Analysis and Prediction of Transient Opacity Spikes Using Dimensional Modeling

Dimensional modeling, GT-Power in particular, has been used for two related purposes-to quantify and understand the inaccuracies of transient engine flow estimates that cause transient smoke spikes and to improve empirical models of opacity or particulate matter used for engine calibration. It has been proposed by dimensional modeling that exhaust gas recirculation flow rate was significantly underestimated and volumetric efficiency was overestimated by the electronic control module during the turbocharger lag period of an electronically controlled heavy duty diesel engine. Factoring in cylinder-to-cylinder variation, it has been shown that the electronic control module estimated fuel-Oxygen ratio was lower than actual by up to 35% during the turbocharger lag period but within 2% of actual elsewhere, thus hindering fuel-Oxygen ratio limit-based smoke control. The dimensional modeling of transient flow was enabled with a new method of simulating transient data in which the manifold pressures and exhaust gas recirculation system flow resistance, characterized as a function of exhaust gas recirculation valve position at each measured transient data point, were replicated by quasi-static or transient simulation to predict engine flows. Dimensional modeling was also used to transform the engine operating parameter model input space to a more fundamental lower dimensional space so that a nearest neighbor approach could be used to predict smoke emissions. This new approach, intended for engine calibration and control modeling, was termed the "nonparametric reduced dimensionality" approach. It was used to predict federal test procedure cumulative particulate matter within 7% of measured value, based solely on steady-state training data. Very little correlation between the model inputs in the transformed space was observed as compared to the engine operating parameter space. This more uniform, smaller, shrunken model input space might explain how the nonparametric reduced dimensionality approach model could successfully predict federal test procedure emissions when roughly 40% of all transient points were classified as outliers as per the steady-state training data.

Power Calculations for Preclinical Studies Using a K-Sample Rank Test and the Lehmann Alternative Hypothesis

Power calculations in a small sample comparative study, with a continuous outcome measure, are typically undertaken using the asymptotic distribution of the test statistic. When the sample size is small, this asymptotic result can be a poor approximation. An alternative approach, using a rank based test statistic, is an exact power calculation. When the number of groups is greater than two, the number of calculations required to perform an exact power calculation is prohibitive. To reduce the computational burden, a Monte Carlo resampling procedure is used to approximate the exact power function of a k-sample rank test statistic under the family of Lehmann alternative hypotheses. The motivating example for this approach is the design of animal studies, where the number of animals per group is typically small.

Collapsed cone convolution and analytical anisotropic algorithm dose calculations compared to VMC++ Monte Carlo simulations in clinical cases

The purpose of this work was to study and quantify the differences in dose distributions computed with some of the newest dose calculation algorithms available in commercial planning systems. The study was done for clinical cases originally calculated with pencil beam convolution (PBC) where large density inhomogeneities were present. Three other dose algorithms were used: a pencil beam like algorithm, the anisotropic analytic algorithm (AAA), a convolution superposition algorithm, collapsed cone convolution (CCC), and a Monte Carlo program, voxel Monte Carlo (VMC++). The dose calculation algorithms were compared under static field irradiations at 6 MV and 15 MV using multileaf collimators and hard wedges where necessary. Five clinical cases were studied: three lung and two breast cases. We found that, in terms of accuracy, the CCC algorithm performed better overall than AAA compared to VMC++, but AAA remains an attractive option for routine use in the clinic due to its short computation times. Dose differences between the different algorithms and VMC++ for the median value of the planning target volume (PTV) were typically 0.4% (range: 0.0 to 1.4%) in the lung and -1.3% (range: -2.1 to -0.6%) in the breast for the few cases we analysed. As expected, PTV coverage and dose homogeneity turned out to be more critical in the lung than in the breast cases with respect to the accuracy of the dose calculation. This was observed in the dose volume histograms obtained from the Monte Carlo simulations.

Conversion of CT numbers into tissue parameters for Monte Carlo dose calculations: a multi-centre study

The conversion of computed tomography (CT) numbers into material composition and mass density data influences the accuracy of patient dose calculations in Monte Carlo treatment planning (MCTP). The aim of our work was to develop a CT conversion scheme by performing a stoichiometric CT calibration. Fourteen dosimetrically equivalent tissue subsets (bins), of which ten bone bins, were created. After validating the proposed CT conversion scheme on phantoms, it was compared to a conventional five bin scheme with only one bone bin. This resulted in dose distributions D(14) and D(5) for nine clinical patient cases in a European multi-centre study. The observed local relative differences in dose to medium were mostly smaller than 5%. The dose-volume histograms of both targets and organs at risk were comparable, although within bony structures D(14) was found to be slightly but systematically higher than D(5). Converting dose to medium to dose to water (D(14) to D(14wat) and D(5) to D(5wat)) resulted in larger local differences as D(5wat) became up to 10% higher than D(14wat). In conclusion, multiple bone bins need to be introduced when Monte Carlo (MC) calculations of patient dose distributions are converted to dose to water.

A multiple source model for 6 MV photon beam dose calculations using Monte Carlo

A multiple source model (MSM) for the 6 MV beam of a Varian Clinac 2300 C/D was developed by simulating radiation transport through the accelerator head for a set of square fields using the GEANT Monte Carlo (MC) code. The corresponding phase space (PS) data enabled the characterization of 12 sources representing the main components of the beam defining system. By parametrizing the source characteristics and by evaluating the dependence of the parameters on field size, it was possible to extend the validity of the model to arbitrary rectangular fields which include the central 3 x 3 cm2 field without additional precalculated PS data. Finally, a sampling procedure was developed in order to reproduce the PS data. To validate the MSM, the fluence, energy fluence and mean energy distributions determined from the original and the reproduced PS data were compared and showed very good agreement. In addition, the MC calculated primary energy spectrum was verified by an energy spectrum derived from transmission measurements. Comparisons of MC calculated depth dose curves and profiles, using original and PS data reproduced by the MSM, agree within 1% and 1 mm. Deviations from measured dose distributions are within 1.5% and 1 mm. However, the real beam leads to some larger deviations outside the geometrical beam area for large fields. Calculated output factors in 10 cm water depth agree within 1.5% with experimentally determined data. In conclusion, the MSM produces accurate PS data for MC photon dose calculations for the rectangular fields specified.

Simple beam models for Monte Carlo photon beam dose calculations in radiotherapy

Monte Carlo (code GEANT) produced 6 and 15 MV phase space (PS) data were used to define several simple photon beam models. For creating the PS data the energy of starting electrons hitting the target was tuned to get correct depth dose data compared to measurements. The modeling process used the full PS information within the geometrical boundaries of the beam including all scattered radiation of the accelerator head. Scattered radiation outside the boundaries was neglected. Photons and electrons were assumed to be radiated from point sources. Four different models were investigated which involved different ways to determine the energies and locations of beam particles in the output plane. Depth dose curves, profiles, and relative output factors were calculated with these models for six field sizes from 5x5 to 40x40cm2 and compared to measurements. Model 1 uses a photon energy spectrum independent of location in the PS plane and a constant photon fluence in this plane. Model 2 takes into account the spatial particle fluence distribution in the PS plane. A constant fluence is used again in model 3, but the photon energy spectrum depends upon the off axis position. Model 4, finally uses the spatial particle fluence distribution and off axis dependent photon energy spectra in the PS plane. Depth dose curves and profiles for field sizes up to 10x10cm2 were not model sensitive. Good agreement between measured and calculated depth dose curves and profiles for all field sizes was reached for model 4. However, increasing deviations were found for increasing field sizes for models 1-3. Large deviations resulted for the profiles of models 2 and 3. This is due to the fact that these models overestimate and underestimate the energy fluence at large off axis distances. Relative output factors consistent with measurements resulted only for model 4.