Speckle statistics of biological tissues in optical coherence tomography

The speckle statistics of optical coherence tomography images of biological tissue have been studied using several historical probability density functions. Here, we propose a new theoretical framework based on power-law functions, where we hypothesize that an underlying power-law distribution governs scattering from tissues. Thus, multi-scale scattering sites including the fractal branching vasculature will contribute to power-law probability distributions of speckle statistics. Specifically, these are the Burr type XII distribution for speckle amplitude, the Lomax distribution for intensity, and the generalized logistic distribution for log amplitude. Experimentally, these three distributions are fitted to histogram data from nine optical coherence tomography scans of various samples and biological tissues, in vivo and ex vivo. The distributions are also compared with classical models such as the Rayleigh, K, and gamma distributions. The results indicate that across OCT datasets of various tissue types, the proposed power-law distributions are more appropriate models yielding novel parameters for characterizing the physics of scattering from biological tissue. Thus, the overall framework brings to the field new biomarkers from OCT measures of speckle in tissues, grounded in basic biophysics and with wide applications to diagnostic imaging in clinical use.