Method for measuring thermal damage of biological tissue based on improved arrhenius model

Abstract

The application relates to a kind of biological tissue heat damage measuring methods based on improved Arrhenius model.The method is according to the relaxation loss principle of magnetic nano-particle with small particle size, utilizes the heat production of magnetic nano-particle in target treatment area excited by external alternating magnetic field, analyzes the temperature distribution of biological tissue during magnetic heat therapy through heat conduction, blood perfusion and biological self metabolism heat production, and finally accurately predicts the apoptosis rate of tumor cells based on the improved Arrhenius model of Vogel-Tammann-Fulcher theory.The application can realize the prediction accuracy of improving the degree of biological tissue heat damage in the process of magnetic heat therapy, and is applied to the link of making scheme before magnetic heat therapy, which greatly improves the accuracy of evaluating heat therapy effect.

Description

Technical Field

[0001] This invention relates to the field of modeling technology for magnetic nanothermotherapy, specifically to a method for measuring thermal damage to biological tissues based on an improved Arrhenius model. Background Technology

[0002] As an emerging cancer treatment method, magnetohydrodynamic (MHD) therapy offers numerous advantages, including non-invasiveness and high heating efficiency. During treatment, an external alternating magnetic field stimulates magnetic nanoparticles, which are injected intravenously or directly into the tumor tissue, to generate a large amount of heat. Tumor cells undergo irreversible apoptosis due to their high thermal sensitivity within the 42-46°C temperature range, while surrounding healthy tissue remains undamaged. Therefore, two unavoidable focuses in MHD research are selecting appropriate mathematical models to predict the temperature of biological tissues and accurately assessing the degree of thermal damage to malignant tumor cells within biological tissues.

[0003] The classic Pennes equation is the most popular model for researchers to describe heat conduction processes in biological tissues due to its simplicity and versatility. Furthermore, the degree of thermal damage to malignant cells within biological tissues can estimate their survival rate; however, the Arrhenius model, commonly used to infer the degree of thermal damage in biological tissues, has certain limitations. Its linear predictions do not accurately reflect experimental data. Summary of the Invention

[0004] The purpose of this invention is to provide a method for measuring thermal damage to biological tissues based on an improved Arrhenius model. Under the assumption that the magnetic nanoparticles are uniformly distributed, this method can simulate the temperature field distribution of biological tissues during magnetic hyperthermia, thereby enabling more accurate prediction of the degree of thermal damage to biological tissues.

[0005] To achieve the above objectives, the technical solution of the present invention is: a method for measuring thermal damage to biological tissues based on an improved Arrhenius model, comprising the following steps:

[0006] Step S1: Create a two-dimensional geometric model of biological tissue;

[0007] Step S2: Construct the actual concentration distribution of magnetic nanoparticles after injection into biological tissue;

[0008] Step S3: Simulate the interstitial flow velocity distribution in biological tissues, and use the interstitial flow velocity as input to solve the concentration transport process of magnetic nanoparticles based on the convection-diffusion equation;

[0009] Step S4: Construct the Pennes bio-thermal conduction model, set boundary conditions according to the actual situation, and simulate the therapeutic temperature field distribution of biological tissues during magnetic nanothermotherapy under the coupled analysis of concentration and temperature.

[0010] Step S5: Combining time and temperature coupling analysis, predict the degree of thermal damage to biological tissues based on the improved Arrhenius model of Vogel-Tammann-Fulcher.

[0011] In one embodiment of the present invention, step S1 specifically includes the following steps:

[0012] Step S11: Create an ellipse with major semi-axis R1 and minor semi-axis R2 to represent the first biological tissue region, and then create a circle with r = R3 to represent the second biological tissue region, wherein the first biological tissue region is contained within the second biological tissue region, and R3 > R1 > R2.

[0013] Step S12: Set the basic material properties for the two different biological tissues and magnetic nanoparticles respectively. The material properties include density, constant pressure specific heat capacity, thermal conductivity, blood perfusion rate and volumetric metabolic heat generation rate. The material properties are different for different tissues.

[0014] In steps S13 and S12, the blood perfusion rate in biological tissue is a material property related to the temperature of the biological tissue, specifically expressed as follows:

[0015]

[0016]

[0017] In this context, superscripts i = 0, 2 represent the first biological tissue region, and i = 1 represent the second biological tissue region. T represents the blood perfusion rate of biological tissues that is closely related to temperature. i Indicates the instantaneous temperature of biological tissue;

[0018] The material properties of biological tissues change during the injection of magnetic nanoparticles, specifically as follows:

[0019]

[0020] Wherein, ρ2 represents the density of the first biological tissue region containing magnetic nanoparticles. ρ0 represents the isobaric specific heat capacity of the first biological tissue region containing magnetic nanoparticles, k2 represents the thermal conductivity of the first biological tissue region containing magnetic nanoparticles, φ represents the volume fraction of the magnetic nanofluid, and ρ0 represents the density of the first biological tissue region. ρ represents the isobaric specific heat capacity of the first biological tissue region, k0 represents the density of the first biological tissue region, and ρ represents the density of the first biological tissue region. h k represents the density of magnetic nanoparticles. h C represents the thermal conductivity of magnetic nanoparticles. p,h This represents the constant-pressure specific heat capacity of magnetic nanoparticles.

[0021] In one embodiment of the present invention, step S2 specifically includes the following steps:

[0022] Step S21: Set a threshold to obtain the actual distribution of magnetic nanoparticles from images of biological tissues containing magnetic nanoparticles.

[0023] Step S22: Perform grayscale processing on the distribution map of magnetic nanoparticles obtained in step S21.

[0024] Step S23: Transform the grayscale image of the magnetic nanoparticle distribution from the pixel coordinate system to the geometric coordinate system.

[0025] In one embodiment of the present invention, step S3 specifically includes the following steps:

[0026] Step S31: The velocity distribution in the interstitial fluid of biological tissues is specifically expressed using the law of conservation of mass for incompressible fluids:

[0027]

[0028] in, Represents the Hamiltonian operator, u i The φ represents the interstitial flow velocity of biological tissues; subscripts i = 0, 2 indicate the first biological tissue region, and i = 1 indicate the second biological tissue region. B φ represents the quality source of the interstitial tissue of biological tissues. L This represents the mass sink of the interstitial tissue in biological tissues;

[0029] Step S32, the quality sources and quality sinks in the interstitial tissue of biological tissues are further specifically represented as follows:

[0030]

[0031]

[0032] Among them, L p S / V represents the permeability coefficient of the quality source, P b P represents the static pressure of blood. i P represents the interstitial pressure in biological tissues. l σ represents the pressure in the space where the mass sink is located. s Represents the osmotic reflection coefficient, π b π represents the pressure exerted by the expansion of blood. i L represents the expansion pressure of biological tissues. pl S L / V represents the permeability coefficient of the mass sink;

[0033] Step S33: Using interstitial flow rate as input, the concentration transport process of magnetic nanoparticles is specifically represented by the convection-diffusion equation:

[0034]

[0035] Among them, c i Indicates the concentration of magnetic nanoparticles. Denotes the Hamiltonian operator, D eff U represents the effective diffusion coefficient. i It indicates the velocity of interstitial flow in biological tissues.

[0036] In one embodiment of the present invention, step S4 specifically includes the following steps:

[0037] Step S41, the Pennes biological heat conduction model is expressed as:

[0038]

[0039] Wherein, subscripts i = 0, 2 represent the first biological tissue region, and i = 1 represent the second biological tissue region; ρ i Indicates the density of biological tissues, kJ represents the constant-pressure specific heat capacity of biological tissues. i Indicates the thermal conductivity of biological tissues. T represents the Hamiltonian operator. i Indicates the instantaneous temperature of biological tissue. ρ represents the isobaric specific heat capacity of blood in biological tissues. b T represents the density of blood in biological tissues. a This indicates the temperature of arterial blood in biological tissues. P represents the volumetric metabolic heat production rate of biological tissues. h This indicates the heat generated by magnetic nanoparticles under the influence of an alternating magnetic field. Indicates the blood perfusion rate in biological tissues;

[0040] Step S42: The Pennes biological heat conduction mathematical model satisfies the following Newman boundary conditions:

[0041]

[0042] Step S43: Apply the coupling analysis method of magnetic nanoparticle concentration and temperature from step S3 to simulate the temperature field distribution of biological tissues during magnetic nanothermotherapy.

[0043] In one embodiment of the present invention, step S5 specifically includes the following steps:

[0044] Step S51, the improved Arrhenius model based on Vogel-Tammann-Fulcher is expressed as:

[0045]

[0046] Where A represents the frequency factor, τ represents the duration of the thermotherapy process, a is the temperature-related activation energy, and T represents the temperature of the biological tissue;

[0047] Step S52: The damage fraction θ of biological tissue is related to the degree of damage to the biological tissue, specifically expressed as follows:

[0048] θ = 1 - e -Ω (7)

[0049] Step S53: Use a time-temperature coupled analysis method to predict the degree of thermal damage to biological tissues.

[0050] In one embodiment of the present invention, the Pennes biological heat conduction mathematical model in step S4 is a partial differential equation, and the biological tissue thermal damage model based on Vogel-Tammann-Fulcher theory in step S5 is a nonlinear equation. The material properties of biological tissue and magnetic nanoparticles are used as inputs to the model, and the Pennes biological heat conduction mathematical model and biological tissue thermal damage are solved by the finite element method.

[0051] Compared with the prior art, the present invention has the following beneficial effects:

[0052] This invention, assuming that the magnetic nanoparticles are uniformly distributed, simulates the temperature field distribution of biological tissues during magnetothermal therapy through a coupled analysis method of concentration and temperature; and, through a coupled analysis method of time and temperature, and based on an improved Arrhenius thermal damage model of the Vogel-Tammann-Fulcher theory, accurately predicts the degree of thermal damage to biological tissues using the finite element method. Attached Figure Description

[0053] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0054] Figure 2 This is a schematic diagram of the two-dimensional geometric model constructed in the embodiments of the present invention;

[0055] Figure 3 This is a schematic diagram of the temperature field distribution of biological tissue using the Pennes biological heat conduction mathematical model in an embodiment of the present invention;

[0056] Figure 4 This is a schematic diagram illustrating the prediction results of the degree of thermal damage to biological tissue based on the improved Arrhenius model of the Vogel-Tammann-Fulcher theory in an embodiment of the present invention. Detailed Implementation

[0057] The technical solution of the present invention will now be described in detail with reference to the accompanying drawings.

[0058] like Figure 1 As shown, this embodiment provides a method for predicting thermal damage to biological tissues based on an improved Arrhenius model, including the following steps:

[0059] Step S1: Create a two-dimensional geometric model of biological tissue;

[0060] Step S2: Construct the actual concentration distribution of magnetic nanoparticles after injection into biological tissue;

[0061] Step S3: Simulate the interstitial flow velocity distribution in biological tissues, and use the interstitial flow velocity as input to solve the concentration transport process of magnetic nanoparticles based on the convection-diffusion equation;

[0062] Step S4: Construct a Pennes biothermal conduction model, set reasonable boundary conditions according to the actual situation, and simulate the therapeutic temperature field distribution of biological tissues during magnetic nanothermotherapy under the coupled analysis of concentration and temperature.

[0063] Step S5: Combining time and temperature coupling analysis, predict the degree of thermal damage to biological tissues based on the improved Arrhenius model of Vogel-Tammann-Fulcher.

[0064] Preferably, in this embodiment, step S1 specifically includes the following steps:

[0065] Step S11: The constructed two-dimensional geometric model of the biological tissue consists of an ellipse with a major semi-axis R1 = 15 mm and a minor semi-axis R2 = 10 mm, and a circle with a radius R3 = 40 mm. For example... Figure 2 As shown, the large circle represents the second tissue region, and the small ellipse represents the first tissue region;

[0066] Step S12: Set the basic material properties for the two different biological tissues and magnetic nanoparticles respectively. The material properties include density, constant pressure specific heat capacity, thermal conductivity, blood perfusion rate and volumetric metabolic heat generation rate. The material properties are different for different tissues.

[0067] Step S13: The blood perfusion rate in the biological tissue in step S12 is a material property related to the temperature of the biological tissue, specifically expressed as follows:

[0068]

[0069]

[0070] Wherein, the superscript i = 0, 2 represents the first tissue region, and i = 1 represents the second tissue region; T represents the blood perfusion rate of biological tissues that is closely related to temperature. i It represents the instantaneous temperature of biological tissues.

[0071] The material properties of biological tissues change during the injection of magnetic nanoparticles, which can be specifically expressed as follows:

[0072]

[0073] Where ρ2 represents the density of the first biological tissue region containing magnetic nanoparticles. ρ0 represents the isobaric specific heat capacity of the first biological tissue region containing magnetic nanoparticles, k2 represents the thermal conductivity of the first biological tissue region containing magnetic nanoparticles, φ represents the volume fraction of the magnetic nanofluid, and ρ0 represents the density of the first biological tissue region. ρ represents the isobaric specific heat capacity of the first biological tissue region, k0 represents the density of the first biological tissue region, and ρ represents the density of the first biological tissue region. h The density of magnetic nanoparticles, k h The thermal conductivity of magnetic nanoparticles, C p,h This represents the constant-pressure specific heat capacity of magnetic nanoparticles.

[0074] Preferably, in this embodiment, step S2 is specifically implemented as follows:

[0075] Step S21: Set a threshold to obtain the actual distribution of magnetic nanoparticles from images of biological tissues containing magnetic nanoparticles.

[0076] Step S22: Perform grayscale processing on the distribution map of magnetic nanoparticles obtained in step S21.

[0077] Step S23: Transform the grayscale image of the magnetic nanoparticle distribution from the pixel coordinate system to the geometric coordinate system.

[0078] Preferably, in this embodiment, step S3 is specifically implemented as follows:

[0079] Step S31: The flow velocity distribution in the interstitial fluid of the biological tissue can be specifically expressed by the law of conservation of mass for incompressible fluids.

[0080]

[0081] in, Represents the Hamiltonian operator, u i This represents the interstitial flow velocity of biological tissues; subscripts i = 0, 2 indicate the first tissue region, and i = 1 indicate the second tissue region; φ B φ represents the quality source of the interstitial tissue of biological tissues. L It represents the mass sink of the interstitial tissue in biological tissues.

[0082] Step S32, the mass source and mass sink in the biological tissue interstitium can be further specifically represented as follows:

[0083]

[0084]

[0085] Among them, L p S / V represents the permeability coefficient of the quality source, P b P represents the static pressure of blood. i P represents the interstitial pressure in biological tissues. l σ represents the pressure in the space where the mass sink is located. s Represents the osmotic reflection coefficient, π b π represents the pressure exerted by the expansion of blood. i L represents the expansion pressure of biological tissues. pl S L / V represents the permeability coefficient of the mass sink.

[0086] Step S33: Using the interstitial flow rate as input, the concentration transport process of the magnetic nanoparticles can be specifically represented by the convection-diffusion equation:

[0087]

[0088] Among them, c i Indicates the concentration of magnetic nanoparticles. Denotes the Hamiltonian operator, D eff U represents the effective diffusion coefficient. i It indicates the velocity of interstitial flow in biological tissues.

[0089] Preferably, in this embodiment, step S4 is specifically implemented as follows:

[0090] Step S41, the Pennes biological heat conduction model is expressed as:

[0091]

[0092] Wherein, subscripts i = 0, 2 represent the first tissue region, and i = 1 represent the second tissue region; ρ i Indicates the density of biological tissues, kJ represents the constant-pressure specific heat capacity of biological tissues. i Indicates the thermal conductivity of biological tissues. T represents the Hamiltonian operator. i Indicates the instantaneous temperature of biological tissue. ρ represents the isobaric specific heat capacity of blood in biological tissues. b T represents the density of blood in biological tissues. a This indicates the temperature of arterial blood in biological tissues. P represents the volumetric metabolic heat production rate of biological tissues. hThis indicates the heat generated by magnetic nanoparticles under the influence of an alternating magnetic field. It represents the blood perfusion rate in biological tissues.

[0093] Step S42: The Pennes biological heat conduction mathematical model satisfies the following Newman boundary conditions:

[0094]

[0095] Step S43, as Figure 3 As shown, the temperature field distribution of biological tissue during magnetic nanothermotherapy is simulated using the coupled analysis method of magnetic nanoparticle concentration and temperature in step S3.

[0096] Preferably, in this embodiment, step S5 specifically includes the following steps:

[0097] Step S51, the improved Arrhenius model based on Vogel-Tammann-Fulcher is expressed as:

[0098]

[0099] Where A represents the frequency factor, τ represents the duration of the thermotherapy process, a is the temperature-related activation energy, and T represents the temperature of the biological tissue.

[0100] Step S52: The damage fraction θ of biological tissue is related to the degree of damage to the biological tissue, which can be specifically expressed as:

[0101] θ = 1 - e -Ω (7)

[0102] Step S53, as follows Figure 4 As shown, a time-temperature coupled analysis method is used to predict the degree of thermal damage to biological tissues.

[0103] Preferably, in this embodiment, the Pennes biological heat conduction mathematical model in step S4 is a partial differential equation, and the biological tissue thermal damage model based on Vogel-Tammann-Fulcher theory in step S5 is a nonlinear equation. The material properties of biological tissue and magnetic nanoparticles are used as inputs to the model, and the Pennes biological heat conduction mathematical model and biological tissue thermal damage are solved by the finite element method.

[0104] The above are preferred embodiments of the present invention. Any changes made to the technical solution of the present invention that do not exceed the scope of the technical solution of the present invention shall fall within the protection scope of the present invention.

Claims

1. A method for measuring thermal damage to biological tissues based on an improved Arrhenius model, characterized in that, Includes the following steps: Step S1: Create a two-dimensional geometric model of biological tissue; Step S2: Construct the actual concentration distribution of magnetic nanoparticles after injection into biological tissue; Step S3: Simulate the interstitial flow velocity distribution in biological tissues, and use the interstitial flow velocity as input to solve the concentration transport process of magnetic nanoparticles based on the convection-diffusion equation; Step S4: Construct the Pennes bio-thermal conduction model, set boundary conditions according to the actual situation, and simulate the therapeutic temperature field distribution of biological tissues during magnetic nanothermotherapy under the coupled analysis of concentration and temperature. Step S5: Combining time and temperature coupling analysis, predict the degree of thermal damage to biological tissues based on the improved Arrhenius model of Vogel-Tammann-Fulcher; specifically including the following steps: Step S51, the improved Arrhenius model based on Vogel-Tammann-Fulcher is expressed as: Where A represents the frequency factor, τ represents the duration of the thermotherapy process, a is the temperature-related activation energy, and T represents the temperature of the biological tissue; Step S52: The damage fraction θ of biological tissue is related to the degree of damage to the biological tissue, specifically expressed as follows: θ=1-e -Ω Step S53: Use a time-temperature coupled analysis method to predict the degree of thermal damage to biological tissues.

2. The method for measuring thermal damage to biological tissues based on the improved Arrhenius model according to claim 1, characterized in that, Step S1 specifically includes the following steps: Step S11: Create an ellipse with major semi-axis R1 and minor semi-axis R2 to represent the first biological tissue region, and then create a circle with r = R3 to represent the second biological tissue region, wherein the first biological tissue region is contained within the second biological tissue region, and R3 > R1 > R2. Step S12: Set the basic material properties for the two different biological tissues and magnetic nanoparticles respectively. The material properties include density, constant pressure specific heat capacity, thermal conductivity, blood perfusion rate and volumetric metabolic heat generation rate. The material properties are different for different tissues. In steps S13 and S12, the blood perfusion rate in biological tissue is a material property related to the temperature of the biological tissue, specifically expressed as follows: In this context, superscripts i = 0, 2 represent the first biological tissue region, and i = 1 represent the second biological tissue region. T represents the blood perfusion rate of biological tissues that is closely related to temperature. i Indicates the instantaneous temperature of biological tissue; The material properties of biological tissues change during the injection of magnetic nanoparticles, specifically as follows: Wherein, ρ2 represents the density of the first biological tissue region containing magnetic nanoparticles. ρ0 represents the isobaric specific heat capacity of the first biological tissue region containing magnetic nanoparticles, k2 represents the thermal conductivity of the first biological tissue region containing magnetic nanoparticles, φ represents the volume fraction of the magnetic nanofluid, and ρ0 represents the density of the first biological tissue region. ρ represents the isobaric specific heat capacity of the first biological tissue region, k0 represents the density of the first biological tissue region, and ρ represents the density of the first biological tissue region. h k represents the density of magnetic nanoparticles. h C represents the thermal conductivity of magnetic nanoparticles. p,h This represents the constant-pressure specific heat capacity of magnetic nanoparticles.

3. The method for measuring thermal damage to biological tissues based on the improved Arrhenius model according to claim 1, characterized in that, Step S2 specifically includes the following steps: Step S21: Set a threshold to obtain the actual distribution of magnetic nanoparticles from images of biological tissues containing magnetic nanoparticles. Step S22: Perform grayscale processing on the distribution map of magnetic nanoparticles obtained in step S21. Step S23: Transform the grayscale image of the magnetic nanoparticle distribution from the pixel coordinate system to the geometric coordinate system.

4. The method for measuring thermal damage to biological tissues based on the improved Arrhenius model according to claim 1, characterized in that, Step S3 specifically includes the following steps: Step S31: The velocity distribution in the interstitial fluid of biological tissues is specifically expressed using the law of conservation of mass for incompressible fluids: in, Represents the Hamiltonian operator, u i The φ represents the interstitial flow velocity of biological tissues; subscripts i = 0, 2 indicate the first biological tissue region, and i = 1 indicate the second biological tissue region. B φ represents the quality source of the interstitial tissue of biological tissues. L This represents the mass sink of the interstitial tissue in biological tissues; Step S32, the quality sources and quality sinks in the interstitial tissue of biological tissues are further specifically represented as follows: Among them, L p S / V represents the permeability coefficient of the quality source, P b P represents the static pressure of blood. i P represents the interstitial pressure in biological tissues. l σ represents the pressure in the space where the mass sink is located. s Represents the osmotic reflection coefficient, π b π represents the pressure exerted by the expansion of blood. i L represents the expansion pressure of biological tissues. pl S L / V represents the permeability coefficient of the mass sink; Step S33: Using interstitial flow rate as input, the concentration transport process of magnetic nanoparticles is specifically represented by the convection-diffusion equation: Among them, c i Indicates the concentration of magnetic nanoparticles. Denotes the Hamiltonian operator, D eff U represents the effective diffusion coefficient. i It indicates the velocity of interstitial flow in biological tissues.

5. The method for measuring thermal damage to biological tissues based on the improved Arrhenius model according to claim 1, characterized in that, Step S4 specifically includes the following steps: Step S41, the Pennes biological heat conduction model is expressed as: Wherein, subscripts i = 0, 2 represent the first biological tissue region, and i = 1 represent the second biological tissue region; ρ i Indicates the density of biological tissues, kJ represents the constant-pressure specific heat capacity of biological tissues. i Indicates the thermal conductivity of biological tissues. T represents the Hamiltonian operator. i The instantaneous temperature of a biological tissue, C p,b ρ represents the isobaric specific heat capacity of blood in biological tissues. b T represents the density of blood in biological tissues. a This indicates the temperature of arterial blood in biological tissues. P represents the volumetric metabolic heat production rate of biological tissues. h This indicates the heat generated by magnetic nanoparticles under the influence of an alternating magnetic field. Indicates the blood perfusion rate in biological tissues; Step S42: The Pennes biological heat conduction mathematical model satisfies the following Newman boundary conditions: Step S43: Apply the coupling analysis method of magnetic nanoparticle concentration and temperature from step S3 to simulate the temperature field distribution of biological tissues during magnetic nanothermotherapy.

6. The method for measuring thermal damage to biological tissues based on the improved Arrhenius model according to claim 1, characterized in that, The Pennes biological heat conduction mathematical model in step S4 is a partial differential equation, and the biological tissue thermal damage model based on the Vogel-Tammann-Fulcher theory in step S5 is a nonlinear equation. The material properties of biological tissue and magnetic nanoparticles are used as inputs to the model, and the finite element method is used to solve the Pennes biological heat conduction mathematical model and the biological tissue thermal damage.

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