# Real-Time Prediction of Transarterial Drug Delivery Based on a Deep Convolutional Neural Network
## 4 Discussion  
This study reports a deep-learning-based reduced-order model for prediction of drug trajectory and concentration field. After further investigations, it is expected to work as an auxiliary tool to assist physicians to direct the drug to the tumor site in clinical chemoembolization therapy treatment. Although the traditional numerical simulation can also give an accurate calculation with the known PDEs, the developed network model can avoid the numerical iterations and, thus, allows for extremely fast predictions of the physical fields, which is essential for a real-time treatment auxiliary tool.  
Furthermore, we propose a purely data-driven modeling method and a CNN architecture for the reduced-order model. Although physics-informed machine learning (PINN) is currently the leading direction in physics research involving machine learning, the proposed purely data-driven model requires far fewer computational resources and time for training to make the model converge. In addition, benefiting from the CNN structure, the model can discretize the flow field as pixel-level figures/matrix; therefore, the CNN-based model can be adapted to any geometry easily, much easier than fully connected network-based PINN. CNN architecture enables the model to accurately predict the drug concentration field with relatively small databases, which is important in the biomedical/clinical field, because, sometimes, the data is limited due to privacy concerns or rare diseases.  
The results show a high accuracy of 99.9% in the most complex geometry, the representative hepatic system, which verifies the great performance of the proposed ROM. The high accuracy is also related to the evaluation method of average accuracy. In this study, the drug injection is concentrated from a very tiny point and the amount is small. Therefore, the drug has a small distribution range. However, we considered the entire flow field in the artery when calculating the accuracy (because it is not easy to define which area should be counted), so the accuracy reaches 99.9%.  
It is acknowledged that this preliminary study has some limitations. We only focused on the injection location without consideration of other potentially influential factors such as injection direction and injection time windows. In addition, only one representative geometry of the human hepatic artery system was studied. However, to assist clinical therapy, patient-specific anatomies should be considered. In other words, a geometry-adaptive model [18] should be explored. Additionally, our study is limited to two dimensions, which is not the case for real drug delivery and mass transfer problems in blood vessels. Hence,  
Figure 12: (**a**) Validation loss during the training; (**b**) minimum values of the validation loss with different learning rates.  
rather than providing a predictive model that can be directly used in the clinic, the main contribution of this study should be the proposition of the new idea and method.  
To the best knowledge of the authors, this is the first work on real-time prediction of drug trajectory and concentration field after injections. However, for the purpose of assisting image-guided clinical therapy, further investigations should be explored, such as predictions under three-dimensional CT or MRI-based patient-specific anatomies and construction of an ROM with the geometry and injection condition adaptive ability.