Statistical estimation of haemodynamic parameters in optical coherence tomography

Abstract

Optical coherence tomography (OCT) is an imaging modality analogous to ultrasound. By using the interference properties of light, one may image to micrometer resolutions using interferometric methods. Most modern systems can acquire A-scans at kHz to MHz speeds, and are capable of real-time 3D imaging. OCT has been used extensively in ophthalmology and has been used in angiography to quantify blood flow. The aim of this research has been to develop statistically optimal estimators for blood flow estimation to take advantage of these hardware advances. This is achieved through a deeper understanding of the noise characteristics of OCT. Through mathematical derivations and simulations, the noise characteristics of OCT Doppler and flow imaging were accurately modelled as additive white noise and multiplicative decorrelation noise. Decorrelation arises due to relative motion of tissue relative to the OCT region of interest and adversely affects Doppler estimation. From these models maximum likelihood estimators (MLEs) that statistically outperform the commonly used Kasai autocorrelation estimator were derived. The Cramer-Rao lower bound (CRLB), which gives the theoretical lowest estimator variance for an unbiased estimator was derived for different noise regimes. It is shown that the AWGN MLE achieves the CRLB for additive white noise dominant conditions, and the decorrelation noise MLE achieves the CRLB under more general noise conditions. The use of computational algorithms that enhance the capabilities of OCT are demonstrated. This shows that this approach for determining parametric estimators may be used in a more general medical imaging context. In addition, the use of decorrelation as a measure of speed is explored, as it is itself proportional to flow speed.