Acoustic holography as a metrological tool for characterizing medical ultrasound sources and fields

Abstract

Acoustic holography is a powerful technique for characterizing ultrasound sources and the fields they radiate, with the ability to quantify source vibrations and reduce the number of required measurements. These capabilities are increasingly appealing for meeting measurement standards in medical ultrasound; however, associated uncertainties have not been investigated systematically. Here errors associated with holographic representations of a linear, continuous-wave ultrasound field are studied. To facilitate the analysis, error metrics are defined explicitly, and a detailed description of a holography formulation based on the Rayleigh integral is provided. Errors are evaluated both for simulations of a typical therapeutic ultrasound source and for physical experiments with three different ultrasound sources. Simulated experiments explore sampling errors introduced by the use of a finite number of measurements, geometric uncertainties in the actual positions of acquired measurements, and uncertainties in the properties of the propagation medium. Results demonstrate the theoretical feasibility of keeping errors less than about 1%. Typical errors in physical experiments were somewhat larger, on the order of a few percent; comparison with simulations provides specific guidelines for improving the experimental implementation to reduce these errors. Overall, results suggest that holography can be implemented successfully as a metrological tool with small, quantifiable errors.

A Prototype Therapy System for Transcutaneous Application of Boiling Histotripsy

“…6, which demonstrates that the hologram can serve as a model boundary condition that accurately captures the linear field in three dimensions. Discrepancies between the holographic representation and independent measurements of the focal region of the beam were on the order of 5% or less, within the uncertainty of the hydrophone calibration [44]. While the main diffraction lobe is symmetric in x and y directions in the focal plane, some difference is observed in the position of side lobes in the transverse structure of the beam due to asymmetry of the 7-element design of the array.…”

“…Holography was used to reconstruct the distribution of vibrational velocity at the surface of the transducer [44]. This distribution was used as a boundary condition to nonlinear modeling.…”

“…The boundary condition to the model was determined from holography measurements of the vibration pattern of the surface of the array [35, 43, 44]. The hologram measured in water in the plane z = 85 mm was linearly back projected to a source hologram in the plane z = 0 using the angular spectrum method.…”

Design of HIFU Transducers for Generating Specified Nonlinear Ultrasound Fields

“…For two array transducers considered in this paper, spatial distributions of the initial pressure amplitude $p_0^{\mathrm{italichol}}(x,y)$ and phase ${\phi }_0^{\mathrm{italichoi}}(x,y)$ were determined from acoustic holography measurements conducted at low output levels [34]. Measurements to define a hologram were made in a planar region perpendicular to the beam axis between the source and the focus [26, 27, 35]. The measured hologram was then linearly backpropagated to define the field in the initial plane of modeling z = 0.…”

“…Geometric parameters of spherically shaped transducers and power outputs were determined to achieve specified focal pressures for three characteristic levels of nonlinear distortion: quasilinear waveforms, waveforms with fully developed shocks, and saturated waveforms. To validate the accuracy of the proposed approach, full diffraction nonlinear Westervelt modeling and high-output characterization measurements were performed for three representative strongly focused HIFU sources: a single-element 1-MHz histotripsy source [25], a custom-built 7-element transducer array designed for boiling histotripsy [26], and a 256-element HIFU array from a clinical MR-guided HIFU system [27]. A relationship was established between each of these sources and an equivalent single-element planar source for the parabolic model or a spherical source for the full diffraction model based on matching measured and modeled axial distributions of acoustic pressure at low output levels.…”