Acoustic field modeling for physiotherapy ultrasound applicators by using approximated functions of measured non-uniform radiation distributions

Abstract

The strongest therapeutic effects in ultrasonic physiotherapy are mainly produced at the first centimeters, i.e. close to the applicator surface and, in general, only in the near-field zone. The acoustic field produced in practice by this type of transducers differs from the classical models because the vibration distribution on the real transducer surfaces is non-uniform. However, neither models using uniform distribution, nor those using typical non-uniform distribution patterns for the source accurately represent the radiation of this kind of transducers. Although this therapy is widely used and many efforts have been made in experimentally studying the patterns of ultrasound radiation produced during physiotherapy applications (IEC-61689, 1998), additional modeling researches still would be needed in order to achieve improved models giving field patterns closer to the measured ultrasonic results. In this paper, acoustic patterns produced from two source radiation functions are proposed and evaluated for field modeling of physiotherapy applicators. Both the functions are approximations to the pressure distribution measured close to the emitting surface and they are based on the modulation of the classical simply-supported function using either sinusoidal or Bessel-type distributions. The simply-supported function is accounted for the radiator-fixing condition and the modulation function simulates the complex vibration distribution of this kind of transducer. The modulator Bessel function is based on reports about Bessel-type vibration distributions found in piezoelectric disk resonators. The use of a selected sinusoidal segment represents another analytical option for obtaining an approximated behavior of the measured data in a real applicator. Both the field models are implemented using the finite element method (FEM) to obtain the numerical solution of wave equation at each point in the radiated space. The solution is reached by considering axisymmetric radiation in attenuation-free media. The results indicate the viability of applying an adequate model for acoustic field calculation by simulating the radiating distribution on the emitting surface as either sinusoidal or Bessel-modulated functions. Models using both the functions describe reasonably real behaviors, but those based on Bessel functions are better correlated with the measurements. The results for three commercial applicators indicate the possibility of representing, with adequate verisimilitude, the acoustic field radiated by physiotherapy ultrasound transducers using linear combinations of Bessel profiles describing the radiation source.