstract

The present application relates to a kind of biological tissue temperature prediction methods based on magnetic nanoparticle polydispersity, comprising the following steps: step S1: the geometric model of biological tissue is constructed;Step S2: based on the geometric model of biological tissue, the geometric model of magnetic nanoparticle with polydispersity is constructed;Step S3: pre-setting the parameter of the geometric model of magnetic nanoparticle with polydispersity;Step S4: based on the geometric model of magnetic nanoparticle with polydispersity, by solving Pennes biological heat transfer equation, the temperature distribution in biological tissue is predicted.The present application realizes the prediction of temperature distribution in biological tissue region under the condition of magnetic nanoparticle polydispersity.

Description

Technical Field

[0001] This invention relates to the field of magnetic nanoparticle modeling technology, and more specifically to a method for predicting temperature within biological tissues based on the polydispersity of magnetic nanoparticles. Background Technology

[0002] Magnetic nanothermotherapy is an emerging tissue thermal ablation technology with advantages such as high safety, accurate positioning, and minimal side effects. Magnetic nanoparticles absorb magnetic field energy and convert it into heat energy due to the relaxation effect under the influence of an alternating magnetic field, thereby achieving tissue thermal ablation. During magnetic nanothermotherapy, the particle size distribution of the magnetic nanoparticles, the properties of the applied magnetic field, and the properties of the biological tissue all affect the therapeutic effect.

[0003] Previous work has mostly considered the impact of magnetic nanoparticles with constant radii on the temperature distribution of magnetothermal therapy. However, due to technological limitations, not all magnetic nanoparticles have the same radius during synthesis; therefore, it is necessary to calculate the average power dissipation based on the particle size distribution. Although the radius of magnetic nanoparticles is not constant, it still exhibits certain patterns. A commonly used and reasonable distribution pattern for magnetic nanoparticles is a log-normal distribution. Summary of the Invention

[0004] In view of this, the purpose of this invention is to provide a method for predicting temperature within biological tissues based on the polydispersity of magnetic nanoparticles, thereby enabling the prediction of temperature distribution within biological tissue regions under the condition of magnetic nanoparticle polydispersity.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] A method for predicting intracellular temperature in biological tissues based on the polydispersity of magnetic nanoparticles includes the following steps:

[0007] Step S1: Construct a geometric model of the biological tissue;

[0008] Step S2: Based on the geometric model of biological tissue, construct a geometric model of magnetic nanoparticles with polydispersity;

[0009] Step S3: Pre-set the parameters of the geometric model of the polydisperse magnetic nanoparticles;

[0010] Step S4: Based on the geometric model of multidispersed magnetic nanoparticles, the temperature distribution inside biological tissues is predicted by solving the Pennes biological heat transfer equation.

[0011] Furthermore, the geometric model of the biological tissue includes a circle with radius R1 and a circle with radius R2, where R1 < R2. The area containing the circle with radius R1 is the first tissue region, and the area outside the circle is the second tissue region.

[0012] Furthermore, step S2 specifically includes:

[0013] Step S21: Generate a radius that conforms to a log-normal distribution;

[0014] Step S22: Draw circular magnetic nanoparticles;

[0015] Step S23: Randomly generate the position coordinates of the magnetic nanoparticles so that the drawn magnetic nanoparticles are distributed in the first tissue region. If the magnetic nanoparticles are distributed outside the first tissue region at this time, the position coordinates of the magnetic nanoparticles need to be regenerated until the magnetic nanoparticles are distributed in the first tissue region.

[0016] Step S24: Determine whether the magnetic nanoparticles in the first tissue region overlap. If the drawn magnetic nanoparticles overlap, repeat step S23 to generate new position coordinates of the magnetic nanoparticles until the magnetic nanoparticles are distributed in the first tissue region and do not overlap.

[0017] Step S25: Repeat steps S21-S24 until the volume of all magnetic nanoparticles exceeds the preset proportion of the first tissue region.

[0018] Furthermore, the radius distribution of the magnetic nanoparticles conforms to a log-normal distribution, and the particle size distribution of the magnetic nanoparticles is expressed as follows:

[0019]

[0020]

[0021] Where g(R) represents the particle size distribution of the magnetic nanoparticles, σ represents the standard deviation of ln R, R represents the radius of the magnetic nanoparticles, and ln R0 represents the median of ln R.

[0022] Furthermore, the parameters include material property parameters and settings for alternating magnetic field strength and frequency, wherein the material property parameters include the constant pressure heat capacity, thermal conductivity, and density of the first and second tissue regions.

[0023] Furthermore, the power dissipation of the magnetic nanoparticles is related to the magnetic field strength and frequency of the alternating magnetic field, and the power dissipation of the magnetic nanoparticles is expressed as follows:

[0024]

[0025] Where P represents the power dissipation of the magnetic nanoparticles, μ0 represents the permeability in vacuum, χ0 represents the actual magnetic susceptibility corresponding to the Langevin equation, f represents the frequency of the alternating magnetic field, H0 represents the intensity of the alternating magnetic field, and τ represents the relaxation time.

[0026] Furthermore, the Pennes biological heat transfer equation is specifically as follows:

[0027]

[0028] Where ρ represents tissue density, c represents tissue specific heat capacity, T represents tissue absolute temperature, t represents heating time, and Q... m α represents the metabolic heat per unit volume in the tissue, α represents the power dissipation correction factor for the magnetic nanoparticles, P represents the power dissipation of the magnetic nanoparticles, and ω represents the power dissipation of the magnetic nanoparticles. b ρ represents the blood perfusion rate. b c represents blood density. b T represents the specific heat capacity of blood. b The value represents the blood temperature, and k represents the thermal conductivity coefficient of the tissue.

[0029] Furthermore, the outer surface of the second tissue region in the Pennes bioheat transfer equation needs to satisfy the following boundary conditions:

[0030] T[r=R2]=37℃ (5)

[0031] Where T represents temperature and R2 is the radius of the second tissue region.

[0032] Compared with the prior art, the present invention has the following advantages:

[0033] This invention enables the prediction of temperature distribution within biological tissue regions under the condition of polydispersity of magnetic nanoparticles. Attached Figure Description

[0034] Figure 1 This is a flowchart of the method of the present invention;

[0035] Figure 2 This is a schematic diagram of the geometric model constructed in one embodiment of the present invention;

[0036] Figure 3 This is a schematic diagram of a geometric model of multidispersed magnetic nanoparticles constructed in one embodiment of the present invention;

[0037] Figure 4 This is a schematic diagram of temperature distribution prediction within a heated biological tissue region according to one embodiment of the present invention. Detailed Implementation

[0038] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0039] Please refer to Figure 1 This invention provides a method for predicting intracellular temperature in biological tissues based on the polydispersity of magnetic nanoparticles, comprising the following steps:

[0040] Step S1: Construct a geometric model of the biological tissue;

[0041] Step S2: Based on the geometric model of biological tissue, construct a geometric model of magnetic nanoparticles with polydispersity;

[0042] Step S3: Pre-set the parameters of the geometric model of the polydisperse magnetic nanoparticles;

[0043] Step S4: Based on the geometric model of multidispersed magnetic nanoparticles, the temperature distribution inside biological tissues is predicted by solving the Pennes biological heat transfer equation.

[0044] Preferably, in this embodiment, the geometric model for constructing biological tissue described in step S1 is as follows: Figure 2 As shown, the geometric model includes a circle with a radius of R1 = 15 mm and a circle with a radius of R2 = 25 mm. The area containing the circle with a radius of R1 = 15 mm is the first tissue region, and the area outside is the second tissue region.

[0045] Preferably, in this embodiment, step S2 specifically includes:

[0046] Step S21: Generate a radius that conforms to a log-normal distribution;

[0047] Step S22: Draw circular magnetic nanoparticles;

[0048] Step S23: Randomly generate the position coordinates of the magnetic nanoparticles so that the drawn magnetic nanoparticles are distributed in the first tissue region. If the magnetic nanoparticles are distributed outside the first tissue region at this time, the position coordinates of the magnetic nanoparticles need to be regenerated until the magnetic nanoparticles are distributed in the first tissue region.

[0049] Step S24: Determine whether the magnetic nanoparticles in the first tissue region overlap. If the drawn magnetic nanoparticles overlap, repeat step S23 to generate new position coordinates of the magnetic nanoparticles until the magnetic nanoparticles are distributed in the first tissue region and do not overlap.

[0050] Step S25: Repeat steps S21, S22, S23, and S24 until the volume of all magnetic nanoparticles exceeds 70% of the first tissue region.

[0051] Preferably, in this embodiment, the radius distribution of the magnetic nanoparticles in step S2 conforms to a log-normal distribution, and the particle size distribution of the magnetic nanoparticles is expressed as follows:

[0052]

[0053]

[0054] Where g(R) represents the particle size distribution of the magnetic nanoparticles, σ = 0.209 represents the standard deviation of ln R, R represents the radius of the magnetic nanoparticles, and ln R0 = 2.699 represents the median of ln R. The geometric model of polydisperse magnetic nanoparticles is as follows: Figure 3 As shown.

[0055] Preferably, in this embodiment, the setting of material property parameters and the setting of alternating magnetic field strength and frequency in step S3, wherein the material property parameters include the constant-pressure heat capacity, thermal conductivity, and density of the first and second microstructure regions. The constant-pressure heat capacity, thermal conductivity, and density of the first microstructure region are 3540 J·kg⁻¹. -1 ·K -1 0.52 W·m -1 ·K -1 1060Kg·m -3 The constant-pressure heat capacity, thermal conductivity, and density of the second tissue region are 4180 J·kg⁻¹. -1 ·K -1 0.59 W·m -1 ·K -1 1064 kg·m -3 .

[0056] Preferably, in this embodiment, the power dissipation of the magnetic nanoparticles in step S3 is related to the magnetic field strength and magnetic field frequency of the alternating magnetic field, and the power dissipation of the magnetic nanoparticles is expressed as follows:

[0057]

[0058] Where P represents the power dissipation of the magnetic nanoparticles, μ0 represents the permeability in vacuum, χ0 represents the actual magnetic susceptibility corresponding to the Langevin equation, f = 300 kHz represents the frequency of the alternating magnetic field, and H0 = 15 kA·m -1 The value represents the intensity of the alternating magnetic field, and τ represents the relaxation time.

[0059] Preferably, in this embodiment, the biological heat transfer mathematical model constructed by Pennes' biological heat transfer theory in step S4 is expressed as follows:

[0060]

[0061] Where ρ represents tissue density, c represents tissue specific heat capacity, T represents tissue absolute temperature, t represents heating time, and Q... m α represents the metabolic heat per unit volume in the tissue, α represents the power dissipation correction factor for the magnetic nanoparticles, P represents the power dissipation of the magnetic nanoparticles, and ω represents the power dissipation of the magnetic nanoparticles. b ρ represents the blood perfusion rate. b c represents blood density. bT represents the specific heat capacity of blood. b The value represents the blood temperature, and k represents the thermal conductivity coefficient of the tissue. Figure 4 This is a tissue temperature distribution map obtained by solving a biological heat transfer model using the finite element method.

[0062] Preferably, in this embodiment, the outer surface of the second tissue region in the biological heat transfer mathematical model needs to satisfy the following boundary conditions:

[0063] T[r=R2]=37℃ (5)

[0064] Where T represents temperature and R2 is the radius of the second tissue region.

[0065] The above description is only a preferred embodiment of the present invention. All equivalent changes and modifications made within the scope of the claims of the present invention should be included in the scope of the present invention.

Claims

1. A method for predicting temperature in biological tissue based on polydispersity of magnetic nanoparticles, characterized by, The method comprises the following steps: Step S1: constructing a geometric model of a biological tissue; Step S2: constructing a geometric model of magnetic nanoparticles with polydispersity based on the geometric model of the biological tissue; Step S3: presetting parameters of the geometric model of the magnetic nanoparticles with polydispersity; Step S4: predicting a temperature distribution inside the biological tissue by solving the Pennes bio-heat equation based on the geometric model of the magnetic nanoparticles with polydispersity; The step S2 is specifically: Step S21: generating radii conforming to a lognormal distribution; Step S22: drawing the magnetic nanoparticles in a circular shape; Step S23: randomly generating position coordinates of the magnetic nanoparticles, so that the drawn magnetic nanoparticles are distributed in the first tissue region, and if the magnetic nanoparticles are distributed outside the first tissue region at this time, the position coordinates of the magnetic nanoparticles need to be regenerated until the magnetic nanoparticles are distributed in the first tissue region; Step S24: judging whether the magnetic nanoparticles in the first tissue region overlap, if the drawn magnetic nanoparticles overlap, repeating step S23 to generate new position coordinates of the magnetic nanoparticles until the magnetic nanoparticles are distributed in the first tissue region and do not overlap; Step S25: repeating steps S21-S24 until the volume of all magnetic nanoparticles exceeds a preset proportion of the first tissue region; The radius distribution of the magnetic nanoparticles conforms to a lognormal distribution, and the particle size distribution of the magnetic nanoparticles is represented as: （1） （2） wherein, represents a particle size distribution of the magnetic nanoparticle, represents a standard deviation of represents a radius of the magnetic nanoparticle, represents a median of 2. The method of predicting temperature in biological tissue based on polydispersity of magnetic nanoparticles according to claim 1, characterized in that, The geometric model of the biological tissue includes a circle with a radius of and a circle with a radius of , < wherein the area in which the circle with a radius of is located is the first tissue area and the area other than this is the second tissue area.

3. The method of predicting temperature in biological tissue based on polydispersity of magnetic nanoparticles according to claim 1, characterized in that, The parameters include material attribute parameters and set alternating magnetic field strength and frequency, wherein the material attribute parameters include constant pressure heat capacity, thermal conductivity, and density of the first tissue region and the second tissue region.

4. The method of predicting temperature in biological tissue based on polydispersity of magnetic nanoparticles according to claim 3, characterized in that, The power dissipation of the magnetic nanoparticles is related to the magnetic field strength and the magnetic field frequency of the alternating magnetic field, and the power dissipation of the magnetic nanoparticles is represented as: （3） wherein, represents the power dissipation of the magnetic nanoparticle, represents the magnetic permeability in vacuum, represents the actual magnetic susceptibility corresponding to the Langevin equation, represents the frequency of the alternating magnetic field, represents the strength of the alternating magnetic field, represents the relaxation time.

5. The method of predicting temperature in biological tissue based on polydispersity of magnetic nanoparticles according to claim 1, wherein, The Pennes bio-heat equation is specifically: （4） wherein, denotes the tissue density, denotes the tissue specific heat capacity, denotes the absolute temperature of the tissue, denotes the heating time, denotes the metabolic heat per volume in the tissue, denotes the magnetic nanoparticle power dissipation correction factor, denotes the magnetic nanoparticle power dissipation, denotes the blood perfusion rate, denotes the blood density, denotes the blood specific heat capacity, denotes the blood temperature, denotes the thermal conductivity of the tissue.

6. The method of predicting temperature in biological tissue based on polydispersity of magnetic nanoparticles according to claim 2, wherein, The outer surface of the second tissue region in the Pennes bio-heat equation needs to satisfy a boundary condition: （5） where T represents temperature, is the radius of the second tissue region.

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