Analytical calculations and Monte Carlo simulations of laser Doppler flowmetry using a cubic lattice model

Abstract

In addition to the static cubic lattice model for photon migration in turbid biological media by Bonner et al. [J. Opt. Soc. Am. A 4, 423-432 (1987)], a dynamic method is presented to calculate the average absolute Doppler shift as a function of the distance between the point of injection of photons into the medium and the point of detection. At every lattice point a moving particle is assumed with a constant velocity in random directions. The velocity direction fluctuates randomly in time. When a photon is scattered at a lattice point it has a finite probability to be Dopper shifted, since in reality not every scattering event occurs with a moving particle. Calculated average absolute Doppler shifts are verified with Monte Carlo simulations. We verified the applicability of the derived formulas for continuous isotropic and continuous anisotropic media. Good agreement is found between the calculated and simulated average absolute Doppler shifts. Small differences between calculated and simulated average abso ute Doppler shifts can be explained by the assumptions made in the theory. Furthermore the calculations of the average absolute Doppler shift confirm the theory of Bonner et al. that the first moment ?omega? of a spectrum S(omega) measured with a blood perfusion meter is linearly proportional to the average number m of scattering events with a moving particle in case of m < 1 and linearly proportional to the square root of m in the case of m > 1. It is confirmed that the average absolute Doppler shift depends on the average number of scattering events at the position of the detection. This effect is, apart from the size and position of the probe volume, essential for the interpretation of the signal measured with a laser Doppler perfusion meter.