Quantitative evaluation of stone fragments in extracorporeal shock wave lithotripsy using a time reversal operator

Extracorporeal shock wave lithotripsy (ESWL) has been used widely in the noninvasive treatment of kidney calculi. The fine fragments less than 2 mm in size can be discharged by urination, which determines the success of ESWL. Although ultrasonic and fluorescent imaging are used to localize the calculi, it’s challenging to monitor the stone comminution progress, especially at the late stage of ESWL when fragments spread out as a cloud. The lack of real-time and quantitative evaluation makes this procedure semi-blind, resulting in either under- or over-treatment after the legal number of pulses required by FDA. The time reversal operator (TRO) method has the ability to detect point-like scatterers, and the number of non-zero eigenvalues of TRO is equal to that of the scatterers. In this study, the validation of TRO method to identify stones was illustrated from both numerical and experimental results for one to two stones with various sizes and locations. Furthermore, the parameters affecting the performanc...