Experimental Validation of k-Wave: Nonlinear Wave Propagation in Layered, Absorbing Fluid Media

Abstract

Models of ultrasound propagation in biologically relevant media have applications in planning and verification of ultrasound therapies and computational dosimetry. To be effective, the models must be able to accurately predict both the spatial distribution and amplitude of the acoustic pressure. This requires that the models are validated in absolute terms, which for arbitrarily heterogeneous media should be performed by comparison with measurements of the acoustic field. In this study, simulations performed using the open-source k-Wave acoustics toolbox, with a measurement-based source definition, were quantitatively validated against measurements of acoustic pressure in water and layered absorbing fluid media. In water, the measured and simulated spatial peak pressures agreed to within 3% under linear conditions and 7% under non-linear conditions. After propagation through a planar or wedge shaped glycerolfilled phantom, the difference in spatial peak pressure was 8.5% and 10.7%, respectively. These differences are within or close to the expected uncertainty of the acoustic pressure measurement. The -6 dB width and length of the focus agreed to within 4% in all cases, and the focal positions were within 0.7 mm for the planar phantom and 1.2 mm for the wedge shaped phantom. These results demonstrate that when the acoustic medium properties and geometry are well known, accurate quantitative predictions of the acoustic field can be made using k-Wave.

Securing Implantable Medical Devices Using Ultrasound Waves

“…k-Wave efficiently solves a system of firstorder, coupled equations that accounts for phenomena such as acoustic absorption and complex tissue-wave interactions that play a part when waves are transmitted through the skin and other layers. Moreover, k-Wave has been validated experimentally and it has become one of the standards for accurate and fast ultrasound simulations [30], [31].…”

Quantitative prediction of the extent of pelvic tumour ablation by magnetic resonance-guided high intensity focused ultrasound

“…The spatial resolution was 196 mm (corresponding to 6.2 grid points per wavelength at minimum), and the time resolution was 29 ns (corresponding to a Courant-Friedrichs-Lewy number [27] of 0.25). These settings were chosen because preliminary validation demonstrated that they provided the fastest simulation in which simulated pressures differed by approximately 7% (i.e., no worse than the uncertainty in hydrophone calibration [10] of the validation model's pressure [31,32]. Simulations were performed on a 20-core (2.6 GHz, 12.8 GB RAM per core) cluster node or a 48-core (2.40 GHz, 8 GB RAM per core) cluster node, depending on which was available.…”

“…These factors suggest that assessment of tumor coverage on its own may be inadequate for identifying whether a patient with a relatively deep-seated tumor is suitable for MRgHIFU therapy and that the percentage of tumor that can be thermally ablated (the 'treatability') should provide a better assessment. Acousto-thermal simulations have been used previously to estimate the extent of tissue ablation within a patient [8,9] however, to the authors' knowledge and probably due to the prohibitive computational costs of these simulations [8][9][10][11], work has not progressed toward estimating the treatability of an entire tumor.…”

Experimental validation of acoustic and thermal modeling in heterogeneous phantoms using the hybrid angular spectrum method

“…For more complex tissue constructs that include voxel-wise inhomogenieties and non-linearities, several beam propagation equations may be applied, including the Khokhlov-Zabolotskaya-Kuznetsov (KZK) [ 15 , 16 ] and Westervelt [ 17 , 18 ] formulations. Simulation methods to account for inhomogeneities and non-linear responses include finite-difference time-domain (FDTD) [ 19 ], the Wen-Breazeale method of Gaussian decomposition [ 20 ] and the pseudospectral k-Wave technique [ 21 ]. There have been significant advances in reducing computational time for many of these techniques using the parallelization advances of graphics processing units.…”