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Machine Learning Approach for Simultaneous Determination of Counting Efficiencies of Strontium-90 and Strontium-89
- 언어ENG
- URLhttps://db.koreascholar.com/Article/Detail/430650
p.365
Radioactivity of radiostrontiums, Sr-89 and Sr-90, which are both pure beta-emitters, are generally measured via Cherenkov counting. However, the determination of Cherenkov counting efficiencies of radiostrontiums requires a complicated procedure due to the presence of Y-90 (also a pure betaemitter) which is the daughter nuclide of Sr-90. In this study, we have developed a machine learning approach using a linear regression model which allows an easier and simultaneous determination of the Cherenkov counting efficiencies of the radiostrontiums. The linear regression model was employed because total net Cherenkov count (Ct) from the three beta-emitters at time t after the separation of Y- 90, can be expressed as a linear combination of their respective time-varying radioactivities with their respective coefficients (parameters) being their counting efficiencies: Ct = εSr-90[ASr-90·exp(–λSr-90·t)] + εSr-89[ASr-89·exp(–λSr-89·t)] + εY-90[ASr-90·exp(1–λSr-90·t)], where ε is a counting efficiency, A is an initial activity, λ is a decay constant and t is time after the separation of Y-90, Thus, if we train the model with multiple Cherenkov counts measured from the three beta emitters, then we can obtain their estimates for counting efficiencies (so-called parameters) straightforward. For this, the model has been trained by two methods: Ordinary Least Squares (OLS) and Bayesian linear regression (BLR), for which two software packages, PyMC3 and Stan were employed to compare their performances. The results showed that the accuracy of the OLS was worse than that of the BLR. Particularly, the counting efficiency of Sr-90 was estimated to be smaller than 0, which is an unrealistic value. On the other hand, the estimates of the BLR gave realistic values which are close to the true values. Additionally, the BLR was able to provide a distribution for each counting efficiency (so-called “posterior”) from which various types of inference can be made including median and credible interval in the Bayesian statistics which is analogous to, but different from confidence interval in the Frequentist statistics. In the results of the BLR, the Stan package gave more accurate estimates than the PyMC3 package. Therefore, it is expected that counting efficiencies of the radiostrontiums including radioyttrium can be determined at the same time, more easily and accurately, by using the BLR with the Stan package and that the activities of radiostrontium also can be determined more easily by using the BLR if we know their counting efficiencies in advance. It is worth noting that the usage of the linear regression model in this study was different from the usual one where the trained model is used to predict a response value (count) from a set of unseen regressor values (activities).
