Objective To address the limitations of conventional physics-informed neural network(PINN)in handling hemodynamic boundary constraints,an improved hard boundary-constrained PINN(HBC-PINN)framework was proposed to achieve precise prediction of blood flow fields within stenotic arteries.Methods An idealized stenosed vessel geometry model was established and computational fluid dynamic simulation was performed to obtain a validation dataset.Appropriate boundary dependent trial functions were designed according to the hard constraint method to embed the flow boundary conditions into the network output.Thus,an HBC-PINN model with the hard boundary constraint method was constructed to predict the velocity field and pressure field of stenosed blood flow.Meanwhile,an original PINN model with the soft constraint method was also built for comparison.By evaluating the accuracy of the two models on the validation dataset,the capability of the HBC-PINN model to simulate hemodynamics without using any labeled data for training was verified.Results The effectiveness of the HBC-PINN method in predicting hemodynamic parameters in stenosed blood flow tasks was validated.The relative L2 errors of the flow velocity and pressure predicted by the HBC-PINN in two different stenosis scenarios were both lower than 0.5％,representing an improvement of over 48.8％in accuracy compared to the original PINN model.Additionally,the prediction accuracy of the transverse velocity also increased by more than 35.4％.Conclusions Implementing hard constraints on boundary conditions in the PINN modeling process can effectively improve the prediction accuracy of hemodynamic parameters and the efficiency of model solving.

Objective To address the limitations of conventional physics-informed neural network(PINN)in handling hemodynamic boundary constraints,an improved hard boundary-constrained PINN(HBC-PINN)framework was proposed to achieve precise prediction of blood flow fields within stenotic arteries.Methods An idealized stenosed vessel geometry model was established and computational fluid dynamic simulation was performed to obtain a validation dataset.Appropriate boundary dependent trial functions were designed according to the hard constraint method to embed the flow boundary conditions into the network output.Thus,an HBC-PINN model with the hard boundary constraint method was constructed to predict the velocity field and pressure field of stenosed blood flow.Meanwhile,an original PINN model with the soft constraint method was also built for comparison.By evaluating the accuracy of the two models on the validation dataset,the capability of the HBC-PINN model to simulate hemodynamics without using any labeled data for training was verified.Results The effectiveness of the HBC-PINN method in predicting hemodynamic parameters in stenosed blood flow tasks was validated.The relative L2 errors of the flow velocity and pressure predicted by the HBC-PINN in two different stenosis scenarios were both lower than 0.5％,representing an improvement of over 48.8％in accuracy compared to the original PINN model.Additionally,the prediction accuracy of the transverse velocity also increased by more than 35.4％.Conclusions Implementing hard constraints on boundary conditions in the PINN modeling process can effectively improve the prediction accuracy of hemodynamic parameters and the efficiency of model solving.

Objective To predict the constitutive parameters of a superelastic model of plantar soft tissues based on random forest(RF)and backpropagation(BP)neural network algorithms to improve the efficiency and accuracy of the method for obtaining constitutive parameters.Methods First,a finite element model for a spherical indentation experiment of plantar soft tissues was established,and the spherical indentation experiment process was simulated to obtain a dataset of nonlinear displacement and indentation force,divided into training and testing sets.The established RF and BP neural network(BPNN)models were trained separately.The constitutive parameters of plantar soft tissues were predicted using experimental data.Finally,the mean square error(MSE)and coefficient of determination(R2)were introduced to evaluate the accuracy of the model prediction,and the effectiveness of the model was verified by comparison with the experimental curves.Results Combining the RF and BPNN models with finite element simulation was an effective and accurate method for determining the superelastic constitutive parameters of plantar soft tissues.After training,the MSE of the RF model reached 1.370 2×10-3,and R2 was 0.982 9,whereas the MSE of the BPNN model reached 4.858 1×10-5,and R2 was 0.999 3.The inverse-determined constitutive parameters of the plantar soft tissues suitable for simulation were obtained.The calculated response curves for the two predicted sets of constitutive parameters were in good agreement with the experimental curves.Conclusions The prediction accuracy for the superelastic constitutive parameters of plantar soft tissues based on an artificial intelligence algorithm model is high,and the relevant research results can be applied to study other mechanical properties of plantar soft tissues.This study provides a new method for obtaining the constitutive parameters of plantar soft tissues and helps to quickly diagnose clinical problems,such as plantar soft tissue lesions.

Objective To investigate the application of machine learning to predict the hemodynamic parameters of combined stenotic left coronary artery(LCA)aneurysms.Methods Parameterized modeling and simulation based on the geometric parameter range of combined stenosis LCA aneurysms in clinical statistics were conducted.The obtained simulation data was used as the dataset,and two common machine learning models were constructed and trained for optimization to predict two key hemodynamic parameters:wall shear stress(WSS)and pressure.By comparing and analyzing the performances of these models on the training and testing sets,the accuracy of each model was evaluated,and the effectiveness of the data-driven prediction of hemodynamic parameters for LCA aneurysms with concomitant stenosis was verified.Results The effectiveness of machine learning method in inverting the hemodynamic parameters of aneurysms was determined.For WSS prediction,the trained deep learning model and random forest model achieved mean squared error(MSE),mean absolute error(MAE),and determination coefficient R2 of 0.052 8,0.032 2,0.988 3,and 0.078 2,0.046 3,and 0.976 6,respectively.For pressure prediction,the accuracies of the deep learning models and random forest models were comparable,with MSE,MAE,and R2 of 4.67×10-6,3×10-4,0.999 7,and 1.07×10-5,5×10-4,and 0.999 3,respectively.Conclusions Machine learning methods show high accuracy in predicting the hemodynamic parameters of combined stenotic coronary artery aneurysm models.The predictive accuracy of the model,computational efficiency,and needs of the application scenarios need to be considered in machine learning prediction so that the appropriate model can be selected according to the specific situation.This study has clinical significance,helping doctors to more accurately evaluate a patient's condition and provide new ideas and method for the diagnosis and treatment of cardiovascular diseases.