Predictive Modeling of Oxygen Gradient in Gut-on-a-Chip Using Machine Learning and Finite Element Simulation

Featured Application

The oxygen gradient prediction model established in this study can be applied to the design optimization of gut-on-a-chip. It provides a foundation for research on gut barrier function, immune responses, or host–microbiome interactions, thereby enhancing the effectiveness of gut-on-a-chip in drug screening, disease modeling, and personalized medicine. Furthermore, the proposed innovative oxygen distribution image prediction model architecture demonstrates broad applicability and can be utilized for image generation tasks in other microfluidic chips.

Abstract

The FDA plans to gradually replace animal testing with organoid and organ-on-a-chip technologies for drug safety assessment, driving surging demand for gut-on-a-chip in food and drug safety evaluation and highlighting the need for efficient, precise chip designs. Oxygen gradients are central to these devices because they shape epithelial metabolism, microbial co-culture, and overall gut homeostasis. We coupled machine learning with finite element analysis to build a parametric COMSOL Multiphysics model linking channel geometry, transport coefficients, and cellular oxygen uptake to the resulting oxygen field. For numerical prediction, three models—Random Forest (RF), XGBoost, and MLP—were employed, with XGBoost achieving the highest accuracy (RMSE = 1.68%). SHAP analysis revealed that medium flow rate (39.7%), external flux (26.9%), and cellular oxygen consumption rate (24.8%) contributed most importantly to the prediction. For oxygen distribution mapping, an innovative Boundary-Guided Generative Network (BG-Net) model was employed, yielding an average concentration error of 0.012 mol/m³ (~4.8%), PSNR of 33.71 dB, and SSIM of 0.9220, demonstrating excellent image quality. Ablation experiment verified the necessity of each architectural component of BG-Net. This pipeline offers quantitative, data-driven guidance for tuning oxygen gradients in gut-on-a-chip. Future work will explore extensions including real experimental data integration, real-time prediction, and multi-task scenarios.

1. Introduction

In recent years, Gut-on-a-Chip has emerged as an innovative bionic platform with promising applications. This platform can reconstruct the gut physical barrier, biochemical gradients, and cell–microbe interaction interfaces at the microscale. These capabilities have opened up broad prospects in drug development, the study of gut–microbiome mechanisms, and personalized therapies [1,2,3]. Organ-on-a-chip technology is a novel tool that more closely mimics human physiological processes than traditional animal testing or two-dimensional cell cultures. It is increasingly being used to find alternatives to animal testing and to create human tissue models in the laboratory. In 2025, the U.S. Food and Drug Administration (FDA) formally launched a new policy to progressively replace animal testing, encouraging the use of “New Approach Methodologies” (NAMs) such as organ-on-a-chip, organoids, and AI simulations for drug safety and efficacy testing [4]. This initiative marks a paradigm shift in global drug evaluation, advancing toward methods that are more human-relevant, reproducible, and ethically sound. Organ-on-a-chip platforms are evolving beyond basic research tools to become critical technologies for preclinical studies and regulatory decision-making. Consequently, the development of efficient and precise chip designs has become an urgent challenge.

For gut-on-a-chip development, microenvironmental factors are critical to replicating in vivo physiological functions—and among these, oxygen gradients stand out as a core variable for maintaining gut homeostasis and regulating microbe–host interactions [5,6]. Consequently, oxygen gradients have become a key indicator in gut-on-a-chip design and evaluation. In the physiological gut, the oxygen concentration gradually decreases from vascularized regions to the lumen, directly affecting epithelial cell metabolic activity and the stability of tight junction proteins, such as the claudin family and occluding, thereby regulating gut barrier integrity and microbial community structure [7,8,9]. The maintenance of gut barrier function depends on the proper expression and localization of tight junctions between epithelial cells. Abnormal oxygen gradients disrupt this equilibrium, leading to barrier dysfunction. This further highlights the importance of precisely replicating oxygen gradients in Gut-on-a-Chip models. Currently, researchers are working to establish stable oxygen gradients on chips through strategies such as microfluidic structure design, oxygen diffusion pathway regulation, and oxygen-barrier material implementation. For instance, Shin et al. [10] used the Finite Element Simulation (FES) to explore how flow rate and diffusion parameters affect oxygen distribution in microchannels. Liu et al. [11] further optimized channel geometry and restricted ambient oxygen infiltration to enhance gradient formation. Ingber’s team [12] introduced a polycarbonate oxygen barrier layer to establish microaerobic conditions, expanding the range of material-based control strategies. Other related studies are summarized in

Table 1. Strategies for Reproducing Physiological Oxygen Gradients in Gut Models.

Model Type	Methodology	References
Intestinal Organoid	The apical side of intestinal organoids is exposed to anaerobic conditions, while the basal side receives dissolved oxygen from the growth medium.	[13]
	By integrating ‘artificial microvessels’ and ‘intestinal organoids’ with microfluidic perfusion and COMSOL simulation, a hypoxic environment is created.	[14]
Gut-on-a-Chip & Related Models	Pure nitrogen gas within the chip isolates oxygen, and channel dimensions are optimized using COMSOL simulation.	[15]
	An oxygen-impermeable plug and collagen scaffold create a self-sustaining oxygen gradient via basal oxygen diffusion and cellular respiration.	[16]
	Using an anaerobic culture system to reduce oxygen concentration below 0.1%, simulating the hypoxic environment of the gut to achieve an oxygen gradient.	[17]
	Using a rigid, oxygen-impermeable flow chamber combined with an anaerobic unit (silicone tube–antioxidant solution)	[18]
	Establish a semi-scaffold system with 3D tubular geometry, achieving oxygen gradient by inverting the stent.	[6]

. However, these studies that rely solely on COMSOL simulations typically depend on trial-and-error methods and limited parameter combinations, failing to generate large-scale datasets and lacking systematic optimization frameworks. Furthermore, existing research often does not adequately consider the interaction effects among parameters involved, nor does it sufficiently explore the interactions between parameters under steady-state conditions in complex microfluidic environments.

FES has been widely applied to simulate fluid flow and mass transfer processes in organ-on-a-chip due to its advantages in multiphysics coupling modeling [19,20]. To improve modeling efficiency and parameter coverage, some studies have incorporated the COMSOL LiveLink for MATLAB interface to automate simulation workflows through scripting, enhancing modeling efficiency and parameter coverage. For example, Junghwan Kook [21] proposed a multiphysics topology optimization framework based on weak formulations, embedding governing equations into COMSOL through MATLAB scripts to automate structural design and sensitivity analysis. Ahmad Jafari [22] adopted the extended FES and level-set strategies for full-process automation in porous media problems. These methods highlight the potential for deep integration between FES and advanced programming environments, but systematic research on oxygen gradient modeling and optimization remains lacking.

Concurrently, the widespread application of machine learning (ML) in engineering prediction and design optimization has sparked interest in data-driven approaches for organ-on-chip research. By integrating mathematical modeling with machine learning, these approaches have demonstrated substantial advantages in multi-parameter optimization for complex biological systems. For instance, in precision nutrition, techniques such as random forests and data augmentation efficiently handle multivariate interaction problems, leading to the precise optimization of complex objectives [23]. This offers valuable insights for the systematic design of organ-on-a-chip systems, specifically in overcoming the limitations of traditional trial-and-error design through data-driven strategies. In the field of organ-on-a-chip technology, James et al. [24] combined principal component analysis with random forests to develop regression models linking vascularized chip morphology to functional performance. Marina et al. [25] employed convolutional neural networks to analyze chip imaging data for tumor progression prediction. They underscore ML’s significant potential for feature extraction and system modeling. However, no studies have yet combined automated finite element simulations with machine learning to systematically model the mapping between chip design parameters and oxygen distribution, thus failing to establish a systematic optimization framework for oxygen gradients in gut-on-a-chip.

To address these limitations, this paper proposes a method for generating COMSOL simulation data driven by MATLAB. This approach overcomes the computational efficiency limitations of traditional numerical modelling. It provides an efficient data generation scheme for machine learning algorithms to predict oxygen gradients under various parameter combinations. The Effective Region Percentage (ERP) was proposed as a quantitative metric for evaluating biomimetic performance. For the numerical prediction of oxygen gradient metrics, RF, XGBoost, and MLP algorithms were employed for numerical prediction of oxygen gradient metrics, while the BG-Net model is utilized for predicting oxygen distribution maps. Furthermore, the SHAP analysis method was applied to interpret the numerical prediction model for oxygen gradient metrics, revealing the relative importance of input features. To validate the effectiveness of the proposed model, the rationality of the innovative architecture design for the oxygen distribution image prediction model was evaluated using ablation experiments. The results demonstrate that this model performs exceptionally well in processing oxygen distribution images from gut-on-a-chip. In conclusion, this dual-prediction model not only accommodated diverse research needs but also supports the design and optimization of oxygen gradients in gut-on-a-chip, advancing their development as high-fidelity in vitro simulation platforms.

2. Methods

2.1. Gut-on-a-Chip Parameters

In the human gut, the epithelial layer forms dense villi to increase the absorption surface area. In addition, a rich microvascular network composed of endothelial cells is distributed in the underlying lamina propria (Figure 1). This compact and ordered structure provides important biomimetic reference for the design of the gut-on-a-chip in this study. A simplified two-dimensional, three-channel gut-on-a-chip was constructed using COMSOL Multiphysics 6.1. The upper and lower microchannels represent the endothelial channels (1 mm wide and 200 μm high), while the middle microchannel represents the epithelial channel (1 mm wide and 500 μm high). A porous membrane (50 μm thick with 7 μm pore diameter) separates the channels. The wavy lines in the epithelial channel represent the intestinal epithelial layer (150 μm thick). The total length of the chip channels is 10 mm [26,27,28].

In COMSOL Multiphysics 6.1, the FES was employed to simulate oxygen distribution within a three-channel gut-on-a-chip model. The simulation combined the Laminar Flow and Transport of Diluted Species modules, which were used to describe both convective and diffusive oxygen transport under varying geometric and physiological conditions, including epithelial channel height ($H_{Ep}$), endothelial channel height ($H_{En}$), external flux ($F_x$), medium flow rate ($V_r$), and cellular oxygen consumption rate ($Q_c$). The governing equations were based on the Navier–Stokes and Fick’s second law, assuming incompressible laminar flow and steady-state diffusion. The interface between the cellular microchannel and the PDMS layer was configured with a no-slip condition. The upper and lower channels flowed in oxygenated medium (0.2 mol/m³), while the middle channel flowed in hypoxic medium 0 mol/m³). Other boundary conditions and material properties were adapted from previous studies on hypoxic-oxygen interface chips. Necessary adjustments were made to accommodate the three-channel configuration [10]. All simulations were conducted at 37 °C and atmospheric pressure (1 atm), with a Standard mesh controlled by the physical field (number of elements:16202). The solver was set to default settings and controls error convergence through residuals. The parameters used in the simulations are listed in

Table 2. Parameters used in COMSOL computational simulation.

Parameter	Description	Quantity	References
Dmedium	The oxygen diffusion coefficient in the medium	$3.0 \times$ 10−9 m2/s	[29]
Dcell	The oxygen diffusion coefficient in the intestinal epithelium	$2.0 \times$ 10−9 m2/s	[29]
DPDMS	Oxygen diffusion coefficient in PDMS	$5.0 \times$ 10−9 m2/s	[30]
QO2 cell	Oxygen consumption rate of the intestinal epithelium	$8.64 \times$ 10−3 mol/m3·s	[31]

Note: Q_{O2 cell} refers to the oxygen consumption rate of Caco-2 cells.

.

This study conducted a systematic parameter scan analysis to identify the key variables influencing the oxygen gradient in the gut-on-a-chip and their corresponding value ranges (

Table 3. Critical Variables and Corresponding Value Ranges.

Variable	Minimum	Maximum	Interval
Epithelial channel height (mm)	0.4	1.0	0.05
Endothelial channel height (mm)	0.05	0.25	0.01
External Flux (mol/m3)	$1.22 \times$ 10−7	$6.1 \times$ 10−7	$1.22 \times$ 10−7
PDMS layer thickness (mm)	1	5	1
Cellular oxygen consumption rate (mol/m3·s)	$4.32 \times$ 10−3	$8.64 \times$ 10−3	$8.64 \times$ 10−4
Medium flow rate (μL/h)	30	200	20

), covering both physiologically relevant ranges and constraints imposed by microfabrication feasibility [10,11,26,32,33,34,35].

To validate the mesh independence of simulation results, this study designed four sets of meshes with progressively increasing density (coarse mesh, standard mesh, fine mesh, ultra-fine mesh). The geometric model, boundary conditions, and physical parameters remained consistent across all meshes, with only the mesh density varying. Oxygen concentration at key physiological locations within the intestinal chip (x = 5 mm, y = 0 mm, corresponding to the endothelial vascular side; x = 5 mm, y = 0.15 mm, corresponding to the villus tip) was selected as the monitoring metric. Relative errors between adjacent mesh groups were calculated to assess the impact of mesh refinement on results. Mesh parameters, element mass, and oxygen concentration test results are presented in

Table 4. Mesh Independence Validation Analysis.

Monitoring Location	Mesh Type	Number of Elements	Minimum Element Quality	Oxygen Concentration (mol/m3)	Relative Error (%)
x = 5 mm, y = 0 mm	Coarse Mesh	12,206	0.3822	0.070	0.70%
	Standard Mesh	16,202	0.3480	0.0707	-
	fine mesh	23,060	0.3440	0.0705	0.16%
	ultra-fine mesh	231,470	0.4471	0.0707	0.06%
x = 5 mm, y = 0.15 mm	Coarse Mesh	12,206	0.3822	0.0545	0.79%
	Standard Mesh	16,202	0.3480	0.0549	-
	fine mesh	23,060	0.3440	0.0547	0.44%
	ultra-fine mesh	231,470	0.4471	0.0547	0.53%

below.

Based on the above results, this study selected the “standard mesh (16,202 elements)” for subsequent simulation experiments. Firstly, its relative error compared to both the fine and ultra-fine meshes was ≤0.36%, which meets the accuracy requirements. Secondly, when compared to the ultra-fine mesh (230,000 elements), the standard mesh significantly reduces computational costs, balancing simulation accuracy and computational efficiency.

2.2. Dataset Generation

To handle high-throughput calculations and structural-parameter analysis, we built an automated bridge between MATLAB (R2018a) and COMSOL Multiphysics. This system consists of two main modules: a finite element solver module and an oxygen gradient interpolation and reconstruction module. These modules work together to loop through batches of geometry settings, extract concentration fields, evaluate them, and render images. The pipeline significantly reduces turnaround time and provides clean, consistent data to the downstream machine-learning models.

2.2.1. Finite Element Solver Module

This study utilizes the MATLAB R2018a LiveLink interface provided by COMSOL Multiphysics 6.1 to automate the solution workflow for the gut-on-a-chip finite element model. The main computational steps include:

• Automatically loading the prebuilt gut-on-a-chip multiphysics model file (*.mph);
• Dynamically injecting input design parameters into the boundary conditions and model settings;
• Performing steady-state calculations for coupled oxygen diffusion and transport using COMSOL’s built-in solvers;
• Solving multiphysics coupled equations with default nonlinear iterative method;
• Automatically extracting oxygen concentration distribution results within specified regions for subsequent interpolation and predictive models training.

2.2.2. Oxygen Gradient Interpolation and Reconstruction Module

To address the irregular spacing of unstructured-grid outputs, we devised a post-processor that relies on Natural Neighbor Interpolation. Borrowing the Voronoi-diagram machinery of computational geometry, the scheme recalculates on the fly how much each neighbor contributes to the interpolated value, thereby sidestepping the spurious oscillations and edge warping that plague bilinear or inverse-distance weighting on non-uniform meshes [36]. Its core steps include:

• Construct the original Voronoi diagram for the discrete finite element node set $\{Pi (xi,yi\left)\right\}$. When inserting the target interpolation point $Q (x,y)$, generate a new Voronoi cells and identify the natural neighbor set $\left\{P_k\right\}$ altered by the insertion operation (Figure 2).
• Dynamic weight calculation: Define the interpolation weight as the proportion of the original Voronoi cell area loss:

$$W_k\left(Q\right)={\displaystyle \frac{ A_k^{original}-A_k^{new}}{{\sum }_{j=1}^n(A_k^{original}-A_j^{new})}}$$

(1)

Here, $A_k^{original}$ and $A_k^{new}$ represent the Voronoi areas of the kth node before and after interpolation by $Q$, respectively. This weight quantifies the spatial dependence intensity of $Q$ on surrounding data points.

3.

Conformal Interpolation Calculation: The concentration value at the interpolation point $Q$ is determined by the weighted average of the concentrations at its natural neighbor points:

$$C\left(Q\right)={\sum }_{k=1}^n{w}_k\left(Q\right)·C\left(P_k\right)$$

(2)

This method strictly satisfies local extremum constraints (interpolation results cannot exceed the extremum range of neighboring points), thereby preventing non-physical oscillations.

4.

Generate a 500 × 500 uniform grid within the target analysis region (for example, the y = 0.00 mm and y = 0.15 mm cross-sections), and reconstruct the oxygen gradient field at submicron resolution by interpolating point by point. Specifically, refine the grid at critical biological interfaces such as the epithelial layer to ensure biologically accurate threshold determination.

2.2.3. Threshold Analysis

Among all organs, the partial pressure of oxygen in adjacent arterial and venous vessels ranges from 0.0945–0.135 mol/m³ (70–100 mmHg) and approximately 0.054 mol/m³ (40 mmHg), respectively. In the gut epithelium, the partial pressure of oxygen decreases sharply along the radial axis. It drops from approximately 0.081 mol/m³ (60 mmHg) in the submucosal arterioles to about 0.0135 mol/m³ (10 mmHg) within the colonic lumen [34,37,38,39] (Figure 3).

To incorporate this complex gradient into our simulations, we simplified the model to two dimensions and selected representative positions for analysis. Due to structural symmetry, only two key y-positions were analyzed. At y = 0, representing the endothelial (vascular) side, the oxygen limits were set to 0.054 mol/m³ and 0.135 mol/m³. At y = 0.15, corresponding to the villus tip of the intestinal epithelium, the limits were 0.0135 mol/m³ and 0.054 mol/m³. For each of these y-positions, all x-coordinates were traversed and the proportion of points meeting the oxygen concentration criteria was calculated. The resulting effective area percentages were visualized using a MATLAB script.

$$Area percentage={\displaystyle \frac{N_{range}}{N_{total}}}\times 100\mathrm{\%}$$

(3)

2.3. Oxygen Gradient Prediction Model Construction

2.3.1. Correlation Analysis

When two or more features are strongly linearly related, multicollinearity appears. In regression tasks, this inflates the standard errors of the coefficients, raises the chance of overfitting, and can push predictions far off the mark [40]. To avoid such redundancy, the features must first be screened for correlation, and the Spearman rank coefficient offers a straightforward gauge of their pairwise association.

The Spearman rank correlation coefficient is obtained by ranking the observations of the two variables [41]. Its value lies between −1 and 1: 1 means perfect positive correlation, −1 perfect negative correlation, and 0 absence of any relationship. Results of the computation are displayed in Figure 4. The horizontal and vertical axes correspond to the feature variables, the numbers are the Spearman coefficients, and the colour intensity reflects the strength of the correlation. As the correlations among the different features are low, multicollinearity is not a concern.

2.3.2. Model Selection

Two types of prediction models were developed to characterize oxygen distribution in the gut-on-a-chip: (1) numerical prediction models based on simulation parameters, and (2) image prediction models reconstructing spatial oxygen concentration images.

For the numerical prediction task, Random Forest (RF), XGBoost, and Multi-Layer Perceptron (MLP) were trained using datasets generated from the COMSOL–MATLAB co-simulation system. RF enhances robustness and noise resistance by aggregating multiple random decision trees. XGBoost achieved high-precision regression performance through its highly optimized gradient boosting algorithm with regularization. MLP captured nonlinear relationships via multi-layer transformations and backpropagation, offering robust fitting capabilities for complex data.

The oxygen concentration distribution within microfluidic systems exhibits unique physical characteristics. Most regions show gradual concentration changes, while sharp concentration gradients exist at fluid interfaces and diffusion boundaries. This property imposes stringent demands on a model’s ability to perceive boundaries. Under these conditions, traditional computer vision models, particularly generic image processing architectures, often fail to meet the requirements for parameter-to-field reconstruction tasks. Architectures like U-Net are fundamentally designed to process spatially correlated image data. When applied to the scalar parameter inputs in this study, they typically require parameter expansion into pseudo-images. This not only introduces significant computational redundancy but also makes it difficult for convolutional operations to efficiently capture global nonlinear couplings between discrete physical parameters, unlike fully connected layers. Standard CNN models like ResNet exhibit translation invariance, treating all image regions equally. However, microfluidic chips possess fixed, highly heterogeneous topologies (e.g., distinct physical properties across top, middle, and bottom layers). General-purpose models lack explicit awareness of such specific geometric topologies, making it difficult to apply differentiated feature processing rules across different physical regions.

To address these limitations, this paper proposes the Boundary-Guided Generation Network (BG-Net) model (Figure 5). This model replaces traditional image encoders with a “Dense-to-Mesh” feature extraction mechanism to adapt to scalar inputs. It also introduces a novel geometry-aware three-branch module and positional encoding to explicitly embed chip physical structure priors into the network. Combined with progressive upsampling and boundary enhancement modules, these components ensure that the model accurately captures complex spatial relationships and boundary gradients.

To rigorously validate the effectiveness of this physical perception architecture, this study selected conditional generative adversarial networks (cGANs) as the core comparative baseline. As a mainstream method in conditional image generation, cGANs offer significant advantages in generating high-frequency details through their adversarial loss, which aligns with the core requirements of this research.

2.3.3. Model Evaluation Methods

The oxygen gradient numerical prediction in this study is a regression task, employing root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) as model performance evaluation metrics. Oxygen distribution image prediction is also a regression task; although its output is in image format, it still predicts continuous numerical values for each pixel point. In addition to the aforementioned metrics, the oxygen distribution image prediction further incorporates the Mean Squared Error (MSE), Similarity Index (SSIM) and Peak Signal-to-Noise Ratio (PSNR) as supplementary performance evaluation criteria.

Root Mean Square Error (RMSE) represents the deviation between predicted values and actual values [42]. A smaller value indicates lower prediction error and better model performance.

$$RMSE=\sqrt{{\displaystyle \frac{1}{n}}{\sum }_{i=1}^n{\left(y_i-{\widehat{y}}_i\right)}^2}$$

(4)

Mean Absolute Error (MAE) is the average of absolute errors, reflecting the actual state of prediction error. A smaller value indicates higher prediction accuracy of the model.

$$MAE={\displaystyle \frac{1}{n}}{\sum }_{i=1}^n\left|{\widehat{y}}_i-y_i\right|$$

(5)

The coefficient of determination measures the model’s fit. A value closer to 1 indicates a higher fit and better performance [43].

$$R^2=1-{\displaystyle \frac{\sum _{i=1}^n{(y_i-{\widehat{y}}_i)}^2}{\sum _{i=1}^n{(y_i-\overline{y})}^2}}$$

(6)

where $n$ represents the number of samples, $y_i$ is the true value, ${\widehat{y}}_i$ is the predicted value, and $\overline{y}$ is the average of the true value.

SSIM is a traditional method for image quality assessment. Generally, the closer the SSIM value is to 1, the better the quality [44].

$$SSIM\left(x,y\right)={\displaystyle \frac{(2{\mu }_x{\mu }_y+C_1)(2{\sigma }_{xy}+C_2)}{({\mu }_x^2+{\mu }_y^2+C_1)({\sigma }_x^2+{\sigma }_y^2+C_2)}}$$

(7)

Here, ${\mu }_x$ and ${\mu }_y$ represent the local means of image components$x$and $y$, respectively; ${\sigma }_x^2$ and ${\sigma }_y^2$ denote the local variances; ${\sigma }_{xy}$ the local covariance; $C_1={\left(K_{1}L\right)}^2$, $C_2={\left(K_{2}L\right)}^2$ are two constants used to stabilize the calculation (preventing denominators from becoming zero), where L is the maximum range of pixel values.

PSNR calculates the signal-to-noise ratio by comparing the error between the original image and the compressed image. A higher PSNR indicates that the image quality is closer to the original image, with less loss [45].

The mean square error (MSE) is typically used as the baseline. The formula for calculating PSNR is as follows:

$$PSNR=10{log}_{10}\left({\displaystyle \frac{L^2}{MSE}}\right)$$

(8)

Here, $L$ represents the maximum value of the image pixels.

MSE stands for Mean Squared Error, representing the average squared difference between the original image and the distorted image.

$$MSE\left(x,y\right)={\displaystyle \frac{1}{N}}{\sum }_{i=1}^N{(x_i-y_i)}^2$$

(9)

Here, $x_i$ and $y_i$ are the pixel values at the $i-\mathrm{t}\mathrm{h}$ position of the original and distorted images, respectively, and $N$ is the total number of pixels in the image.

2.3.4. Data Preprocessing and Model Structure Design

During the data preprocessing stage, the RF and XGBoost models did not require feature scaling and thus utilized raw numerical values directly. In contrast, the MLP model required the data to undergo Z-score normalization. The preprocessing workflow for the BG-Net model was more complex. Simulation outputs underwent a custom conversion pipeline to generate normalized tensors: physical parameters were automatically extracted from filenames, the primary concentration field was cropped, and pixel colors were mapped to concentration values via nearest-neighbor mapping within the Lab color space. The detailed workflow is illustrated in Figure 6.

Table 5. Model Configurations and Hyperparameters.

Model	Optimizer	Learning Rate	Batch Size	Regularization Strategy
XGBoost	Gradient Boosting	0.2	--	Depth Limit [3, 5, 10, None], Sampling [2, 5, 10]
RF	--	--	--	Min Samples Split [2, 5, 10], Depth Limit [3, 5, 10, None], Min Samples Leaf [1, 2, 4], Ensemble Averaging [50, 100, 200]
MLP	Adam	0.0005	--	L2 Regularization, Dropout
cGAN	Adam	0.0003	32	Dropout (0.3), BatchNorm, EarlyStopping, Gradient Clipping, Data Augmentation
BG-Net	Adam	0.0003	32	Dropout (0.3), BatchNorm, EarlyStopping, Gradient Clipping, Data Augmentation

summarizes the core structural configurations for each model. For numerical predictions, tree-based models (Random Forest and XGBoost) were trained directly on raw physical parameters, with hyperparameters optimized via cross-validation and grid search. The Multilayer Perceptron (MLP) utilized Z-score normalization to ensure training stability. This model employed the Adam optimizer with a learning rate of 0.001, and a Dropout layer (rate = 0.2) was incorporated into the MLP architecture.

All physical parameters input to the BG-Net model were Z-score-normalized. Oxygen flux underwent logarithmic transformation (log₁₀). Concentration field images were uniformly resampled to 256 × 256 pixels and normalized to the range [0, 1]. The model is trained using a boundary enhancement loss function that combines L1 loss (weight 0.2), mean squared error (MSE) (weight 0.1), gradient loss (weight 0.2), boundary loss (weight 0.4), and structural similarity index SSIM (weight 0.1). This combined loss function was designed to enhance perceptual quality and prediction accuracy at boundaries, with a 5x weighting applied specifically to high-concentration regions at the input of the vertical channels. The model employed the Adam optimizer with an initial learning rate of 0.0003 and a batch size of 32. A learning rate scheduler (reducing the learning rate to 60% of its original value if the validation loss does not improve over 10 consecutive epochs, with a minimum learning rate of 10⁻⁷) and an early stopping mechanism (terminating training and restoring optimal weights if the validation loss improvement is less than 10⁻⁵ over 20 consecutive epochs) were introduced to effectively prevent overfitting. Gradient clipping (clipnorm = 1.0) was applied during training to prevent gradient explosion. The model was dynamically optimized via tf.data.AUTOTUNE to enhance GPU utilization. Data preprocessing was performed on the CPU. The experimental environment configured pytesseract to assist in extracting parameter information contained within certain image data (OCR parsing). During training, an NVIDIA RTX 2080 Ti GPU was used, with each training session exceeding 4 h.

cGAN and BG-Net maintain consistent hyperparameter settings across optimizers, learning rate scheduling, batch size, and gradient clipping, ensuring fairness in comparative experiments. Their primary differences lie in distinct loss functions and network architectures. cGAN employs a conditional generative adversarial network architecture, featuring a fully connected deconvolutional decoder for the generator and a multi-layer convolutional neural network (CNN) for the discriminator. To accommodate the Tanh activation function in the generator, cGAN normalizes images to the range [−1, 1], whereas BG-Net normalizes to [0, 1]. Furthermore, cGAN employs a hybrid loss function during training, combining adversarial loss (Binary Cross Entropy) with L1 loss, with L1 loss assigned a higher weight (100.0). This differs from BG-Net’s boundary enhancement loss function design.

The numerical model dataset, containing over 4500 samples, was split into training and test sets in an 8:2 ratio. The image model dataset was constructed using 4180 PNG images depicting oxygen concentration distributions and expanded to approximately 5225 samples through data augmentation techniques. Following a 7:1.5:1.5 ratio, this image dataset is further partitioned into: a training set (≈3657 samples), a validation set (≈784 samples), and a test set (≈784 samples). Gaussian noise was introduced to a portion of the training data to enhance the model’s generalization capability and robustness, with the standard deviation set to 0.01.

2.3.5. Ablation Experiment Design

To validate the effectiveness of each component within the BG-Net model, this study designed systematic ablation experiments. By progressively removing or replacing key components, the experiments assessed the contribution of each component to the overall performance.

The experiment designed six ablation variants to validate the contributions of key model components. These include: removing multi-scale branches (selecting a single fully connected layer), removing boundary enhancement loss (using only L1 loss, MSE, gradient loss, and SSIM), removing positional encoding, reducing Dropout ratio (from 0.3 to 0.1), simplifying network depth (removing the Dense2048 layer in the feature extraction module), and simplifying the loss function (using only MSE). The baseline model is the BG-Net architecture, with the same dataset partitioning ratio as the baseline model: 7.0:1.5:1.5 (training set: test set: validation set). Evaluation metrics included: MAE, MSE, SSIM, PSNR.

All variants employ identical training configurations to the baseline model to ensure fair comparison. The Adam optimizer is used with an initial learning rate of 0.0003, β₁ = 0.9, β₂ = 0.999, and a gradient clipping threshold of 1.0. The batch size is set to 32, with a maximum of 100 epochs, employing early stopping and learning rate decay strategies (Patience = 10, Factor = 0.6).

3. Results and Discussion

3.1. Validation of the Numerical Simulation Model

The gut-on-a-chip simulation model developed in this study demonstrates the oxygen concentration trends at three representative locations—the inlet, middle, and outlet—which closely align with the computational simulation results reported by Shin et al. [10] (Figure 7a). Specifically, our model brings these three locations closer to physiological gut oxygen concentrations. Shin et al. simplified the porous membrane to a thin film, which allowed the oxygenated medium in the endothelial channel to readily contact the hypoxic medium in the epithelial channel. Consequently, low oxygen concentrations (0.0083–0.0088 mol/m³) were observed at the inlet (0 mm and 0.15 mm positions) (gray points in Figure 7a). In contrast, our study accounts for the actual diffusion resistance of the porous membrane. The hypoxic medium in the epithelial channel cannot rapidly obtain oxygen diffusion from the endothelial side in the inlet segment. Therefore, the oxygen concentration at the inlet is 0 mol/m³, which is consistent with the inlet concentration reported by Liu et al. [11], who also simulated an gut-on-a-chip considering porous membrane structures (red points in Figure 7a).

The central region constitutes the core functional zone of the gut villi. The results of this study exhibit high quantitative consistency with experimental data from Shin et al.: Vascular side (0 mm): Experimental value 0.072191 mol/m³, reference value 0.072400 mol/m³, relative error only 0.29%; Villus tip (0.15 mm position): Experimental value 0.057138 mol/m³, reference value 0.059900 mol/m³, relative error 4.61%. These results demonstrate that the simulation model developed in this study predicts oxygen concentrations with high precision, consistent with the physical laws of oxygen gradient transport.

Due to the porous membrane restricting oxygen transfer from the endothelium to the epithelial channel, coupled with continuous oxygen consumption by cells within the flow channel, the outlet concentration is lower (closer to the hypoxic environment at the gut end). In contrast, Shin’s simplified membrane model leads to faster oxygen diffusion, resulting in a relatively higher outlet oxygen concentration. The relative error in the outlet region is significant (22.03–30.42%). Overall, the simulation dataset generated in this study exhibits high reliability, providing effective numerical support for modeling oxygen distribution in gut-on-a-chip.

PO₂ profiles along these sites showed a steady decrease toward the villus tips, where the gradient flattened to its lowest value (Figure 7b), mirroring earlier experimental findings [46].

3.2. Comparison of Simulation Results

Figure 8a displays the unstructured finite-element oxygen concentration field obtained from COMSOL, whereas Figure 8b shows the corresponding two-dimensional map reconstructed in MATLAB with natural-neighbor interpolation. The original data, constrained by intricate geometry and boundary conditions, contain pronounced irregularities. Interpolation projects the scattered values onto a uniform grid, yielding a noticeably smoother and continuous concentration field.

Comparing the color scales, we find that the interpolated gradients are consistent with the original simulation results, particularly in key regions like the upper and lower channel boundaries. The 0.05–0.15 mol m⁻³ concentration band remains intact. By smoothing the field, the interpolation not only sharpens visualization but also supplies a regular grid, which can be ingested by later machine-learning models, thus closing the loop between simulation and data-driven analysis.

To check whether the predicted oxygen field is physiologically plausible, we examined two reference lines: y = 0 and y = 0.15. In Figure 8c the orange-red trace shows the profile at y = 0, close to the vascular bed; the pink band marks the accepted tissue interval of 0.054–0.135 mol m⁻³ (40–100 mmHg). The blue trace, taken at y = 0.15 near the villus tip, is paired with a blue band indicating 0.0135–0.054 mol m⁻³ (10–40 mmHg). White patches, where the computed concentration lies outside these ranges, probably indicate model limitations rather than genuine physiology.

MATLAB scripts were used to calculate the percentage of values within the physiological range. The results showed that 67.3% of concentrations at y = 0 and 63.9% at y = 0.15 fall within the expected range. Overall, the model successfully reproduced the expected gradient from high to low oxygen levels.

3.3. Performance Evaluation of the Numerical Prediction Models

Figure 9 presents the root mean square error (RMSE), mean absolute error (MAE), and coefficient of determination (R²) for each model on the test set, while Figure 10a shows the linear regression fitting results.

The results indicate that XGBoost outperforms both RF and MLP across all metrics, achieving an R² of 0.9945. This superior performance can be attributed to XGBoost’s adaptability to structured data, strong nonlinear modeling capabilities, and the use of regularization and subsampling techniques, which enhance both model stability and generalization. While Random Forest demonstrates good robustness, its ability to capture complex interactions is limited. The MLP model shows weaker fitting performance and lower training stability.

Figure 10b displays the residual distribution. XGBoost residuals are tightly clustered around zero and exhibit an approximately normal distribution. The standard deviation of residuals in the middle region (y_mid) is 1.3942, lower than the standard deviation of 1.9148 in the bottom region (y_bot), suggesting better prediction accuracy in the central area. In contrast, the RF model shows a larger residual standard deviation at y_bot (3.5165), indicating lower stability. MLP exhibits the greatest residual fluctuations, particularly at y_bot, where the standard deviation reaches 4.1006, reflecting weak fitting stability.

Based on the prediction results, the XGBoost model achieved the highest predictive accuracy. To clarify how each variable shapes the predicted oxygen gradient, we applied SHAP analysis to the same model. Figure 11 ranks the input variables by their influence on the XGBoost output. Medium flow rate dominates, contributing 39.7% of the total SHAP importance, followed by external flux (26.9%), cellular oxygen consumption rate (24.8%), endothelial channel height (5.5%), and epithelial channel height (3.1%). Existing experimental studies have shown that by reducing the oxygen permeability of PDMS (external flux) and controlling flow rate, cells can achieve a steady-state oxygen gradient through natural oxygen consumption within channels. This finding aligns with the results of SHAP analysis in this study [11,34]. Furthermore, the research by Jomezadeh Kheibary et al. [47] also indicates that oxygen transfer is influenced not only by diffusion but also by fluid flow rate and channel geometry. In microfluidic systems, increasing flow velocity enhances the convective effects, which helps oxygen spread and distribute more rapidly. This explains why flow rate emerged as the most significant feature in predicting oxygen gradients within this model.

To eliminate the influence of feature scaling or variable range differences on SHAP results, Figure 12 further validates the robustness of the SHAP analysis. Figure 12a,b respectively display the SHAP relative importance proportions for raw data and standardized data. Identical results confirm that SHAP feature importance rankings remain unaffected by feature dimensions and numerical ranges. Figure 12c presents the results of the permutational feature importance analysis. The core influential features remain $V_r, { F}_x$, and $Q_c$, and their importance ranking fully consistent with the SHAP analysis results. This high consistency between different interpretation methods further validates the reliability of the model’s key feature identification.

Figure 13 visualizes, for the XGBoost model, how every feature shapes the quantitative oxygen-gradient metric on the test set. Each dot is one test instance, and its horizontal position gives the SHAP value, i.e., the feature’s signed contribution to the predicted outcome. Colour encodes the feature’s magnitude: red for high, blue for low. Positive SHAP scores push the prediction upward, negative scores pull it downward. The plot reveals that a higher medium flow rate lifts the prediction and spans a wide value range; endothelial channel height also raises the output, though less broadly; cellular oxygen consumption can act in either direction; while external flux and epithelial channel height consistently reduce the predicted value.

Through SHAP interaction analysis, we further explored the synergistic and antagonistic relationships among features (Figure 14). Figure 14a displays the SHAP interaction matrix, revealing that the strongest interactions occur between $V_r$and itself (15.09), $F_x$and $Q_c$(7.62), and $Q_c$and itself (6.27). These results indicate significant nonlinear synergistic effects among these core features. Figure 14b details the$V_r$-$F_x$ interaction: at low $V_r$, increasing $F_x$ substantially enhances the oxygen gradient; at high $V_r$, $F_x$’s effect reverses, attenuating the oxygen gradient. This finding complements the physical mechanism of “cooperative regulation of oxygen gradient by flow velocity and flux,” further enhancing the model’s interpretability.

3.4. Performance Evaluation of the Image Prediction Models

To evaluate the performance of the constructed image prediction model in the oxygen concentration distribution prediction task, both quantitative and qualitative analyses were conducted. Figure 15a presents a comparison between the original oxygen concentration distribution and the BG-Net model-generated predicted image. The two images exhibited a high degree of consistency in the overall gradient shape, distribution region, and boundary transition features. This consistency indicates that the model effectively captures the continuous variation in oxygen concentration distribution. However, slight differences were observed in the boundary transition details: the original image shows clearer transitions, while the predicted image exhibits somewhat blurred and less accurate boundary transitions. This suggested that the model may have limitations in reproducing complex boundary transition details, failing to fully capture the intricate variations present in the original image.

Figure 15b illustrates the changes in the loss function and mean absolute error (MAE) during training and validation of the BG-Net model. In the early stages, both training and validation losses decreased rapidly. Training loss dropped sharply from approximately 0.19 to below 0.05, while validation loss decreased from around 0.13 to near 0.03. At the same time, training MAE and validation MAE showed higher initial values (approximately 0.13 and 0.12, respectively), but also declined rapidly. During the early training phase (first 10 epochs), the validation MAE exhibited significant fluctuations, peaking at around 0.04. This was potentially related to the model’s adaptation to the features in the validation set during the learning process. As training progressed (after approximately 20 epochs), all metrics gradually stabilized. Lastly, both training loss and validation loss converged to around 0.02, while training MAE and validation MAE stabilized within the 0.01–0.015 range, showing very close values. This indicated that the oxygen concentration image prediction model demonstrated robust predictive performance on both the training and validation sets. The high consistency between training and validation losses suggested the model effectively learned data features while maintaining strong generalization capabilities, without exhibiting significant overfitting.

The model was further assessed with SSIM and PSNR (Figure 16). Mean SSIM reached 0.9220 and mean PSNR 33.71 dB, confirming that structural fidelity and visual quality were well preserved. The strong positive correlation between the two metrics reinforces this consistency. Box plots showed tight distributions with few outliers, underscoring stable performance across varied image-prediction tasks.

To further validate BG-Net’s superiority in oxygen distribution prediction, a comparative analysis was conducted against the cGAN baseline model using both quantitative metrics and qualitative visualization. Figure 17 displays oxygen distribution prediction images generated by the BG-Net and cGAN models. Both models show similar overall gradient patterns and concentration distributions, capturing the continuous variations in oxygen distribution. However, subtle differences appear at boundaries: the BG-Net model’s predictions show clearer boundary transitions, whereas the cGAN model shows blurred transitions in certain regions. Overall, the BG-Net model achieves superior image quality.

Table 6. Performance Comparison between BG-Net and cGAN.

Evaluation Metrics	cGAN	BG-Net	Performance Comparison
MSE	0.0017	0.0005	−70.29%
MAE	0.0161	0.0107	−33.39%
SSIM	0.89	0.92	+4.11%
PSNR(dB)	28.36	33.70	+18.83

compares the performance of the two models on the test set. Compared to cGAN, BG-Net reduces MAE by 70.29% and MSE by 33.39%, while improving SSIM by 4.11% and PSNR by 18.83%. These error reductions suggest that BG-Net’s boundary-enhancement and multi-scale feature-fusion modules effectively reduce local prediction errors. The higher SSIM and PSNR further indicate better structural fidelity and visual consistency with the simulated data, alleviating cGAN’s tendency to produce over-smoothed images.

3.5. Ablation Experiment Results Analysis

Figure 18 compares the performance of each model variant against the baseline. Dropping the boundary-enhancement module caused the sharpest drop: MSE rose 46.1% and MAE 16.9%, underscoring that boundary-aware design is indispensable. SSIM, in contrast, barely moved (+0.55%). The metric captures global structural similarity, so the concentration field still shows the correct large-scale pattern even when fine boundary detail is missing. MSE, penalizing squared error, is far more reactive to local mismatches at the boundary. Thus, it provides a clearer readout of how much the enhancement module contributes in microfluidic tasks.

When the multi-scale feature fusion module was dropped, MAE rose by 9.1%, confirming that merging cues across spatial scales is essential for recovering concentration patterns. Positional encoding had a smaller effect: removing it lifted MAE by only 3.4%, implying that the convolutional layers already absorb most of the required spatial relationships and that explicit position signals add little in this task.

Among the dropout regularization tests, lowering the dropout rate from 0.3 to 0.1 was the only change that cut MAE by 6.6% and simultaneously lifted SSIM by 0.65%. This suggests that the baseline model had begun to overfit. When the network was trained with plain MSE loss, the MSE itself dropped 12.0%, yet MAE rose 15.6% and SSIM fell 1.60%; the training loss also collapsed to 0.00054, a clear sign of overfitting. These results confirm that a single pixel-wise loss cannot jointly preserve point accuracy, structural detail, and sharp boundaries in concentration-field reconstruction. Full metrics for every variant are given in

Table 7. Ablation Experiment Results.

Model	Test MAE	Test MSE	Test SSIM	Test PSNR
Baseline (BG-Net)	0.01073	0.000505	0.9223	33.70 (dB)
No Boundary Enhancement	0.01254	0.000737	0.9273	32.31 (dB)
No Multi-scale Branches	0.01170	0.000530	0.9181	33.47 (dB)
No Positional Encoding	0.01109	0.000472	0.9205	34.06 (dB)
Less Dropout (0.1)	0.01002	0.000532	0.9283	33.20 (dB)
Shallow Network	0.01136	0.000625	0.9203	32.62 (dB)
Simple MSE Loss	0.01240	0.000444	0.9075	34.40 (dB)

.

4. Discussion

This study introduces a MATLAB-driven COMSOL simulation data generation method. It effectively overcomes the computational efficiency limitations of traditional numerical simulations, providing an efficient data generation solution for machine learning algorithms to predict oxygen gradients under different parameter combinations.

For quantitative oxygen gradient prediction, three models—RF, XGBoost, and MLP—were employed. Among these models, XGBoost demonstrated the optimal predictive accuracy, achieving an RMSE of 1.68%. SHAP analysis revealed that medium flow rate (39.7%), external flux (26.9%), and cellular oxygen consumption rate (24.8%) significantly influenced prediction outcomes. Additionally, the analysis highlighted how these factors interact synergistically, offering a more profound understanding for the optimization and regulation of the oxygen gradient.

For spatial mapping, BG-Net was adopted to predict full oxygen images; the reconstructions matched experimental quality. Ablation experiments validated the rationality of the innovative architecture design for the oxygen distribution image prediction model. Results indicated that modules such as boundary enhancement and multi-scale feature fusion within the BG-Net model positively contributed to oxygen distribution image generation for gut-on-a-chip. The contrast with the cGAN baseline model further validates the domain-specific innovative value of BG-Net in predicting oxygen distribution in gut-a-chip. Future efforts may explore transferring this model to image generation tasks for other microfluidic chips.

The numerical prediction model provides the pass rate of oxygen concentration in chip channels corresponding to parameter combinations, while the image prediction model delivers the specific oxygen distribution patterns in chip channels under given parameter sets. This dual-prediction model not only meets the diverse needs of different researchers but also provides robust support for oxygen gradient design and optimization in gut-on-a-chip. This advancement promotes greater biological realism in organ-on-a-chip, enhancing their effectiveness in drug screening, disease research, and personalized medicine. Actually, this dual-prediction framework can accelerate the rational design process of gut-on-a-chip for preclinical drug screening and personalized gut microbiome therapy. Future research will focus on integrating in vitro experimental data to enable real-time prediction and extending the BG-Net architecture to the study of other microfluidic organ chips.