Nonuniform Bessel-Based Radiation Distributions on A Spherically Curved Boundary for Modeling the Acoustic Field of Focused Ultrasound Transducers  
[PERSON]  
1 CONACYT--Instituto Nacional de Rehabilitacion, Subdireccion de Investigacion Biotecnologica, Division de Investigacion en Ingenieria Medica, Calz. Mexico-Xochimilco 289, Tlalpan, Mexico City 14389, Mexico; [EMAIL_ADDRESS]  
[PERSON]  
2 Consejo Superior de Investigaciones Cientificas, CSIC, Instituto de Tecnologias Fisicas y de la Informacion, R&D Group. Ultrasonic Signals, Systems and Technologies, C/Serrano 144, 28006 Madrid, Spain; [EMAIL_ADDRESS]  
[PERSON]  
3 Instituto Nacional de Rehabilitacion, Subdireccion de Investigacion Biotecnologica, Division de Investigacion en Ingenieria Medica, Calz. Mexico-Xochimilco 289, Tlalpan, Mexico City 14389, Mexico  
4 Centro de Investigacion y de Estudios Avanzados del IPN, Cinvestav-IPN, Department of Electrical Engineering, Bioelectronics Section, Av. IPN 2508, Gustavo A. Madero, Mexico City 07360, Mexico; [EMAIL_ADDRESS] (A.V. ); [EMAIL_ADDRESS] (L.L)  
4 Consejo Superior de Investigaciones Cientificas, CSIC, Instituto de Tecnologias Fisicas y de la Informacion, R&D Group. Ultrasonic Signals, Systems and Technologies, C/Serrano 144, 28006 Madrid, Spain; [EMAIL_ADDRESS]  
Instituto Nacional de Rehabilitacion, Subdireccion de Investigacion Biotecnologica, Division de Investigacion en Ingenieria Medica, Calz. Mexico-Xochimilco 289, Tlalpan, Mexico City 14389, Mexico  
4 Centro de Investigacion y de Estudios Avanzados del IPN, Cinvestav-IPN, Department of Electrical Engineering, Bioelectronics Section, Av. IPN 2508, [PERSON], Mexico City 07360, Mexico; [EMAIL_ADDRESS] (A.V. ); [EMAIL_ADDRESS] (L.L)
reported in literature can be mentioned the low-intensity pulsed ultrasound (LIPUS) using focused transducers [8], drug delivery in deep tissues (as blood-brain barrier disruption) [10], gene transfer therapy [11], and sonothrombysis [12; 13], among others. In all these applications, the control of the dose in the target volume should be precise during long periods of time to avoid cell death in non-treated zones [12; 14]. Noninvasive (and non-expensive) technologies to monitor the temperature in the treated zone [12], more precise and simpler calibration techniques for FUS transducers to determine effective radiating parameters [15; 16], in conjunction with accurate and simple computational models capable of effectively representing the acoustic fields of real FUS transducers are required. This could provide more information to adequately study the produced effects along the ultrasound pathway and to quantify undesired consequences in surrounding tissues, previous the application of the therapy. However, in medical applications, the use of simple, but inefficient, ideal models for the acoustic field of FUS transducers is a common and not very questioned practice [17; 18; 19]. One of the first approaches to calculate the acoustic field of curved radiators is the O'Neil solution proposed in 1949 [20]. This solution is based on the Rayleigh integral, and it assumes a spherically curved uniform radiator (SCUR) oscillating with a uniform velocity distribution. Although this approximation could be appropriate for many modern transducers at the focus, in the regions where the pressure amplitudes are highly affected by diffraction, e.g., before the focus, the discrepancies are very evident [17]. These variations between \"ideal\" theory and experiments occur because the assumption of a normal uniform velocity distribution is very conservative and, usually, unreal [17; 21; 22].