Refractive index of solutions of human hemoglobin from the near-infrared to the ultraviolet range: Kramers-Kronig analysis

Abstract

Because direct measurements of the refractive index of hemoglobin over a large wavelength range are challenging, indirect methods deserve particular attention. Among them, the Kramers-Kronig relations are a powerful tool often used to derive the real part of a refractive index from its imaginary part. However, previous attempts to apply the relations to solutions of human hemoglobin have been somewhat controversial, resulting in disagreement between several studies. We show that this controversy can be resolved when careful attention is paid not only to the absorption of hemoglobin but also to the dispersion of the refractive index of the nonabsorbing solvent. We present a Kramers-Kroning analysis taking both contributions into account and compare the results with the data from several studies. Good agreement with experiments is found across the visible and parts of near-infrared and ultraviolet regions. These results reinstate the use of the Kramers-Kronig relations for hemoglobin solutions and provide an additional source of information about their refractive index.

Determining the refractive index of human hemoglobin solutions by Kramers–Kronig relations with an improved absorption model

“…However, due to our different ansatz for the absorption, where we take into account the excluded water volume, we obtain a different result for B(λ) with an additional term (n H 2 O (λ) − 1)/ρ Hb for the concentration dependence. We discuss the differences between the results obtained in [9], [10] and the result with our improved model in section 3 B.…”

“…Other researchers [9,10] have previously relied on the data compiled from various sources by Prahl [15]. However, since not all of the compiled sources used human hemoglobin, these data are not used here.…”

“…For our model, it suffices to add to the spectrum a delta-peak of unknown amplitude located at zero wavelength, which accounts for the influence of extreme UV absorption by a constant offset in the real RI: α δ (λ) = lim λ δ →0 + π 2 a δ λ δ δ(λ − λ δ ). In this respect, our approach is not different from [9,10]: We cannot predict the absolute value of the RI of Hb, but we need to determine a constant by comparing to experimental data. However, we apply non-local fitting to optimize this constant, instead of using just one single data point.…”

Blood equivalent phantom vs whole human blood, a comparative study

“…This e®ect is caused by the change in the scattering of the sample which in°uences the overall attenuation of light. The higher scattering is caused by higher refractive index mismatch 34 between the RBCs [35][36][37] and the medium surrounding them, caused by exchange of plasma with saline, of the refractive index value 1.330 and 1.328 at 930 nm, respectively (see Fig. 7).…”

Photoacoustic measurement of refractive index of dye solutions and myoglobin for biosensing applications

“…Using Kramers-Kroenig analysis (mathematical relationships that relate the complex and real parts of a physical system) it is possible to estimate many material properties, including refractive index. However, in recent years, the legitimacy of this analysis has been questioned for heterogenous biological materials, such as hemaglobin, due to the complex nature of the analysis [1]. Measurement of the refractive index is based upon the fundamental Fresnel equations, which describe the refraction, reflection, and transmission of light at an interface between two media with non-matching refractive indices.…”