AN ALGORITHM FOR LOCALIZATION OF OPTICAL STRUCTURE DISTURBANCES IN BIOLOGICAL TISSUE USING TIME-RESOLVED DIFFUSE OPTICAL TOMOGRAPHY Potlov A.Yu, Frolov S.V., Proskurin S.G. Biomedical Engineering, TSTU http://bmt.tstu.ru/ http://spros.tamb.ru/ spros@tamb.ru Saratov Fall Meeting 2017

OBJECTIVES The purpose of our study was to develop an algorithm for localizing inhomogeneities in time-resolved Diffuse Optical Tomography, which combining increased speed (dialog mode) with acceptable accuracy.   The method is based on the initial approximation formed from the results of the analysis of late photons (LAPs) of all temporal point spread functions (TPSF)s. 2

SELECTING A METHOD FOR SOLUTION OF THE FORWARD PROBLEM It is generally accepted to model the migration of photons in highly scattering media, such as biological tissues, using a diffusion approximation by the Monte Carlo method or the Kubelka–Munk method (manyflux model). Monte Carlo simulation is characterized by much higher accuracy (especially on the boundaries and near the source) than the Kubelka–Munk method and diffusion approximation. However, the Monte Carlo method calls for large computational resources. At the same time, the needs of the diffusion approximation for computational resources are rather moderate, and it describes well the propagation of radiation in the bulk of biological tissues. In this context, it is proposed to use the diffusion approximation to form theoretical TPSFs within the solution of the inverse problem. 3

SOLUTION OF THE FORWARD PROBLEM Diffusion approximation, as applied to simulation of photon migration in biological tissues, is a parabolic-type partial differential equation, which describes the balance energy in a medium containing scattering and absorbing particles: The Robin boundary condition (of the third type) is used to describe the photon flux at the boundary of modeled object : 4 Quantum Electronics (2015), p. 540

where: 5

SOLUTION OF THE INVERSE PROBLEM To select LAPs, the initial regions, corresponding to early photons, and the middle regions, corresponding to photons with an intermediate time of flight, are removed from all TPSFs: where: Then is calculated photon flux density on the detector: 6 Optics and spectroscopy (2016), p. 9

Then we find the time-averaged LAP flux density on detector: Finally, we obtain homogeneity index, which is the dependence of the mean LAP density on the angle between the directions of the light source fiber and the detector fiber, corresponding to the TPSF: 7

INITIAL APPROXIMATION TO THE SPATIAL DISTRIBUTION OF THE ABSORPTION AND SCATTERING COEFFICIENTS The found homogeneity index is transformed into a step function as follows: For each such portion of the step function, it is successively assumed that the modeled object contains a spherical absorbing inhomogeneity with a diameter equal to the halflength of the chord between the angles corresponding to the beginning and end of the portion of the step function. Note that the inhomogeneity is assumed to be equidistant from the center of the object studied and from the point on the boundary of this object, located at the angle corresponding to the middle of the portion step function. 8 Laser Physics (2015), p. 035601

ALGORITHM OF TWO-DIMENSIONAL LAYER-BY-LAYER AND THREE-DIMENSIONAL VOLUME LOCALIZATION OF INHOMOGENEITIES 9 Optics and spectroscopy (2016), p. 9

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FAST (DIALOG MODE) LOCALIZATIONS OF INHOMOGENEITIES IN BIOMEDICAL OBJECT (a) (b) MRI scan of a patient with a glioblastoma (a), the result of the glioblastoma localization (b). Inverse problem was solved on an HP Z640 Workstation for less than 3 s. 12 Advanced Laser Technologies (2016), BP-P-7

CONCLUSIONS The investigated algorithm for localizing inhomogeneities in time-resolved Diffuse Optical Tomography provides rapidly adequate results. The assumption that optical inhomogeneities in an object studied are spherical and homogeneous with respect to the absorption and scattering coefficients is valid for most of diagnosed tumor angiogenesis regions. The suggested algorithm can be used for fast (dialog mode) localizations of absorbing and scattering inhomogeneities in biomedical objects for brain structures diagnostics, traumatology, and mammography using Diffuse Optical Tomography.   Our further study will be focused on the improvement of the initial approximation to the spatial distribution of absorbing and scattering inhomogeneities, adaptation of the algorithm to simultaneous calculations on graphical processors, and consideration of cases with more complex geometric and optical structures. 13