Simulation of optical coherence tomography to determine refractive indices of retinal layers in different organisms

doi:10.21203/rs.3.rs-4929459/v1

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Simulation of optical coherence tomography to determine refractive indices of retinal layers in different organisms

https://doi.org/10.21203/rs.3.rs-4929459/v1

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Optical coherence tomography (OCT) is a non-invasive imaging technique capable to produce two-dimensional (2D) images or three-dimensional (3D) reconstructions of inhomogeneous samples. OCT is mainly used in ophthalmology as a powerful tool for early diagnosis of eye diseases. The main goal of this article is to simulate the interferogram of OCT images and obtain the refractive index related to each retina layers in different organisms, including human, monkey, cow and dog. To achieve this goal, by simulating the interferogram of OCT images in the time and frequency domains for a supergaussian light source, different retinal samples are studied and for the given layer thicknesses, the refractive indices of different retina layers are determined.

Optical coherence tomography

interferogram

retina

refractive index

organisms

Optical coherence tomography (OCT), introduced by David Huang in 1991 and named by James Fujimoto, represents a relatively new advancement in medical imaging [1]. Utilizing the analysis of light interference from a low-coherence source, OCT is a high-resolution, non-invasive technique. Standard OCT achieves a resolution of 10–15 µm, while specialized sources can enhance this to 1–5 µm [2–3]. This technology allows for cross-sectional imaging with a penetration depth of 2–3 mm, contingent on the specific OCT setup. Initially applied in ophthalmology [4], OCT systems have recently shown potential in various other medical fields such as cardiology [5–6], dermatology [7], and gastroenterology [8].

OCT can act as sampling and provide information about tissue pathology in a precise location and time without the need to destroy the tissue. In general, broadband light sources are used in OCT, including: broadband fluorescent, Ti:AL₂O₃ laser [9], femtosecond KLM laser, laser diodes with infrared bandwidth, etc. [10] with different wavelengths.

Optical coherence tomography (OCT) facilitates high-resolution tomographic imaging of the internal microstructures within biological materials by detecting backscattered or reflected light. OCT produces two-dimensional data sets that depict optical backscattering across a tissue's cross-sectional area. Analogous to ultrasound imaging, OCT constructs cross-sectional images or B-scans by combining multiple linear A-scans. However, OCT uses light energy instead of sound waves, with image generation depending on the tissue's optical properties. Direct measurement of the signal delay from tissue echoes is infeasible due to light's high speed. Therefore, OCT employs low coherence interferometry, utilizing superluminescent diodes or femtosecond lasers for this purpose [10]. This technique achieves image resolutions ranging from 1 to 15 µm, which is significantly higher than traditional ultrasound imaging. Imaging can be conducted in situ and in real time, broadening the scope for both research and clinical applications. Examples of in vitro OCT imaging include studies of the human retina and atherosclerotic plaque, demonstrating its effectiveness in both low-scattering transparent media and high-scattering opaque media [11–12].

Originally, OCT was utilized for ocular imaging, and it remains most impactful in the field of ophthalmology. This technology allows for non-invasive and non-contact imaging of the anterior segment of the eye, as well as detailed visualization of the retina's morphology, including structures like the cavity and optic disc [13–14].

Optical methods are often pivotal in the medical field due to their cost-effectiveness and safety compared to alternative techniques. Recent advancements in OCT technology have expanded its capability to image opaque tissues, making it applicable across various medical specialties. The imaging depth is constrained by optical attenuation caused by tissue absorption and scattering. Nevertheless, OCT can typically achieve imaging depths of 2 to 3 mm in most tissues, which aligns with the scale typically observed in vector tissue and conventional histology. While OCT's imaging depth may not match that of ultrasound, its resolution surpasses standard clinical ultrasound by 10 to 100 times [15].

Imaging studies have been conducted under laboratory conditions to explore applications across various medical disciplines such as dermatology, gastroenterology, urology, gynecology, surgery, neurosurgery, and rheumatology [16]. OCT is particularly valuable in developmental biology as it enables repeated imaging of evolving morphology without the need to sacrifice samples. Furthermore, significant advancements have been achieved in OCT technology, including demonstrations of high-speed real-time imaging at acquisition rates of several frames per second. New laser light sources have enabled high-resolution and ultra-high-resolution OCT imaging, achieving axial resolutions as fine as 1µm [17].

This article aims to determine the refractive index of each retinal layer by leveraging the known thickness of each layer, which corresponds to the peaks in the simulated OCT interferogram. We propose a method to calculate refractive indices for different retinal layers across various organisms, including humans, monkeys, cows, and dogs, where refractive index data are scarce in the existing literature.

OCT is an advanced technology used for high-resolution cross-sectional imaging of biological tissues, particularly in ophthalmology [18]. It operates based on interferometric principles, relying on the interference between two light beams typically in the infrared wavelength range. Figure 1 illustrates the schematic setup of an OCT system.

Light emitted from a source is split by a beam splitter into reference and sample paths. The reference beam reflects off a mirror, while the sample beam reflects from various layers within the sample [19]. These reflected beams are then recombined and detected by an optical detector, in the interferogram correspond to changes in refractive index between sample layers, revealing the sample's internal structure.

In this work, in the first step to simulate an OCT system, we define a supergaussian light source with the amplitude of $\:E=\text{exp}\:\left(-\frac{1}{2}{\left(\frac{\omega\:-{\omega\:}_{c}}{\sigma\:}\right)}^{2m}\right)$ where by changing the value of m, one can creates several sources with different spectral flatness for a given bandwidth (standard deviation) of 𝜎. Also, 𝜔_𝑐 is the center frequency and 𝜎 is obtained according to the formula $\:{\sigma\:}=\frac{2\pi\:c\frac{\varDelta\:\lambda\:}{{\lambda\:}_{0}}}{\sqrt{8ln2}}$ ; where 𝑐 represents the speed of light in a vacuum [21].

For simulation purpose, the center wavelength is set at 𝜆₀ = 850 𝑛𝑚 and the linewidth is Δ𝜆=100 𝑛𝑚. The simulated source spectra for different supergaussian orders m = 1,2,3,4,5,6,10,15,20 are shown in Fig. 2. As it is obvious, by increasing the supergaussian order, the flatness of the source spectrum increases.

Then, in the second step, we the define the sample function as [22]:

$$\:H\left(\omega\:\right)=\sum\:_{j=1}^{N}{r}_{p}exp[2i\frac{\omega\:}{c}{n}_{j}{z}_{j}\left]\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\right(1)$$

$$\:{r}_{p}=\frac{{n}_{j+1}-{n}_{j}}{{n}_{j+1}+{n}_{j}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(2\right)$$

where r_p is the amplitude reflection coefficient of p’th sample layer, which is calculated from the refractive index of adjacent layers, and z_j is the thickness of p’th layer. The matrix of the refractive index and the thickness of the layers are respectively defined as $\:n=[{n}_{1},\:{n}_{2},\:{n}_{3},\dots\:]$ and $\:z=[{z}_{1},{z}_{2},\:{z}_{3},\dots\:]$ and H[𝜔] is computed for each value within the optical frequency array 𝜔.

To simulate OCT interferogram in Fourier domain (FD-OCT), the source spectrum S[𝜔] illustrated in Fig. 2 and the sample function defined by H[𝜔], are used to simulate the OCT intensity through the Eq. (3) as follows [21]:

$$\:{I}_{FD}=\frac{1}{4}S\left[\omega\:\right]|H{\left[{\omega\:}\right]|}^{2}+\frac{1}{4}S\left[\omega\:\right]+\frac{1}{2}\mathfrak{R}\left\{S\left[\omega\:\right]H\left[\omega\:\right]\right\}\:\:\:\:\:\:\:\:\:\:\:\:\:\:(3)$$

A graphical representation of the OCT A-scan can be achieved by implementing a Discrete Fourier Transform (DFT) algorithm, where as the order of the supergaussian increases, the peak values at different depths of the sample increases, which means achieving greater longitudinal resolution. The results of the FD-OCT simulation agree well with those obtained for the time domain (TD-OCT) simulation, aside from a few slight variations in the peak positions.

This section starts with a test sample consisting of four layers (except the top air layer) with the refractive indices and thicknesses listed in Table 1. The aim of the test sample is to validate our model for accurate prediction of the refractive indices. After validating our model, the refractive index and thickness of the retinal layers, including the nerve fiber layer (NFL), inner plexiform and ganglion cell layers (IPL + GCL), inner nuclear layer (INL), outer plexiform layer (OPL), outer nuclear layer and photoreceptor inner segments (ONL + PIS), and photoreceptor outer segments (POS) [23].

Table 1

Refractive index and thickness of the test layers.
Layer Number	Refractive Index	Thickness z ($\:\varvec{\mu\:}\varvec{m}$)
1	1.00	5
2	1.25	12
3	1.30	24
4	1.45	32
5	1.00	0

Figure 3. (a) Time-domain (TD); and (b) Frequency-domain (FD) OCT simulations for the test sample.

The main goal is simulating the OCT interferograms and determining the refractive indices of humans’ retina, cows, monkeys and dogs. To do this, the estimated average values of each layer's refractive index were considered and incorporated in the numerical model and by adjusting each refractive index, corresponding peaks in the OCT interferograms are shifted so that the right thickness layer as the initial given thickness is obtained via Eq. (4):

$$\:{n}_{p}=\frac{{d}_{p}-{d}_{p-1}}{{\varDelta\:z}_{p}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(4\right)$$

where $\:{d}_{p-1\:\:}$and $\:{d}_{p}\:$are two successive peaks in the OCT interferogram and $\:{\varDelta\:z}_{p}$ is the initial known the thickness of the p’th layer, where the refractive index is $\:{n}_{p}$.

Table 2 presents the simulated parameters, including the layer thicknesses and refractive indices.

Table 2

Simulated refractive indices and thickness of human, dog, monkey and cow retinal layers.
	POS		ONL + PIS		OPL		INL		IPL + GCL		NFL
Sample	z ($\:\varvec{\mu\:}\varvec{m}$)	n	z ($\:\varvec{\mu\:}\varvec{m}$)	n	z ($\:\varvec{\mu\:}\varvec{m}$)	n	z ($\:\varvec{\mu\:}\varvec{m}$)	n	z ($\:\varvec{\mu\:}\varvec{m}$)	n	z ($\:\varvec{\mu\:}\varvec{m}$)	n
Human	60	1.358	100	1.36	10	1	30	1.361	50	1.367	10	1.376
Monkey	60	1.357	120	1.355	12	2	35	1.360	50	1.365	12	1.374
Cow	70	1.355	150	1.340	15	3	40	1.355	60	1.345	15	1.380
Dog	60	1.346	120	1.364	12	4	35	1.380	50	1.329	12	1.355

In fact, refractive indices listed in Table 2 are obtained via corresponding interferograms related to humans and other animals as below.

The retina consists of multiple layers, with the refractive index varying between them. Hence, we considered the human and animals’ retinas by the following layers: nerve fiber layer, inner plexiform layer and ganglion cell layer, inner nuclear layer, outer plexiform layer, outer nuclear layer, photoreceptor inner segments and photoreceptor outer segments.

For obtaining the refractive index of the layers of the human eye and other animals mentioned in the Table 2, it was done by first considering the center wavelength as 1000 nm for the human retina and 850 nm for other animals and FWHM equal to 100 nm and m = 3 for all samples. We set the trial refractive indices for all six layers and in the next step we set the thickness of each layer as well as the thickness of the air and executed the numerical program. Further, according to the peaks obtained in the interferogram and considering the given thickness, we obtained the refractive index corresponding to the peak in such a way that the result of the difference of the two successive peaks divided by the refractive index of the layer gives us the proper layer thickness (Eq. 4). If the answer is the same as the given thickness, it means that the refractive index choice is correct, otherwise, we change the refractive indices so that the correct values are reached. Finally, two matrices corresponding to refractive indices and retina layers thicknesses, are obtained; e.g., for the human retina as n=[1,1.358,1.36,1.364,1.361,1.367,1.376,1] and z=[5$\:\varvec{\mu\:}\varvec{m}$,60$\:\varvec{\mu\:}\varvec{m}$,100$\:\varvec{\mu\:}\varvec{m}$,10$\:\varvec{\mu\:}\varvec{m}$,30$\:\varvec{\mu\:}\varvec{m}$,50$\:\varvec{\mu\:}\varvec{m}$,10$\:\varvec{\mu\:}\varvec{m}$,0$\:\varvec{\mu\:}\varvec{m}$]. The simulated TD-OCT interferogram is shown in Fig. 4 where the peaks are indicated by arrows.

To get the retina OCT interferogram for other animals, the same process was done as for the human retina, but with a different light source, λ₀ = 850 nm so that the results are depicted in Figs. 5–7 for the retina of monkey cow and dog, respectively.

To obtain the simulated refractive index of the monkey retina layers, two matrices for refractive indices and thicknesses have been calculated as n = [1, 1.357, 1.355, 1.363, 1.360, 1.365, 1.374, 1]; and z = [5$\:\:\varvec{\mu\:}\varvec{m}$, 60$\:\:\varvec{\mu\:}\varvec{m}$, 120$\:\:\varvec{\mu\:}\varvec{m}$,12$\:\:\varvec{\mu\:}\varvec{m},$ 35$\:\:\varvec{\mu\:}\varvec{m},$ 50$\:\:\varvec{\mu\:}\varvec{m},$ 12$\:\:\varvec{\mu\:}\varvec{m},$ 0$\:\:\varvec{\mu\:}\varvec{m}$]; with the corresponding TD-OCT interferogram shown in Fig. 5.

To obtain the simulated refractive index of the Cow retinal layers, two matrices for refractive index and thickness have been calculated as n = [1, 1.355, 1.34, 1.35, 1.355, 1.345, 1.38, 1]; and z = [5$\:\:\varvec{\mu\:}\varvec{m},$ 70$\:\:\varvec{\mu\:}\varvec{m},$ 150$\:\:\varvec{\mu\:}\varvec{m},$ 15$\:\:\varvec{\mu\:}\varvec{m},$ 40$\:\:\varvec{\mu\:}\varvec{m},$ 60$\:\:\varvec{\mu\:}\varvec{m},$ 15$\:\:\varvec{\mu\:}\varvec{m},$ 0$\:\:\varvec{\mu\:}\varvec{m}$]; with the corresponding TD-OCT interferogram shown in Fig. 6.

To determine the refractive index of the retinal layers in the final sample, the dog's retina, the same process was performed as the other samples. Two matrices consisting of refractive indices and thicknesses were obtained, n = [1, 1.406, 1.364, 1.376, 1.380, 1.329, 1.355, 1]; z = [5$\:\:\varvec{\mu\:}\varvec{m},$ 60$\:\:\varvec{\mu\:}\varvec{m},$ 120$\:\:\varvec{\mu\:}\varvec{m},$ 12$\:\:\varvec{\mu\:}\varvec{m},$ 35$\:\:\varvec{\mu\:}\varvec{m},$ 50$\:\:\varvec{\mu\:}\varvec{m},$ 12$\:\:\varvec{\mu\:}\varvec{m},$ 0$\:\:\varvec{\mu\:}\varvec{m}$] where the TD-OCT interferogram is shown in Fig. 7.

The primary objective of this article was to simulate the OCT image interferogram and obtain the refractive index related to each retina layer in different organisms, including human, monkey, cow and dog. To achieve this goal, by simulating the interferogram of OCT images in the time and frequency domains for a supergaussian light source, different retinal samples were studied and assuming given layer thickness, the refractive indices of different layers were obtained. Also, according to observations, it was seen that as the peaks in the TD-OCT interferogram were more pronounced (for example for the case of dog retina), the refractive index values of the sample can be determined with higher accuracy.

Conflict of interest

The authors declare no conflict of interest.

Funding

There is no fund.

Author Contribution

All authors contributed to the study, conception and design. Material preparation, simulation results and analysis were performed by H. P and M.G. The first draft of the manuscript was written by M. G and all authors commented on previous versions of the manuscript. H.P supervised and approved the final manuscript.

Data Availability Statement

Data available on request from the authors.

Fujimoto, J., & Swanson, E. (2016). The Development, Commercialization, and Impact of Optical Coherence Tomography. Investig Opthalmology Vis Sci, 57(9), OCT1.
Herz, P. R., et al. (2004). Ultrahigh resolution optical biopsy with endoscopic optical coherence tomography. Optics Express, 12(15), 3532.
Drexler, W., Morgner, U., Kärtner, F. X., Pitris, C., Boppart, S. A., Li, X. D., Ippen, E. P., & Fujimoto, J. G. (1999). In vivo ultrahigh-resolution optical coherence tomography. Optics Letters, 24(17), 1221.
Ahmed, H., Zhang, Q., Donnan, R., & Alomainy, A. (2024). Denoising of Optical Coherence Tomography Images in Ophthalmology Using Deep Learning: A Systematic Review. J Imaging, 10(4), 86.
Chandramohan, N., Hinton, J., O’Kane, P., & Johnson, T. W. (2024). Artificial Intelligence for the Interventional Cardiologist: Powering and Enabling OCT Image Interpretation. Interv Cardiol Rev Res Resour, 19, e03.
Yonetsu, T., & Jang, I. K. (2023). Cardiac Optical Coherence Tomography. JACC Asia, p. S2772374723002892.
Latriglia, F., et al. (2023). Line-Field Confocal Optical Coherence Tomography (LC-OCT) for Skin Imaging in Dermatology. Life, 13(12), 2268.
Otuya, D. O. (2022). Sep., Passively scanned, single-fiber optical coherence tomography probes for gastrointestinal devices, Lasers Surg. Med., vol. 54, no. 7, pp. 935–944.
Kowalevicz, A., Ko, T., Hartl, I., Fujimoto, J., Pollnau, M., & Salath, R. (2002). Ultrahigh resolution optical coherence tomography using a superluminescent light source. Optics Express, 10(7), 349.
Photiou, C., Kassinopoulos, M., & Pitris, C. (2023). Extracting Morphological and Sub-Resolution Features from Optical Coherence Tomography Images, a Review with Applications in Cancer Diagnosis. Photonics, 10(1), 51.
Liu, Y., et al. (2024). Enhanced properties of the mid-infrared superluminescent emitter with a composite waveguide. Applied Optics, 63(12), 3174.
Fujimoto, J. G., Pitris, C., Boppart, S. A., & Brezinski, M. E. (2000). Optical Coherence Tomography: An Emerging Technology for Biomedical Imaging and Optical Biopsy. Neoplasia (New York, N.Y.), 2(1–2), 9–25.
Gora, M. J., Suter, M. J., Tearney, G. J., & Li, X. (2017). Endoscopic optical coherence tomography: technologies and clinical applications [Invited]. Biomed Opt Express, 8(5), 2405.
Zheng, F., et al. (2023). Advances in swept-source optical coherence tomography and optical coherence tomography angiography. Adv Ophthalmol Pract Res, 3(2), 67–79.
Shahalinejad, S., & Seifi Majdar, R. (2021). Macular Hole Detection Using a New Hybrid Method: Using Multilevel Thresholding and Derivation on Optical Coherence Tomographic Images, Comput. Intell. Neurosci., vol. pp. 1–8, 2021.
Wang, Y., Liu, S., Lou, S., Zhang, W., Cai, H., & Chen, X. (2020). Application of optical coherence tomography in clinical diagnosis. Journal Of X-Ray Science And Technology, 27(6), 995–1006.
Rajinikanth, V., Satapathy, S. C., Fernandes, S. L., & Nachiappan, S. (2017). Entropy based segmentation of tumor from brain MR images – a study with teaching learning based optimization. Pattern Recognition Letters, 94, 87–95.
Pakarzadeh, H., & Fatemipanah, Z. (2023). Arun Kumar. Super-continuum Generation in Silica-Based Photonic Crystal Fibers for High-Resolution Ophthalmic Optical Coherence Tomography. Silicon, 15, vol, 6655–6661.
Keksel, A., Bulun, G., Eifler, M., Idrizovic, A., & Seewig, J. (2020). Physical Modeling of Full-Field Time-Domain Optical Coherence Tomography, OASIcs Vol. 89 IPMVM vol. 89, p. 14:1–14:22, 2021.
Drexler, W., & Fujimoto, J. G. (Eds.). (2008). Optical coherence tomography: technology and applications. Springer Science & Business Media.
Carvalho, P. M., & Silva (2016). Optical coherence tomography Layout Simulation Using MATLAB, PMS Carvalho-2016-estudogeral.uc.pt.
Tomlins, P. H., & Wang, R. K. (2005). Theory, developments and applications of optical coherence tomography. J Phys Appl Phys, 38(15), 2519–2535.
Bagci, A. M., Shahidi, M., Ansari, R., Blair, M., Blair, N. P., & Zelkha, R. Thickness Profiles of Retinal Layers by Optical Coherence Tomography Image Segmentation. American Journal Of Ophthalmology, 146, 5, pp. 679–687.e1, 2008.

No competing interests reported.

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Simulation of optical coherence tomography to determine refractive indices of retinal layers in different organisms

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2 Theoretical Framework of OCT

3 Simulation Results and Discussion

4 Conclusion

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	POS		ONL + PIS		OPL		INL		IPL + GCL		NFL
Sample	z (\(\:\varvec{\mu\:}\varvec{m}\))	n	z (\(\:\varvec{\mu\:}\varvec{m}\))	n	z (\(\:\varvec{\mu\:}\varvec{m}\))	n	z (\(\:\varvec{\mu\:}\varvec{m}\))	n	z (\(\:\varvec{\mu\:}\varvec{m}\))	n	z (\(\:\varvec{\mu\:}\varvec{m}\))	n
Human	60	1.358	100	1.36	10	1	30	1.361	50	1.367	10	1.376
Monkey	60	1.357	120	1.355	12	2	35	1.360	50	1.365	12	1.374
Cow	70	1.355	150	1.340	15	3	40	1.355	60	1.345	15	1.380
Dog	60	1.346	120	1.364	12	4	35	1.380	50	1.329	12	1.355