### Abstract

Purpose: To determine the x-ray photon energy dependence of the anatomic power spectrum of the breast when imaged with dedicated breast computed tomography (CT). Methods: A theoretical framework for scaling the empirically determined anatomic power spectrum at one x-ray photon energy to that at any given x-ray photon energy when imaged with dedicated breast CT was developed. Theory predicted that when the anatomic power spectrum is fitted with a power curve of the form k f^{-β}, where k and β are fit coefficients and f is spatial frequency, the exponent β would be independent of x-ray photon energy (E), and the amplitude k scales with the square of the difference in energy-dependent linear attenuation coefficients of fibroglandular and adipose tissues. Twenty mastectomy specimens based numerical phantoms that were previously imaged with a benchtop flat-panel cone-beam CT system were converted to 3D distribution of glandular weight fraction (f_{g}) and were used to verify the theoretical findings. The 3D power spectrum was computed in terms of f_{g} and after converting to linear attenuation coefficients at monoenergetic x-ray photon energies of 20-80 keV in 5 keV intervals. The 1D power spectra along the axes were extracted and fitted with a power curve of the form k f^{-β}. The energy dependence of k and β were analyzed. Results: For the 20 mastectomy specimen based numerical phantoms used in the study, the exponent β was found to be in the range of 2.34-2.42, depending on the axis of measurement. Numerical simulations agreed with the theoretical predictions that for a power-law anatomic spectrum of the form k f^{-β}, β was independent of E and k(E) = k _{1}[μ_{g}(E) - μ_{a}(E)]^{2}, where k_{1} is a constant, and μ_{g}(E) and μ_{a}(E) represent the energy-dependent linear attenuation coefficients of fibroglandular and adipose tissues, respectively. Conclusions: Numerical simulations confirmed the theoretical predictions that in dedicated breast CT, the spatial frequency dependence of the anatomic power spectrum will be independent of x-ray photon energy, and the amplitude of the anatomic power spectrum scales by the square of difference in linear attenuation coefficients of fibroglandular and adipose tissues.

Original language | English (US) |
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Article number | 011901 |

Journal | Medical physics |

Volume | 40 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2013 |

Externally published | Yes |

### Keywords

- anatomic noise
- breast computed tomography
- cascaded linear systems
- mammography

### ASJC Scopus subject areas

- Biophysics
- Radiology Nuclear Medicine and imaging

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## Cite this

*Medical physics*,

*40*(1), [011901]. https://doi.org/10.1118/1.4769408