Monte Carlo investigation on the effect of air gap under bolus in post-mastectomy radiotherapy

ObjectivesTo investigate the dosimetric effect of air gaps under bolus on skin dose for left-sided post-mastectomy radiotherapy with loco regional involvement.MethodsEight patients were planned retrospectively with volume modulated arc therapy (VMAT) and conventional static Field-in-Field (FinF) methods. Three different setups were applied for the 5-mm bolus over the chest wall having 0, 5 or 10 mm air gap under the bolus. The dose calculation was performed using Monte Carlo (MC) simulation. In addition, Analytic Anisotropic Algorithm (AAA) was used to demonstrate the differences observed in clinical setting.ResultsThe investigated air gaps under the bolus had minimal effect on surface dose for FinF plans (relative difference ≤ 2.6%), whereas for VMAT plans the surface dose decreased 13.6% when compared to the case with no air gap. In both FinF and VMAT, the largest differences between AAA and MC were seen at the surface where AAA underestimated the dose by 1.5 Gy (p < 0.05) on average; while the dose in the target volume excluding the surface was relatively similar being on average 0.3 Gy (p > 0.05) larger with AAA than with MC calculations.ConclusionsThe surface dose was significantly lower with VMAT technique than with FinF technique. Possible air gaps under the bolus reduced the surface dose significantly further for VMAT but not for FinF treatments, which may have clinical impact on recurrence rate. AAA was shown to underestimate the surface dose when compared to MC calculation.     

A Monte Carlo approach to estimate the uncertainty in soil CO2 emissions caused by spatial and sample size variability

The soil CO₂ emission is recognized as one of the largest fluxes in the global carbon cycle. Small errors in its estimation can result in large uncertainties and have important consequences for climate model predictions. Monte Carlo approach is efficient for estimating and reducing spatial scale sampling errors. However, that has not been used in soil CO₂ emission studies. Here, soil respiration data from 51 PVC collars were measured within farmland cultivated by maize covering 25 km² during the growing season. Based on Monte Carlo approach, optimal sample sizes of soil temperature, soil moisture, and soil CO₂ emission were determined. And models of soil respiration can be effectively assessed: Soil temperature model is the most effective model to increasing accuracy among three models. The study demonstrated that Monte Carlo approach may improve soil respiration accuracy with limited sample size. That will be valuable for reducing uncertainties of global carbon cycle.     

On power and sample size calculations for likelihood ratio tests in generalized linear models

A direct extension of the approach described in Self, Mauritsen, and Ohara (1992, Biometrics 48, 31-39) for power and sample size calculations in generalized linear models is presented. The major feature of the proposed approach is that the modification accommodates both a finite and an infinite number of covariate configurations. Furthermore, for the approximation of the noncentrality of the noncentral chi-square distribution for the likelihood ratio statistic, a simplification is provided that not only reduces substantial computation but also maintains the accuracy. Simulation studies are conducted to assess the accuracy for various model configurations and covariate distributions.     

A Monte Carlo study of the chlorophyll fluorescence emission and its effect on the leaf spectral reflectance and transmittance under various conditions.

Spectral hemispherical reflectance R(lambda) and transmittance T(lambda) are affected by chlorophyll (Chl) fluorescence which may complicate the evaluation of optical parameters of leaves. Measured Chl a fluorescence spectral emission F(lambda) is itself affected by several distortion effects on the leaf level (fluorescence reabsorption, secondary fluorescence, inner filter, surface and subsurface reflections etc.). In this work we propose a Monte Carlo photon transport (MCPT) model capable for treating a variety of optical distortion effects on the leaf level. In the forward mode the model decouples R(lambda), T(lambda) and their fluorescence contributions FR(T)(lambda). To obtain the absorption and scattering spectra of the leaf, utilized in the forward modeling, we have suggested an inversion procedure employing the experimental R(lambda), T(lambda). The attention was paid on the correction of the leaf absorption and scattering spectra caused by the optical effects on the sample level including Chl fluorescence contribution to measured R(lambda), T(lambda).     

A Monte Carlo investigation of the dosimetric properties of monoenergetic neutron beams for neutron capture therapy

A Monte Carlo simulation study has been carried out to investigate the suitability of neutron beams of various energies for therapeutic efficacy in boron neutron capture therapy. The dosimetric properties of unidirectional, monoenergetic neutron beams of varying diameters in two different phantoms (a right-circular cylinder and an ellipsoid) made of brain-equivalent material were examined. The source diameter was varied from 0.0 to 20.0 cm; neutron energies ranged from 0.025 eV up to 800 keV, the maximum neutron energy generated by a tandem cascade accelerator using 2.5-MeV protons in a 7Li(p,n)7Be reaction. Such a device is currently under investigation for use as a neutron source for boron neutron capture therapy. The simulation studies indicate that the maximum effective treatment depth (advantage depth) in the brain is 10.0 cm and is obtainable with a 10-keV neutron beam. A useful range of energies, defined as those neutron energies capable of effectively treating to a depth of 7 cm in brain tissue, is found to be 4.0 eV to 40.0 keV. Beam size is shown not to affect advantage depth as long as the entire phantom volume is used in determining this depth. Dose distribution in directions parallel to and perpendicular to the beam direction are shown to illustrate this phenomenon graphically as well as to illustrate the differences in advantage depth and advantage ratio and the contribution of individual dose components to tumor dose caused by the geometric differences in phantom shape.     

Power and sample size for testing homogeneity of relative risks in prospective studies

Power and sample-size formulas for testing the homogeneity of relative risks using the score method are presented. The homogeneity score test (Gart, 1985, Biometrika 72, 673-677) is formally equivalent to the Pearson chi-square test, although they look different. Results of this paper may be useful in assessing the validity of the model of a common relative risk before combining several 2 x 2 tables or in designing a prospective study for detecting heterogeneity of relative risks.     

Performance of the Peto odds ratio compared to the usual odds ratio estimator in the case of rare events

For the calculation of relative measures such as risk ratio (RR) and odds ratio (OR) in a single study, additional approaches are required for the case of zero events. In the case of zero events in one treatment arm, the Peto odds ratio (POR) can be calculated without continuity correction, and is currently the relative effect estimation method of choice for binary data with rare events. The aim of this simulation study is a variegated comparison of the estimated OR and estimated POR with the true OR in a single study with two parallel groups without confounders in data situations where the POR is currently recommended. This comparison was performed by means of several performance measures, that is the coverage, confidence interval (CI) width, mean squared error (MSE), and mean percentage error (MPE). We demonstrated that the estimator for the POR does not outperform the estimator for the OR for all the performance measures investigated. In the case of rare events, small treatment effects and similar group sizes, we demonstrated that the estimator for the POR performed better than the estimator for the OR only regarding the coverage and MPE, but not the CI width and MSE. For larger effects and unbalanced group size ratios, the coverage and MPE of the estimator for the POR were inappropriate. As in practice the true effect is unknown, the POR method should be applied only with the utmost caution.     

A revisit on tests for homogeneity of the risk difference

Lipsitz et al. (1998, Biometrics 54, 148-160) discussed testing the homogeneity of the risk difference for a series of 2 x 2 tables. They proposed and evaluated several weighted test statistics, including the commonly used weighted least squares test statistic. Here we suggest various important improvements on these test statistics. First, we propose using the one-sided analogues of the test procedures proposed by Lipsitz et al. because we should only reject the null hypothesis of homogeneity when the variation of the estimated risk differences between centers is large. Second, we generalize their study by redesigning the simulations to include the situations considered by Lipsitz et al. (1998) as special cases. Third, we consider a logarithmic transformation of the weighted least squares test statistic to improve the normal approximation of its sampling distribution. On the basis of Monte Carlo simulations, we note that, as long as the mean treatment group size per table is moderate or large (> or = 16), this simple test statistic, in conjunction with the commonly used adjustment procedure for sparse data, can be useful when the number of 2 x 2 tables is small or moderate (< or = 32). In these situations, in fact, we find that our proposed method generally outperforms all the statistics considered by Lipsitz et al. Finally, we include a general guideline about which test statistic should be used in a variety of situations.