Hybrid Theory For Photon Transport in Tissue - Hybrid Theory

Hybrid Theory

The Hybrid Theory combines the Diffusion Theory and the Monte Carlo method in order to increase accuracy near the source and boundaries while reducing computation time. In the previous example for the Diffusion Theory, a semi-infinite scattering medium with only one boundary was assumed. If the geometry is a slab, the second boundary must be taken into account. The fluence rate at the extrapolated boundaries must be approximately 0. Using an array of image sources fulfills this boundary condition. The extrapolated boundary is located at distance . The coordinates for the source pairs are where is the coordinate for the point source and is the slab thickness. Only 2-3 pairs are usually necessary to achieve good accuracy.

A Monte Carlo approach can be used to make up for the Diffusion Theory's inherently poor accuracy near the boundaries. As mentioned before, the Monte Carlo simulation is time consuming. When a photon packet is within a critical depth the Monte Carlo simulation tracks all packets but within the center region the photon packet is transformed to an isotropic source and subsequently treated with Diffusion Theory. Just like in the Monte Carlo simulation, any photon packet that gets reemitted is added to the diffuse reflectance .

When a photon packet is scattered into the center zone, it is conditionally converted to an isotropic point source. The photon packet must still be in the center region after one transport mean free path 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. The resulting weight is recorded as a source function . This is the accumulated weight distribution which can be converted to relative source density function by:

where is the grid volume and is the number of photon packets.

The additional diffuse reflectance from the sources is calculated as:

where is from the diffusion theory approximation for a slab and is the azimuthal angle. The total diffuse reflectance would be and added together.