Physics of ultrasonography

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László Gulyás
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1 Physis o ultrasonography US imaging. Modes o sonography. Doppler-eho Spallanzani: bat's navigation Eho priniple Eho priniple Colladen measured the speed o sound in water Δt = d+d = 2d 10 miles bottlenose dolphin 3 4

A-image - Amplitúdó Y Z Deletion / ontroling A-image egy dimenziós B-kép két dimenziós B-kép Time ( axial distane) Y Amplitude ( I rel ) - Laterális távolság One-dimensional only Z (Brightness)

2 A-image - Amplitúdó Y Z Deletion / ontroling A-image egy dimenziós B-kép két dimenziós B-kép Time ( axial distane) Y Amplitude ( I rel ) - Laterális távolság One-dimensional only Z (Brightness) Fényesség ( I rel ) Fényesség ( I rel ) 5 Δt = d+d = 2d 6 B-image - Brightness Y transduer pulse Z s eho Eltérítés / szabályozás A-kép egydimenziós B-kép kétdimenziós B-kép A-mode (Amplitude) only 1-dimensional B-mode (Brightness) only 1-dimensional τ = 2s/ time Y Amplitúdó ( I rel ) - Laterális távolság Z (Fényesség) Fényesség ( I rel ) Fényesség ( I rel ). Textbook Fig. VIII

3 2-dimensional B-mode moving transduer Z Y Eltérítés / szabályozás A-kép egydimenziós B-kép kétdimenziós B-kép Y Amplitúdó ( I rel ) - Laterális távolság Z (Fényesség) Fényesség ( I rel ) Fényesség ( I rel ) 9 10 TM-mode TM-mode B-mode ECG signal or reerene time (vertial) time-dependent 1-dimensional B-mode (T)M-mode Time Motion Textbook Fig. VIII

2-dimensional B-mode and A-mode (used in opthamology) Resolving limit, resolution real speed o propagation or the aurate determination o distanes: ornea: 1641 m/s aqueos humour: 1532 m/s rystalline

4 2-dimensional B-mode and A-mode (used in opthamology) Resolving limit, resolution real speed o propagation or the aurate determination o distanes: ornea: 1641 m/s aqueos humour: 1532 m/s rystalline lens: 1641 m/s vitreous body: 1532 m/s 13 Resolving limit is the distane between two objet details whih an be just resolved as distint objets (the smaller the better). Resolution (resolving power): the reiproal o the resolving limit (the greater the better) Axial resolving limit - is the minimum separation o two interaes aligned along the ultrasound beam. Lateral resolving limit - is the minimum separation o two I nteraes aligned along a diretion perpendiular to the ultrasound beam. 14 Axial resolving limit depends on the pulse length. Pulse length is inversely proportional to the requeny. Resolving limit, resolution Typial parameters Lateral resolving limit depends on the beam width requeny (MHz): 2 15 wavelength (in musle) (mm): penetration depth (m): lateral resolving limit (mm): Axial resolving limit axial resolving limit (mm): τ d 1 τ 2 τ = τ pulse length δ τ = d resolving limit 2 ax = τ : pulse duration The axial resolving limit is the hal o the pulse length. The ehos rom the adjaent suraes in this ase just hit another. 1 τ ~ T =

Lateral resolving limit multi unit linear array Sanning multi unit urved array δ lat F ~ 2R λ F: oal length 2R: diameter o the transduer λ: wavelength 17. Textbook Fig. VII.

5 Lateral resolving limit multi unit linear array Sanning multi unit urved array δ lat F ~ 2R λ F: oal length 2R: diameter o the transduer λ: wavelength 17. Textbook Fig. VII Doppler phenomenon The pith o a train whistle seems to get higher as it approahes, then seems to lower as the train whistle moves away. (C. Doppler, 1842) Doppler phenomenon The pith o a train whistle seems to get higher as it approahes, then seems to lower as the train whistle moves away. (C. Doppler, 1842) Moving soure v ' = 1 ± T = λ, = λ : initial requeny : altered requeny v: speed o soure : speed o US Teextbook Fig. VIII

Moving releting objet (surae), Doppler-shit D = ' 0 2v = 1 ± ' 0 Doppler shit is proportional to the speed o releting surae 21 : observed requeny, : original requeny (a) standing soure and moving

releting objet (surae), (i v R << ) v ' = 1 ± O ' = vs 1m v 1± ' = v 1m 2v ' = 1 ± O S R 22 Doppler requeny = requeny hange = requeny shit i v i, v R << (i= S or O) rearranging equation (a) moving

6 Moving releting objet (surae), Doppler-shit D = ' 0 2v = 1 ± ' 0 Doppler shit is proportional to the speed o releting surae 21 : observed requeny, : original requeny (a) standing soure and moving observer (v O ) +: observer approhes the soure : observer moves away rom the soure (b) moving soure and standing observer (i v S <<, then same as (a)) () moving soure and moving observer (d) moving releting objet (surae), (i v R << ) v ' = 1 ± O ' = vs 1m v 1± ' = v 1m 2v ' = 1 ± O S R 22 Doppler requeny = requeny hange = requeny shit i v i, v R << (i= S or O) rearranging equation (a) moving soure or observer: Δ = D = ± vi 1-dimensional Doppler apparatus or measuring average low veloity. CW: ontinuous wave soure and detetor are separated rearranging equation (d) moving releting objet or surae: Δ = v D = ±2 R Sinusuidal osillator Red blood ells as sound satterers. i v and are not parallel, then v osθ should be used instead o v (remark: i Θ = 90, D = 0) 23 Tkv. VIII.41. ábra dierene signal 1 khz 24

7 Colour oding towards the transduer: warm olours away rom the transduer: old olours BART: Blue Away Red Towards power Doppler Reonstrution o the ae o a etus 3D reonstrution arotis bladder 27 28

8 Saety intensity (W/m 2 ) Question o the week in the diagnostis: 10 mw/m 2 = 100 W/m 2. pain threshold: 10 W/m 2 probably unsae range What is the untion o ouplant materials in US diagnostis? in the therapy: 1 W/m 2 sae range (no damage) exposure time (s) Kapsolódó ejezetek: Damjanovih, Fidy, Szöllősi: Orvosi Bioizika II VIII

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