Computed Tomography Physics, Instrumentation, and Imaging Module E Computed Tomography Physics, Instrumentation, and Imaging

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Attenuation The reduction in the intensity of a radiographic beam as it travels through matter. Remnant radiation

X-ray Interactions Coherent scatter Compton Effect Photoelectric Effect Pair Production Triplet Production Photodisintegration

Diagnostic x-ray Interactions Compton – non-diagnostic Photoelectric Effects – the x-ray interaction which will result in a diagnostic image

Attenuation in CT Depends on: the effective atomic density in atoms/volume The Z-number of the absorber (atomic number) The energy of the x-ray photons

Linear Attenuation Coefficient Although the Photoelectric effect is more predominant…. The Compton interaction must be considered when developing mathematical formulas to determine the changes of x-ray attenuation through different tissue and then reconstruct images of the anatomy scanned. Requires: The application of physics Complex mathematics and Computer science WHY………….

CT and x-ray attenuation The determination of x-ray attenuation in body tissue and the use of that information to reconstruct images of the anatomy scanned is the basic problem in CT.

Homogeneous / Monochromatic Gamma radiation source with a pencil beam configuration was initially used in Hounsfield’s tests. A radiation source with 1 frequency was needed to use the Lambert-Beer Law for calculations. The attenuation characteristic of the homogeneous radiation source interacting with human tissue causes absorption of photons but no loss in the quality or energy of the beam. This allowed accurate calculations to be made determining the linear attenuation coefficients for human tissue.

Iin = Iout e -μx Lambert-Beer Law CT attenuation depends on Effective atomic density in atoms/volume The Z-number of the absorber (atomic number) The energy of the x-ray photons

Monochromatic vs. Polychromatic Original experiments using monochromatic – quality of the beam remained the same after interaction with tissue. Only the quantity changed allowing for the requirements necessary to use the Lambert-Beer Law for mathematic computations. Polychromatic beam (x-ray) attenuates at various rates….. Quantity and Quality are both changed. In addition, the beam geometry also changed from pencil to Fan-beam by using polychromatic x-ray radiation. The differences in beam energy frequencies creates the fan beam configuration of a divergent x-ray source.

New Equation N = Noe-μx N = the number of transmitted x-ray photons No = the number of x-ray photons entering body tissue (incidental photons) μ = equals the linear attenuation coefficients of the tissue (μp +μc) e = the base of the natural logarithm (Euler’s Constant of 2.718)

Because the x-ray beam in CT does not travel through a uniform block of tissue, the equation was modified to:

CT vs. Conventional radiography Cross-sectional imaging Eliminates superimposition Sensitive to subtle variations in x-ray attenuation Digital imaging processing technique Images produced from topographic maps of the x-ray linear attenuation coefficients.

Maxrix -an array of numbers composed of rows and columns -512 x 512 = 262,144 pixels -1024 x 1024 = 1,042,576 pixels

Matrix Pixels within the matrix represent various tissue types. Tissue differences are represented by CT numbers or Hounsfield units. A pixel is considered a two-dimensional representation

P (mm2) = DFOV (mm2) / Matrix Size Pixel size / Voxel size P (mm2) = DFOV (mm2) / Matrix Size Voxel Size (mm3) = DFOV (mm2) (slice thickness in mm) / Matrix Size

Pixel and Voxel

Sampling Process for determining attenuation values Type of measurement technique Enables CT to change analog information into digital information without losing information. Two types of Sampling Angular ray

Nyquist Theorem “Sampling must be performed at least twice the spatial frequency of the object scanned”.

Angular / Ray Sampling Angular Sampling- Ray Sampling- Determined by the distance between each view obtained during the scan Ray Sampling- Determined by the angle between each pair of rays within a view

Rays and Views 4th generation scans- View is a set of rays that strike a single (specific) detector (remember the tube is rotating around the patient in 4th generation scanners) The value of each ray is directly proportional to the transmitted photon measured and characterized as a CT number. Data from each view is called “Raw Data”