Evaluation of algorithms for microperfusion assessment by fast simulations of laser Doppler power spectral density

In classical laser Doppler (LD) perfusion measurements, zeroth- and first-order moments of the power spectral density of the LD signal are utilized for the calculation of a signal corresponding to the concentration, speed and flow of red blood cells (RBCs). We have analysed the nonlinearities of the moments in relation to RBC speed distributions, parameters of filters utilized in LD instruments and the signal-to-noise ratio. We have developed a new method for fast simulation of the spectrum of the LD signal. The method is based on a superposition of analytically calculated Doppler shift probability distributions derived for the assumed light scattering phase function. We have validated the method by a comparison of the analytically calculated spectra with results of Monte Carlo (MC) simulations. For the semi-infinite, homogeneous medium and the single Doppler scattering regime, the analytical calculation describes LD spectra with the same accuracy as the MC simulation. The method allows for simulating the LD signal in time domain and furthermore analysing the index of perfusion for the assumed wavelength of the light, optical properties of the tissue and concentration of RBCs. Fast simulations of the LD signal in time domain and its frequency spectrum can be utilized in applications where knowledge of the LD photocurrent is required, e.g. in the development of detectors for tissue microperfusion monitoring or in measurements of the LD autocorrelation function for perfusion measurements. The presented fast method for LD spectra calculation can be used as a tool for evaluation of signal processing algorithms used in the LD method and/or for the development of new algorithms of the LD flowmetry and imaging. We analysed LD spectra obtained by analytical calculations using a classical algorithm applied in classical LD perfusion measurements. We observed nonlinearity of the first moment M₁ for low and high speeds of particles (v < 2 mm s⁻¹, v > 10 mm s⁻¹). It was also noted that the first moment M(1) is less sensitive to the change of the mean RBC speed for flat speed distributions. The low-pass filter frequency f₂ implemented in the LD instrument has a significant influence on the first moment of the spectrum. In particular, for a cut-off frequency lower than 10 kHz the M₁ value is strongly underestimated.