Biliary tract flow multi-parameter intelligent prediction method based on CFD and PIV data fusion

Abstract

The invention provides a CFD and PIV data fusion-based biliary tract flow multi-parameter intelligent prediction method. The method comprises the following steps of constructing a multi-modal data set according to each biliary tract structure model and PIV + CFD joint supervision data corresponding to the biliary tract structure model; coding each biliary tract structure model; training a deep learning model by using each encoded biliary tract structure model and the plurality of key fluid dynamic parameters so as to obtain a trained deep learning model; obtaining a to-be-predicted biliary tract structure model, and obtaining a plurality of key fluid dynamic parameters of internal flow behaviors of the to-be-predicted biliary tract structure model through the trained deep learning model; the method has the beneficial effects that a structure-flow mapping model is constructed, that is, nonlinear mapping from the biliary tract form to the fluid parameters is learned based on a graph neural network or convolutional neural network architecture, so that a rapid online prediction mechanism is realized, and clinical personalized pathological analysis or clinical medical science research and evaluation requirements are facilitated.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of biomedical engineering, computational fluid dynamics and artificial intelligence, and in particular to a multi-parameter intelligent prediction method for biliary flow based on the fusion of CFD and PIV data. Background Technology

[0002] The biliary system has a complex structure, and different pathological conditions (such as congenital dilatation, stone obstruction, and stenosis) significantly affect bile flow characteristics. Traditional methods mainly rely on computational fluid dynamics (CFD) for numerical simulation or particle image velocimetry (PIV) to obtain experimental data. Both of these methods have limitations such as high computational cost, long data acquisition cycle, and difficulty in rapid evaluation.

[0003] With the development of artificial intelligence, using machine learning methods to extract patterns from existing experimental and simulation data and predict flow behavior under new structures has become a trend. However, a mature solution has yet to be developed in the field of biliary tract diseases. In particular, there are no systematic solutions for how to integrate and utilize multi-source data from CFD and PIV, how to encode complex biliary tract structures into a form recognizable by machine learning models, and how to output prediction results that combine visualization and numerical analysis. Therefore, there is an urgent need for a multi-parameter intelligent prediction method for biliary tract flow based on the fusion of CFD and PIV data to address the following problems in existing technologies:

[0004] 1. Traditional simulation methods are time-consuming and difficult to adapt to individualized structures: The diagnosis and mechanism research of biliary tract diseases rely on high-precision assessment of bile flow, while existing CFD simulation methods require a lot of computing resources and have a long cycle, making it difficult to quickly deal with diverse pathological structures, which limits their promotion in clinical real-time decision-making and preoperative assessment.

[0005] 2. Lack of structural representation methods that can be used for AI modeling: The morphology of the bile duct has significant individual differences, and existing research has not yet formed a unified structural encoding method suitable for deep learning modeling, especially in how to efficiently transform anatomical features (such as branches, curvature, diameter, etc.) into learnable inputs, there is a technical gap.

[0006] 3. A high-quality experimental-simulation-learning fusion framework has not yet been established: In current research, PIV experimental data and CFD simulation data are mostly used independently, lacking a systematic fusion mechanism, failing to leverage their complementary advantages, and failing to develop a deep learning method for simultaneous prediction of multiple fluid physical quantities (velocity, pressure, shear force).

[0007] 4. Clinical application currently only allows for assessment of the condition through three-dimensional models: At present, clinical assessment of biliary tract lesions mainly relies on the doctor's personal experience and observation of three-dimensional structural models, lacking quantitative analysis methods, and cannot accurately judge the hydrodynamic risks (such as local high pressure, abnormal shear force, etc.) of the lesion area; this method can easily lead to increased uncertainty in the treatment of key pathological areas during actual surgery, affecting the accuracy of preoperative decision-making and the individualization of surgical plans. Summary of the Invention

[0008] In view of the shortcomings of the prior art described above, the purpose of this invention is to provide a multi-parameter intelligent prediction method for biliary flow based on the fusion of CFD and PIV data. This method addresses the problems of traditional simulation methods in the prior art, such as long cycle time, difficulty in adapting to individualized structures, lack of structural expression methods that can be used for AI modeling, lack of a high-quality experimental-simulation-learning fusion framework, and the fact that current clinical applications can only assess the condition through three-dimensional models.

[0009] To achieve the above and other related objectives, the present invention provides the following technical solution:

[0010] A multi-parameter intelligent prediction method for biliary flow based on CFD and PIV data fusion includes the following steps: acquiring PIV+CFD joint supervision data corresponding to each biliary structure model, and constructing a multimodal dataset based on each biliary structure model and its corresponding PIV+CFD joint supervision data, wherein the PIV+CFD joint supervision data includes multiple key hydrodynamic parameters concerning the flow behavior inside the biliary tract; encoding each biliary structure model, wherein the encoding method includes graph structure encoding and voxel grid encoding of each biliary structure model;

[0011] The deep learning model is trained using encoded biliary structure models and several key hydrodynamic parameters concerning the internal flow behavior of the biliary tract. The trained deep learning model is obtained based on the training results. The biliary structure model to be predicted is obtained and input into the trained deep learning model. The trained deep learning model performs structural analysis and intelligent prediction on the biliary structure model to be predicted, thereby obtaining several key hydrodynamic parameters of the internal flow behavior of the biliary structure model to be predicted.

[0012] In one embodiment of the present invention, before acquiring the PIV+CFD joint supervision data corresponding to each biliary structure model and constructing a multimodal dataset based on each biliary structure model and its corresponding PIV+CFD joint supervision data, the method includes: acquiring the patient's CT or MRI images and performing three-dimensional reconstruction on the patient's CT or MRI images, obtaining the patient's biliary structure model based on the three-dimensional reconstruction results; performing a PIV experiment based on the patient's biliary structure model, and obtaining the planar velocity vector distribution of the fluid inside the biliary tract based on the PIV experiment results.

[0013] Based on the patient's biliary structure model, CFD simulation was performed. The three-dimensional flow velocity field, pressure distribution, and biliary wall shear force of the fluid inside the biliary tract were obtained from the CFD simulation results. The CFD simulation results were projected onto the PIV observation plane through spatial interpolation and coordinate mapping. The PIV experimental data and CFD simulation results were registered and complemented based on the projection results, thus obtaining PIV+CFD joint supervision data.

[0014] In one embodiment of the present invention, the graph structure encoding of each biliary tract structure model includes: extracting the centerline of the biliary tract structure model and constructing a graph structure of the biliary tract structure model based on the centerline; calibrating the centerline of the biliary tract structure model with the PIV observation plane using rigid registration or ICP algorithm, and ensuring that the graph structure and CFD / PIV data are located in the same reference coordinate system based on the calibration result; determining node features and edge features in the calibrated graph structure, wherein the node features include branch length, average tube diameter, local maximum / minimum curvature and anatomical level, and the edge features include connection angle and flow rate ratio.

[0015] In one embodiment of the present invention, the voxel mesh encoding of each biliary structure model includes: standardizing the biliary structure model and converting it into a voxel mesh, wherein the voxel mesh contains a multi-channel structure, and the multi-channel structure includes geometric contours, normal vectors, spatial coordinates and region masks.

[0016] In one embodiment of the present invention, training a deep learning model using encoded bile duct structure models and multiple key fluid dynamic parameters relating to the internal flow behavior of the bile duct, and obtaining a trained deep learning model based on the training results, includes: using the encoded bile duct structure models as input to the deep learning model, and using the corresponding multiple key fluid dynamic parameters relating to the internal flow behavior of the bile duct as output of the deep learning model; calculating the multi-task loss of the multiple key fluid dynamic parameters relating to the internal flow behavior of the bile duct according to a loss function, and automatically calculating the gradient according to the backpropagation operation function; using an optimizer to update the parameters of the deep learning model according to the gradient of the current batch, until the multi-task loss is less than a preset threshold, thereby completing the training of the deep learning model and obtaining a trained deep learning model.

[0017] In one embodiment of the present invention, the deep learning model includes a graph neural network model and a convolutional neural network model; the graph neural network model is trained using graph-encoded models of various biliary structures and multiple key fluid dynamic parameters relating to the flow behavior within the biliary tract; the convolutional neural network model is trained using voxel grid-encoded models of various biliary structures and multiple key fluid dynamic parameters relating to the flow behavior within the biliary tract.

[0018] In one embodiment of the present invention, each bile duct structure model encoded by the graph structure is used as the input of a graph neural network model, and the corresponding key fluid dynamic parameters concerning the internal flow behavior of the bile duct are used as the output of the graph neural network model; each bile duct structure model encoded by the voxel grid is used as the input of a convolutional neural network model, and the corresponding key fluid dynamic parameters concerning the internal flow behavior of the bile duct are used as the output of the convolutional neural network model.

[0019] As described above, the intelligent multi-parameter prediction method for biliary flow based on the fusion of CFD and PIV data of the present invention has the following beneficial effects:

[0020] This invention combines CFD simulation data with PIV experimental data to supervise a deep learning model. PIV data enhances the reliability of CFD simulation data, and a large amount of CFD simulation data expands the data source, improving the ability to fit real physical flows. The invention encodes the biliary structure model, constructing a structural representation suitable for neural network modeling by integrating biliary topology, geometric features, and local morphology. It constructs a structure-flow mapping model, based on a graph neural network (GNN) or convolutional neural network (CNN) architecture, learning a nonlinear mapping from biliary morphology to fluid parameters (flow velocity, pressure drop, shear force). This achieves a rapid online prediction mechanism, where the deployed model supports inputting any new biliary structure and outputs a complete predicted flow feature map and quantitative indicators within a certain time, facilitating personalized clinical pathological analysis or clinical medical scientific research evaluation. Attached Figure Description

[0021] Figure 1 The diagram shows the overall process of the intelligent prediction method for multi-parameter bile duct flow based on the fusion of CFD and PIV data disclosed in this embodiment of the invention.

[0022] Figure 2 The diagram shown is a schematic of one of the biliary structure models in the intelligent prediction method for multi-parameter biliary flow based on CFD and PIV data fusion disclosed in this embodiment of the invention.

[0023] Figure 3 This also shows a schematic diagram of one of the biliary structure models in the intelligent prediction method for multi-parameter biliary flow based on the fusion of CFD and PIV data disclosed in the embodiments of the present invention. Detailed Implementation

[0024] The following specific examples illustrate the implementation of the present invention. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. It should be noted that, unless otherwise specified, the following embodiments and features described herein can be combined with each other.

[0025] This invention relates to an intelligent multi-parameter prediction method for biliary flow based on the fusion of CFD and PIV data. It is used to rapidly predict the internal flow behavior of a patient's biliary tract based on a biliary structure model, including key fluid dynamic parameters such as velocity field distribution, pressure drop, and shear force. This method can be applied to scenarios such as research on the pathogenesis of biliary tract diseases, preoperative personalized assessment, individualized treatment plan development, and the design and evaluation of novel medical devices. The process is as follows: Figure 1 As shown, the details are as follows:

[0026] Step 101: Obtain the PIV+CFD joint supervision data for each biliary tract structure model, and construct a multimodal dataset based on each biliary tract structure model and its corresponding PIV+CFD joint supervision data.

[0027] Specifically, data preparation and fusion: Based on the established three-dimensional biliary tract structure model, this invention obtains the corresponding experimental observations and simulation results, and constructs a multimodal dataset for training deep learning models. The specific process is as follows:

[0028] First, the biliary tract structure model is reconstructed in three dimensions from the patient's CT or MRI images. Please refer to section 2 for details. Figure 3 Then, based on the physical model, a PIV experiment is conducted to obtain the planar velocity vector distribution. Simultaneously, CFD simulation is performed under the same geometric structure to obtain complete three-dimensional flow field, pressure distribution, and bile duct wall shear force results. Through spatial interpolation and coordinate mapping, the CFD results are projected onto the PIV observation plane to achieve registration and complementarity between the PIV experimental data and the CFD simulation results, thereby constructing higher-quality supervised data. Each data sample consists of an input bile duct structure model and multiple key output fluid dynamic parameters, forming a complete supervised learning sample.

[0029] Step 102: Encode each biliary tract structure model.

[0030] Specifically, to adapt to deep learning models and improve structural feature extraction capabilities, this invention proposes two encoding schemes for biliary tract structure models: graph structure encoding and voxel grid encoding. The specific process of graph encoding of biliary tract structures is as follows: Graph structure encoding (applicable to graph neural networks GNN): 1) First, extract the centerline: extract the centerline from the reconstructed three-dimensional biliary tract structure model and construct a graph G = (V, E). The graph structure can be automatically constructed by the centerline extraction algorithm, which has good scalability and interpretability; 2) Coordinate alignment: ensure that the graph structure and CFD / PIV data use the same reference coordinate system; use rigid registration or ICP algorithm to calibrate the centerline and the experimental observation plane; 3) The biliary tract structure is abstracted as an undirected graph model, where nodes represent branch segments (such as the left hepatic duct, common hepatic duct, etc.) and edges represent connection relationships; Node features: each node (vv) includes branch length, average diameter, local maximum / minimum curvature, and anatomical level; Edge features: each edge (ee) includes connection angle and flow rate ratio (which can be derived from simulation data).

[0031] Voxel grid encoding (suitable for convolutional neural networks CNN) can be used as input to 3D CNNs to achieve end-to-end modeling of complex spatial structures: the 3D biliary tract structure model is standardized and converted into a voxel grid, that is, the 3D model is resampled into a voxel grid of uniform size (such as 64364^3 or 1283128^3); the multi-channel structure includes geometric contours, normal vectors, spatial coordinates, region masks, etc.; error control: Signed Distance Field (SDF) or multi-resolution pyramid method is used to reduce geometric errors introduced by interpolation;

[0032] Through the above structural encoding method, the complex anatomical information of the bile duct is effectively converted into a format that can be recognized and processed by machine learning models, providing a foundation for subsequent predictive modeling.

[0033] Step 103: Train the deep learning model using the encoded bile duct structure models and several key fluid dynamic parameters concerning the internal flow behavior of the bile duct, and obtain the trained deep learning model based on the training results.

[0034] Specifically, the model construction and training steps are as follows: This invention adopts a deep learning framework, selecting GNN or CNN as the main modeling structure; the network input is a structural graph encoding, and the output is multiple flow parameter fields, including: two-dimensional or three-dimensional velocity vector field, pressure distribution, and bile duct wall shear force distribution map; the loss function design adopts a multi-task joint regression strategy, including velocity vector field L2 error, pressure drop mean square error, and shear force heatmap structural similarity index (such as SSIM); during model training, PIV experimental results serve as a reference for real physical observations, and CFD simulation serves as a global supplement to the flow field, improving prediction accuracy and physical rationality through joint supervision; to improve the model's generalization ability, data augmentation techniques such as structural perturbation and fluid boundary condition changes are introduced.

[0035] More specifically, the GNN architecture (based on PyTorch Geometric / DGL): 1) Graph convolutional layers: GCN, GAT, or GraphSAGE can be selected, with multiple layers stacked to extract node embeddings; 2) Global / local readout: After aggregating node features, local shear force and overall pressure drop are predicted respectively; 3) Activation and normalization: ReLU+BatchNorm is applied after each layer to improve training stability; 3DCNN architecture: 1) Convolutional modules: Conv3D→BatchNorm→ReLU→MaxPool, repeatedly stacked to capture spatial features at different scales; 2) Upsampling / skip connections: U-Net-style structure is adopted to restore high-resolution prediction; or a fully convolutional network (FCN) directly outputs a physical field with the same size as the input voxels; Multi-task output: Velocity field: 3D vector tensor; Pressure distribution: scalar field; Shear force heatmap: 2D surface projection or 3D distribution.

[0036] To elaborate further, the loss function and training process are as follows: 1) Joint loss design: 1) SSIM loss is used in conjunction with L1 / L2 to balance structural and pixel accuracy; 2) Optimizer and hyperparameters: Adam (learning rate 1e-4) is commonly used, combined with learning rate decay and early stopping strategies; multi-task weights α, β, γ can be automatically tuned through grid search or dynamic methods (such as UncertaintyWeighting); 3) Training details: Batch organization: GNN uses graph batch processing (batch of graphs), CNN uses voxel tensor batch; Data augmentation: Graph: random DropEdge, node perturbation; Voxel: geometric scaling, rotation, noise injection; Validation and early stopping: monitor various losses on the validation set to prevent overfitting.

[0037] Step 104: Obtain the bile duct structure model to be predicted, and input the bile duct structure model to be predicted into the trained deep learning model. The trained deep learning model performs structural analysis and intelligent prediction on the bile duct structure model to be predicted, thereby obtaining multiple key fluid dynamic parameters of the internal flow behavior of the bile duct structure model to be predicted.

[0038] Specifically, the steps for model deployment and prediction output are as follows: After model training, it is deployed on a high-performance inference platform; users can input any biliary structure model online (such as STL, DICOM, etc.), and the system will automatically perform structural analysis and graphical encoding; the model performs rapid inference on the structure and outputs the following within seconds: flow velocity vector diagram (two-dimensional cross-section or three-dimensional volume), overall and local pressure drop values, heat map of biliary wall shear force distribution; table of numerical indicators for key areas (such as the maximum shear force point, the steepest pressure drop segment, etc.); the output results can be used for clinical auxiliary diagnosis, preoperative risk analysis, bionic device design verification, and other scenarios.

[0039] In practical applications, the specific steps of the intelligent prediction method for multi-parameter biliary flow based on CFD and PIV data fusion are as follows: Step 1: Data Preparation: Collect registered and aligned pairs of [structure encoding + CFD / PIV labels]: 1) Graph structure encoding (node / edge features); 2) Voxel grid encoding (multi-channel 3D tensor); 3) Corresponding velocity field, pressure field, and shear force heatmaps; Step 2: Batch Construction: Use DataLoader (or PyG / DGL graph batch processing) to divide the samples into batches (batch_size) to ensure that the graph and voxel tensors can be parallelized and accelerated by GPU; Step 3: Model Forward: Input the graph encoding into a GNN, or the voxel tensor into a 3D CNN, to obtain multi-task outputs: (Velocity vector field); (Pressure distribution); (Shear force heatmap) Step 4: Loss Calculation: Calculate multi-task loss: Step 5, Backpropagation: Call loss.backward() on Ltotal to automatically calculate the gradient; Step 6, Parameter Update: Use Adam (or SGD) to execute optimizer.step(), and you can do lr_scheduler.step() every N steps.

[0040] Step 7, Validation and Early Stopping: Repeat steps 3–4 on the validation set for each epoch, monitoring L. total Changes; if there is no improvement for several consecutive rounds, Early Stopping is triggered; Step 8, Model Saving: When the performance is optimal on the validation set, export the model weights using torch.save() (or equivalent); Step 9, Deployment Testing: Export the model as ONNX / TensorRT format, input the new structure encoding, and verify the correctness of the second-level inference and output.

[0041] In summary, this invention combines CFD simulation data with PIV experimental data to supervise deep learning models. PIV data enhances the reliability of CFD simulation data, and a large amount of CFD simulation data expands the data source, improving the ability to fit real physical flows. This invention encodes the biliary structure model, constructing a structural representation suitable for neural network modeling by integrating biliary topology, geometric features, and local morphology. This invention constructs a structure-flow mapping model, based on a graph neural network (GNN) or convolutional neural network (CNN) architecture, learning a nonlinear mapping from biliary morphology to fluid parameters (flow velocity, pressure drop, shear force). This achieves a rapid online prediction mechanism, meaning the deployed model supports inputting any new biliary structure and outputs a complete predicted flow feature map and quantitative indicators within a certain time, facilitating personalized clinical pathological analysis or clinical medical scientific research evaluation.

[0042] The above embodiments are merely illustrative of the principles and effects of the present invention and are not intended to limit the invention. All equivalent modifications or alterations made by those skilled in the art without departing from the spirit and technical concept disclosed in this invention should still be covered by the claims of this invention.

Claims

1. A multi-parameter intelligent prediction method for biliary flow based on the fusion of CFD and PIV data, characterized in that, The method includes the following steps: The PIV+CFD joint supervision data corresponding to each biliary tract structure model is obtained, and a multimodal dataset is constructed based on each biliary tract structure model and its corresponding PIV+CFD joint supervision data. The PIV+CFD joint supervision data includes multiple key hydrodynamic parameters related to the flow behavior inside the biliary tract. Each biliary tract structure model is encoded, wherein the encoding method includes graph structure encoding and voxel grid encoding of each biliary tract structure model; The deep learning model is trained using the encoded bile duct structure models and several key fluid dynamic parameters concerning the internal flow behavior of the bile duct. The trained deep learning model is obtained based on the training results. The bile duct structure model to be predicted is obtained and input into a trained deep learning model. The trained deep learning model performs structural analysis and intelligent prediction on the bile duct structure model to be predicted, thereby obtaining several key fluid dynamic parameters of the internal flow behavior of the bile duct structure model to be predicted.

2. The intelligent prediction method for multiple parameters of biliary flow based on CFD and PIV data fusion as described in claim 1, characterized in that: Before acquiring the PIV+CFD joint supervision data corresponding to each biliary tract structure model, and constructing a multimodal dataset based on each biliary tract structure model and its corresponding PIV+CFD joint supervision data, the following steps are included: Acquire the patient's CT or MRI images and perform three-dimensional reconstruction of the patient's CT or MRI images to obtain the patient's biliary tract structure model based on the three-dimensional reconstruction results; Based on the patient's biliary structure model, a PIV experiment was performed, and the planar velocity vector distribution of the fluid inside the biliary tract was obtained from the PIV experiment results. Based on the patient's biliary structure model, CFD simulation was performed, and the three-dimensional flow velocity field of the fluid inside the biliary tract, the pressure distribution inside the biliary tract, and the shear force of the biliary wall were obtained according to the CFD simulation results. The CFD simulation results are projected onto the PIV observation plane through spatial interpolation and coordinate mapping. Based on the projection results, the PIV experimental data and CFD simulation results are registered and complemented, thus obtaining PIV+CFD joint supervision data.

3. The intelligent prediction method for multiple parameters of biliary flow based on CFD and PIV data fusion according to claim 1, characterized in that: The graph structure encoding of each biliary tract structure model includes: Extract the centerline of the biliary tract structure model and construct a graphical structure of the biliary tract structure model based on the centerline; The centerline of the biliary tract structure model is calibrated to the PIV observation plane using rigid registration or ICP algorithm, and the calibration results are used to ensure that the graph structure and CFD / PIV data are located in the same reference coordinate system. In the calibrated graph structure, node features and edge features are determined, wherein the node features include branch length, average pipe diameter, local maximum / minimum curvature and anatomical level, and the edge features include connection angle and flow rate ratio.

4. The intelligent prediction method for multiple parameters of biliary flow based on CFD and PIV data fusion as described in claim 1, characterized in that: The process of performing voxel grid encoding on each biliary tract structure model includes: The bile duct structure model is standardized and converted into a voxel mesh, wherein the voxel mesh contains a multi-channel structure, and the multi-channel structure includes geometric contours, normal vectors, spatial coordinates and region masks.

5. The intelligent prediction method for multiple parameters of biliary flow based on CFD and PIV data fusion according to claim 1, characterized in that: The deep learning model is trained using the encoded biliary structure models and several key hydrodynamic parameters regarding the flow behavior within the biliary tract. Based on the training results, a trained deep learning model is obtained, including: The encoded bile duct structure models are used as inputs to the deep learning model, and the corresponding key fluid dynamic parameters concerning the internal flow behavior of the bile duct are used as outputs of the deep learning model. The multi-task loss is calculated based on the loss function for multiple key hydrodynamic parameters concerning the flow behavior inside the bile duct, and the gradient is automatically calculated based on the backpropagation operation function. The optimizer updates the parameters of the deep learning model based on the gradient of the current batch until the multi-task loss is less than a preset threshold, thus completing the training of the deep learning model and obtaining a trained deep learning model.

6. The intelligent prediction method for multiple parameters of biliary flow based on CFD and PIV data fusion according to claim 5, characterized in that: The deep learning model includes a graph neural network model and a convolutional neural network model; The graph neural network model was trained using graph-encoded models of various biliary structures and several key hydrodynamic parameters relating to the flow behavior within the biliary tract; the convolutional neural network model was trained using voxel-grid encoded models of various biliary structures and several key hydrodynamic parameters relating to the flow behavior within the biliary tract.

7. The intelligent prediction method for multiple parameters of biliary flow based on CFD and PIV data fusion according to claim 6, characterized in that: Each bile duct structure model after being encoded by the graph structure is used as the input of the graph neural network model, and the corresponding key fluid dynamic parameters concerning the internal flow behavior of the bile duct are used as the output of the graph neural network model. Each bile duct structure model encoded by the voxel grid serves as the input to the convolutional neural network model, while the corresponding key hydrodynamic parameters concerning the internal flow behavior of the bile duct serve as the output of the convolutional neural network model.

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