Quantitative assessment of bone mineral by photon scattering: Calibration considerations

Abstract

The ratio of the coherent-to-Compton photons scattered from bone can be used to measure its mineral density. Conversion of this ratio (R) to bone mineral density (BMD) requires calibration using bone simulating phantoms. The widely used aqueous solution of K2HPO4 proved unsatisfactory for calibration purposes when using the coherent-to-Compton technique. These solutions differ markedly in their scatter spectra and composition from trabecular bone. In this study a new and more realistic series of phantoms is proposed which simulates well the trabecular bone of the calcaneum. These phantoms are made of bone ash suspended in white petrolatum in varying concentrations. A calibration curve has been established using these phantoms with a range of BMD values of 0 to 347 mg/cm3. The scatter spectra, and range of R values and BMD of these phantoms are in very good agreement with those of real trabecular bone. A measuring device has been built for the determination of the BMD of the calcaneum by using the established calibration curve.

Radioactivity Control of Composite Materials Using Low Energy Photon Radiation

“…If an angle θ is smaller than the "characteristic" angle (θ<θ 0 ), then if the "characteristic" angle θ 0 approaches 0, the scattering ratio is proportional to Z 2 and does not depend on the energy E. It is important to note that the ratio ⁄ increases with increasing atomic number Z and decreasing energy E. Taking the Thomas-Fermi approach into consideration, for the distribution of electron, the differential cross-section of the coherent scattering can be written as (Manninen, Pitkänen et al 1984 23 2 2 In this approach the differential cross-section ⁄ is proportional to , however, this is only correct for scattering angles bigger than the characteristic angle (Manninen and Koikkalainen 1984;Leichter, Karellas et al 1985). Based on the angular frequencies of incident photons and scattered photons the Klein-Nishina formula is approximated by the relation (Manninen, Pitkänen et al 1984;Perumallu, Rao et al 1985): …”

“…It is known (Karellas, Leichter et al 1983;Manninen and Koikkalainen 1984;Gigante, Pedraza et al 1985;Leichter, Karellas et al 1985;Perumallu, Rao et al 1985;Duvauchelle, Peix et al 1999), that the value of exponent n for large scattering angles is: n=3. The determination of Z eff from the ratio ⁄ depends on the separation of the spectrum lines of the coherently and incoherently scattered γ-quanta.…”

“…The exponential dependence of coherent to incoherent effective cross-sections scattering ratio from the is not obvious consequence of eq. (19), however it is expressed in functions F (Z) and S (Z) (Leichter, Karellas et al 1985). The values of index n depend on the value of the given scattering angle (the transfer of momentum during scattering is higher for larger values of the scattering angle).…”

How to improve x‐ray scattering techniques to quantify bone mineral density using spectroscopy

“…1 In these and other early studies, it was determined theoretically and verified experimentally that the intensity ratio of coherent to Compton scattered beams (CCSR) was strongly dependent upon the effective (or mean) atomic number of the scattering material, [2][3][4][5][6] Z eff . In particular, the theoretical proportionality between CCSR (R), the atomic number (Z), and the magnitude of the momentum transfer (x) is governed by the ratio of form factors [F(x, Z] 2 =S(x, Z), where F(x, Z) is the atomic form factor and S(x, Z) is the incoherent scattering function.…”

“…The origin of the incident gamma radiation in early CCSR studies was a radionuclide, 241 Am, source with a high activity of a few giga-becquerels and a long half-life of 432 years that requires strict radiation safety measures. Scattered beams were measured at a variety of angles, [8][9][10] from 22.5 to 135 , and CCSR was tested using K 2 HPO 4 water solutions 2,4,11 on phantoms made from trabecular bone ash and petrolatum 5,12 and on human subjects 13,14 where trabecular bone in the calcaneous (the heel) served as the scattering material. Most previous CCSR studies obtained good energy resolution and sensitivity through the use of large scattering angles (around 90 ).…”