PowerPoint - Ultrasound Imaging - Instituts für Medizinische Physik

Wave Equation
• Assumptions
– Particle speed low compared to speed of sound:
∂ v + ( v ⋅∇)
v
t
≈
∂
t
v
– Particle speed dominates the spatial derivative:
∇ ⋅ ρv ≈ ρ∇
⋅v
• Simplified equations:
∂
t
ρ + ρ∇ ⋅v
∇p
+ ρ ∂
t
v
=
=
0
0
∂ t
∇ ⋅
⋅
• Wave equation:
∂
2
t
ρ
− ∇
2
p
=
0
2 2 2
2 dp
( ∂ − c ∇ ) ρ = 0 with
t
c = ≈ const.
d ρ
Ultrasound Imaging