### 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) |
---|---|

Article number | 011901 |

Journal | Medical physics |

Volume | 40 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2013 |

Externally published | Yes |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Biophysics
- Radiology Nuclear Medicine and imaging

### Cite this

*Medical physics*,

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

**Scaling-law for the energy dependence of anatomic power spectrum in dedicated breast CT.** / Vedantham, Srinivasan; Shi, Linxi; Glick, Stephen J.; Karellas, Andrew.

Research output: Contribution to journal › Article

*Medical physics*, vol. 40, no. 1, 011901. https://doi.org/10.1118/1.4769408

}

TY - JOUR

T1 - Scaling-law for the energy dependence of anatomic power spectrum in dedicated breast CT

AU - Vedantham, Srinivasan

AU - Shi, Linxi

AU - Glick, Stephen J.

AU - Karellas, Andrew

PY - 2013/1

Y1 - 2013/1

N2 - 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 (fg) and were used to verify the theoretical findings. The 3D power spectrum was computed in terms of fg 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[μg(E) - μa(E)]2, where k1 is a constant, and μg(E) and μa(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.

AB - 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 (fg) and were used to verify the theoretical findings. The 3D power spectrum was computed in terms of fg 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[μg(E) - μa(E)]2, where k1 is a constant, and μg(E) and μa(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.

KW - anatomic noise

KW - breast computed tomography

KW - cascaded linear systems

KW - mammography

UR - http://www.scopus.com/inward/record.url?scp=84872050801&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872050801&partnerID=8YFLogxK

U2 - 10.1118/1.4769408

DO - 10.1118/1.4769408

M3 - Article

C2 - 23298092

AN - SCOPUS:84872050801

VL - 40

JO - Medical Physics

JF - Medical Physics

SN - 0094-2405

IS - 1

M1 - 011901

ER -