ABSTRACT
Monte Carlo radiation transport approaches the image formation process as a set of probabilities. The x-ray source, including focal spot shape, energy spectrum, and any added spatially varying filtration such a bow-tie filter, is defined as a set of probability density functions. An x-ray, for example, is generated with a probability of having a specific energy according to the specified energy spectrum, is initiated from a location specified by a probability density function describing the spatial distribution of the focal spot, and has a direction according to an angular emission probability. Given those initial conditions, the location of the next interaction is determined based on the interaction cross sections of the current material. Once the location of the next interaction is determined, the particle is transported to that location using the geometric model used by the Monte Carlo code. Monte Carlo packages also test for material boundary intersections and reevaluate the probability of interaction. Once an interaction has occurred, the type of interaction, such as coherent, incoherent, photoelectric, or pair production, is determined; secondaries are generated and added to the particle stack. A particle is usually followed until its initial energy drops below a certain threshold. Detector models also make use of spatial and statistical probability distributions. For each interaction, Monte Carlo codes use both analytical and empirical probability distributions and scatter cross-section models. The materials involved in the imaging chain are usually defined using databases of published properties. Each particle arriving at the detector will have a log with information about the interactions it has experienced, the materials it has crossed, and its current state. The particle log is used to develop numerous detector models, such as ideal energy-integrating, detectors with simple spread and depth of interaction models or complex indirect optical and direct scintillator models. Because of the statistical nature of each interaction, any resulting image will have inherent noise and will include scatter from the object to be imaged as well as scatter in the detector. Depending on the accuracy of the physical models used, the resulting image, quantum noise, and scatter estimates can be very accurate and realistic. Because of the electron tracking, Monte Carlo can report the energy deposited in each of the materials or phantom voxels in the simulation; therefore, organ and patient dose can be estimated at the same time as the image generation (Rupcich et al. 2012).
