Contents
% 2D simulation of linear array % % This example demonstrates the use of k-Wave simulation of ultrasounic % beams in a 2D domain and how it can interact with USTB structures. % % authors: Alfonso Rodriguez-Molares <alfonso.r.molares@ntnu.no> % % Based on code by Bradley Treeby k-Wave Toolbox (http://www.k-wave.org) % Copyright (C) 2009-2017 Bradley Treeby % % Last updated: 30.10.2018 close all;
Basic definitions
We define some constants to be used on the script
f0 = 2e6; % pulse center frequency [Hz] cycles=2; % number of cycles in pulse c0 = 1540; % medium speed of sound [m/s] rho0 = 1020; % medium density [kg/m3] F_number = 1.7; % F number for CPWC sequence (i.e. maximum angle) N=1; % number of plane waves in CPWC sequence
uff.probe
We define the ultrasound probe as a USTB structure.
prb=uff.linear_array(); prb.N=128; % number of elements prb.pitch=300e-6; % probe pitch in azimuth [m] prb.element_width=300e-6; % element width [m] prb.element_height=5000e-6; % element height [m] fig_handle = prb.plot([],'Linear array');
Computational grid
We can define the computational grid as a uff.linear_scan strcuture. We set different resolution options depending on frequency reference speed of sound.
f_max = 1.2*f0; lambda_min = c0/f_max; % mesh resolution, choose one mesh_resolution='element2'; switch mesh_resolution case 'element2' % around 50 sec per wave dx=prb.pitch/2; % 2 elements per pitch case 'element4' % around 6min sec per wave dx=prb.pitch/4; % 2 elements per pitch otherwise error('Not a valid option'); end % mesh size PML_size = 20; % size of the PML in grid points Nx=round(40e-3/dx); Nx=Nx+mod(Nx,2); Nz=round(40e-3/dx); Nz=Nz+mod(Nz,2); grid_width=Nx*dx; grid_depth=Nz*dx; domain=uff.linear_scan('x_axis', linspace(-grid_width/2,grid_width/2,Nx).', 'z_axis', linspace(0,grid_depth,Nz).'); kgrid = kWaveGrid(domain.N_z_axis, domain.z_step, domain.N_x_axis, domain.x_step);
Propagation medium
We define the medium based by setting the sound speed and density in every pixel of the uff.scan. Here we set an hyperechoic cyst at the center of the domain.
% transparent background medium.sound_speed = c0*ones(domain.N_z_axis, domain.N_x_axis); % sound speed [m/s] medium.density = rho0.*ones(domain.N_z_axis, domain.N_x_axis); % density [kg/m3] % include fat layer fat_std = 3/100; cn=abs(domain.z-(10e-3 + 0.025e-3*sin(2*pi*domain.x/5e-3)))<0.5e-3; medium.sound_speed(cn) = random('normal',1450,1450*fat_std,size(medium.sound_speed(cn))); % sound speed [m/s] medium.density(cn) = random('normal',950,950*fat_std,size(medium.density(cn))); % density [kg/m3] % include cyst cyst_std = 3/100; cx=0; cz=20e-3; cr = 5e-3; cn=sqrt((domain.x-cx).^2+(domain.z-cz).^2)<cr; medium.sound_speed(cn) = random('normal',1540,1540*cyst_std,size(medium.sound_speed(cn))); % sound speed [m/s] medium.density(cn) = random('normal',1020,1020*cyst_std,size(medium.density(cn))); % density [kg/m3] % include point if true cx=0; cz=20e-3; cr = 0.06125e-3; cn=sqrt((domain.x-cx).^2+(domain.z-cz).^2)<cr; medium.sound_speed(cn) = 1450; % sound speed [m/s] medium.density(cn) = 1020; % density [kg/m3] end % attenuation medium.alpha_coeff = 0.3; % [dB/(MHz^y cm)] medium.alpha_power = 1.5; % show physical map: speed of sound and density figure; subplot(1,2,1); imagesc(domain.x_axis*1e3,domain.z_axis*1e3,medium.sound_speed); colormap gray; colorbar; axis equal tight; xlabel('x [mm]'); ylabel('z [mm]'); title('c_0 [m/s]'); subplot(1,2,2); imagesc(domain.x_axis*1e3,domain.z_axis*1e3,medium.density); colormap gray; colorbar; axis equal tight; xlabel('x [mm]'); ylabel('z [mm]'); title('\rho [kg/m^3]');
Time vector
We define the time vector depending on the CFL number, the size of the domain and the mean speed of sound.
cfl=0.3; t_end=2*sqrt(grid_depth.^2+grid_depth.^2)/mean(medium.sound_speed(:)); kgrid.makeTime(medium.sound_speed,cfl,t_end);
Sequence
We define a sequence of plane-waves
alpha_max=1/2/F_number; % maximum angle span [rad] if N>1 angles=linspace(-alpha_max,alpha_max,N); % angle vector [rad] else angles = 0; end seq=uff.wave(); for n=1:N seq(n)=uff.wave(); seq(n).apodization = uff.apodization('f_number',1,'window',uff.window.rectangular,'focus',uff.scan('xyz',[0 0 10e-3])); seq(n).source.azimuth=angles(n); seq(n).source.distance=-Inf; seq(n).probe=prb; seq(n).sound_speed=1540; % reference speed of sound [m/s] seq(n).delay = min(seq(n).delay_values); seq(n).source.plot(fig_handle); end
Source & sensor mask
Based on the uff.probe we find the pixels in the domain that must work as source and sensors.
% find the grid-points that match the element source_pixels={}; element_sensor_index = {}; n=1; for m=1:prb.N_elements plot((prb.x(m)+[-prb.width(m)/2 prb.width(m)/2])*1e3,[0 0],'k+-'); hold on; grid on; source_pixels{m}=find(abs(domain.x-prb.x(m))<prb.width(m)/2 & abs(domain.y-prb.y(m))<prb.height(m) & abs(domain.z-prb.z(m))<=domain.z_step/2); element_sensor_index{m} = n:n+numel(source_pixels{m})-1; n=n+numel(source_pixels{m}); end % sensor mask sensor.mask = zeros(domain.N_z_axis, domain.N_x_axis); for m=1:prb.N_elements sensor.mask(source_pixels{m}) = sensor.mask(source_pixels{m}) + 1; end % source mask source.u_mask=sensor.mask; figure; h=pcolor(domain.x_axis,domain.z_axis,source.u_mask); axis equal tight; title('Source/Sensor mask') set(h,'edgecolor','none'); set(gca,'YDir','reverse'); xlabel('x [mm]'); ylabel('z [mm]');
Calculation
We are ready to launch the k-Wave calculation
disp('Launching kWave. This can take a while.'); for n=1:N delay=seq(n).delay_values-seq(n).delay; denay=round(delay/kgrid.dt); seq(n).delay = seq(n).delay - cycles/f0/2; % offsets tone_burst_offset = []; for m=1:prb.N_elements tone_burst_offset = [tone_burst_offset repmat(denay(m),1,numel(source_pixels{m}))]; end source.ux = toneBurst(1/kgrid.dt, f0, cycles, 'SignalOffset', tone_burst_offset); % create the tone burst signals source.uy = 0.*source.ux; source.u_mode ='dirichlet'; % set the input arguements: force the PML to be outside the computational % grid; switch off p0 smoothing within kspaceFirstOrder2D input_args = {'PMLInside', false, 'PMLSize', PML_size, 'PlotPML', false, 'Smooth', false}; % run the simulation sensor_data(:,:,n) = permute(kspaceFirstOrder2D(kgrid, medium, source, sensor, input_args{:}),[2 1]); end sensor_data(isnan(sensor_data))=0;
Index exceeds the number of array elements (1).
Error in CPWC_linear_array_cyst_fat (line 182)
disp('Launching kWave. This can take a while.');
Gather element signals
After calculaton we combine the signal recorded by the sensors according to the corresponding element
element_data=zeros(numel(kgrid.t_array),prb.N_elements,numel(seq)); for m=1:prb.N_elements if ~isempty(element_sensor_index{m}) element_data(:,m,:)=bsxfun(@times,sqrt(1./kgrid.t_array).',trapz(kgrid.y(source_pixels{m}),sensor_data(:,element_sensor_index{m},:),2)); end end
Band-pass filter
We remove some numerical noise by band-pass filtering
filtered_element_data=tools.band_pass(element_data,1/kgrid.dt,[0 1e6 8e6 10e6]);
Channel_data
We can now store the simulated data into a uff.channel_data class
channel_data = uff.channel_data();
channel_data.probe = prb;
channel_data.sequence = seq;
channel_data.initial_time = 0;
channel_data.sampling_frequency = 1/kgrid.dt;
channel_data.data = filtered_element_data;
% taking care of NaNs
channel_data.data(isnan(channel_data.data))=0;
Beamforming
To beamform we define a new (coarser) uff.linear_scan. We also define the processing pipeline and launch the beamformer
domain=uff.linear_scan('x_axis',linspace(domain.x_axis(1),domain.x_axis(end),512).',... 'z_axis',linspace(domain.z_axis(1),domain.z_axis(end),512).'); pipe = pipeline(); pipe.channel_data = channel_data; pipe.scan = domain; pipe.receive_apodization.window = uff.window.hanning; pipe.receive_apodization.f_number = F_number; b=postprocess.coherent_compounding(); b.dimension = dimension.both; das = pipe.go({midprocess.das b}); das.plot([],'DAS'); hold on;