Simple, accurate equations for human blood O2 dissociation computations

TLDR

Hill’s equation can be modified to fit the human blood O₂ dissociation curve within ±0.0055 fractional saturation across the physiologic range. The authors present modified Hill equations and related expressions for calculating Po₂ from saturation, temperature, and pH effects, and describe iterative procedures to determine Po₂, saturation, and P₅₀ from a single blood sample. Explicit equations for Po₂, temperature, and pH dependence, as well as iterative calculation procedures, are supplied.

Abstract

Hill's equation can be slightly modified to fit the standard human blood O2 dissociation curve to within plus or minus 0.0055 fractional saturation (S) from O less than S less than 1. Other modifications of Hill's equation may be used to compute Po2 (Torr) from S (Eq. 2), and the temperature coefficient of Po2 (Eq. 3). Variations of the Bohr coefficient with Po2 are given by Eq. 4. S = (((Po2(3) + 150 Po2)(-1) x 23,400) + 1)(-1) (1) In Po2 = 0.385 In (S-1 - 1)(-1) + 3.32 - (72 S)(-1) - 0.17(S6) (2) DELTA In Po2/delta T = 0.058 ((0.243 X Po2/100)(3.88) + 1)(-1) + 0.013 (3) delta In Po2/delta pH = (Po2/26.6)(0.184) - 2.2 Procedures are described to determine Po2 and S of blood iteratively after extraction or addition of a defined amount of O2 and to compute P50 of blood from a single sample after measuring Po2, pH, and S.