k-Wave

1. emanuelepeschiera
   

   Member
   Joined: Mar '20
   Posts: 1

   Hi,
   for a thesis project we are simulating ultrasound waves propagation in bubbly media, focusing on multiple scattering phenomena.
   The background medium is set to muscle.

   We're currently trying to introduce attenuation in muscle using
   alpha_coeff = 0.57,
   alpha_power = 0.99 (or alpha_power = 1.01).

   What we notice is an increase/decrease of the wave velocity (depending on alpha_power being >/< 1) respect to the case without attenuation.
   We know that attenuation is made by absorption + dispersion, and dispersion could change the velocity of the different harmonic components (Kramers-Kronig relationships). This would result in a 'distorsion' of the transmitted pulse, and this effect would be more evident as frequency increases.
   Nevertheless, in our code the velocity of the harmonics seems to be constant, resulting in a progressive shift, as space increases, independent from the frequency (we use central frequencies ranging from 1 to 5 MHz).

   Our question is: is the velocity variation due to dispersion? Or is it related to other reasons such as numerical ones?

   Another thing we tried is to set alpha_mode to 'no_dispersion'. This didn't change the results, making it seem like the delay is not due to dispersion.
   The doubt here is that we don't know if 'no_dispersion' works: for instance, the documentation suggests to set alpha_mode = 'no_dispersion' if you want to model an alpha_power exactly 1. Trying this, the code returns the same error of the case alpha_power = 1 and dispersion present.

   Thank you for the answers!

   Posted 5 years ago #

2. Bradley Treeby
   

   Developer
   Joined: Mar '10
   Posts: 1,643

   Hi emanuelepeschiera,

   For power law values very close to 1, there is a strong dependence of the sound speed on frequency.

   Try opening the http://www.k-wave.org/documentation/example_na_modelling_absorption.php and replacing the absorption properties (around line 91) with your values:

   % define the absorption properties of the propagation medium
   switch loop
       case 1
           medium.alpha_coeff = 0.57;
           medium.alpha_power = 1.01;
       case 2
           medium.alpha_coeff = 0.57;
           medium.alpha_power = 0.99;
       case 3
           medium.alpha_coeff = 0.57;
           medium.alpha_power = 1.01;
           medium.alpha_mode = 'no_dispersion';
   end

   This more or less confirms exactly what you're seeing. For the case of no_dispersion, the sound speed comes out at the background value (i.e., unchanged). If you move the power law exponent a bit further away from 1, the effect is much less pronounced.

   The no dispersion flag just turns off one of the terms in the absorption operator. If you read the original paper, to first order, one of the terms accounts for absorption and the other to dispersion.

   Brad

   Posted 5 years ago #

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