k-Wave Toolbox |

## Simulations In One Dimension Example

On this page…
Overview Creating the k-space grid and defining the medium properties Defining the initial pressure distribution and sensor mask Running the simulation

### Overview

This example provides a simple demonstration of using k-Wave for the simulation and detection of the pressure field generated by an initial pressure distribution within a one-dimensional heterogeneous propagation medium. It builds on the Homogeneous Propagation Medium and Heterogeneous Propagation Medium examples.

- open the file in the MATLAB Editor
- run the file in MATLAB

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### Creating the k-space grid and defining the medium properties

Simulations in one-dimension are performed in an analogous fashion to those in two-dimensions. The medium discretisation is again performed by `makeGrid` using the inputs for a single dimension. The properties of a heterogeneous acoustic propagation medium are also given as one-dimensional column vectors.

    % create the computational grid
    Nx = 512;       % number of grid points in the x (row) direction
    dx = 0.05e-3;   % grid point spacing in the x direction [m]
    kgrid = makeGrid(Nx, dx);

    % define the properties of the propagation medium
    medium.sound_speed = 1500*ones(Nx, 1);      % [m/s]
    medium.sound_speed(1:round(Nx/3)) = 2000;   % [m/s]
    medium.density = 1000*ones(Nx, 1);          % [kg/m^3]
    medium.density(round(4*Nx/5):end) = 1500;   % [kg/m^3]

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### Defining the initial pressure distribution and sensor mask

As in two-dimensions, the initial pressure distribution is set using a vector which contains the initial pressure values for each grid point within the computational domain. Here a smoothly varying pressure function is defined using a portion of a sinusoid.

    % create initial pressure distribution using a smoothly shaped sinusoid
    x_pos = 280;    % [grid points]
    width = 100;    % [grid points]
    height = 1;     % [Pa]
    in = (0:pi/(width/2):2*pi).';
    source.p0 = [zeros(x_pos, 1); ((height/2)*sin(in-pi/2)+(height/2)); zeros(Nx - x_pos  - width - 1, 1)];

Again both Cartesian and binary sensor masks can be used to define the locations where the pressure field is recorded at each time-step. In this example, a Cartesian sensor mask with two points is defined.

    % create a Cartesian sensor mask
    sensor.mask = [-10e-3, 10e-3];  % [mm]

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### Running the simulation

The computation is started by passing the four input structures, `kgrid`, `medium`, `source`, and `sensor` to `kspaceFirstOrder1D`. To record long enough to capture the reflections from the heterogeneous interfaces, `kgrid.t_array` is created using `makeTime`, with the total simulation time set explicitly. By default, a visualisation of the propagating wave-field and a status bar are displayed.

    % set the simulation time to capture the reflections
    t_end = 2.5*kgrid.x_size/max(medium.sound_speed(:));

    % define the time array
    [kgrid.t_array, dt] = makeTime(kgrid, medium.sound_speed, [], t_end);

    % run the simulation
    sensor_data = kspaceFirstOrder1D(kgrid, medium, source, sensor, 'PlotLayout', true);

As the function runs, status updates and computational parameters are printed to the command line.

    Running k-Wave simulation...
      start time: 18-Oct-2011 09:27:02
      reference sound speed: 2000m/s
      dt: 7.5ns, t_end: 31.995us, time steps: 4267
      input grid size: 512 pixels (25.6mm)
      maximum supported frequency: 15MHz
      smoothing p0 distribution...
      precomputation completed in 0.5824s
      starting time loop...
      estimated simulation time 1.9824s...
      computation completed in 5.1936s

A plot of the initial pressure distribution, sensor mask, and medium properties (returned using `'PlotLayout'` set to `true`) is given below.

When the time loop has completed, the function returns the recorded time series at each of sensor points defined by `sensor_mask`. The ordering is again dependent on whether a Cartesian or binary sensor mask is used. A visualisation of the recorded sensor data is given below.

Note, in some cases the animated visualisation can significantly slow down the simulation. The computational speed can be increased by switching off the animations by setting the optional input `'PlotSim'` to `false`.

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© 2009-2012 Bradley Treeby and Ben Cox.