title: Scaling-law for the energy dependence of anatomic power spectrum in dedicated breast CT.
abstract: OBJECTIVE
  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.
authors.affiliation: Department of Radiology, University of Massachusetts Medical School, Worcester, MA 01655, USA. srinivasan.vedantham@umassmed.edu
authors.forename: Srinivasan
authors.initials: S
authors.lastname: Vedantham
authors.forename: Linxi
authors.initials: L
authors.lastname: Shi
authors.forename: Stephen J
authors.initials: SJ
authors.lastname: Glick
authors.forename: Andrew
authors.initials: A
authors.lastname: Karellas
mesh_terms: D001940:Breast / Q000033:anatomy & histology*; D008327:Mammography / Q000379:methods*; D008962:Models, Theoretical; D013057:Spectrum Analysis; D014057:Tomography, X-Ray Computed / Q000379:methods*