Simulation of Ultrasound signals on a 3D Brain model using K-Wave MATLAB toolbox .

The brain model was downloaded from scalablebrainatlas.
A rough model with the skull can be created using the CreateSkull.m script, which uses morfological dilation operations.
The simulation medium proprieties can be set using masked operations using the values from the brain model.

A simple focusing algorithm was created in order to assert wether or not ultrasound signals could be focused, from an array of transducers, on a brain region, through the skull.

The algorithm works by sending an ultrasound pulse from the target, which reaches the transducers at diferent points in time. The diferent travel times are then used to calculate the delays between the ultrasound transducers. In practice, due to interface reflections, the same signal can reach a transducer multiple times, so all but the maximum value are ignored. The algorithm assumes the same travel path in both directions, which is not true in most cases, despite this, it achieves satisfatory results.

The transducers can be "placed" on the top of the skull/brain, by only to defining the number and spacing between array elements.

The maximum signal pressure was recorded at every point in the simulation array in order to determine the highest intensity points. VolumeViewer was then used to better visualize the results.

Written by Bradley Treeby, Ben Cox, and Jiri Jaros

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.
[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.
[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.