A practical and theoretical definition of very small field size for radiotherapy output factor measurements

Purpose This work introduces the concept of very small field size. Output factor (OPF) measurements at these field sizes require extremely careful experimental methodology including the measurement of dosimetric field size at the same time as each OPF measurement. Two quantifiable scientific definitions of the threshold of very small field size are presented. Methods A practical definition was established by quantifying the effect that a 1 mm error in field size or detector position had on OPFs, and setting acceptable uncertainties on OPF at 1%. Alternatively, for a theoretical definition of very small field size, the OPFs were separated into additional factors to investigate the specific effects of lateral electronic disequilibrium, photon scatter in the phantom and source occlusion. The dominant effect was established and formed the basis of a theoretical definition of very small fields. Each factor was obtained using Monte Carlo simulations of a Varian iX linear accelerator for various square field sizes of side length from 4 mm to 100 mm, using a nominal photon energy of 6 MV. Results According to the practical definition established in this project, field sizes < 15 mm were considered to be very small for 6 MV beams for maximal field size uncertainties of 1 mm. If the acceptable uncertainty in the OPF was increased from 1.0 % to 2.0 %, or field size uncertainties are 0.5 mm, field sizes < 12 mm were considered to be very small. Lateral electronic disequilibrium in the phantom was the dominant cause of change in OPF at very small field sizes. Thus the theoretical definition of very small field size coincided to the field size at which lateral electronic disequilibrium clearly caused a greater change in OPF than any other effects. This was found to occur at field sizes < 12 mm. Source occlusion also caused a large change in OPF for field sizes < 8 mm. Based on the results of this study, field sizes < 12 mm were considered to be theoretically very small for 6 MV beams. Conclusions Extremely careful experimental methodology including the measurement of dosimetric field size at the same time as output factor measurement for each field size setting and also very precise detector alignment is required at field sizes at least < 12 mm and more conservatively < 15 mm for 6 MV beams. These recommendations should be applied in addition to all the usual considerations for small field dosimetry, including careful detector selection.

Output feedback optimal control with contraints

In Chapters 1 through 9 of the book (with the exception of a brief discussion on observers and integral action in Section 5.5 of Chapter 5) we considered constrained optimal control problems for systems without uncertainty, that is, with no unmodelled dynamics or disturbances, and where the full state was available for measurement. More realistically, however, it is necessary to consider control problems for systems with uncertainty. This chapter addresses some of the issues that arise in this situation. As in Chapter 9, we adopt a stochastic description of uncertainty, which associates probability distributions to the uncertain elements, that is, disturbances and initial conditions. (See Section 12.6 for references to alternative approaches to model uncertainty.) When incomplete state information exists, a popular observer-based control strategy in the presence of stochastic disturbances is to use the certainty equivalence [CE] principle, introduced in Section 5.5 of Chapter 5 for deterministic systems. In the stochastic framework, CE consists of estimating the state and then using these estimates as if they were the true state in the control law that results if the problem were formulated as a deterministic problem (that is, without uncertainty). This strategy is motivated by the unconstrained problem with a quadratic objective function, for which CE is indeed the optimal solution (˚Astr¨om 1970, Bertsekas 1976). One of the aims of this chapter is to explore the issues that arise from the use of CE in RHC in the presence of constraints. We then turn to the obvious question about the optimality of the CE principle. We show that CE is, indeed, not optimal in general. We also analyse the possibility of obtaining truly optimal solutions for single input linear systems with input constraints and uncertainty related to output feedback and stochastic disturbances.We first find the optimal solution for the case of horizon N = 1, and then we indicate the complications that arise in the case of horizon N = 2. Our conclusion is that, for the case of linear constrained systems, the extra effort involved in the optimal feedback policy is probably not justified in practice. Indeed, we show by example that CE can give near optimal performance. We thus advocate this approach in real applications.

Monte Carlo simulations of small field output factors in solid phantoms

Introduction Total scatter factor (or output factor) in megavoltage photon dosimetry is a measure of relative dose relating a certain field size to a reference field size. The use of solid phantoms has been well established for output factor measurements, however to date these phantoms have not been tested with small fields. In this work, we evaluate the water equivalency of a number of solid phantoms for small field output factor measurements using the EGSnrc Monte Carlo code. Methods The following small square field sizes were simulated using BEAMnrc: 5, 6, 7, 8, 10 and 30 mm. Each simulated phantom geometry was created in DOSXYZnrc and consisted of a silicon diode (of length and width 1.5 mm and depth 0.5 mm) submersed in the phantom at a depth of 5 g/cm2. The source-to-detector distance was 100 cm for all simulations. The dose was scored in a single voxel at the location of the diode. Interaction probabilities and radiation transport parameters for each material were created using custom PEGS4 files. Results A comparison of the resultant output factors in the solid phantoms, compared to the same factors in a water phantom are shown in Fig. 1. The statistical uncertainty in each point was less than or equal to 0.4 %. The results in Fig. 1 show that the density of the phantoms affected the output factor results, with higher density materials (such as PMMA) resulting in higher output factors. Additionally, it was also calculated that scaling the depth for equivalent path length had negligible effect on the output factor results at these field sizes. Discussion and conclusions Electron stopping power and photon mass energy absorption change minimally with small field size [1]. Also, it can be seen from Fig. 1 that the difference from water decreases with increasing field size. Therefore, the most likely cause for the observed discrepancies in output factors is differing electron disequilibrium as a function of phantom density. When measuring small field output factors in a solid phantom, it is important that the density is very close to that of water.

A diode for correction-less small field output factor measurements

Introduction Due to their high spatial resolution diodes are often used for small field relative output factor measurements. However, a field size specific correction factor [1] is required and corrects for diode detector over-response at small field sizes. A recent Monte Carlo based study has shown that it is possible to design a diode detector that produces measured relative output factors that are equivalent to those in water. This is accomplished by introducing an air gap at the upstream end of the diode [2]. The aim of this study was to physically construct this diode by placing an ‘air cap’ on the end of a commercially available diode (the PTW 60016 electron diode). The output factors subsequently measured with the new diode design were compared to current benchmark small field output factor measurements. Methods A water-tight ‘cap’ was constructed so that it could be placed over the upstream end of the diode. The cap was able to be offset from the end of the diode, thus creating an air gap. The air gap width was the same as the diode width (7 mm) and the thickness of the air gap could be varied. Output factor measurements were made using square field sizes of side length from 5 to 50 mm, using a 6 MV photon beam. The set of output factor measurements were repeated with the air gap thickness set to 0, 0.5, 1.0 and 1.5 mm. The optimal air gap thickness was found in a similar manner to that proposed by Charles et al. [2]. An IBA stereotactic field diode, corrected using Monte Carlo calculated kq,clin,kq,msr values [3] was used as the gold standard. Results The optimal air thickness required for the PTW 60016 electron diode was 1.0 mm. This was close to the Monte Carlo predicted value of 1.15 mm2. The sensitivity of the new diode design was independent of field size (kq,clin,kq,msr = 1.000 at all field sizes) to within 1 %. Discussion and conclusions The work of Charles et al. [2] has been proven experimentally. An existing commercial diode has been converted into a correction-less small field diode by the simple addition of an ‘air cap’. The method of applying a cap to create the new diode leads to the diode being dual purpose, as without the cap it is still an unmodified electron diode.

Effects of small field output factors on IMRT optimisation and dose calculation

Introduction Given the known challenges of obtaining accurate measurements of small radiation fields, and the increasing use of small field segments in IMRT beams, this study examined the possible effects of referencing inaccurate field output factors in the planning of IMRT treatments. Methods This study used the Brainlab iPlan treatment planning system to devise IMRT treatment plans for delivery using the Brainlab m3 microMLC (Brainlab, Feldkirchen, Germany). Four pairs of sample IMRT treatments were planned using volumes, beams and prescriptions that were based on a set of test plans described in AAPM TG 119’s recommendations for the commissioning of IMRT treatment planning systems [1]: • C1, a set of three 4 cm volumes with different prescription doses, was modified to reduce the size of the PTV to 2 cm across and to include an OAR dose constraint for one of the other volumes. • C2, a prostate treatment, was planned as described by the TG 119 report [1]. • C3, a head-and-neck treatment with a PTV larger than 10 cm across, was excluded from the study. • C4, an 8 cm long C-shaped PTV surrounding a cylindrical OAR, was planned as described in the TG 119 report [1] and then replanned with the length of the PTV reduced to 4 cm. Both plans in each pair used the same beam angles, collimator angles, dose reference points, prescriptions and constraints. However, one of each pair of plans had its beam modulation optimisation and dose calculation completed with reference to existing iPlan beam data and the other had its beam modulation optimisation and dose calculation completed with reference to revised beam data. The beam data revisions consisted of increasing the field output factor for a 0.6 9 0.6 cm2 field by 17 % and increasing the field output factor for a 1.2 9 1.2 cm2 field by 3 %. Results The use of different beam data resulted in different optimisation results with different microMLC apertures and segment weightings between the two plans for each treatment, which led to large differences (up to 30 % with an average of 5 %) between reference point doses in each pair of plans. These point dose differences are more indicative of the modulation of the plans than of any clinically relevant changes to the overall PTV or OAR doses. By contrast, the maximum, minimum and mean doses to the PTVs and OARs were smaller (less than 1 %, for all beams in three out of four pairs of treatment plans) but are more clinically important. Of the four test cases, only the shortened (4 cm) version of TG 119’s C4 plan showed substantial differences between the overall doses calculated in the volumes of interest using the different sets of beam data and thereby suggested that treatment doses could be affected by changes to small field output factors. An analysis of the complexity of this pair of plans, using Crowe et al.’s TADA code [2], indicated that iPlan’s optimiser had produced IMRT segments comprised of larger numbers of small microMLC leaf separations than in the other three test cases. Conclusion: The use of altered small field output factors can result in substantially altered doses when large numbers of small leaf apertures are used to modulate the beams, even when treating relatively large volumes.

Effects of wireless sensor network uncertainties on output-only modal analysis employing merged data of multiple tests

The use of Wireless Sensor Networks (WSNs) for vibration-based Structural Health Monitoring (SHM) has become a promising approach due to many advantages such as low cost, fast and flexible deployment. However, inherent technical issues such as data asynchronicity and data loss have prevented these distinct systems from being extensively used. Recently, several SHM-oriented WSNs have been proposed and believed to be able to overcome a large number of technical uncertainties. Nevertheless, there is limited research verifying the applicability of those WSNs with respect to demanding SHM applications like modal analysis and damage identification. Based on a brief review, this paper first reveals that Data Synchronization Error (DSE) is the most inherent factor amongst uncertainties of SHM-oriented WSNs. Effects of this factor are then investigated on outcomes and performance of the most robust Output-only Modal Analysis (OMA) techniques when merging data from multiple sensor setups. The two OMA families selected for this investigation are Frequency Domain Decomposition (FDD) and data-driven Stochastic Subspace Identification (SSI-data) due to the fact that they both have been widely applied in the past decade. Accelerations collected by a wired sensory system on a large-scale laboratory bridge model are initially used as benchmark data after being added with a certain level of noise to account for the higher presence of this factor in SHM-oriented WSNs. From this source, a large number of simulations have been made to generate multiple DSE-corrupted datasets to facilitate statistical analyses. The results of this study show the robustness of FDD and the precautions needed for SSI-data family when dealing with DSE at a relaxed level. Finally, the combination of preferred OMA techniques and the use of the channel projection for the time-domain OMA technique to cope with DSE are recommended.

Enhanced stochastic mobility prediction with multi-output Gaussian processes

Outdoor robots such as planetary rovers must be able to navigate safely and reliably in order to successfully perform missions in remote or hostile environments. Mobility prediction is critical to achieving this goal due to the inherent control uncertainty faced by robots traversing natural terrain. We propose a novel algorithm for stochastic mobility prediction based on multi-output Gaussian process regression. Our algorithm considers the correlation between heading and distance uncertainty and provides a predictive model that can easily be exploited by motion planning algorithms. We evaluate our method experimentally and report results from over 30 trials in a Mars-analogue environment that demonstrate the effectiveness of our method and illustrate the importance of mobility prediction in navigating challenging terrain.

The technical efficiency of the Japanese banks : non-radial directional performance measurement with undesirable output

The paper analyses technical efficiency of the Japanese banks from 2000 to 2007. The estimation technique is based on the Russell directional distance function that takes into consideration not only desirable outputs but also an undesirable output that is represented by non-performing loans (NPLs). The results indicate that NPLs remain a significant burden as for banks' performance. We show that banks' inputs have to be utilised more efficiently, particularly labour and premises. We also argue that a further restructuring process is needed in the segment of Regional Banks. We conclude that the Japanese banking system is still far away from being fully consolidated and restructured.

Stochastic output feedback model predictive control

This paper addresses the issue of output feedback model predictive control for linear systems with input constraints and stochastic disturbances. We show that the optimal policy uses the Kalman filter for state estimation, but the resultant state estimates are not utilized in a certainty equivalence control law

Methods to improve the energy output of dye sensitized solar cell arrays

The work examined the operation and optimisation of dye-sensitised solar cell arrays, informing ways to improve performance through materials choices and geometrical design. Methods to improve the output of solar arrays under shading by external objects like trees or building were developed.

Clinical use of diodes and micro-chambers to obtain accurate small field output factor measurements

There have been substantial advances in small field dosimetry techniques and technologies, over the last decade, which have dramatically improved the achievable accuracy of small field dose measurements. This educational note aims to help radiation oncology medical physicists to apply some of these advances in clinical practice. The evaluation of a set of small field output factors (total scatter factors) is used to exemplify a detailed measurement and simulation procedure and as a basis for discussing the possible effects of simplifying that procedure. Field output factors were measured with an unshielded diode and a micro-ionisation chamber, at the centre of a set of square fields defined by a micro-multileaf collimator. Nominal field sizes investigated ranged from 6×6 to 98×98 mm2. Diode measurements in fields smaller than 30 mm across were corrected using response factors calculated using Monte Carlo simulations of the full diode geometry and daisy-chained to match micro-chamber measurements at intermediate field sizes. Diode measurements in fields smaller than 15 mm across were repeated twelve times over three separate measurement sessions, to evaluate the to evaluate the reproducibility of the radiation field size and its correspondence with the nominal field size. The five readings that contributed to each measurement on each day varied by up to 0.26%, for the “very small” fields smaller than 15 mm, and 0.18% for the fields larger than 15 mm. The diode response factors calculated for the unshielded diode agreed with previously published results, within 1.6%. The measured dimensions of the very small fields differed by up to 0.3 mm, across the different measurement sessions, contributing an uncertainty of up to 1.2% to the very small field output factors. The overall uncertainties in the field output factors were 1.8% for the very small fields and 1.1% for the fields larger than 15 mm across. Recommended steps for acquiring small field output factor measurements for use in radiotherapy treatment planning system beam configuration data are provided.

Design and fabrication of linear pixel arrays for organic photovoltaic modules to achieve scalable power output

We describe a design and fabrication method to enable simpler manufacturing of more efficient organic solar cell modules using a modified flat panel deposition technique. Many mini-cell pixels are individually connected to each other in parallel forming a macro-scale solar cell array. The pixel size of each array is optimized through experimentation to maximize the efficiency of the whole array. We demonstrate that integrated organic solar cell modules with a scalable current output can be fabricated in this fashion and can also be connected in series to generate a scalable voltage output.

Exploring the nexus between tourism and output in Cook Islands: An ARDL bounds approach

Tourism plays an important role in the development of Cook Islands. In this paper we examine the nexus between tourism and growth using quarterly data over the period 2009Q1–2014Q2 using the recently upgraded ARDL bounds test to cointegration tool, Microfit 5.01, which provides sample adjusted bounds and hence is more reliable for small sample size studies. We perform the cointegration using the ARDL bounds test and examine the direction of causality. Using visitor arrival and output in per capita terms as respective proxy for tourism development and growth, we examine the long-run association and report the elasticity coefficient of tourism and causality nexus, accordingly. Using unit root break tests, we note that 2011Q1 and 2011Q2 are two structural break periods in the output series. However, we note that this period is not statistically significant in the ARDL model and hence excluded from the estimation. Subsequently, the regression results show the two series are cointegrated. The long-run elasticity coefficient of tourism is estimated to be 0.83 and the short-run is 0.73. A bidirectional causality between tourism and income is noted for Cook Islands which indicates that tourism development and income mutually reinforce each other. In light of this, socio-economic policies need to focus on broad-based, inclusive and income-generating tourism development projects which are expected to have feedback effect.

Efficient Output-Sensitive Construction of Reeb Graphs

The Reeb graph tracks topology changes in level sets of a scalar function and finds applications in scientific visualization and geometric modeling. This paper describes a near-optimal two-step algorithm that constructs the Reeb graph of a Morse function defined over manifolds in any dimension. The algorithm first identifies the critical points of the input manifold, and then connects these critical points in the second step to obtain the Reeb graph. A simplification mechanism based on topological persistence aids in the removal of noise and unimportant features. A radial layout scheme results in a feature-directed drawing of the Reeb graph. Experimental results demonstrate the efficiency of the Reeb graph construction in practice and its applications.

Using Alkanes to Predict Voluntary Intake, Faecal Output and Digestibility of Buffel Grass Hay Fed to Steers

The cuticular waxes of forage plants contain long chain n-alkanes with odd carbon chain lengths in the range C25-C37 which are quantitatively recovered in faeces. When these concentrations are used with the concentrations of administered synthetic even chain length alkanes, the voluntary intake (VI), faecal output (FO) and digestibility (DMD) of forages can be estimated (Dove and Mayes 1991, 1996).