Academic journal article Environmental Health Perspectives

Calculating Bone-Lead Measurement Variance

Academic journal article Environmental Health Perspectives

Calculating Bone-Lead Measurement Variance

Article excerpt

The technique of [sup.109]Cd-based X-ray fluorescence (XRF) measurements of lead in bone is well established. A paper by some XRF researchers [Gordon CL, et al. The Reproducibility of [sup.109]Cd-based X-ray Fluorescence Measurements of Bone Lead. Environ Health Perspect 102:690-694 (1994)] presented the currently practiced method for calculating the variance of an in vivo measurement once a calibration line has been established. This paper corrects typographical errors in the method published by those authors; presents a crude estimate of the measurement error that can be acquired without computational peak fitting programs; and draws attention to the measurement error attributable to covariance, an important feature in the construct of the currently accepted method that is flawed under certain circumstances. Key words: bone, lead, measurement error, X-ray fluorescence. Environ Health Perspect 108:383-386 (2000). [Online 15 March 1999] http://ehpnet1.niehs.nih.gov/docs/2000/108p383-386todd/abstract.html

The in vivo measurement of lead in human bone using [sup.109]Cd-based fluorescence of the K-shell X-rays of lead (KXRF) is a well-established technique that has been widely applied to studies of the human health effects of lead and has been reviewed, most recently, by Todd and Chettle (1) in a technical manner and by Hu et al. (2) in a conceptual manner. This paper addresses the method for calculating the measurement uncertainty in a bone-lead measurement given in a 1994 paper by Gordon et al. (3).

In [sup.109]Cd-based KXRF, the 88.034 keV [Gamma]-rays from [sup.109]Cd are used to fluoresce the K-shell X-rays of lead (in increasing energy, those with Siegbahn notation: K[[Alpha].sub.2], K[[Alpha].sub.1], K[[Beta].sub.1], K[[Beta].sub.3], and K[[Beta].sub.2]). The [sup.109]Cd [Gamma]-rays can also elastically scatter off of the calcium and phosphorus (and, to a lesser extent, oxygen) atoms in bone and inelastically scatter off all of the elements in the sample undergoing measurement (principally the bone, soft tissue, and skin). The photons are recorded by a spectroscopy system that yields an energy distribution of the recorded photons that is then fitted using a nonlinear least-squares technique with a mathematical function to extract the amplitudes of the X-ray and elastic scatter peaks. The ratio of the X-ray-to-elastic peaks is the response of the system and is regressed, for each X-ray peak under analysis, against the lead concentration of the calibration standards to produce a calibration line.

The in vivo signal from a subject is measured for each lead X-ray to be analyzed and is compared to the established calibration line to obtain one or more estimates of the subject's bone-lead level. The individual X-ray estimates are then combined, usually in an inverse-variance weighted manner, to produce the result.

The remainder of this paper addresses methods for the mathematical treatment of the measurement uncertainty; corrects typographical errors in the published method of Gordon et al. (3); presents a crude estimate of the measurement error that can be acquired without computational peak-fitting programs; and addresses the measurement error attributable to covariance.

Materials and Methods

Gordon et al. (3) published a study of the reproducibility of [sup.109]Cd-based X-ray fluorescence (XRF) measurements of bone lead. Their paper contained an "Appendix" wherein they gave a near-complete description of the mathematical method by which they calculated the variance of an in vivo bone-lead measurement. In brief, they made multiple measurements of a series of plaster-of-paris phantoms doped with a range of lead concentrations. The spectrum of scattered radiation showed characteristic peaks from the emission of lead K X-rays that varied in size depending, in part, on the lead concentration of the phantom. Gordon et al. used four of the lead K X-rays for analysis: those with Siegbahn (International Union of Pure and Applied Chemistry notation in parentheses) K[[Alpha]. …

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