http://www.k-wave.org/forum/topic/volume-rate-of-heat-deposition-as-divergence-of-intensity Support for the k-Wave MATLAB toolbox en-US Thu, 14 May 2026 23:25:18 +0000 http://bbpress.org/?v=1.0.2 q http://www.k-wave.org/forum/search.php http://www.k-wave.org/forum/topic/volume-rate-of-heat-deposition-as-divergence-of-intensity#post-8692 Wed, 11 Jan 2023 00:26:48 +0000 Manuel Vielma 8692@http://www.k-wave.org/forum/ <p>In equation 6 of their recent (October 2022) paper [1], Kleparnik, Zemcik, Treeby and Jaros define the volume rate of heat deposition, Q, as</p> <p>Q = -div(I_avg) = - d(Ix_avg)/dx - d(Iy_avg)/dy - d(Iz_avg)/dz (1),</p> <p>(the second equality has been introduced by me for explicitness). This is in line with early expressions such as e.g. the one given by Nyborg in [2].</p> <p>To my knowledge, eq. (1) is not used in any of the k-wave examples. When I use it to compare with the temperature output that other expressions, such as</p> <p>Q = p^2/(density*sound_speed) (2) -- plane wave approximation<br /> or<br /> Q = alpha_np * abs(I_avg) (3),</p> <p>lead to in example_diff_focused_ultrasound_heating, I get very different results -- the ones given by (1) seem particularly odd. More precisely, what I am doing is running this example for the different Qs shown below:</p> <p>============================<br /> <pre><code>% Heating By A Focused Ultrasound Transducer [...] % set the sensor mask to cover the entire grid sensor.mask = ones(Nx, Ny); sensor.record = {&#39;p&#39;, &#39;p_max_all&#39;, &#39;I_avg&#39;}; %Include I_avg in recorded data [...] % ========================================================================= % CALCULATE HEATING % ========================================================================= % convert the absorption coefficient to nepers/m alpha_np = db2neper(medium.alpha_coeff, medium.alpha_power) * ... (2 * pi * freq).^medium.alpha_power; % extract the pressure amplitude at each position p = extractAmpPhase(sensor_data.p, 1/kgrid.dt, freq); % reshape the data, and calculate the volume rate of heat deposition p = reshape(p, Nx, Ny); %Q = alpha_np .* p.^2 ./ (medium.density .* medium.sound_speed); % Plane wave approximation I_avg_x = reshape(sensor_data.Ix_avg, Nx,Ny); I_avg_y = reshape(sensor_data.Iy_avg, Nx,Ny); %Q = alpha_np .* sqrt(I_avg_x.^2 + I_avg_y.^2); Q = -divergence(I_avg_x, I_avg_y); [...]</code></pre> <p>====================================</p> <p>MY QUESTION IS: how should eq. (1) be used in a thermal simulation in k-wave? Any idea why seemingly inconsistent answers are obtained when using it in the aforementioned example?</p> <p>This post mentions the gradient (?) of the intensity, but no further details are provided: <a href="http://www.k-wave.org/forum/topic/doubts-converting-pressure-into-heat-deposition" rel="nofollow">http://www.k-wave.org/forum/topic/doubts-converting-pressure-into-heat-deposition</a></p> <p>Many thanks in advance for any clarification you may provide.</p> <p>Manuel<br /> ______________________________</p> <p>[1] Kleparnik, P., Zemcik, P., Treeby, B. E., &amp; Jaros, J. (2022). On-the-Fly Calculation of Time-Averaged Acoustic Intensity in Time-Domain Ultrasound Simulations Using a k-Space Pseudospectral Method. IEEE transactions on ultrasonics, ferroelectrics, and frequency control, 69(10), 2917–2929. <a href="https://doi.org/10.1109/TUFFC.2022.3199173" rel="nofollow">https://doi.org/10.1109/TUFFC.2022.3199173</a></p> <p>[2] Nyborg (1981). Heat generation by ultrasound in a relaxing medium. The Journal of the Acoustical Society of America 70, 310 (1981); <a href="https://doi.org/10.1121/1.386778" rel="nofollow">https://doi.org/10.1121/1.386778</a> </p>