Ultrasound field estimation method using a secondary source-array numerically constructed from a limited number of pressure measurements

Nonuniform Bessel-Based Radiation Distributions on A Spherically Curved Boundary for Modeling the Acoustic Field of Focused Ultrasound Transducers

Therapeutic focused ultrasound is a technique that can be used with different intensities depending on the application. For instance, low intensities are required in nonthermal therapies, such as drug delivering, gene therapy, etc.; high intensity ultrasound is used for either thermal therapy or instantaneous tissue destruction, for example, in oncologic therapy with hyperthermia and tumor ablation. When an adequate therapy planning is desired, the acoustic field models of curve radiators should be improved in terms of simplicity and congruence at the prefocal zone. Traditional ideal models using uniform vibration distributions usually do not produce adequate results for clamped unbacked curved radiators. In this paper, it is proposed the use of a Bessel-based nonuniform radiation distribution at the surface of a curved radiator to model the field produced by real focused transducers. This proposal is based on the observed complex vibration of curved transducers modified by Lamb waves, which have a non-negligible effect in the acoustic field. The use of Bessel-based functions to approximate the measured vibration instead of using plain measurements simplifies the rationale and expands the applicability of this modeling approach, for example, when the determination of the effects of ultrasound in tissues is required.

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

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.

Extension of the distributed point source method for ultrasonic field modeling

The distributed point source method (DPSM) was recently proposed for ultrasonic field modeling and other applications. This method uses distributed point sources, placed slightly behind transducer surface, to model the ultrasound field. The acoustic strength of each point source is obtained through matrix inversion that requires the number of target points on the transducer surface to be equal to the number of point sources. In this work, DPSM was extended and further developed to overcome the limitations of the original method and provide a solid mathematical explanation of the physical principle behind the method. With the extension, the acoustic strength of the point sources was calculated as the solution to the least squares minimization problem instead of using direct matrix inversion. As numerical examples, the ultrasound fields of circular and rectangular transducers were calculated using the extended and original DPSMs which were then systematically compared with the results calculated using the theoretical solution and the exact spatial impulse response method. The numerical results showed the extended method can model ultrasonic fields accurately without the scaling step required by the original method. The extended method has potential applications in ultrasonic field modeling, tissue characterization, nondestructive testing, and ultrasound system optimization.