A 3D pencil-beam-based superposition algorithm for photon dose calculation in heterogeneous media.

In this work, a novel three-dimensional superposition algorithm for photon dose calculation is presented. The dose calculation is performed as a superposition of pencil beams, which are modified based on tissue electron densities. The pencil beams have been derived from Monte Carlo simulations, and are separated into lateral and depth-directed components. The lateral component is modeled using exponential functions, which allows accurate modeling of lateral scatter in heterogeneous tissues. The depth-directed component represents the total energy deposited on each plane, which is spread out using the lateral scatter functions. Finally, convolution in the depth direction is applied to account for tissue interface effects. The method can be used with the previously introduced multiple-source model for clinical settings. The method was compared against Monte Carlo simulations in several phantoms including lung- and bone-type heterogeneities. Comparisons were made for several field sizes for 6 and 18 MV energies. The deviations were generally within (2%, 2 mm) of the field central axis d(max). Significantly larger deviations (up to 8%) were found only for the smallest field in the lung slab phantom for 18 MV. The presented method was found to be accurate in a wide range of conditions making it suitable for clinical planning purposes.

Determination of parameters for a multiple-source model of megavoltage photon beams using optimization methods.

Accurate modelling of the radiation output of a medical linear accelerator is important for radiotherapy treatment planning. The major challenge is the adjustment of the model to a specific treatment unit. One approach is to use a multiple-source model containing a set of physical parameters. In this work, the parameters were derived from standard beam data measurements using optimization methods. The source model used includes sub-sources for bremsstrahlung radiation from the target, extra-focal photon radiation and electron contamination. The cost function includes a gamma error measure between measurements and current dose calculations. The procedure was applied to six beam data sets (6 MV to 23 MV) measured with accelerators from three vendors, but the results focus primarily on Varian accelerators. The obtained average gamma error (1%, 1 mm) between dose calculations and measurements used in optimization was smaller than 0.7 for each studied treatment beam and field size, and a minimum of 83% of measurement points passed the gamma < 1 criterion. For experiments made at different SSDs and for asymmetric fields, the average gamma errors were smaller than 1.1. For irregularly shaped MLC apertures, the differences in point doses were smaller than 1.0%. This work demonstrates that the source model parameters can be automatically derived from simple measurements using optimization methods. The developed procedure is applicable to a wide range of accelerators, and has an acceptable accuracy and processing time.

Two-electron quantum dot molecule: composite particles and the spin phase diagram.

We study a two-electron quantum dot molecule in a magnetic field by the direct diagonalization of the Hamiltonian matrix. The ground states of the molecule with the total spin S = 0 and S = 1 provide a possible realization for a qubit of a quantum computer. Switching between the states is best achieved by changing the magnetic field. Based on an analysis of the wave function, we show that the system consists of composite particles formed by an electron and flux quanta attached to it. This picture can also be used to explain the spin phase diagram.