Modeling the pressure pulse shape of piezoelectric lithotripters

Abstract

Piezoelectric focusing transducers are widely used in extracorporeal lithotripsy. To optimize the therapeutically relevant focal pressure pulse it is necessary to affect the generated pulse shape at the transducer surface. Therefore a modeling approach is required containing the acousto-mechanical properties of the transducer structure as well as the influence of the electrical drive. The procedure presented here uses three dimensional transient finite element simulations to calculate an electro-acoustical impulse response of the transducer structure and linear systems theory to model the influence of the driving circuit on the emitted acoustical signal. Applying a short electrical pulse an acoustical impulse response can be simulated under plane wave conditions, which is valid at sufficiently large distances from the transducer. Focal pressures are estimated rapidly by linear calculations or accurately by a nonlinear propagation model. The influence of electrical drive conditions on the emitted acoustical signal is investigated very efficiently by a convolution with the desired electrical input, avoiding FEM simulations for each case. Reverting this process the required driving voltage course for a given pressure signal is determined. Alterations of the pressure signal in terms of pulse width and tensile components are demonstrated theoretically, varying the design parameters of the transducer.