DETERMINATION OF THE TISSUE ANISOTROPY FACTOR DURING THE PHOTOMETRY BY ELLIPSOIDAL REFLECTORS

62 ɉɊɂɅȺȾɈȻɍȾɍȼȺɇɇə ɌȺ ȱɇɎɈɊɆȺɐȱɃɇɈ-ȼɂɆȱɊɘȼȺɅɖɇȺ ɌȿɏɇȱɄȺ DOI: 10.20535/kpi-sn.2019.4.177082 UDC 535.2:616-71 M.O. Bezuglyi , N.V. Bezugla, D.V. Horban Igor Sikorsky Kyiv Polytechnic Institute, Kyiv, Ukraine correspondingauthor: DETERMINATION OF THE TISSUE ANISOTROPY FACTOR DURING THE PHOTOMETRY BY ELLIPSOIDAL REFLECTORS 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. Keywords: ellipsoidal reflector; photometry; scattering anisotropy factor; tissue anisotropy factor. Introduction Scattering anisotropy factor is one of the indicators, determining optical properties of biological tissue. Scattering and absorption coefficients, and refractive index form the biometrical basis, with the help of which the identification of biological media is possible. The goal of such identification is determination of changes, caused by various pathologic processes [1—6]. From the analytic interpretation standpoint, the tissue anisotropy factor is the probability characteristic, which reveals the phase scattering function in the main equation of radiative transfer theory [7, 8]. For biophotonics methods and means for various biological tissues, the one-time Mie scattering and Reynolds-McCormick (RMPF), Eddington and Delta-Eddington, and Henyey-Greenstein (HGPF) phase functions are most widely used. Besides, the HGPF is considered as the best standard for ©TheAuthor(s). ThearticleisdistributedunderthetermsofthelicenseCCBY4.0. simulation of light propagation in biological tissues (BT), and, therefore, for solution of inverse tasks in optical biomedical diagnostics [9—12]. During the transition to the one-time scattering function based on the measured scattering indicatrix on the thick biological samples, mathematical apparatus for goniometric measurements is used [13—17]. Among used technical tools for determining the optical properties of tissues based on the measured optical coefficients of transmittance and reflectance, photometers with ellipsoidal reflectors (ER) can be considered as the most informative ones [18]. They can be considered as the successful alternative for integrating spheres. Photometers with ellipsoidal reflectors, used in combination with ray-tracing principles in biological tissue and ellipsoidal reflector [19], and Monte Carlo simulation of light propagation, allow estimating the spatial distribution of forward and back scattered light on various laser source parameters [20]. 63 ɉɊɂɅȺȾɈȻɍȾɍȼȺɇɇə ɌȺ ȱɇɎɈɊɆȺɐȱɃɇɈ-ȼɂɆȱɊɘȼȺɅɖɇȺ ɌȿɏɇȱɄȺ The proceedings [21—23] represent that the scattering anisotropy has non-axial symmetry character, which is extremely true for fiber biological tissues. In such case, photometry by ellipsoidal reflectors is used as the method of preliminary estimation of the asymmetry of scattering indicatrix in the solid angle range of 4Ɏ, and the quantity of cross sections is determined [22], which is necessary to perform the averaging of anisotropy factor. From the other side, the Monte Carlo simulation of light propagation in the system “BT + ER” occurs from the standpoint of the scattering phase function axial symmetry. The differential estimation of spatial distribution by cross section can be ensured similar to the real experiment [21—23]. However, authors of the current research consider that the use of photometric images, which were derived from the method of mirror ellipsoids of revolution during the modal experiment in reflected and transmitted light, is feasible for specifying the tissue anisotropy factor, which was received during the real experiment. Problem statement Considering the mentioned information, the goal of the current investigation is development of the method for determination of tissue scattering anisotropy factor by the analysis of illuminance of different zones of photometric images, received during the photometry by ellipsoidal reflectors. Photometer with ellipsoidal reflectors In the current research the modification of the photometer with ellipsoidal reflectors was used, which was similar to ones, used in the proceedings [18—22, 24]. Fig.1 represents the photometer scheme, which contains ellipsoidal reflectors for transmitted (ER1) and reflected (ER2) light, optical hoods OH1 and OH2, adjusting optical systems L1 and L2, and cameras CCD1 and CCD2. L1 OH1 ER1 Ellipsoidal reflector is a mirror ellipsoid of revolution with internal reflecting surface, which was cut by focal planes orthogonally to its major semi-axis; at the same time its minor semi-axes are equal. By means of the reflecting prism P, which was fitted in the laser sourc (...truncated)