Mathematical modelling of the manganese level in the muscle tissue of cattle

Abstract

The results of determining the most effective model for predicting the level of manganese in the muscle tissue of Hereford cattle for in vivo assessment of the elemental status of animals by low invasive methods are presented. The experiment was carried out using hematological and biochemical blood tests and atomic absorption analysis of the muscle tissue of cattle. The data obtained are used to fit the regression model using the least square method. Skeletal muscle samples weighing 100 g from the diaphragm muscle of the Hereford cattle bred in the southern part of Western Siberia in the conditions of industrial complex were taken for analysis. Manganese concentration in tissues was assessed by atomic absorption analysis on an MGA-1000 spectrometer. The content of erythrocytes, leukocytes, and hemoglobin was determined on an automatic hematology analyzer PCE-90VET. Protein, albumin, globulin, urea, uric acid, and cholesterol levels were determined by photometric methods on a Photometer-5010 semi-automatic biochemical analyzer. The effects of regression models were calculated using the least square method. Selection of the best model for efficiency and accuracy of model estimation was based on a comprehensive assessment of the values of internal and external quality criteria. Statistically significant associations ( p < 0.05) were found between the dependent and independent variables. Within the pool of predictors, correlation ( p < 0.05) was observed. As a result of model fitting, an optimal regression equation including two indicators (erythrocyte sedimentation rate and globulin level) for predicting manganese levels in bovine muscle tissue was obtained. There are no signs of multicollinearity between the main effects of the model, which confirms the values of the variance inflation factor 1.2. The resulting model satisfies the necessary assumptions about the residuals. The distributions of the model residuals fall within the confidence intervals of the normal distribution curve. The autocorrelation coefficient was 0.039 ( p > 0.05), indicating the independence of the residuals. The resulting model can be used for in vivo assessment of manganese concentration in bovine muscle tissue.