Localized light absorption by hemoglobins of an erythrocyte suspension

Abstract

A correction factor accounting for the differences between the absorption spectra of an erythrocyte suspension and hemolyzed blood (hemoglobin solution) has been calculated. Erythrocytes and their aggregates are simulated by "soft" cylindrical (disk-shaped) particles. The anomalous diffraction approximation is used. At equal absorbing mass, the absorption coefficient of the suspension in the blue spectral region is shown to be capable of being several times lower than that of the solution due to localization of the absorber in erythrocytes.The hemoglobin localization effect is less important for λ em > 600 nm. Approximate analytical equations that are valid for cylindrical particles with a length-to-diameter ratio l/d > 3-4 are proposed for calculating the correction factor. More cumbersome formulas of anomalous diffraction must be used at smaller l/d values. It is shown that these formulas transform at the limit into the analytical equations. The spectra of the correction factor for cylindrical and spherical particles are compared. The simple approximation for spherical particles is demonstrated to work well for rather long aggregates when the cylinder volume-to-surface area ratio is the same as for a spherical particle. The results can be used to solve various problems of erythrocyte optics, e.g., to reproduce sizes of aggregates by measuring their spectral absorption.Introduction. Light of spectral range 300-1000 nm is absorbed in blood mainly by various forms of hemoglobins, e.g., oxy-, deoxy-, met-, sulf-, and carboxyhemoglobin among others. Variations of their molecular structures causes their absorption coefficients μ i (λ) (i is the hemoglobin form) to assume different properties depending on the wavelength of the light [1-4] although the absolute values are usually much greater than those of other blood chromophores (thrombocytes, plasma) [5, 6]. Therefore, blood absorption spectra μ b (λ) are often used for optical monitoring of its hemoglobin composition and the bulk concentration of derivatives [1,[7][8][9][10][11]. Multi-component analysis [1,3,10,11], least-squares methods, and other well developed mathematical procedures are used to deduce the concentration from the measured function μ b (λ) and known μ i (λ). The principal issue with experimental determination of μ b (λ) is the structure of the blood sample, namely, is the hemoglobin in solution after hemolysis of the blood or is it dispersed, concentrating on erythrocytes. Herein we propose a method for calculating the absorption coefficient of a suspension of erythrocytes and evaluate differences between the absorption spectra of hemoglobin suspension and solution.Current State of the Problem. The problem of finding the relationship between the absorption coefficient of a substance and its dispersed phase has been solved historically using two approaches. These are the theory of light scattering on individual particles (Maxwell's equations) and the theory of radiation transfer in the medium. It is well known in the theory of light scattering on...

Effect of scattering and absorbing inclusions in dispersive medium on the optical parameters of an elementary volume

“…1 are close to each other. The calculations using formulas (4) and (5) show that a similar conclusion can be drawn for the remaining inclusions in Fig. 1 (ellipsoids, parallelepipeds, and cylinders with q ≈ 1).…”

“…Denominators in formulas (3) are interpreted as effective optical thicknesses of extinction, absorption, etc. The following quantities are introduced as correction coefficients: (4) When С = 1, we employ the Lambert-Beer law, otherwise the law must be corrected using coefficient С. Note that coefficients С depend on the optical characteristics of the inclusion material.…”

“…Various shapes and orientations of inclusions relative to the incident beam are possible. Regular objects are rare in nature, and objects in radiation transfer problems are often approximated using cylinders (blood vessels of biological tissues [1][2][3] and erythrocytes [4]), spheres (algae in water [5]), paraboloids (cumulus clouds in atmosphere [6]), and parallelepipeds (snow surface [7]). Light propagation in such media differs from the propagation under uniform distribution of the same amount of material, since the presence of inclusions implies the presence of pores or holes in which radiation does not interact with medium [8,9].…”

“…Direct numerical integration along the optical path in inclusion or the Monte Carlo simulation can be employed. Analytical formulas of [3,4] characterize the absorption coefficient of tissue that contains oriented or chaotically distributed blood vessels and aggregates of erythrocytes with arbitrary length. The relationships of [3,4] generalize the results of [16] that were obtained for infinite cylindrical inclusions irradiated along the normal to the longitudinal axis.…”

“…Analytical formulas of [3,4] characterize the absorption coefficient of tissue that contains oriented or chaotically distributed blood vessels and aggregates of erythrocytes with arbitrary length. The relationships of [3,4] generalize the results of [16] that were obtained for infinite cylindrical inclusions irradiated along the normal to the longitudinal axis. Optical measurements in model and natural media yield experimental results on the effect of localized vessels on the absorption coefficient of biological tissue [17,18].…”