I got some counter-intuitive results that I could use some insight on.
I ran 3D simulations with a single-element transducer facing towards an example skull. The simulations were done over two different areas of the skull for comparison: parietal bone (thick, curved) and temporal bone (flatter, thinner). Voxels within skull were set to medium properties of skull (bulk), and everything else was set to properties of brain. An average of peak pressures past the skull (within “brain”) were noted. This average peak was compared to the average peak in an identical simulation with medium properties set to those of water. A mean of peak values in water were noted, creating an estimate of attenuation: pressure peak ratio (brain / water). This was done on 9 different example skulls.
Counter to my expectations, the peak pressure ratio for the simulation over temporal bone (flatter, thinner) was lower than that of parietal bone (thicker, curved)—about 0.4 and 0.5 respectively. In other words, lower peak pressures were seen after passing through the flatter, thinner temporal bone.
Of note: The grid points per wavelength were lower than minimum suggested levels:
Brain: 3.9 grid points per wavelength
Skull: 7.5 grid points per wavelength
Water: 3.7 grid points per wavelength
My questions: Are these results to be expected? Can the relationship between the wavelength and the width of a solid medium create non-linear levels of attenuation (as in, energy absorbed does not simply drop linearly as a function of mm the wave must pass through, at least in values ranging from 3-13 mm). Is it result of too few grid points per wavelength?
(Some additional details):
Single-element transducer [makeBowl()]
Single frequency: 0.5 MHz
alpha_power: 1 (no dispersion)
BonA: not defined
CFL number for simulations
0.3
Grid points per wavelength
brain: 3.8657
skull: 7.5000
water: 3.7050