Theoretical model for optical oximetry at the capillary level: Exploring hemoglobin oxygen saturation through backscattering of single red blood cells

Oxygen saturation (sO₂) of red blood cells (RBCs) in capillaries can indirectly assess local tissue oxygenation and metabolic function. For example, the altered retinal oxygenation in diabetic retinopathy and local hypoxia during tumor development in cancer are reflected by abnormal sO₂ of local capillary networks. However, it is far from clear whether accurate label-free optical oximetry (i.e., measuring hemoglobin sO₂) is feasible from dispersed RBCs at the single capillary level. The sO₂-dependent hemoglobin absorption contrast present in optical scattering signal is complicated by geometry-dependent scattering from RBCs. We present a numerical study of backscattering spectra from single RBCs based on the first-order Born approximation, considering practical factors: RBC orientations, size variation, and deformations. We show that the oscillatory spectral behavior of RBC geometries is smoothed by variations in cell size and orientation, resulting in clear sO₂-dependent spectral contrast. In addition, this spectral contrast persists with different mean cellular hemoglobin content and different deformations of RBCs. This study shows for the first time the feasibility of, and provides a theoretical model for, label-free optical oximetry at the single capillary level using backscattering-based imaging modalities, challenging the popular view that such measurements are impossible at the single capillary level.