Interactions with 3D isotropic and homogeneous radiation fields: a Monte Carlo simulation algorithm

Monte Carlo techniques have become important tools for many biomedical applications. Many of these involve simulations of radiation fields that rely on the isotropy and homogeneity of the radiation source. The current study proposes a general algorithm to simulate such a radiation field around a fixed object. The idea is to surround the object with a sphere and to limit the source of radiation to the surface of that sphere. To insure the isotropy of the radiation source, each point on the sphere surface as seen from the object defines a direction at which a unidirectional field of particles is created. The combination of all unidirectional fields approaching from all points on the source sphere creates the effect of an isotropic and homogeneous radiation source. The algorithm is first presented without mathematical detail. Next, the expressions for the position and direction of the particles that compose the field are derived using analytical geometry. The radius of the source sphere is the only parameter needed for this algorithm. The randomness of each particle is simulated by the choice of four random numbers. Two algorithms using these analytical results are proposed, and an example of a C program is given for each. Both algorithms can be easily adapted to any situation that involves the Monte Carlo simulation of radiation interactions of a fixed object immersed within an isotropic and homogeneous radiation field.