Depth-dependent attenuation and backscattering characterization of optical coherence tomography by stationary iterative method

Abstract

Significance: Extracting optical properties of tissue [e.g., the attenuation coefficient ($\mu$) and the backscattering fraction] from the optical coherence tomography (OCT) images is a valuable tool for parametric imaging and related diagnostic applications. Previous attenuation estimation models depend on the assumption of the uniformity of the backscattering fraction ($R$) within layers or whole samples, which does not accurately represent real-world conditions.

Aim: Our aim is to develop a robust and accurate model that calculates depth-wise values of attenuation and backscattering fractions simultaneously from OCT signals. Furthermore, we aim to develop an attenuation compensation model for OCT images that utilizes the optical properties we obtained to improve the visual representation of tissues.

Approach: Using the stationary iteration method under suitable constraint conditions, we derived the approximated solutions of $\mu$ and $R$ on a single scattering model. During the iteration, the estimated value of $\mu$ can be rectified by introducing the large variations of $R$, whereas the small ones were automatically ignored. Based on the calculation of the structure information, the OCT intensity with attenuation compensation was deduced and compared with the original OCT profiles.

Results: The preliminary validation was performed in the OCT A-line simulation and Monte Carlo modeling, and the subsequent experiment was conducted on multi-layer silicone-dye-${\mathrm{TiO}}_2$ phantoms and ex vivo cow eyes. Our method achieved robust and precise estimation of $\mu$ and $R$ for both simulated and experimental data. Moreover, corresponding OCT images with attenuation compensation provided an improved resolution over the entire imaging range.

Conclusions: Our proposed method was able to correct the estimation bias induced by the variations of $R$ and provided accurate depth-resolved measurements of both $\mu$ and $R$ simultaneously. The method does not require prior knowledge of the morphological information of tissue and represents more real-life tissues. Thus, it has the potential to help OCT imaging based disease diagnosis of complex and multi-layer biological tissue.

Keywords: attenuation coefficient; attenuation compensation; backscattering fraction; multiple scattering; optical coherence tomography; single scattering.

Fig. 1

Example of locating and removing the noise floor by signal fitting extrapolation: (a) representative OCT signal intensity and (b) measured attenuation coefficient $\mu$ with and without extrapolation. The OCT signal intensity in red is extrapolated to infinity.

Fig. 2

Numerical simulation result of (a), (b) OCT signal intensity of (a) first phantom and (b) second phantom before and after signal compensation on a logarithmic scale; (c) measured backscattering fraction $R$ of the first phantom during iteration; (d), (e) measured attenuation coefficient $\mu$ of (d) first phantom and (e) second phantom with and without iteration; (f) example of the partial average algorithm when calculating backscattering fraction $R$ of the first phantom. The ideal backscattering fraction $R$ of the second phantom is 0.005, 0.007, 0.006, and 0.004, respectively. Other theoretical values are represented by dashed lines.

Fig. 3

(a) The experimentally obtained real OCT image of the bovine retinal tissue for comparison. (b) The simulated OCT image of the bovine retinal tissue obtained using Monte Carlo modeling. The image size is set to $800\times 400\text{\hspace{0.17em}\hspace{0.17em}pixels}$ with resolutions of $0.7\mu \mathrm{m}$ per pixel axially and $10\mu \mathrm{m}$ per pixel laterally. (c) A representative OCT A-line signal within RoI indicated as a red dashed box in (b). (d)–(f) Measured attenuation coefficient $\mu$ and representative A-line $\mu$ of the red dashed RoI with and without iterations. (g)–(h) The comparison between measured backscattering fraction $R$ of the red dashed RoI and the measured backscattering map obtained using our iterative method.

Fig. 4

(a) Measured average attenuation coefficient $\mu$ that changes with the particle concentration by fitting an exponential curve. (b) Measured average backscattering fraction $R$ that changes with the particle concentration using Eq. (21). The signal trend is marked by a solid line. (c) Representative OCT A-line signal intensity of the finalized home-made two-layer phantoms.

Fig. 5

Phantom experiment results. (a) and (h) OCT signal intensity of the first and second phantoms. (b) and (i) Measured attenuation coefficient $\mu$ without iteration. (c) and (f) The comparison between calculated $\mu$ using different methods. (d) Measured backscattering fraction $R$ of the first phantom using our method. (e) and (j) Measured attenuation coefficient $\mu$ with iteration. (g) The comparison between calculated $R$ and ideal $R$ in the dashed red RoI of (a) and (h).

Fig. 6

Experiment result of bovine retinal tissue. (a) and (c) OCT signal intensity of bovine retinal tissue (a) before and (c) after our intensity compensation method. (b) and (d) Measured attenuation coefficient $\mu$ (b) without and (d) with iteration. (e) Measured backscattering fraction $R$ using our method. (f) The comparison between calculated $R$ and ideal $R$ of red RoI in (e). (g) Representative OCT A-line signal intensity of red RoI in (a). (h) The comparison between calculated $\mu$ using different methods of red RoI in (d).

Fig. 7

(a) The mean percentage errors between the estimated attenuation coefficients ${\mu }_k$ and true attenuation coefficients ${\mu }_g$ within all red dashed RoIs of phantoms and tissues in Figs. 3, 5, and 6. (b) The mean percentage errors between the estimated backscattering fractions $R_k$ and true backscattering fractions $R_g$ within all red dashed RoIs of phantoms and tissues in Figs. 3, 5, and 6.