Introduction au cours

Fund BioImag 20132-12: Ultrasound imaging and x-raysHow does ultrasound imaging work ?What is ionizing electromagnetic radiation ?Definition of ionizing radiation How are x-rays produced ?BremsstrahlungAuger electron

After this course you understand the basic principle of ultrasound imaging Are able to estimate the influence of frequency on resolution and penetration. are capable of calculating echo amplitudes based on acoustic impedance; know which parts of the electromagnetic spectrum are used in bio-imaging know the definition of ionizing radiation; understand the principle of generation of ionizing radiation and control of energy and intensity of x-ray production;Fund BioImag 20132-2What do these have in common ?

OrcaBatShip

Human HairSingle CrystalMicroscopic view of scanhead Ultrasound transducerUS scannerFund BioImag 20132-3Reflection (echo formation) is key to imaging2-1. What are the main fates of US waves in matter ?Sound wave travels through the substance but loses energy I(x)

1. Attenuation2. Refraction3. ScatterSound wave dispersed in all directions4. ReflectionSound wave bounces back to probe

Attenuation coefficient a [dB/(cm Mhz)]a is usually given in dB: dB=10logI(x)/I0 [3dB=2fold increase in I(x): 100.3=2]Typically a~0.5dB/(cm MHz) 6MHz signal will lose 3dB per cm of travel (2 fold loss in wave energy)Materiala [dB/cm MHz]Water0.002Blood0.2Tissue0.7Bone15Lung40Sound wave bends as it hits an interface at an oblique angleFund BioImag 20132-4What is the basic principle of US imaging ?UItrasound: frequency f=1-20MHz (not 20kHz)Sound wave propagation velocity c [c=lf] ~330m/s (air) = 0.33 mm/s~1.45-1.6 mm/s (tissue) (1cm~7s)(increases with density r, bone ~ 4 mm/s)The basic principle of imaging using sound waves :Emit sound pulse (length [1-5 s] is a multiple of cycle time 1/f)Measure time and intensity of echo Reconstruct using known wave propagation velocity cDistance of tissue boundary from probe (transducer)

Distance=speed x time/2transducerFund BioImag 20132-5What determines the resolution in US imaging ?Pulse duration Dt = N/fWavelength l determines minimal resolutionTo have defined frequency:Pulse length = N/f l Separation of return echoes, e.g. DT > 2 pulse length 1. Resolution increases with f2. Penetration (cf. attenuation)decreases with fFree lunchmin. echo separation, e.g., DT 2 DtT1=2x1/cT2=2x2/cDT=T1-T2=2Dx/cOverlap:No Gap,No separate echoesGap: Separate echoesxFund BioImag 20132-6When does an acoustic echo occur ? Acoustic impedance and reflection ratioDefinition:Z= rc [kg/m2s=rayls]Amount of reflected wave energy Iref=I0RIAt interface between objects with different acoustical propertiesAcoustic impedance Z

Z1Z2Reflection coefficientTransmission

Probability of reflection + transmission is = 1:

Fund BioImag 20132-7What are the reflection coefficients RI between tissues ?RIFatMuscleSkinBrainLiverBloodCranial bonePlexi-glassWater0.0470.020.0290.0070.0350.0070.570.35Fat0.0670.0760.0540.0490.0470.610.39Muscle0.0090.0130.0150.020.560.33Skin0.0220.0060.0290.560.32Brain0.0280.000.570.34Liver0.0280.550.32Blood0.570.35Cranial bone0.29Reflection by solid material e.g. bone-tissue interface Shadow formation: ~45% of energy transmitted

US shadow due to gallstone

Dolphin fetus100%45%45%20%bone(TI=1-RI)Fund BioImag 20132-8What is the optimal choice of US frequency ?SNR:Signal returned from an echo-generating tissue interface at distance x from transducer

Maximum is where derivative with respect to f is zero

f0=1/(2ax)The optimal frequency decreases with tissue depth and with increasing absorptionHow critical is the choice of f0 ?f0=0f: US frequency (experimental parameter)a: attenuation coefficient (tissue parameter)ResolutionSNRResolution:Dx decreases with increasing frequency f : 1/f Resolution fFind the optimal f Maximize fSD(fS) EKmin : ionizinghn < EKmin : non-ionizingIonizing radiation is above 13.6 eV

Electron (some useful constants)me = mass = 9e-31kgqe = charge = 1.6e-19 C (As)Rest energy mec2 = 511 keVFund BioImag 20132-15

13.6eVNon-Ionizing

Ionizing

What is ionizing radiation ?Fund BioImag 20132-162-3. How are x-rays generated (scheme) ?

Negatively charged cathode = electron sourceElectrical current (filament current) heats up the cathode (why is that necessary ?)Electrons are liberated and accelerated by electric field (Energy of e-= qDV)

Anode = metal target (tungsten)accelerated electrons hit anode generate X-rays(tube current with voltage difference up to 150 kV)

Intensity of beam = Power/Area Number of X-rays (proportional to tube current)Energy of X-rays hn(proportional to voltage)Fund BioImag 20132-17

Emission of x-rays I: What is Bremsstrahlung ?Elastic scattering: Probability ~ Z2/Ee-2 Inelastic scattering: n releaseProbability ~ Z2

Max. Energy: EeiConsider the interaction of e- with stationary atom as collision :pi=pf+pphotonpipfpphoton-Decreasing energyCoulomb:a ~ qeZ/mer2 PBrems = qe2a2/6pe0c3No info on directionality of radiation(but maximum energy is defined, how?)

High Z: Tungsten is a good targetFund BioImag 20132-18Emission of x-rays II: What are Characteristic (fluorescent) X-rays ?

Impacting e- liberates inner shell e-Atom is excited (higher energy state)VacancyFilled by outer shell electron (cascading)Emission of characteristic x-ray

Auger emissionThe excited atom can also reduce energy by liberating an additional e- (Auger e-):

Fund BioImag 20132-19Generation of x-rays revisited