Document Type


Date of Degree

Fall 2012

Degree Name

MS (Master of Science)

Degree In

Biomedical Engineering

First Advisor

John J. Sunderland


The phenomenon of x-ray beam hardening (BH) has significant impact on preclinical micro-CT imaging systems. The causal factors are the polyenergetic nature of x-ray beam used for imaging and the energy dependence of linear attenuation coefficient of the imaged material. With increase in length of propagation of beam in the imaged object, lower energy photons in the projected beam become preferentially absorbed. The beam "hardens" (as average energy increases) and progressively becomes more penetrating, causing underestimation of the attenuation coefficient. When this phenomenon is not accounted for during CT reconstruction, it results in images with nonuniform CT number values across regions of uniform density. It leads to severe errors in quantitative applications of micro-CT and degradation in diagnostic quality of images. Hence, correction for beam hardening effect is of foremost importance and has been an active area of research since the advent of micro -CT.

The Siemens Inveon micro-CT system uses a common linearization approach for BH correction. It provides a set of standard default coefficients to be applied during CT reconstruction. However, our initial experiments with uniform water phantoms of varying diameters indicated that the correction coefficients provided by default in the Inveon system are applicable for imaging mouse-size (~28 mm) objects only. For larger objects the correction factors yielded incorrect CT values along with characteristic 'cupping' observed in the uniform region in the center of the phantom. This study provides an insight into the nature and characteristics of beam hardening on the Inveon CT system using water phantoms of varying sizes. We develop and test a beam hardening correction scheme based on linearization using cylindrical water phantoms of two different diameters - 28 mm and 71 mm, selected to represent mouse and rat sizes respectively. The measured non-linear relationship between attenuation and length of propagation is fitted to a polynomial function, which is used to estimate the effective monoenergetic attenuation coefficient for water. The estimated effective linear attenuation coefficient value is used to generate the expected sum of attenuation coefficients along each x-ray path through the imaged object. The acquired poly-energetic data is then linearized to expected projections using a third order polynomial fit, which is consistent with the Inveon BH model and software. The coefficients of this trinomial are then applied for BH correction during CT reconstruction.

Correction achieved with the proposed model demonstrates effective removal of the characteristic cupping artifact that was observed when default BHC coefficients were applied. In addition to water phantoms, we also test the effectiveness of the proposed scheme using solid cylindrical phantoms of three different densities and composition. The proposed method was also used to measure the BH effect for 12 different kVp/filtration combinations. By generating twelve distinct sets of BHC coefficients, for each setting, we achieve a significant expansion in the quantitative performance of the Inveon CT system.


Attenuation, Beam Hardening, Linearization, Micro Computed Tomorgraphy, Polynomial, X-ray Spectrum


xii, 77 pages


Includes bibliographical references (pages 75-77).


Copyright 2012 Sucheta Mohapatra