Computed Tomography PDF

RANZCR AIT Computed Tomography Lucy Cartwright Senior Medical Physics Specialist (Radiology) Westmead Hospital Lecture Overview 1....

RANZCR AIT Computed Tomography Lucy Cartwright Senior Medical Physics Specialist (Radiology) Westmead Hospital Lecture Overview 1. Basic principles of cross sectional imaging 2. Image reconstruction and display 3. CT components 4. CT design and operation 5. Image quality 6. Artefacts 7. CT dose 1  Basic Principles Cross‐sectional imaging Computed tomography (CT) is an imaging technique where two‐dimensional cross sectional images (“slices”) are created from three‐dimensional body structures. – Mathematical principle developed by Radon in 1917: An image of an unknown object can be produced if one has an infinite number of projections through the object. – Made possible by computers (imagine interpreting 360 chest X‐rays taken from different angles!). Basic Principles Attenuation X‐ray images, in general, are obtained by measuring the intensity of an X‐ray beam that has been attenuated by the patient. – Attenuation is a reduction in beam intensity. In X‐ray imaging, this is due to the interaction of the X‐ray photons with the object (i.e. person) it passes through. 2 https://radiologykey.com/image‐production/  Basic Principles Attenuation Coefficient The fraction of photons removed from an X‐ray beam is characterised by the linear attenuation coefficient, µ. – µ is the sum of the individual linear attenuation coefficients for each type of interaction. 𝜇 𝜇 𝜇 𝜇 µ ‐ Water Basic Principles Attenuation Coefficient  is dependant on: Photoelectric ‐ 1/E3, Z3, ρ Compton ‐ 1/E, ρ – Density The relationship between density and attenuation is linear. – Atomic Number Only relevant for the photoelectric effect. Photoelectric attenuation is much higher in high atomic number tissue (e.g. bones). – Energy Attenuation decreases with increasing energy. – Photoelectric effect decreases significantly with energy, Compton effect is ~constant in the diagnostic energy range. 3  Basic Principles Attenuation Typical average CT X‐ray energy is ~ 60 keV Source: ARPANSA Accelerating Average Potential Photon Energy – Higher than other diagnostic imaging Mammography 26‐30 kV 20 keV modalities, heavily filtered “hard” spectrum. General 50‐140 kV 40 keV Effective Z of bone is ~12.3, tissue ~6.5 CT 80‐140 kV 60 keV (NIST). Attenuation in CT is caused predominantly by Compton Scattering, and some Photoelectric Effect. – At ~ 75 keV, Compton interactions account for; ~ 91% in muscle, ~ 94% for fat, ~ 74% in bone. Basic Principles Attenuation CT contrast is therefore mainly from physical properties that influence Compton scatter; – Physical density (dominant role). – Electron density (approximately constant for tissues other than lung). The photoelectric effect also has a minor effect; – Atomic number (minor role). Can be important for dual energy CT (discussed later). 4  Basic Principles Attenuation The reduction in intensity of an X‐ray beam is given by Beer’s Law; Incident Intensity Path length Average linear Transmitted attenuation Intensity coefficient Basic Principles Attenuation Solving Beer’s law for μ; 1 𝐼 𝜇 ln 𝑥 𝐼 5  Basic Principles Attenuation Can calculate µ from the measured X‐ray intensity: Generated 1 𝐼 𝜇 ln 𝑥 𝐼 Path length Measured Basic Principles Attenuation Coefficient Corrections  is a constant for a homogeneous material and monochromatic x‐rays and is a measure of the total interaction probability per unit length of material. In real world situations, µ needs corrections for inhomogeneous objects and polychromatic radiation. – X‐ray production is polychromatic. – Characteristic X‐rays are produced. Kα – Somewhat mitigated by filtration Relative intensity Characteristic Peaks (more later) and calibration, but can Kβ still lead to beam hardening artefacts (more later). 0 20 40 60 80 100 120 140 Energy, keV 6  Basic Principles Attenuation Coefficient Corrections  is a constant for a homogeneous material and monochromatic x‐rays and is a measure of the total interaction probability per unit length of material. In real world situations, µ needs corrections for inhomogeneous objects and polychromatic radiation. –  is the average linear attenuation coefficient. 0.8 Average µ= 0.163 cm‐1 0.6 µ 0.4 0.2 0 0 5 10 15 20 25 1 𝐼 𝐼 𝑒 0.8 I 0.6 I= 0.018, or 1.8% 0.4 0.2 0 0 5 10 15 20 25 Basic Principles Attenuation Coefficient Corrections  is a constant for a homogeneous material and monochromatic x‐rays and is a measure of the total interaction probability per unit length of material In real world situations, µ needs corrections for inhomogeneous objects and polychromatic radiation –  is the average linear attenuation coefficient. – CT reconstruction recovers the distribution of . 7  CT Image Formation µ is calculated through a ray line from the source to the detector: – Raw data is corrected for variations in detector sensitivity, gain, X‐ray inhomogeneities e.g. anode‐heel, ISL, bow‐tie filter, dead elements (interpolated) etc. – Logarithmic transformation to convert attenuation to µ. Attenuation Detector CT Image Formation µ is calculated through a ray line from the source to the detector: Many ray lines → projec on image. – Assumes parallel data. Attenuation Detector 8  CT Image Formation Parallel Beam Re‐binning µ is calculated through a ray line from the source to the detector: Many ray lines → projec on image. – Assumes parallel data. Modern CT scanners are fan beam geometry. Need to re‐bin the fan‐beam data into parallel beam format. – Combine data from adjacent detectors in subsequent views. CT Image Formation µ is calculated through a ray line from the source to the detector: Many ray lines → projec on image. Many projec ons → Sinogram. – Obtain 2D ‘projections’ at all angles around the patient. – At each angle, sample µ at each detector. – Tube and detectors rotate around Projections the patient. – Generate a series of projections (sinogram). Rays 9  CT Image Formation µ is calculated through a ray line from the source to the detector: Many ray lines → projec on image. Many projec ons → Sinogram. Reconstruct data → CT images. – Several reconstruction methods are available: Back Projection. Filtered Back Projection. Iterative. – Scatter correction can be applied to the data. – Adaptive noise filtering (smoothing out the noisiest areas) can also be applied before reconstruction (the reconstruction is limited by the nosiest ray). Data Processing Reconstruction Data is the total attenuation along a ray line (average ). Need to convert to initial distribution. 10  Reconstruction Algorithms Back Projection Start with an empty matrix. I0 I0 I0 µ1 µ2 7 ? ? I0 µ3 µ4 9 ? ? 4 3 5 4 12 11 8 1 Reconstruction Algorithms Back Projection Each projection is ‘smeared’ across the image: – The  value from each ray is added to each pixel in a line through the image corresponding to the ray’s path. µ1 µ2 7 7 7 I0 µ3 µ4 9 9 9 11  Reconstruction Algorithms Back Projection Each projection is ‘smeared’ across the image: – The  value from each ray is added to each pixel in a line through the image corresponding to the ray’s path. I0 µ1 µ2 18 11 µ3 µ4 10 20 4 11 1 Reconstruction Algorithms Back Projection Each projection is ‘smeared’ across the image: – The  value from each ray is added to each pixel in a line through the image corresponding to the ray’s path. I0 µ1 µ2 22 23 µ3 µ4 14 32 4 12 12  Reconstruction Algorithms Back Projection Each projection is ‘smeared’ across the image: – The  value from each ray is added to each pixel in a line through the image corresponding to the ray’s path. I0 µ1 µ2 25 28 µ3 µ4 19 40 3 5 8 Reconstruction Algorithms Back Projection The final values are then normalised. µ1 µ2 3 4 µ3 µ4 1 8 Subtract an offset (16) Normalise (÷3) 13  Reconstruction Algorithms Back Projection Produces blurred trans‐axial images. Copyright © NSW Hospital and University Radiation Safety Officers Group Reconstruction Algorithms Filtered Back Projection Need to mathematically filter projection data to remove the blurring. – Can be performed before, after or during backprojection. – Involves convolving the projection data with a convolution kernel (not covered here). Projection data Filtered Projection data 14  Reconstruction Algorithms Filtered Back Projection The easiest way to apply this filter is by doing a Fourier Transform. – Spa al data → frequency data. – Convolution in the spatial domain = multiplication in the frequency domain. The higher frequency components (edges/noise) are scaled down, then the inverse Fourier Transform is applied. – There are many different filters used for varying clinical applications. – Detailed design of filters is often proprietary. Filtering FT + IFT Filtered Projection data Projection data Reconstruction Algorithms Filtered Back Projection 1/r blurring is removed. 15 Copyright © NSW Hospital and University Radiation Safety Officers Group  Filtered Back Projection Filters Soft tissue (smooth) filter; Bone (sharp) filter; – High frequency cut‐off. – Less high frequency cut‐off. Less noise. More noise. Lower spatial resolution. Higher spatial resolution. Improved contrast resolution. Hamming Shepp‐Logan Amplitude Amplitude Frequency Frequency Reconstruction Algorithms Iterative Measured Projections The idea: – Measure some data – Make a first guess of the image – Derive what data would result in our guess – Compare derived data with measured data – Update the guess (1 iteration) – Continue until certain criteria is met Compute Projections 16 First guess – could be blank or FBP  Reconstruction Algorithms Iterative Measured Projections The idea: – Measure some data – Make a first guess of the image – Derive what data would result in our guess – Compare derived data with measured data – Update the guess (1 iteration) – Continue until certain criteria is met Compare! First guess – could be blank or FBP Reconstruction Algorithms Iterative Measured Projections The idea: – Measure some data – Make a first guess of the image – Derive what data would result in our guess – Compare derived data with measured data – Update the guess (1 iteration)* – Continue until certain criteria is met Compute Update *How the update is 17 computed is beyond the Updated guess scope of material here.  Reconstruction Algorithms Iterative 1 2 3 4 5 6 Reconstruction Algorithms Comparison (simulated) Actual FBP Iterative Error ‐ MSE 94 10 Time ‐ Secs 0.7 18 18  Pixels & Voxels Resulting images are axial “slices” through the body. The image is divided up into individual picture elements (Pixels). Each pixel in a CT image represents a volume (Voxels) with the depth as the reconstructed slice thickness. Slice thickness Reconstruction Matrix Images are typically 512x512 pixels. – A larger reconstruction matrix (e.g. 1024x1024) gives better spatial resolution (pixels are smaller), but the reconstruction will take longer (more complex), and the noise in each pixel will increase (less photons used = higher relative noise). 512 x 512 50 x 50 19  Field of View The physical area of the patient to be reconstructed is determined by the field of view (FOV). – E.g. Head ~250 mm, Body ~500 mm. – A smaller FOV will improve spatial resolution (matrix is fixed so the effective pixel size is smaller) 512 x 512 Matrix 512 x 512 Matrix 250 mm FOV 125 mm FOV 0.5 mm pixel size 0.25 mm pixel size https://www.upstate.edu/radiology/education/rsna/ct/reconstruction.php Data CT Numbers The reconstructed value in each pixel represents the linear attenuation coefficient. –  values (linear attenuation coefficient) are scaled to water to give a CT Number (expressed in Hounsfield units). tissue ‐ water CT Number (HU) = x 1000 water 20  Data CT Numbers CT numbers are quantitative: 3000 Blood – Water = 0 Liver 60 Tumor – Air = ‐1000 Spleen Kidneys Heart – Bone = ~1000 40 Bone Pancreas Bladder Adrenal Gland Intestine Water 0 -100 Mamma -200 Fat -900 Air Lung -1000 Copyright © NSW Hospital and University Radiation Safety Officers Group Multiplanar Reconstruction (MPR) The native format of CT is axial slice images. Can recompute images to be sagittal or coronal. – Z‐axis resolution limited by the reconstructed slice thickness. – Use thinner slices if MPR images are needed. 21  3D Reconstruction Slice data can also be rendered to form 3D surfaces. – A hypothetical observer point is created. – Rays are projected from this observer through a virtual monitor screen (defines displayed pixels) and then through the reconstructed (and interpolated) CT volume. Luccichenti, G. et al. 3D reconstruction techniques made easy: know‐how and pictures. Eur Radiol (2005). 3D Reconstruction Slice data can also be rendered to form 3D surfaces. – The final displayed value can be: The sum of all values along the ray (similar to a conventional X‐ray). The maximum value (maximum intensity projection MIP) (or minimum). The value of the point closest to the screen and above a threshold (can display surfaces). The sum of all values along the ray BUT the values have been adjusted by some amount based on their value so that only particular tissues are included (volume rendering). 22 Luccichenti, G. et al. 3D reconstruction techniques made easy: know‐how and pictures. Eur Radiol (2005). End CT 1/3 Home time 23