Monte Carlo calculation of specific absorbed fractions: variance reduction techniques

Abstract

The purpose of the present work is to calculate specific absorbed fractions using variance reduction techniques and assess the effectiveness of these techniques in improving the efficiency (i.e. reducing the statistical uncertainties) of simulation results in cases where the distance between the source and the target organs is large and/or the target organ is small. The variance reduction techniques of interaction forcing and an ant colony algorithm, which drives the application of splitting and Russian roulette, were applied in Monte Carlo calculations performed with the code penelope for photons with energies from 30 keV to 2 MeV. In the simulations we used a mathematical phantom derived from the well-known MIRD-type adult phantom. The thyroid gland was assumed to be the source organ and urinary bladder, testicles, uterus and ovaries were considered as target organs. Simulations were performed, for each target organ and for photons with different energies, using these variance reduction techniques, all run on the same processor and during a CPU time of 1.5 · 10(5) s. For energies above 100 keV both interaction forcing and the ant colony method allowed reaching relative uncertainties of the average absorbed dose in the target organs below 4% in all studied cases. When these two techniques were used together, the uncertainty was further reduced, by a factor of 0.5 or less. For photons with energies below 100 keV, an adapted initialization of the ant colony algorithm was required. By using interaction forcing and the ant colony algorithm, realistic values of the specific absorbed fractions can be obtained with relative uncertainties small enough to permit discriminating among simulations performed with different Monte Carlo codes and phantoms. The methodology described in the present work can be employed to calculate specific absorbed fractions for arbitrary arrangements, i.e. energy spectrum of primary radiation, phantom model and source and target organs.

A Pseudo-Analytical Mix Sampling Strategy for Reliability Assessment of Power Girds

“…In formula (17), Fi k (X) denotes the value of the system experimental function under the condition that the event Bi occurs in the kth interval. The reliability index of the system can be calculated with formula (16) after respective sampling of each interval.…”

“…The experimental function F(Xk) of the subinterval [(k-1)/h), k/h] can be calculated by substituting these experimental functions and the corresponding probabilities of the sample space into the formula (18), and then the experimental functions of all subintervals can be calculated. 5) F*(X) is calculated according to formula (17). The experimental functions of the system, namely the reliability index, can be gotten by substituting all the F(Xk) required in step 4) into the formula (17).…”

“…5) F*(X) is calculated according to formula (17). The experimental functions of the system, namely the reliability index, can be gotten by substituting all the F(Xk) required in step 4) into the formula (17). 6) β is calculated based on formula (7) and Ns=Ns+1.…”

“…In fact, there is a large number of scientific works have been published on improving computing efficiency in the past few years [16]. For example, in some works, variance reduction techniques [17][18][19] are adopted to accelerate convergence speed and improve calculation efficiency of Monte Carlo based simulation, among which control variable (CV) [20], [21], average-and-scattered sampling (ASS) [22], importance sampling (IS) [23], antithetic variable (AV) [24] are commonly adopted. The ASS is adopted in reference [25] to reduce variance by averaging the experimental function in each interval (gotten by evenly dividing the interval [0, 1]) of each sampling as the new experimental function of the system.…”

PENGEOM —A general-purpose geometry package for Monte Carlo simulation of radiation transport in material systems defined by quadric surfaces

“…Figure 3 shows 2D and 3D images of an example quadric geometry included in the distribution package, a mathematical anthropomorphic phantom representing an adult, in which organs with the average shapes and dimensions are defined by quadric surfaces [35; 36; 37; 38]. This kind of phantom is used in Monte Carlo dosimetry studies [39] because it allows fast calculation of 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 ray-surface intersections 1 The method used to generate a two-dimensional image (2DView) consists of following a particle that moves on a plane perpendicular to an axis of the reference frame, which is mapped on the window. The particle starts from a position that corresponds to the leftmost pixel of each row and moves along a straight trajectory to the right of the window.…”