Abstract
Abstract: :
Purpose: Previously, laser Doppler velocimetry (LDV) analysis was based on a rectangular shape of the Doppler shift power spectrum (DSPS), i.e., assuming uniform illumination of a parabolic velocity profile. The aim of this work was to develop a new ray–tracing model that characterizes the DSPS properties for Gaussian laser beams and takes into account light absorption. Methods: This analytical model was developed using Mathematica 5. A laser beam of given wavelength and width is computationally made to intersect a blood vessel carrying laminar flow at a selectable eccentricity. We assume pseudo–single backscattering with a fixed scattering geometry. For each point within the "measuring volume" (i.e., the 3–D intersection between beam and vessel) the Doppler shift, the total path length of the light inside the blood vessel and the intensity scattered towards the detector are calculated. The contributions to the photocurrent from all points of the measuring volume are then integrated, and the resulting DSPS is determined. Model parameters (wavelength, scattering angles, beam size, intersection eccentricity, extinction coefficient) can be varied independently. Results: First, the model shows that the DSPS for a Gaussian beam deviates markedly from the rectangular shape already for a beam size comparable to the vessel size. For smaller beam sizes, the differences become even more pronounced. Second, the expected DSPS shape for eccentric intersection (e.g., as seen with a small laser beam scanning across the vessel) can now be quantified precisely and applied to the analysis of velocity profile measurements. Third, the calculated area under the DSPS curve differs by as much as 40%, due to differences in light absorption between oxy– and deoxy–hemoglobin, depending on the wavelength. Conclusions: With the recent advances in technology, the size of the LDV probing volume can be decreased to a fraction of a vessel diameter, in which case the light intensity distribution within the vessel is clearly not uniform. This produces DSPS that require an entirely new approach to LDV analysis. This work provides the appropriate models to fit the data obtained with various LDV configurations, potentially opening a new avenue for the measurement of blood oxygen saturation in retinal vessels.
Keywords: computational modeling • blood supply • laser