k-Wave

1. H_Frechen
   

   Member
   Joined: Nov '16
   Posts: 3

   Hi,

   I have a setup, where I measure and simulate ultrasonics on multi-layer polymeric structures. The materials can have high attenuation coefficients, e.g y = 1.18, alpha_coeff = 4 dB/(MHz^y*cm) or even higher. Furthermore the exponent is not always the same for all materials. For my larger samples (d=20.5 mm) I expected an amplitude reduction of the initial 5 MHz impulse based on the acoustical paramters of the main material:
   alpha = 4*5^1.18 = 26.7 dB/cm
   Resulting amplitude reduction ca. 110 dB (alpha*2*d)

   For verification, I first compared measurement results with a simple A-Scan model, where a plane wave and just reflection/transmission and attenuation coefficients of the different layers are taken into account (cf. H. Azhari, Basics of biomedical ultrasound for engineers). I could get a good agreement for the amplitude reduction, i.e. the amplitude of a reflection at an inner interface is in the range of 5e-6 compared to the reflection on the surface of the sample (amplitude normalized to 1). But this simplified model of course does not contain a frequency dependent attenuation. Thus, the shape of the measured and simulated signal differed greatly.

   After that I performed 1D and 3D k-wave simulations with the same sample setup and acoustical parameters. CFL was varied down to 0.1. In all cases I could achieve a frequency dependent attenuation and the signal shape showed an improved resemblance to the measured signal. But the amplitude of the k-wave simulated signal is in the range of 2e-2, which is four orders of magnitude larger than the measurement/simplified model results.

   Therefore three questions:
   1.) In many comments it was written, that the k-wave toolbox may not function properly at high attenuation values. Could this already be the explanation for the amplitude difference?
   2.) The alpha_power exponent can only be put as a scalar for the whole domain. Since the materials in the domain have different exponents, I chose the exponent of the material of the thickest layer in the domain. All other attenuation coefficients are therefore slightly off (e.g. y1 = 1.18, y2 = 1.01). Is there any experience how large the effect of different exponents is?
   3.) Will a variation of the alpha_power exponent across the simulation domain be possible in the future?

   Kind regards
   Henning

   Posted 6 years ago #

2. Bradley Treeby
   

   Developer
   Joined: Mar '10
   Posts: 1,640

   Hi Henning,

   If you are modelling very high attenuation values, you need to adjust the parameters you input into k-Wave. You can get the adjusted values using the function fitPowerLawParams. There is an example of this here (see Fig. 2). However, this is not going to change the amplitude by four orders of magnitude. Have you double checked against your simple model when no attenuation is included?

   You are correct that only one power law can be used. One option is to then adjust the alpha_coeff parameters for the other layers so you can get the correct absorption at a particular frequency, e.g.,

   alpha_coeff_new = alpha_coeff * f_ref^(alpha_power - alpha_power_ref);

   In principle, it is possible to have spatially varying alpha_power, however, this means we would have to compute the inverse transform using a spatially-weighted Fourier transform, which has to be implemented as a matrix multiplication rather than an FFT (the same holds for the k-space operator). We don't have any immediate plans to do this. Although at some point we might add it as an option.

   Hope that helps,

   Brad.

   Posted 6 years ago #

3. H_Frechen
   

   Member
   Joined: Nov '16
   Posts: 3

   Hi Brad,

   many thanks for your reply and your great support in this forum. I already learned alot just by reading the different posts of other authors.

   I tried the fitPowerLawParams function and got the new y_fit = 1.2041 and a0_fit = 4.3499 using the above mentioned values. But as you said, this will most probably not explain the four orders of magnitude.

   I also tried your approach with different values for alpha_power_ref
   alpha_coeff_new = alpha_coeff * f_ref^(alpha_power - alpha_power_ref);
   But this also did not improve the results.

   Lastly, I did double check the simple model another time. But since the amplitude reduction fits really well to the values of the lab measurements on the sample, I am currently a little bit confused.

   If by any chance, you have the time to look on my code I uploaded it here (since it is rather long):
   https://git.rwth-aachen.de/frechen/US_Simulation

   Best regards
   Henning

   Posted 6 years ago #

4. Bradley Treeby
   

   Developer
   Joined: Mar '10
   Posts: 1,640

   Hi Henning,

   I took a brief look at your code (although didn't run it), and no immediate red flags. As you have quite large sound speed changes, you will need to watch out for numerical dispersion. A good approach is to set the reference sound speed to the background medium, and then make sure your time step is small enough for stability.

   Did you double check that your k-Wave simulation gives you the expected results when no absorption is included?

   If you can replicate your problem in a simple script that's fast to run (e.g., in 2D), I can dig a bit further.

   Brad.

   Posted 6 years ago #

5. H_Frechen
   

   Member
   Joined: Nov '16
   Posts: 3

   Hi Brad,

   I made a few more investigations. I uploaded the scripts for the 2D case and comparison figures between simple model and 2D-k-Wave for the cases:
   1. No Absorption (k-Wave CFL 0.2)
   2. Absorption (k-Wave CFL 0.2)
   3. Absorption (k-Wave CFL 0.1)

   You can find the on my gitlab.

   For the first case without absorption, both models agree rather well. Of course there are some smaller deviations due to the geometry of the sample, which cannot be represented by the simple model. For cases 2 and 3 on the other hand, there is still the huge deviation in amplitude. A change of the CFL from 0.2 to 0.1 did not change the results very much.

   Best regards
   Henning

   Posted 6 years ago #

6. Bradley Treeby
   

   Developer
   Joined: Mar '10
   Posts: 1,640

   Hi Henning,

   Are you comparing the amplitude of the time trace, or the spectrum? If I run your absorbing simulation, and then replace medium.alpha_coeff with alpha_coef_water and compare the spectrum of the two signals using:

   spect(scan(19000:23000), 1/kgrid.dt, 'Plot', [true, false]);

   At 5 MHz, the signal reduction is around 128 dB, which is roughly what you might expect given the absorption in the layers.

   Hope that helps,

   Brad.

   Posted 6 years ago #

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