Stochastic modelling of T cell homeostasis for two competing clonotypes via the master equation

Stochastic models for competing clonotypes of T cells by multivariate, continuous-time, discrete state, Markov processes have been proposed in the literature by Stirk, Molina-París and van den Berg (2008). A stochastic modelling framework is important because of rare events associated with small populations of some critical cell types. Usually, computational methods for these problems employ a trajectory-based approach, based on Monte Carlo simulation. This is partly because the complementary, probability density function (PDF) approaches can be expensive but here we describe some efficient PDF approaches by directly solving the governing equations, known as the Master Equation. These computations are made very efficient through an approximation of the state space by the Finite State Projection and through the use of Krylov subspace methods when evolving the matrix exponential. These computational methods allow us to explore the evolution of the PDFs associated with these stochastic models, and bimodal distributions arise in some parameter regimes. Time-dependent propensities naturally arise in immunological processes due to, for example, age-dependent effects. Incorporating time-dependent propensities into the framework of the Master Equation significantly complicates the corresponding computational methods but here we describe an efficient approach via Magnus formulas. Although this contribution focuses on the example of competing clonotypes, the general principles are relevant to multivariate Markov processes and provide fundamental techniques for computational immunology.

Monte Carlo verification of gel dosimetry measurements for stereotactic radiotherapy

The quality assurance of stereotactic radiotherapy and radiosurgery treatments requires the use of small-field dose measurements that can be experimentally challenging. This study used Monte Carlo simulations to establish that PAGAT dosimetry gel can be used to provide accurate, high resolution, three-dimensional dose measurements of stereotactic radiotherapy fields. A small cylindrical container (4 cm height, 4.2 cm diameter) was filled with PAGAT gel, placed in the parietal region inside a CIRS head phantom, and irradiated with a 12 field stereotactic radiotherapy plan. The resulting three-dimensional dose measurement was read out using an optical CT scanner and compared with the treatment planning prediction of the dose delivered to the gel during the treatment. A BEAMnrc DOSXYZnrc simulation of this treatment was completed, to provide a standard against which the accuracy of the gel measurement could be gauged. The three dimensional dose distributions obtained from Monte Carlo and from the gel measurement were found to be in better agreement with each other than with the dose distribution provided by the treatment planning system's pencil beam calculation. Both sets of data showed close agreement with the treatment planning system's dose distribution through the centre of the irradiated volume and substantial disagreement with the treatment planning system at the penumbrae. The Monte Carlo calculations and gel measurements both indicated that the treated volume was up to 3 mm narrower, with steeper penumbrae and more variable out-of-field dose, than predicted by the treatment planning system. The Monte Carlo simulations allowed the accuracy of the PAGAT gel dosimeter to be verified in this case, allowing PAGAT gel to be utilised in the measurement of dose from stereotactic and other radiotherapy treatments, with greater confidence in the future.

The Remnant Emergency Artlab

The REMNANT/EMERGENCY Artlab was funded by the Australia Council InterArts ArtLab Program in 2010 and involves 22 months of rigorous research and experimentation in several countries. The process will be developed between a core transdisciplinary team of practicing media artists, designers and engineers where possible working in consultation and collaboration with local creatives at each venue. Our team asserts that today’s environmental crisis is underpinned by a deep cultural crisis - and so to get our ‘house in order’ we urgently need to create better and more powerful ‘images’ of what a ‘citizen-led’, sustainable world might be. This ArtLab’s core aim is therefore to begin to understand how to develop and create such ‘powerful images’.

Understanding evaluation of learning support in mathematics and statistics

With rapid and continuing growth of learning support initiatives in mathematics and statistics found in many parts of the world, and with the likelihood that this trend will continue, there is a need to ensure that robust and coherent measures are in place to evaluate the effectiveness of these initiatives. The nature of learning support brings challenges for measurement and analysis of its effects. After briefly reviewing the purpose, rationale for, and extent of current provision, this article provides a framework for those working in learning support to think about how their efforts can be evaluated. It provides references and specific examples of how workers in this field are collecting, analysing and reporting their findings. The framework is used to structure evaluation in terms of usage of facilities, resources and services provided, and also in terms of improvements in performance of the students and staff who engage with them. Very recent developments have started to address the effects of learning support on the development of deeper approaches to learning, the affective domain and the development of communities of practice of both learners and teachers. This article intends to be a stimulus to those who work in mathematics and statistics support to gather even richer, more valuable, forms of data. It provides a 'toolkit' for those interested in evaluation of learning support and closes by referring to an on-line resource being developed to archive the growing body of evidence. © 2011 Taylor & Francis.

Pollutant concentrations within households in Lao PDR and association with housing characteristics and occupants' activities

The paper presents the results of a study conducted to investigate indoor air quality within residential dwellings in Lao PDR. Results from PM 10, CO, and NO2 measurements inside 167 dwellings in Lao PDR over a five month period (December 2005-April 2006) are discussed as a function of household characteristics and occupant activities. Extremely high PM10 and NO2 concentrations (12 h mean PM10 concentrations 1275 ± 98 μg m-3 and 1183 ± 99 μg m-3 in Vientiane and Bolikhamxay provinces, respectively; 12 h mean NO2 concentrations 1210 ± 94 μg m-3 and 561 ± 45 μg m-3 in Vientiane and Bolikhamxay, respectively) were measured within the dwellings. Correlations, ANOVA analysis (univariate and multivariate), and linear regression results suggest a substantial contribution from cookingandsmoking.The PM10 concentrations were significantly higher in houses without a chimney compared to houses in which cooking occurred on a stove with a chimney. However, no significant differences in pollutantconcentrations were observed as a function of cooking location. Furthermore, PM10 and NO2 concentrations were higher in houses in which smoking occurred, suggestive of a relationship between increased indoor concentrations and smoking (0.05 < p < 0.10). Resuspension of dust from soil floors was another significant source of PM10 inside the house (634 μg m-3, p < 0.05).

Monte Carlo modeling of a 4 mm conical collimator for a Novalis Tx Linear Accelerator

The work presented in this poster outlines the steps taken to model a 4 mm conical collimator (BrainLab, Germany) on a Novalis Tx linear accelerator (Varian, Palo Alto, USA) capable of producing a 6MV photon beam for treatment of Stereotactic Radiosurgery (SRS) patients. The verification of this model was performed by measurements in liquid water and in virtual water. The measurements involved scanning depth dose and profiles in a water tank plus measurement of output factors in virtual water using Gafchromic® EBT3 film.

Interplay effects during enhanced dynamic wedge deliveries

In this study the interplay effects for Enhanced Dynamic Wedge (EDW) treatments are experimentally investigated. Single and multiple field EDW plans for different wedge angles were delivered to a phantom and detector on a moving platform, with various periods, amplitudes for parallel and perpendicular motions. A four field 4D CT planned lung EDW treatment was delivered to a dummy tumor over four fractions. For the single field parallel case the amplitude and the period of motion both affect the interplay resulting in the appearance of a step function and penumbral cut off with the discrepancy worst where collimator-tumor speed is similar. For perpendicular motion the amplitude of tumor motion is the only dominant factor. For large wedge angle the dose discrepancy is more pronounced compared to the small wedge angle for the same field size and amplitude-period values. For a small field size i.e. 5 × 5 cm2 the loss of wedged distribution was observed for both 60º and 15º wedge angles for of parallel and perpendicular motions. Film results from 4D CT planned delivery displayed a mix of over and under dosages over 4 fractions, with the gamma pass rate of 40% for the averaged film image at 3%/1 mm DTA (Distance to Agreement). Amplitude and period of the tumor motion both affect the interplay for single and multi-field EDW treatments and for a limited (4 or 5) fraction delivery there is a possibility of non-averaging of the EDW interplay.