Method for constructing and analyzing bubble kinetic model in liquid cavity in viscoelastic tissue and simulation system

Abstract

The invention discloses a construction and analysis method and a simulation system of a dynamic model of bubbles in a liquid cavity in a viscoelastic tissue, and a numerical simulation system for performing a cavitation effect in high-intensity focused ultrasound therapy based on the model, and the method comprises the following steps: firstly, establishing a modified microbubble dynamic model based on a Keller-Miksis equation; microbubbles are placed in a liquid cavity wrapped by viscoelastic tissue, the constraint relation of the radius of the liquid cavity to the radius of the bubbles is introduced, and the viscoelastic stress-strain relation of the tissue is described by adopting a Voigt model, so that a cavitation kinetic model closer to the actual biological tissue is constructed. Secondly, the sound pressure waveform of the focus area is obtained through HIFU sound field simulation; and finally, taking the simulated sound pressure as a drive input kinetic model, and solving to obtain a microbubble oscillation behavior, tissue internal stress distribution and maximum compression stress. The system comprises a model building module, a sound field simulation module and a dynamics simulation module. According to the method, the cavitation dynamic process in the tissue under the action of the HIFU can be more accurately simulated, and an effective numerical analysis tool is provided for analyzing the tissue damage related to cavitation.

Description

[0001] Construction, Analysis Methods, and Simulation System of Bubble Dynamics Model in Liquid Cavities of Viscoelastic Organizations Technical Field

[0002] This invention relates to the field of simulated ultrasonic cavitation dynamics technology, and in particular to a method and simulation system for constructing and analyzing a dynamic model of bubbles in a liquid cavity of a viscoelastic tissue. Background Technology

[0003] Existing technical solutions employ the classical Keller-Miksis (KM) equation to describe the dynamic behavior of bubbles in an infinitely large, unconstrained liquid medium. However, this approach has the following shortcomings when simulating the microbubble dynamics in high-intensity focused ultrasound (HIFU) therapy: 1. The classic KM equation does not take into account the actual situation during HIFU treatment, where microbubbles exist within finite fluid cavities enclosed by viscoelastic tissue (such as biological soft tissue). It ignores the crucial influence of cavity geometry constraints and tissue viscoelasticity on microbubble oscillation behavior, and therefore cannot accurately simulate the cavitation process and related mechanical responses within the tissue.

[0004] 2. Neglecting the geometric constraint effect of the cavity: The classical KM equation assumes that the liquid medium space is infinite and does not consider the constraint effect of the finite liquid cavity or the boundary of the adjacent tissue on the sound field propagation and microbubble oscillation. It is difficult to reflect the influence of cavity size changes on microbubble dynamics.

[0005] 3. Failure to reflect tissue-bubble coupling: In actual HIFU treatment, microbubble oscillation induces significant mechanical responses in tissues (such as stress, strain, and local damage), while the classic KM equation does not establish the coupling relationship between bubble dynamics and tissue mechanical response.

[0006] 4. Insufficient accuracy in predicting the mechanical effects of cavitation within tissues: Due to the lack of comprehensive consideration of geometric constraints and tissue viscoelasticity factors, existing technologies are unable to accurately predict the cavitation process within tissues and the mechanical responses it induces.

[0007] 5. Failure to consider tissue stress changes caused by tissue liquefaction under high-intensity ultrasound: During high-intensity focused ultrasound (HIFU), cavitation can lead to local tissue liquefaction or mechanical property degradation, resulting in significant changes in the internal stress distribution of the tissue. However, the existing KM equation assumes that the mechanical properties of the surrounding medium are constant and does not consider the tissue liquefaction process and its influence on the evolution of stress state, making it difficult to accurately describe the actual changes in tissue stress with cavitation under high-intensity ultrasound conditions. Summary of the Invention

[0008] In view of this, the purpose of this invention is to provide a method and digital simulation system for constructing and analyzing a bubble dynamics model in a liquid cavity encapsulated by viscoelastic tissue. This method utilizes a modified classical bubble vibration model, introducing geometric constraints of the liquid cavity and tissue viscoelasticity (Voigt model), to make it more closely resemble the biological tissue environment, thereby accurately simulating the HIFU cavitation process.

[0009] To achieve the above objectives, the present invention provides the following technical solution: The present invention provides a method for constructing and analyzing a bubble dynamics model within a liquid cavity in a viscoelastic tissue, comprising the following steps: S1. Establish the microbubble dynamics control equation based on the Keller-Miksis equation, which considers that microbubbles exist in liquid cavities enclosed by viscoelastic tissue, and their oscillations are subject to the geometric constraints of the cavity and the influence of tissue viscoelasticity. S2. Determine the internal pressure of the bubbles in the liquid cavity, the liquid boundary conditions between the microbubbles and the cavity, and the instantaneous pressure of the liquid at the inner wall of the cavity; S3. The Voigt model is used to describe the stress-strain relationship of the tissue outside the cavity under the action of sound waves, and the radial velocity, stress and strain of the tissue are correlated. S4. Introduce an acoustic-thermal damage coupling mechanism into the dynamic model, and couple the transient heat source term generated by microbubble oscillation dissipation to the biological heat conduction equation to simulate the effect of tissue temperature changes on viscoelastic parameters; S5. Construct a dynamic model of bubbles within a liquid cavity encapsulated by a viscoelastic tissue based on the above relationships; S6. Using the model described above, combined with preset high-intensity focused ultrasound acoustic field parameters, analyze the dynamic behavior of the bubbles and the resulting tissue stress response; S7. Implement a real-time feedback control strategy during model application to monitor the internal stress state of the organization and dynamically adjust the acoustic field driving parameters in the simulation according to the preset stress threshold.

[0010] Furthermore, the specific form of the microbubble dynamics governing equation in step S1 is as follows: ; In the formula, The radius of the cavitation bubble; , They are respectively The first and second derivatives with respect to time; ρ is the density of the liquid; c is the speed of sound in the medium; For the medium Stress in the direction, Indicates the internal pressure of the bubble; This indicates the boundary liquid conditions between the microbubble and the cavity.

[0011] Furthermore, in step S2, the internal pressure of the bubble... Represented as: ; in, The static pressure of the liquid; The radius of the cavitation bubble; Let be the initial radius of the bubble; The adiabatic index of the gas; is the surface tension of the liquid.

[0012] Furthermore, in step S2, the boundary liquid conditions between the microbubbles and the cavity... for: ; in, The surface tension of the liquid, The radius of the cavitation bubble; for The first derivative with respect to time; The static pressure of the liquid. The viscosity coefficient of the liquid; To drive sound pressure; The instantaneous pressure of the liquid at the inner wall of the cavity is expressed as: ; in, This indicates the instantaneous pressure of the liquid at the inner wall of the cavity; This represents the radial coordinate at a fixed spatial location; Indicates the radius of the liquid cavity; This indicates the stress-strain relationship of the soft tissue on the outer side of the liquid cavity wall.

[0013] Furthermore, in step S3, the tissue stress-strain relationship described by the Voigt model is as follows: ; In the formula, and These are the shear modulus and viscosity coefficient of the medium, respectively. and For the stress and strain of the organization; Wherein, stress and strain are respectively: ; ; The stress-strain relationship of the soft tissue on the outer side of the cavity wall is expressed as follows: ; in, This represents the radial coordinate at a fixed spatial location; Indicates the radius of the liquid cavity; To represent the initial radius of the liquid cavity; express The first derivative with respect to time.

[0014] Furthermore, the relationship between the radius of the liquid cavity and the radius of the bubble satisfies: ; in, Indicates the radius of the liquid cavity; Indicates the bubble radius; Indicates the initial radius of the liquid cavity; Indicates the initial radius of the bubble; The velocity of a liquid is expressed as: ; ; In the formula, This represents the rate of change of the velocity of a liquid volume element at a fixed spatial position r over time. The time function representing the motion of the bubble interface. Indicates the radial velocity at the bubble interface. This represents the radial coordinate at a fixed spatial location.

[0015] Furthermore, in step S5, the bubble dynamics model within the liquid cavity is expressed as: in, Indicates the internal pressure of the bubble; This indicates the boundary liquid conditions between the microbubbles and the cavity. For the medium Stress in the direction, The static pressure of the liquid. Let be the initial radius of the bubble. The surface tension of the liquid, Let be the radius of the cavitation bubble. Let be the initial radius of the bubble. Let be the viscosity coefficient of the liquid. Indicates the radial velocity at the bubble interface. To drive sound pressure, and These are the shear modulus and viscosity coefficient of the medium, respectively. Represents the radius of the liquid cavity. To represent the initial radius of the liquid cavity, This represents the radial velocity of the liquid cavity boundary. This indicates the gas polyhedral index.

[0016] The present invention provides a simulation system for realizing biomechanical response under high-intensity focused ultrasound using the above-mentioned bubble dynamics model based on the liquid cavity dynamics model in viscoelastic tissue. The system includes a parameter input module, a sound field simulation calculation module, a coupled dynamics model processor, and a tissue mechanical response analysis module. The parameter input module is used to receive or set physical parameters related to biological tissues, fluid cavities, and bubbles, as well as acoustic field driving parameters of high-intensity focused ultrasound. The sound field simulation calculation module is used to simulate and calculate the nonlinear sound field formed by high-intensity focused ultrasound in tissue based on a layered medium model, and output the sound pressure parameters of the focal region. The coupled dynamics model processor has a pre-stored dynamics model of bubbles in the liquid cavity of a viscoelastic tissue constructed by the above method. It is used to receive the sound pressure parameters and calculate the dynamic change of the bubble radius under the drive of the sound field. The tissue mechanical response analysis module is connected to the coupled dynamics model processor and is used to calculate and output the spatial and temporal distribution data of the internal stress field of the tissue caused by bubble oscillation based on the dynamic changes of the bubble radius.

[0017] Furthermore, it also includes a results visualization module: The result visualization module is used to graphically display the dynamic change curve of the bubble radius and the spatial distribution and time change curve of the stress field inside the tissue.

[0018] Furthermore, the sound field simulation calculation module is specifically configured to use water-liver-water as the layered medium model, and calculate and output the peak positive pressure, peak negative pressure and shock wave amplitude of the focal region by solving the nonlinear sound wave propagation equation; The output data of the tissue mechanical response analysis module includes at least the curves of compressive stress versus time at different locations within the tissue, and the maximum tissue stress calculated based on different initial bubble radii. The output results of the dynamic simulation module include: microbubble radius variation curve over time, spatial distribution cloud map of internal tissue stress, and maximum stress and cumulative tissue damage data at different locations or with different initial bubble radii.

[0019] The beneficial effects of this invention are as follows: The present invention provides a method for constructing and analyzing a dynamic model of bubbles within a viscoelastic tissue-encapsulated liquid cavity, which is used to simulate the biomechanical response of tissue liquefaction under high-intensity focused ultrasound. This method can more closely simulate the cavitation dynamics process within the tissue under HIFU, providing a theoretical model and numerical analysis tool for quantitative analysis of local tissue damage (such as stress distribution and maximum compressive stress) caused by microbubble oscillation.

[0020] The method provided by this invention introduces a viscoelastic tissue constraint effect: the biological soft tissue surrounding the liquid cavity is modeled as a viscoelastic medium, which can take into account the damping and energy dissipation effects of the tissue's elasticity and viscosity on microbubble oscillation, thereby more realistically reflecting the dynamic behavior of microbubbles in a finite cavity.

[0021] Considering the impact of tissue liquefaction on stress distribution: It can simulate the local tissue liquefaction process under high-intensity focused ultrasound and its impact on tissue stress state, and can predict the stress distribution, maximum compressive stress and strain changes in the liquefaction area, providing a quantitative basis for assessing tissue damage caused by microbubble cavitation.

[0022] Establishing a bubble-tissue coupling model: By coupling bubble dynamics with the mechanical response of the surrounding tissue, this method can reflect the immediate impact of microbubble oscillations on tissue mechanics, as well as the feedback modulation effect of tissue on bubble oscillations, thus achieving a multi-scale description of cavitation effects.

[0023] Quantitative analysis applicable to high-intensity acoustic excitation conditions: This scheme can simulate the nonlinear oscillation and collapse process of microbubbles under HIFU conditions, revealing the influence of factors such as acoustic power, frequency and cavity constraint on local mechanical effects, providing theoretical and numerical support for treatment parameter optimization and safety assessment.

[0024] This approach provides numerical analysis tools and theoretical models; it offers numerical models and calculation methods that can be directly used for simulation analysis to study local tissue damage induced by high-intensity focused ultrasound microbubbles, and can support systematic research on microbubble dynamics, tissue stress-strain analysis and cavitation effect assessment.

[0025] The above and other objects, advantages, and features of the present invention will be more fully set forth and demonstrated through the following detailed description of specific embodiments in conjunction with the accompanying drawings. Those skilled in the art, upon referring to the following detailed description and the accompanying drawings, will be able to better understand and realize the above advantages of the present invention. Other objects, features, and advantages of the present invention will become clearer after being described in detail in the detailed description section in conjunction with the accompanying drawings. Attached Figure Description

[0026] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the following drawings are provided for illustration.

[0027] Figure 1 A flowchart illustrating the construction and analysis of a dynamic model of air bubbles within a liquid cavity in a viscoelastic tissue; Figure 2 A schematic diagram of a numerical simulation system for biomechanical response under high-intensity focused ultrasound; Figure 3 The sound pressure distribution at the focal point of the liquid cavity where the microbubble used in the simulation is located; Figure 4 This is a schematic diagram illustrating the change in microbubble radius; Figure 5 This is a schematic diagram of the spatial distribution of stress. Figure 6 This is a schematic diagram showing the stress changes at different locations; Figure 7 This is a schematic diagram showing the stress changes of different tissue parameters during tissue liquefaction.

[0028] Figure 8 This is a diagram showing the area of ​​tissue damage and cumulative damage. Detailed Implementation

[0029] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0030] Example 1 like Figure 1 As shown in this embodiment, the method for constructing and analyzing the bubble dynamics model within the liquid cavity of a viscoelastic tissue, used to simulate the biomechanical response under high-intensity focused ultrasound, includes the following steps: S1. Establish the microbubble dynamics control equation based on the Keller-Miksis equation, which considers that microbubbles exist in liquid cavities enclosed by viscoelastic tissue, and their oscillations are subject to the geometric constraints of the cavity and the influence of tissue viscoelasticity. S2. Determine the internal pressure of the bubbles in the liquid cavity, the liquid boundary conditions between the microbubbles and the cavity, and the instantaneous pressure of the liquid at the inner wall of the cavity; S3. The Voigt model is used to describe the stress-strain relationship of the tissue outside the cavity under the action of sound waves, and the radial velocity, stress and strain of the tissue are correlated. S4. Introduce an acoustic-thermal damage coupling mechanism into the dynamic model, and couple the transient heat source term generated by microbubble oscillation dissipation to the biological heat conduction equation to simulate the effect of tissue temperature changes on viscoelastic parameters; This embodiment couples the microbubble dynamics equation with the tissue mechanics equation to predict the tissue stress, strain and liquefaction region induced by bubble oscillation, and can reflect the stress evolution after tissue liquefaction under high-intensity ultrasound. The nonlinear viscoelastic properties of tissues are considered in the coupling model, which enables accurate simulation of the damping and energy dissipation effects of microbubble oscillations under different tissue mechanical conditions. Simulating the multi-scale mechanical interaction between the liquid cavity and the surrounding tissue can simultaneously reflect the coupling effect between the microbubble micro-oscillation behavior and the macro-mechanical response of the tissue. In this embodiment, the liquid cavity can be an interstitial fluid cavity.

[0031] Considering the tissue liquefaction process caused by cavitation under high-intensity ultrasound, and feeding back the changes in tissue mechanical parameters in the liquefaction area to the microbubble dynamics equation, the accuracy of tissue damage prediction is improved. This approach enables quantitative analysis of local tissue stress and cumulative damage induced by microbubble oscillation, providing a theoretical model and numerical analysis tool for research on microbubble-assisted drug delivery or tissue disruption during high-intensity focused ultrasound therapy.

[0032] In this embodiment, the liquid cavity has a nonlinear viscoelastic and deformable cavity wall; In this embodiment, a corresponding dynamic model of the deformable cavity wall is constructed based on the deformable cavity wall. Its constitutive relation is described by a viscoelastic model with fractional derivatives, and the coupling relationship between cavity wall deformation and intracavitary liquid pressure distribution is solved. The dynamic model of the deformable cavity wall in this embodiment is used to simulate the mechanical response of biological tissue cavities (such as blood vessels, glands or cysts). Its stress-strain relationship is defined by a fractional-order viscoelastic model. When solving the model, the pressure change inside the cavity caused by the movement of bubbles and liquid is used as the driving load, and the calculated cavity wall deformation is fed back in real time to update the boundary and spatial domain of the liquid flow.

[0033] S5. By combining the above equations and relationships, a complete dynamic model of bubbles within a liquid cavity encapsulated by a viscoelastic tissue is constructed; This embodiment can also be based on the acoustic-thermal-damage coupling theory, introducing a transient heat source term generated by microbubble oscillation dissipation into the model, and defining the tissue viscoelastic parameters (shear modulus G, viscosity μ) as a continuous function of local temperature; thus constructing a strongly coupled multiphysics dynamic model. This embodiment uses the acoustic-thermal-damage coupling theory, combined with the biological heat conduction equation, to construct a multiphysics model, introducing a transient heat source term Q generated by microbubble oscillation dissipation into the model. bubble As a local heat source in the biological heat conduction equation, it simulates the instantaneous contribution of acoustic energy released during microbubble oscillation to tissue temperature. The acoustic-thermal-damage coupling theoretical mechanism in this embodiment is a feedback loop of microbubble oscillation dissipation (acoustic) - local temperature rise (thermal) - tissue parameter change / damage threshold triggering (damage).

[0034] S6. Using the model described above, combined with preset high-intensity focused ultrasound acoustic field parameters, analyze the dynamic behavior of the bubbles and the resulting tissue stress response.

[0035] S7. Implement a real-time feedback control strategy during model application to monitor the internal stress state of the tissue and dynamically adjust the acoustic field driving parameters in the simulation according to the preset stress threshold; In this embodiment, a real-time feedback control strategy is implemented during the simulation: the maximum shear stress inside the tissue obtained by simulation is monitored, and if its value exceeds the preset safety threshold, the HIFU sound pressure amplitude input in the simulation is dynamically reduced until the stress is lower than the threshold.

[0036] In this embodiment, tissue liquefaction refers to changes after thermal coagulation necrosis, or it can also refer to viscoelastic failure or local tissue failure areas.

[0037] This implementation case employs a real-time feedback control strategy during the simulation process. Its features include: real-time monitoring of local tissue stress during the calculation of the coupled microbubble dynamics and tissue mechanics model; when the tissue stress is less than a set threshold (e.g., 0.27 MPa for liver tissue, 0.11 MPa for heart tissue), the local tissue damage process is stopped, thus achieving dynamic control of the damage process. This strategy avoids excessive tissue damage while ensuring that the simulation results conform to the mechanical tolerance characteristics of actual tissues, and enables quantitative assessment of the extent of local tissue damage caused by microbubble oscillation.

[0038] In this embodiment, the specific form of the microbubble dynamics control equation in step S1 is as follows: ; In the formula, The radius of the cavitation bubble; , They are respectively The first and second derivatives with respect to time; The density of the liquid; c is the speed of sound in the medium; The stress in the r-direction within the medium; In step S2 of this embodiment, the internal pressure of the bubble... Represented as: ; in, The static pressure of the liquid; Let be the initial radius of the bubble; The adiabatic index of the gas; The surface tension of the liquid; The boundary conditions for the microbubble-cavity are: in, The viscosity coefficient of the liquid; To drive sound pressure; The instantaneous pressure of the liquid at the inner wall of the cavity is expressed as: ; in, This indicates the instantaneous pressure of the liquid at the inner wall of the cavity; Indicates the hydrostatic pressure of a liquid; Indicates direction; Indicates the radius of the liquid cavity; This indicates the stress in the soft tissue on the outer side of the fluid cavity wall; In step S3 of this embodiment, the stress-strain relationship described by the Voigt model is as follows: ; In the formula, and These are the shear modulus and viscosity coefficient of the medium, respectively. and For the stress and strain of the organization and ; The radial velocity of the soft tissue medium is expressed as: ; The stress and strain are respectively: ; ; The soft tissue stress on the outer side of the cavity wall is expressed as ; In this embodiment, if the compressibility of the liquid inside the cavity is ignored, the relationship between the radius of the liquid cavity and the radius of the bubble satisfies: ; in, Indicates the radius of the liquid cavity; Indicates the bubble radius; Indicates the initial radius of the liquid cavity; Indicates the initial radius of the bubble; The velocity of a liquid is expressed as: ; ; In the formula, Let r be the radial velocity of the liquid volume element at point r in a coordinate system with the center of the liquid cavity as the origin; This represents the rate of change of the velocity of a liquid volume element at a fixed spatial position r over time. The time function representing the motion of the bubble interface. Indicates the instantaneous radius of the bubble. Indicates the radial velocity at the bubble interface; In this embodiment, r represents the radial coordinate at a fixed spatial location, that is, the distance from a spatial point radiating outward from the bubble center to the bubble center. It is used to describe the velocity distribution at any point in the liquid (located at a distance r from the bubble center) during the expansion or contraction of the bubble. This represents the rate of change of the velocity of the liquid element at that location with time.

[0039] In step S5 of this embodiment, the dynamic model of the bubble in the liquid cavity is expressed as follows: in, Indicates the gas polyhedral index; Represents the radial velocity of the liquid cavity boundary; Indicates the radial velocity at the bubble interface; Therefore, the above formula is a dynamic model of bubbles in the liquid cavity of a viscoelastic organization based on the Keller-Miksis equation; Example 2 like Figure 2 As shown, the numerical simulation system for biomechanical response under high-intensity focused ultrasound based on the dynamic model of bubbles in the liquid cavity of viscoelastic tissue provided in this embodiment includes a parameter input module, a sound field simulation calculation module, a coupled dynamic model processor, a tissue mechanical response analysis module, and a result visualization module. The parameter input module is used to receive or set physical parameters related to biological tissues, fluid cavities, and bubbles, as well as acoustic field driving parameters of high-intensity focused ultrasound. The sound field simulation calculation module is used to simulate and calculate the nonlinear sound field formed by high-intensity focused ultrasound in tissue based on a layered medium model, and output the sound pressure parameters of the focal region. The coupled dynamics model processor has a pre-stored dynamics model of bubbles in the liquid cavity of a viscoelastic tissue constructed by the above method. It is used to receive the sound pressure parameters and calculate the dynamic change of the bubble radius under the drive of the sound field. The tissue mechanical response analysis module is connected to the coupled dynamics model processor and is used to calculate and output the spatial and temporal distribution data of the internal stress field of the tissue caused by bubble oscillation based on the dynamic change of the bubble radius. The result visualization module is used to graphically display the dynamic change curve of the bubble radius and the spatial distribution and time change curve of the stress field inside the tissue.

[0040] In this embodiment, the sound field simulation calculation module is specifically configured to use water-liver-water as the layered medium model, and calculate and output the peak positive pressure, peak negative pressure and shock wave amplitude of the focal region by solving the nonlinear sound wave propagation equation.

[0041] The output data of the tissue mechanical response analysis module in this embodiment includes at least the curves of the change of compressive stress over time at different locations within the tissue, and the maximum compressive stress of the tissue calculated based on different initial bubble radii.

[0042] In this embodiment, the system is configured to simulate and compare the bubble dynamics and tissue stress response under different conditions by iterating over the initial radius of the bubble or the acoustic field driving parameters.

[0043] The output results of the dynamic simulation module include: microbubble radius variation curve over time, spatial distribution cloud map of internal stress in tissue, and maximum compressive stress data at different locations or with different initial bubble radii.

[0044] The model in this embodiment simulates the oscillatory behavior of microbubbles within a liquid cavity encapsulated by viscoelastic tissue. The oscillations are influenced by the cavity's geometric constraints and the tissue's viscoelasticity. It simulates tissue cavitation under high sound pressure levels and provides a theoretical basis for analyzing local tissue damage caused by microbubble oscillations.

[0045] Example 3 This embodiment details the construction process of the bubble dynamics model within the liquid cavity of a viscoelastic tissue, and the simulation process of using the model to realize the dynamics of bubbles within the liquid cavity and the mechanical response of the tissue under high-intensity focused ultrasound: 1. Reasoning Process for Establishing the Cavitation Dynamics Model: In experiments, observation of tissue sections revealed local tissue damage after HIFU treatment. To approximate this reality, this embodiment constructs a modified microbubble dynamics model based on the classic Keller-Miksis (KM) equations. In this model, microbubbles exist within liquid cavities enclosed by viscoelastic tissue, and their oscillation behavior is influenced by the cavity's geometric constraints and the tissue's viscoelasticity. This model can simulate the tissue cavitation process under high sound pressure levels and provides a theoretical basis for analyzing local tissue damage caused by microbubble oscillations.

[0046] In the formula, Let be the radius of the cavitation bubble. , They are respectively The first and second derivatives with respect to time; Let be the density of the liquid, and c be the speed of sound in the medium. This represents the stress in the r-direction within the medium.

[0047] internal pressure of the bubble Represented as: ,in The static pressure of the liquid. Let be the initial radius of the bubble. The adiabatic index of the gas is . is the surface tension of the liquid.

[0048] For the boundary conditions of microbubbles-cavities, the viscosity coefficient of the liquid is considered. Drive sound pressure ; ; The vibration of bubbles within the cavity affects the fluid motion and the viscoelastic response of the external medium. The instantaneous pressure of the fluid at the inner wall of the cavity during this vibration process is expressed as: ; The stress-strain relationship of a tissue under the action of sound waves is described by the Voigt model, i.e. ; In the formula, and These are the shear modulus and viscosity coefficient of the medium, respectively. and For the stress and strain of the organization and ; The radial velocity of the soft tissue medium is expressed as: ; The stress and strain are respectively: , ; The soft tissue stress on the outer side of the cavity wall is expressed as ; Ignoring the compressibility of the liquid inside the cavity, the relationship between the radius of the liquid cavity and the radius of the bubble satisfies: ; If the fluid inside the cavity is incompressible, then the velocity of the fluid can be expressed as: , ; In the formula, Let r be the radial velocity of the liquid volume element at point r in a coordinate system with the center of the liquid cavity as the origin.

[0049] The final result is: ; Therefore, based on the above steps, a dynamic model of bubbles in the liquid cavity of a viscoelastic organization based on the Keller-Miksis equation can be established.

[0050] 2. Conduct HIFU beam simulation experiments using the model. The nonlinear sound field distribution and sound pressure waveform at the focal point of high-intensity focused ultrasound (HIFU) in tissue were obtained through HIFU Beam simulation. Based on a "water-liver-water" layered medium model, the sound focusing position was set at a certain depth from the tissue surface. Acoustic characteristics such as peak positive and negative sound pressure levels and shock wave amplitude in the focal region were calculated using nonlinear propagation equations. The results were used to characterize the sound field energy distribution characteristics under macroscopic HIFU action. The peak positive pressure was significantly higher than the peak negative pressure, and the distribution was concentrated in a significantly small region around the focal point.

[0051] In this embodiment, in order to accurately simulate the nonlinear propagation process of high-intensity focused ultrasound in tissues, the nonlinear wide-angle parabolic equation (WAPE) is selected as the sound field control equation to describe the propagation behavior of ultrasound in layered non-uniform media.

[0052] The nonlinear wide-angle parabolic equation introduces thermoviscous absorption and power-law absorption terms during the modeling process, which can describe the frequency-dependent attenuation characteristics of sound energy in biological tissues as the propagation distance increases, and thus more realistically reflect the absorption and dissipation process of ultrasound energy by tissues.

[0053] The focused ultrasound source was set as an axisymmetric focused transducer, with a center frequency of 0.982MHz, an aperture size of 0.15mm, a focal length of 170mm, and an acoustic power of 1000W. At the same time, the acoustic focusing position was set to be at a certain depth below the tissue surface to simulate the situation where HIFU forms a focal point inside the tissue.

[0054] During the simulation, it is also necessary to pay attention to the continuity of sound wave propagation under layered medium conditions, the stability of numerical calculation under nonlinear propagation conditions, and the influence of time step and spatial grid settings on the accuracy of sound field calculation, so as to ensure the accuracy and reliability of the obtained sound field results.

[0055] like Figure 3-8 As shown, Figure 3 This is a sound pressure distribution map of the high-intensity focused ultrasound sound field at the focal point, obtained based on HIFU Beam simulation, used to characterize the acoustic excitation intensity in the focal region.

[0056] Figure 4The curves show the changes in cavitation bubble radius and vibration velocity within the liquid cavity over time under the influence of the acoustic field at the focal point in the HIFU beam simulation, representing the variation of the microbubble radius. It can be seen that the cavitation bubble radius reaches its peak during the expansion phase and then rapidly decreases, while the wall velocity increases sharply at the moment of collapse, forming a sharp velocity peak, which can reach hundreds of meters per second. This process indicates that the kinetic energy of the bubble is intensely concentrated during the collapse phase and is instantaneously converted into high-amplitude pressure in the surrounding medium.

[0057] Figure 5 To illustrate the spatial distribution of stress, under ultrasonic excitation, the bubble undergoes periodic expansion and collapse, and its radial motion induces a significant transient stress field in the surrounding medium. The stress exhibits a non-uniform distribution in both time and space. Furthermore, the temporal variation of the stress is highly consistent with the bubble expansion-collapse process, generating transient high-amplitude compressive and tensile stresses during the collapse phase. This stress field repeats under periodic excitation, allowing for the application of controllable transient mechanical loading to localized areas.

[0058] Figure 6 Due to stress changes at different locations, the oscillation of microbubbles within the encapsulated cavity during bubble cavitation will generate significant mechanical stress on the surrounding tissue. Figure 6 Stress curves over time are presented at three observation points at distances of 10 μm, 20 μm, and 30 μm from the bubble center. This result indicates that the mechanical damage from microbubble cavitation is mainly confined to the near-field region surrounding the liquid cavity, and the stress exhibits a rapid decay characteristic with distance.

[0059] Figure 7 This diagram illustrates the stress changes of different tissue parameters during tissue liquefaction, showing the maximum stress changes at the liquid-tissue interface of different tissues as tissue liquefaction increases. By measuring or estimating tissue parameters, the stress level that the tissue may experience during cavitation can be predicted. Conversely, by setting damage stress thresholds for different tissues, the damage effects and selectivity of cavitation therapy on different types of tissues can be theoretically predicted.

[0060] Figure 8 This diagram illustrates the relationship between tissue damage area and cumulative damage, showing the correlation between tissue liquefaction damage area and cumulative damage energy (ICD) under high-intensity focused ultrasound (HIFU). As the liquefaction area continues to expand, the growth rate of ICD gradually slows down and tends to stabilize, indicating that within a larger liquefaction range, local tissue mechanical constraint weakens, and the contribution of new damage to cumulative damage energy gradually decreases. By establishing a quantitative relationship between cumulative damage energy and tissue liquefaction damage area, this embodiment can characterize the evolution process of tissue damage from an energy perspective, providing a quantitative indicator for assessing the degree of tissue damage induced by microbubble oscillation.

[0061] The embodiments described above are merely preferred embodiments for fully illustrating the present invention, and the scope of protection of the present invention is not limited thereto. Equivalent substitutions or modifications made by those skilled in the art based on the present invention are all within the scope of protection of the present invention. The scope of protection of the present invention is defined by the claims.

Claims

1. A method for constructing and analyzing a dynamic model of bubbles within a liquid cavity in a viscoelastic tissue, characterized in that, Includes the following steps: S1. Establish the microbubble dynamics control equation based on the Keller-Miksis equation, which considers that microbubbles exist in liquid cavities enclosed by viscoelastic tissue, and their oscillations are subject to the geometric constraints of the cavity and the influence of tissue viscoelasticity. S2. Determine the internal pressure of the bubbles in the liquid cavity, the liquid boundary conditions between the microbubbles and the cavity, and the instantaneous pressure of the liquid at the inner wall of the cavity; S3. The Voigt model is used to describe the stress-strain relationship of the tissue outside the cavity under the action of sound waves, and the radial velocity, stress and strain of the tissue are correlated. S4. Introduce an acoustic-thermal damage coupling mechanism into the dynamic model, and couple the transient heat source term generated by microbubble oscillation dissipation to the biological heat conduction equation to simulate the effect of tissue temperature changes on viscoelastic parameters; S5. Construct a dynamic model of bubbles within a liquid cavity encapsulated by a viscoelastic tissue based on the above relationships; S6. Using the model described above, combined with preset high-intensity focused ultrasound acoustic field parameters, analyze the dynamic behavior of the bubbles and the resulting tissue stress response; S7. Implement a real-time feedback control strategy during model application to monitor the internal stress state of the organization and dynamically adjust the acoustic field driving parameters in the simulation according to the preset stress threshold.

2. The method for constructing and analyzing the dynamic model of bubbles within the liquid cavity of a viscoelastic tissue as described in claim 1, characterized in that, The specific form of the microbubble dynamics control equation in step S1 is as follows: ； In the formula, The radius of the cavitation bubble; , They are respectively The first and second derivatives with respect to time; ρ is the density of the liquid; c is the speed of sound in the medium; For the medium Stress in the direction, Indicates the internal pressure of the bubble; This indicates the boundary liquid conditions between the microbubble and the cavity.

3. The method for constructing and analyzing the dynamic model of bubbles within the liquid cavity of a viscoelastic tissue as described in claim 1, characterized in that, In step S2, the internal pressure of the bubble Represented as: ； in, The static pressure of the liquid; The radius of the cavitation bubble; Let be the initial radius of the bubble; The adiabatic index of the gas; is the surface tension of the liquid.

4. The method for constructing and analyzing the dynamic model of bubbles within the liquid cavity of a viscoelastic tissue as described in claim 1, characterized in that, In step S2, the boundary liquid conditions between the microbubbles and the cavity... for: ； in, The surface tension of the liquid, The radius of the cavitation bubble; for The first derivative with respect to time; The static pressure of the liquid. The viscosity coefficient of the liquid; To drive sound pressure; The instantaneous pressure of the liquid at the inner wall of the cavity is expressed as: ； in, This indicates the instantaneous pressure of the liquid at the inner wall of the cavity; This represents the radial coordinate at a fixed spatial location; Indicates the radius of the liquid cavity; This indicates the stress-strain relationship of the soft tissue on the outer side of the liquid cavity wall.

5. The method for constructing and analyzing the dynamic model of bubbles within the liquid cavity of a viscoelastic tissue as described in claim 1, characterized in that, In step S3, the tissue stress-strain relationship described by the Voigt model is as follows: ； In the formula, and These are the shear modulus and viscosity coefficient of the medium, respectively. and For the stress and strain of the organization; Wherein, stress and strain are respectively: ； ； The stress-strain relationship of the soft tissue on the outer side of the cavity wall is expressed as follows: ; in, This represents the radial coordinate at a fixed spatial location; Indicates the radius of the liquid cavity; To represent the initial radius of the liquid cavity; express The first derivative with respect to time.

6. The method for constructing and analyzing the dynamic model of bubbles within the liquid cavity of a viscoelastic tissue as described in claim 1, characterized in that, The radius of the liquid cavity and the radius of the bubble are related by the following: ； in, Indicates the radius of the liquid cavity; Indicates the bubble radius; Indicates the initial radius of the liquid cavity; Indicates the initial radius of the bubble; The velocity of a liquid is expressed as: ； ； In the formula, This represents the rate of change of the velocity of a liquid volume element at a fixed spatial position r over time. This represents a time function related to the motion of the bubble interface. Indicates the radial velocity at the bubble interface. This represents the radial coordinate at a fixed spatial location.

7. The method for constructing and analyzing the dynamic model of bubbles within a liquid cavity in a viscoelastic tissue as described in claim 1, characterized in that, In step S5, the dynamic model of bubbles in the liquid cavity is expressed as follows: in, Indicates the internal pressure of the bubble; This indicates the boundary liquid conditions between the microbubbles and the cavity. For the medium Stress in the direction, The static pressure of the liquid. Let be the initial radius of the bubble. The surface tension of the liquid, Let be the radius of the cavitation bubble. Let be the initial radius of the bubble. Let be the viscosity coefficient of the liquid. Indicates the radial velocity at the bubble interface. To drive sound pressure, and These are the shear modulus and viscosity coefficient of the medium, respectively. Represents the radius of the liquid cavity. To represent the initial radius of the liquid cavity, This represents the radial velocity of the liquid cavity boundary. This indicates the gas polyhedral index.

8. A simulation system for realizing biomechanical response under high-intensity focused ultrasound using the bubble dynamics model within a liquid cavity in viscoelastic tissue as described in any one of claims 1 to 7, characterized in that, It includes a parameter input module, a sound field simulation calculation module, a coupled dynamics model processor, and a tissue mechanical response analysis module; The parameter input module is used to receive or set physical parameters related to biological tissues, fluid cavities, and bubbles, as well as acoustic field driving parameters of high-intensity focused ultrasound. The sound field simulation calculation module is used to simulate and calculate the nonlinear sound field formed by high-intensity focused ultrasound in tissue based on a layered medium model, and output the sound pressure parameters of the focal region. The coupled dynamics model processor has a pre-stored dynamics model of bubbles in the liquid cavity of a viscoelastic tissue constructed by the above method. It is used to receive the sound pressure parameters and calculate the dynamic change of the bubble radius under the drive of the sound field. The tissue mechanical response analysis module is connected to the coupled dynamics model processor and is used to calculate and output the spatial and temporal distribution data of the internal stress field of the tissue caused by bubble oscillation based on the dynamic changes of the bubble radius.

9. The simulation system as described in claim 8, characterized in that, It also includes a results visualization module: The result visualization module is used to graphically display the dynamic change curve of the bubble radius and the spatial distribution and time change curve of the stress field inside the tissue.

10. The simulation system as described in claim 8, characterized in that, The sound field simulation calculation module is specifically configured to use water-liver-water as the layered medium model, and calculate and output the peak positive pressure, peak negative pressure and shock wave amplitude of the focal region by solving the nonlinear sound wave propagation equation. The output data of the tissue mechanical response analysis module includes at least the curves of compressive stress versus time at different locations within the tissue, and the maximum tissue stress calculated based on different initial bubble radii. The output results of the dynamic simulation module include: microbubble radius variation curve over time, spatial distribution cloud map of internal tissue stress, and maximum stress and cumulative tissue damage data at different locations or with different initial bubble radii.

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