Determination of sodium, chlorine, and bromine concentrations in breast milk using neutron activation: Correlation, regression, and machine learning predictions

Breast milk plays a vital role in infant health, providing essential nutrients that directly impact nutrition and development. Understanding its elemental composition, as well as the relationships among these elements, is crucial for assessing its nutritional adequacy. This study focused on determining the concentrations of sodium (Na), chlorine (Cl), and bromine (Br) in the breast milk of lactating mothers in Tehran, Iran, during early lactation. The primary objectives were to analyze the concentrations of these elements, investigate their interrelationships, and employ machine-learning techniques to predict their concentrations in breast milk. Neutron activation analysis (NAA) was used to precisely measure the levels of Na, Cl, and Br, while statistical methods, including correlation and regression analyses, were applied to further explore these relationships. Machine-learning models, specifically Random Forest and Linear Regression, were utilized to predict the concentrations of these elements based on their interdependencies. The study revealed mean concentrations of 5.12 mg/g for Na, 8.14 mg/g for Cl, and 11.84 mg/kg for Br in the breast milk samples. A strong positive correlation was observed between Na and Cl (r = 0.976, p < 0.001), while moderate positive correlations were found between Na and Br (r = 0.558, p < 0.001) and Cl and Br (r = 0.606, p < 0.001). Multiple regression models showed that 94.7 % of the variance in Na concentration could be explained by Cl and Br levels (R-squared = 0.947), with a strong positive association between Cl and Na, and a slight inverse relationship between Br and Na. A similar model for Cl concentrations showed strong predictive power, with Na being a significant predictor. However, the model for Br concentrations explained a smaller proportion of variance (R-squared = 0.318), suggesting that additional factors influencing Br levels were not captured in this study. Furthermore, multicollinearity was observed between Na and Cl (VIF = 20.675), indicating potential interactions between these elements. This study highlights the significant correlations between Na, Cl, and Br in breast milk, with particularly strong predictive models for Na and Cl concentrations. The findings also suggest the need for further investigation into the factors affecting Br concentrations. Overall, this research provides valuable insights into the elemental composition of breast milk and its implications for infant nutrition and health.