An analysis of geometric uncertainty calculations for prostate radiotherapy in clinical practice.

Margins are used in radiotherapy to assist in the calculation of planning target volumes. These margins can be determined by analysing the geometric uncertainties inherent to the radiotherapy planning and delivery process. An important part of this process is the study of electronic portal images collected throughout the course of treatment. Set-up uncertainties were determined for prostate radiotherapy treatments at our previous site and the new purpose-built centre, with margins determined using a number of different methods. In addition, the potential effect of reducing the action level from 5 mm to 3 mm for changing a patient set-up, based on off-line bony anatomy-based portal image analysis, was studied. Margins generated using different methodologies were comparable. It was found that set-up errors were reduced following relocation to the new centre. Although a significant increase in the number of corrections to a patient's set-up was predicted if the action level was reduced from 5 mm to 3 mm, minimal reduction in patient set-up uncertainties would be seen as a consequence. Prescriptive geometric uncertainty analysis not only supports calculation and justification of the margins used clinically to generate planning target volumes, but may also best be used to monitor trends in clinical practice or audit changes introduced by new equipment, technology or practice. Simulations on existing data showed that a 3 mm rather than a 5 mm action level during off-line, bony anatomy-based portal imaging would have had a minimal benefit for the patients studied in this work.

Using Coxian Phase-Type Distributions to Identify Patient Characteristics for Duration of Stay in Hospital

Coxian phase-type distributions are a special type of Markov model that describes duration until an event occurs in terms of a process consisting of a sequence of latent phases. This paper considers the use of Coxian phase-type distributions for modelling patient duration of stay for the elderly in hospital and investigates the potential for using the resulting distribution as a classifying variable to identify common characteristics between different groups of patients according to their (anticipated) length of stay in hospital. The identification of common characteristics for patient length of stay groups would offer hospital managers and clinicians possible insights into the overall management and bed allocation of the hospital wards.

Simulating Coxian Phase-type Distributions for Patient Survival

Coxian phase-type distributions are a special type of Markov model that can be used to represent survival times in terms of phases through which an individual may progress until they eventually leave the system completely. Previous research has considered the Coxian phase-type distribution to be ideal in representing patient survival in hospital. However, problems exist in fitting the distributions. This paper investigates the problems that arise with the fitting process by simulating various Coxian phase-type models for the representation of patient survival and examining the estimated parameter values and eigenvalues obtained. The results indicate that numerical methods previously used for fitting the model parameters do not always converge. An alternative technique is therefore considered. All methods are influenced by the choice of initial parameter values. The investigation uses a data set of 1439 elderly patients and models their survival time, the length of time they spend in a UK hospital.

Role of behaviour in biological invasions and species distributions; lessons from interactions between the invasive Gammarus pulex and the native G-duebeni (Crustacea : Amphipoda)

In attempting to understand the distributions of both introduced species and the native species on which they impact, there is a growing trend to integrate studies of behaviour with more traditional life history/ecological approaches. The question of what mechanisms drive the displacement of the freshwater amphipod Gammarus duebeni by the often introduced G pulex is presented as a case study Patterns of displacement are well documented throughout Europe, but the speed and direction of displacement between these species can be varied. From early studies proposing interspecific competition as causal in these patterns, I review research progress to date. I show there has been no evidence for interspecific competition operating, other than the field patterns themselves, a somewhat tautological argument. Rather, the increased recognition of behavioural attributes with respect to the cannibalistic and predatory nature of these species gave rise to a series of studies unravelling the processes driving field patterns. Both species engage in 'intraguild predation' (IGP), with moulting females particularly vulnerable to predation by congeneric males. G pulex is more able both to engage in and avoid this interaction with G duebeni. However, several factors mediate the strength and asymmetry of this IGP, some biotic (e.g. parasitism) and others abiotic (e.g. water chemistry). Further, a number of alternative hypotheses that may account for the displacement (hybridization; parasite transmission) have been tested and rejected. While interspecific competition has been modelled mathematically and found to be a weak interaction relative to IGP, mechanisms of competition between these Gammarus species remain largely untested empirically. Since IGP may be finely balanced in some circumstances, I conclude that the challenge to detect interspecific competition remains and we require assessment of its role, if any, in the interaction between these species. Appreciation of behavioural attributes and their mediation should allow us to more fully understand, and perhaps predict, species introductions and resultant distributions.

Modeling the geometric characteristics of five-dimensionally woven composites

An analytical modeling approach for the prediction of the geometric characteristics of five-dimensional (5D) woven composites has been formulated. The model is driven by readily available data including the weaving parameters and constituent material properties. The new model calculates the individual proportions of fiber in each direction, areal density, overall fiber volume fraction, and laminate thickness. This information is useful for the engineer in the design and manufacture of 5D woven composites. In addition the present model outputs the mathematical definition of the 5D woven composite unit cell, which could be implemented as the geometric input for a downstream analytical model that is capable of predicting the elastic stiffness of 5D woven composites. Input parameters have been sourced from existing published work and the subsequent predictions made by the model are compared with the available experimental data on 5D woven composites.

Laplace transforms of probability distributions and their inversions are easy on logarithmic scales

It is shown that, when expressing arguments in terms of their logarithms, the Laplace transform of a function is related to the antiderivative of this function by a simple convolution. This allows efficient numerical computations of moment generating functions of positive random variables and their inversion. The application of the method is straightforward, apart from the necessity to implement it using high-precision arithmetics. In numerical examples the approach is demonstrated to be particularly useful for distributions with heavy tails, Such as lognormal, Weibull, or Pareto distributions, which are otherwise difficult to handle. The computational efficiency compared to other methods is demonstrated for an M/G/1 queueing problem.