Deep Learning to Localize Photoacoustic Sources in Three Dimensions: Theory and Implementation.

Surgical tool tip localization and tracking are essential components of surgical and interventional procedures. The cross sections of tool tips can be considered as acoustic point sources to achieve these tasks with deep learning applied to photoacoustic channel data. However, source localization was previously limited to the lateral and axial dimensions of an ultrasound transducer. In this article, we developed a novel deep learning-based 3-D photoacoustic point source localization system using an object detection-based approach extended from our previous work. In addition, we derived theoretical relationships among point source locations, sound speeds, and waveform shapes in raw photoacoustic channel data frames. We then used this theory to develop a novel deep learning instance segmentation-based 3-D point source localization system. When tested with 4000 simulated, 993 phantom, and 1983 ex vivo channel data frames, the two systems achieved F1 scores as high as 99.82%, 93.05%, and 98.20%, respectively, and Euclidean localization errors (mean ± one standard deviation) as low as ${1.46} \; \pm \; {1.11}$ mm, ${1.58} \; \pm \; {1.30}$ mm, and ${1.55} \; \pm \; {0.86}$ mm, respectively. In addition, the instance segmentation-based system simultaneously estimated sound speeds with absolute errors (mean ± one standard deviation) of ${19.22} \; \pm \; {26.26}$ m/s in simulated data and standard deviations ranging 14.6-32.3 m/s in experimental data. These results demonstrate the potential of the proposed photoacoustic imaging-based methods to localize and track tool tips in three dimensions during surgical and interventional procedures.