Numerical schemes and multivariate extrapolation of a two-dimensional anomalous sub-diffusion equation

Anomalous dynamics in complex systems have gained much interest in recent years. In this paper, a two-dimensional anomalous subdiffusion equation (2D-ASDE) is considered. Two numerical methods for solving the 2D-ASDE are presented. Their stability, convergence and solvability are discussed. A new multivariate extrapolation is introduced to improve the accuracy. Finally, numerical examples are given to demonstrate the effectiveness of the schemes and confirm the theoretical analysis.

Typical accuracy and quality control of a process for creating CT-Based virtual bone models

A pragmatic method for assessing the accuracy and precision of a given processing pipeline required for converting computed tomography (CT) image data of bones into representative three dimensional (3D) models of bone shapes is proposed. The method is based on coprocessing a control object with known geometry which enables the assessment of the quality of resulting 3D models. At three stages of the conversion process, distance measurements were obtained and statistically evaluated. For this study, 31 CT datasets were processed. The final 3D model of the control object contained an average deviation from reference values of −1.07±0.52 mm standard deviation (SD) for edge distances and −0.647±0.43 mm SD for parallel side distances of the control object. Coprocessing a reference object enables the assessment of the accuracy and precision of a given processing pipeline for creating CTbased 3D bone models and is suitable for detecting most systematic or human errors when processing a CT-scan. Typical errors have about the same size as the scan resolution.

Image acquisition and manipulation protocols for CT-PET fusion to improve the accuracy of gross tumour volume localisation for 3D conformal radiotherapy for lung cancer

Aims: To develop clinical protocols for acquiring PET images, performing CT-PET registration and tumour volume definition based on the PET image data, for radiotherapy for lung cancer patients and then to test these protocols with respect to levels of accuracy and reproducibility. Method: A phantom-based quality assurance study of the processes associated with using registered CT and PET scans for tumour volume definition was conducted to: (1) investigate image acquisition and manipulation techniques for registering and contouring CT and PET images in a radiotherapy treatment planning system, and (2) determine technology-based errors in the registration and contouring processes. The outcomes of the phantom image based quality assurance study were used to determine clinical protocols. Protocols were developed for (1) acquiring patient PET image data for incorporation into the 3DCRT process, particularly for ensuring that the patient is positioned in their treatment position; (2) CT-PET image registration techniques and (3) GTV definition using the PET image data. The developed clinical protocols were tested using retrospective clinical trials to assess levels of inter-user variability which may be attributed to the use of these protocols. A Siemens Somatom Open Sensation 20 slice CT scanner and a Philips Allegro stand-alone PET scanner were used to acquire the images for this research. The Philips Pinnacle3 treatment planning system was used to perform the image registration and contouring of the CT and PET images. Results: Both the attenuation-corrected and transmission images obtained from standard whole-body PET staging clinical scanning protocols were acquired and imported into the treatment planning system for the phantom-based quality assurance study. Protocols for manipulating the PET images in the treatment planning system, particularly for quantifying uptake in volumes of interest and window levels for accurate geometric visualisation were determined. The automatic registration algorithms were found to have sub-voxel levels of accuracy, with transmission scan-based CT-PET registration more accurate than emission scan-based registration of the phantom images. Respiration induced image artifacts were not found to influence registration accuracy while inadequate pre-registration over-lap of the CT and PET images was found to result in large registration errors. A threshold value based on a percentage of the maximum uptake within a volume of interest was found to accurately contour the different features of the phantom despite the lower spatial resolution of the PET images. Appropriate selection of the threshold value is dependant on target-to-background ratios and the presence of respiratory motion. The results from the phantom-based study were used to design, implement and test clinical CT-PET fusion protocols. The patient PET image acquisition protocols enabled patients to be successfully identified and positioned in their radiotherapy treatment position during the acquisition of their whole-body PET staging scan. While automatic registration techniques were found to reduce inter-user variation compared to manual techniques, there was no significant difference in the registration outcomes for transmission or emission scan-based registration of the patient images, using the protocol. Tumour volumes contoured on registered patient CT-PET images using the tested threshold values and viewing windows determined from the phantom study, demonstrated less inter-user variation for the primary tumour volume contours than those contoured using only the patient’s planning CT scans. Conclusions: The developed clinical protocols allow a patient’s whole-body PET staging scan to be incorporated, manipulated and quantified in the treatment planning process to improve the accuracy of gross tumour volume localisation in 3D conformal radiotherapy for lung cancer. Image registration protocols which factor in potential software-based errors combined with adequate user training are recommended to increase the accuracy and reproducibility of registration outcomes. A semi-automated adaptive threshold contouring technique incorporating a PET windowing protocol, accurately defines the geometric edge of a tumour volume using PET image data from a stand alone PET scanner, including 4D target volumes.

An investigation of dose calculation accuracy in intensity-modulated radiotherapy of sites in the head & neck

Knowledge of the accuracy of dose calculations in intensity-modulated radiotherapy of the head and neck is essential for clinical confidence in these highly conformal treatments. High dose gradients are frequently placed very close to critical structures, such as the spinal cord, and good coverage of complex shaped nodal target volumes is important for long term-local control. A phantom study is presented comparing the performance of standard clinical pencil-beam and collapsed-cone dose algorithms to Monte Carlo calculation and three-dimensional gel dosimetry measurement. All calculations and measurements are normalized to the median dose in the primary planning target volume, making this a purely relative study. The phantom simulates tissue, air and bone for a typical neck section and is treated using an inverse-planned 5-field IMRT treatment, similar in character to clinically used class solutions. Results indicate that the pencil-beam algorithm fails to correctly model the relative dose distribution surrounding the air cavity, leading to an overestimate of the target coverage. The collapsed-cone and Monte Carlo results are very similar, indicating that the clinical collapsed-cone algorithm is perfectly sufficient for routine clinical use. The gel measurement shows generally good agreement with the collapsed-cone and Monte Carlo calculated dose, particularly in the spinal cord dose and nodal target coverage, thus giving greater confidence in the use of this class solution.

Pattern recognition using invariants defined from higher order spectra - one-dimensional inputs

A new approach to pattern recognition using invariant parameters based on higher order spectra is presented. In particular, invariant parameters derived from the bispectrum are used to classify one-dimensional shapes. The bispectrum, which is translation invariant, is integrated along straight lines passing through the origin in bifrequency space. The phase of the integrated bispectrum is shown to be scale and amplification invariant, as well. A minimal set of these invariants is selected as the feature vector for pattern classification, and a minimum distance classifier using a statistical distance measure is used to classify test patterns. The classification technique is shown to distinguish two similar, but different bolts given their one-dimensional profiles. Pattern recognition using higher order spectral invariants is fast, suited for parallel implementation, and has high immunity to additive Gaussian noise. Simulation results show very high classification accuracy, even for low signal-to-noise ratios.

Effective shear modulus approach for two dimensional solids and plate bending problems by meshless point collocation method

For the analysis of material nonlinearity, an effective shear modulus approach based on the strain control method is proposed in this paper by using point collocation method. Hencky’s total deformation theory is used to evaluate the effective shear modulus, Young’s modulus and Poisson’s ratio, which are treated as spatial field variables. These effective properties are obtained by the strain controlled projection method in an iterative manner. To evaluate the second order derivatives of shape function at the field point, the radial basis function (RBF) in the local support domain is used. Several numerical examples are presented to demonstrate the efficiency and accuracy of the proposed method and comparisons have been made with analytical solutions and the finite element method (ABAQUS).

Next generation low-cost motion capture systems can provide comparable spatial accuracy to high-end systems

The objective quantification of three-dimensional kinematics during different functional and occupational tasks is now more in demand than ever. The introduction of new generation of low-cost passive motion capture systems from a number of manufacturers has made this technology accessible for teaching, clinical practice and in small/medium industry. Despite the attractive nature of these systems, their accuracy remains unproved in independent tests. We assessed static linear accuracy, dynamic linear accuracy and compared gait kinematics from a Vicon MX20 system to a Natural Point OptiTrack system. In all experiments data were sampled simultaneously. We identified both systems perform excellently in linear accuracy tests with absolute errors not exceeding 1%. In gait data there was again strong agreement between the two systems in sagittal and coronal plane kinematics. Transverse plane kinematics differed by up to 3 at the knee and hip, which we attributed to the impact of soft tissue artifact accelerations on the data. We suggest that low-cost systems are comparably accurate to their high-end competitors and offer a platform with accuracy acceptable in research for laboratories with a limited budget.

Computational analysis of laminated glass panels under blast loads: A comparison of two dimensional and three dimensional modelling approaches

This paper illustrates the use of finite element (FE) technique to investigate the behaviour of laminated glass (LG) panels under blast loads. Two and three dimensional (2D and 3D) modelling approaches available in LS-DYNA FE code to model LG panels are presented. Results from the FE analysis for mid-span deflection and principal stresses compared well with those from large deflection plate theory. The FE models are further validated using the results from a free field blast test on a LG panel. It is evident that both 2D and 3D LG models predict the experimental results with reasonable accuracy. The 3D LG models give slightly more accurate results but require considerably more computational time compared to the 2D LG models.

Magnetic resonance imaging: An accurate, radiation-free, alternative to computed tomography for the primary imaging and three-dimensional reconstruction of the bony orbit

Purpose: To determine the extent to which the accuracy of magnetic resonance imaging (MRI) based virtual 3-dimensional (3D) models of the intact orbit can approach that of the gold standard, computed tomography (CT) based models. The goal was to determine whether MRI is a viable alternative to CT scans in patients with isolated orbital fractures and penetrating eye injuries, pediatric patients, and patients requiring multiple scans in whom radiation exposure is ideally limited. Materials and Methods: Patients who presented with unilateral orbital fractures to the Royal Brisbane and Women’s Hospital from March 2011 to March 2012 were recruited to participate in this cross-sectional study. The primary predictor variable was the imaging technique (MRI vs CT). The outcome measurements were orbital volume (primary outcome) and geometric intraorbital surface deviations (secondary outcome)between the MRI- and CT-based 3D models. Results: Eleven subjects (9 male) were enrolled. The patients’ mean age was 30 years. On average, the MRI models underestimated the orbital volume of the CT models by 0.50 0.19 cm3 . The average intraorbital surface deviation between the MRI and CT models was 0.34 0.32 mm, with 78 2.7% of the surface within a tolerance of 0.5 mm. Conclusions: The volumetric differences of the MRI models are comparable to reported results from CT models. The intraorbital MRI surface deviations are smaller than the accepted tolerance for orbital surgical reconstructions. Therefore, the authors believe that MRI is an accurate radiation-free alternative to CT for the primary imaging and 3D reconstruction of the bony orbit. �

Numerical treatment of a two-dimensional variable-order fractional nonlinear reaction-diffusion model

A two-dimensional variable-order fractional nonlinear reaction-diffusion model is considered. A second-order spatial accurate semi-implicit alternating direction method for a two-dimensional variable-order fractional nonlinear reaction-diffusion model is proposed. Stability and convergence of the semi-implicit alternating direct method are established. Finally, some numerical examples are given to support our theoretical analysis. These numerical techniques can be used to simulate a two-dimensional variable order fractional FitzHugh-Nagumo model in a rectangular domain. This type of model can be used to describe how electrical currents flow through the heart, controlling its contractions, and are used to ascertain the effects of certain drugs designed to treat arrhythmia.

A second order control-volume finite-element least-squares strategy for simulating diffusion in strongly anisotropic media

An unstructured mesh �nite volume discretisation method for simulating di�usion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume �nite-element method and it retains the local continuity of the ux at the control volume faces. A least squares function recon- struction technique together with a new ux decomposition strategy is used to obtain an accurate ux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it signi�cantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes, and appears independent of the mesh quality.

Clinical Accuracy of the MedGem Indirect Calorimeter for Measuring Resting Energy Expenditure in Cancer Patients

OBJECTIVE: To compare, in patients with cancer and in healthy subjects, measured resting energy expenditure (REE) from traditional indirect calorimetry to a new portable device (MedGem) and predicted REE. DESIGN: Cross-sectional clinical validation study. SETTING: Private radiation oncology centre, Brisbane, Australia. SUBJECTS: Cancer patients (n = 18) and healthy subjects (n = 17) aged 37-86 y, with body mass indices ranging from 18 to 42 kg/m(2). INTERVENTIONS: Oxygen consumption (VO(2)) and REE were measured by VMax229 (VM) and MedGem (MG) indirect calorimeters in random order after a 12-h fast and 30-min rest. REE was also calculated from the MG without adjustment for nitrogen excretion (MGN) and estimated from Harris-Benedict prediction equations. Data were analysed using the Bland and Altman approach, based on a clinically acceptable difference between methods of 5%. RESULTS: The mean bias (MGN-VM) was 10% and limits of agreement were -42 to 21% for cancer patients; mean bias -5% with limits of -45 to 35% for healthy subjects. Less than half of the cancer patients (n = 7, 46.7%) and only a third (n = 5, 33.3%) of healthy subjects had measured REE by MGN within clinically acceptable limits of VM. Predicted REE showed a mean bias (HB-VM) of -5% for cancer patients and 4% for healthy subjects, with limits of agreement of -30 to 20% and -27 to 34%, respectively. CONCLUSIONS: Limits of agreement for the MG and Harris Benedict equations compared to traditional indirect calorimetry were similar but wide, indicating poor clinical accuracy for determining the REE of individual cancer patients and healthy subjects.