Kinetics and Transient Times of Fluorescence Optical Sensors (Optodes) for Blood Gas Analysis (O₂, CO₂, pH)

Abstract

Oxygen measurements with optical sensors (O₂ optodes) (Lubbers and Opitz, 1983; Opitz and Lubbers, 1984) are based on fluorescence quenching of certain indicator molecules by molecular oxygen in a diffusion-controlled collisional process (Vaughan and Weber, 1970; Knopp and Longmuir, 1972). The functional dependence follows Stern-Volmer’s equation (Stern and Volmer, 1919) : S (P O₂) = S₀/ (1+KηPO₂), where K is overall quenching constant, PO₂, oxygen partial pressure, and S and S_o, relative fluorescence intensity in the presence and absence of oxygen, respectively. Since fluorescence optical sensors incorporate membrane-protected indicator layers, an exponential time course of the PO₂ within these layers can be assumed (Jost, 1960), if a rectangular PO₂ step, ΔP O₂ = PO₂″ − PO₂′, is induced in front of the sensor membrane. Insertion of this time course into the hyperbolic calibration curve brings about asymmetrical kinetics of reversible reactions with different transient times, e.g. to 90% of final value (t₉₀):

$$\begin{matrix}t_{90,02}^{\downarrow }={{k}^{-1}}\cdot \log \left( 10-\left( 9\cdot k\cdot \Delta P{{O}_{2}} \right)/\left( 1+k\cdot P{{O}_{2}}\prime\prime \right) \right) \\t_{90,02}^{\uparrow }={{k}^{-1}}\cdot \log \left( 10+\left( 9\cdot k\cdot \Delta P{{O}_{2}} \right)/\left( 1+k\cdot P{{O}_{2}}\prime\right) \right) \\\end{matrix}$$

(4.1)

where k⁻¹ ~ D₀₂/1², D₀₂, oxygen diffusion coefficient and, 1, thickness of the sensor membrane.