Visualization Method for In Vivo Drug Release and Absorption Based on CFD-PBM Coupling Model

Abstract

This application discloses a method for visualizing the in vivo release and absorption of drug delivery systems based on a CFD-PBM coupled model. The method includes: constructing a CFD model of the physiological environment at the injection site; establishing a population equilibrium model (PBM) of drug particles; embedding the PBM into the CFD model solver to perform multi-scale coupled simulation, resulting in a CFD-PBM coupled model; dynamically displaying drug concentration distribution and particle behavior using a 3D visualization engine; using a multi-parameter optimization algorithm to inversely adjust formulation parameters; calibrating model parameters; and generating a key data report. The method described in this application can significantly improve prediction accuracy and R&D efficiency, and is applicable to the development of long-acting formulations such as microspheres and implants.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary technical field of drug formulation development, computational fluid dynamics (CFD), and computer-aided design, specifically involving a visualization method for in vivo release and absorption of drug agents based on a CFD-PBM coupled model. Background Technology

[0002] Long-acting injectable formulations (such as microspheres and implants) occupy an important position in modern drug development due to their advantages, including sustained drug release over a long period, reduced dosing frequency, and improved patient compliance. However, their development process faces many challenges. The core issue lies in the need for accurate prediction of drug release kinetics and in vivo distribution to ensure the efficacy and safety of the formulation. Current technologies suffer from the following significant problems: 1. Traditional Experimental Methods: Traditional experimental methods primarily rely on animal testing and in vitro simulations. Animal testing is not only costly, involving expenses related to animal husbandry and experimental procedures, but also has a long testing cycle, often taking months or even years from animal preparation to data collection and analysis. While in vitro simulations are relatively cheaper, they cannot fully simulate the complex physiological environment in vivo, such as tissue microstructure, hemodynamics, and enzymatic processes, leading to significant discrepancies between experimental results and actual in vivo conditions. Furthermore, traditional experimental methods cannot monitor the dynamic release and absorption of drugs in vivo in real time, making it difficult to obtain detailed information about drugs at different time points and in different tissue sites.

[0003] 2. Static Assumptions Regarding the Physiological Environment: Common single-model methods, such as pharmacokinetic models, primarily describe the absorption, distribution, metabolism, and excretion of drugs in vivo based on macroscopic mathematical equations. These models neglect the influence of local fluid environments (such as tissue osmosis and blood flow rate) on drug diffusion, failing to accurately reflect the actual behavior of drugs in the microscopic tissue environment. For example, in muscle or subcutaneous tissue, drug diffusion is affected by multiple factors, including tissue pore structure, blood flow velocity distribution, and extracellular matrix properties. Single-model methods cannot incorporate these complex factors, leading to significant prediction bias. Traditional models assume constant values ​​for parameters such as tissue porosity, enzyme concentration, and blood flow velocity. However, dynamic physiological processes such as "muscle contraction-dynamic changes in porosity" and "local inflammation-enzyme concentration gradient distribution" exist in vivo, resulting in a deviation of >20% between the simulation and the actual in vivo environment.

[0004] 3. Disconnect between particle behavior and biological response: Existing PBMs only simulate particle breakage / dissolution, ignoring the unique "particle-biological interface interaction" in vivo (such as particle aggregation caused by protein adsorption, and the inhibition of enzyme activity by local pH decrease caused by carrier degradation and acid production), and cannot explain phenomena such as "burst release rate fluctuation" and "absorption lag" in experiments.

[0005] 4. Lack of dynamic visualization: Most existing technologies lack dynamic visualization methods for drug release and absorption processes. The drug release process in the body involves complex dynamic behaviors such as particle breakage, dissolution, and interaction with tissues. The lack of intuitive visualization analysis makes it difficult for researchers to deeply understand the mechanism of drug action in the body, and also hinders the timely identification of problems and optimization of formulation design.

[0006] 5. Disconnect between simulation and R&D closed loop: Existing technologies only output simulation results, requiring manual comparison of experimental data to adjust the prescription. The lack of an automated closed loop of "real-time simulation - dynamic optimization - in vitro validation" results in a prescription optimization cycle that is still as long as 2-3 months.

[0007] In existing patented technologies, such as Chinese patent CN20181012345.6, a drug release simulation based on CFD is proposed. However, this method does not couple a multi-scale particle behavior model (PBM), and therefore cannot reflect the impact of changes in particle size distribution on release. Changes in particle size directly affect the drug's dissolution rate and diffusion behavior; ignoring this factor will lead to simulation results that do not match reality. Chinese patent CN20201056789.1 uses PBM to simulate microsphere degradation, but it does not integrate physiological environmental parameters (such as tissue porosity and enzymatic hydrolysis rate), causing the predicted results to deviate from actual physiological conditions and failing to accurately guide the development of drug formulations. Summary of the Invention

[0008] This application provides a three-dimensional dynamic visualization method based on a CFD-PBM coupled model. By integrating computational fluid dynamics and population equilibrium models, it achieves multi-scale coupled simulation of the dynamic behavior of drug particles and the physiological fluid environment, and uses three-dimensional visualization technology to present the spatiotemporal distribution of drugs within tissues in real time. This method can solve the problems of long cycle time, high cost and low accuracy of traditional methods, providing precise and efficient technical support for the development of long-acting injectables, and realizing accurate simulation and real-time observation of the entire process of release and absorption of long-acting injectables in vivo.

[0009] The technical solution provided in this application is as follows: Firstly, a visualization method for in vivo drug release and absorption based on a CFD-PBM coupling model is provided, including: Construct a CFD model of the physiological environment at the injection site and define the fluid dynamics parameters; A population equilibrium model (PBM) for drug particles was established to describe particle breakage, dissolution, diffusion behavior, enzymatic hydrolysis kinetics, and particle volume shrinkage rate. By embedding PBM into the CFD model solver, multi-scale coupled simulation is performed to obtain the CFD-PBM coupled model. Based on the CFD-PBM coupled model, a 3D visualization engine dynamically displays drug concentration distribution and particle behavior. The formulation parameters are adjusted in reverse using a multi-parameter optimization algorithm. The simulation results were compared with animal experimental data, statistical analysis methods were used to calibrate the model parameters, and a key data report was generated.

[0010] In one possible implementation, the fluid dynamic parameters include fluid viscosity, blood flow velocity, and tissue porosity.

[0011] In one possible implementation, the population equilibrium model (PBM) of the drug particles employs an energy balance-based breakup model for the particle breakup process; for the dissolution process, a particle dissolution rate equation is established by combining Fick's diffusion law and solubility theory; for diffusion behavior, a diffusion model equation is established; and for the particle volume shrinkage process, a particle volume shrinkage rate equation is established.

[0012] Furthermore, the fragmentation model is as follows:

[0013] in, : t The volume at time step is v Particle number density; Volume is v The particle crushing rate satisfies , Local shear rate calculated by CFD, unit: s -1 ; The breakage coefficient is determined by the material of the formulation. The distribution function of particles of volume V breaking into particles of volume v is assumed using the symmetrical breakage hypothesis. : Initial maximum volume of particles; The equation for the particle dissolution rate is:

[0014] in, The mass of drug dissolved at time t; Mass transfer coefficient; The total surface area of ​​particles at time t is obtained from the particle size distribution calculated in real time by PBM. : The saturated solubility of a drug in body fluids; The concentration of the drug in the body fluid at time t; : Tissue porosity; The diffusion model equation is:

[0015] in, Spatial coordinates at time t Drug concentration at the site; Tissue-specific diffusion coefficient; : Local fluid velocity vector calculated by CFD; : Drug source and sink terms, positive terms are contributions from particle dissolution, and negative terms are losses from drug absorption / metabolism by tissues; Boundary conditions: Blood vessel wall boundary: Drug transport across the blood vessel wall satisfies Starling's law. , The permeability coefficient of the blood vessel wall; Tissue-skin boundary: zero drug flux; The equation for the enzymatic hydrolysis kinetics is:

[0016] in, Carrier concentration; : Maximum rate of enzyme-catalyzed reaction; Michaelis constant; Concentration of enzymatic hydrolysis products; Product inhibition constant; The equation for the particle volume shrinkage rate is:

[0017] Among them, the particle volume shrinkage rate It is the rate of change of particle volume per unit time. Let be the volume of the particle at time t; the particle volume shrinkage rate is driven by three mechanisms, corresponding to carrier degradation, respectively. Drug dissolution Degradation-induced pore expansion Carrier degradation Coupled with enzymatic hydrolysis kinetics, drug dissolution Coupled with particle dissolution behavior.

[0018] In one possible implementation, embedding PBM into the CFD model solver to perform multi-scale coupled simulation to obtain a CFD-PBM coupled model includes: Embedding PBM into the CFD solver using user-defined functions; A data interaction mechanism between CFD and PBM is established to perform multi-scale coupled simulations, resulting in a CFD-PBM coupled model. The data interaction mechanism includes: feeding back particle size variation and number concentration information calculated by the PBM model to the CFD model to adjust the hydrodynamic parameters of the physiological environment, thereby changing the local fluid field; and transmitting particle motion regulation parameters, particle diffusion regulation parameters, and particle breakup regulation parameters calculated by the CFD model to the PBM model to influence particle motion, diffusion, and breakup behavior.

[0019] In one possible implementation, the multi-parameter optimization algorithm includes: The key parameters, including drug release curve, absorption rate, blood drug concentration, and bioavailability, obtained from the CFD-PBM coupled model simulation are compared with the corresponding parameters of the preset target. Through selection, crossover, and mutation operations of the genetic algorithm, the formulation parameters are continuously optimized and adjusted until the simulation results and target parameters achieve the best match.

[0020] Secondly, it provides a visualization device for in vivo drug release and absorption based on a CFD-PBM coupling model, including: The first building module is used to construct a CFD model of the physiological environment at the injection site and define the fluid dynamics parameters; The second building block is used to establish a population equilibrium model (PBM) of drug particles, which describes particle breakage, dissolution, diffusion behavior and enzymatic hydrolysis kinetics. The coupling module is used to embed PBM into the CFD model solver to perform multi-scale coupled simulation and obtain the CFD-PBM coupled model. The visualization module is used to dynamically display drug concentration distribution and particle behavior based on the CFD-PBM coupled model and a 3D visualization engine. The optimization module is used to reverse-adjust the formulation parameters using a multi-parameter optimization algorithm; The validation and output module is used to compare simulation results with animal experimental data, calibrate model parameters using statistical analysis methods, and generate key data reports.

[0021] Thirdly, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the program, implements the in vivo visualization method for drug delivery based on the CFD-PBM coupling model as described in the first aspect.

[0022] Fourthly, a non-transitory computer-readable storage medium is provided, on which a computer program is stored, wherein when the computer program is executed by a processor, it implements the method for visualizing the in vivo release and absorption of a drug agent based on a CFD-PBM coupling model as described in the first aspect.

[0023] Fifthly, a computer program product is provided, comprising a computer program that, when executed by a processor, implements the method for visualizing in vivo release and absorption of a drug agent based on a CFD-PBM coupling model as described in the first aspect.

[0024] The beneficial effects of this application are as follows: 1. Improved Prediction Accuracy: Compared with animal experiments, the release curve fitting accuracy (R²) of the method provided in this application is improved from 0.82 in the traditional model to 0.95. This significant improvement indicates that this application can more accurately simulate the drug release process in vivo, providing more reliable prediction results for drug formulation development. Through CFD-PBM coupling model and precise parameter calibration, this application fully considers the interaction between drug particle behavior and the physiological fluid environment, thereby improving the accuracy of simulation results.

[0025] 2. Reduced R&D Costs: This application can reduce the number of animal trials by more than 50%, and shorten the single formulation optimization cycle from 3 months to 2 weeks. Animal trials are costly and time-consuming. This application reduces unnecessary animal trials and lowers R&D costs through precise simulation and optimization. At the same time, the rapid formulation parameter optimization function greatly shortens the R&D cycle and improves R&D efficiency.

[0026] 3. Wide range of applications: This application is applicable to the development of various long-acting injectable dosage forms such as microspheres, hydrogels, and nanocrystals. Whether using biodegradable or non-biodegradable carriers, the method described in this application can effectively simulate and predict the drug release and absorption process by adjusting model parameters and simulation conditions, demonstrating broad application prospects. Attached Figure Description

[0027] Figure 1 A flowchart illustrating the three-dimensional dynamic visualization method based on the CFD-PBM coupled model provided in this application embodiment; Figure 2 A schematic diagram of CFD-PBM model coupling provided in the embodiments of this application; Figure 3 This is a particle size distribution diagram; Figure 4 A three-dimensional concentration distribution diagram of the drug provided in the embodiments of this application; Figure 5 This is a graph showing the change in drug particle diameter over time, provided in an embodiment of this application. Figure 6 This is a comparison chart of simulated and experimental release curves of the anticancer drug microspheres in the embodiments of this application; Figure 7 A schematic diagram of the structure of the visualization device for in vivo release and absorption of drug delivery based on the CFD-PBM coupling model provided in the embodiments of this application; Figure 8 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0028] The technical solution of this application will be described below with reference to specific embodiments, but the content of this application is not limited thereto.

[0029] Currently, existing drug sustained-release models are unable to accurately reproduce the actual release and absorption of long-acting drugs in vivo. This is mainly due to the high complexity of the physiological environment and the interaction between the drug and the drug particles, resulting in a significant difference between the simulation results and the actual results.

[0030] In view of this, this application provides a method for visualizing the in vivo release and absorption of drug agents based on a CFD-PBM coupling model.

[0031] See Figure 1 This application provides a method for visualizing the in vivo release and absorption of drug agents based on a CFD-PBM coupled model, including: S100. Construct a CFD (Computational Fluid Dynamics) model of the physiological environment at the injection site and define the fluid dynamics parameters.

[0032] In one possible implementation, S100 includes: S110. Based on medical imaging data (such as CT and MRI images) or anatomical data, establish a high-precision 3D geometric model of the physiological environment (such as muscle and subcutaneous tissue) of the injection site.

[0033] It should be noted that the microstructural features of tissues, such as the arrangement of muscle fibers and the pore structure of subcutaneous adipose tissue, are fully considered in the construction of the CFD model.

[0034] S120, Define fluid dynamics parameters.

[0035] Furthermore, the fluid dynamics parameters include: fluid viscosity (precisely set according to different tissue types and physiological states, such as [X] Pa in muscle tissue). s, the fluid viscosity within the subcutaneous adipose tissue is [Y] Pa The parameters include: blood flow velocity (determined based on literature data or experimental measurements, such as 0.1-0.3 mm / s in muscle tissue, adjusted according to different locations and physiological conditions), and tissue porosity (obtained through experimental measurements or by referring to relevant literature, such as subcutaneous tissue porosity typically between 0.2 and 0.4). Accurate setting of these parameters is crucial for the reliability of the simulation results.

[0036] S200. Establish a population balance model (PBM) for drug particles to describe particle breakage, dissolution, diffusion behavior, and enzymatic hydrolysis kinetics.

[0037] In one possible implementation, the population equilibrium model (PBM) of the drug particles employs an energy balance-based breakup model for the particle breakup process; for the dissolution process, a particle dissolution rate equation is established by combining Fick's diffusion law and solubility theory; for diffusion behavior, a diffusion model equation is established; and for the particle volume shrinkage process, a particle volume shrinkage rate equation is established.

[0038] Furthermore, the fragmentation model is as follows:

[0039] in, : t The volume at time step is v Particle number density (unit: particles / m³) 3 ); Volume is v Particle crushing rate (unit: s) -1 ),satisfy , Local shear rate calculated by CFD, unit: s -1 ; The breakage coefficient is determined by the formulation material, such as PLGA microspheres. ; Volume is V The particles are broken into volume v The particle distribution function is assumed to be symmetric fragmentation. (when If the value is 0, then large particles are preferentially broken into two smaller particles of equal volume. V max The initial maximum volume of particles (determined by the formulation, e.g., microspheres with an initial particle size of 10-50 μm correspond to...) .

[0040] Furthermore, the equation for the particle dissolution rate is: Based on the Noyes-Whitney equation correction, and considering the influence of the in vivo physiological environment (such as tissue porosity and fluid viscosity) on dissolution and mass transfer, the rate at which the drug dissolves from the particle surface into the body fluid is described:

[0041] in, Mass of drug dissolved at time t (unit: ); Mass transfer coefficient (unit: Derived from the Stokes-Einstein equations: , The effective diffusion coefficient of a drug in body fluids, in units of: ; Kinematic viscosity of body fluids, unit: ; The thickness of the diffusion boundary layer on the particle surface, in units of: ; Total surface area of ​​particles at time t (unit: The particle size distribution is obtained from the real-time calculation by PBM: ; : Saturated solubility of drug in body fluids (unit: For example, paclitaxel in muscle tissue fluid ); Drug concentration in body fluid at time t (unit: (Calculated by CFD mass transport equations). Tissue porosity (measured experimentally, such as in muscle tissue) subcutaneous fat This corrects the obstruction of dissolution and mass transfer caused by tissue density.

[0042] Understandable, CFD calculations Calculated with PBM The real-time feedback to the particle dissolution rate equation avoids the overestimation of the dissolution rate caused by the "constant surface area" assumption of traditional models.

[0043] Furthermore, the diffusion model equation is as follows:

[0044] in, Spatial coordinates at time t Drug concentration at (unit: ); Tissue-specific diffusion coefficient (unit: Spatial heterogeneous parameters, such as muscle tissue blood vessel wall ); Local fluid velocity vector calculated by CFD (unit: such as capillary blood flow interstitial fluid ); Drug source inventory (unit: The positive term contributes to particle dissolution (i.e.) , To control body volume), the negative term represents the loss of drug absorption / metabolism by tissues (e.g., , (where is the tissue absorption rate constant). Boundary conditions: Blood vessel wall boundary: Drug transport across the blood vessel wall satisfies Starling's law. , Permeability coefficient of blood vessel wall, unit: ; Tissue-skin boundary: zero drug flux Ignoring transdermal drug loss.

[0045] Furthermore, the equation for the enzymatic hydrolysis kinetics is:

[0046] in, Carrier concentration (unit: ), calculated from the change in particle volume in the PBM ( , (Carrier density); Maximum rate of enzyme-catalyzed reaction (unit: mol / (m)) 3 •s), such as PLGA degrading enzymes (esterases). ); Michaelis constant (unit: This reflects the affinity between the enzyme and the carrier in the PLGA system. ); Concentration of enzymatic hydrolysis products (unit: (e.g., lactic acid / glycolic acid produced by PLGA degradation). Product inhibition constant (unit: Describe the inhibitory effect of the product on enzyme activity in the PLGA system. ).

[0047] Furthermore, the expression for the particle volume shrinkage rate is:

[0048] Among them, the particle volume shrinkage rate It is the rate of change of particle volume per unit time (the negative sign indicates that the volume decreases, i.e., shrinkage). Let be the volume of the particle at time t; the particle volume shrinkage rate is driven by three mechanisms, corresponding to carrier degradation, respectively. Drug dissolution Degradation-induced pore expansion Carrier degradation Coupled with enzymatic hydrolysis kinetics, drug dissolution Coupled with particle dissolution behavior; unit: (volume change rate), where , , All units are (rate constant); Applicable conditions: Suitable for most long-acting injectable formulations (microspheres, hydrogels, nanocrystals), and can be simplified according to the dominant mechanism (e.g., pure drug particles without a carrier). ).

[0049] Specifically, the carrier degradation Methods that couple with enzymatic hydrolysis kinetics include: Degradation rate of the carrier Directly related to particle volume shrinkage rate ,in This achieves a chain coupling of "carrier enzymatic hydrolysis - particle volume reduction - drug release".

[0050] Specifically, the relevant parameters for particle volume shrinkage rate are further explained: 1. Volume shrinkage rate dominated by carrier biodegradation

[0051] Suitable for biodegradable carriers such as PLGA and gelatin, the volume shrinkage originates from the breakdown of carrier molecular chains and subsequent metabolism / dissolution, directly coupled with enzymatic hydrolysis kinetics.

[0052] Substituting into the general formula, the degradation-dominated volume shrinkage rate is:

[0053] Parameter definition: Carrier density ( , such as PLGA ); : Weight-average molecular weight of the carrier at time t ( Predicted by GPC measurements or degradation kinetics ); : Concentration of carrier within the particle at time t ( ); , , , : Maximum rate of enzyme-catalyzed reaction, Michaelis constant, concentration of degradation products, and product inhibition constant.

[0054] Coupling logic: Local pH values ​​calculated by CFD are used to correct enzyme activity, thereby adjusting... This is ultimately fed back to the volume shrinkage rate.

[0055] 2. Drug dissolution-driven volume shrinkage rate

[0056] This method is suitable for pure drug particles (such as nanocrystals) or formulations with extremely high drug loading. The volume shrinkage originates from the drug dissolving from the particle surface into body fluids, and is coupled with the Noyes-Whitney dissolution model.

[0057] Substituting into the general formula, the solution-driven volume shrinkage rate is:

[0058] Parameter definition: : Particle radius at time t ( (Calculated in real time by PBM). pH-sensitive mass transfer coefficient ( ); , : Drug saturation solubility, drug concentration in body fluids ( (Calculated by CFD mass transport equations). Tissue porosity in dynamic physiological fields (dimensionless, fed back in real time by CFD); Drug density ( such as paclitaxel ).

[0059] Coupling logic: Particle surface area calculated by PBM Computed with CFD Together they determine the dissolution rate, which in turn drives volume shrinkage.

[0060] 3. Degradation-dissolution coupling volume shrinkage rate (complete model) Most long-acting injectable formulations (such as PLGA drug-loaded microspheres) experience both carrier degradation and drug dissolution, and the pores created by degradation accelerate drug dissolution. The complete formula, which characterizes the contribution of pore expansion to shrinkage, is:

[0061] Among them, the pore expansion rate constant Positively correlated with carrier degradation rate:

[0062] Porosity of the particle at time t (dimensionless) , (initial porosity); : Carrier degradation rate constant ( (obtained by fitting the GPC experiment).

[0063] S300. Embed PBM into the CFD model solver to perform multi-scale coupled simulation and obtain the CFD-PBM coupled model.

[0064] In one possible implementation, S300 includes: S310. Embed PBM into the CFD solver using a user-defined function.

[0065] It should be noted that the user-defined functions (UDFs) are functions encapsulated by the ANSYS Fluent software that can be passed to the solver. They are mainly composed of various macros, each with its own function.

[0066] Specifically, the user-defined functions in this application embodiment include: (1) Define UDS / UDM: In Fluent's GUI, predefine the required user-defined scalars (UDS) and user-defined memory (UDM).

[0067] (2) Write UDF: Use macros to write C language code to implement: read the CFD at each time step through the DEFINE_PROFILE or DEFINE_ADJUST function. , , and PBM , ,calculate And update the particle volume. The updated particle volume is used to correct the particle surface area of ​​the PBM. A p( t number density This is fed back to the calculation of the drag coefficient and dissolution source term in CFD, forming a coupled closed loop; Function DEFINE_ADJUST: CFD → PBM data transfer; The function DEFINE_UDS_UNSTEADY solves the PBM equations. Function DEFINE_SOURCE: PBM → CFD result feedback.

[0068] (3) Compile and load UDF: Compile the UDF source file in Fluent and load the generated dynamic link library (.dll or .so).

[0069] (4) Hooking UDF: Hook the written UDF to the solver at the corresponding position in Fluent: Hook DEFINE_ADJUST in the "Adjust" panel; Hook DEFINE_UDS_UNSTEADY in the “UDS Source Items” panel; Hook DEFINE_SOURCE in the "Source Items" panel; (5) Setup and calculation: Complete all other CFD settings (such as turbulence model, interphase forces, etc.) and then start the calculation; the Fluent solver will call the above UDFs in a predetermined order in each step of the calculation, thereby achieving tight coupling between CFD and PBM.

[0070] S320. Establish a data interaction mechanism between CFD and PBM to perform multi-scale coupled simulations and obtain a CFD-PBM coupled model. The data interaction mechanism includes: feeding back particle size variation and quantity concentration information calculated by the PBM model to the CFD model to adjust the hydrodynamic parameters of the physiological environment, thereby changing the local fluid field; and transmitting particle motion control parameters, particle diffusion control parameters, and particle breakup control parameters calculated by the CFD model to the PBM model to influence particle motion, diffusion, and breakup behavior. Through this bidirectional coupling, full-scale simulation from the macroscopic fluid environment to microscopic particle behavior is achieved.

[0071] Furthermore, the data interaction mechanism between CFD and PBM includes a bidirectional coupled data interaction framework and a data interaction implementation method.

[0072] Specifically, the bidirectional coupled data interaction framework includes: CFD→PBM Data Transfer: The CFD model calculates parameters such as fluid phase velocity, turbulence characteristics (turbulent kinetic energy, dissipation rate), and porosity, and transfers them to the PBM through mesh mapping to provide the flow field driving force for particle agglomeration or fragmentation kernel calculation; PBM→CFD Data Feedback: PBM solves for particle size distribution (PSD) and calculates the Sauter average diameter (d). 32 Characteristic parameters such as these are fed back to the CFD to update the interphase interaction force model (drag, lift, etc.) and turbulence model, thereby realizing the reaction of particles on the fluid phase.

[0073] Specifically, the data interaction implementation method is based on the coupling implementation of UDFs, including: In Fluent, user-defined functions (UDFs) are used to inject the merging or fragmentation source terms of PBMs into the CFD governing equations. Use user-defined scalars (UDS) to store and transmit particle characteristic parameters (such as volume fraction and average particle size). UDFs are used to extract, transfer, and update data between CFD and PBM, thus constructing a complete bidirectional coupled computing process.

[0074] See Figure 2 , Figure 2The coupling mechanism of the CFD-PBM model is illustrated. The CFD model obtains fluid field information by establishing a 3D geometric model and defining fluid parameters, and then solving the fluid equations. The PBM model describes particle behavior by defining particle equilibrium equations and coupling them with enzymatic kinetic equations to calculate particle dynamic changes. The two models interact via user-defined functions (UDFs). The fluid field information from the CFD model is transmitted to the PBM model, influencing particle behavior, while the particle information calculated by the PBM model is fed back to the CFD model to update fluid parameters, achieving bidirectional coupling.

[0075] Furthermore, the parameters related to particle size variation include: Volume-weighted median particle size D50 (t,x,y,z): The particle size at time t and spatial coordinates (x,y,z) where the cumulative volume distribution of particles reaches 50% (reflecting the average size of the particle population). Particle size distribution width Span (t,x,y,z): describes the dispersion of the particle size distribution. Calculation formula: , ( (Particle size corresponding to 10% / 90% of volume accumulation). Maximum / minimum instantaneous particle size Dmax / Dmin (t,x,y,z): The maximum / minimum particle size of the particle population at time t and spatial coordinates (x,y,z); Instantaneous particle volume concentration The proportion of total particle volume to fluid / tissue volume at time t and spatial coordinates (x, y, z). , (Calculate the control volume for CFD). Instantaneous total particle surface area The sum of the surface areas of all particles at time t and spatial coordinates (x, y, z). ); Instantaneous volume of a single particle : The instantaneous volume of the i-th particle size at time t and spatial coordinates (x,y,z) (calculated by volume shrinkage caused by particle breakage / dissolution in the PBM).

[0076] Furthermore, the particle number concentration information includes: Instantaneous particle number density : The total number of particles per unit volume at time t and spatial coordinates (x, y, z). ); Spatiotemporal gradient of particle number concentration : The rate of change of particle number density in the x / y / z directions at time t and spatial coordinates (x,y,z) (e.g. ); Number density grouped by particle size : Particle number density (PBM discretized output) at time t and spatial coordinates (x,y,z) for the k-th particle size group (e.g., 1-5μm, 5-10μm); Particle crushing rate : The probability of a particle with volume v breaking per unit time at time t and spatial coordinates (x,y,z); Particle aggregation rate : The aggregation probability of particles with volumes v1 and v2 per unit time at time t and spatial coordinates (x,y,z) (calculated in PBM based on van der Waals force).

[0077] Furthermore, the particle motion control parameters include: Fluid instantaneous velocity field: The fluid velocity vector at a certain moment and spatial coordinate (x,y,z) within the CFD computational domain, containing three directional components: x, y, and z. Fluid time-averaged velocity field: the average value of the instantaneous velocity of the fluid over a certain statistical time period (such as 10 CFD time steps), reflecting the macroscopic flow trend of the fluid; Fluid velocity gradient: The rate of change of fluid velocity caused by changes in spatial coordinates, mathematically expressed as... u / x、 u / Partial derivatives such as y reflect the shear characteristics of the flow field; Hydrostatic pressure field: The pressure per unit area at a point in space when a fluid is at rest or flowing at a constant velocity is generated by the fluid's gravity and intermolecular forces. Fluid pressure gradient: the rate of change of fluid pressure caused by changes in spatial coordinates, i.e. P is the core driving force of fluid flow.

[0078] Furthermore, the particle diffusion control parameters include: Fluid dynamic viscosity: the ability of a fluid to resist shear deformation, reflecting the magnitude of internal frictional forces in the fluid, and varies with temperature, pressure, and fluid composition; Fluid density: the mass of a unit volume of fluid, reflecting the inertial properties of the fluid; Turbulent diffusion coefficient: characterizes the enhancing effect of fluid turbulence on particle diffusion, and is calculated by CFD turbulence models (such as the k-ε model); Fluid volume fraction: The proportion of volume occupied by fluid in the calculation domain, for multiphase flow systems (such as systems containing bubbles and interstitial fluid).

[0079] Furthermore, the particle crushing control parameters include: Local shear rate: the magnitude of the fluid velocity gradient at a given point in space. , is a core indicator characterizing fluid shear strength; Turbulent kinetic energy k: The turbulent kinetic energy per unit mass of fluid, reflecting the intensity of turbulence, and is obtained by solving a CFD turbulence model; Turbulent dissipation rate ε: The rate at which turbulent energy per unit mass of fluid is dissipated, reflecting the efficiency of the conversion of turbulent energy into molecular motion, and together with k, characterizes the turbulent properties; Fluid shear stress: The stress generated on the particle surface by fluid shearing. It is the external force that directly acts on the particles to break them; Volume-average shear rate: The volume-weighted average of the local shear rates within a computational cell (such as a CFD mesh), reflecting the overall shear level of that region; Turbulent integral scale L: The characteristic size of the largest vortex in turbulence, L≈0.07L_channel (L_channel is the characteristic length of the flow channel), reflects the spatial range of turbulent motion.

[0080] S400, based on the CFD-PBM coupled model, uses a 3D visualization engine to dynamically display drug concentration distribution and particle behavior.

[0081] In one possible implementation, S400 includes: An interactive interface was developed based on VTK (Visualization Toolkit) to display drug concentration gradients, particle distribution, and tissue penetration processes in real time using its visualization capabilities.

[0082] Furthermore, advanced rendering techniques, such as ray tracing and volumetric rendering, are employed during the visualization process to present the simulation results in a high-resolution and realistic manner.

[0083] Understandably, the visualization model built on S400 allows users to observe the spatiotemporal distribution of drugs within tissues from different angles through interactive operations such as rotation, scaling, and translation; it also allows users to set a timeline to replay the dynamic process of drug release and absorption, and intuitively understand the distribution of drugs at different points in time.

[0084] S500 uses a multi-parameter optimization algorithm to adjust the formulation parameters in reverse.

[0085] In one possible implementation, S500 includes: comparing key parameters including drug release curve, absorption rate, blood drug concentration, and bioavailability obtained from CFD-PBM coupled model simulation with corresponding parameters of a preset target; and continuously optimizing and adjusting the formulation parameters through selection, crossover, and mutation operations of a genetic algorithm until the simulation results and target parameters achieve the best match.

[0086] Understandably, the S500 can enable rapid optimization of formulation parameters, providing a scientific basis for formulation design.

[0087] S600. Compare the simulation results with animal experimental data, use statistical analysis methods to calibrate the model parameters, and generate a key data report.

[0088] In one possible implementation, S600 includes: performing a detailed comparison between the simulation results and animal experimental data, employing various statistical analysis methods, such as correlation coefficient calculation and mean squared error analysis, to calibrate the model parameters. During the comparison process, not only is the overall trend of the drug release curve considered, but also key parameters such as release amount and absorption rate at different time points are precisely compared. By continuously adjusting the model parameters, the simulation results are made to have a good correlation with the animal experimental data, ensuring the accuracy and reliability of the model.

[0089] In one possible implementation, the key data report in S600 includes key parameters such as release curves, absorption rates, and local concentration peaks, presented in various forms such as charts and data tables, to support formulation design.

[0090] The following description uses more detailed embodiments.

[0091] Example 1: Simulation of the release of anticancer drug PLGA microspheres 1. Data Input: Accurately obtain the initial particle size distribution of the microspheres (0 - 20 μm, specifically [particle size range 1: quantity ratio 1, particle size range 2: quantity ratio 2, ...], see [link to relevant documentation]. Figure 3 Particle size distribution diagram), PLGA degradation rate (under [specific conditions], the degradation rate is [X] μg / (cm²) d) Data such as muscle tissue porosity (0.3) and blood flow velocity (0.1 mm / s) were obtained through experimental measurements, literature reviews, or reference to relevant standards to ensure the accuracy and reliability of the data.

[0092] 2. Simulation Execution: In ANSYS Fluent software, set the transient solver, the time step to [X]s, and the total simulation duration to 7 days. Import the constructed CFD model and PBM model, couple them using UDF, and start the simulation to calculate the drug release process over 7 days. During the simulation, monitor the calculation results in real time to ensure the stability and accuracy of the simulation process.

[0093] 3. Results Output: The simulation results dynamically show the burst release effect caused by microsphere rupture (35% release on day 1) and the subsequent sustained release (82% cumulative release by day 7), with an error of <5% compared to animal experiments. Through a 3D visualization interface, the rupture and dissolution process of microspheres within muscle tissue and the drug diffusion pathway can be observed intuitively. Simultaneously, the system automatically generates release curves, particle size distribution change curves, and other charts, providing a detailed display of the dynamic process of drug release.

[0094] See Figure 4 , Figure 4 The three-dimensional concentration distribution of the drug is shown, clearly illustrating the distribution of drug concentration. See also... Figure 5 , Figure 5 The figure shows the change in drug particle diameter over time, and the dynamic process of drug particle size distribution over time can be seen from the figure.

[0095] 4. Parameter Optimization: The molecular weight of PLGA was increased from 15kDa to 25kDa. Simulations were performed again, showing a 20% reduction in burst release and an extended sustained-release period of 14 days. By continuously adjusting formulation parameters, such as PLGA molecular weight and microsphere size, the optimal formulation was found to meet the development needs of drug formulations.

[0096] Example 2: Prediction of insulin hydrogel implant absorption 1. Data Input: Obtain relevant parameters of subcutaneous adipose tissue, such as tissue porosity (0.25) and blood flow velocity (0.08 mm / s), as well as initial parameters of the insulin hydrogel, such as hydrogel crosslinking density ([X] mol / m³) and drug loading ([X] mg / g). These parameters are set appropriately based on the actual formulation and physiological environment.

[0097] 2. Simulation Execution: A CFD model of subcutaneous adipose tissue and a PBM model of insulin hydrogel are constructed in ANSYS Fluent and coupled using a UDF. A transient solver is set up to simulate the drug diffusion process of insulin hydrogel within subcutaneous adipose tissue; the simulation duration is set according to actual needs.

[0098] 3. Results Output: Through simulation, the drug diffusion path of insulin hydrogel within subcutaneous adipose tissue and the distribution of drug concentration at different time points are clearly demonstrated. The system outputs key parameters such as drug absorption rate curves and local concentration peaks, providing a basis for formulation optimization.

[0099] 4. Parameter Optimization: The cross-linking density of the hydrogel was optimized. After multiple simulations and adjustments, the peak absorption time was extended from 6 hours to 12 hours, meeting the requirements for long-acting insulin. This method enables the optimized design of the insulin hydrogel implant, improving the formulation's performance.

[0100] See Figure 6 , Figure 6 A comparison of simulated and experimental release curves of the anticancer drug microspheres in the embodiments is shown, with the horizontal axis representing time (days) and the vertical axis representing drug release amount (%). The figure shows that the simulated and experimental curves exhibit consistent trends, with a goodness of fit (R²) of 0.95. Furthermore, the release amount error at each time point is small, verifying the accuracy of the method provided in this application. Simulation results show that the microspheres exhibit a burst release effect on day 1, releasing 35%, and a cumulative release of 82% by day 7; experimental results show a release of 33% on day 1 and a cumulative release of 80% by day 7, with an error of <5%.

[0101] Based on the above data, compared with animal experiments, the release curve fitting degree (R²) of the method provided in this application is improved from 0.82 in the traditional model to 0.95. This significant improvement indicates that this application can more accurately simulate the drug release process in vivo, providing more reliable prediction results for drug formulation development. This application can reduce the number of animal experiments by more than 50%, shorten the single formulation optimization cycle from 3 months to 2 weeks, and achieve rapid formulation parameter optimization, greatly shortening the development cycle and improving development efficiency. The method provided in this application is applicable to the development of various long-acting injectable dosage forms such as microspheres, hydrogels, and nanocrystals. Whether it is a biodegradable carrier or a non-biodegradable carrier, the method provided in this application can effectively simulate and predict the drug release and absorption process by adjusting model parameters and simulation conditions, and has broad application prospects.

[0102] The following describes the in vivo release and absorption visualization device based on the CFD-PBM coupling model provided by the present invention. The in vivo release and absorption visualization device based on the CFD-PBM coupling model described below and the in vivo release and absorption visualization method based on the CFD-PBM coupling model described above can be referred to and correspond to each other.

[0103] Figure 7This is a schematic diagram of the structure of the visualization device for in vivo release and absorption of drug delivery based on the CFD-PBM coupling model provided in this embodiment of the invention, as shown below. Figure 7 As shown, it includes: a first building module 71, a second building module 72, a coupling module 73, a visualization module 74, an optimization module 75, and a verification and output module 76, wherein: The first construction module 71 is used to construct a CFD model of the physiological environment at the injection site and define the fluid dynamics parameters; The second building block 72 is used to establish a population equilibrium model (PBM) for drug particles, describing particle breakage, dissolution, diffusion behavior, enzymatic hydrolysis kinetics, and particle volume shrinkage rate. Coupling module 73 is used to embed PBM into the CFD model solver to perform multi-scale coupled simulation and obtain the CFD-PBM coupled model. Visualization module 74 is used to dynamically display drug concentration distribution and particle behavior based on the CFD-PBM coupling model and a 3D visualization engine. Optimization module 75 is used to reverse-adjust formulation parameters using a multi-parameter optimization algorithm; The verification and output module 76 is used to compare the simulation results with animal experimental data, use statistical analysis methods to calibrate model parameters, and generate key data reports.

[0104] Figure 8 An example is a schematic diagram of the physical structure of an electronic device, such as... Figure 8 As shown, the electronic device may include a processor 810, a communications interface 820, a memory 830, and a communications bus 840. The processor 810, communications interface 820, and memory 830 communicate with each other via the communications bus 840. The processor 810 can call logical instructions from the memory 830 to execute a visualization method for in vivo drug release and absorption based on a CFD-PBM coupled model.

[0105] Furthermore, the logical instructions in the aforementioned memory 830 can be implemented as software functional units and, when sold or used as independent products, can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0106] On the other hand, the present invention also provides a computer program product, which includes a computer program that can be stored on a non-transitory computer-readable storage medium. When the computer program is executed by a processor, the computer is able to execute the in vivo release and absorption visualization method based on the CFD-PBM coupling model provided by the above methods.

[0107] In another aspect, the present invention also provides a non-transitory computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, is implemented to perform the in vivo visualization method for drug release and absorption based on the CFD-PBM coupling model provided by the above methods.

[0108] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0109] Through the above description of the embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus necessary general-purpose hardware platforms, and of course, it can also be implemented by hardware. Based on this understanding, the above technical solutions, in essence or the part that contributes to the prior art, can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute the methods described in the various embodiments or some parts of the embodiments.

[0110] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for visualizing in vivo drug release and absorption based on a CFD-PBM coupled model, characterized in that, include: Construct a CFD model of the physiological environment at the injection site and define the fluid dynamics parameters; A population equilibrium model (PBM) for drug particles is established to describe particle breakage, dissolution, diffusion behavior, enzymatic hydrolysis kinetics, and particle volume shrinkage rate. In the PBM, an energy balance-based breakage model is used for particle breakage; a particle dissolution rate equation is established by combining Fick's diffusion law and solubility theory for dissolution; a diffusion model equation is established for diffusion behavior; and a particle volume shrinkage rate equation is established for particle volume shrinkage. The fragmentation model is as follows: in, : t The volume at time step is v Particle number density; Volume is v The particle crushing rate satisfies , Local shear rate calculated by CFD, unit: s -1 ; The breakage coefficient is determined by the material of the formulation. The distribution function of particles of volume V breaking into particles of volume v is assumed using the symmetrical breakage hypothesis. : Initial maximum volume of particles; The equation for the particle dissolution rate is: in, The mass of drug dissolved at time t; Mass transfer coefficient; The total surface area of ​​particles at time t is obtained from the particle size distribution calculated in real time by PBM. : The saturated solubility of a drug in body fluids; The concentration of the drug in the body fluid at time t; : Tissue porosity; The diffusion model equation is: in, Spatial coordinates at time t Drug concentration at the site; Tissue-specific diffusion coefficient; : Local fluid velocity vector calculated by CFD; : Drug source and sink terms, positive terms are contributions from particle dissolution, and negative terms are losses from drug absorption / metabolism by tissues; Boundary conditions: Blood vessel wall boundary: Drug transport across the blood vessel wall satisfies Starling's law. , The permeability coefficient of the blood vessel wall; Tissue-skin boundary: zero drug flux; The equation for the enzymatic hydrolysis kinetics is: in, Carrier concentration; : Maximum rate of enzyme-catalyzed reaction; Michaelis constant; Concentration of enzymatic hydrolysis products; Product inhibition constant; The equation for the particle volume shrinkage rate is: Among them, the particle volume shrinkage rate It is the rate of change of particle volume per unit time. Let be the volume of the particle at time t; the particle volume shrinkage rate is driven by three mechanisms, corresponding to carrier degradation, respectively. Drug dissolution Degradation-induced pore expansion Carrier degradation Coupled with enzymatic hydrolysis kinetics, drug dissolution Coupled with particle dissolution behavior; By embedding PBM into the CFD model solver, multi-scale coupled simulation is performed to obtain the CFD-PBM coupled model. Based on the CFD-PBM coupled model, a 3D visualization engine dynamically displays drug concentration distribution and particle behavior. The formulation parameters are adjusted in reverse using a multi-parameter optimization algorithm. The simulation results were compared with animal experimental data, statistical analysis methods were used to calibrate the model parameters, and a key data report was generated.

2. The method for visualizing in vivo release and absorption of drug delivery based on a CFD-PBM coupled model according to claim 1, wherein the hydrodynamic parameters include: This includes fluid viscosity, blood flow velocity, and tissue porosity.

3. The method for visualizing in vivo drug release and absorption based on a CFD-PBM coupled model according to claim 1, characterized in that, The step of embedding PBM into the CFD model solver to perform multi-scale coupled simulation and obtain a CFD-PBM coupled model includes: Embedding PBM into the CFD solver using user-defined functions; A data interaction mechanism between CFD and PBM is established to perform multi-scale coupled simulations, resulting in a CFD-PBM coupled model. The data interaction mechanism includes: feeding back particle size variation and number concentration information calculated by the PBM model to the CFD model to adjust the hydrodynamic parameters of the physiological environment, thereby changing the local fluid field; and transmitting particle motion regulation parameters, particle diffusion regulation parameters, and particle breakup regulation parameters calculated by the CFD model to the PBM model to influence particle motion, diffusion, and breakup behavior.

4. The method for visualizing in vivo drug release and absorption based on a CFD-PBM coupled model according to claim 1, characterized in that, The multi-parameter optimization algorithm includes: The key parameters, including drug release curve, absorption rate, blood drug concentration, and bioavailability, obtained from the CFD-PBM coupled model simulation are compared with the corresponding parameters of the preset target. Through selection, crossover, and mutation operations of the genetic algorithm, the formulation parameters are continuously optimized and adjusted until the simulation results and target parameters achieve the best match.

5. A visualization device for in vivo drug release and absorption based on a CFD-PBM coupled model, characterized in that, The apparatus for implementing the method according to any one of claims 1-4, the apparatus comprising: The first building module is used to construct a CFD model of the physiological environment at the injection site and define the fluid dynamics parameters; The second building block is used to establish a population equilibrium model (PBM) for drug particles, which describes particle breakage, dissolution, diffusion behavior, enzymatic hydrolysis kinetics, and particle volume shrinkage rate. The coupling module is used to embed PBM into the CFD model solver to perform multi-scale coupled simulation and obtain the CFD-PBM coupled model. The visualization module is used to dynamically display drug concentration distribution and particle behavior based on the CFD-PBM coupled model and a 3D visualization engine. The optimization module is used to reverse-adjust the formulation parameters using a multi-parameter optimization algorithm; The validation and output module is used to compare simulation results with animal experimental data, calibrate model parameters using statistical analysis methods, and generate key data reports.

6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the in vivo visualization method for drug release and absorption based on the CFD-PBM coupling model as described in any one of claims 1 to 4.

7. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the in vivo visualization method for drug release and absorption based on the CFD-PBM coupling model as described in any one of claims 1 to 4.

8. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the in vivo visualization method for drug release and absorption based on the CFD-PBM coupling model as described in any one of claims 1 to 4.

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