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Simulations In Three Dimensions Example

Overview

This example provides a simple demonstration of using k-Wave for the simulation and detection of a time varying pressure source within a three-dimensional heterogeneous propagation medium. It builds on the Monopole Point Source In A Homogeneous Propagation Medium Example and Simulations In Three Dimensions examples.

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Defining the time varying pressure source

As in one and two dimensions, a time varying pressure source is defined by assigning a binary matrix (i.e., a matrix of 1's and 0's with the same dimensions as the computational grid) to source.p_mask, where the 1's represent the grid points that form part of the source. The time varying input signal is then assigned to source.p. This can have any number of time points (it doesn't need to be the same length as kgrid.t_array) and can be defined as either a single time series (in which case it is applied to all of the source points), or a matrix of time series following the source points using MATLAB's standard column-wise linear matrix index ordering. Here a sinusoidal input is assigned to a square source element. To avoid aliasing, the input should first be filtered using filterTimeSeries (see the Filtering A Delta Function Input Signal Example for more information).

% define a square source element
source_radius = 5;  % [grid points]
source.p_mask = zeros(Nx, Ny, Nz);
source.p_mask(Nx/4, Ny/2 - source_radius:Ny/2 + source_radius, Nz/2 - source_radius:Nz/2 + source_radius) = 1;

% define a time varying sinusoidal source
source_freq = 2e6;  % [Hz]
source_mag = 1;     % [Pa]
source.p = source_mag*sin(2*pi*source_freq*kgrid.t_array);

% smooth the source
source.p = filterTimeSeries(kgrid, medium, source.p);

A plot of the source and sensor masks using voxelPlot is shown below.

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Running the simulation

To allow visualisation of the source elements within the grid, the source mask is assigned to the optional input parameter 'DisplayMask'. This mask is overlaid onto the plot during the simulation. The optional input 'DataCast' is also set to 'single' to reduce the computation time.

% input arguments
input_args = {'DisplayMask', source.p_mask, 'DataCast', 'single'};

% run the simulation
sensor_data = kspaceFirstOrder3D(kgrid, medium, source, sensor, input_args{:});

A plot of the display during simulation is shown below.

The effective visualisation of three-dimensional matrix data remains an important part of data exploration and presentation. An animated slice-by-slice visualisation of the final pressure field can be viewed using flyThrough.

% view final pressure field slice by slice
flyThrough(p_final);

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© 2009-2014 Bradley Treeby and Ben Cox.