Evolutionary model of flexible exponential function to characterize decay pattern of OCT signal in turbid tissues

Conventional analyses of OCT signal measurements resolve the signal decay profile in terms of single discrete exponential function with distinct exponential model. In symmetrical medium, mono-exponential decay function can appear to provide a well fit to OCT signal decay data, but the assuption of symmetrical components is essentially arbitrary and is often erroneous. Actually, the real biological samples such as tissue contained more complex components and are more heterogeneous. To avoid the shortages of mono-exponential decay function fitting to OCT signal decay data from heterogeneous biological tissues, a novel model of flexible exponential function has been developed. The main idea of the flexible exponential function modle is based on the assuption that heterogeneous biological tissue can be considered as a multi-layered tissue. Each layer is symmetric and the OCT signal decay profile in each layer obeies to a distinct single exponential function. If we can find out all the distinct single exponential function for each layer, the total flexible exponential function is determined by summing up all the single exponential functions. As pilot studies on the practical application of flexibleexponential decay model for monitoring and quantifying the diffusion of different analytes in turbid biological tissues in vivo by using OCT system, we demonstrate an experiment of monitoring of glucose diffusion in agar gel. In addition, the flexible-exponential decay model can provide a direct measure of the heterogeneity of the sample, and the analysis of turbid tissues OCT map using the flexible-exponential decay model can reveal subtle tissue differences that other models fail to show.