http://www.k-wave.org/forum/topic/seems-attenuation-settings-following-power-law-affect-signals-time-of-arrival Support for the k-Wave MATLAB toolbox en-US Tue, 12 May 2026 23:34:20 +0000 http://bbpress.org/?v=1.0.2 q http://www.k-wave.org/forum/search.php http://www.k-wave.org/forum/topic/seems-attenuation-settings-following-power-law-affect-signals-time-of-arrival#post-9221 Mon, 14 Jul 2025 07:59:55 +0000 NicholasHorton 9221@http://www.k-wave.org/forum/ <p>Hi everyone,<br /> I was working on the simulation of ultrasound propagation. I designed three homogeneous mediums. Their speed-of-sounds were 1500 m/s. Their densities were 1000 kg/m^3. Their alpha_power were set as 1.1. Their alpha_coeff were 0.002, 0.7, and 3.0, respectively.<br /> A sensor was set to record transmitted signal.<br /> I just found that with different alpha_coeff, the time-of-arrivals of the signals were different. The larger alpha_coeff was, the earlier the signal arrived.<br /> The change was so significant that it was counter-intuitive. I wonder if dispersion can explain this phenomenon.<br /> I would like to ask you, is this simulation result consistent with the physical phenomenon? If not, how should I correct my code?<br /> The code has been attached below.<br /> Thanks a lot.<br /> <pre><code>% To compare TOFs of transmitted signals, with different [constant] att.s or wvfroms. % * The 2-D numerical simulations are based on k-Wave toolbox % * Emitted pulse: a 3-cycle tone-burst whose centre-frequency is 2 MHz % * Emitter and receiver: two points about 25 cm apart, recording transmitted signal % * Medium: homogeneous, whose attenuation power is 1.1, and attenuation coefficient % is 0.002, 0.7 or 3.0 dB/cm/MHz^1.1 clc;clear close all %% Define Params % default medium params sos_ref = 1500; % [m/s] density_ref = 1000; % [kg/m^3] att_power = 1.1; % y % define k-Wave Grid Nx = 3072; dx = 1e-4; kgrid = kWaveGrid(Nx, dx, Nx, dx); t_end = Nx * dx / sos_ref * 2; kgrid.makeTime(sos_ref, 0.5, t_end); % CFL = 0.5 % different wvforms and att.s small_att = 0.002; % dB/cm/MHz^y big_att = 0.7; bigger_att = 3.0; wv_tb = toneBurst(1./kgrid.dt, 2e6, 3, &#39;SignalLength&#39;, kgrid.Nt); %% Define numerical phantom %------------define Medium One, no attenuation at all medium_noAtt.sound_speed = sos_ref * ones(Nx); medium_noAtt.density = density_ref * ones(Nx); %------------define Medium Two, with a small atten. coeff., medium_smallAtt = medium_noAtt; medium_smallAtt.alpha_power = att_power; medium_smallAtt.alpha_coeff = small_att * ones(Nx); %------------define Medium Three, with a big atten. coeff., medium_bigAtt = medium_smallAtt; medium_bigAtt.alpha_coeff = big_att * ones(Nx); %------------define Medium Three, with a big atten. coeff., medium_biggerAtt = medium_smallAtt; medium_biggerAtt.alpha_coeff = bigger_att * ones(Nx); %% Define source &amp; sensor source.p_mask = zeros(Nx, Nx); source.p_mask(Nx / 2, 250) = 1; sensor.mask = zeros(Nx, Nx) sensor.mask(Nx / 2, Nx - 250) = 1; % source.p not defined %% Execute the simulations input_args = {&#39;PMLSize&#39;, &#39;auto&#39;,... &#39;PMLInside&#39;, false,... &#39;PlotPML&#39;, false,... &#39;DisplayMask&#39;, &#39;off&#39;,... &#39;DataPath&#39;, pwd,... &#39;DeleteData&#39;, false}; for medium_name = {&#39;smallAtt&#39;, &#39;bigAtt&#39;, &#39;biggerAtt&#39;} cmd = [&#39;medium = medium_&#39;, medium_name{1}, &#39;;&#39;]; eval(cmd) source.p = wv_tb; rf_data = kspaceFirstOrder2DC(kgrid, medium, source, sensor, input_args{:}); cmd = [&#39;sig_&#39;, medium_name{1}, &#39; = rf_data;&#39;]; eval(cmd) end %% Visulaization f1 = figure(&#39;Units&#39;,&#39;centimeters&#39;, &#39;Position&#39;, [2, 2, 25, 40]); plt_cnt = 0; plt_c = 3; plt_r = 1; range_ = [160, 175] * 1e-6; % unit: s for medium_name = { &#39;smallAtt&#39;, &#39;bigAtt&#39;, &#39;biggerAtt&#39;} cmd = [&#39;sig = sig_&#39;, medium_name{1}, &#39;;&#39;]; eval(cmd) env = abs(hilbert(sig)); % ---------- plt_cnt = plt_cnt + 1; subplot(plt_c, plt_r, plt_cnt) plot(kgrid.t_array * 1e6, env, &#39;color&#39;,&#39;r&#39;, &#39;lineWidth&#39;, 1.5) grid on grid minor xlabel(&#39;Time [\mus]&#39;) xlim(range_ * 1e6) title(medium_name{1}, &#39;Interpreter&#39;, &#39;none&#39;) end sgtitle(&#39;Signal Envelope&#39;)</code></pre>