Journal of Radioanalytical and Nuclear Chemistry, Vol. 269, No.2 (2006) 325–329 0236–5731/USD 20.00 Akadémiai Kiadó, Budapest © 2006 Akadémiai Kiadó, Budapest Springer, Dordrecht Curve fitting using a genetic algorithm for the X-ray fluorescence measurement of lead in bone L. Luo, 1,2* D. R. Chettle, 2 H. Nie, 2 F. E. McNeill, 2 M. Popovic 2 1 National Research Center of Geoanalysis, 100037, Beijing, P.R. China 2 Department of Medical Physics and Applied Radiation Sciences, McMaster University, Hamilton, Canada (Received April 6, 2006) We investigated the potential application of the genetic algorithm in the analysis of X-ray fluorescence spectra from measurement of lead in bone. Candidate solutions are first designed based on the field knowledge and the whole operation, evaluation, selection, crossover and mutation, is then repeated until a given convergence criterion is met. An average-parameters based genetic algorithm is suggested to improve the fitting precision and accuracy. Relative standard deviation (RSD%) of fitting amplitude, peak position and width is 1.3–7.1, 0.009–0.14 and 1.4–3.3, separately. The genetic algorithm was shown to make a good resolution and fitting of K lines of Pb and γ elastic peaks. Introduction In the in vivo X-ray fluorescence measurement of trace lead in bone, continuous efforts are made to lower the minimum detectable limit of lead thus improving the measurement precision particularly in individuals with low exposure. 1 Such improvements are partially limited by the energy resolution of the XRF system, which can be insufficient to resolve the overlap of lead K-series X- rays and the Compton peak. The resolution of overlapped peaks may provide a robust foundation of predicting accurately the concentrations of trace Pb in phantoms and in bone. A trend in research involving curve fitting is to find a global optimum solution and to avoid falling into a local minimum. The genetic algorithm (GA) was first suggested by HOLLAND in 1975, 2 and since then genetic algorithms have been extensively studied and have found a wide range of applications. 3–7 It has been confirmed that GAs are a useful tool in solving real problems in many scientific fields, involving optimization and curve fitting. GAs are also of great value in identifying the fittest model by natural evolution. Generally, GAs have good search accuracy, but are flawed by poor precision. Thus, improving the search precision is a task that requires addressing before GAs can be reliably applied to X-ray spectrometry. In this work, a GA has been investigated and used to resolve the overlapping peaks in the X-ray fluorescence measurement of lead in bone. Special attention has been paid to improving fitting precision. Theory GA is based on the principle of biological evolution and survival of the fittest. Entities capable of adapting to the environmental changes are able to live longer. GA * E-mail: luoliqiang@ccsd.org.cn pays attention to the evolution of biological genus in order to avoid the degradation of a system. GA usually includes the initialization of data, evaluation of fitting and genetic operations. A convergence criterion is assigned prior to the evaluation. Candidate solutions, or chromosomes, are first designed based on the field knowledge and then are initialized randomly. The initial solutions or parameters are limited within upper and low boundaries. Then they are forwarded to genetic operations to go through selection and crossover procedures. The optimal solutions are kept and worse ones excluded. The whole operation, evaluation, selection, crossover and mutation, is then repeated until a given convergence criterion is met. In principle, the crossover and mutation are the mathematical operations of exchanging positions or values of parameters fitted. In general, criteria are the number of generations, or small error values predefined by a user. The population size is usually from 50 to 500 strings, the crossover probability is in the region 0.5–0.9 and the mutation probability is between 0.001 and 0.05. The key difference between GA and common classical methods are that GA approaches search whole space of solutions rather than a small range of parameters as done by the common methods. Experimental Two major cases of overlapped peaks are encountered when Pb in bone is measured by XRF. One is due to the coherent scatter peak from 109 Cd source, which overlaps nearly completely with Pb Kβ2. Secondly, there is an overlap between Pb peaks and the Compton peak, which causes the main obstacle in the determination of trace Pb in bone. Pb Kα 1 peak at trace content, a prominent lead feature, is difficult to distinguish from a large tail of Compton peak.