Monte Carlo method for photon transport
In contrast, Monte Carlo simulations can be made arbitrarily accurate by increasing the number of photons traced.
For example, see the movie, where a Monte Carlo simulation of a pencil beam incident on a semi-infinite medium models both the initial ballistic photon flow and the later diffuse propagation.
The Monte Carlo method is necessarily statistical and therefore requires significant computation time to achieve precision.
In addition Monte Carlo simulations can keep track of multiple physical quantities simultaneously, with any desired spatial and temporal resolution.
Thus, while computationally inefficient, Monte Carlo methods are often considered the standard for simulated measurements of photon transport for many biomedical applications.
Microscopy techniques (including confocal, two-photon, and optical coherence tomography) have the ability to image these properties with high spatial resolution, but, since they rely on ballistic photons, their depth penetration is limited to a few millimeters.
Monte Carlo methods provide a flexible framework that has been used by different techniques to reconstruct optical properties deep within tissue.
Due to the nature of PDT, it is useful to use Monte Carlo methods for modeling scattering and absorption in the tissue in order to ensure appropriate levels of light are delivered to activate chemotherapy agents.
In addition for a semi-infinite medium (in which photons are considered lost if they exit the top boundary), special consideration must be taken.
We will solve the problem using an infinitely small point source (represented analytically as a Dirac delta function in space and time).
Responses to arbitrary source geometries can be constructed using the method of Green's functions (or convolution, if enough spatial symmetry exists).
Time-resolved responses are found by keeping track of the total elapsed time of the photon's flight using the optical path length.
Any number of photon packets can be launched and modeled, until the resulting simulated measurements have the desired signal-to-noise ratio.
Below is a basic form of photon step size selection (derived using the inverse distribution method and the Beer–Lambert law) from which we use for our homogeneous model: where
To keep total energy constant, a Russian roulette technique is often employed for photons below a certain weight threshold.
The parallel nature of this special type of Monte Carlo simulation renders it highly suitable for execution on a graphics processing unit (GPU).
The release of programmable GPUs started such a development, and since 2008 there have been a few reports on the use of GPU for high-speed Monte Carlo simulation of photon migration.
