Hybrid theory for photon transport in tissue
The MCML is a numerical way to simulate photon transport in biological tissue.
By averaging multiple independent random walks, MCML estimates the ensemble-averaged quantities such as reflectance, transmittance, absorption, and fluence.
The parameters of photon transport, including the step size and deflection angle due to scattering, are determined by random sampling from probability distributions.
A fraction of weight, determined by the scattering and absorption coefficients is deposited at the interaction site.
The photon packet continues propagating until the weight left is smaller than a certain threshold.
If this packet of photon hits the boundary during the propagation, it is either reflected or transmitted, determined by a pseudorandom number.
Statistically sufficient numbers of photon packets must be simulated to obtain the expected values accurately.
[1] Advantages and Disadvantages This Monte Carlo method is rigorous and flexible.
However, because of its statistical nature, this method requires tracking a large number of photon packets, making it computationally expensive.
The Diffusion Theory is an approximation of the radiative transfer equation (RTE), and an analytical way to simulate photon transport.
As an example, one way to attain a solution for a pencil beam that is vertically incident on a semi-infinite homogeneous scattering medium is by taking three approximation steps as follows: Advantages and Disadvantages Diffusion Theory is more computationally efficient than MCML.
In the previous example for the Diffusion Theory, a semi-infinite scattering medium with only one boundary was assumed.
A Monte Carlo approach can be used to make up for the Diffusion Theory's inherently poor accuracy near the boundaries.
Just like in the Monte Carlo simulation, any photon packet that gets reemitted is added to the diffuse reflectance
along the direction of the photon packet propagation for it to be converted to a point source, otherwise the Monte Carlo simulation continues.
Before the conversion to an isotropic point source, the photon packet reduces its weight due to its interaction with the scattering medium.
This is the accumulated weight distribution which can be converted to relative source density function
from the sources is calculated as: A trade-off between simulation speed and accuracy exists; choosing a critical depth
becomes the deciding factor for simulation speed with a deeper critical depth resulting in slower times due to packets needing to be tracked for a longer distance before the transition to diffusion theory.
