k-Wave

1. DanR
   

   Member
   Joined: Mar '11
   Posts: 9

   Hi Brad,
   I cannot explain the differences I am getting between two different types of sources in absorbing media with different alphas. I set up a test situation with a plane wave CW (1 MHz) source 10 cm from a single sensor and looked at the sensor data. I recorded relative pressure values of .43 and .032 for alpha of 0.75 and 3.0, respectively, compared to the value I got with no absorption. These values are virtually the same as those I calculate from the known distance and alpha coefficients. The simulation and I seem to be on the same page here.

   The problem comes when I switch to an initial value disk source with the same sensor distance. Now I measure the relative pressures (determined by the peak value of the sensor data) as 0.83 and 0.65. Absorption is having a much smaller effect here. By looking at the relative measurements, I have assumed that the geometric spreading will be common to all. These results were for ideal wide-BW transducers, and were comparable for disks sources of 1.6 and 4 mm diameter, with a high resolution grid of 0.2 mm/voxel.

   Do these results make sense to you? I appreciate any insight you can offer.
   Thanks,
   Dan

   Posted 12 years ago #

2. Bradley Treeby
   

   Developer
   Joined: Mar '10
   Posts: 1,640

   Hi Dan,

   The difference arises because of the frequency content in the source. The CW source has a single frequency and thus the absorption can be extracted by examining the magnitude of the pressure signal at different positions as you have done. The initial value disk creates a broadband source which contains many frequencies (the exact frequency content will depend on the size and shape of the source, the properties of the grid, and any smoothing that has been done). Because the specified absorption is typically dependent on frequency, using the overall magnitude of the pressure signal at different positions no longer corresponds to the absorption of the individual frequency components.

   If you look at the amplitude spectrum at the two different positions (using spectrum or similar), you should see the same relative decay of the 1 MHz frequency component. However, because the initial value disk also contains low frequency components which are not attenuated very much, the overall magnitude of the pressure may give the impression that absorption is having a smaller effect.

   I hope that helps. Let me know if you have any more questions.

   Brad.

   Posted 12 years ago #

3. DanR
   

   Member
   Joined: Mar '11
   Posts: 9

   Hi Brad,
   Thanks for reminding me of the broadband nature of the photoacoustic pulse. I did not fully appreciate how much of the energy is in the lower frequency range where attenuation is substantially lower. I ran simulations with disc sources, 0.6 and 1 mm diameter, and looked at the spectra for a medium with no attenuation and attenuation equivalent to breast tissue (alpha = 0.75). I also varied the frequency response of the sensors from an ideal wide bandwidth to one with a 2 MHz bandwidth. Here is the link to the resulting spectra on imageshack:
   

   For absorbing tissue, higher wavelengths are significantly more reduced, as expected, but a lot of low frequency content remains. The pressure at the sensors is therefore higher than the pressure I found with the single wavelength plane wave.

   As you suggested, I looked at one frequency, 1 MHz for example, and found the reduction in signal does agree with the plane wave simulation and the calculated attenuation. All is right again!

   My simulations show that objects that I consider to be pretty small, 0.6 mm and 1 mm, still have a lot of frequency content below the sensitivity of transducers that we typically use, about 2-5 MHz. It is impressive how little of the signal we are apparently using.

   Thanks again for your help,
   Dan

   Posted 12 years ago #

4. Bradley Treeby
   

   Developer
   Joined: Mar '10
   Posts: 1,640

   Hi Dan,

   Thanks for getting back to us with the results of your simulations, the results look very interesting (this sort of feedback is also really useful for us to know what k-Wave is being used for).

   We have also noticed the very broadband nature of experimental photoacoustic signals. For example, see here, Fig. 1(a) and here, Fig. 2(b).

   Kind regards,

   Brad.

   Posted 12 years ago #

5. WXia
   

   Member
   Joined: Aug '11
   Posts: 4

   Hi Brad and Dan,

   It is a very interesting discussion. I have made similar simulations and have got similar results. There is something that still not clear for me. For example in the simulation results from Dan, the signal generated from 0.6 mm object has frequency peak around 500 kHz, is this suppose to be too low? Might it has something to do with a 2D simulation instead of 3D?

   Another question is about choosing the pixel size in 2D simualtions. If I wanted to simulate a 0.2 mm object, is pixel size 0.1 mm enough? When I simulate a 0.2 mm object with 0.1 mm pixel size, the signal has frequency peak also around 500 kHz, which is strange for me.

   Do you have any idea about this?

   Thanks!
   Wenfeng

   Posted 12 years ago #

6. bencox
   

   Developer
   Joined: Mar '10
   Posts: 285

   Dear Wenfeng,

   Apologies for the delay in replying - we've both been away.

   There will certainly be differences in the temporal signals when your initial pressure distribution is a disc in 2D and when it is a ball (filled sphere) in 3D, eg. the free space Green's functions have quite different forms in 2D and 3D. Some analytical work has been done on this by G. Diebold and his collaborators, which would be worth looking up.

   Thinking for a moment about the frequency content from a photoacoustic signal generated in real life - not in the model - the frequencies generated will depend on the frequencies in the temporal heating pulse and on the shape (size, sharpness of edges, etc) of the object being illuminated. In the simulation, the number of pixels representing the object will dictate (or limit) the edge sharpness, so you will need to think about that.

   Hope that helps,

   Ben

   Posted 12 years ago #

7. Yan
   

   Member
   Joined: Dec '19
   Posts: 6

   Dear Bencox,

   Is there any paper demonstrating the relationship of the frequencies generated by a specified source being illuminated and the frequencies of the temporal heating pulse?

   It would be grateful if you can give some your insight on this!

   Thanks!

   Yan

   Posted 4 years ago #

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