CT Chapter 4: Principles of Computed Tomography

Radiography vs. CT Both based on differential attenuation of x-rays passing through body Radiography “Shadowgraph” using x-ray light source CT Cross-sectional image Image computed from pencil beam intensity measurements through only slice of interest

Limitations of Radiography 3D body rendered in 2D Structures superimposed on film Must view structure of interest through underlying / overlying structures Multiple views often required to adequately visualize a structure. Patient X-ray Beam Film

Limitations of Radiography Optical density dictated by total attenuation encountered by beam Thin highly-attenuating objects appear to be same density as thicker low- attenuating object. Patient X-ray Beam Film Thin dense object Thick less dense object

Early Solution: Conventional Tomography Tube and film move Rotate around fulcrum Image produced on film Objects above or below fulcrum plane change position on film & thus blur

Limitations of Conventional Tomography Overlying / underlying structures blurred, not removed 5-10% subject contrast difference required for objects to appear different many anatomic systems do not have this subject contrast

CT Advantages View anatomy without looking through underlying / overlying structures improves contrast Uses tightly collimated beam minimizes scattered radiation improves contrast Demonstrates very small contrast differences reliable & repeatedly CT X-ray Beam Conventional X-ray Beam

Film as a Radiation Detector Analog not quantitative Not sensitive enough to distinguish small differences in incident radiation Applications film badges therapy dosimetry

CT Detectors electronic / quantitative extremely sensitive small radiation input differences reliably & repeatedly measured & discerned output digitized & sent to computer

Data Aquisition Slice by slice One slice at a time Volume acquisition data for an entire volume collected patient moves in axial direction during scan tube traces spiral-helical path through patient

Scanning X-ray tube rotates around patient detectors also rotate for 3rd generation CT Detectors measure radiation transmitted through patient for various pencil beam projections Relative transmissions calculated Fraction of beam exiting patient Patient X-Ray beams

Scanning Patient X-Ray beam X-Ray detector Intensity measurements Computer Memory

Photon Phate What can happen to an x-ray photon passing through a material (tissue)? Material Incoming X-ray Photon ???

Photon Phate #1: Nothing Photon exits unaffected same energy same direction Material Incoming X-ray Photon Outgoing X-ray Photon

Photon Phate #2: Absorption Photon disappears Its energy is absorbed by material Material Incoming X-ray Photon

Photon Phate #3: Scatter Lower energy photon emerges energy difference deposited in material Photon usually emerges in different direction Material Incoming X-ray Photon Outgoing X-ray Photon

Photon Beam Attenuation Anything which removes original photon from beam absorption scatter Material Incoming X-ray Photon Material Incoming X-ray Photon Outgoing X-ray Photon

Example Beam Attenuation (Mono-energy source) Each cm of material reduces beam intensity 20% exiting beam intensity 80% of incident for 1 cm absorber 1cm *.8 = *.8 = *.8 = *.8 = 41

Attenuation Equation for Mono-energetic Photon Beams I = I o e -  x I = Exiting beam intensity I o = Incident beam intensity e = constant (2.718…)  = linear attenuation coefficient property of absorber material beam energy x = absorber thickness Material IoIo I x For photons which are neither absorbed nor scattered

Example Beam Attenuation Using equation to calculate beam intensity for various absorber thicknesses (  =.223) 1cm I = I o e -  x 100*e -(0.223)(1) = %

Example Beam Attenuation Using equation to calculate beam intensity for various absorber thicknesses (  =.223) 1cm I = I o e -  x 100*e -(0.223)(2) = %

Example Beam Attenuation Using equation to calculate beam intensity for various absorber thicknesses (  =.223) 1cm I = I o e -  x 100*e -(0.223)(3) = %

Example Beam Attenuation Using equation to calculate beam intensity for various absorber thicknesses (  =.223) 1cm I = I o e -  x 100*e -(0.223)(4) = %

More Realistic CT Example Beam Attenuation for non-uniform Material 4 different materials 4 different attenuation coefficients #1#2#3#4 11 22  44 IoIo I x I = I o e -(   +   +   +   )x

Effect of Beam Energy on Attenuation Low energy photons more easily absorbed High energy photons more penetrating All materials attenuate a larger fraction of low than high energy photons Material Higher-energy mono-energetic beam 30 Material Lower-energy mono-energetic beam 100

Mono vs. Poly-energetic X-ray Beam Equations below assume Mono-energetic x-ray beam #1#2#3#4 11 22  44 IoIo I x I = I o e -(   +   +   +   )x I = I o e -  x

Mono-energetic X-ray Beams Available from radionuclide sources Not used in CT because beam intensity much lower than that of an x-ray tube

X-ray Tube Beam High intensity Produces poly-energetic beam #1#2#3#4 11 22  44 IoIo I x I = I o e -(   +   +   +   )x

Beam Hardening Complication Attenuation coefficients  n depend on beam energy!!! Beam energy incident on each block unknown Four  ’s, each for a different & unknown energy 11 22  44 1cm I = I o e -(   +   +   +   )x

Beam Hardening Complication Beam quality changes as it travels through absorber greater fraction of low-energy photons removed from beam Average beam energy increases 1cm Fewer Photons But higher avg kV than A Fewer Photons But higher avg kV than B A B Fewer Photons But higher avg kV than C CD Fewer Photons But higher avg kV than D E

Your Job: Stop People at the Gate Set up multiple gates, one behind the other Catch as many as you can at first gate Catch as many as you can who got through gate #1 at gate #2 Monitor average weight of crowd getting through each gate

Reconstruction Scanner measures “I” for thousands of pencil beam projections Computer calculates tens of thousands of attenuation coefficients one for each pixel Computer must correct for beam hardening effect of increase in average beam energy from one side of projection to other I = I o e -(   +   +   +   +  )x

Data Acquisition Geometries All CT generations obtain same set of multi- line transmission measurements in many directions Generational differences Protocol for obtaining line transmissions geometry / location of tube / detector motion # of line transmissions obtained simultaneously speed

Why is CT done with High kV’s? Less dependence of attenuation coefficient on photon energy Attenuation coefficient changes less at higher kV’s Reduce contrast of bone relative to soft tissue Produce high radiation flux at detector

Common Data-Acquisition Geometries Tube rotates around patient Detector system Rotates with x-ray tube (3rd generation) Stationary (4th generation) 360 o ring of detectors

3rd Generation Geometry Patient Tube / Collimator Rotating Detector Array

3rd Generation Geometry Patient Z-axis orientation perpendicular to page

4th Generation Geometry Patient Tube / Collimator Stationary Detector Array

4th Generation Geometry Patient

Image Reconstruction One of these equations for every projection line I A = I o e -(   +   +   +   +  )x Projection #A I C = I o e -(  C  +  C  +  C  +  C  +  )x Projection #C Projection #B I B = I o e -(   +   +   +   +  )x

Image Reconstruction I A = I o e -(   +   +   +   +  )x I B = I o e -(   +   +   +   +  )x I C = I o e -(  C  +  C  +  C  +  C  +  )x Projection #A Projection #B Projection #C I A, I B, I C,... What We Measure:  A1,  A2,  A3,... Reconstruction Calculates:  B1,  B2,  B3,...  C1,  C2,  C3,... Etc. *

CT Number Calculated from reconstructed pixel attenuation coefficient  t -  W ) CT # = 1000 X  W Where: u t = linear attenuation coefficient for tissue in pixel u W = linear attenuation coefficient for water

CT Numbers for Special Stuff Bone: Water: 0 Air:  t -  W ) CT # = 1000 X  W

Display & Windowing Gray shade assigned to each pixel value (CT #) Windowing Assignment of display brightness to pixel values does not disturb original pixel values in memory Operator controllable window level 47 93

Display & Display Matrix: Resolution CT images usually 512 X 512 pixels Display resolution better often 1024 X 1024 can be as high as 2048 X 2048 $$$

Display & Display Matrix: Contrast CT #range to 3000 Monitor can display far fewer gray shades Eye can discern few gray shades Purpose of Window & Leveling display only portion of CT # values Emphasize only those CT #’s display of CT #’s above & below window all black OR all white

Pixel Values & Gray Shades # of valid pixel values depends on bit depth 1 bit: 2 values 2 bits: 4 values 3 bits: 8 values 8 bits: 256 values 10 bits: 1024 values n bits: 2 n values

Pixel Values & Gray Shades CT can discern ~ 4000 gray shades Typical bit depth: 10 bits = 1024 gray shades Single gray shade represents range of pixel values

Silly CT # Display Example: 10 Gray Shades > <301

CT # Level Change Darks lighter lights lighter

CT # Level Change > <301 > (-49)-0 (-99)-(-50) (-149)-(-100) (-199)-(-150) <(-199)

CT # Level Change > <301 > (-49)-0 (-99)-(-50) (-149)-(-100) (-199)-(-150) <(-199) Window: 400 Level: 500 Window: 400 Level: 0

CT # Window Change Darks darker, lights lighter

CT # Window Change > <301 > <101

CT # Window Change > < > <101 Window: 800 Level: 500 Window: 400 Level: 500

Pixels & Voxels Pixel is 2D component of an image Voxel is 3D cube of anatomy CT reconstruction calculates attenuation coefficients of Voxels CT displays CT numbers of Pixels as gray shades

Pixel & Voxel Size Voxel depth same as slice thickness Pixel dimension field of view / matrix size FOV = 12 inches 256 pixels 12 inches Pixel size = pixels Pixel size =.047”

CT Systems X-Ray Production X-Ray Detection Computer Systems Reconstruction X-Ray Tube Detectors A - D Conversion Display & Format Printing Archiving Generator

CT Advantages Excellent low-contrast resolution sensitive detectors small beam size produces little scatter Much better than film

CT Advantages Adjustable contrast scale window / level Other digital image manipulations filters bone / soft tissue edge enhancement Region of interest analysis

CT Advantages Spiral volume data acquisition in single breath hold no delay between slices improved 3D imaging improved multi-planar image reformatting Special applications bone mineral content radiation treatment planning CT angiography

CT Advantages Muti-slice Scans at much greater speed OR Allows scanning of same volume with thin slices Makes possible additional clinical applications

CT Disadvantages Poorer spatial resolution than film Higher dose to in-slice tissue Physical set-up can limit to axial / near-axial slices Artifacts at abrupt transitions bone / soft tissue interfaces metallic objects