Ilkka Nissil 3.10.2019 Aalto University School of Science Department - PowerPoint PPT Presentation

Ilkka Nissilä 3.10.2019 Aalto University School of Science Department of Neuroscience and Biomedical Engineering (NBE)

Practicalities  Lectures: 3.10. and 10.10.  Exercise sessions: 4.10., 9.10., 11.10. and 16.10.  Teachers: Ilkka Nissilä and Tuomas Mutanen  The assignment involves familiarization with X ‐ ray propagation and computed tomography  Return the exercise by 17.10. and the learning journal by 21.10.

X ‐ ray imaging Computed tomography – three ‐ dimensional imaging using x ‐ rays 1979 Nobel Prize in Medicine: Hounsfield and Cormack

Applications of CT

This week’s lecture  Physics of X ‐ ray imaging  Generation of X ‐ rays  Interaction between X ‐ rays and tissue  Detection of X ‐ rays  Imaging geometry and forward model  Planar imaging (2D)  Computed Tomography (3D imaging)

Principle of 2D X ‐ ray imaging (planar imaging) Planar X ‐ ray imaging creates a 2D projection of the tissue • Photoelectric effect (absorption) Scintillator creates contrast between tissues Photodiode array TFT matrix • Scattered x ‐ ray photons reduce contrast

What are x ‐ rays? • X ‐ rays are electromagnetic radiation in the gamma range • Photon energy E = h ν = hc/ λ ~ 6e ‐ 34*3e8/1e ‐ 10J ~ 2 fJ ~ 10keV • X ‐ rays penetrate tissue quite well but are attenuated due to photoelectric effect and Compton scattering • High ‐ energy gamma rays have higher probability of Compton scattering than x ‐ rays

Radiation dose in clinical use • Effective dose equivalents HE = Biological effect of radiation – Dental 0.01 mSv 1 Gy = 1 J/kg absorbed dose – Breast 0.05 mSv 1 Sv = 1 J/kg ”equivalent” in – Chest 0.02 ‐ 0.2 mSv terms of biological effect – Skull 0.15 mSv For gamma and x ‐ ray, – Abdominal 1.0 mSv 1 Gy => 1 Sv – Barium fluoroscopy 5 mSv – Head CT 3 mSv For alpha, 1 Gy => 20 Sv – Body CT 10 mSv • Natural background radiation 0.3 ‐ 3 mSv/year in Finland • Diagnostic x ‐ ray amounts to 14% increase in total radiation worldwide

X ‐ ray source: the x ‐ ray tube 10 ‐ 7 atm pressure • • 15 to 150 kV rectified alternating voltage between cathode and anode • Cathode heated (~2200 deg C) tungsten Number of x ‐ ray photons in � ) � (mA) the beam � ∝ ��� filament wire kVp = accelerating (peak) voltage • Thermionic emission mA = filament current • Anode: rotating disc, covered by a layer of tungsten, tungsten ‐ rhenium or molybdenum, liquid cooling

X ‐ ray tube output energy spectra Different filters Peaks correspond to affect x ‐ ray energy characteristic X ‐ rays content (anode material property) Brehmsstrahlung Electrons hop from outer continuous spectrum Aluminum filter to inner shell => X ‐ ray (deflection of incoming = standard beam electron) energy content (e.g. for imaging the torso) X ‐ ray tube housing Molybdenum filter absorbs = low energy content low ‐ energy (used e.g. in X ‐ rays mammography)

X ‐ ray interaction with tissue Mass attenuation coefficient is absorption coefficient [1/cm] divided by density [g/cm^3] • Interaction of x ‐ rays with tissue includes absorption (photoelectric effect); Compton scattering and Rayleigh scattering • Photoelectric effect is the most frequent event in tissue ‐ x ‐ ray interaction and it produces useful diagnostic contrast • Probability of each event type depends on the energy of the radiation and the material properties

Photoelectric interaction  In the photoelectric interaction between X ‐ ray and tissue, an inner electron is ejected by the X ‐ ray  An outer electron takes up the vacancy and emits a low ‐ energy characteristic X ‐ ray which is absorbed quickly. � � ��� � ������������� ∝ � � �

Photoelectric absorption in tissue K edge: • Probability of PE event is more likely when the energy of incoming X ‐ ray is just above binding energy of K electron • Contrast between bone and soft tissue increased • Dual ‐ energy imaging can highlight the contrast

Compton scattering  In Compton scattering, an outer electron is ejected from a molecule  The original X ‐ ray is deflected by an angle θ

Rayleigh scattering  Rayleigh scattering is elastic i.e. the emitted X ‐ ray has the same wavelength as the incoming X ‐ ray  The angle of deflection is small.

Half ‐ Value Layer (HVL) How thick a slab of given tissue reduces the X ‐ ray beam intensity by 50%? Higher energy X ‐ rays are needed to get a useful image of the torso In mammography, the breast is compressed to a thickness of ~ 4 cm

Dual ‐ energy imaging  By starting from images obtained using X ‐ rays generated with two different tube voltages, it is possible to produce different weightings of bone and soft tissue, enhancing contrast  Can also suppress artifacts due to metal objects  Measurement of electron density

Instrumentation for planar x ‐ ray imaging

Digital Radiography TFT Array Detectors  TFT array detectors can be large  Indirect method: use scintillator and optical coupling to TFT matrix  Direct method: X ‐ rays release ion pairs; electrical coupling to TFT matrix

Anti ‐ scatter grids Lead strips Aluminium Length = h Thickness = t Separation = d Grid ratio = h/d Grid frequency = 1/(d+t) If the X ‐ ray source is close the beam divergence should be considered

Noise in x ‐ ray imaging: photon shot noise   n shot N  N    SNR N n  Photon shot noise is a key image quality parameter  η is the quantum efficiency, N number of photons hitting the detector during the exposure  N follows Poissonian statistics

Additional sources of noise in x ‐ ray detection  In addition to photon shot noise, detectors and electronics introduce additional noise sources  Dark current is the current that the detector generates when not exposed to X ‐ rays  Thermal electrons are separated from the photodetector material and amplified  The amplifiers add some noise of their own to the signal  In this course we can model these additional noise sources optionally with a Gaussian white noise term added to the photon count or intensity

Instrumentation for CT First and second generation devices used synchronized  translation of both the X-ray source and detector on opposite sides of patient First generation used a pencil beam  Second generation used a narrow fan beam 

Instrumentation for CT Third generation devices use a rotating assembly with an arc of  detectors and X-ray source on opposite side Fourth generation systems use a rotating X-ray source and a full  ring of detectors

Detectors in CT systems Scintillator crystals convert X-ray into light  Optical filler material between each crystal to prevent cross talk  Photodiodes convert the light into electrical signals 

Mathematical principles of CT ‐ measured data  Considering only the PE effect for simplicity, the reduction of the intensity of the x ‐ ray beam along the projection line is proportional to the absorption  The measured intensity at a single point at the detector is � � � � � �� � �  I 0 = source intensity  I = intensity at detector; n = noise

Projection �� � ����� �� � � ���� � � � �� � � � ��� � � � � � � log ��0� ���� � log � � � � � ��� � The projection p is an integral of the absorption coefficient along the line of propagation of the x ‐ rays

Calculating the projections Model of an axial slice with 3 x 3 resolution 4 9 6 Detectors Anti ‐ scatter grid 1 3 2 6 6 X ‐ ray tube positions for 3 2 5 10 5 the second orientation 3 0 1 2 4 Scanning 1 2 3 Rotate tube and order detector array X ‐ ray tube positions for the second orientation Measurements are electrical signals which are proportional to intensities � � � � � � � � � � �� = � � � �� � � � p � log � � � � � � � �� � � �Δ� � ���

Ray ‐ by ‐ ray image reconstruction 2nd iteration 1st iteration � ����,� �� �,� � ����,� �� �,� Correct by Correct by Original Initial guess � � � � 4 6 9 4 6 9 4 6 9 0 0 0 y 6 0 1 3 2 0 0 0 1.33 2 3 1.22 1.89 2.89 6.33 6 10 0 3 2 5 0 0 0 1.33 2 3 2.56 3.22 4.22 6.33 10 3 0 0 1 2 0 0 0 1.33 2 3 0.22 0.89 1.89 6.33 3 x 4 4 0 4 6 6 0 6 � ����,� 9 9 0 9 � � � � ���� � � ����,� � � � � � � � 6.33 3 0 3 6.33 10 0 10 6.33 6 0 6

Projection with multiple directions  For the first projection angle � � ���� � � � �, � ∆� ��� r y s �  For a general projection direction α x � � � � � � � �, � � ∆� �� � First projection along y axis; translation along x axis. � ��� � � � � ∆� r and s replace x and y in a rotated coordinate system

Sinogram First projection incidated by arrow Original image: attenuation varies between 0 and 1.5 The sinogram contains the measured (or simulated) projections; each row corresponds to a different projection angle and each column to a different translational position