Monte Carlo modelling of X-ray absorptiometry and its application to body composition studies

This thesis applies Monte Carlo techniques to the study of X-ray absorptiometric methods of bone mineral measurement. These studies seek to obtain information that can be used in efforts to improve the accuracy of the bone mineral measurements. A Monte Carlo computer code for X-ray photon transport at diagnostic energies has been developed from first principles. This development was undertaken as there was no readily available code which included electron binding energy corrections for incoherent scattering and one of the objectives of the project was to study the effects of inclusion of these corrections in Monte Carlo models. The code includes the main Monte Carlo program plus utilities for dealing with input data. A number of geometrical subroutines which can be used to construct complex geometries have also been written. The accuracy of the Monte Carlo code has been evaluated against the predictions of theory and the results of experiments. The results show a high correlation with theoretical predictions. In comparisons of model results with those of direct experimental measurements, agreement to within the model and experimental variances is obtained. The code is an accurate and valid modelling tool. A study of the significance of inclusion of electron binding energy corrections for incoherent scatter in the Monte Carlo code has been made. The results show this significance to be very dependent upon the type of application. The most significant effect is a reduction of low angle scatter flux for high atomic number scatterers. To effectively apply the Monte Carlo code to the study of bone mineral density measurement by photon absorptiometry the results must be considered in the context of a theoretical framework for the extraction of energy dependent information from planar X-ray beams. Such a theoretical framework is developed and the two-dimensional nature of tissue decomposition based on attenuation measurements alone is explained. This theoretical framework forms the basis for analytical models of bone mineral measurement by dual energy X-ray photon absorptiometry techniques. Monte Carlo models of dual energy X-ray absorptiometry (DEXA) have been established. These models have been used to study the contribution of scattered radiation to the measurements. It has been demonstrated that the measurement geometry has a significant effect upon the scatter contribution to the detected signal. For the geometry of the models studied in this work the scatter has no significant effect upon the results of the measurements. The model has also been used to study a proposed technique which involves dual energy X-ray transmission measurements plus a linear measurement of the distance along the ray path. This is designated as the DPA( +) technique. The addition of the linear measurement enables the tissue decomposition to be extended to three components. Bone mineral, fat and lean soft tissue are the components considered here. The results of the model demonstrate that the measurement of bone mineral using this technique is stable over a wide range of soft tissue compositions and hence would indicate the potential to overcome a major problem of the two component DEXA technique. However, the results also show that the accuracy of the DPA( +) technique is highly dependent upon the composition of the non-mineral components of bone and has poorer precision (approximately twice the coefficient of variation) than the standard DEXA measurements. These factors may limit the usefulness of the technique. These studies illustrate the value of Monte Carlo computer modelling of quantitative X-ray measurement techniques. The Monte Carlo models of bone densitometry measurement have:- 1. demonstrated the significant effects of the measurement geometry upon the contribution of scattered radiation to the measurements, 2. demonstrated that the statistical precision of the proposed DPA( +) three tissue component technique is poorer than that of the standard DEXA two tissue component technique, 3. demonstrated that the proposed DPA(+) technique has difficulty providing accurate simultaneous measurement of body composition in terms of a three component model of fat, lean soft tissue and bone mineral,4. and provided a knowledge base for input to decisions about development (or otherwise) of a physical prototype DPA( +) imaging system. The Monte Carlo computer code, data, utilities and associated models represent a set of significant, accurate and valid modelling tools for quantitative studies of physical problems in the fields of diagnostic radiology and radiography.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by a Caputo fractional derivative, and the second order space derivative by a symmetric fractional derivative. First, a method of separating variables expresses the analytical solution of the TSS-FDE in terms of the Mittag--Leffler function. Second, we propose two numerical methods to approximate the Caputo time fractional derivative: the finite difference method; and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Analytical and numerical solutions for the time and space-symmetric fractional diffusion equation

We consider a time and space-symmetric fractional diffusion equation (TSS-FDE) under homogeneous Dirichlet conditions and homogeneous Neumann conditions. The TSS-FDE is obtained from the standard diffusion equation by replacing the first-order time derivative by the Caputo fractional derivative and the second order space derivative by the symmetric fractional derivative. Firstly, a method of separating variables is used to express the analytical solution of the tss-fde in terms of the Mittag–Leffler function. Secondly, we propose two numerical methods to approximate the Caputo time fractional derivative, namely, the finite difference method and the Laplace transform method. The symmetric space fractional derivative is approximated using the matrix transform method. Finally, numerical results are presented to demonstrate the effectiveness of the numerical methods and to confirm the theoretical claims.

Effect of the Summer Months on Body Weight and Composition in College Women

BACKGROUND AND OBJECTIVES: College students and young adults are experiencing the greatest increases in rates of obesity, and 20% of college students are classified as obese. The objective of this study was to compare changes and rates of change in body weight and body composition between the freshman academic year and the summer after the freshman year among female college students. METHODS: Participants were recruited early in their freshman year of college to participate in a prospective longitudinal study examining changes in body weight and composition over the college years. Height and weight were measured, and body composition was assessed using dual energy x-ray absorptiometry (DEXA) at the beginning and end of the freshman year. Upon return from the summer for their sophomore year, participants returned to have all measurements repeated. Sixty-nine female participants completed all three visits. RESULTS: Body weight increased 1.3 kg during the academic period and an additional 0.1 kg during the summer period. Body mass index (BMI) increased between the first two visits but did not change between the last two visits. However, percent fat increased at each visit. Fat-free mass significantly increased 0.5 kg over the academic year but decreased by 1.1 kg over the summer (p<0.05). Greater rates of change were detected in percent fat, fat-free mass, and BMI during the summer compared with the academic year (p<0.05). CONCLUSIONS: Differences in body composition between the academic and summer periods may reflect changes in living situations between these periods. Unfavorable changes during the summer suggest the need to promote healthy lifestyles to freshman women before they leave campus for the summer

Craft, process and art : teaching and learning music composition in higher education

This paper explores models of teaching and learning music composition in higher education. It analyses the pedagogical approaches apparent in the literature on teaching and learning composition in schools and universities, and introduces a teaching model as: learning from the masters; mastery of techniques; exploring ideas; and developing voice. It then presents a learning model developed from a qualitative study into students’ experiences of learning composition at university as: craft, process and art. The relationship between the students’ experiences and the pedagogical model is examined. Finally, the implications for composition curricula in higher education are presented.

Theoretical analysis of the motion and evaporation of exhaled respiratory droplets of mixed composition

The dynamics of droplets exhaled from the respiratory system during coughing or talking is addressed. A mathematical model is presented accounting for the motion of a droplet in conjunction with its evaporation. Droplet evaporation and motion are accounted for under two scenarios: 1) A well mixed droplet and 2) A droplet with inner composition variation. A multiple shells model was implemented to account for internal mass and heat transfer and for concentration and temperature gradients inside the droplet. The trajectories of the droplets are computed for a range of conditions and the spatial distribution and residence times of such droplets are evaluated.

Response of tall buildings with symmetric setbacks under blast loading

This study explores three-dimensional nonlineardynamic responses of typical tall buildings with and without setbacks under blast loading. These 20 storey reinforced concrete buildings have been designed for normal (dead, live and wind)loads. The influence of the setbacks on the lateral load response due to blasts in terms of peak deflections, accelerations, inter-storey drift and bending moments at critical locations (including hinge formation) were investigated. Structural response predictions were performed with a commercially available three-dimensional finite element analysis programme using non-linear direct integration time history analyses. Results obtained for buildings with different setbacks were compared and conclusions made. The comparisons revealed that buildings have setbacks that protect the tower part above the setback level from blast loading show considerably better response in terms of peak displacement and interstorey drift, when compared to buildings without setbacks. Rotational accelerations were found to depend on the periods of the rotational modes. Abrupt changes in moments and shears are experienced near the levels of the setbacks. Typical twenty storey tall buildings with shear walls and frames that are designed for only normaln loads perform reasonably well, without catastrophic collapse, when subjected to a blast that is equivalent to 500 kg TNT at a standoff distance of 10 m.

Genetic Composition and Complexity of Virus Populations at Tungro-Endemic and Outbreak Rice Sites

We have recently demonstrated the geographic isolation of rice tungro bacilliform virus (RTBV) populations in the tungro-endemic provinces of Isabela and North Cotabato, Philippines. In this study, we examined the genetic structure of the virus populations at the tungro-outbreak sites of Lanao del Norte, a province adjacent to North Cotabato. We also analyzed the virus populations at the tungro-endemic sites of Subang, Indonesia, and Dien Khanh, Vietnam. Total DNA extracts from 274 isolates were digested with EcoRV restriction enzyme and hybridized with a full-length probe of RTBV. In the total population, 22 EcoRV-restricted genome profiles (genotypes) were identified. Although overlapping genotypes could be observed, the outbreak sites of Lanao del Norte had a genotype combination distinct from that of Subang or Dien Khanh but a genotype combination similar to that identified earlier from North Cotabato, the adjacent endemic province. Sequence analysis of the intergenic region and part of the ORF1 RTBV genome from randomly selected genotypes confirms the geographic clustering of RTBV genotypes and, combined with restriction analysis, the results suggest a fragmented spatial distribution of RTBV local populations in the three countries. Because RTBV depends on rice tungro spherical virus (RTSV) for transmission, the population dynamics of both tungro viruses were then examined at the endemic and outbreak sites within the Philippines. The RTBV genotypes and the coat protein RTSV genotypes were used as indicators for virus diversity. A shift in population structure of both viruses was observed at the outbreak sites with a reduced RTBV but increased RTSV gene diversity