Effect of Scattering on the Image. Reducing Compton Scatter with a Grid

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1 Effect of Scattering on the Image Increasing Compton scattering degrades image. Webb 21 Reducing Compton Scatter with a Grid Grids Parallel (focused at infinity) Linear Focused (see figure) Moving grids avoid grid lines. Grid increases exposure by grid conversion factor (GCF) (typically 3-8) Scattering worse for high kv photons and thick body parts. Linear Focused Grid 22 1

2 Air Gaps and Scanning Slits Air Gaps Increasing space between patient and the detector reduces scatter, because scattered photons diverge at a given angle. Must trade off with increased unsharpness as will be seen. Scanning Slits Mechanical slits that move together in front and in back of the patient. Only photons traveling a straight path make it through. Requires longer exposure, but not greater radiation to patient. 23 Film-Screen Detectors Intensifying screens consist of a phosphor and a mirror on both sides of the photographic film to convert x-rays into visible photons. Luminescence (photons generated by something besides heat, which is incandescence) 2 types of Luminescence involved here, both caused by incoming high energy photons (x-rays). Fluorescence - good (fast re-emission of lower energy photon) Phosphorescence - bad (much slower re-emission due to forbidden energy state transitions) Conversion Efficiency # light photons per x-ray photon (typically 10 3 ) 24 2

3 From Film To Detectors Film is basically almost completely gone UPMC is now filmless Detectors have great advantages Ability to adjust gain and offset afterwards Permits computational techniques such as Dual-Energy, which eliminates ribs from the chest X-ray by using two scans with different KeV. Linear combination (subtraction) to eliminate bones. Much easier to store, retrieve, and transmit the images. Dual Energy X-ray 25 X-ray Image Intensifier (Fluoroscopy) Fluoroscopy - like night vision goggles, but with extra input phosphor to convert x-rays to light photons, Light photons hit photocathode, generating electrons 26 Electrons are accelerated and focused at anode on output phosphor. 3

4 X-ray Image Intensifier (Fluoroscopy) Curved input phosphor/photocathode produces photoelectrons, which are focused by electrostatic lenses (dynodes) onto a fluorescent screen (output phosphor). Huge amplification ~200,000 light photons per x-ray photon. Magnification can be changed dynamically by voltage on dynodes. Webb 27 Image Formation - Linear Attenuation Recall Intensity = Energy x Flux As we have seen, attenuation of polyenergetic x-ray source (Bremsstrahlung) by a non-homogeneous structure yields where r(x,y) is the length of the path, S 0 (E) is spectrum of the incident x-rays, s is the distance from the x-ray source along the path and I(x,y) is the intensity of x-rays remaining. 28 4

5 Geometric Effects - Beam Divergence Diverging beam of x-rays yields inverse square law; r varies with (x,y). Uneven intensity between I O at detector origin and I r elsewhere on a flat detector, even before object attenuation. 29 Flat detector is not orthogonal to the beam except at the detector origin causing intensity on the detector I d to be lower than that at origin by Combines with beam divergence on previous slide to yield Geometric Effects - Obliquity 30 5

6 Anode Heel Effect stronger intensity beam in the cathode direction and no variation orthogonal to the cathode-anode direction Less attenuation from anode itself in this direction. Can be compensated for by a filter or used to compensate for variations in patient thickness 31 Path length through patient Consider homogeneous flat slab of thickness L Ignoring anode heel, and combining with obliquity and beam divergence: 32 6

7 Effect of shading artifact The preceding geometric effects create a gradual change in intensity with position that can be ignored by the radiologist, who can just concentrate locally. However this low frequency shading artifact can be undesirable for automated image analysis, and the models just presented may be used to cancel the effect, insofar as the models are accurate. 33 Depth-dependent object magnification Example of stick object object magnification M(z) 34 7

8 Imaging Equation with Geometric Effects When object is located at detector face, intensity at detector is When Things closer to x-ray origin appear larger 35 Blur due to extended source (geometric unsharpness) Non-zero spot size of the x-ray emission source, needed to prevent it from melting. 36 8

9 Blur due to extended source (geometric unsharpness) The physical extent of blurring caused by an extend source depends on the size of the source and the location of the object. Larger source, or greater distance from patient to detector, means more blur. penumbra (Latin for partial shadow) Webb 37 Principle of Source Magnification For a given z, convolution of the source shape with the object shape (with magnification effects also included). source magnification m(z) (negative because image is inverted) as opposed to object magnification M(z) disk function Ignoring geometric effects, including 1/r 2, so that all rays are passing through hole where k is constant for a given z 38 9

10 Solving for k as a function of z (this is more detail than you really need to know ) Recall that geometric effects are being ignored (including 1/r 2 ) integration yields DC component To find k take the Fourier transform, using the scale law As object approaches detector, integrated intensity independent of z dilution from source magnification so that no blurring occurs 39 Superposition of pin holes in one z plane Convolving the magnified (by M) object s transmittivity by the magnified (by m) and scaled (by geometric factors) source function. geometric factors source magnification object magnification see k in previous slide For objects close to the detector, convolution in 3D over entire object the object will have unity magnification, and will not be blurred by the source focal spot regardless of the focal spot size (convolution with impulse function)

11 PA / AP chest X-ray PA (posterior-anterior) X-rays hit the back first. AP (anterior-posterior) heart is blurred and magnified. from Lucy Squire 41 Mammography Very low X-ray energy Lower radiation dose Better soft tissue (PE effect) Less Compton scattering Looking for micro-calcifications. Very small focal spot. Minimize geometric unsharpness by Large focal-spot-to-film distance Small film-to-patient distance May use magnifying glass to see micro-calcifications. sprojects.mmi.mcgill.ca 42 11

12 Film-Screen Blurring Isotropic shower of light photons form spot on the film. Film-screen impulse response h(x,y) to x-ray photon impulse. Cascades with previous response derived for a single plane transmittivity. 43 Film-Screen Blurring typical MTF Thin phosphor, less blurring so higher resolution, but lower efficiency (% of x-ray photons stopped) thus higher noise. Thus a thicker phosphor may actually be better

13 Digital detectors have replaced film Large, high resolution digital cameras (like film) Still need phosphor to convert x-ray to visible light Permits dynamic adjustment of contrast after the fact Enables digital storage and distribution Radiographs were last hold-out in medical imaging Kodak has filed for bankruptcy Enables use of Pulsed X-Ray tubes (specialized scan) Very short pulses (12 nanosecond) High intensity but short duration, so reasonable dose. Permits movies like fluoroscopy, but much higher shutter speed Need digital detector to store sequence of snapshots Used in dynamic studies of motion in spine, joints, etc

14 Chapter 6 Computed Tomography Originally Computed Axial Tomography ( CAT scan) 1 Before computed tomography Motion tomogram produced by moving source and film in opposite directions to focus on a particular plane different planes temporomandibular joint exostosis in auditory canal CT has almost completely replaced this. Though CT has poorer in-plane resolution, it eliminated overlapping structures 2 1

15 Computed Tomography Invented mid-1960s Through 1970s and 1980s profound change in diagnostic imaging. Reduced exploratory surgery. CT numbers in Hounsfield units for quantitative analysis. Same fundamental physics. We will discuss geometries of generations of CT scanners. Mathematics of reconstruction Same can be used in SPECT, PET, MRI. gantry 3 Subdural Hematoma Note the midline shift and distorted ventricles

16 Lung Tumor contrast (iodine) in vasculature CT always seen from the patients feet, tumor in left lung. 5 Liver Tumors Liver is on patient s right. 6 3

17 Kidney and Intestines Oral and intravenous contrast were administered prior to the image. 7 Hepatic veins with contrast Reconstructed in the coronal plane. 8 4

18 First Generation (1G) CT scanner Single source and detector move in unison along a linear path. Then whole apparatus rotated around patient in the gantry. Arbitrary number of rays (paths). Arbitrary number of angular projections. Scattering goes mostly undetected and no collimators required No longer manufactured. 9 Second Generation (2G) CT scanner Additional detectors in an array. Still move linearly in unison, but can make larger rotation, reducing time (because multiple angles captured with each scan). Now scattering a problem and collimators required. This reduces efficiency and increases noise for a given dose. Payoff in reducing time is worth it. 10 5

19 Third Generation (3G) CT scanner More detectors in array, so fan beam covers entire patient. Linear motion no longer needed. Much faster. Collimators required to reduce scattering. Detectors smaller so less efficient. So for same SNR, higher dose required, but savings in time still win. 11 Fourth Generation (4G) CT scanner Complete ring of stationary detectors. Only the source rotates. Large detectors, since they lie on a large ring, so high detection efficiency. But collimators (between detectors) cannot be used, so noise is a problem. (Collimators still used axially to restrict beam to detectors overall) Overall image quality comparable to 3G 12 6

20 Fifth Generation (5G) CT scanner Electron Beam CT (EBCT) ultra-fast or cine CT Only ~150 in the world; 1 in Oakland Electronically steers beam across ring of stationary detectors No moving parts, 50ms per image Can image beating heart without gating to electrocardiogram US patent Sixth Generation (6G) CT scanner Helical (spiral) CT Rapid volumetric data acquisition (full torso in 30 seconds) Table moves smoothly as source (and in some scanners detectors) rotate continuously using slip rings. Fast enough for single breath-hold, reducing motion artifact. Becoming quite common. 14 7

21 Seventh Generation (7G) CT scanner Multislice CT Multiple rows of detectors, can detect simultaneously. Faster, higher resolution, many tricks can be played with combining detectors dynamically trading off resolution against signal-to-noise. Beautiful high-resolution cardiac studies gated to electrocardiogram. 15 Seventh Generation (7G) CT scanner Multislice CT

22 Cone-Beam CT Recent addition, a portable machine that spins around patient. Not as high quality an image, but used in the OR to guide intervention. Reconstructs 3D data sets from multiple projections on a flat sensor array X-ray source Most CT scanners have a single x-ray source (except EBCT) Expensive (need to be replaced frequently) Need to be constantly calibrated CT requires x-ray source to be approximated as monoenergetic. More filtering employed than with projection radiography Hardening the beam (removing lower energy x-rays) before it hits the patient (using aluminum and copper filter combinations). 18 9

23 CT Detectors All use photo-electric effect to produce photoelectrons, detected electronically. (a) Solid-state detectors, thicker crystals for higher efficiency. (b) Xenon gas tubes, less efficient, but highly directional (3G). (c) Multiple solid-state detector array, most common today. 19 Image Formation - Line Integrals Mathematically intractable for CT image reconstruction So we assume a single effective energy The basic measurement of a CT scanner is a line integral of the linear attenuation coefficient at the effective energy of the scanner (notice that I 0 is calibrated away)

24 Calibration and CT numbers Reference Intensity I 0 must be measured for each detector. However, Effective Energy still varies with each x-ray tube. To compensate, we normalize to The CT number in Hounsfield units (HU) is defined as Air HU Water 0 HU Bone ~1000 HU Metal > 3000 HU Contrast > 3000 HU because μ Air 0 Godfrey Hounsfield Reproducible across scanners +/- 2 HU 21 Parallel-Ray Reconstruction Project along a line Parametric form of projection Alternate form of projection using sifting 22 11

25 Radon Transform To characterize CT measurement, Johann Radon 1917 Attenuation coefficient of underlying unknown object. CT measurements along a given line at a given angle. 23 Example - Radon transform of unit disk due to symmetry, only need consider 24 12