Résumé: © 2018 Institute of Physics and Engineering in Medicine. Ultrasound shock wave therapy is increasingly used for non-invasive surgery. It requires the focusing of very high pressure amplitude in precisely controlled focal spots. In transcostal therapy of the heart or the liver, the high impedance mismatch between the bones and surrounding tissues gives rise to strong aberrations and attenuation of the therapeutic wavefront, with potential risks of injury at the tissue-bone interface. An adaptive propagation of the ultrasonic beam through the intercostal spaces would be required. Several solutions have been developed so far, but they require a prior knowledge of the patient's anatomy or an invasive calibration process, not applicable in clinic. Here, we develop a non-invasive adaptive focusing method for ultrasound therapy through the ribcage using a time reversal cavity (TRC) acting as an ultrasonic beam amplifier. This method is based on ribcage imaging through the TRC and a projection orthogonally to the strongest identified reflectors. The focal pressure of our device was improved by up to 30% using such self-adaptive processing, without degrading the focal spots size and shape. This improvement allowed lesion formation in an Ultracal®phantom through a ribcage without invasive calibration of the device. This adaptive method could be particularly interesting to improve the efficiency and the safety of pulsed cavitational therapy of the heart or the liver.

Résumé: © 2018, SBMAC – Sociedade Brasileira de Matemática Aplicada e Computacional. Our goal is to propose an efficient approach to characterize the eigenvalues and eigenfunctions of the Helmholtz equation with mixed (Dirichlet and Neumann) boundary conditions. Our approach is based on layer potentials. We extend the eigenvalue characterization known for Neumann boundary conditions to the case of mixed boundary conditions. The problem is motivated by the need of such methods for real-time wave-field shaping by electronically tunable surfaces.