1. 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
Saratov Fall Meeting 2016

2. 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.

3. 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

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

5. 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:

6. 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

7. Inhomogeneity localization in a cylindrical object

8. 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

9. 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

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

11. 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

12. 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

13. 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

14. 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

15. 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.