Effects of overlying soft tissue on X-ray fluorescence bone lead measurement uncertainty

Effective atomic number of soft tissue, water and air for interaction of various hadrons, leptons and isotopes of hydrogen

PURPOSE

Characterization of soft tissue, water and air in terms of effective atomic number (Z_eff) with respect to the interactions of hadrons, leptons and isotopes of hydrogen.

METHOD

Mass collision stopping powers (MCSPs) were calculated first using Bethe formula. Then, these values were used to estimate Z_eff using linear-logarithmic interpolation. A scale equation was also used to calculate MCSP.

RESULTS

Variation in Z_eff, over the 0.5-50 MeV energy range considered, is minimum for muon and pion (π meson) interactions (relative difference [RD] ≤ 7%), while maximum variation has been noticed in Z_efffor heavy charged particles, i.e. alpha particle (RD ≤ 26%). The highest values of Z_eff were obtained for muon particle, the lightest particle while the minimum values of Z_eff were obtained for alpha particle interaction. Except for very low kinetic energies, water equivalence of soft tissue is very satisfactory (RD ≤ 3%). The Z_eff of water relative to air was found to be almost constant at high energies. The present results should be valid for especially high energies where the Bethe formula can be applied. This applies to relatively higher energies (>2 MeV) for heavier particles such as alpha particles and applies to relatively lower energies (>0.5 MeV) for lighter particles such as protons.

CONCLUSIONS

In view of the importance of water equivalence in particle therapy, new data on Z_eff in soft tissue, water and air for fundamental particle interaction should be important. Results revealed that soft tissue could be considered as water equivalent for interaction of various fundamental particles.

Monte Carlo simulation of an anthropometric phantom used for calibrating in vivo K-XRF spectroscopy measurements of stable lead in bone

An anthropometric surrogate (phantom) of the human leg was defined in the constructs of the Monte Carlo N Particle (MCNP) code to predict the response when used in calibrating K x-ray fluorescence (K-XRF) spectrometry measurements of stable lead in bone. The predicted response compared favorably with measurements using the anthropometric phantom containing a tibia with increasing stable lead content. These benchmark measurements confirmed the validity of a modified MCNP code to accurately simulate K-XRF spectrometry measurements of stable lead in bone. A second, cylindrical leg phantom was simulated to determine whether the shape of the calibration phantom is a significant factor in evaluating K-XRF performance. Simulations of the cylindrical and anthropometric calibration phantoms suggest that a cylindrical calibration standard overestimates lead content of a human leg up to 4%. A two-way analysis of variance determined that phantom shape is a statistically significant factor in predicting the K-XRF response. These results suggest that an anthropometric phantom provides a more accurate calibration standard compared to the conventional cylindrical shape, and that a cylindrical shape introduces a 4% positive bias in measured lead values.

A 4×500mm2 cloverleaf detector system forin vivobone lead measurement

A 4 x 500 mm2 "cloverleaf" low energy germanium detector array has been assembled for the purpose of in vivo bone lead measurement through x-ray fluorescence. Using 109Cd as an exciting source, results are reported from a leg phantom simulating measurement of lead in a human tibia. For high activity (4.0-4.4 GBq) and low activity (0.18-0.19 GBq) sources, measurement results are reported for both the cloverleaf system and a conventional single detector system of equivalent surface area (2000 mm2). The mean uncertainty and reproducibility of measurement were both significantly improved for the cloverleaf system with a high activity 109Cd source. When using a source activity of 4.4 GBq, measurement of the phantom resulted in an average bone lead uncertainty of 0.79 microg/g and a reproducibility of 0.84 microg/g. These results represent the highest precision yet reported from a bone lead x-ray fluorescence system.