Data Processing in CO-Oximeters That Use Overdetermined Systems

CO-oximeters are specialized spectrophotometers that automatically determine hemoglobin (Hb) derivatives by measuring absorbance at selected wavelengths (1). We believe that a good understanding of the relevant theory may allow users to avoid many pitfalls during operation of these instruments. The mathematical basis of their operation has not, however, been fully explained by the manufacturers apart from Instrumentation Laboratory (Lexington, MA) at the introduction of their first CO-Oximeter™ (2). Here, we discuss what mathematical methods for data processing might be used in commercial CO-oximeters, particularly in those models that use an “overdetermined” system. CO-oximeters depend on the observation that Hb solutions obey the Lambert–Beer Law; thus, the absorbance measured at a given wavelength is the sum of the absorbance of each Hb derivative at the same wavelength (2). When we measure n wavelengths to determine the m Hb derivatives χ i , we get n equations: \batchmode \documentclass[fleqn,10pt,legalpaper]{article} \usepackage{amssymb} \usepackage{amsfonts} \usepackage{amsmath} \pagestyle{empty} \begin{document} \[\ A\_{j}{=}\ {{\sum}\_{i{=}1}^{m}}{\epsilon}\_{ji}C\_{i}l\mathrm{\ for\ 1}{\leq}j{\leq}n,\] \end{document} where A j is the absorbance at wavelength λ j , C i is the concentration of derivative χ i , and l is the pathlength. e ji is the molar absorptivity at wavelength λ j for derivative χ i . When n = m , we can solve Eq. 1 to get C i . This is termed an “exactly determined” system (3) and has been implemented in the IL 482 CO-Oximeter (Instrumentation Laboratory), the IL 282 (its predecessor), and the Radiometer OSM3 Hemoximeter™ (Radiometer, Copenhagen, Denmark). The IL 482 uses four wavelengths for four Hb derivatives, whereas the OSM3 uses six wavelengths for six unknowns: five Hb derivatives plus one for noise (attributed to “turbidity”). The report by Steinke and Shepherd (4) illustrates how the full exposition of the algorithms used in specific instruments is useful not only to users but also to manufacturers. After measuring absorptive spectra of Hb derivatives … [↵][1]bAuthor for correspondence. [1]: #xref-corresp-2-1