Model for the Diffuse Reflectance in Spatial Frequency Domain Imaging

Overview

Journal J Biomed Opt

Specialties Biomedical Engineering
Ophthalmology

Date 2023 Apr 10

PMID 37035029

Authors

Anouk L Post

Dirk J Faber

Ton G van Leeuwen

Affiliations

Soon will be listed here.

Abstract

Significance: In spatial frequency domain imaging (SDFI), tissue is illuminated with sinusoidal intensity patterns at different spatial frequencies. For low spatial frequencies, the reflectance is diffuse and a model derived by Cuccia et al. (doi 10.1117/1.3088140) is commonly used to extract optical properties. An improved model resulting in more accurate optical property extraction could lead to improved diagnostic algorithms.

Aim: To develop a model that improves optical property extraction for the diffuse reflectance in SFDI compared to the model of Cuccia et al.

Approach: We derive two analytical models for the diffuse reflectance, starting from the theoretical radial reflectance for a pencil-beam illumination under the partial current boundary condition (PCBC) and the extended boundary condition (EBC). We compare both models and the model of Cuccia et al. to Monte Carlo simulations.

Results: The model based on the PCBC resulted in the lowest errors, improving median relative errors compared to the model of Cuccia et al. by 45% for the reflectance, 10% for the reduced scattering coefficient and 64% for the absorption coefficient.

Conclusions: For the diffuse reflectance in SFDI, the model based on the PCBC provides more accurate results than the currently used model by Cuccia et al.

Citing Articles

Tutorial on methods for estimation of optical absorption and scattering properties of tissue.

Tao R, Grohl J, Hacker L, Pifferi A, Roblyer D, Bohndiek S J Biomed Opt. 2024; 29(6):060801.

PMID: 38864093 PMC: 11166171. DOI: 10.1117/1.JBO.29.6.060801.

Relevance and utility of the and optical properties of the skin reported in the literature: a review [Invited].

Setchfield K, Gorman A, Simpson A, Somekh M, Wright A Biomed Opt Express. 2023; 14(7):3555-3583.

PMID: 37497524 PMC: 10368038. DOI: 10.1364/BOE.493588.

References

Farrell T, Patterson M, Wilson B . A diffusion theory model of spatially resolved, steady-state diffuse reflectance for the noninvasive determination of tissue optical properties in vivo. Med Phys. 1992; 19(4):879-88. DOI: 10.1118/1.596777. View

Furutsu , Yamada . Diffusion approximation for a dissipative random medium and the applications. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 1994; 50(5):3634-3640. DOI: 10.1103/physreve.50.3634. View

Gioux S, Mazhar A, Cuccia D . Spatial frequency domain imaging in 2019: principles, applications, and perspectives. J Biomed Opt. 2019; 24(7):1-18. PMC: 6995958. DOI: 10.1117/1.JBO.24.7.071613. View

Angelo J, van de Giessen M, Gioux S . Real-time endoscopic optical properties imaging. Biomed Opt Express. 2017; 8(11):5113-5126. PMC: 5695957. DOI: 10.1364/BOE.8.005113. View

Kanick S, McClatchy 3rd D, Krishnaswamy V, Elliott J, Paulsen K, Pogue B . Sub-diffusive scattering parameter maps recovered using wide-field high-frequency structured light imaging. Biomed Opt Express. 2014; 5(10):3376-90. PMC: 4206309. DOI: 10.1364/BOE.5.003376. View

Post A, Faber D, Sterenborg H, van Leeuwen T . Subdiffuse scattering and absorption model for single fiber reflectance spectroscopy. Biomed Opt Express. 2020; 11(11):6620-6633. PMC: 7687961. DOI: 10.1364/BOE.402466. View

Haskell R, Svaasand L, Tsay T, Feng T, McAdams M, Tromberg B . Boundary conditions for the diffusion equation in radiative transfer. J Opt Soc Am A Opt Image Sci Vis. 1994; 11(10):2727-41. DOI: 10.1364/josaa.11.002727. View

Panigrahi S, Gioux S . Machine learning approach for rapid and accurate estimation of optical properties using spatial frequency domain imaging. J Biomed Opt. 2018; 24(7):1-6. PMC: 6995874. DOI: 10.1117/1.JBO.24.7.071606. View

Nakai T, Nishimura G, Yamamoto K, Tamura M . Expression of optical diffusion coefficient in high-absorption turbid media. Phys Med Biol. 1998; 42(12):2541-9. DOI: 10.1088/0031-9155/42/12/017. View

10.

Graaff R, Ten Bosch J . Diffusion coefficient in photon diffusion theory. Opt Lett. 2007; 25(1):43-5. DOI: 10.1364/ol.25.000043. View

11.

Stier A, Goth W, Hurley A, Brown T, Feng X, Zhang Y . Imaging sub-diffuse optical properties of cancerous and normal skin tissue using machine learning-aided spatial frequency domain imaging. J Biomed Opt. 2021; 26(9). PMC: 8459901. DOI: 10.1117/1.JBO.26.9.096007. View

12.

Svaasand L, Spott T, Fishkin J, Pham T, Tromberg B, Berns M . Reflectance measurements of layered media with diffuse photon-density waves: a potential tool for evaluating deep burns and subcutaneous lesions. Phys Med Biol. 1999; 44(3):801-13. DOI: 10.1088/0031-9155/44/3/020. View

13.

Streeter S, Maloney B, Zuurbier R, Wells W, Barth R, Paulsen K . Optical scatter imaging of resected breast tumor structures matches the patterns of micro-computed tomography. Phys Med Biol. 2021; 66(11). PMC: 9161376. DOI: 10.1088/1361-6560/ac01f1. View

14.

Cuccia D, Bevilacqua F, Durkin A, Ayers F, Tromberg B . Quantitation and mapping of tissue optical properties using modulated imaging. J Biomed Opt. 2009; 14(2):024012. PMC: 2868524. DOI: 10.1117/1.3088140. View

15.

Bassani M, Martelli F, Zaccanti G, Contini D . Independence of the diffusion coefficient from absorption: experimental and numerical evidence. Opt Lett. 1997; 22(12):853-5. DOI: 10.1364/ol.22.000853. View

16.

Zhao Y, Deng Y, Bao F, Peterson H, Istfan R, Roblyer D . Deep learning model for ultrafast multifrequency optical property extractions for spatial frequency domain imaging. Opt Lett. 2018; 43(22):5669-5672. DOI: 10.1364/OL.43.005669. View

17.

Cuccia D, Bevilacqua F, Durkin A, Tromberg B . Modulated imaging: quantitative analysis and tomography of turbid media in the spatial-frequency domain. Opt Lett. 2005; 30(11):1354-6. DOI: 10.1364/ol.30.001354. View

18.

Aronson R, Corngold N . Photon diffusion coefficient in an absorbing medium. J Opt Soc Am A Opt Image Sci Vis. 1999; 16(5):1066-71. DOI: 10.1364/josaa.16.001066. View

19.

Li Y, Guo M, Qian X, Lin W, Zheng Y, Yu K . Single snapshot spatial frequency domain imaging for risk stratification of diabetes and diabetic foot. Biomed Opt Express. 2020; 11(8):4471-4483. PMC: 7449725. DOI: 10.1364/BOE.394929. View

20.

Faber D, Post A, Sterenborg H, van Leeuwen T . Analytical model for diffuse reflectance in single fiber reflectance spectroscopy. Opt Lett. 2020; 45(7):2078-2081. DOI: 10.1364/OL.385845. View