The Use of Different Statistical Metrics to Detect Physiological Changes in Metal-Overloaded Avian Bone

Abstract

Slag from nickel smelting operations in the Sudbury basin in Ontario, Canada, has become ubiquitous. This material rich in heavy metals -particularly iron -upon ingestion has the potential to effect changes in physiology. In previous work, we analyzed the effects of dietary slag ingestion on several quantitative parameters of the tibio-tarsal bones in pigeons, including density, cortical thickness, bone mineral density, calcium and iron concentrations, Young's Moduli, and breaking strength. In the present work, we compute the Pearson correlation coefficients for all possible sets of bivariations of the measured parameters for a control group fed a normal diet, and an experimental group fed a slag-based diet. Furthermore, the Pearson distance, which is a metric associated with the degree of "clustering" between two independent sets of bivariate correlations, was calculated for all corresponding pairs of bivariations. A new metric -the Distance correlation R -is a measure of multivariate correlation which tests for any type of correlation, including linear correlation (or anticorrelation). In analogy to the Pearson distance, we introduce in this work the Distance correlation dR, and a criterion for its statistical significance. On the existing data set, the Distance correlation R was also calculated for all 42 bivariations, and the associated 21 values of dR were computed. In the control group, the Pearson correlation revealed an anticorrelation between cortical thickness and breaking strength. In the experimental group, the metric revealed a correlation between breaking strength and bone mineral density, and an anticorrelations between: i) Young's Moduli and iron concentration, and ii) between cortical thickness and bone mineral density. Significant Pearson distances between: i) cortical thickness vs. breaking strength, ii) cortical thickness vs. bone mineral density, iii) density vs. bone mineral density, and iv) breaking strength vs. bone mineral density, were indicative of fundamental changes in bone physiology in the experimental group. The Pearson distance metric was thus effective in detecting physiological changes associated with the presence of metal overload in bone. The Distance correlation R revealed a significant correlation between cortical thickness and breaking strength in the control group, and between the calcium and iron concentrations in the experimental group. The dR metric revealed significant loss in correlation between calcium concentration and bone mineral density in the experimental group. In summary, the statistical metrics used -and introduced in this work -are efficacious in detecting physiological changes in metaloverloaded bone.

Energy Dispersive Spectroscopy (EDS) Measurements of Sulfur Uptake in Pigeon Bone Associated with the Intake of Slag, and the Induction of Homocystinuria

“…A control group was fed a slag-free diet. Selection, feeding, husbandry, and sample preparation, have been described extensively elsewhere [1,2,4]. This work was performed in accordance with an animal care protocol approved by the University of Guelph Animal Care Committee (where husbandry, and organ harvesting of the samples took place), on behalf of the Canadian Council on Animal Care.…”