# Image Human Thorax Using Ultrasound Traveltime Tomography with Supervised Descent Method
## 5 Conclusions  
In this paper, we verify the feasibility of imaging the human thorax using ultrasound traveltime tomography with SDM and detecting the change of acoustic velocity distribution resulting from respiratory diseases. A training set containing training models with homogeneous background and a high-velocity block covering the whole DoI is introduced. The average descent direction is learned from the training set and all elements in the DoI are sensed. Thanks to the offline training process, the online predicting process is fast and stable. In numerical experiments, SDM traveltime inversion is compared with the traditional gradient-based method on a normal thorax model. A slightly better result is obtained in half the time as the Gauss-Newton method, which means SDM traveltime inversion can be used to image human thorax efficiently. Then, we test its ability to detect the change in acoustic velocity distribution resulting from respiratory diseases. Thorax velocity distribution of pleural effusion and pneumothorax is assumed and inversed by our method. The results show that the synthetic change in acoustic velocity distribution can be detected. SDM also shows good generalization ability. No prior information about thorax structure is added to the training set and the learned descent direction can be applied to inverse thorax at different states. Computing the acoustic velocity distribution can help to monitor human respiratory system, as the acoustic velocity is closely related to tissues' physical properties. In conclusion, ultrasound traveltime tomography with SDM can be used to image human thorax and detect the change in thorax acoustic velocity distribution efficiently. It might be helpful for the diagnosis and quantitative evaluation of respiratory diseases and the localization of the lesion area.  
Figure 12: Thorax acoustic velocity distribution of a pleural effusion patient breathing in air and a pneumothorax patient breathing out air and the corresponding reconstruction results. (**a**) Thorax acoustic velocity distribution of a pleural effusion patient when breathing in air. (**b**) Thorax acoustic velocity distribution of a pneumothorax patient when breathing out air. (**c**) SDM inversion result of the thorax model (**a**). (**d**) SDM inversion result of the thorax model (**b**). (**e**) Gauss–Newton inversion result of the thorax model (**a**). (**f**) Gauss–Newton inversion result of the thorax model (**b**). Colorbar: 1200–2200 m/s.  
**Author Contributions:** Project administration, T.Z., M.L., F.Y. and S.X.; Resources, T.Z.; software, T.Z., R.G., H.Z. ([PERSON]), H.Z. ([PERSON]) and Y.C.; Supervision, M.L.; Writing--original draft preparation, T.Z. All authors have read and agreed to the published version of the manuscript.  
**Funding:** This research was funded by National Natural Science Foundation of China (61971263), the National Key R&D Program of China (2018 YFC0603604), and Institute for Precision Medicine, Tsinghua University, Beijing, China, and Biren Tech, Beijing, China.  
**Conflicts of Interest:** The authors declare no conflict of interest.