Final answer:
The relationship between the CT number and Hounsfield units involves a simple linear transformation using the attenuation coefficients of the material, water, and air.
Step-by-step explanation:
The conversion equation that relates Hounsfield units (HU) to the CT number is essentially a linear transformation. Hounsfield unit is a quantitative scale for describing radiodensity in medical computed tomography (CT), and it's defined using the following equation:
HU = 1000 * ((μ - μwater) / (μwater - μair))
Where μ represents the linear attenuation coefficient of the material being scanned, μwater is the linear attenuation coefficient of water, and μair is the linear attenuation coefficient of air. In this equation, pure water has been assigned a value of 0 Hounsfield units, while air is assigned a value of -1000 Hounsfield units. This scale provides a measurable framework for identifying the different tissues within a scan based on their radiodensity relative to water and air.