Probability density function formalism for optical coherence tomography signal analysis: a controlled phantom study

Abstract

The distribution of backscattered intensities as described by the probability density function (PDF) of tissue-scattered light contains information that may be useful for tissue assessment and diagnosis, including characterization of its pathology. In this Letter, we examine the PDF description of the light scattering statistics in a well characterized tissue-like particulate medium using optical coherence tomography (OCT). It is shown that for low scatterer density, the governing statistics depart considerably from a Gaussian description and follow the K distribution for both OCT amplitude and intensity. The PDF formalism is shown to be independent of the scatterer flow conditions; this is expected from theory, and suggests robustness and motion independence of the OCT amplitude (and OCT intensity) PDF metrics in the context of potential biomedical applications.

K‐distribution three‐dimensional mapping of biological tissues in optical coherence tomography

“…where w confocal is the 1/e-Gaussian-beam-intensity radius, which is 1/√2 of the 1/e 2 -intensity (1/e-amplitude) radius w 1 . This factor of 1/√2 (thus factor of 2 for the volume) originates from the confocal setup of the OCT imager in which the overlap integral of the illumination and collection optical mode fields should be taken into account [13][14][15]; this formulation also corrects our slight inconsistency published previously [7]. For the microspheres-in-water phantom examined here, the average number of particles N within the coherence volume V was~1.9.…”

“…The coherence volume of this OCT imager was calculated as V = π 3/2 · w confocal 2 · w 2 = ~(12 μm) 3 , defined by a volume integral of the 3D Gaussian point spread function (PSF) for OCT signal amplitude : where w confocal is the 1/e‐Gaussian‐beam‐intensity radius, which is 1/√2 of the 1/e 2 ‐intensity (1/e‐amplitude) radius w 1 . This factor of 1/√2 (thus factor of 2 for the volume) originates from the confocal setup of the OCT imager in which the overlap integral of the illumination and collection optical mode fields should be taken into account ; this formulation also corrects our slight inconsistency published previously . For the microspheres‐in‐water phantom examined here, the average number of particles N within the coherence volume V was ~1.9.…”

“…We thus expect the resultant α maps to be homogeneous, and from the resultant fluctuations we can evaluate the range of random errors. Further, knowing N permits the accuracy assessment of the K‐distribution approach through its expected dependence N = α/2 . Studies in this control phantom also enable examination of optimal and practical conditions for the size of the 3D evaluation window.…”

“…We thus expect the resultant α maps to be homogeneous, and from the resultant fluctuations we can evaluate the range of random errors. Further, knowing N permits the accuracy assessment of the K-distribution approach through its expected dependence N = α/2 [7,8].…”

“…After selecting a suitably sized 3D evaluation window, and verifying methodology in phantoms, the resultant parametric α images obtained in different animal tissues (rat liver and brain) show new contrasting ability not seen in conventional OCT intensity images. In optical investigations of turbid media, the K-distribution has been employed to represent the non-Gaussian optical scattering regime in both theoretical and experimental studies [1][2][3][4][5][6] Among the variety of optical measurement and analysis methodologies with the K-distribution model, its application to optical coherence tomography (OCT) analysis of the intensity probability density function (PDF) has yielded successful estimation of the number of scatterers within the coherence volume (eg, in the microspheres-inwater phantom system, ranging from a few to >50) [7,8]. Initial possibilities for biological tissue characterization have also been demonstrated in in vivo human skin and nail [8].…”