Radial basis function proxy model-based optimization method and system for enteric organ-on-chip

Abstract

This invention proposes an optimization method and system for intestinal organ-on-a-chip based on a radial basis function surrogate model, belonging to the field of microfluidic organ-on-a-chip design and optimization. The method includes: determining the core design variables, dual-physics optimization objectives, and defining the optimization range of the core design variables; generating an experimental design matrix using Latin hypercube sampling, and constructing a sample database after obtaining response values ​​through simulation; constructing a radial basis function surrogate model based on the database, and performing global multi-objective optimization on the surrogate model using a non-dominated sorting genetic algorithm to generate a Pareto front solution set; remodeling the representative solutions in the Pareto front and performing CFD numerical simulations, obtaining the objective function value, comparing it with the representative solutions, and selecting the optimal design scheme as the final optimization result. This invention effectively solves the physical field conflict between shear force and oxygen gradient in intestinal organ-on-a-chip, achieving coordinated optimization of chip structure and operating parameters.

Description

Technical Field

[0001] This invention belongs to the field of microfluidic organ-on-a-chip design and optimization technology, and particularly relates to an intestinal organ-on-a-chip optimization method and system based on a radial basis function surrogate model. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Microfluidic organ-on-a-chip technology represents a significant breakthrough in biomedical engineering in recent years, enabling the simulation of key structures and physiological microenvironments of human organs within a micro- and nano-scale space. Among these, the intestinal organ-on-a-chip serves as a crucial model for drug absorption and barrier defense research, playing an irreplaceable role in improving the accuracy of preclinical pharmacokinetic assessments. However, the core challenge of intestinal organ-on-a-chip technology lies in accurately mimicking the complex mechanical and biochemical environment of the gut in vivo.

[0004] Current organ-on-a-chip designs largely rely on trial and error based on experience or adjustments to single-variable parameters, making it difficult to systematically resolve the inherent conflict between fluid dynamics and mass transfer processes. The root of the problem lies in the highly coupled and conflicting nature of fluid dynamics and mass transfer characteristics in conventional designs: increasing flow rate or decreasing channel height, while enhancing shear stimulation to meet cellular mechanical demands, can instantaneously introduce excessive dissolved oxygen, disrupting the existing oxygen gradient; conversely, decreasing flow rate or increasing channel height to maintain the oxygen gradient may lead to insufficient shear force, affecting cell phenotype maintenance and barrier function maturation. This mutually constraining relationship makes design methods relying on repeated parameter modifications based on human experience extremely inefficient, and even unlikely to achieve ideal design results. Directly employing computational fluid dynamics (CFD) simulations for multi-parameter analysis results in lengthy calculation times and high computational costs, making it difficult to meet the needs of engineering applications. Existing technologies typically use discrete probes or global average concentrations as evaluation indicators, failing to accurately quantify the morphological characteristics of oxygen gradients in complex spaces.

[0005] In recent years, surrogate models and multi-objective optimization algorithms have demonstrated significant advantages in optimizing complex systems in fields such as aerospace and automotive manufacturing. By constructing efficient surrogate models to replace time-consuming computational fluid dynamics (CFD) simulations, and combining them with intelligent optimization algorithms to automatically search for optimal solutions in multi-parameter spaces, it is hoped that a shift from passive trial and error to proactive design can be achieved. However, no research has yet systematically applied these methods to the multiphysics structure optimization of intestinal organ-on-a-chip, and there is a lack of systematic solutions for the dual-objective synergistic optimization of oxygen gradient and shear force. Furthermore, existing technologies generally lack mechanisms to accurately map complex biological requirements (such as oxygen coverage in specific physiological regions) into calculable mathematical evaluation indicators, thus failing to address the problem of solving multiphysics conflicts that conventional general optimization algorithms struggle to accomplish. Summary of the Invention

[0006] To overcome the shortcomings of the prior art, this invention provides an intestinal organ-on-a-chip optimization method and system based on a radial basis function surrogate model. By introducing a multi-objective optimization design framework based on a surrogate model and a non-dominated sequence genetic algorithm (NSGA-II), it can effectively solve the problems of multi-physics objective conflict, low optimization efficiency, and reliance on experience trial and error in existing designs.

[0007] To achieve the above objectives, one or more embodiments of the present invention provide the following technical solutions: The first aspect of this invention provides an intestinal organ-on-a-chip optimization method based on a radial basis function surrogate model; An intestinal organ-on-a-chip optimization method based on a radial basis function surrogate model includes: The core design variables and dual-physics optimization objectives of the intestinal organ-on-a-chip were determined, and the optimization range of the core design variables was defined. Based on the optimization range of the defined core design variables, Latin hypercube sampling is used to generate the experimental design matrix, and a sample database is constructed after obtaining the response values ​​through numerical simulation. A radial basis function surrogate model based on multiple quadratic kernel functions is constructed based on the sample database. A non-dominated sorting genetic algorithm is used to perform global multi-objective optimization on the radial basis function surrogate model to generate a Pareto front solution set. The representative solution in the Pareto front is remodeled and CFD numerical simulation is performed. The objective function value is obtained and compared with the representative solution. The design scheme with the best comprehensive performance is selected as the final optimization result.

[0008] As a further technical solution, the core design variables of the intestinal organ chip include inlet flow rate, upper channel aspect ratio, lower channel aspect ratio, distance from lower channel to bottom of chip, and distance from upper channel to top of chip; The dual-physics optimization objectives include maximizing the coverage area of ​​the physiologically suitable oxygen concentration range and minimizing the absolute deviation between the average shear force on the cell surface and the physiological target value.

[0009] As a further technical solution, based on the defined optimization range of the core design variables, Latin hypercube sampling is used to generate the experimental design matrix. After obtaining the response values ​​through numerical simulation, a sample database is constructed, including: Based on defining the optimization range of the core design variables, the Latin hypercube sampling method is used to generate sample points in the five-dimensional design space composed of the core design variables. After inverse normalization and modeling of the sample points, they are imported in batches into the computational fluid dynamics simulation platform for multi-physics coupling solution. The suitable oxygen coverage and average surface shear force of each group of samples are extracted through post-processing. Using design variables as input and optimization objectives as output, a sample database containing sample points and their corresponding objective function values ​​is constructed.

[0010] As a further technical solution, the mathematical expression of the radial basis function surrogate model is:

[0011] in, For unknown test points; Let i be the i-th sample point; is the predicted value of the radial basis surrogate model for the unknown point; N is the total number of samples in the Latin hypercube sampling. Let be the Euclidean distance from the test point to the i-th sample point. These are the weighting coefficients to be solved; For the radial basis surrogate model, it is the kernel function; The quadratic kernel function of the radial basis function surrogate model is:

[0012] in, The kernel function is a quadratic kernel function; r is the Euclidean distance between the two points; For shape parameters.

[0013] As a further technical solution, the method of using a non-dominated sorting genetic algorithm to perform global multi-objective optimization on the radial basis function surrogate model and generate a Pareto front solution set includes: Using the radial basis function surrogate model as the objective function surrogate model, a non-dominated sorting genetic algorithm is employed for global multi-objective optimization. The non-dominated sorting genetic algorithm introduces Pareto dominance theory to divide individuals in the population into non-dominated levels and uses the crowding distance method to maintain the diversity of the solution set. Its execution process includes: Initialize the population by setting the population size, number of generations, crossover probability, and mutation probability parameters; The objective function value for each individual in the population is calculated using a radial basis function surrogate model. The objective function value includes the oxygen suitability concentration coverage and the deviation of the average surface shear force. Perform non-dominated ranking on the individuals in the population, assign a non-dominated level to each individual and calculate the crowding distance for each individual; An elite retention strategy is adopted, merging the parent and offspring populations, prioritizing individuals with lower non-dominant levels to enter the next generation, and prioritizing individuals with larger crowding distances when individuals of the same non-dominant level cannot be accommodated. The final Pareto front solution set is output by iterating until the preset number of generations or convergence condition is reached.

[0014] As a further technical solution, the representative solution in the Pareto front is remodeled and subjected to CFD numerical simulation. The objective function value is then compared with the representative solution, and the design scheme with the best overall performance is selected as the final optimization result, including: The K-means clustering algorithm is used to partition and classify the Pareto front solution set, dividing the Pareto front into several feature sub-regions, and extracting representative solutions from each cluster. The design variable parameters corresponding to the extracted representative solutions are substituted back into the computational fluid dynamics simulation platform to perform multi-physics coupling solution and obtain the suitable oxygen concentration coverage and average surface shear force of each representative solution. The simulation target value obtained from computational fluid dynamics simulation is compared with the predicted value of the radial basis function surrogate model, the relative error is calculated, and the prediction accuracy of the surrogate model is evaluated. Based on the simulation target value, a comprehensive performance evaluation of each representative solution is performed. The optimal solution that maximizes the coverage of suitable oxygen concentration and minimizes the shear force deviation is selected as the final optimization result. The design variable parameters and performance indicators corresponding to the final optimization result are output.

[0015] A second aspect of the present invention provides an intestinal organ-on-a-chip optimization system based on a radial basis function surrogate model.

[0016] An intestinal organ-on-a-chip optimization system based on a radial basis function surrogate model includes: The parameter setting module is configured to: determine the core design variables and dual-physics field optimization objectives of the intestinal organ chip, and define the optimization range of the core design variables; The sample generation module is configured to: generate an experimental design matrix based on the optimization range of the defined core design variables, and construct a sample database after obtaining the response values ​​through numerical simulation; The optimization solution module is configured to: construct a radial basis function surrogate model based on multiple quadratic kernel functions based on the sample database, and use a non-dominated sorting genetic algorithm to perform global multi-objective optimization on the radial basis function surrogate model to generate a Pareto front solution set; The verification output module is configured to: remodel the representative solution in the Pareto front and perform CFD numerical simulation, obtain the objective function value and compare it with the representative solution, and select the design scheme with the best comprehensive performance as the final optimization result.

[0017] A third aspect of the present invention provides a computer-readable storage medium having a program stored thereon, which, when executed by a processor, implements the steps of the intestinal organ-on-a-chip optimization method based on a radial basis function surrogate model as described in the first aspect of the present invention.

[0018] A fourth aspect of the present invention provides an electronic device, including a memory, a processor, and a program stored in the memory and executable on the processor, wherein the processor executes the program to implement the steps in the intestinal organ-on-a-chip optimization method based on a radial basis function surrogate model as described in the first aspect of the present invention.

[0019] The fifth aspect of the present invention provides a computer program product, including a computer program / instruction that, when executed by a processor, implements the steps in the intestinal organ-on-a-chip optimization method based on a radial basis function surrogate model described in the first aspect of the present invention.

[0020] The above one or more technical solutions have the following beneficial effects: (1) A customized optimization framework for multi-physics field conflicts in organ-on-a-chip was constructed. This invention breaks through the limitations of traditional "general algorithm application" and systematically performs in-depth mathematical deconstruction and modeling of the physical field conflict between "fluid shear force stimulation" and "oxygen gradient maintenance" in intestinal microarrays. By revealing the constraints between the characteristic dimensions (channels, walls) of intestinal organ-on-a-chip and the culture operation parameters (flow rate of culture medium, dissolved oxygen), a leap from passive trial and error to active design is achieved.

[0021] (2) It achieves a precise mapping from biological indicators to mathematical evaluation indicators. This invention innovatively transforms spatial image morphological features (i.e., the proportion of oxygen pixel area falling into a specific physiological range) into a negative objective function, and constructs a multi-objective optimization framework with the goal of maximizing the coverage area of ​​the physiologically suitable oxygen concentration range and minimizing shear force deviation. It solves the technical problem that traditional discrete probes or average concentrations cannot characterize the "gradient spatial morphology", and provides a reliable optimization target for multi-objective optimization algorithms.

[0022] (3) Traditional intestinal organ-on-a-chip design relies on a large number of trial-and-error computational fluid dynamics simulations, which take a long time to complete a single simulation and are difficult to support global optimization of multiple parameters and multiple objectives. This invention generates an experimental design matrix through Latin hypercube sampling, obtains response values ​​through numerical simulation, constructs a sample database, and builds a radial basis function surrogate model based on the sample data. Compared with the optimization path that simply relies on the traditional CFD trial-and-error method, this invention avoids the computational overhead of thousands of expensive nonlinear fluid simulations, achieving the dual technical effects of improved computational efficiency and high-fidelity reconstruction of the physical field, reducing the multi-physics optimization computation time by several orders of magnitude. In addition, compared with the traditional polynomial response surface model and Kriging model, the radial basis function surrogate model adopted in this invention has stronger fitting ability and better small sample stability when dealing with flow field problems with high nonlinearity and multi-peak response, and is particularly suitable for modeling complex fluid-mass coupling problems in microfluidic chips.

[0023] (4) This invention scientifically defines the optimization range of the five core design variables through rigorous univariate sensitivity analysis, ensuring the physical rationality of the optimization space; it extracts feature solutions covering different preference regions from the Pareto front using the K-means clustering algorithm, and ensures the physical reliability of the optimization results through computational fluid dynamics back-substitution verification. This invention obtains an asymmetric topological structure of upper and lower channel heights and oxygen barrier wall thickness through global optimization of five-dimensional parameters. The optimized chip forms clear recommended values ​​for parameters such as upper and lower channel heights and top and bottom wall thicknesses, which facilitates the preparation and verification of intestinal organ-on-a-chip. In terms of parameter optimization, it can accurately quantify operating parameters such as inlet flow rate, improving the uniformity of shear force distribution and oxygen gradient reconstruction effect of the optimized chip.

[0024] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0025] The accompanying drawings, which form part of this invention, are used to provide a further understanding of the invention. The illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an improper limitation of the invention.

[0026] Figure 1 This is a flowchart of the method in the first embodiment.

[0027] Figure 2 This is a diagram showing the distribution of sample points generated from the Latin hypercube sampling data in the first embodiment in the multidimensional parameter space.

[0028] Figure 3 This is a schematic diagram showing the comparison results between the radial basis function surrogate model in the first embodiment and the other models.

[0029] Figure 4 This is a flowchart of the non-dominated sequence genetic algorithm for solving the radial basis function model in the first embodiment.

[0030] Figure 5 This is a schematic diagram of the Pareto front solution set obtained in the first embodiment.

[0031] Figure 6 The first embodiment is a schematic diagram of selecting five representative solutions from the Pareto front solution set using the K-means clustering algorithm.

[0032] Figure 7 The first embodiment shows the oxygen concentration gradient cloud maps of five representative solutions obtained from the numerical simulation, along with corresponding post-processing diagrams.

[0033] Figure 8The values ​​represent the average shear force and deviation (y2) of the five representative solutions obtained from the numerical simulation in the first embodiment.

[0034] Figure 9 The simulated values ​​of the proportion of oxygen suitable concentration ranges (y1) of the five representative solutions in the first embodiment are compared with the predicted values ​​of the surrogate model. Detailed Implementation

[0035] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0036] It should be noted that the terminology used herein is for the purpose of describing particular implementations only and is not intended to limit the exemplary implementations of the present invention.

[0037] Where there is no conflict, the embodiments and features in the embodiments of the present invention can be combined with each other.

[0038] The overall approach proposed in this invention addresses the challenges of fluid shear force and oxygen gradient interdependence, coupled with low efficiency of manual trial and error in intestinal organ-on-a-chip design. It defines five core design variables, including inlet velocity and channel aspect ratio, and establishes dual-physics optimization objectives. A sample dataset is constructed using Latin hypercube sampling combined with CFD simulation. A radial basis function surrogate model is built to replace time-consuming CFD simulations, reducing computational costs. Subsequently, the NSGA-II algorithm is used to perform global multi-objective optimization to generate a Pareto front solution set. Representative solutions are extracted using K-means clustering and verified through CFD back-substitution. Finally, the optimal solution with the best overall performance is selected, achieving synergistic optimization of the chip's dual-physics fields and improving biomimetic performance and design efficiency.

[0039] Example 1 This embodiment discloses an optimized design method for intestinal organ-on-a-chip structures. By introducing a multi-objective optimization design framework based on a radial basis function surrogate model and the NSGA-II algorithm, it can effectively solve the problems of multi-physics objective conflict, low optimization efficiency, and reliance on experience trial and error in existing designs.

[0040] Specifically, such as Figure 1 As shown, the intestinal organ-on-a-chip optimization method based on the radial basis function surrogate model includes: Step S1: Determine the core design variables and dual-physics field optimization objectives of the intestinal organ-on-a-chip, and define the optimization range of the core design variables.

[0041] Step S1.1: Determine the core design variables and dual-physics field optimization objectives for the intestinal organ-on-a-chip.

[0042] Key physical parameters of the in vivo microfluidic and mass transfer fields of the human gut were extracted. To achieve accurate mapping of the in vitro microenvironment, the primary task is to quantitatively characterize the physical structure and hydrodynamic boundaries of the gut. For example, during actual digestion, the physical properties of chyme in the gut exhibit high dynamic complexity. Based on existing research, the dynamic viscosity of chyme ranges from approximately 0.01 to 1 Pa·s, and its density is between 1000 and 1400 kg / m³. 3 The propulsion velocity of the small intestine within the intestinal lumen is typically between 0.005 and 0.02 m / s, while the average diameter of the adult small intestine is approximately 0.025 m. Based on the aforementioned core physical properties, envelope calculations for the limiting condition using the Reynolds number equation (Re = ρul / μ) show that the Reynolds number in the in vivo small intestine is between 0.125 and 70, falling within the typical low-velocity laminar flow range.

[0043] Related studies have shown that when the surface of intestinal epithelial cells is subjected to approximately 0.02 dyne / cm 2 (2×10) -3 When subjected to fluid shear stress of (Pa), cell polarization is significantly induced and the formation of 3D villous structures is promoted. Simultaneously, due to the unidirectional oxygen supply from the basal vessels and the intense consumption by the cells, a steep physiological oxygen gradient, ranging from 59 mmHg to less than 10 mmHg, is formed from the base of the crypt to the intestinal lumen junction. These parameters collectively constitute the rigid physical benchmark for the biomimetic design in this study.

[0044] In this embodiment, a "sandwich" type (Transwell) dual-channel topology is used as the initial physical model. The main body of the model consists of two parallel microfluidic channels. The upper and lower channels have the same width, both set to 1.5 mm. The upper channel directly simulates the intestinal lumen, while the lower channel simulates the capillary network of the submucosa of the intestine. A porous flexible polymer membrane coated with extracellular matrix is ​​embedded between the two channels. In addition, vacuum stretching chambers are symmetrically arranged on both sides of the microchannels. The flexible membrane is deformed by applying periodic negative pressure to accurately reproduce the mechanical peristaltic characteristics of the intestine.

[0045] Based on the constructed Transwell-type dual-channel topology of the intestinal organ-on-a-chip, the governing equations of the oxygen concentration field and the cell surface shear force field were deconstructed.

[0046] The spatial functional relationship of the oxygen concentration field can be characterized as follows:

[0047] in, This is the spatial functional relationship expression for the oxygen concentration field; The oxygen concentration is affected by the average flow velocity of the fluid; The diffusion coefficient of oxygen in the culture medium; This represents the cell's maximum oxygen consumption rate. The overall mass transfer coefficient of the wall surface; The partial pressure of atmospheric oxygen in the external incubator; The thickness of the mass transfer barrier in the chip; The seeding cell density, i.e., the oxygen concentration, is constrained by the parameters mentioned above.

[0048] Dominant intestinal epithelial cell surface fluid shear stress ( The functional relationship of ) can be characterized as:

[0049] Among them, shear stress is affected by the fluid density of the culture medium ( ), dynamic viscosity ( ), average fluid velocity ( ) and the characteristic hydraulic diameter of microchannels ( () direct control.

[0050] To save computational costs and from the perspective of engineering controllability, the variable space was reduced in dimensionality. First, the fluid density, viscosity, oxygen diffusion coefficient, wall oxygen permeability coefficient, and external oxygen concentration in the above formulas are inherent physical properties of the culture medium and PDMS material or external environmental constants, while the maximum oxygen consumption rate and cell density are inherent biological characteristics. These parameters are rigidly locked in a specific in vitro culture system, and therefore were removed as constant terms.

[0051] Finally, from an engineering adjustment perspective, five core design variables were identified: inlet flow rate (x1), upper channel aspect ratio (x2), lower channel aspect ratio (x3), distance from lower channel to bottom of chip (x4), and distance from upper channel to top of chip (x5). The aspect ratio is defined as the ratio of channel height to width. Since the width of the upper and lower channels is fixed at 1.5mm in this embodiment, the channel height can be determined by optimizing the aspect ratio. These five variables constitute the core parameters of the chip structure design.

[0052] After establishing the five-dimensional design vector, to ensure that subsequent univariate sensitivity analysis and multi-objective optimization algorithms have clear optimization directions and quantitative standards, the biological requirement of reconstructing the real human microenvironment must be transformed into a rigorous mathematical objective function. Specifically, based on the baseline of the human intestinal physiological microenvironment, a dual-physics field optimization objective is determined. The first is to maximize the suitable oxygen concentration range, that is, to maximize the area within the chip cell culture region that falls within the physiological oxygen concentration range of 0.013~0.077 mol / m³ (corresponding to 10~59 mmHg), accurately reconstructing the steep oxygen gradient of the intestine; the second is to ensure that the average shear force on the surface of intestinal cells is within the physiologically safe range of 0.002 - 0.08 dyne / cm². 2(2×10) -4 - 8×10 -3 Under the premise of Pa), that is, at 0.02 dyne / cm² (2×10 -3 The shear force (Pa) is the physiological target value. This value is most suitable for inducing intestinal cells to form a villous structure in the organ-on-a-chip, so as to minimize the absolute deviation between the average shear force on the surface of the intestinal epithelial cells of the chip and this target value, and ensure the normal physiological phenotype of the cells.

[0053] Based on the principle of minimization in multi-objective optimization algorithms, the aforementioned dual-physics optimization objective is transformed into a computable mathematical objective, meaning all sub-objectives are unified into a minimization form. Therefore, in this embodiment, the problem of maximizing the proportion of suitable oxygen concentration is transformed into a minimization problem by introducing a negative sign, thus enabling the algorithm to uniformly solve for the minimum value. Therefore, the proportion of the area of ​​the negative suitable oxygen concentration region and the absolute deviation between shear force and physiological target value are used as quantitative evaluation indicators to lay the foundation for subsequent optimization calculations. Based on this, the objective evaluation function system F(x) for the aforementioned dual-physics optimization objective is constructed:

[0054] Where y1 is the area ratio of the suitable oxygen concentration range, taking a negative value allows the multi-objective optimization algorithm to uniformly solve for the minimum value; y2 is the objective of minimizing the surface average shear force deviation (dyne / cm²). Target represents the average shear force on the cell surface, and Target is the optimized rigid reference target.

[0055] Step S1.2 involves performing univariate sensitivity analysis on the five core design variables (inlet velocity x1, upper channel aspect ratio x2, lower channel aspect ratio x3, distance from lower channel to chip bottom x4, and distance from upper channel to chip top x5). The control variable method is used to change each design variable one by one. With the other variables fixed, computational fluid dynamics simulations are used to obtain two optimization target values ​​corresponding to different variable levels (the proportion of the negative physiological oxygen concentration range and the absolute deviation of shear force from the physiological target value), thereby establishing the response relationship between each variable and the objective function.

[0056] Based on the simulation results, sensitivity curves of each design variable are plotted, and the influence of each variable on oxygen concentration distribution and shear force field is analyzed, thereby initially selecting the reasonable range of variation for each variable.

[0057] Univariate sensitivity analysis of the inlet flow rate (x1) revealed that as the inlet flow rate increased from 500 μL / h to 1300 μL / h, the mean shear force deviation on the intestinal cell surface (y2) showed a trend of first decreasing and then increasing. The shear force deviation reached its minimum value, closest to 0.02 dyne / cm² (2×10⁻⁶), when the flow rate was around 930 μL / h. -3The physiological target value for shear force (Pa) was determined; however, when the flow rate deviated from this range (below 700 μL / h or above 1100 μL / h), the shear force deviation increased significantly. This data quantitatively illustrates the direct impact of flow rate changes on the shear force environment.

[0058] Step S1.3: Define the optimization range of the core design variables. Based on the univariate sensitivity analysis results of the five-dimensional core design variables, and combined with the influence of each variable on the oxygen concentration field and shear force field of the intestinal organ-on-a-chip, as well as the actual engineering constraints, the optimization boundaries of each design variable are defined, namely, inlet flow rate (800~1000 uL / h), upper channel aspect ratio (0.25~0.75), lower channel aspect ratio (0.05~0.2), distance from lower channel to chip bottom (1.5~2.5 mm), and distance from upper channel to chip top (2.5~4.0 mm). This avoids invalid parameter space and limits a reasonable physical range for subsequent sampling and optimization.

[0059] Step S2: Based on the optimization range of the defined core design variables, an experimental design matrix is ​​generated using Latin hypercube sampling. After obtaining the response values ​​through numerical simulation, a sample database is constructed.

[0060] Step S2.1: Based on the defined design space of the five core parameters, to ensure that the sampled data has excellent representativeness in the above five-dimensional input space, this embodiment uses the Latin Hypercube Sampling (LHS) method to efficiently generate 80 sets of experimental design sample points, divided into 15 validation sets and 65 training sets, forming the experimental design matrix for training the surrogate model, as shown below. Figure 2 The figure shows the distribution of the generated sample points in the multidimensional parameter space.

[0061] Step S2.2, in the microfluidic chip optimization process based on the surrogate model, the quality of the sample points directly determines the prediction accuracy and generalization ability of the approximate model. Because three-dimensional computational fluid dynamics simulation takes a long time per calculation, for the above five design variables, if each variable has five levels, it requires... The computational cost of such simulations is unacceptable. Therefore, in this embodiment, in order to maximize the extraction of feature information from the design space within a limited computational budget, Latin hypercube sampling is selected as the core sampling strategy, taking into account the multi-physics coupling characteristics of the intestinal organ-on-a-chip.

[0062] Specifically: Set the design space as D Dimension (D=5 in this embodiment), the number of samples to be generated is N .

[0063] Next, intervals are divided, and each design variable is... The normalized range of values ​​[0, 1] is divided into equal parts. NThere are three non-overlapping subintervals, each with the same probability density, i.e., the interval length is 1 / N .

[0064] Each design variable was sampled independently. N A value is randomly selected from each sub-interval, ensuring that each interval in each dimension is sampled only once.

[0065] Finally, the extracted values ​​from each dimension are randomly arranged and combined to form... N indivual D Dimensional vector.

[0066] For the value of the i-th sample point in the j-th dimension The calculation formula is as follows:

[0067]

[0068] in, It is a random arrangement. It is an independent random variable that follows a uniform distribution in [0, 1].

[0069] Step S2.3: Subsequently, the 80 sets of discrete geometric structures and fluid parameter matrices are subjected to inverse normalization modeling. The reconstructed models are then imported into the CFD simulation platform in batches for solving. The five-dimensional core design variables are used as input features, and the oxygen suitability coverage and the average shear force deviation of the cell surface are used as output optimization targets.

[0070] Step S2.4 involves mapping the design parameters of the 80 sample points to their corresponding response values ​​to construct a complete "input-output" sample database. This database is then divided into a training set and a validation set in a 13:3 ratio. These sets are used for the subsequent construction of the surrogate model and accuracy verification, respectively, providing high-quality data support for the surrogate model training.

[0071] Step S3: Construct a radial basis function surrogate model based on multiple quadratic kernel functions based on the sample database, and use a non-dominated sorting genetic algorithm to perform global multi-objective optimization on the radial basis function surrogate model to generate a Pareto front solution set.

[0072] Step S3.1: Using the sample database constructed in step S2 as the training basis, a multiple quadratic radial basis function (MQ-RBF) surrogate model is built as an optimization evaluation engine to replace CFD simulation. The core mathematical expression of the model is:

[0073] in, For unknown test points; Let i be the i-th sample point; is the predicted value of the radial basis surrogate model for the unknown point; N is the total number of samples in the Latin hypercube sampling. Let be the Euclidean distance from the test point to the i-th sample point. These are the weighting coefficients to be solved; This is the kernel function for the radial basis surrogate model.

[0074] The model kernel function uses a quadratic kernel function, expressed as follows:

[0075] in, The kernel function is a quadratic kernel function; r is the Euclidean distance between the two points; The shape parameter is used. To further improve the prediction accuracy and generalization ability of the surrogate model, this embodiment uses the minimum sum of squared prediction errors on the validation set as the target fitness. Through iterative search, the shape parameter of the quadratic kernel function of the radial basis function surrogate model is determined. Global adaptive optimization was performed. The shape parameters of the multi-quadratic kernel function in this embodiment... The value was determined to be 0.2981.

[0076] Furthermore, to verify the effectiveness of the radial basis function surrogate model used in this embodiment, based on the coefficient of determination (… Using the radial basis function (RBF) model and root mean square error (RMSE) as core evaluation metrics, a systematic accuracy comparison was conducted between the RBF model and the polynomial response surface model (PR) and the Kriging model in this embodiment. Figure 3 As shown. For the complex multiphysics coupling in the intestinal organ-on-a-chip microenvironment, although polynomial models can capture the global evolution trend, errors are inevitable due to the lack of local residual compensation mechanisms in algebraic equations. This leads to limitations in predicting oxygen gradient y1 and shear force y2. The values ​​are 0.832 and 0.872, respectively. The Kriging model encounters a significant convergence bottleneck when approaching the limiting physical boundary, and its predictions... The RMSE is only at a low level of 0.710 and 0.716, and exhibits the highest root mean square error among the three, facing a significant risk of underfitting. In contrast, the radial basis function surrogate model configured with multiple quadratic basis functions demonstrates a superior approximation advantage, with its prediction coefficients for the dual-physics objective reaching 0.973 and 0.965, respectively, approaching the theoretical value of 1, and the corresponding RMSE is reduced to the lowest value, achieving a good balance between error minimization and high accuracy in global nonlinear mapping. This proves that compared with the polynomial response surface model and the Kriging model, the radial basis function surrogate model has stronger fitting ability and better small-sample stability when dealing with highly nonlinear, multi-peak response flow field problems, and is more suitable for modeling complex fluid-mass coupling problems in microfluidic chips.

[0077] Step S3.2: Using the constructed radial basis function surrogate model as the objective function surrogate model, initiate the non-dominated sorting genetic algorithm for global multi-objective optimization. The flowchart for the non-dominated sorting genetic algorithm to solve the radial basis function model is as follows: Figure 4 As shown.

[0078] (i) Set the core parameters of the algorithm, including randomly initializing the population within the five-dimensional design variable optimization range, setting the population size, maximum number of generations, and genetic operation parameters such as crossover probability and mutation probability, to lay the foundation for iterative optimization of the algorithm. Specifically, in this embodiment, to balance the global search and local convergence capabilities of the algorithm, the population size is set to 200 and the maximum number of generations is set to 500; a simulated binary crossover and polynomial mutation strategy is adopted, wherein the crossover probability is set to 0.9 and the crossover distribution index is set to 20; the mutation probability is set to 0.2 and the mutation distribution index is set to 20.

[0079] (ii) Input the five-dimensional design parameters of each individual in the initial population into the radial basis function surrogate model. The model quickly calculates the objective function value corresponding to each individual, namely, minimizing the negative value corresponding to the oxygen suitability coverage, and minimizing the mean shear force on the cell surface to 0.02 dyne / cm² (2×10⁻⁶). -3 Pa) Minimizes the deviation of physiological target values, uses two objective function values ​​as the basis for evaluating individual fitness, replaces time-consuming CFD simulation, and greatly improves optimization efficiency.

[0080] (iii) represents the population. Each individual in Define two parameters and .in Record the dominant individual The total number of individuals, and Records by individuals A collection of dominant individuals. Through iterative comparison, all... Individuals that are not subject to the control of any individual are selected to form the first level of non-dominated set. :

[0081] Remove individuals from P1 from the current population. Virtual elimination. For each individual in P1... The members in the group, their number of subjects Subtract 1; if after subtracting 1 If the individual is found to be a non-dominated set, then it is assigned to the second-level non-dominated set P2. This dimensionality-reducing recursive method is then used to calculate P3, P4, ..., until every individual in the population is assigned a fixed non-dominated rank. This improved algorithm only requires iterating through the entire population to calculate the required values. and This reduces the computational complexity of the original sorting process from O(rN) 3 The value was significantly reduced to O(rN). 2 This greatly improves the efficiency of optimization.

[0082] (iv) To address the issue of maintaining the uniformity and diversity of the population distribution within the solution set, NSGA-II abandons the fitness sharing parameter, which was difficult to set in the first-generation algorithm, and proposes the crowding distance method. Crowding distance measures the clustering density of other solutions around a specific individual. In the objective function space, an individual... The clustering distance can be intuitively understood as the sum of the length and width of the largest rectangle (or hypercube) centered on the individual and excluding any other individuals. For an optimization problem with r sub-objectives, the individuals in the population need to be quickly sorted according to the function values ​​of each sub-objective. The formula for calculating the clustering distance pdist(i) of individual pi is:

[0083] In the formula, and These represent the function values ​​of the two individuals adjacent to the individual at the k-th target. By sorting and summing, the computational complexity of calculating the cluster distance for each individual is only O(rNlog N).

[0084] (v) In the breeding and updating phase of the algorithm, NSGA-II introduces an elite preservation strategy and a partially ordered set mechanism. When a new population is generated, the parent and offspring populations are first merged, and then individuals with the lowest non-dominant rank (smallest Rank value, representing the more excellent the individual) are preferentially selected to enter the next generation.

[0085] When individuals at a certain level cannot be fully accommodated into the preset population size, the system will initiate a partial order comparison: among individuals at the same non-dominant level, those with larger cluster distances will be preferentially retained. Larger individuals (representing lower density of surrounding individuals) are selected. This dual selection mechanism ensures that excellent genetic material (approaching the Pareto front) is not lost, while also ensuring that the final intestinal organ-on-a-chip design can broadly and uniformly cover the entire Pareto front, providing a wealth of physical structure options for engineering decisions.

[0086] (vi) Repeat the above process of fitness evaluation - non-dominated sorting - crowding distance calculation - genetic operations - individual selection to iterate the algorithm; when the number of iterations reaches the preset maximum number of generations, or the population solution set tends to converge (no obvious optimization space), terminate the iteration and output the Pareto non-dominated optimal solution set curve in the two-dimensional target space, such as... Figure 5 As shown, each individual in this solution set represents the optimal design that cannot optimize one objective without sacrificing another, providing a complete solution space for subsequent chip structure optimization.

[0087] Step S4: Remodel the representative solution in the Pareto front and perform CFD numerical simulation. After obtaining the objective function value, compare it with the representative solution, and then select the design scheme with the best comprehensive performance as the final optimization result.

[0088] Step S4.1, for the Pareto optimal solution set output in step S3, to solve the engineering decision-making difficulties caused by a massive number of solutions.

[0089] Step S4.2: In this embodiment, the K-means clustering algorithm is used to classify and partition the Pareto front solution set in the two-dimensional target space, dividing the continuous Pareto front into 5 feature sub-regions ( Figure 6 As shown in Table 1, each region corresponds to the optimal oxygen coverage, the minimum shear force deviation, and the dual-objective trade-off features with different weights. One optimal solution with the most regional representativeness is extracted from each cluster, resulting in a total of 5 representative solutions, as shown in Table 1. These solutions cover the full range of Pareto front features and provide typical samples for subsequent accurate verification.

[0090] Table 1. Five representative solutions for cluster partitioning

[0091] Step S4.3 involves taking the five-dimensional design variable parameters (inlet velocity, aspect ratio of upper and lower channels, and top and bottom boundary wall thickness) corresponding to the five representative solutions extracted, and using computational fluid dynamics simulation one by one. Following the same multiphysics coupling solution parameter settings as in step S2, fluid dynamics and mass transfer solutions are performed to obtain the oxygen concentration distribution cloud map and cell surface shear force distribution curve of each representative solution under the physical field, providing objective physical data for performance verification.

[0092] The same customized post-processing algorithm as in step S2 was used to quantitatively analyze the CFD back-substitution simulation results. Pixel-level binarization was performed on the oxygen concentration field to extract the suitable oxygen coverage falling within the physiological range of 0.013–0.077 mol / m³, such as... Figure 7The image in the middle (e) represents the post-processing results of oxygen concentration distribution on the intestinal organ-on-a-chip under different parameter configurations (R1–R5). The left column (I) shows the numerical simulation cloud map after removing pixels that do not conform to the specified intervals; the right column (II) shows the image extracted using MATLAB image analysis algorithms, where white pixel areas represent the spatial coverage range of physiologically suitable oxygen concentration intervals. Additionally, 100 discrete points were uniformly selected along the arc length of the microchannel culture area, and the spatial evolution curve of the bottom wall shear stress was plotted, as shown below. Figure 8 As shown in Figures a-e, the blue dashed lines in the figures precisely indicate the magnitude of the average shear stress across the entire surface. Figure 8 Figure f in the figure shows the calculated average shear force deviation (y2). It should be noted that the unit of shear stress in Figures (a)-(e) is the international standard unit Pascal (Pa), while the deviation value in Figure (f) uses the biologically common unit dyne per square centimeter (dyne / cm²). The conversion relationship between the two is 1 Pa = 10 Dyne / cm².

[0093] The two simulation target values ​​obtained from the CFD simulation are compared one by one with the predicted values ​​of each representative solution by the radial basis function surrogate model. The relative error of each group of solutions is calculated, and the comparison results are as follows: Figure 9 As shown in Table 2, where Figure 9 The simulation values ​​of the proportion of suitable oxygen concentration range obtained from numerical simulation are compared with the predicted values ​​of the surrogate model. Table 2 shows that the model prediction deviation values ​​of the average shear force of five representative solutions are in high agreement with the CFD simulation deviation values, and the relative error is strictly controlled within the safe range of 2.02% to 7.24%.

[0094] Table 2 Comparison of simulated and predicted values ​​of average shear force deviation

[0095] Step S4.4: Using the simulation target value obtained from CFD back-substitution simulation as the core evaluation criterion, a comprehensive evaluation is conducted on 5 representative solutions. The comprehensive evaluation criterion for the representative solutions in this embodiment is: ensuring that the average shear force on the real cell surface falls within the physiologically safe range of 0.002~0.08 dyne / cm² (2×10⁻⁶). -4 - 8×10 -3 Under the premise of (Pa), the coverage area of ​​the physiological oxygen gradient microenvironment is expanded to the maximum extent.

[0096] Based on the above criteria and through multi-dimensional comparison, this embodiment preferentially selects scheme R1 as the design scheme for the intestinal organ-on-a-chip. Scheme R1 (inlet flow rate 999.8 μL / h, upper channel height 659.4 μm, lower channel height 155 μm, upper PDMS oxygen barrier wall thickness 3161.8 μm, lower PDMS oxygen barrier wall thickness 2195.3 μm) has an oxygen suitability concentration coverage of 71.58% and an average cell surface shear force of 0.0272 dyne / cm² (2.72 × 10⁻⁶). -3 Pa) was used as the final optimized design scheme for the intestinal organ-on-a-chip. Finally, the PDMS chip was fabricated strictly according to the geometric parameters of scheme R1 using soft lithography or 3D printing technology, and the inlet flow rate of the micro-injection pump was set to 999.8 μL / h to complete the physical fabrication and fluid control of the intestinal organ-on-a-chip.

[0097] For a conventional "sandwich" type (Transwell) intestinal organ-on-a-chip design, the inlet flow rate was set to 800 μL / h, the upper channel height to 500 μm, the lower channel height to 200 μm, the distance from the lower channel to the bottom of the chip to 2 mm, and the distance from the upper channel to the top of the chip to 3 mm. Calculations showed that this conventional design achieved only 42.3% oxygen suitability coverage, with an average cell surface shear stress of 0.032 dyne / cm² (0.0032 Pa). Compared to the unoptimized conventional design, the optimized design R1 reduced the average shear stress on the surface of intestinal epithelial cells within the chip by 17.65%, significantly improved the uniformity of shear stress distribution, and significantly increased the area of ​​the physiologically suitable oxygen concentration region by 30.78%. This effectively resolved the coupling conflict between fluid shear stress and oxygen gradient, significantly improving the consistency between the cell culture environment and the in vivo environment.

[0098] Example 2 This embodiment discloses an intestinal organ-on-a-chip optimization system based on a radial basis function surrogate model; An intestinal organ-on-a-chip optimization system based on a radial basis function surrogate model includes: The parameter setting module is configured to: determine the core design variables and dual-physics field optimization objectives of the intestinal organ chip, and define the optimization range of the core design variables; The sample generation module is configured to: generate an experimental design matrix based on the optimization range of the defined core design variables, and construct a sample database after obtaining the response values ​​through numerical simulation; The optimization solution module is configured to: construct a radial basis function surrogate model based on multiple quadratic kernel functions based on the sample database, and use a non-dominated sorting genetic algorithm to perform global multi-objective optimization on the radial basis function surrogate model to generate a Pareto front solution set; The verification output module is configured to: remodel the representative solution in the Pareto front and perform CFD numerical simulation, obtain the objective function value and compare it with the representative solution, and then select the design scheme with the best comprehensive performance as the final optimization result.

[0099] Example 3 The purpose of this embodiment is to provide a computer-readable storage medium.

[0100] A computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps in the intestinal organ-on-a-chip optimization method based on a radial basis function surrogate model as described in Example 1.

[0101] Example 4 The purpose of this embodiment is to provide an electronic device.

[0102] An electronic device includes a memory, a processor, and a program stored in the memory and executable on the processor. When the processor executes the program, it implements the steps in the intestinal organ-on-a-chip optimization method based on a radial basis function surrogate model as described in Embodiment 1.

[0103] Example 5 Embodiment 5 of the present invention provides a computer program product, including a computer program / instruction, which, when executed by a processor, implements the steps in the intestinal organ-on-a-chip optimization method based on a radial basis function surrogate model as described in Embodiment 1.

[0104] The steps and methods involved in the apparatuses of Embodiments 2, 3, 4, and 5 above correspond to those in Embodiment 1. For specific implementation details, please refer to the relevant description section of Embodiment 1. The term "computer-readable storage medium" should be understood as a single medium or multiple media including one or more instruction sets; it should also be understood as including any medium capable of storing, encoding, or carrying an instruction set for execution by a processor and enabling the processor to perform any of the methods in this invention.

[0105] Those skilled in the art will understand that the modules or steps of the present invention described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, thereby allowing them to be stored in a storage device for execution by a computer device, or they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. The present invention is not limited to any particular combination of hardware and software.

[0106] Furthermore, it should be noted that although the above embodiments are described in detail using the intestinal organ-on-a-chip as an example, the customized optimization framework of "multi-physics conflict modeling—mathematical mapping of bioindicators—global optimization of surrogate models" proposed in this invention is not limited to the intestinal model. This method is also applicable to other organ-on-a-chip systems with highly coupled requirements of fluid shear force and material transport (such as oxygen and drug molecule concentration gradients), such as liver-on-a-chip, kidney-on-a-chip, and blood-brain barrier-on-a-chip, and has broad engineering application value.

[0107] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of the present invention are still within the scope of protection of the present invention.

Claims

1. An intestinal organ-on-a-chip optimization method based on a radial basis function surrogate model, characterized in that, include: The core design variables and dual-physics optimization objectives of the intestinal organ-on-a-chip were determined, and the optimization range of the core design variables was defined. Based on the optimization range of the defined core design variables, Latin hypercube sampling is used to generate the experimental design matrix, and a sample database is constructed after obtaining the response values ​​through numerical simulation. A radial basis function surrogate model based on multiple quadratic kernel functions is constructed based on the sample database. A non-dominated sorting genetic algorithm is used to perform global multi-objective optimization on the radial basis function surrogate model to generate a Pareto front solution set. The representative solution in the Pareto front is remodeled and CFD numerical simulation is performed. The objective function value is obtained and compared with the representative solution. The design scheme with the best comprehensive performance is selected as the final optimization result.

2. The intestinal organ-on-a-chip optimization method based on the radial basis function surrogate model as described in claim 1, characterized in that, The core design variables of the intestinal organ chip include inlet flow rate, upper channel aspect ratio, lower channel aspect ratio, distance from lower channel to bottom of chip, and distance from upper channel to top of chip; The dual-physics optimization objectives include maximizing the coverage area of ​​the physiologically suitable oxygen concentration range and minimizing the absolute deviation between the average shear force on the cell surface and the physiological target value.

3. The intestinal organ-on-a-chip optimization method based on the radial basis function surrogate model as described in claim 1, characterized in that, Based on the defined optimization range of the core design variables, Latin hypercube sampling is used to generate the experimental design matrix. After obtaining the response values ​​through numerical simulation, a sample database is constructed, including: Based on defining the optimization range of the core design variables, the Latin hypercube sampling method is used to generate sample points in the five-dimensional design space composed of the core design variables. After inverse normalization and modeling of the sample points, they are imported in batches into the computational fluid dynamics simulation platform for multi-physics coupling solution. The suitable oxygen coverage and average surface shear force of each group of samples are extracted through post-processing. Using design variables as input and optimization objectives as output, a sample database containing sample points and their corresponding objective function values ​​is constructed.

4. The intestinal organ-on-a-chip optimization method based on the radial basis function surrogate model as described in claim 1, characterized in that, The mathematical expression for the radial basis function surrogate model is: in, For unknown test points; Let i be the i-th sample point; is the predicted value of the radial basis surrogate model for the unknown point; N is the total number of samples in the Latin hypercube sampling. Let be the Euclidean distance from the test point to the i-th sample point. These are the weighting coefficients to be solved; For the radial basis surrogate model, it is the kernel function; The quadratic kernel function of the radial basis function surrogate model is: in, The kernel function is a quadratic kernel function; r is the Euclidean distance between the two points; For shape parameters.

5. The intestinal organ-on-a-chip optimization method based on the radial basis function surrogate model as described in claim 1, characterized in that, The method employs a non-dominated sorting genetic algorithm to perform global multi-objective optimization on the radial basis function surrogate model, generating a Pareto front solution set, including: Using the radial basis function surrogate model as the objective function surrogate model, a non-dominated sorting genetic algorithm is employed for global multi-objective optimization. The non-dominated sorting genetic algorithm introduces Pareto dominance theory to divide individuals in the population into non-dominated levels and uses the crowding distance method to maintain the diversity of the solution set. Its execution process includes: Initialize the population by setting the population size, number of generations, crossover probability, and mutation probability parameters; The objective function value for each individual in the population is calculated using a radial basis function surrogate model. The objective function value includes the oxygen suitability concentration coverage and the deviation of the average surface shear force. Perform non-dominated ranking on the individuals in the population, assign a non-dominated level to each individual and calculate the crowding distance for each individual; An elite retention strategy is adopted, merging the parent and offspring populations, prioritizing individuals with lower non-dominant levels to enter the next generation, and prioritizing individuals with larger crowding distances when individuals of the same non-dominant level cannot be accommodated. The final Pareto front solution set is output by iterating until the preset number of generations or convergence condition is reached.

6. The intestinal organ-on-a-chip optimization method based on the radial basis function surrogate model as described in claim 1, characterized in that, The representative solution in the Pareto front is remodeled and subjected to CFD numerical simulation. The objective function value is then compared with the representative solution, and the design scheme with the best overall performance is selected as the final optimization result, including: The K-means unsupervised clustering algorithm is used to partition and classify the Pareto front solution set, dividing the Pareto front into several feature sub-regions, and extracting representative solutions from each cluster. The design variable parameters corresponding to the extracted representative solutions are substituted back into the computational fluid dynamics simulation platform to perform multiphysics coupling solution and obtain the simulated suitable oxygen concentration coverage and average surface shear force of each representative solution. The simulation target value obtained from computational fluid dynamics simulation is compared with the predicted value of the radial basis function surrogate model, the relative error is calculated, and the prediction accuracy of the surrogate model is evaluated. Based on the simulation target value, a comprehensive performance evaluation is performed on each representative solution. The optimal solution that maximizes the coverage of suitable oxygen concentration and minimizes the shear force deviation is selected as the final optimization result. The design variable parameters and dual-physics performance index corresponding to the final optimization result are output.

7. An intestinal organ-on-a-chip optimization system based on a radial basis function surrogate model, characterized in that, include: The parameter setting module is configured to: determine the core design variables and dual-physics field optimization objectives of the intestinal organ chip, and define the optimization range of the core design variables; The sample generation module is configured to: generate an experimental design matrix based on the optimization range of the defined core design variables, and construct a sample database after obtaining the response values ​​through numerical simulation; The optimization solution module is configured to: construct a radial basis function surrogate model based on multiple quadratic kernel functions based on the sample database and use it as the objective function surrogate model; use a non-dominated sorting genetic algorithm to perform global multi-objective optimization on the radial basis function surrogate model and generate a Pareto front solution set; The verification output module is configured to: remodel the representative solution in the Pareto front and perform CFD numerical simulation, obtain the objective function value and compare it with the representative solution, and select the design scheme with the best comprehensive performance as the final optimization result.

8. A computer-readable storage medium having a program stored thereon, characterized in that, When executed by the processor, the program implements the steps in the intestinal organ-on-a-chip optimization method based on the radial basis function surrogate model as described in any one of claims 1-6.

9. An electronic device comprising a memory, a processor, and a program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps in the intestinal organ-on-a-chip optimization method based on the radial basis function surrogate model as described in any one of claims 1-6.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps in the intestinal organ-on-a-chip optimization method based on the radial basis function surrogate model as described in any one of claims 1-6.

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