2021-2022 1
Inleiding tot de medische beeldvorming
Pixelgrootte
𝐹𝑂𝑉
∆𝑟 = ∆𝑟 = 𝑝𝑖𝑥𝑒𝑙𝑔𝑟𝑜𝑜𝑡𝑡𝑒
𝑁
𝐹𝑂𝑉 = 𝑓𝑖𝑒𝑙𝑑 𝑜𝑓 𝑣𝑖𝑒𝑤 [cm]
𝑁 = 𝑏𝑟𝑒𝑒𝑑𝑡𝑒 [#punten]
SNR
𝑔𝑒𝑚𝑖𝑑𝑑𝑒𝑙𝑑𝑒 𝑣𝑎𝑛 ℎ𝑒𝑡 𝑜𝑏𝑗𝑒𝑐𝑡 𝑆𝑁𝑅 = 𝑠𝑖𝑔𝑛𝑎𝑎𝑙 − 𝑟𝑢𝑖𝑠 − 𝑣𝑒𝑟ℎ𝑜𝑢𝑑𝑖𝑛𝑔
𝑆𝑁𝑅 =
𝑠𝑡𝑎𝑛𝑑𝑎𝑎𝑟𝑑𝑎𝑓𝑤𝑖𝑗𝑘𝑖𝑛𝑔 𝑣𝑎𝑛 𝑑𝑒 𝑎𝑐ℎ𝑡𝑒𝑟𝑔𝑟𝑜𝑛𝑑 𝑖𝑛 𝑑𝑒 𝑟𝑒𝑔𝑖𝑜
CNR
𝑔𝑒𝑚𝑖𝑑𝑑𝑒𝑙𝑑𝑒𝑟𝑒𝑔𝑖𝑜 1 − 𝑔𝑒𝑚𝑖𝑑𝑑𝑒𝑙𝑑𝑒𝑟𝑒𝑔𝑖𝑜 2 𝐶𝑁𝑅 = 𝑐𝑜𝑛𝑡𝑟𝑎𝑠𝑡 − 𝑟𝑢𝑖𝑠 − 𝑣𝑒𝑟ℎ𝑜𝑢𝑑𝑖𝑛𝑔
𝐶𝑁𝑅 =
𝑠𝑡𝑎𝑛𝑑𝑎𝑎𝑟𝑑𝑎𝑓𝑤𝑖𝑗𝑘𝑖𝑛𝑔 𝑣𝑎𝑛 𝑑𝑒 𝑎𝑐ℎ𝑡𝑒𝑟𝑔𝑟𝑜𝑛𝑑 𝑖𝑛 𝑑𝑒 𝑟𝑒𝑔𝑖𝑜
Ultrasound beeldvorming
Kalibratiewaarde van de golfsnelheid in weefsels
𝑐 = 1540 𝑚/𝑠
Golfsnelheid in weefsels
𝑎𝑓𝑔𝑒𝑙𝑒𝑔𝑑𝑒 𝑤𝑒𝑔 2 ∙ 𝑑𝑖𝑒𝑝𝑡𝑒 𝑐 = 𝑔𝑜𝑙𝑓𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑐= =
𝑡 𝑡 𝑑𝑖𝑒𝑝𝑡𝑒 = 𝑎𝑓𝑠𝑡𝑎𝑛𝑑 𝑣𝑎𝑛 𝑑𝑒 𝑏𝑟𝑜𝑛 𝑡𝑜𝑡 ℎ𝑒𝑡 𝑤𝑒𝑒𝑓𝑠𝑒𝑙 [m]
𝑡 = 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑒𝑡𝑖𝑗𝑑 [s]
Dikte
𝜆 𝑐 𝜆 = 𝑔𝑜𝑙𝑓𝑙𝑒𝑛𝑔𝑡𝑒 [m]
𝑑𝑖𝑘𝑡𝑒 = =
2 2∙𝑓 𝑐 = 𝑔𝑜𝑙𝑓𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 [Hz]
Resolutie
𝑐 𝜆 = 𝑔𝑜𝑙𝑓𝑙𝑒𝑛𝑔𝑡𝑒 [m]
𝑟𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑒~𝜆 =
𝑓 𝑐 = 𝑔𝑜𝑙𝑓𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 = 1540 [m/s]
𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 [Hz]
Akoestische impedantie
𝑍 =𝜌∙𝑐 𝑍 = 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑘𝑒 𝑎𝑘𝑜𝑒𝑠𝑡𝑖𝑠𝑐ℎ𝑒 𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑡𝑖𝑒 [kg/m²s]
𝜌 = 𝑑𝑖𝑐ℎ𝑡ℎ𝑒𝑖𝑑 𝑣𝑎𝑛 ℎ𝑒𝑡 𝑤𝑒𝑒𝑓𝑠𝑒𝑙 [kg/m³]
𝑐 = 𝑔𝑜𝑙𝑓𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
Reflectiecoëfficiënt
𝐼𝑟 𝑍2 − 𝑍1 2 𝛼𝑟 = 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑒𝑐𝑜ë𝑓𝑓𝑖𝑐𝑖ë𝑛𝑡
𝛼𝑟 = =( )
𝐼𝑖 𝑍2 + 𝑍1 𝐼𝑟 = 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑟𝑒𝑛𝑑𝑒 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑒𝑖𝑡 [1/m²]
𝐼𝑖 = 𝑖𝑛𝑣𝑎𝑙𝑙𝑒𝑛𝑑𝑒 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑒𝑖𝑡 [1/m²]
𝑍1 = 𝑎𝑘𝑜𝑒𝑠𝑡𝑖𝑠𝑐ℎ𝑒 𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑡𝑖𝑒 𝑣𝑎𝑛 𝑠𝑡𝑜𝑓 1 [kg/m²s]
𝑍2 = 𝑎𝑘𝑜𝑒𝑠𝑡𝑖𝑠𝑐ℎ𝑒 𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑡𝑖𝑒 𝑣𝑎𝑛 𝑠𝑡𝑜𝑓 2 [kg/m²s]
Transmissiecoëfficiënt
𝐼𝑡 4𝑍1 ∙ 𝑍2 𝛼𝑡 = 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑒𝑐𝑜ë𝑓𝑓𝑖𝑐𝑖ë𝑛𝑡
𝛼𝑡 = =
𝐼𝑖 (𝑍2 + 𝑍1 )2 𝐼𝑡 = 𝑔𝑒𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑒𝑟𝑑𝑒 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑒𝑖𝑡 [1/m²]
𝐼𝑖 = 𝑖𝑛𝑣𝑎𝑙𝑙𝑒𝑛𝑑𝑒 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑒𝑖𝑡 [1/m²]
𝑍1 = 𝑎𝑘𝑜𝑒𝑠𝑡𝑖𝑠𝑐ℎ𝑒 𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑡𝑖𝑒 𝑣𝑎𝑛 𝑠𝑡𝑜𝑓 1 [kg/m²s]
𝑍2 = 𝑎𝑘𝑜𝑒𝑠𝑡𝑖𝑠𝑐ℎ𝑒 𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑡𝑖𝑒 𝑣𝑎𝑛 𝑠𝑡𝑜𝑓 2 [kg/m²s]
Formularium medische beeldvorming Céline De Munter
, 2021-2022 2
Attenuatie van de intensiteit na doorgang door het weefsel
𝐼(𝑥) = 𝐼0 ∙ 𝑒 −(𝜇∙𝑥) 𝐼0 = 𝑖𝑛𝑖𝑡𝑖ë𝑙𝑒 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑒𝑖𝑡 𝑣𝑜𝑜𝑟 𝑑𝑜𝑜𝑟𝑔𝑎𝑛𝑔 𝑣𝑎𝑛 ℎ𝑒𝑡 𝑤𝑒𝑒𝑓𝑠𝑒𝑙 [1/m²]
𝜇 = 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑒𝑖𝑡 − 𝑣𝑒𝑟𝑧𝑤𝑎𝑘𝑘𝑖𝑛𝑔𝑠𝑐𝑜ë𝑓𝑓𝑖𝑐𝑖ë𝑛𝑡 [1/cm]
𝑥 = 𝑎𝑓𝑔𝑒𝑙𝑒𝑔𝑑𝑒 𝑤𝑒𝑔 [m]
Absorptie
𝜇𝑎 ≈ 𝑓 𝑏 𝜇𝑎 = 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑒𝑣𝑒𝑟𝑧𝑤𝑎𝑘𝑘𝑖𝑛𝑔𝑠𝑐𝑜ë𝑓𝑓𝑖𝑐𝑖ë𝑛𝑡 [1/cm]
𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 𝑣𝑎𝑛 𝑑𝑒 𝑔𝑜𝑙𝑓 [Hz]
𝑏 = 𝑏𝑒𝑟𝑒𝑖𝑘 𝑡𝑢𝑠𝑠𝑒𝑛 [0.7 ; 1.2]
Ultrasound Doppler-effect – stationaire zender
𝑐 ± 𝑣 ∙ cos 𝛼 𝑓1 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 𝑤𝑎𝑎𝑟𝑔𝑒𝑛𝑜𝑚𝑒𝑛 𝑑𝑜𝑜𝑟 𝑑𝑒 𝑐𝑒𝑙 [Hz]
𝑓1 = ( ) ∙ 𝑓0
𝑐 𝑐 = 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑖𝑛 ℎ𝑒𝑡 𝑔𝑒𝑘𝑒𝑛𝑑𝑒 𝑚𝑒𝑑𝑖𝑢𝑚 [m/s]
𝑣 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣/𝑒 𝑏𝑒𝑤𝑒𝑔𝑒𝑛𝑑 𝑜𝑏𝑗𝑒𝑐𝑡 [m/s]
𝛼 = ℎ𝑜𝑒𝑘 𝑡𝑜𝑣 𝑑𝑒 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑏𝑟𝑜𝑛 [rad of °]
𝑓0 = 𝑧𝑒𝑛𝑑𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 [Hz]
Ultrasound Doppler-effect – stationaire ontvanger
𝑐 𝑓2 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 𝑤𝑎𝑎𝑟𝑔𝑒𝑛𝑜𝑚𝑒𝑛 𝑑𝑜𝑜𝑟 𝑑𝑒 𝑜𝑛𝑡𝑣𝑎𝑛𝑔𝑒𝑟 [Hz]
𝑓2 = ( ) ∙ 𝑓1
𝑐 ∓ 𝑣 ∙ cos 𝛽
𝑓1 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 𝑤𝑎𝑎𝑟𝑔𝑒𝑛𝑜𝑚𝑒𝑛 𝑑𝑜𝑜𝑟 𝑑𝑒 𝑐𝑒𝑙 [Hz]
𝑐 = 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑖𝑛 ℎ𝑒𝑡 𝑔𝑒𝑘𝑒𝑛𝑑𝑒 𝑚𝑒𝑑𝑖𝑢𝑚 [m/s]
𝑣 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣/𝑒 𝑏𝑒𝑤𝑒𝑔𝑒𝑛𝑑 𝑜𝑏𝑗𝑒𝑐𝑡 [m/s]
𝛽 = ℎ𝑜𝑒𝑘 𝑡𝑜𝑣 𝑑𝑒 𝑜𝑛𝑡𝑣𝑎𝑛𝑔𝑒𝑟 [rad of °]
Frequentieverschuiving
(±𝑣 ∙ cos 𝛼 ± 𝑣 ∙ cos 𝛽) 𝑓2 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 𝑤𝑎𝑎𝑟𝑔𝑒𝑛𝑜𝑚𝑒𝑛 𝑑𝑜𝑜𝑟 𝑑𝑒 𝑜𝑛𝑡𝑣𝑎𝑛𝑔𝑒𝑟 [Hz]
∆𝑓 = 𝑓2 − 𝑓0 = ∙ 𝑓0
𝑐 𝑐 = 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑖𝑛 ℎ𝑒𝑡 𝑔𝑒𝑘𝑒𝑛𝑑𝑒 𝑚𝑒𝑑𝑖𝑢𝑚 [m/s]
𝑣 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣/𝑒 𝑏𝑒𝑤𝑒𝑔𝑒𝑛𝑑 𝑜𝑏𝑗𝑒𝑐𝑡 [m/s]
𝛼 = ℎ𝑜𝑒𝑘 𝑡𝑜𝑣 𝑑𝑒 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑏𝑟𝑜𝑛 [rad of °]
𝛽 = ℎ𝑜𝑒𝑘 𝑡𝑜𝑣 𝑑𝑒 𝑜𝑛𝑡𝑣𝑎𝑛𝑔𝑒𝑟 [rad of °]
𝑓0 = 𝑧𝑒𝑛𝑑𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 [Hz]
Bloedstroomsnelheid
±∆𝑓 ∙ 𝑐 𝑣 = 𝑏𝑙𝑜𝑒𝑑𝑠𝑡𝑟𝑜𝑜𝑚𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑣=
2 ∙ 𝑓0 ∙ cos 𝛼 ∆𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒𝑣𝑒𝑟𝑠𝑐ℎ𝑢𝑖𝑣𝑖𝑛𝑔 [Hz]
𝑐 = 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑖𝑛 ℎ𝑒𝑡 𝑔𝑒𝑘𝑒𝑛𝑑𝑒 𝑚𝑒𝑑𝑖𝑢𝑚 [m/s]
𝛼 = ℎ𝑜𝑒𝑘 𝑡𝑜𝑣 𝑑𝑒 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑏𝑟𝑜𝑛 [rad of °]
𝑓0 = 𝑧𝑒𝑛𝑑𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 [Hz]
±2 ∙ 𝑣 ∙ cos 𝛼 𝑣 = 𝑏𝑙𝑜𝑒𝑑𝑠𝑡𝑟𝑜𝑜𝑚𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
∆𝑓 = ∙ 𝑓0
𝑐 ∆𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒𝑣𝑒𝑟𝑠𝑐ℎ𝑢𝑖𝑣𝑖𝑛𝑔 [Hz]
𝑐 = 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑖𝑛 ℎ𝑒𝑡 𝑔𝑒𝑘𝑒𝑛𝑑𝑒 𝑚𝑒𝑑𝑖𝑢𝑚 [m/s]
𝛼 = ℎ𝑜𝑒𝑘 𝑡𝑜𝑣 𝑑𝑒 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑏𝑟𝑜𝑛 [rad of °]
𝑓0 = 𝑧𝑒𝑛𝑑𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 [Hz]
Formularium medische beeldvorming Céline De Munter
Inleiding tot de medische beeldvorming
Pixelgrootte
𝐹𝑂𝑉
∆𝑟 = ∆𝑟 = 𝑝𝑖𝑥𝑒𝑙𝑔𝑟𝑜𝑜𝑡𝑡𝑒
𝑁
𝐹𝑂𝑉 = 𝑓𝑖𝑒𝑙𝑑 𝑜𝑓 𝑣𝑖𝑒𝑤 [cm]
𝑁 = 𝑏𝑟𝑒𝑒𝑑𝑡𝑒 [#punten]
SNR
𝑔𝑒𝑚𝑖𝑑𝑑𝑒𝑙𝑑𝑒 𝑣𝑎𝑛 ℎ𝑒𝑡 𝑜𝑏𝑗𝑒𝑐𝑡 𝑆𝑁𝑅 = 𝑠𝑖𝑔𝑛𝑎𝑎𝑙 − 𝑟𝑢𝑖𝑠 − 𝑣𝑒𝑟ℎ𝑜𝑢𝑑𝑖𝑛𝑔
𝑆𝑁𝑅 =
𝑠𝑡𝑎𝑛𝑑𝑎𝑎𝑟𝑑𝑎𝑓𝑤𝑖𝑗𝑘𝑖𝑛𝑔 𝑣𝑎𝑛 𝑑𝑒 𝑎𝑐ℎ𝑡𝑒𝑟𝑔𝑟𝑜𝑛𝑑 𝑖𝑛 𝑑𝑒 𝑟𝑒𝑔𝑖𝑜
CNR
𝑔𝑒𝑚𝑖𝑑𝑑𝑒𝑙𝑑𝑒𝑟𝑒𝑔𝑖𝑜 1 − 𝑔𝑒𝑚𝑖𝑑𝑑𝑒𝑙𝑑𝑒𝑟𝑒𝑔𝑖𝑜 2 𝐶𝑁𝑅 = 𝑐𝑜𝑛𝑡𝑟𝑎𝑠𝑡 − 𝑟𝑢𝑖𝑠 − 𝑣𝑒𝑟ℎ𝑜𝑢𝑑𝑖𝑛𝑔
𝐶𝑁𝑅 =
𝑠𝑡𝑎𝑛𝑑𝑎𝑎𝑟𝑑𝑎𝑓𝑤𝑖𝑗𝑘𝑖𝑛𝑔 𝑣𝑎𝑛 𝑑𝑒 𝑎𝑐ℎ𝑡𝑒𝑟𝑔𝑟𝑜𝑛𝑑 𝑖𝑛 𝑑𝑒 𝑟𝑒𝑔𝑖𝑜
Ultrasound beeldvorming
Kalibratiewaarde van de golfsnelheid in weefsels
𝑐 = 1540 𝑚/𝑠
Golfsnelheid in weefsels
𝑎𝑓𝑔𝑒𝑙𝑒𝑔𝑑𝑒 𝑤𝑒𝑔 2 ∙ 𝑑𝑖𝑒𝑝𝑡𝑒 𝑐 = 𝑔𝑜𝑙𝑓𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑐= =
𝑡 𝑡 𝑑𝑖𝑒𝑝𝑡𝑒 = 𝑎𝑓𝑠𝑡𝑎𝑛𝑑 𝑣𝑎𝑛 𝑑𝑒 𝑏𝑟𝑜𝑛 𝑡𝑜𝑡 ℎ𝑒𝑡 𝑤𝑒𝑒𝑓𝑠𝑒𝑙 [m]
𝑡 = 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑒𝑡𝑖𝑗𝑑 [s]
Dikte
𝜆 𝑐 𝜆 = 𝑔𝑜𝑙𝑓𝑙𝑒𝑛𝑔𝑡𝑒 [m]
𝑑𝑖𝑘𝑡𝑒 = =
2 2∙𝑓 𝑐 = 𝑔𝑜𝑙𝑓𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 [Hz]
Resolutie
𝑐 𝜆 = 𝑔𝑜𝑙𝑓𝑙𝑒𝑛𝑔𝑡𝑒 [m]
𝑟𝑒𝑠𝑜𝑙𝑢𝑡𝑖𝑒~𝜆 =
𝑓 𝑐 = 𝑔𝑜𝑙𝑓𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 = 1540 [m/s]
𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 [Hz]
Akoestische impedantie
𝑍 =𝜌∙𝑐 𝑍 = 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑒𝑘𝑒 𝑎𝑘𝑜𝑒𝑠𝑡𝑖𝑠𝑐ℎ𝑒 𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑡𝑖𝑒 [kg/m²s]
𝜌 = 𝑑𝑖𝑐ℎ𝑡ℎ𝑒𝑖𝑑 𝑣𝑎𝑛 ℎ𝑒𝑡 𝑤𝑒𝑒𝑓𝑠𝑒𝑙 [kg/m³]
𝑐 = 𝑔𝑜𝑙𝑓𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
Reflectiecoëfficiënt
𝐼𝑟 𝑍2 − 𝑍1 2 𝛼𝑟 = 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑖𝑒𝑐𝑜ë𝑓𝑓𝑖𝑐𝑖ë𝑛𝑡
𝛼𝑟 = =( )
𝐼𝑖 𝑍2 + 𝑍1 𝐼𝑟 = 𝑟𝑒𝑓𝑙𝑒𝑐𝑡𝑒𝑟𝑒𝑛𝑑𝑒 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑒𝑖𝑡 [1/m²]
𝐼𝑖 = 𝑖𝑛𝑣𝑎𝑙𝑙𝑒𝑛𝑑𝑒 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑒𝑖𝑡 [1/m²]
𝑍1 = 𝑎𝑘𝑜𝑒𝑠𝑡𝑖𝑠𝑐ℎ𝑒 𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑡𝑖𝑒 𝑣𝑎𝑛 𝑠𝑡𝑜𝑓 1 [kg/m²s]
𝑍2 = 𝑎𝑘𝑜𝑒𝑠𝑡𝑖𝑠𝑐ℎ𝑒 𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑡𝑖𝑒 𝑣𝑎𝑛 𝑠𝑡𝑜𝑓 2 [kg/m²s]
Transmissiecoëfficiënt
𝐼𝑡 4𝑍1 ∙ 𝑍2 𝛼𝑡 = 𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑠𝑠𝑖𝑒𝑐𝑜ë𝑓𝑓𝑖𝑐𝑖ë𝑛𝑡
𝛼𝑡 = =
𝐼𝑖 (𝑍2 + 𝑍1 )2 𝐼𝑡 = 𝑔𝑒𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑒𝑟𝑑𝑒 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑒𝑖𝑡 [1/m²]
𝐼𝑖 = 𝑖𝑛𝑣𝑎𝑙𝑙𝑒𝑛𝑑𝑒 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑒𝑖𝑡 [1/m²]
𝑍1 = 𝑎𝑘𝑜𝑒𝑠𝑡𝑖𝑠𝑐ℎ𝑒 𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑡𝑖𝑒 𝑣𝑎𝑛 𝑠𝑡𝑜𝑓 1 [kg/m²s]
𝑍2 = 𝑎𝑘𝑜𝑒𝑠𝑡𝑖𝑠𝑐ℎ𝑒 𝑖𝑚𝑝𝑒𝑑𝑎𝑛𝑡𝑖𝑒 𝑣𝑎𝑛 𝑠𝑡𝑜𝑓 2 [kg/m²s]
Formularium medische beeldvorming Céline De Munter
, 2021-2022 2
Attenuatie van de intensiteit na doorgang door het weefsel
𝐼(𝑥) = 𝐼0 ∙ 𝑒 −(𝜇∙𝑥) 𝐼0 = 𝑖𝑛𝑖𝑡𝑖ë𝑙𝑒 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑒𝑖𝑡 𝑣𝑜𝑜𝑟 𝑑𝑜𝑜𝑟𝑔𝑎𝑛𝑔 𝑣𝑎𝑛 ℎ𝑒𝑡 𝑤𝑒𝑒𝑓𝑠𝑒𝑙 [1/m²]
𝜇 = 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑒𝑖𝑡 − 𝑣𝑒𝑟𝑧𝑤𝑎𝑘𝑘𝑖𝑛𝑔𝑠𝑐𝑜ë𝑓𝑓𝑖𝑐𝑖ë𝑛𝑡 [1/cm]
𝑥 = 𝑎𝑓𝑔𝑒𝑙𝑒𝑔𝑑𝑒 𝑤𝑒𝑔 [m]
Absorptie
𝜇𝑎 ≈ 𝑓 𝑏 𝜇𝑎 = 𝑎𝑏𝑠𝑜𝑟𝑝𝑡𝑖𝑒𝑣𝑒𝑟𝑧𝑤𝑎𝑘𝑘𝑖𝑛𝑔𝑠𝑐𝑜ë𝑓𝑓𝑖𝑐𝑖ë𝑛𝑡 [1/cm]
𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 𝑣𝑎𝑛 𝑑𝑒 𝑔𝑜𝑙𝑓 [Hz]
𝑏 = 𝑏𝑒𝑟𝑒𝑖𝑘 𝑡𝑢𝑠𝑠𝑒𝑛 [0.7 ; 1.2]
Ultrasound Doppler-effect – stationaire zender
𝑐 ± 𝑣 ∙ cos 𝛼 𝑓1 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 𝑤𝑎𝑎𝑟𝑔𝑒𝑛𝑜𝑚𝑒𝑛 𝑑𝑜𝑜𝑟 𝑑𝑒 𝑐𝑒𝑙 [Hz]
𝑓1 = ( ) ∙ 𝑓0
𝑐 𝑐 = 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑖𝑛 ℎ𝑒𝑡 𝑔𝑒𝑘𝑒𝑛𝑑𝑒 𝑚𝑒𝑑𝑖𝑢𝑚 [m/s]
𝑣 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣/𝑒 𝑏𝑒𝑤𝑒𝑔𝑒𝑛𝑑 𝑜𝑏𝑗𝑒𝑐𝑡 [m/s]
𝛼 = ℎ𝑜𝑒𝑘 𝑡𝑜𝑣 𝑑𝑒 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑏𝑟𝑜𝑛 [rad of °]
𝑓0 = 𝑧𝑒𝑛𝑑𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 [Hz]
Ultrasound Doppler-effect – stationaire ontvanger
𝑐 𝑓2 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 𝑤𝑎𝑎𝑟𝑔𝑒𝑛𝑜𝑚𝑒𝑛 𝑑𝑜𝑜𝑟 𝑑𝑒 𝑜𝑛𝑡𝑣𝑎𝑛𝑔𝑒𝑟 [Hz]
𝑓2 = ( ) ∙ 𝑓1
𝑐 ∓ 𝑣 ∙ cos 𝛽
𝑓1 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 𝑤𝑎𝑎𝑟𝑔𝑒𝑛𝑜𝑚𝑒𝑛 𝑑𝑜𝑜𝑟 𝑑𝑒 𝑐𝑒𝑙 [Hz]
𝑐 = 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑖𝑛 ℎ𝑒𝑡 𝑔𝑒𝑘𝑒𝑛𝑑𝑒 𝑚𝑒𝑑𝑖𝑢𝑚 [m/s]
𝑣 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣/𝑒 𝑏𝑒𝑤𝑒𝑔𝑒𝑛𝑑 𝑜𝑏𝑗𝑒𝑐𝑡 [m/s]
𝛽 = ℎ𝑜𝑒𝑘 𝑡𝑜𝑣 𝑑𝑒 𝑜𝑛𝑡𝑣𝑎𝑛𝑔𝑒𝑟 [rad of °]
Frequentieverschuiving
(±𝑣 ∙ cos 𝛼 ± 𝑣 ∙ cos 𝛽) 𝑓2 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 𝑤𝑎𝑎𝑟𝑔𝑒𝑛𝑜𝑚𝑒𝑛 𝑑𝑜𝑜𝑟 𝑑𝑒 𝑜𝑛𝑡𝑣𝑎𝑛𝑔𝑒𝑟 [Hz]
∆𝑓 = 𝑓2 − 𝑓0 = ∙ 𝑓0
𝑐 𝑐 = 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑖𝑛 ℎ𝑒𝑡 𝑔𝑒𝑘𝑒𝑛𝑑𝑒 𝑚𝑒𝑑𝑖𝑢𝑚 [m/s]
𝑣 = 𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑣/𝑒 𝑏𝑒𝑤𝑒𝑔𝑒𝑛𝑑 𝑜𝑏𝑗𝑒𝑐𝑡 [m/s]
𝛼 = ℎ𝑜𝑒𝑘 𝑡𝑜𝑣 𝑑𝑒 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑏𝑟𝑜𝑛 [rad of °]
𝛽 = ℎ𝑜𝑒𝑘 𝑡𝑜𝑣 𝑑𝑒 𝑜𝑛𝑡𝑣𝑎𝑛𝑔𝑒𝑟 [rad of °]
𝑓0 = 𝑧𝑒𝑛𝑑𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 [Hz]
Bloedstroomsnelheid
±∆𝑓 ∙ 𝑐 𝑣 = 𝑏𝑙𝑜𝑒𝑑𝑠𝑡𝑟𝑜𝑜𝑚𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
𝑣=
2 ∙ 𝑓0 ∙ cos 𝛼 ∆𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒𝑣𝑒𝑟𝑠𝑐ℎ𝑢𝑖𝑣𝑖𝑛𝑔 [Hz]
𝑐 = 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑖𝑛 ℎ𝑒𝑡 𝑔𝑒𝑘𝑒𝑛𝑑𝑒 𝑚𝑒𝑑𝑖𝑢𝑚 [m/s]
𝛼 = ℎ𝑜𝑒𝑘 𝑡𝑜𝑣 𝑑𝑒 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑏𝑟𝑜𝑛 [rad of °]
𝑓0 = 𝑧𝑒𝑛𝑑𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 [Hz]
±2 ∙ 𝑣 ∙ cos 𝛼 𝑣 = 𝑏𝑙𝑜𝑒𝑑𝑠𝑡𝑟𝑜𝑜𝑚𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 [m/s]
∆𝑓 = ∙ 𝑓0
𝑐 ∆𝑓 = 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒𝑣𝑒𝑟𝑠𝑐ℎ𝑢𝑖𝑣𝑖𝑛𝑔 [Hz]
𝑐 = 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑠𝑛𝑒𝑙ℎ𝑒𝑖𝑑 𝑖𝑛 ℎ𝑒𝑡 𝑔𝑒𝑘𝑒𝑛𝑑𝑒 𝑚𝑒𝑑𝑖𝑢𝑚 [m/s]
𝛼 = ℎ𝑜𝑒𝑘 𝑡𝑜𝑣 𝑑𝑒 𝑔𝑒𝑙𝑢𝑖𝑑𝑠𝑏𝑟𝑜𝑛 [rad of °]
𝑓0 = 𝑧𝑒𝑛𝑑𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑡𝑖𝑒 [Hz]
Formularium medische beeldvorming Céline De Munter
