Medical biophysics II. X-ray. X-ray. Generation, Spectral features Interaction with matter

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1 Medical biophysics II Medical biophysics II X-ray - generation and properties X-ray - diagnostic foundations Medical use of electronics Thermodynamics - equilibrium, change, laws Diffusion, Brown-motion, Osmosis Flow of fluids and gases. Hemodynamics Bioelectric phenomena Sound, ultrasound Biophysics of sensory organs. Vision and hearing Building blocks of life: water, macromolecules, supramolecular systems Methods of investigating biomolecular structure and dynamics. MRI Molecular mechanisms of biomolecular motion. Biomechanics, biomolecular and tissue elasticity Respiratory and cardiac biophysics. Physical examination X-ray X-ray Generation, Spectral features Interaction with matter Wilhelm Konrad Röntgen ( ) Nobel prize, 1901 Hand mit Ringen (Hand with Ring): print of Wilhelm Röntgen's first "medical" X-ray, of his wife's hand, taken on 22 December 1895 and presented to Professor Ludwig Zehnder of the Physik Institut, University of Freiburg, on 1 January The dark oval on the third finger is a shadow produced by her ring.

2 Paper funnel radioscope Medical diagnostics Late 1890s I. World war today Shoe-fitting fluoroscope ( ) X-rays are electromagnetic waves Wavelength nm. Frequency 30x x10 18 Hz. Energy 120 ev kev.

3 X-rays Generation of X-ray (non-conventional) Generation of X-rays Triboluminescence: light emission evoked by scratching or rubbing. Francis Bacon, X-ray spectrum Interaction with matter 1: diffraction Interaction with matter 2: absorption X-ray absorption mechanisms: Photoelectric effect Compton scatter Pair production Peeling away sticky tape emits light......and X-rays. (Nature News, October 2008) Generation of X-ray: in Cathode Ray Tube Bremsstrahlung I anode anode (anticathode) X- rays U anode cathode ray Photo of a Coolidge x-ray tube, from the early 1900s. The heated cathode is on the left, the anode target is on the right. The x-rays are emitted in a downward direction. cathode I heating U heating Rotating anode X-ray tube Electrons decelerate, thereby loose their kinetic energy, when interacting with the atoms of the anode ( braking radiation ).

4 Spectrum of Bremsstrahlung Characteristic X-ray eu anode = ε max = hf max λ min = hc e 1 U anode Maximal photon energy (ε max) h =Planck s constant; c = speed of light; e = charge of electron; eu anode = work of acceleration Limiting wavelength (λ min) (Duane-Hunt Law) Continuous spectrum ΔP Δε = c' Z ε max ε ( ) P tot = 1 2 c' Z ε 2 max Energy spectrum (energy dependence of power) 2 = c Z U anode e 2 Total power (based on area of triangle) Knocked-out inner-shell electron is replaced by one on a higher-energy shell 2 P tot = C Rtg I anode U anode Z Total power Auger electron η = P tot P in = C I U 2 Rtg anode anode Z = C Rtg U anode Z I anode U anode Efficiency <1% Energy of electron transition may be used for the escape of an outershell electron: Auger electron hole energy exchange Spectrum of characteristic X-ray X-ray spectrum characterizes the element Because inner-shell electrons participate in characteristic X-radiation, only the atomic (and not the molecular) properties are revealed Line spectrum Electronic transitions in a calcium atom. Energy dispersive X-ray fluorescence spectrum.

5 Detection of characteristic X-ray X-ray diffraction λ X-raybeam Crystal Experiment Condition of constructive interference: 2dsinθ = nλ +1 N.B.: electron microscope Electron probe microanalyzer X-ray spectroscope 0-1 3D structure X-ray absorption X-ray photoeffect Incident intensity J 0 x absorbent Outgoing intensity J Exponential attenuation principle J J 0 J = J 0 e μx x incoming X-ray photon (hf) Binding energy (A) 100 kev photon 66 kev photoelectron may participate in X-ray generation Main effect in diagostic X-ray Photoeffect attenuation coefficient: τ = τ m ρ μ = μ m ρ μ=attenuation coefficient μ m=mass attenuation coefficient (cm 2 /g) ρ=density (g/cm 3 )

6 Photoeffect attenuation depends strongly on atomic number Compton scatter wavelength (pm) τ m = const Z 3 ε 3 = C λ3 Z 3 valence electrons Compton electron For multi-component system: effective atomic number (Z eff) Z eff = 3 3 w i Z i n i=1 ε=photon energy Z=atomic number w=mole fraction n=number of components Arthur Holly Compton ( ) Material Zeff Air 7.3 hf = A + hf scatt + E kin incoming photon photon energy (kev) Water 7.7 Soft tissue 7.4 Bone 13.8 scattered photon Pair production incoming photon pair production (relevant only in therapeutic x-ray) attenuation mechanisms Dependence on photon energy and material Energy balance: Lead Water β - (electron) hf = 2m e c 2 + 2E kin β + (positron) m e=mass of electron c=speed of light E photon (MeV) E photon (MeV) radiation Pair production relevant in highenergy X-ray photons, γ- radiation. μ = τ + σ +κ μ m=mass attenuation coefficient τ m=photoeffect mass attenuation coefficient σ m=compton effect mass attenuation coefficient κ m=pair production mass attenuation coefficient

7 Summary of attenuation mechanisms Future trends of X-ray applications Mechanism Variation of μ m with E Variation of μ m with Z Energy range in tissue Rayleigh ~ 1 / E ~Z kev Spiral CT photoelectric ~1 / E 3 ~Z kev Compton falls gradually with E independent ~Z MeV pair production rises slowly with E ~ Z 2 > 5 MeV Virtual endoscopy Main contrast mechanism in diagnostic X-ray: photoelectric effect (~Z 3 ) 3D reconstruction Angiography