k-Wave is an open source MATLAB toolbox designed for the time-domain simulation of propagating acoustic waves in 1D, 2D, or 3D [1]. The toolbox has a wide range of functionality, but at its heart is an advanced numerical model that can account for both linear and nonlinear wave propagation, an arbitrary distribution of heterogeneous material parameters, and power law acoustic absorption.

The numerical model is based on the solution of three coupled first-order partial differential equations which are equivalent to a generalised form of the Westervelt equation [2]. The equations are solved using a k-space pseudospectral method, where spatial gradients are calculated using a Fourier collocation scheme, and temporal gradients are calculated using a k-space corrected finite-difference scheme. The temporal scheme is exact in the limit of linear wave propagation in a homogeneous and lossless medium, and significantly reduces numerical dispersion in the more general case.

Power law acoustic absorption is accounted for using a linear integro-differential operator based on the fractional Laplacian [3]. A split-field perfectly matched layer (PML) is used to absorb the waves at the edges of the computational domain. The main advantage of the numerical model used in k-Wave compared to models based on finite-difference time domain (FDTD) schemes is that fewer spatial and temporal grid points are needed for accurate simulations. This means the models run faster and use less memory. A detailed description of the model is given in the k-Wave User Manual and the references below.



[1] B. E. Treeby and B. T. Cox, "k-Wave: MATLAB toolbox for the simulation and reconstruction of photoacoustic wave-fields," J. Biomed. Opt., vol. 15, no. 2, p. 021314, 2010. download pdf

[2] B. E. Treeby, J. Jaros, A. P. Rendell, and B. T. Cox, "Modeling nonlinear ultrasound propagation in heterogeneous media with power law absorption using a k-space pseudospectral method," J. Acoust. Soc. Am., vol. 131, no. 6, pp. 4324-4336, 2012. download pdf

[3] B. E. Treeby and B. T. Cox, "Modeling power law absorption and dispersion for acoustic propagation using the fractional Laplacian," J. Acoust. Soc. Am., vol. 127, no. 5, pp. 2741-2748, 2010. download pdf (see also erratum)