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In this study, we derive a fast, novel time-domain algorithm to compute the nth-order moment of the power spectral density of the photoelectric current as measured in laser-Doppler flowmetry (LDF). It is well established that in the LDF literature these moments are closely related to fundamental physiological parameters, i.e. concentration of moving erythrocytes and blood flow. In particular, we take advantage of the link between moments in the Fourier domain and fractional derivatives in the temporal domain. Using Parseval's theorem, we establish an exact analytical equivalence between the time-domain expression and the conventional frequency-domain counterpart. Moreover, we demonstrate the appropriateness of estimating the zeroth-, first- and second-order moments using Monte Carlo simulations. Finally, we briefly discuss the feasibility of implementing the proposed algorithm in hardware.

Monte Carlo (MC) simulations significantly contributed to a better understanding of laser-Doppler flowmetry (LDF). Here it is shown that the data obtained from standard MC simulations can be reinterpreted and used to extract more information such as the photo-electric current (i(t)). This is important because i(t) is the starting point for evaluating any existing or new algorithm to be used in LDF instrumentation. This circumvents the tedious procedure of generating a specific model (often approximated if possible at all) each time a different algorithm is considered. By a series of tutorial examples, the influence of various parameters is investigated, e.g. sampling rate, total acquisition time and dc filtering. These cases also demonstrate the fundamental role played by the photons' random phase in the shaping of the LDF signal. In particular, it is demonstrated by MC simulation that when the number of photon-moving red blood cell interactions is too low, then the Siegert relation that exists between the field and photo-electric current autocorrelation functions does not hold. This is an important point because the validity of the Siegert relation is implicitly admitted in the majority of the classical analytical models for the autocorrelation function in LDF (the classical MC approach does not allow one to study this problem). The proposed method and examples could stimulate new ideas and help the scientific community develop, test and validate new approaches in LDF.

Based on quasi-elastic scattering theory (and random walk on a lattice approach), a model of laser-Doppler flowmetry (LDF) has been derived which can be applied to measurements in large tissue volumes (e.g. when the interoptode distance is >30 mm). The model holds for a semi-infinite medium and takes into account the transport-corrected scattering coefficient and the absorption coefficient of the tissue, and the scattering coefficient of the red blood cells. The model holds for anisotropic scattering and for multiple scattering of the photons by the moving scatterers of finite size. In particular, it has also been possible to take into account the simultaneous presence of both Brownian and pure translational movements. An analytical and simplified version of the model has also been derived and its validity investigated, for the case of measurements in human skeletal muscle tissue. It is shown that at large optode spacing it is possible to use the simplified model, taking into account only a 'mean' light pathlength, to predict the blood flow related parameters. It is also demonstrated that the 'classical' blood volume parameter, derived from LDF instruments, may not represent the actual blood volume variations when the investigated tissue volume is large. The simplified model does not need knowledge of the tissue optical parameters and thus should allow the development of very simple and cost-effective LDF hardware.