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 Receptor Contrast vs latitude: required film dynamic range limits film contrast Superposition/Conspicuity: overlapping structures with 3D anatomy rendered on 2D image

Focal Plane Tomography: Bocage 1921

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.

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

Pixels and Voxels

1st Generation Data Collection

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.

Hounsfield’s Experimental CT

Specimen Scan with Lab Device

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

EMI Mark 1

Image Reconstuction

Image Reconstuction

Backprojection

Backprojection (con’t)

Convolution

Filtered Backprojection

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

CT Numbers