Image Cross-Correlation Analysis of Time Varying Flows

In vivo studies of blood circulation pathologies have great medical relevance and need methods for the characterization of time varying flows at high spatial and time resolution in small animal models. We test here the efficacy of the combination of image correlation techniques and single plane illumination microscopy (SPIM) in characterizing time varying flows in vitro and in vivo. As indicated by numerical simulations and by in vitro experiments on straight capillaries, the complex analytical form of the cross-correlation function for SPIM detection can be simplified, in conditions of interest for hemodynamics, to a superposition of Gaussian components, easily amenable to the analysis of variable flows. The possibility to select a wide field of view with a good spatial resolution along the collection optical axis and to compute the cross-correlation between regions of interest at varying distances on a single time stack of images allows one to single out periodic flow components from spurious peaks on the cross-correlation functions and to infer the duration of each flow component. We apply this cross-correlation analysis to the blood flow in Zebrafish embryos at 4 days after fertilization, measuring the average speed and the duration of the systolic and diastolic phases.