Thermal damage measurement method for porous biological tissue based on local nonequilibrium heat transfer

Abstract

The present invention relates to a method for measuring thermal damage of porous biological tissues based on local thermal non-equilibrium heat transfer, comprising the following steps: step S1: constructing a geometric model of biological tissues; step S2: setting the distribution of magnetic nanoparticles in biological tissues as a Gaussian distribution model; step S3: assuming that the biological tissue is a porous structure containing interstitial tissue and blood, through the local thermal non-equilibrium theory, constructing a mathematical model of the temperature distribution of interstitial tissue and blood in the biological tissue and setting boundary conditions; step S4: using a multi-physics field analysis method of concentration-temperature coupling to solve the temperature distribution of biological tissues after heat generation under the interaction of magnetic nanoparticles and alternating magnetic fields; step S5: using the biological tissue temperature distribution result as input, applying the finite element method to calculate the biological tissue thermal damage equivalent dose based on the Vogel-Tammann-Fulcher behavior theory. The method is conducive to realizing the temperature distribution of interstitial tissue and blood in biological tissues in local thermal non-equilibrium, and accurately predicting the biological tissue thermal damage equivalent dose.

Description

Technical Field

[0001] The invention belongs to the technical field of magnetic nanoparticle modeling, and in particular relates to a method for measuring thermal damage of porous biological tissues based on local thermal non-equilibrium heat transfer. Background Art

[0002] Recently, the emerging technology of magnetic nanoparticles has made magnetic fluid hyperthermia a highly efficient and non-invasive method for local thermal ablation of biological tissues. The process is that the magnetic nanoparticles injected into the target tissue area are exposed to the alternating magnetic field applied by the outside world to generate heat, and the temperature of the target area is increased to 42℃-46℃ through the magnetothermal mechanism, ultimately achieving the purpose of thermal ablation.

[0003] The classic Pennes equation is widely used in bioheat transfer research due to its simplicity, but it ignores the influence of the microvascular system. In order to simplify the complex heterogeneous structure of biological tissues, the anatomical model of biological tissues is regarded as a porous medium infiltrated by fluids based on porous media theory. However, the temperatures of blood and interstitial tissues are not always the same during hyperthermia. Therefore, the local thermal nonequilibrium bioheat transfer equation is more suitable as a simple model for predicting the temperature of biological tissues.

[0004] At the same time, accurate quantification of thermal damage helps in planning before hyperthermia, monitoring during hyperthermia, and evaluation after hyperthermia, so the prediction of thermal damage is crucial for the practical application of hyperthermia. The equivalent thermal dosimetry equation represented by temperature equivalent time is often used to quantify thermal damage to biological tissues, but it still has shortcomings in effectiveness and accuracy. The equivalent thermal dose equation based on Vogel-Tammann-Fulcher behavior has significantly improved accuracy. Summary of the invention

[0005] The purpose of the present invention is to provide a method for measuring thermal damage to porous biological tissue based on local thermal nonequilibrium heat transfer, which is conducive to realizing the temperature distribution of the interstitium and blood of biological tissue in local thermal nonequilibrium and accurately predicting the equivalent dose of thermal damage to biological tissue.

[0006] To achieve the above object, the technical solution adopted by the present invention is: a method for measuring thermal damage of porous biological tissue based on local thermal non-equilibrium heat transfer, comprising the following steps:

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

[0008] Step S2: setting the distribution of magnetic nanoparticles in biological tissues to a Gaussian distribution model;

[0009] Step S3: Assume that the biological tissue is a porous structure containing interstitial fluid and blood. Based on the local thermal non-equilibrium theory, construct a mathematical model for the temperature distribution of the interstitial fluid and blood in the biological tissue, and set boundary conditions for the mathematical model.

[0010] Step S4: Use a multi-physics analysis method coupling concentration and temperature to solve the temperature distribution of the biological tissue after heat generation under the interaction of magnetic nanoparticles and alternating magnetic fields.

[0011] Step S5: Take the result of the biological tissue temperature distribution obtained in Step S4 as the input, and apply the finite element method to calculate the equivalent dose of thermal damage of the biological tissue based on the Vogel-Tammann-Fulcher behavior theory.

[0012] Further, Step S1 specifically includes the following steps:

[0013] Step S11: Construct a geometric model of the biological tissue, and the geometric model is a two-dimensional axisymmetric model; the geometric model includes a first tissue region r = R1 and a second tissue region r = R2, where R1 is the radius of the first tissue region, R2 is the radius of the second tissue region, R1 < R2, and the first tissue region is contained inside the second tissue region.

[0014] Step S12: Set basic material parameters for two different biological tissues respectively. The basic material parameters include density, thermal conductivity, specific heat capacity at constant pressure, blood perfusion rate, and porosity, and the material parameters of different tissue regions are different.

[0015] Further, in Step S2, the Gaussian distribution model is expressed as:

[0016]

[0017] where C0 represents the concentration at the center point of the geometric model, r and z are the two coordinate variables of the two-dimensional axisymmetric coordinate system of the constructed geometric model, and R0 represents the distance of the magnetic nanoparticles injected into the biological tissue diffusing outward from the center of the geometric model.

[0018] Further, the specific implementation method of Step S3 is as follows:

[0019] Assume that the biological tissue is a porous structure containing interstitial fluid and blood. The local thermal non-equilibrium heat transfer model used to describe the temperature change of the blood in the biological tissue is expressed as:

[0020]

[0021] where ε represents the blood volume fraction of the biological tissue, ρ b represents the density of the blood in the biological tissue, c brepresents the constant pressure specific heat capacity of blood in biological tissue, ω represents the blood perfusion rate of biological tissue, k b represents the thermal conductivity of blood in biological tissue, represents the Hamiltonian operator, <T b > represents the volume average of blood temperature, <T t > represents the volume average of the interstitial temperature, represents the volume average of blood flow velocity, h represents the surface heat transfer coefficient between interstitial tissue and blood, a represents the volume heat transfer area between interstitial tissue and blood, Q MNP It represents the heat generated by magnetic nanoparticles under the action of alternating magnetic field;

[0022] The local thermal nonequilibrium heat transfer model used to describe the temperature change of the interstitial tissue in biological tissue is expressed as:

[0023]

[0024] Among them, ρ t represents the density of the matrix in biological tissues, c t represents the constant-pressure specific heat capacity of the matrix in biological tissues, k t It represents the thermal conductivity of the matrix in biological tissues;

[0025] Set corresponding boundary conditions for the obtained local thermal non-equilibrium heat transfer mathematical model.

[0026] Furthermore, in step S4, the magnetic nanoparticle Gaussian distribution model obtained in step S2 is used as input, and a concentration-temperature coupled multi-physics field analysis method is applied to solve the temperature distribution of blood in biological interstitial tissue and tissue after heat generation under the interaction of magnetic nanoparticles and alternating magnetic field.

[0027] Furthermore, in step S5, the biological tissue thermal damage equivalent dose model based on the Vogel-Tammann-Fulcher behavior theory is expressed as:

[0028]

[0029] Where τ represents the duration of the hyperthermia process and T represents the interstitial temperature of the biological tissue.

[0030] Furthermore, the two local thermal non-equilibrium heat transfer models in step S3 are both partial differential equations, and the biological tissue thermal damage equivalent dose model based on Vogel-Tammann-Fulcher behavior theory in step S5 is a nonlinear equation. The material parameters of the biological tissue and the parameters of the magnetic nanoparticles are used as input, and the local thermal non-equilibrium heat transfer model is solved by finite element analysis to obtain the temperature distribution and the biological tissue thermal damage equivalent dose.

[0031] Compared with the prior art, the present invention has the following beneficial effects: the present invention, under the assumption that biological tissue is a porous medium, realizes the coupled analysis of concentration and temperature using the finite element analysis method, can predict the temperature distribution of the interstitial and blood of biological tissue in local thermal non-equilibrium, and can more accurately predict the equivalent dose of thermal damage to biological tissue based on the Vogel-Tammann-Fulcher behavior theory. Therefore, the present invention has strong practicality and broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 is a flow chart of a method implementation of an embodiment of the present invention;

[0033] Figure 2 A schematic diagram of a geometric model of a biological tissue constructed in an embodiment of the present invention;

[0034] Figure 3 Schematic diagram of interstitial temperature distribution in a biological tissue region based on the local thermal non-equilibrium theory in an embodiment of the present invention;

[0035] Figure 4 Schematic diagram of blood temperature distribution in a biological tissue region based on the local thermal non-equilibrium theory in an embodiment of the present invention;

[0036] Figure 5 Schematic diagram of equivalent dose distribution of thermal damage in biological tissue region based on Vogel-Tammann-Fulcher behavior theory in an embodiment of the present invention. DETAILED DESCRIPTION

[0037] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0038] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0039] 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 form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, it indicates the presence of features, steps, operations, devices, components and / or combinations thereof.

[0040] like Figure 1 As shown, this embodiment provides a method for measuring thermal damage of porous biological tissue based on local thermal non-equilibrium heat transfer, comprising the following steps:

[0041] Step S1: Construct a geometric model of the biological tissue.

[0042] Step S2: Set the distribution of magnetic nanoparticles in the biological tissue as a Gaussian distribution model.

[0043] Step S3: Assume that the biological tissue is a porous structure containing interstitial fluid and blood. Based on the local thermal non-equilibrium theory, construct a mathematical model for the temperature distribution of interstitial fluid and blood in the biological tissue, and set reasonable boundary conditions for the mathematical model according to the actual situation.

[0044] Step S4: Use a multi-physics field analysis method coupling concentration and temperature to solve the temperature distribution of the biological tissue after heat generation under the interaction of magnetic nanoparticles and alternating magnetic fields.

[0045] Step S5: Take the temperature distribution result of the biological tissue obtained in Step S4 as the input, and use the finite element method to calculate the equivalent dose of thermal damage of the biological tissue based on the Vogel-Tammann-Fulcher behavior theory.

[0046] In this embodiment, Step S1 specifically includes the following steps:

[0047] Step S11: Construct a geometric model of the biological tissue. The geometric model is a two-dimensional axisymmetric model. The geometric model includes a first tissue region r = R1 and a second tissue region r = R2, where R1 is the radius of the first tissue region, R2 is the radius of the second tissue region, R1 < R2, and the first tissue region is included inside the second tissue region. As Figure 2 shown, in this embodiment, the two-dimensional axisymmetric model is composed of two semi-circles with radii of 6.2 mm and 31 mm respectively. The small semi-circle is the first tissue region, and the large semi-circle is the second tissue region.

[0048] Step S12: Set the basic material parameters for two different biological tissues. The basic material parameters include density, thermal conductivity, specific heat capacity at constant pressure, blood perfusion rate, and porosity. The material parameters of different tissue regions are different.

[0049] In this embodiment, in Step S2, the Gaussian distribution model is expressed as:

[0050]

[0051] where C0 represents the concentration at the center point of the geometric model, r and z are the two coordinate variables of the two-dimensional axisymmetric coordinate system of the constructed geometric model, and R0 represents the distance of the magnetic nanoparticles injected into the biological tissue diffusing outward from the center of the geometric model. Here, R0 is set to 2.

[0052] In this embodiment, the specific implementation method of step S3 is:

[0053] First, it is assumed that biological tissue is a porous structure containing interstitial tissue and blood. The local thermal non-equilibrium heat transfer model used to describe the temperature change of blood in biological tissue is expressed as:

[0054]

[0055] Where ε represents the blood volume fraction of biological tissue, ρ b Represents the density of blood in biological tissue, c b represents the constant pressure specific heat capacity of blood in biological tissue, ω represents the blood perfusion rate of biological tissue, k b represents the thermal conductivity of blood in biological tissue, represents the Hamiltonian operator, <T b > represents the volume average of blood temperature, <T t > represents the volume average of the interstitial temperature, represents the volume average of blood flow velocity, h represents the surface heat transfer coefficient between interstitial tissue and blood, a represents the volume heat transfer area between interstitial tissue and blood, Q MNP It represents the heat generated by magnetic nanoparticles under the action of alternating magnetic field.

[0056] The local thermal nonequilibrium heat transfer model used to describe the temperature change of the interstitial tissue in biological tissue is expressed as:

[0057]

[0058] Where ε represents the blood volume fraction of biological tissue, <T t > represents the volume average of the interstitial temperature, ρ t represents the density of the matrix in biological tissues, c t represents the constant-pressure specific heat capacity of the matrix in biological tissues, ρ b Represents the density of blood in biological tissue, c b represents the constant pressure specific heat capacity of blood in biological tissue, ω represents the blood perfusion rate of biological tissue, k t represents the thermal conductivity of the matrix in biological tissues, represents the Hamiltonian operator, <T b > represents the volume average of blood temperature, h represents the surface heat transfer coefficient between interstitial tissue and blood, a represents the volume heat transfer area between interstitial tissue and blood, Q MNP It represents the heat generated by magnetic nanoparticles under the action of alternating magnetic field.

[0059] Set corresponding boundary conditions for the obtained local thermal non-equilibrium heat transfer mathematical model.

[0060] In this embodiment, in step S4, the Gaussian distribution model of magnetic nanoparticles obtained in step S2 is used as input, and a concentration-temperature coupled multi-physics field analysis method is applied to solve the temperature distribution of blood in biological interstitial tissue and tissue after heat is generated under the interaction between magnetic nanoparticles and alternating magnetic fields.

[0061] In this embodiment, in step S5, the biological tissue thermal damage equivalent dose model based on the Vogel-Tammann-Fulcher behavior theory is expressed as:

[0062]

[0063] Wherein, τ represents the duration of the thermal therapy process, which is set to 100 s here; T represents the interstitial temperature of the biological tissue.

[0064] In this embodiment, the local thermal non-equilibrium heat transfer model used to describe the temperature change of blood in biological tissue and the local thermal non-equilibrium heat transfer model used to describe the temperature change of interstitial tissue in biological tissue in step S3 are both partial differential equations, and the biological tissue thermal damage equivalent dose model based on Vogel-Tammann-Fulcher behavior theory in step S5 is a nonlinear equation. The material parameters of the biological tissue and the parameters of the magnetic nanoparticles are used as input, and the finite element analysis method is used to solve the local thermal non-equilibrium heat transfer model to obtain the temperature distribution and the biological tissue thermal damage equivalent dose.

[0065] Figure 3 , Figure 4 They are schematic diagrams of interstitial and blood temperature distribution in the biological tissue region of this embodiment based on the local thermal non-equilibrium theory. Figure 5 Schematic diagram of equivalent dose distribution of thermal damage in biological tissue region based on Vogel-Tammann-Fulcher behavior theory in this embodiment.

[0066] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented in one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that include computer-usable program code.

[0067] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0068] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0069] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0070] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A method for measuring thermal damage of porous biological tissue based on local thermal non-equilibrium heat transfer, characterized in that: It includes the following steps: Step S1: Construct a geometric model of the biological tissue; Step S2: Set the distribution of magnetic nanoparticles in the biological tissue as a Gaussian distribution model; Step S3: Assume that the biological tissue is a porous structure containing interstitial fluid and blood. Based on the local thermal non-equilibrium theory, construct a mathematical model for the temperature distribution of interstitial fluid and blood in the biological tissue, and set boundary conditions for the mathematical model at the same time; Step S4: Use a multi-physics field analysis method coupling concentration and temperature to solve the temperature distribution of the biological tissue after heat generation under the interaction of magnetic nanoparticles and alternating magnetic field; Step S5: Take the result of the temperature distribution of the biological tissue obtained in Step S4 as the input, and use the finite element method to calculate the equivalent dose of thermal damage of the biological tissue based on the Vogel-Tammann-Fulcher behavior theory; The specific implementation of Step S1 includes the following steps: Step S11: Construct a geometric model of the biological tissue. The geometric model is a two-dimensional axisymmetric model; the geometric model includes a first tissue region r = R1 and a second tissue region r = R2, where R1 is the radius of the first tissue region, R2 is the radius of the second tissue region, and R1 < R2. The first tissue region is included inside the second tissue region; Step S12: Set basic material parameters for two different biological tissues respectively. The basic material parameters include density, thermal conductivity, specific heat capacity at constant pressure, blood perfusion rate, and porosity. The material parameters of different tissue regions are different; In Step S2, the Gaussian distribution model is expressed as: where C0 represents the concentration at the center point of the geometric model, r and z are the two coordinate variables of the two-dimensional axisymmetric coordinate system of the constructed geometric model, and R0 represents the distance of the magnetic nanoparticles injected into the biological tissue diffusing outward from the center of the geometric model; The specific implementation method of Step S3 is: Assume that the biological tissue is a porous structure containing interstitial fluid and blood. The local thermal non-equilibrium heat transfer model for describing the temperature change of blood in the biological tissue is expressed as: Where ε represents the blood volume fraction of biological tissue, ρ b Represents the density of blood in biological tissue, c b represents the constant pressure specific heat capacity of blood in biological tissue, ω represents the blood perfusion rate of biological tissue, k b represents the thermal conductivity of blood in biological tissue, represents the Hamiltonian operator, <T b > represents the volume average of blood temperature, <T t > represents the volume average of the interstitial temperature, represents the volume average of blood flow velocity, h represents the surface heat transfer coefficient between interstitial tissue and blood, a represents the volume heat transfer area between interstitial tissue and blood, Q MNP It represents the heat generated by magnetic nanoparticles under the action of alternating magnetic field; The local thermal non-equilibrium heat transfer model for describing the temperature change of interstitial fluid in the biological tissue is expressed as: Among them, ρ t represents the density of the matrix in biological tissues, ct represents the constant pressure specific heat capacity of the matrix in biological tissues, k t It represents the thermal conductivity of the matrix in biological tissues; Set corresponding boundary conditions for the obtained local thermal non-equilibrium heat transfer mathematical model; In Step S4, take the Gaussian distribution model of magnetic nanoparticles obtained in Step S2 as the input, and use a multi-physics field analysis method coupling concentration and temperature to solve the temperature distribution of interstitial fluid and blood in the biological tissue after heat generation under the interaction of magnetic nanoparticles and alternating magnetic field; In Step S5, the equivalent dose model of thermal damage of the biological tissue based on the Vogel-Tammann-Fulcher behavior theory is expressed as: where τ represents the duration of the hyperthermia process, and T represents the interstitial temperature of the biological tissue; The two local thermal non-equilibrium heat transfer models in step S3 are both partial differential equations, and the biological tissue thermal damage equivalent dose model based on the Vogel-Tammann-Fulcher behavior theory in step S5 is a nonlinear equation. The material parameters of the biological tissue and the parameters of the magnetic nanoparticles are used as inputs, and the local thermal non-equilibrium heat transfer model is solved by the finite element analysis method to obtain the temperature distribution and the biological tissue thermal damage equivalent dose.

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