### Abstract

**Purpose:**

The attenuation coefficient,*μ*(*E*) of substances, at any energy (*E*) of the x-rayphoton, 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*.

**Methods:** 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.

**Results:** 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.

**Conclusions:** 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}.

Received 07 June 2010
Revised 31 July 2011
Accepted 01 August 2011
Published online 09 September 2011

Acknowledgments: Ms. Rezvan Ravanfar Haghighi would like to thank the Shiraz University of Medical Sciences for granting leave and constant encouragement in the present work. The authors would like to acknowledge the help that she received from the Indian Institute of Astrophysics during her recent visit to the institute. Dr. J.M Boone is thanked for providing us with the computer programs to calculate the photon intensity distribution in the x-ray source, which is used in the present work. The referees of the paper are thanked for their careful, critical review, and encouragement, which improved the final version of the paper. The authors thank Dr. Vani V.C. for discussions on statistical tests. The Indian Council of Medical Research is thanked for financing the project.

Article outline:

I. INTRODUCTION

II. MATERIALS AND METHODS

II.A. Theoretical background

II.B. Estimate for the exponent *y*

II.C. Experimental study

II.D. Numerical process for data analysis

II.D.1. Estimate of (V) and (V)

II.D.2. Calibration

III. RESULTS

IV. CONCLUSION

Commenting has been disabled for this content