Response surface calibration of (CO2)-C-13-NDIR offset values: A 'random coefficients' approach
The offset or basal value of (CO2)-C-13/(CO2)-C-12 ratio determinations for breath-gas analysis using non dispersive infrared (NDIR)-technology shows a nonlinear dependence on sample O-2 and CO2 content, which is empirically described and corrected with polynomial functions. The corresponding coefficients are usually determined by regression and measurements at nodes, which cover the entire working range. A sparse grid causes interpolation problems and dense grids increase the calibration effort. As a way out the covariance of coefficients of earlier calibrations is estimated using a 'random coefficient' approach and decomposed into 4-6 principal components. Each component describes the device variability and refers to a polynomial, which covers the entire working range. An actual calibration surface is explained by an overlay of these components, which obviates a systematic variation of the interferences and allows to design a plausibility check. When applied on the two gaseous interferences it gives a root-mean-squared error in (CO2)-C-13/(CO2)-C-12 ratios smaller 10(-5) over the entire working range. With only a few coefficients to be identified by regression, the approach is robust against random measurements errors and paves the way for flexible on-line delta C-13 metabolic measurements with NDIR technology under increased O-2 content. (C) 2011 Elsevier B.V. All rights reserved.
principal components hierarchical models polynomial regression