Mikhail O. Bezuglyi, Natalia V. Bezugla, Denys V. Horban


Background. The features of scattering anisotropy factor determination in the research of thick biological tissue samples.

Objective. The purpose of the paper is development and testing of new method of tissue scattering anisotropy factor determination. The method is based on the analysis of illuminance of different zones of photometric images, received during the photometry by ellipsoidal reflectors.

Methods. For implementation of ideas and assumptions, the paper applies basics of photometry by ellipsoidal reflectors for real and model experiments, with the implementation of direct and inverse Monte Carlo method for light propagation in biological tissue. Additionally, principles of zone analysis of photometric images illuminance, received during the photometry by ellipsoidal reflectors, are applied.

Results. Based on the results of real experiment, the research represents input data set for Monte Carlo simulation of light propagation in biomedical photometer with ellipsoidal reflectors. Considering the modeling, the selection of critical thickness of samples of chicken and porcine muscle tissues was reasoned for further comparison with the results of real experiment. Dependencies of illuminance of different zones of photometric images for the selected thicknesses in the significant range of anisotropy factor value change were received. Anisotropy factors were determined in the spatial scattering cross sections. There was performed the comparative evaluation of character of photometric image zone illumination dependency for samples of various muscle tissues of similar thickness, and different thicknesses of selected tissue. Based on the developed method the specificities of real experiment results reproduction during the determination of scattering anisotropy factor by the illuminance values of photometric images, received during the simulation are shown.

Conclusions. Method of the mirror ellipsoid of revolution (which was used during the experiment with biological tissues samples in reflected and transmitted light) isn’t limited by the functionality of preliminary estimation of quantity of cross section for further spatial analysis and investigation of scattering indicatrix. Photometry by ellipsoidal reflectors can be applied as the separate method for determination of the magnitude of the scattering anisotropy factor based on the results of model and numerical experiments, and the developed procedure.


Ellipsoidal reflector; Photometry; Scattering anisotropy factor; Tissue anisotropy factor

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V.V. Tuchin, Optical Biomedical Diagnostics, part 1. Moscow: Russia: Physmathlit, 2007.

O. Nadiarnykh et al., “Alterations of the extracellular matrix in ovarian cancer studied by Second Harmonic Generation imaging microscopy”, BMC Cancer, vol. 10, p. 94, 2010. doi: 10.1186/1471-2407-10-94

R.B. La Comb et al., “Quantitative second harmonic generation imaging of the diseased state osteogenesi imperfecta: Experiment and simulation”, Biophys. J., vol. 94, no. 11, pp. 4504–4514, 2008. doi: 10.1529/biophysj.107.114405

H. Key et al., “Optical attenuation characteristics of breast tissues at visible and near-infrared wavelengths”, Phys Med Biol., vol. 36, no. 5, pp. 579–590, 1991. doi: 10.1088/0031-9155/36/5/002

A.N. Yaroslavsky et al., “Optical properties of selected native and coagulated human brain tissues in vitro in the visible and near infrared spectral range”, Phys. Med. Biol., vol. 47, no. 12, pp. 2059–2073, 2002. doi: 10.1088/0031-9155/47/12/305

P. D. Verhaegenetal., “A reliable, non-invasive measurement tool for anisotropy in normal skin and scar tissue”, Skin Res. Technol., vol. 16, no. 3, pp. 325–331, 2010. doi: 10.1111/j.1600-0846.2010.00436.x

S. Chandrasekhar, Radiative Transfer. Dover Publications, 1960.

A. Ishimaru, Wave Propagation and Scattering in Random Media. New York: Academic, 1978, 604 p.

W.J. Wiscombe, “Improved Mie scattering algorithms”, Appl. Opt., vol. 19, no. 9, pp. 1505–1509, 1980. doi: 10.1364/ao.19.001505

L.O. Reynolds and N.J. McCormick, “Approximate two-parameter phase function for light scattering”, J. Opt. Soc. Am., vol. 70, no. 10, pp. 1206–1212, 1980. doi: 10.1364/josa.70.001206

J.H. Joseph et al., “The delta-Eddington approximation for radiative flux transfer”, J. Atmos. Sci., vol. 33, no. 12, pp. 2452–2459, 1976. doi: 10.1175/1520-0469(1976)033<2452:tdeafr>;2

L.C. Chickenyey and J.L. Greenstein, “Diffuse radiation in the galaxy”, Astrophys. J., vol. 93, pp. 70–83, 1941. doi: 10.1086/144246

S.L. Jacques et al., “Angular dependence of chickene laser light scattering by human dermis”, Lasers in the Life Sciences, vol. 1, no. 4, pp. 309–333, 1987.

G. Hall et al., “Goniometric measurements of thick tissue using Monte Carlo simulations to obtain the single scattering anisotropy coefficient”, Biomed. Optics Express, vol. 3, no. 11, 2707–2719, 2012. doi: 10.1364/boe.3.002707

P. Saccomandi et al., “Goniometric measurement for the estimation of anisotropy coefficient of human and animal pancreas”, in Proc. 37th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2015, pp. 1283–1286. doi: 10.1109/embc.2015.7318602

D. Fukutomi et al., “Determination of the scattering coefficient of biological tissue considering the wavelength and absorption dependence of the anisotropy factor”, Optical Rev., vol. 23, no. 2, pp. 291–298, 2015. doi: 10.1007/s10043-015-0161-y

P. Saccomandi et al., “Estimation of anisotropy coefficient of swine pancreas, liver and muscle at 1064 nm base dongoniometric technique”, J. Biophoton., vol. 8, no. 5, pp. 422–428, 2015. doi: 10.1002/jbio.201400057

M.A. Bezuglyi and N.V. Bezuglaya, “Ellipsoidal reflectors in biomedical diagnostic”, in Proc. SPIE, vol. 9032, 2013. doi: 10.1117/12.2044606

M.A. Bezuglyi et al., “Ray tracing in ellipsoidal reflectors for optical biometry of media”, Appl Opt., vol. 56, no. 30, pp. 8520–8526, 2017. doi: 10.1364/AO.56.008520

M.A. Bezuglyi et al., “Influence of laser beam profile on light scattering by human skin during photometry by ellipsoidal reflectors”, Devices and Methods of Measurements, vol. 9, no. 1, pp. 56–65, 2018. doi: 10.21122/2220-9506-2018-9-1-56-65

N.V. Bezuglaya et al., “The influence of the axial anisotropy of the scattering by biological media on the accuracy of determination the optical coefficients by Monte Carlo method”, Naukovi Visti NTUU KPI, no. 1, pp. 85–91, 2015.

N.V. Bezuglaya et al., “Features of anisotropy of light scattering on fibrous biological tissues”, Bulletin of NTUU “KPI”. Series Instrument Making, vol. 50, no. 1, pp. 169–175, 2015.

N.V. Bezuglaya and M.A. Bezuglyi, “Spatial photometry of scattered radiation by biological objects”, in Proc. SPIE, 2013, vol. 9032, pp. Q1–Q5. doi:

M.A. Bezuglyi, “The non-invasive optical glucometer prototype with ellipsoidal reflectors”, in Proc. 59th International Scientific Conference on Power and Electrical Engineering of Riga Technical University, 2018, pp. 1–4. doi: 10.1109/RTUCON.2018.8659864

M.A. Bezuglyi et al., “Image processing at ellipsoidal photometry”, Devices and Methods of Measurements, vol. 7, no. 1, pp. 67–76, 2016. doi: 10.21122/2220-9506-2016-7-1-67-76

S. Grabtchak et al., “Optical absorption and scattering properties of bulk porcine muscle phantoms from interstitial radiance measurements in 650–900 nm range”, Physics in Medicine and Biology, vol. 59, no. 10, pp. 2431–2444, 2014. doi: 10.1088/0031-9155/59/10/2431

A.N. Bashkatov et al., “Optical properties of skin, subcutaneous, and muscle tissues: a review”, J. Innov. Optical Health Sci., vol. 4, no. 1, pp. 9–38, 2011. doi: 10.1142/s1793545811001319

S.L. Jacques, “Optical properties of biological tissues: a review”, Physics in Medicine and Biology, vol. 58, no. 11, pp. 5007–5008, 2013. doi:10.1088/0031-9155/58/11/r37

S.A. Prahl, “Light transport in tissue”, Ph.D. dissertation, University of Texas at Austin, 1988.

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