Specific features of motion of the photon density normalized maximum in highly scattering media with tissue-like optical properties Potlov A.Yu., Frolov S.V., Proskurin S.G. Biomedical engineering, TSTU, Russia http://bmt.tstu.ru/ http://spros.tamb.ru/ spros@tamb.ru Saratov Fall Meeting 2016

Objectives The regularities of motion of the Photon Density Normalized Maximum (PDNM) in highly scattering media such as biological tissues are described. Improved model of the optical properties of turbid media based on the diffusion approximation to the Radiative Transfer Equation (RTE) is used for identifying regularities of PDNM movement. Monte Carlo simulation is applied to verify diffusion approximation results.

Numerical simulation of photon migration using Model of a Drop Photon distribution densities were obtained numerically using the Model of a Drop: the laser pulse containing a fixed initial number of photons appears near the object surface and diffuses within it, decaying exponentially and moving primarily to its centre. According to the diffusion approximation to RTE, photon density is described as follows: Photonics and Lasers in Medicine (2013 ) p.139

Boundary condition of the third kind (the Robin condition): where, Quantum Electronics (2015), p.540

Monte Carlo simulation of photon migration The probability of scattering of a photon by a particle: The probability of absorbing of a photon by a particle: The distance between two consecutive acts of interaction: "Weight" of a photon:

if the angle of incidence of the photon beam is close to the normal Updating the coordinates: where , , – direction cosines if the angle of incidence of the photon beam is close to the normal at the initial time in all other cases

Inhomogeneity localization in a cylindrical object

Simulated TPSF (Model of a Drop) (a) (b) 3D representation of Time Point Spread Functions (TPSF) for homogenous (a) and inhomogeneous (b) cases Quantum Electronics (2011), p.402

Photon density in a cylinder Simulation results (Model of a Drop) See attached video file (a) (b) Photons density distribution in a slice of homogeneous (a) and inhomogeneous (b) cylindrical objects 0.75 ns after light pulse injection Quantum Electronics (2014) p.174

for homogenous (a) and inhomogeneous (b) cases Simulated TPSF (Monte Carlo) (a) (b) for homogenous (a) and inhomogeneous (b) cases

Photon density in a cylinder Simulation results (Monte Carlo) See attached video file (a) (b)   Photons density distribution in the same slice of homogeneous (a) and inhomogeneous (b) cylindrical objects 0.75 ns after light pulse injection

Photon density normalized maximum After completion of the iterative process the ф(x, y, z, t) function is normalized with respect to its maximum: then a following transform is performed: where P is the number showing the top part of photon density distribution (PDNM), 0<P 1. Laser Physics (2015), p.035601

of diffuse photon migration Specific features of diffuse photon migration In the homogeneous case, independently of the values of absorption and scattering coefficients, the photon density maximum moves towards the geometric centre of the object. In the presence of an absorbing inhomogeneity, PDNM moves towards the point symmetric to the geometric centre of this inhomogeneity with respect to the centre of the cylindrical object. The distance at which PDNM moves away from the object geometric axis can be calculated using this formula: Laser Physics (2015), p.035601

of diffuse photon migration Specific features of diffuse photon migration In the case of a scattering inhomogeneity, PDNM moves towards the centre of the latter. The distance at which PDNM moves away from the object geometric axis can be calculated using this formula: Quantum Electronics (2015), p.540

Conclusion Both numerical simulations has confirmed that, in homogeneous objects PDNM always moves to the geometric centre of the object. In the case of single absorbing inhomogeneity PDNM moves towards the point which is symmetrical to the geometric centre of it with respect to the center of the object. In the presence of a single scattering inhomogeneity PDNM moves towards its geometric centre.