k-Wave Toolbox

• Getting Started
• Run the First Example
• Build Your Own Simulation
• Troubleshooting
• Reference List
• Examples
• Initial Value Problems
• Example: Homogenous Propagation Medium
• Example: Using A Binary Sensor Mask
• Example: Defining A Sensor Mask By Opposing Corners
• Example: Loading External Image Maps
• Example: Heterogeneous Propagation Medium
• Example: Saving Movie Files
• Example: Recording The Particle Velocity
• Example: Defining A Gaussian Sensor Frequency Response
• Example: Comparison Of Modelling Functions
• Example: Setting An Initial Pressure Gradient
• Example: Simulations In One Dimension
• Example: Simulations In Three Dimensions
• Example: Photoacoustic Waveforms in 1D, 2D and 3D
• Time Varying Source Problems
• Example: Monopole Point Source In A Homogeneous Propagation Medium
• Example: Dipole Point Source In A Homogeneous Propagation Medium
• Example: Simulating Transducer Field Patterns
• Example: Steering A Linear Array
• Example: Snell's Law And Critical Angle Reflection
• Example: The Doppler Effect
• Example: Diffraction Through A Slit
• Example: Simulations In Three-Dimensions
• Sensor Directivity
• Example: Focussed Detector in 2D
• Example: Focussed Detector in 3D
• Example: Modelling Sensor Directivity in 2D
• Example: Modelling Sensor Directivity in 3D
• Example: Sensor Element Directivity in 2D
• Example: Focussed 2D Array with Directional Elements
• Photoacoustic Image Reconstruction
• Example: 2D FFT Reconstruction For A Line Sensor
• Example: 3D FFT Reconstruction For A Planar Sensor
• Example: 2D Time Reversal For A Line Sensor
• Example: 2D Time Reversal For A Circular Sensor
• Example: 3D Time Reversal For A Planar Sensor
• Example: 3D Time Reversal For A Spherical Sensor
• Example: Image Reconstruction With Directional Sensors
• Example: Image Reconstruction With Bandlimited Sensors
• Example: Iterative Image Improvement Using Time Reversal
• Example: Attenuation Compensation Using Time Reversal
• Example: Attenuation Compensation Using Time Variant Filtering
• Example: Automatic Sound Speed Selection
• Diagnostic Ultrasound Simulation
• Example: Defining An Ultrasound Transducer
• Example: Simulating Ultrasound Beam Patterns
• Example: Using An Ultrasound Transducer As A Sensor
• Example: Simulating B-mode Ultrasound Images
• Example: Simulating B-mode Images Using A Phased Array
• Numerical Analysis
• Example: Controlling The Absorbing Boundary Layer
• Example: Source Smoothing
• Example: Filtering A Delta Function Input Signal
• Example: Modelling Power Law Absorption
• Example: Modelling Nonlinear Wave Propagation
• Example: Optimising k-Wave Performance
• Using The C++ Code
• Example: Running C++ Simulations
• Example: Saving Input Files in Parts
• Elastic Wave Propagation
• Example: Explosive Source In A Layered Medium
• Example: Plane Wave Absorption
• Example: Shear Waves And Critical Angle Reflection
• Example: Simulations In Three Dimensions
• Functions - By Category
• Functions - Alphabetical List
• Release Notes
• License

k-Wave Toolbox

kspaceSecondOrder

Fast time-domain simulation of wave propagation for homogeneous media

Syntax

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

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

Description

kspaceSecondOrder simulates the time-domain propagation of linear compressional waves through a one, two, or three dimensional homogeneous acoustic medium given four input structures: kgrid, medium, source, and sensor. The computation is based on an exact second-order k-space model for media with power law absorption. 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. To prevent wave wrapping, the computational domain can be automatically expanded by a factor of two by setting the optional input 'ExpandGrid' to true.

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. An initial pressure gradient can similarly be specified using source.dp0dt. The pressure is returned as an array of time series at the sensor locations defined by sensor.mask. This is specified as a binary matrix (i.e., a matrix of 1's and 0's the same size as the computational grid) representing the grid points within the computational grid that will collect the data. The sensor_data is returned using MATLAB's standard column-wise linear matrix index ordering with the recorded data indexed as sensor_data(sensor_position, time). The final pressure field over the complete computational grid can also be obtained by setting sensor.record to {'p', 'p_final'}. In this case, the output sensor_data is returned as a structure with the outputs appended as the structure fields sensor_data.p and sensor_data.p_final.

Compared to the first-order simulation functions kspaceFirstOrder1D, kspaceFirstOrder2D, and kspaceFirstOrder3D, kspaceSecondOrder is restricted to homogeneous media and has less functionality. However, it is also more computationally efficient and allows an initial pressure gradient to be specified.

Inputs

kgrid	k-Wave 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	homogeneous sound speed within the acoustic medium [m/s]
medium.alpha_power	power law absorption exponent
medium.alpha_coeff	power law absorption coefficient [dB/(MHz^y cm)]
source.p0	initial pressure within the acoustic medium
source.dp0dt	initial pressure gradient within the acoustic medium
sensor.mask	binary grid specifying where the pressure is recorded at each time-step
sensor.record	cell array of the acoustic parameters to record in the form sensor.record = {'p'}; valid inputs are:   'p' (acoustic pressure)   'p_final' (final pressure field at all grid points)

Optional Inputs

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

Input	Valid Settings	Default	Description
'ExpandGrid'	(Boolean scalar)	false	Boolean controlling whether the grid size is expanded on two sides to delay the time before wave wrapping occurs.
'MeshPlot'	(Boolean scalar)	false	Boolean controlling whether mesh is used in place of imagesc to plot the pressure field.
'PlotFrames'	(Boolean scalar)	false	Boolean controlling whether the pressure field for each time step is plotted in a new window.
'PlotFreq'	(integer numeric scalar)	10	The number of iterations which must pass before the simulation plot is updated.
'PlotScale'	(numeric two element vector)	[-1, 1]	[min, max] values used to control the scaling for imagesc (visualisation).
'PlotSim'	(Boolean scalar)	true	Boolean controlling whether the simulation iterations are progressively plotted.
'Smooth'	(Boolean scalar)	true	Boolean controlling whether source.p0 is smoothed using smooth before computation.

Outputs

If sensor.record is not defined by the user:

sensor_data

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

If sensor.record is defined by the user:

sensor_data.p	time varying pressure recorded at the sensor positions given by sensor.mask (returned if 'p' is set)
sensor_data.p_final	final pressure field at all grid points within the domain (returned if 'p_final' is set)

Examples

• Comparison Of Modelling Functions
• Setting An Initial Pressure Gradient
• Modelling Power Law Absorption

See Also

kspaceFirstOrder1D, kspaceFirstOrder2D, kspaceFirstOrder3D, makeGrid, makeTime, smooth

kspacePlaneRecon

loadImage

© 2009-2014 Bradley Treeby and Ben Cox.