Mathematics and Physics of Emerging Biomedical Imaging

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Table 3.1 Technological Improvements in the First 20 Years of Computed Tomography

Scan Parameter	Typical Values, 1972	Typical Values, 1994
Matrix size	80 x 80	1024 x 1024
Spatial resolution	3 line pairs/cm	15 line pairs/cm
Contrast resolution	5 mm/5 HU/50 mGy	3 mm/3 HU/30 mGy
Scan time	5 min	< 1 sec
Data size per scan	50 kByte	2 MByte
X-ray power	2 kW	40 kW
Definitions: mGy = milligrays, where a gray is the SI unit for radiation dose. HU = Hounsfield units; the contrast scale used in CT is defined by zero attenuation (air) = -1000 HU and attenuation coefficient of water = 0 HU (see equation 3.3).

three-dimensional representation of anatomical structures.

3.1.2 Principle of Operation

The attenuation of monochromatic x-rays in homogeneous objects is governed by

where I is the x-ray intensity behind the object, I ₀ is the x-ray intensity without the object, x is the length of the x-ray path through the object, and a is the linear attenuation coefficient of the material for the x-ray energy employed.

For inhomogeneous objects like the human body, the attenuation of x-rays consequently can be described by

This model is explored further in section 14.1.1.

In CT scanners the x-ray attenuation according to equation 3.2 is measured along a variety of lines within a plane perpendicular to the long axis of the patient with the goal of reconstructing a map of the attenuation coefficients a for this plane. The resulting attenuation coefficients are usually expressed with reference to water:

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