: Ultrasound imaging and x-rays 1. How does ultrasound imaging work?. What is ionizing electromagnetic radiation? Definition of ionizing radiation 3. How are x-rays produced? Bremsstrahlung Auger electron After this course you 1. understand the basic principle of ultrasound imaging. Are able to estimate the influence of frequency on resolution and penetration. 3. are capable of calculating echo amplitudes based on acoustic impedance; 4. know which parts of the electromagnetic spectrum are used in bio-imaging 5. know the definition of ionizing radiation; 6. understand the principle of generation of ionizing radiation and control of energy and intensity of x-ray production; -1-1. What are the main fates of US waves in matter? 1. Attenuation. Refraction 3. Scatter Sound wave travels through the substance but loses energy I(x) Material [db/cm MHz] Water. Sound wave bends as it hits an interface at an oblique angle Sound wave dispersed in all directions I( x) I e kxf Attenuation coefficient [db/(cm Mhz)] is usually given in db: db=1logi(x)/i [3dB=fold increase in I(x): 1.3 = Unit conversion: k=ln1/1] Typically ~.5dB/(cm MHz) Blood. Tissue.7 Bone 15 Lung 4 ( fold loss in wave energy) 4. Reflection Sound wave bounces back to probe Reflection (echo formation) is key to imaging -3
What is the basic principle of US imaging? The basic principle of imaging using sound waves : 1. Emit sound pulse (length [1-5 μs] is a multiple of cycle time 1/f). Measure time and intensity of echo 3. Reconstruct using known wave propagation velocity c Distance of tissue boundary from probe (transducer) UItrasound: frequency f=1-mhz transducer (not khz) Sound wave propagation velocity c [c=f] ~33m/s (air) =.33 mm/μs ~1.45-1.6 mm/μs (tissue) (1cm~7μs) (increases with density bone ~ 4 mm/μs) Distance=speed x time/ -4 What determines the resolution in US imaging? x Gap: Separate echoes Overlap: No Gap, No separate echoes T 1 =x 1 /c T =x /c T=T 1 -T =x/c min. echo separation, e.g., T t Pulse duration t = N/f Wavelength determines minimal resolution 1. To have defined frequency: Pulse length = N/f. Separation of return echoes, e.g. T > pulse length 1. Resolution increases with f. Penetration (cf. attenuation) decreases with f -5
When does an acoustic echo occur? Acoustic impedance and reflection ratio Acoustic impedance Z Definition: Z= c [kg/m s=rayls] Amount of reflected wave energy I ref =I R I At interface between objects with different acoustical properties Probability of reflection + transmission is = 1: Z 1 Z Reflection coefficient Transmission I I R I Z1 Z Z1 Z T 1 R -6 What are the reflection coefficients R I between tissues? R I Fat Muscle Skin Brain Liver Blood Cranial bone Plexiglass Water.47..9.7.35.7.57.35 Fat.67.76.54.49.47.61.39 Muscle.9.13.15..56.33 Skin.6.9.56.3 Brain.8..57.34 Liver.8.55.3 Blood.57.35 Cranial bone.9 Reflection by solid material e.g. bone-tissue interface Shadow formation: ~45% of energy transmitted 1% 45% (T I =1-R I ) Dolphin fetus % 45% bone -7
-. What is the optimal choice of US frequency? SNR Resolution Resolution: x decreases with increasing frequency f : 1/f Resolution f SNR: Signal returned from an echo-generating tissue interface at distance x from transducer S( f,, x) S e kf x I is constant f: US frequency (experimental parameter) : attenuation coefficient (tissue parameter) Find the optimal f Maximize f S R is constant d RI S fe fs( f,, x) d kf x df Maximum is where derivative with respect to f is zero df d df kf x fe kf x e 1 fkx f =1/(kx) The optimal frequency decreases with tissue depth and with increasing absorption How critical is the choice of f? fexp(-fx) [normalized] 1. 1.8.6.4. = 1 3 f fkx -8 Ex. 3-D US Imaging & Contrast agents 3D US Physical Principle: 1. the transducer is moved during exposure (linear shift, swinging, rotation). received echoes are stored in the memory 3. the image in the chosen plane is reconstructed mathematically Contrast agents: gas-filled Bubbles Gas : most contrast (plus resonance and higher harmonic imaging) I ~1) Umbilical cord -1
How can Ultrasound detect moving blood? Doppler effect Motion (Doppler): Frequency shift f D of moving tissue, results in shifted US frequency (demodulation for detection) (where is this also used?) stationary Source moving with v In a period T, source moves closer by v T f =(c-v )T =ct Doppler frequency shift f D f D fv cos c c: speed of US, e.g. 15 m/s v : speed of source, e.g. 5 cm/s f : frequency of moving source, e.g. 5MHz : Rel. angle at which blood is moving r =(c+v )T Example: f D = 5 1 6 [Hz].5 [m/s]/15 [m/s] ~ 3kHz ~.5% of f -11-3. Basis of x-ray imaging useful relationships Electromagnetic radiation c = 8 m/s) E = h=hc/ (h = Planck s Constant) h= 1-34 Js =4 1-18 kevs 1eV = energy of e - in acquired in 1V electric field E = hc/ = 1.keV/nm -13
With which elements of matter does EM radiation interact mainly? (in imaging mainly with electrons) Electron binding energy Binding energy 1. decreases with shell distance. increases with Z (Why?) Lowest K-shell binding e - energy: E K min = 13.6eV ( 1 H) h >E K min : ionizing h <E K min : non-ionizing Electron (some useful constants) m e = mass = 9 1-31 kg q e = charge = 1.6 1-19 C (As) Rest energy m e c = 511 kev Ionizing radiation is above 13.6 ev -14-4. How are x-rays generated (scheme)? Negatively charged cathode = electron source Electrical current (filament current) heats up the cathode (why is that necessary?) Electrons are liberated and accelerated by electric field (Energy of e - = qv) Anode = metal target (tungsten) accelerated electrons hit anode generate X-rays (tube current with voltage difference up to 15 kv) Intensity of beam = Power/Area 1. Number of X-rays (proportional to tube current). Energy of X-rays h (proportional to voltage) -16
Emission of x-rays I: What is Bremsstrahlung? Consider the interaction of e - with stationary atom as collision : p i p i =p f +p photon Coulomb: a ~ q e Z/m e r P Brems = q e a /6 c 3 No info on directionality of radiation (but maximum energy is defined, how?) p f p photon Max. Energy: E e i Elastic scattering: Probability ~ Z /E e- Inelastic scattering: release Probability ~ Z Decreasing energy High Z: Tungsten is a good target -17 Emission of x-rays II: What are Characteristic (fluorescent) X-rays? Impacting e - liberates inner shell e - 1. Atom is excited (higher energy state). Vacancy 3. Filled by outer shell electron (cascading) 4. Emission of characteristic x-ray Auger emission The excited atom can also reduce energy by liberating an additional e- (Auger e-): -18