Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations

Maximum-likelihood estimates of the parameters of stochastic differential equations are consistent and asymptotically efficient, but unfortunately difficult to obtain if a closed-form expression for the transitional probability density function of the process is not available. As a result, a large number of competing estimation procedures have been proposed. This article provides a critical evaluation of the various estimation techniques. Special attention is given to the ease of implementation and comparative performance of the procedures when estimating the parameters of the Cox–Ingersoll–Ross and Ornstein–Uhlenbeck equations respectively.

Laser doppler imaging in a paediatric burns population

Objective Laser Doppler imaging (LDI) was compared to wound outcomes in children's burns, to determine if the technology could be used to predict these outcomes. Methods Forty-eight patients with a total of 85 burns were included in the study. Patient median age was 4 years 10 months and scans were taken 0–186 h post-burn using the fast, low-resolution setting on the Moor LDI2 laser Doppler imager. Wounds were managed by standard practice, without taking into account the scan results. Time until complete re-epithelialisation and whether or not grafting and scar management were required were recorded for each wound. If wounds were treated with Silvazine™ or Acticoat™ prior to the scan, this was also recorded. Results The predominant colour of the scan was found to be significantly related to the re-epithelialisation, grafting and scar management outcomes and could be used to predict those outcomes. The prior use of Acticoat™ did not affect the scan relationship to outcomes, however, the use of Silvazine™ did complicate the relationship for light blue and green scanned partial thickness wounds. Scans taken within the 24-h window after-burn also appeared to be accurate predictors of wound outcome. Conclusion Laser Doppler imaging is accurate and effective in a paediatric population with a low-resolution fast-scan.

Improved image quality for x-ray CT imaging of gel dosimeters

Purpose: This study provides a simple method for improving precision of x-ray computed tomography (CT) scans of irradiated polymer gel dosimetry. The noise affecting CT scans of irradiated gels has been an impediment to the use of clinical CT scanners for gel dosimetry studies. Method: In this study, it is shown that multiple scans of a single PAGAT gel dosimeter can be used to extrapolate a ‘zero-scan’ image which displays a similar level of precision to an image obtained by averaging multiple CT images, without the compromised dose measurement resulting from the exposure of the gel to radiation from the CT scanner. Results: When extrapolating the zero-scan image, it is shown that exponential and simple linear fits to the relationship between Hounsfield unit and scan number, for each pixel in the image, provides an accurate indication of gel density. Conclusions: It is expected that this work will be utilised in the analysis of three-dimensional gel volumes irradiated using complex radiotherapy treatments.