X-ray attenuation coefficient of mixtures: inputs for dual-energy CT

The attenuation coefficient, μ(E) of substances, at any energy (E) of the x-ray photon, is known to depend on the electron density (ρ(e)) and the effective atomic number (Z(eff)) of the material. While the dependence on ρ(e) is known to be linear, that of Z(eff) is found to follow a power law (Z(eff))(x) which makes it very sensitive to the index "x". Several different values, lying between 3 and 4 have been suggested for the exponent x, in the existing literature. The purpose of the present investigations is to ascertain empirically the value that should be assigned to x.

This is done by measuring the HU value of different mixtures, having different values for ρ(e) and Z(eff) (calculated from their known chemical compositions) and thus determining the dependence of their attenuation coefficients (μ) on the above two quantities.

The experimental results show the dependence of μ on Z(eff) to be of the power law type, [ρ(e)(Z(eff))(x)/E(y)], where y = 3.0669 but no single value for the index x, can be assigned to fit the observed data. It is seen in different mixtures that the value of x predominantly decreases as Z(eff) increases from 7.5 to 12.

This result points out that very large errors can occur in calculating Z(eff) from the values of μ if a fixed value for x is used. The importance of this result to dual energy computed tomography is pointed out and it is concluded that the proper values for x are required to be incorporated in the inversion algorithms, for the different regimes of Z(eff).