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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