Relationship between Blood and Expiration Alcohol Concentration and Establishment of Mathematical Model

Abstract

Objective: To study the relationship between concentration of alcohol in the exhaled breath at end-exhalation (BrAC) determined by breathalyzer and blood alcohol concentration (BAC) determined by HS-GC and to establish a linear model in order to achieve the prediction of BAC by BrAC.

Methods: From February to December in 2016, 53 healthy drivers who were suspected of drunk driving in Guiyang were selected. The BrAC and BAC were determined. A scatter plot was drawn and a linear model was established with BrAC as the independent variable X and BAC as the dependent variable Y.

Results: The curve equation was obtained by fitting the data of BrAC and BAC: Y=1.298 2X-5.017 5, R2=0.95. A simple random sampling method was used to extract 11 samples. The linear model was used to predict the samples, and the results were compared with the samples′ real values. The predicted values were in great deviation from the true ones. Removed the constant, modified the model, and got the curve equation: Y=1.229 4X, R2=0.99. The predicted values of 2, 3 and 8 samples differed greatly from the true values, and the sum of squared errors of prediction (SSE) =621.70. Took the logarithm of BAC and got the linear equation: lnY=0.016 6X+3.218 5, R2=0.93. There was little difference between the predicted and the true values, SSE=239.06.

Conclusion: The model lnY=0.016 6X+3.218 5 can be used to achieve the prediction of BAC by BrAC.