How to improve x-ray scattering techniques to quantify bone mineral density using spectroscopy
The ratio of CCSR(Z = 12)/CCSR(Z = 7) as a function of scattering angle at an incident energy of 60 keV. Tabular values (Ref. 26) for the form factor F(x, Z) were used in this simulation.
(a) A schematic of the experimental setup used for the FS–BS studies performed in this study. Included are collimators made from steel blocks, narrow shielded channels called beam-lines at forward angles of 10°, 15°, and 20°, at (complimentary) backward angles equal to 170°, 165°, and 160°, and at 90° and 180°, and 6 cm diameter central holes for samples including bone phantoms. Channels were about 20 cm long on either side of the sample hole. Widths were 1, 2, and 3 mm for the 10°, 15°, and 20° forward scattered, and for the 170°, 165°, and 160° backward scattered channels. (b) A photograph showing the FS–T configuration with the x-ray tube inside a shielded box, collimator channels for θ = 20° FS and T beams with the upper plate removed in order to show the beam channels, and two CdTe detectors to collect the FS and T radiation, and phantom #10 in the sample hole. A detector can be placed at the opposite end of the channel containing the FS beam to collect the BS beam.
Incident, forward scattered at 15°, and backscattered at 165° spectra recorded from a test object containing a mineral concentration of 166.7 mg/cm3 using a maximum voltage of 76.5 kV are shown. The endpoint energy of the incident beam appears to be slightly higher due to the summing effect as a consequence of high count rates.
The measured relative intensity of θ = 15° FS radiation as a function of the mineral density of the trabecular bone phantoms used in this study for five different fixed energies of 20, 30, 40, 50, and 60 keV.
The experimentally obtained relative intensity of θ = 165° backward scattered radiation as a function of the mineral density of the trabecular bone phantoms at energies of 20, 30, 40, 50, and 60 keV.
The FS–BS ratio measured at a fixed forward scattering angle of θ = 15°and a backscatter angle of θ = 165° as a function of the mineral density of the trabecular bone phantoms is plotted in this figure for each of five different fixed energies (20, 30, 40, 50, and 60 keV).
The relative intensity of the transmitted radiation as a function of the mineral density of the trabecular bone phantoms is given at each of five different energies (20, 30, 40, 50, and 60 keV).
The relative FS–T ratio measured at a forward scattering angle of θ = 15° as a function of the mineral density of the trabecular bone phantoms for each of three different fixed energies (20, 30, and 60 keV). Beginning at 35 keV, all relative FS–T ratios have almost an identical slope; therefore, only the 60 keV curve is given.
The ratio of the FS–T for the trabecular bone phantom of lowest mineral concentration (phantom #1) to that of the phantom of highest mineral concentration (phantom #10) FS–T (1)/FS–T(10) as a function of x-ray energy for a scattering angle of θ = 10°. This ratio is compared with a transmission index (the ratio of the intensity of radiation transmitted through phantom #1 to that of phantom #10 as a function of x-ray energy (E), T(1)/T(10)).
(a) A simulation of the attenuation correction for the FS–BS geometry (at 15° forward and 165° backward angles) with aluminum and Plexiglas attenuators located on opposite sides of the scattering materials with mean atomic numbers ranging from Z = 7 to Z = 12. (b) The attenuation correction factor measured for θ = 15° forward scattered and θ = 165° backward scattered beams for each of four energies (30, 40, 50, and 60 keV). In order to make this correction, ten phantoms were inserted between the aluminum and Plexiglas attenuators.
Accuracy, precision, and dosage of various present modalities for bone assessment and the CCSR methods used in the past.
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