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Principles of CT

Principles of CT. Limitations of Radiography. Inefficient x-ray absorption: typically ~25% for par speed cassette (prior to rare earth technology) High Scatter-to-Primary Ratios: may have >50% scatter at receptor with large beams even with high ratio grid

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Principles of CT

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  1. Principles of CT

  2. Limitations of Radiography • Inefficient x-ray absorption: typically ~25% for par speed cassette (prior to rare earth technology) • High Scatter-to-Primary Ratios: may have >50% scatter at receptor with large beams even with high ratio grid • Receptor Contrast vs latitude: required film dynamic range limits film contrast • Superposition/Conspicuity: overlapping structures with 3D anatomy rendered on 2D image

  3. Focal Plane Tomography: Bocage 1921

  4. Early Attempts at CT • Gabriel Frank: 1940 Patent: described CT principles using optical backprojection reconstr (but no filter) • Takahashi (Japan, ‘40s, published 1956): describes equipment to image slices by backprojection • Tetel’baum et al (Russia, 1957): Accurate formulation of inverse Radon Transform; TV-based reconstruct • Kuhl & Edwards: (1963): cross-sectional NM images by back-projecting transmission data on oscilloscope • Alan Cormack: built simple CT to measure densities for radiotherapy. Shared Nobel Prize.

  5. Godfrey Hounsfield and EMI: 1967 • Considered areas where much information available but inefficiently used: radiography • Estimated that if efficient detection/analysis, attenuation coefficients measurable within 0.5% from transmission measurements ---> sufficient to distinguish soft tissue differences • Invisioned “slice” divided in small “voxels” • Experiments using Americium source (9-day acquisition) verified 0.5% accuracy achievable

  6. Pixels and Voxels

  7. 1st Generation Data Collection

  8. Hounsfield’s CT Formulation • Measurement Ni written as sum of attenuation of pixel along path • Solve simultan-eous equations from data at many positions and angles • Experiments achieved 0.5% accuracy.

  9. Hounsfield’s Experimental CT

  10. Specimen Scan with Lab Device

  11. 1st Generation Data Collection • 1 Pencil Beam and 1 NaI detector • 160 samples/traverse • 1o increms over 180o • 28,800 samples • Solved simultaneous equations (Fortran) • 1602 image matrix but reduced to 802 for practical clinical use

  12. EMI Mark 1

  13. Image Reconstuction

  14. Image Reconstuction

  15. Backprojection

  16. Backprojection (con’t)

  17. Convolution

  18. Filtered Backprojection

  19. CT Numbers: Hounsfield Units • Example 1: voxel contains water (up= uw): • CT# = 1000 x (uw - uw)/ uw = 0 • Example: voxel contains air (up≈ 0): • CT# = 1000 x (0 - uw)/ uw = 1000 x (-1) = -1000

  20. CT Numbers

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