What is the proper statistical model for laser speckle flowmetry?

Abstract

The ultimate objective of laser speckle flowmetry (and a host of specific implementations such as Laser Speckle Contrast Analysis-LASCA or LSCA, Laser Speckle Spatial Contrast Analysis-LSSCA, Laser Speckle Temporal Contrast Analysis-LSTCA, etc.) is to infer flow velocity from the observed speckle contrast. A proper inversion of this association depends critically on the correct model for the statistical relationship between motion of the scatterers and the resulting spatial and temporal speckle contrast. Many researchers use the Lorentzian model for such a relationship. In fact, the Lorentzian is a homogeneous line profile appropriate only for Brownian motion. In such a case, the dynamics of a single particle are representative of the ensemble. The other extreme is an inhomogeneous (Gaussian) profile which corresponds to a process in which the dynamics are particular to the individual scatterers. The proper model for complex motion such as blood flow is undoubtedly intermediate between these two extremes. One such model for the net effect of these two stochastically independent processes is a Voigt profile. In this paper we explore the quantitative relationship between the statistics of speckle contrast and ordered flow. The study addresses the effects of speckle size relative to that of the pixel, temporal integration time relative to the decorrelation times associated with ordered and un-ordered motion, and the spatio-temporal processing schemes used to quantify speckle contrast.