k-Wave

1. Mucong Li
   

   Member
   Joined: Dec '14
   Posts: 2

   Hi, I'm using the k-wave toolbox to simulate the receiving pressure of a transducer. An acoustic source was put at the acoustic axis. A single pulse was transmitted from the source and its frequency was set to be 10MHz, which is within the supported maximal frequency (13.2MHz).

   I noticed that the waveform I got from the transducer is quite different from the waveform transmitted from the source, which seems to affect the beam-forming results significantly. And when I alter the frequency of the source, the received waveform also changed. I think it's mainly caused by the impulse response of the transducer.

   So I would like to know the define of the impulse response of the transducer. Or can I define it by myself?

   Thanks~

   Mucong Li

   Posted 9 years ago #

2. Mucong Li
   

   Member
   Joined: Dec '14
   Posts: 2

   Recently, I'm doing some simulations to compare the transmission pressure and receiving pressure differences between the focused and unfocused transducers. I did the transmission simulation in FIELD II and the receiving simulation in K-Wave (a single source put at the focus), and compared the two results.

   The maximal pressure ratios of the focused and unfocused transducers should be nearly the same in transmission and receiving process intuitively. But the results indicates big difference between these two values, and this difference seems to increase as the growth of the signal frequency (pulsed signal).

   On the other hand, what also confuses me is that the maximal pressure ratio between the focused and unfocused transducer is much smaller than I expected,like 2.7291 at 5MHz and 3.029 at 6.75MHz.

   My guess is that K-Wave leaves out some higher frequencies because of the grid space, especially in high frequency pulses whose bandwidth is broader. And I'm not sure if the K-Wave has taken the effect of near field into consideration.

   Eager to know if my guess is right. Thank you in advance for your reply!!

   Posted 9 years ago #

3. bencox
   

   Developer
   Joined: Mar '10
   Posts: 292

   Hi Mucong Li,

   Thanks for your post, and sorry for the delay in replying. We've all been on holiday for Christmas.

   k-Wave solves the acoustic wave equation so will include the near field, but (like any model) it is bandlimited, ie. it only includes frequencies below some maximum frequency. This is because of the grid spacing, as you say. For example, if you put in a time series which contains frequencies higher than can be supported by the grid, they will not propagate, and so, to that extent, the signal will be low-pass filtered and you may see some 'ringing' where the signal changes rapidly. If using a single cycle of a sine wave you may see spurious oscillations at the ends of the cycle where the signal changes sharply to zero. This can be dealt with by removing those frequencies from the source signal by usingfilterTimeSeries.

   There are two ways in which sources can be applied in k-Wave and they are selected by setting source.p_mode to either 'additive', which is the default, or 'dirichlet'. 'Additive' mode adds each successive value of source.p to the existing value of the pressure at the source points, whereas 'Dirichlet' mode replaces them, ie. discards the current value and forces the source points to take the value in source.p. There are two significant differences between these modes. First, waves are reflected by the source points when in 'Dirichlet' mode - effectively the source points behave like a Dirichlet boundary with an imposed time varying pressure (given by source.p), but waves are not reflected when in 'additive' mode. Second, the amplitude of the source at the source point when in 'Dirichlet' mode will be the same as the amplitude defined in source.p; they must be as these values are imposed directly on the source points. In 'additive' mode, however, it is a bit more involved.

   In 'additive' mode, the value in source.p is added to the pressure already at the source point, and the resulting pressure at any given point will be the convolution of source.p with the k-Wave impulse response function. In the case of a homogeneous medium k-Wave's impulse response function will be the convolution of the free space Green's function with the bandlimited interpolant (see the k-Wave manual.) This will have the effect of changing the effective amplitude of the source. k-Wave includes a scaling factor which accounts for this when source.p is sufficiently long (also described in the Manual).

   Hope that helps.

   Ben

   Posted 9 years ago #

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