Bayesian analysis of depth resolved OCT attenuation coefficients

Lionel D Fiske,Maurice C G Aalders,Dirk J Faber,Mitra Almasian,Oliver Cossairt,Aggelos K Katsaggelos,Ton G Van Leeuwen

doi:10.1038/s41598-021-81713-7

Abstract

Optical coherence tomography (OCT) is an optical technique which allows for volumetric visualization of the internal structures of translucent materials. Additional information can be gained by measuring the rate of signal attenuation in depth. Techniques have been developed to estimate the rate of attenuation on a voxel by voxel basis. This depth resolved attenuation analysis gives insight into tissue structure and organization in a spatially resolved way. However, the presence of speckle in the OCT measurement causes the attenuation coefficient image to contain unrealistic fluctuations and makes the reliability of these images at the voxel level poor. While the distribution of speckle in OCT images has appeared in literature, the resulting voxelwise corruption of the attenuation analysis has not. In this work, the estimated depth resolved attenuation coefficient from OCT data with speckle is shown to be approximately exponentially distributed. After this, a prior distribution for the depth resolved attenuation coefficient is derived for a simple system using statistical mechanics. Finally, given a set of depth resolved estimates which were made from OCT data in the presence of speckle, a posterior probability distribution for the true voxelwise attenuation coefficient is derived and a Bayesian voxelwise estimator for the coefficient is given. These results are demonstrated in simulation and validated experimentally.

Highlights

Optical coherence tomography (OCT) is an imaging modality which allows for the visualization of internal structures of tissues and other translucent materials volumetrically
To verify the likelihood model from Eq (17), the depth resolved (DR) attenuation formula is applied to phantom data and a histogram is computed to compare against theory
Using these values and Eq (22) we can see that the expected variance for the attenuation coefficient is μoct · ζ = 0.0020 mm−2 which is very small when compared with the variance of the exponential distribution which is μoct 2 = 11.5 mm−2

Summary

Introduction

Optical coherence tomography (OCT) is an imaging modality which allows for the visualization of internal structures of tissues and other translucent materials volumetrically. The layers of media are segmented, and an exponentially decaying model is fit to each A-scan of the OCT signal in the least squares sense[3,4,5] From this perspective, the attenuation coefficient is a bulk measure which assigns a single, deterministic number to each segment of an A-scan. The DR approach assumes the material is weakly absorbing, making this technique related to voxelwise OCT scattering parameter inference m ethods[15,16,17] which have a long history in OCT signal processing This method has been further refined by L iu[18] to better handle boundary effects caused by finite imaging depth. This approach opens the door to probabilistic tissue classification tasks such as tumor grading where the likelihood of various outcomes must be compared

Objectives

Methods

Results

Conclusion