Whitman College, Mathematical Sciences Foundry Talks, Walla Walla, WA, September 19, 2022

Martin Šefl gave a seminar presentation to undergraduate students from Whitman College in Walla Walla, Washington. His presentation was a part of the Mathematical Sciences Foundry Talks series, organized by the mathematics and statistics department. It described how a principal component regression can be used to estimate the total amount of plutonium in the entire skeleton, based on the activity concentrations in a limited subset of bones.

Application of principal component regression at the U.S. Transuranium and Uranium Registries

Martin Šefl

The United States Transuranium and Uranium Registries (USTUR) studies actinide (Pu, Am, and U) biokinetics and tissue dosimetry by following up former nuclear workers with documented internal deposition of these radioactive elements. The USTUR research relies heavily upon postmortem autopsy findings and radiochemical analyses of donated tissues. Plutonium is a radioactive element first produced and isolated in the 1940s. The skeleton is a major plutonium retention site in the human body. The estimation of the total plutonium activity in the skeleton is a challenging problem. For most tissue donors at the USTUR, a limited number of bone samples is available. Typically, the total skeleton activity is calculated using plutonium activity concentration (C_skel) and skeleton weight. If limited number of bone samples was analyzed, C_skel could be estimated using multiple linear regression (MLR) of data from whole-body donors, where C_skel were estimated based on the analysis of the half of the skeleton. The caveat of MLR is that individual bone sample concentrations are correlated. Multicollinearity can be addressed by principal component regression (PCR). PCR consist of two steps, principal component analysis (PCA) and regression. PCA enables to reduce the number of variables for regression while retaining information. A brief introduction into PCR and its application of PCR for estimates of plutonium concentration in the skeleton will be discussed. [USTUR-0623-22P]

Seminar slides (PPTX with animation)
Seminar slides (PDF)