Skip to main content

Table 2 Analytical and numerical calculations of the reflection R and transmission T coefficients for the nine different cases. In the analytical case, the coefficients are calculated based on the acoustic impedance of the two media. The numerical calculations are based on the ratios between the pressure amplitudes of the reflected and transmitted waves to the amplitude of the incident wave

From: Full-wave acoustic and thermal modeling of transcranial ultrasound propagation and investigation of skull-induced aberration correction techniques: a feasibility study

Setup Analytical Numerical
Medium A Medium B Angles Coefficients p [MPa] Coefficients
c [m s −1] ρ [kg m −3] Z c [m s −1] ρ [kg m −3] Z θ i θ t T R p i p t p r T R
1500 1000 1.5 2000 1900 3.8 0 0.00 1.43 0.43 1.00 1.43 0.43 1.43 0.43
1500 1000 1.5 1400 600 0.84 0 0.00 0.72 −0.28 1.00 0.72 −0.28 0.72 −0.28
1500 1000 1.5 1200 600 0.72 0 0.00 0.65 −0.35 1.00 0.65 −0.35 0.65 −0.35
1500 1000 1.5 2000 1900 3.8 15 20.19 1.45 0.45 1.00 1.44 0.44 1.44 0.44
1500 1000 1.5 1400 600 0.84 15 13.98 0.72 −0.28 1.00 0.72 −0.28 0.72 −0.28
1500 1000 1.5 1200 600 0.72 15 11.95 0.64 −0.36 1.00 0.65 −0.35 0.65 −0.35
1500 1000 1.5 2000 1900 3.8 30 41.81 1.49 0.49 1.00 1.50 0.49 1.50 0.49
1500 1000 1.5 1400 600 0.84 30 27.82 0.71 −0.29 1.00 0.71 −0.28 0.71 −0.28
1500 1000 1.5 1200 600 0.72 30 23.58 0.62 −0.38 1.00 0.63 −0.37 0.63 −0.37