Alternating direction implicit numerical method for the space and time fractional Bloch-Torrey equation in 3-D

Recently, some authors have considered a new diffusion model–space and time fractional Bloch-Torrey equation (ST-FBTE). Magin et al. (2008) have derived analytical solutions with fractional order dynamics in space (i.e., _ = 1, β an arbitrary real number, 1 < β ≤ 2) and time (i.e., 0 < α < 1, and β = 2), respectively. Yu et al. (2011) have derived an analytical solution and an effective implicit numerical method for solving ST-FBTEs, and also discussed the stability and convergence of the implicit numerical method. However, due to the computational overheads necessary to perform the simulations for nuclear magnetic resonance (NMR) in three dimensions, they present a study based on a two-dimensional example to confirm their theoretical analysis. Alternating direction implicit (ADI) schemes have been proposed for the numerical simulations of classic differential equations. The ADI schemes will reduce a multidimensional problem to a series of independent one-dimensional problems and are thus computationally efficient. In this paper, we consider the numerical solution of a ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. A fractional alternating direction implicit scheme (FADIS) for the ST-FBTE in 3-D is proposed. Stability and convergence properties of the FADIS are discussed. Finally, some numerical results for ST-FBTE are given.

A new implicit numerical method for the space and time fractional Bloch-Torrey equation

In recent years, it has been found that many phenomena in engineering, physics, chemistry and other sciences can be described very successfully by models using mathematical tools from fractional calculus. Recently, noted a new space and time fractional Bloch-Torrey equation (ST-FBTE) has been proposed (see Magin et al. (2008)), and successfully applied to analyse diffusion images of human brain tissues to provide new insights for further investigations of tissue structures. In this paper, we consider the ST-FBTE on a finite domain. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we propose a new effective implicit numerical method (INM) for the STFBTE whereby we discretize the Riesz fractional derivative using a fractional centered difference. Secondly, we prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent, and the order of convergence of the implicit numerical method is ( T2 - α + h2 x + h2 y + h2 z ). Finally, some numerical results are presented to support our theoretical analysis.

Analytical and numerical solutions of the space and time fractional bloch-torrey equation

Fractional order dynamics in physics, particularly when applied to diffusion, leads to an extension of the concept of Brown-ian motion through a generalization of the Gaussian probability function to what is termed anomalous diffusion. As MRI is applied with increasing temporal and spatial resolution, the spin dynamics are being examined more closely; such examinations extend our knowledge of biological materials through a detailed analysis of relaxation time distribution and water diffusion heterogeneity. Here the dynamic models become more complex as they attempt to correlate new data with a multiplicity of tissue compartments where processes are often anisotropic. Anomalous diffusion in the human brain using fractional order calculus has been investigated. Recently, a new diffusion model was proposed by solving the Bloch-Torrey equation using fractional order calculus with respect to time and space (see R.L. Magin et al., J. Magnetic Resonance, 190 (2008) 255-270). However effective numerical methods and supporting error analyses for the fractional Bloch-Torrey equation are still limited. In this paper, the space and time fractional Bloch-Torrey equation (ST-FBTE) is considered. The time and space derivatives in the ST-FBTE are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Firstly, we derive an analytical solution for the ST-FBTE with initial and boundary conditions on a finite domain. Secondly, we propose an implicit numerical method (INM) for the ST-FBTE, and the stability and convergence of the INM are investigated. We prove that the implicit numerical method for the ST-FBTE is unconditionally stable and convergent. Finally, we present some numerical results that support our theoretical analysis.

"Candidatus Similichlamydia laticola", a novel Chlamydia-like agent of epitheliocystis in seven consecutive cohorts of farmed Australian barramundi, lates calcarifer (Bloch)

Six consecutively hatched cohorts and one cohort of pre-hatch eggs of farmed barramundi (Lates calcarifer) from south Australia were examined for Chlamydia-like organisms associated with epitheliocystis. To identify and characterise the bacteria, 59 gill samples and three pre-hatch egg samples were processed for histology, in situ hybridisation and 16S rRNA amplification, sequencing and comprehensive phylogenetic analysis. Cases of epitheliocystis were observed microscopically and characterised by membrane-enclosed basophilic cysts filled with a granular material that caused hypertrophy of the epithelial cells. In situ hybridisation with a Chlamydiales-specific probe lead to specific labelling of the epitheliocystis inclusions within the gill epithelium. Two distinct but closely related 16S rRNA chlamydial sequences were amplified from gill DNA across the seven cohorts, including from pre-hatch eggs. These genotype sequences were found to be novel, sharing 97.1 - 97.5% similarity to the next closest 16S rRNA sequence, Ca. Similichlamydia latridicola, from Australian striped trumpeter. Comprehensive phylogenetic analysis of these genotype sequences against representative members of the Chlamydiales order and against other epitheliocystis agents revealed these Chlamydia-like organisms to be novel and taxonomically placed them within the recently proposed genus Ca. Similichlamydia. Following Fredricks and Relman's molecular postulates and based on these observations, we propose the epitheliocystis agents of barramundi to be known as "Candidatus Similichlamydia laticola" (sp. nov.).

Characterization of anomalous relaxation using the time-fractional Bloch equation and multiple echo T2 *-weighted magnetic resonance imaging at 7T

PURPOSE To study the utility of fractional calculus in modeling gradient-recalled echo MRI signal decay in the normal human brain. METHODS We solved analytically the extended time-fractional Bloch equations resulting in five model parameters, namely, the amplitude, relaxation rate, order of the time-fractional derivative, frequency shift, and constant offset. Voxel-level temporal fitting of the MRI signal was performed using the classical monoexponential model, a previously developed anomalous relaxation model, and using our extended time-fractional relaxation model. Nine brain regions segmented from multiple echo gradient-recalled echo 7 Tesla MRI data acquired from five participants were then used to investigate the characteristics of the extended time-fractional model parameters. RESULTS We found that the extended time-fractional model is able to fit the experimental data with smaller mean squared error than the classical monoexponential relaxation model and the anomalous relaxation model, which do not account for frequency shift. CONCLUSIONS We were able to fit multiple echo time MRI data with high accuracy using the developed model. Parameters of the model likely capture information on microstructural and susceptibility-induced changes in the human brain.

PTEN inactivation is rare in melanoma tumours but occurs frequently in melanoma cell lines

Deletions detected in cytogenetic and loss of heterozygosity (LOH) studies indicate that at least one tumour suppressor gene maps to the long arm of chromosome 10. Previous deletion mapping studies have observed LOH on 10q in about 30% of melanomas analysed. The PTEN gene, mapping to chromosome band 10q23.3, encodes a protein with both lipid and protein phosphatase activity. Somatic mutations and deletions in have been detected in a variety of cell lines and tumours, including melanoma samples. We performed mutation analyses and extensive allelic loss studies to investigate the role this gene plays in melanoma pathogenesis. We found that a total of 34 out of 57 (60%) melanoma cell lines carried hemizygous deletions of chromosome 10q encompassing the PTEN locus. A further three cell lines carried smaller deletions excluding PTEN. Inactivation of both PTEN alleles by exon-specific homozygous deletion or mutation was observed in 13 out of 57 (23%) melanoma cell lines. The mutation spectrum observed does not indicate an important role for ultraviolet radiation in the genesis of these mutations, and evidence from three cell lines supports the acquisition of PTEN aberrations in culture. Ten out of 49 (20%) matched melanoma tumour/normal samples harboured hemizygous deletions of either the whole chromosome or most of the long arm. Mutations within were detected in only one of the 10 tumours demonstrating LOH at 10q23 that were analysed. These results suggest that PTEN inactivation may be important for the propagation of melanoma cells in culture, and that another chromosome 10 tumour suppressor gene may be important for melanoma pathogenesis.

Surface plasmon hybridization and exciton coupling

We derive a semianalytical model to describe the interaction of a single photon emitter and a collection of arbitrarily shaped metal nanoparticles. The theory treats the metal nanoparticles classically within the electrostatic eigenmode method, wherein the surface plasmon resonances of collections of nanoparticles are represented by the hybridization of the plasmon modes of the noninteracting particles. The single photon emitter is represented by a quantum mechanical two-level system that exhibits line broadening due to a finite spontaneous decay rate. Plasmon-emitter coupling is described by solving the resulting Bloch equations. We illustrate the theory by studying model systems consisting of a single emitter coupled to one, two, and three nanoparticles, and we also compare the predictions of our model to published experimental data. ©2012 American Physical Society.

Numerical simulation of anomalous diffusion with application to medical imaging

The first objective of this project is to develop new efficient numerical methods and supporting error and convergence analysis for solving fractional partial differential equations to study anomalous diffusion in biological tissue such as the human brain. The second objective is to develop a new efficient fractional differential-based approach for texture enhancement in image processing. The results of the thesis highlight that the fractional order analysis captured important features of nuclear magnetic resonance (NMR) relaxation and can be used to improve the quality of medical imaging.

Out of the frying pan and into the fire – forging a career in a temporary workplace : a new perspective for HR?

Recent literature acknowledges the need for new career development models to support the way that careers evolve in the 21st century workplace (Bloch 2005). This is particularly so within temporary organisation forms, and for those pursuing a career in project management (Hölzle 2010). Our research, explores how project managers working on projects and within temporary organisation forms and those working on project-linked contracts access the development opportunities they require to remain employable in an era of project-by-project employment. Set in Australia where a project-based economy (Crawford, French and Lloyd-Walker 2013) and contract work have led to casualisation of the workforce (Connell & Burgess, 2006; McKeown & Hanley (2009) the results suggest new approaches to career development may be required.