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kspaceFirstOrder2D

2D time-domain simulation of wave propagation

Syntax

sensor_data = kspaceFirstOrder2D(kgrid, medium, source, sensor)
sensor_data = kspaceFirstOrder2D(kgrid, medium, source, sensor, ...) 

[sensor_data, field_data] = kspaceFirstOrder2D(kgrid, medium, source, sensor)
[sensor_data, field_data] = kspaceFirstOrder2D(kgrid, medium, source, sensor, ...) 

kspaceFirstOrder2D(kgrid, medium, source, [])
kspaceFirstOrder2D(kgrid, medium, source, [], ...) 

Description

kspaceFirstOrder2D simulates the time-domain propagation of linear compressional waves through a two-dimensional homogeneous or heterogeneous acoustic medium given four input structures: kgrid, medium, source, and sensor. The computation is based on a first-order k-space model which accounts for power law absorption and a heterogeneous sound speed and density. If medium.BonA is specified, cumulative nonlinear effects are also modelled. At each time-step (defined by kgrid.t_array), the pressure at the positions defined by sensor.mask are recorded and stored. If kgrid.t_array is set to 'auto', this array is automatically generated using makeTime. An anisotropic absorbing boundary condition called a perfectly matched layer (PML) is implemented to prevent waves that leave one side of the domain being reintroduced from the opposite side (a consequence of using the FFT to compute the spatial derivatives in the wave equation). This allows infinite domain simulations to be computed using small computational grids.

For a homogeneous medium the formulation is exact and the time-steps are only limited by the effectiveness of the perfectly matched layer. For a heterogeneous medium, the solution represents a leap-frog pseudospectral method with a Laplacian correction that improves the accuracy of computing the temporal derivatives. This allows larger time-steps to be taken without instability compared to conventional pseudospectral time-domain methods. The computational grids are staggered both spatially and temporally.

An initial pressure distribution can be specified by assigning a matrix (the same size as the computational grid) of arbitrary numeric values to source.p0. A time varying pressure source can similarly be specified 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 signals are then assigned to source.p. This must be the same length as kgrid.t_array and can be a single time series (in which case it is applied to all source elements), or a matrix of time series following the source elements using MATLAB's standard column-wise linear matrix index ordering. A time varying velocity source can be specified in an analogous fashion, where the source location is specified by source.u_mask, and the time varying input velocity is assigned to source.ux and source.uy.

The pressure is returned as an array of time series at the sensor locations defined by sensor.mask. This can be given either as a binary grid (i.e., a matrix of 1's and 0's with the same dimensions as the computational grid) representing the grid points within the computational grid that will collect the data, or as a series of arbitrary Cartesian coordinates within the grid at which the pressure values are calculated at each time step via interpolation. The Cartesian points must be given as a 2 by N matrix corresponding to the x and z positions, respectively. The final pressure field over the complete computational grid can also be obtained using the output field_data. If no output is required, the sensor input can be replaced with an empty array [].

If sensor.mask is given as a set of Cartesian coordinates, the computed sensor_data is returned in the same order. If sensor.mask is given as a binary grid, sensor_data is returned using MATLAB's standard column-wise linear matrix index ordering. In both cases, the recorded data is indexed as sensor_data(sensor_position, time). For a binary sensor mask, the pressure values at a particular time can be restored to the sensor positions within the computation grid using unmaskSensorData.

By default, the recorded pressure field is passed directly to the output arguments sensor_data and field_data. However, the particle velocity can also be recorded by setting the optional input parameter 'ReturnVelocity' to true. In this case, the output arguments sensor_data and field_data are returned as structures with the pressure and particle velocity appended as separate fields. In two dimensions, these fields are given by sensor_data.p, sensor_data.ux, and sensor_data.uy, and field_final.p, field_final.ux, and field_final.uy.

kspaceFirstOrder2D may also be used for time reversal image reconstruction by assigning the time varying pressure recorded over an arbitrary sensor surface to the input field sensor.time_reversal_boundary_data. This data is then enforced in time reversed order as a time varying Dirichlet boundary condition over the sensor surface given by sensor.mask. The boundary data must be indexed as sensor.time_reversal_boundary_data(sensor_position, time). If sensor.mask is given as a set of Cartesian coordinates, the boundary data must be given in the same order. An equivalent binary sensor mask (computed using nearest neighbour interpolation) is then used to place the pressure values into the computational grid at each time step. If sensor.mask is given as a binary grid of sensor points, the boundary data must be ordered using MATLAB's standard column-wise linear matrix indexing. If no additional inputs are required, the source input can be replaced with an empty array [].

Acoustic attenuation compensation can also be included during time reversal image reconstruction by assigning the absorption parameters medium.alpha_coeff and medium.alpha_power and reversing the sign of the absorption term by setting medium.alpha_sign = [-1, 1]. This forces the propagating waves to grow according to the absorption parameters instead of decay. The reconstruction should then be regularised by assigning a filter to medium.alpha_filter (this can be created using getAlphaFilter).

Inputs

The minimum fields that must be assigned to run an initial value problem (for example, a photoacoustic forward simulation) are marked with a *.

kgrid*

k-space grid structure returned by makeGrid containing Cartesian and k-space grid fields

kgrid.t_array*

evenly spaced array of time values [s] (set to 'auto' by makeGrid)

 

 

medium.sound_speed*

sound speed distribution within the acoustic medium [m/s]

medium.sound_speed_ref

reference sound speed used within the k-space operator (phase correction term) [m/s]

medium.density*

density distribution within the acoustic medium [kg/m^3]

medium.BonA

parameter of nonlinearity

medium.alpha_power

power law absorption exponent

medium.alpha_coeff

power law absorption coefficient [dB/(MHz^y cm)]

medium.alpha_mode

optional input to force either the absorption or dispersion terms in the equation of state to be excluded; valid inputs are 'no_absorption' or 'no_dispersion'

medium.alpha_filter

frequency domain filter applied to the absorption and dispersion terms in the equation of state

medium.alpha_sign

two element array used to control the sign of absorption and dispersion terms in the equation of state

 

 

source.p0*

initial pressure within the acoustic medium

source.p

time varying pressure at each of the source positions given by source.p_mask

source.p_mask

binary grid specifying the positions of the time varying pressure source distribution

source.p_mode

optional input to control whether the input pressure is injected as a mass source or enforced as a dirichlet boundary condition; valid inputs are 'additive' (the default) or 'dirichlet'

source.ux

time varying particle velocity in the x-direction at each of the source positions given by source.u_mask

source.uy

time varying particle velocity in the y-direction at each of the source positions given by source.u_mask

source.u_mask

binary grid specifying the positions of the time varying particle velocity distribution

source.u_mode

optional input to control whether the input velocity is applied as a force source or enforced as a dirichlet boundary condition; valid inputs are 'additive' (the default) or 'dirichlet'

 

 

sensor.mask*

binary grid or a set of Cartesian points where the pressure is recorded at each time-step

sensor.time_reversal_boundary_data

time varying pressure enforced as a Dirichlet boundary condition over sensor.mask

sensor.frequency_response

two element array specifying the center frequency and percentage bandwidth of a frequency domain Gaussian filter applied to the sensor_data

sensor.record_mode

optional input to save the statistics of the wave field at the sensor elements rather than the time series; valid inputs are 'statistics' or 'time_history' (the default)

sensor.directivity_angle

matrix of directivity angles (direction of maximum response) for each sensor element defined in sensor.mask. The angles are in radians where 0 = max sensitivity in x direction (up/down) and pi/2 or -pi/2 = max sensitivity in y direction (left/right)

sensor.directivity_size

equivalent element size (the larger the element size the more directional the response)

Optional Inputs

Optional 'string', value pairs that may be used to modify the default computational settings.

Input Valid Settings Default Description

'CartInterp'

'linear'
'nearest'

'linear'

Interpolation mode used to extract the pressure when a Cartesian sensor mask is given. If set to 'nearest' and more than one Cartesian point maps to the same grid point, duplicated data points are discarded and sensor_data will be returned with less points than that specified by sensor.mask.

'CreateLog'

(Boolean scalar)

false

Boolean controlling whether the command line output is saved using the diary function with a date and time stamped filename.

'DataCast'

(string of data type)

'off'

String input of the data type that variables are cast to before computation. For example, setting to 'single' will speed up the computation time (due to the improved efficiency of fft2 and ifft2 for this data type) at the expense of a loss in precision. This variable is also useful for utilising GPU parallelisation through libraries such as GPUmat or AccelerEyesJacket by setting 'DataCast' to 'GPUsingle' or 'gsingle'.

'DisplayMask'

(binary matrix) or
'off'

sensor.mask

Binary matrix overlayed onto the animated simulation display. Elements set to 1 within the display mask are set to black within the display.

'LogScale'

(Boolean scalar) or
(numeric scalar)

false

Boolean controlling whether the pressure field is log compressed before display. The data is compressed by scaling both the positive and negative values between 0 and 1 (truncating the data to the given plot scale), adding a scalar value (compression factor) and then using the corresponding portion of a log10 plot for the compression (the negative parts are remapped to be negative thus the default color scale will appear unchanged). The amount of compression can be controlled by adjusting the compression factor which can be given in place of the Boolean input. The closer the compression factor is to zero, the steeper the corresponding part of the log10 plot used, and the greater the compression (the default compression factor is 0.02).

'MeshPlot'

(Boolean scalar)

false

Boolean controlling whether mesh is used in place of imagesc to plot the pressure field. When 'MeshPlot' is set to true, the default display mask is set to 'off'.

'MovieArgs'

(string cell array)

{}

Settings for movie2avi. Parameters must be given as {param, value, ...} pairs within a cell array.

'MovieName'

(string)

'date-time-kspaceFirstOrder2D'

Name of the movie produced when 'RecordMovie' is set to true.

'MovieType'

'frame'
'image'

'frame'

Parameter controlling whether the image frames are captured using getframe ('frame') or im2frame ('image'). If set to 'image', the size of the movie will depend on the size of the simulation grid.

'PlotFreq'

(integer numeric scalar)

10

The number of iterations which must pass before the simulation plot is updated.

'PlotLayout'

(Boolean scalar)

false

Boolean controlling whether a four panel plot of the initial simulation layout is produced (initial pressure, sensor mask, sound speed, density).

'PlotPML'

(Boolean scalar)

true

Boolean controlling whether the perfectly matched layer is shown in the simulation plots. If set to false, the PML is not displayed.

'PlotScale'

(numeric two element vector) or
'auto'

[-1, 1]

[min, max] values used to control the scaling for imagesc (visualisation) and im2frame (movie capture). If set to 'auto', a symmetric plot scale is chosen automatically for each plot frame.

'PlotSim'

(Boolean scalar)

true

Boolean controlling whether the simulation iterations are progressively plotted.

'PMLAlpha'

(numeric scalar or two element vector)

2

Absorption within the perfectly matched layer in Nepers per metre.

'PMLInside'

(Boolean scalar)

true

Boolean controlling whether the perfectly matched layer is inside or outside the grid. If set to false, the input grids are enlarged by PMLSize before running the simulation.

'PMLSize'

(integer numeric scalar or two element vector)

20

Size of the perfectly matched layer in grid points. By default, the PML is added evenly to all sides of the grid, however, both PMLSize and PMLAlpha can be given as two element arrays to specify the x and y properties, respectively. To remove the PML, set the appropriate PMLAlpha to zero rather than forcing the PML to be of zero size.

'RecordMovie'

(Boolean scalar)

false

Boolean controlling whether the displayed image frames are captured and stored as a movie using movie2avi.

'ReturnVelocity'

(Boolean scalar)

false

Boolean controlling whether the acoustic particle velocity at the positions defined by sensor.mask are also returned. If set to true, the output argument sensor_data is returned as a structure with the pressure and particle velocity appended as separate fields. In two dimensions, these fields are given by sensor_data.p, sensor_data.ux, and sensor_data.uy. The field data is similarly returned as field_data.p, field_data.ux, and field_data.uy.

'Smooth'

(Boolean scalar or three element vector)

[true, false, false]

Boolean controlling whether source.p0, medium.sound_speed, and medium.density are smoothed using smooth before computation. 'Smooth' can either be given as a single Boolean value or as a 3 element array to control the smoothing of source.p0, medium.sound_speed, and medium.density, independently.

Outputs

If 'ReturnVelocity' is set to false:

sensor_data

time varying pressure recorded at the sensor positions given by sensor.mask

field_data

final pressure field

If 'ReturnVelocity' is set to true:

sensor_data.p

time varying pressure recorded at the sensor positions given by sensor.mask

sensor_data.ux

time varying particle velocity in the x-direction recorded at the sensor positions given by sensor.mask

sensor_data.uy

time varying particle velocity in the y-direction recorded at the sensor positions given by sensor.mask

field_data.p

final pressure field

field_data.ux

final field of the particle velocity in the x-direction

field_data.uy

final field of the particle velocity in the y-direction

Examples

See Also

fft2, ifft2, im2frame, imagesc, kspaceFirstOrder1D, kspaceFirstOrder3D, makeGrid, makeTime, movie2avi, smooth, unmaskSensorData


© 2009-2012 Bradley Treeby and Ben Cox.