Mathematical analysis of hemoglobin spectrophotometry in microvessels

Spectrophotometry of hemoglobin in microvessels is commonly performed by collecting light either from a small region around the vessel centerline or from the entire lumen of the vessel. In the latter instance, parallel rays of light may not encounter the same amount of absorbing species. Hence, a phenomenon similar to the sieve effect reported in the literature on hemoglobin spectrophotometry may be expected to occur. Although it has been observed that under such circumstances nonlinearities in calibration characteristics arise, the implications of this effect on the interpretation of the spectrophotometric mean concentration have never been addressed so far. Mathematical analysis of hemoglobin spectrophotometry in microvessels, performed in this study, reveals that for practical situations the calibration curve is indeed nonlinear. Moreover, the spectrophotometric mean oxygen saturation is an overestimate of the mean oxygen saturation during oxygenation and an underestimate of the mean oxygen saturation during deoxygenation. These deviations depend upon the manner in which the total heme concentration is distributed within the lumen. Application of the analysis to artificial microvessels showed that the observed superior oxygen transport characteristics of flowing erythrocyte suspensions and hemoglobin solution mixtures could in part be due to the assumptions underlying the procedure used to interpret the experimental results. The implications of this result on models for oxygen transport in microvessels are discussed along with possible resolutions.