Improved estimates of percolation and anisotropic permeability from 3-D X-ray microtomography using stochastic analyses and visualization

X-ray microtomography (micro-CT) with micron resolution enables new ways of characterizing microstructures and opens pathways for forward calculations of multiscale rock properties. A quantitative characterization of the microstructure is the first step in this challenge. We developed a new approach to extract scale-dependent characteristics of porosity, percolation, and anisotropic permeability from 3-D microstructural models of rocks. The Hoshen-Kopelman algorithm of percolation theory is employed for a standard percolation analysis. The anisotropy of permeability is calculated by means of the star volume distribution approach. The local porosity distribution and local percolation probability are obtained by using the local porosity theory. Additionally, the local anisotropy distribution is defined and analyzed through two empirical probability density functions, the isotropy index and the elongation index. For such a high-resolution data set, the typical data sizes of the CT images are on the order of gigabytes to tens of gigabytes; thus an extremely large number of calculations are required. To resolve this large memory problem parallelization in OpenMP was used to optimally harness the shared memory infrastructure on cache coherent Non-Uniform Memory Access architecture machines such as the iVEC SGI Altix 3700Bx2 Supercomputer. We see adequate visualization of the results as an important element in this first pioneering study.

Comparison between analytical and 3D finite element solutions for borehole stresses in anisotropic elastic rock

We present a rigorous validation of the analytical Amadei solution for the stress concentration around an arbitrarily orientated borehole in general anisotropic elastic media. First, we revisit the theoretical framework of the Amadei solution and present analytical insights that show that the solution does indeed contain all special cases of symmetry, contrary to previous understanding, provided that the reduced strain coefficients b11 and b55 are not equal. It is shown from theoretical considerations and published experimental data that the b11 and b55 are not equal for realistic rocks. Second, we develop a 3D finite element elastic model within a hybrid analytical–numerical workflow that circumvents the need to rebuild and remesh the model for every borehole and material orientation. Third, we show that the borehole stresses computed from the numerical model and the analytical solution match almost perfectly for different borehole orientations (vertical, deviated and horizontal) and for several cases involving isotropic, transverse isotropic and orthorhombic symmetries. It is concluded that the analytical Amadei solution is valid with no restriction on the borehole orientation or the symmetry of the elastic anisotropy.

Measuring mechanical properties of tendon in vivo

Introduction: Understanding the mechanical properties of tendon is an important step to guiding the process of improving athletic performance, predicting injury and treating tendinopathies. The speed of sound in a medium is governed by the bulk modulus and density for fluids and isotropic materials. However, for tendon,which is a structural composite of fluid and collagen, there is some anisotropy requiring an adjustment for Poisson’s ratio. In this paper, these relationships are explored and modelled using data collected, in vivo, on human Achilles tendon. Estimates for elastic modulus and hysteresis based on speed of sound data are then compared against published values from in vitro mechanical tests. Methods: Measurements using clinical ultrasound imaging, inverse dynamics and acoustic transmission techniques were used to determine dimensions, loading conditions and longitudinal speed of sound for the Achilles tendon during a series of isometric plantar flexion exercises against body weight. Upper and lower bounds for speed of sound versus tensile stress in the tendon were then modelled and estimates derived for elastic modulus and hysteresis. Results: Axial speed of sound varied between 1850 to 2090 m.s−1 with a non-linear, asymptotic dependency on the level of tensile stress in the tendon 5–35 MPa. Estimates derived for the elastic modulus ranged between 1–2 GPa. Hysteresis derived from models of the stress-strain relationship, ranged from 3–11%. These values agree closely with those previously reported from direct measurements obtained via in vitro mechanical tensile tests on major weight bearing tendons. Discussion: There is sufficiently good agreement between these indirect (speed of sound derived) and direct (mechanical tensile test derived) measures of tendon mechanical properties to validate the use of this non-invasive acoustic transmission technique. This non-invasive method is suitable for monitoring changes in tendon properties as predictors of athletic performance, injury or therapeutic progression.

Cell migration and proliferation on homogeneous and non-homogeneous domains : modelling on the scale of individuals and populations

Cell migration is a behaviour critical to many key biological effects, including wound healing, cancerous cell invasion and morphogenesis, the development of an organism from an embryo. However, given that each of these situations is distinctly different and cells are extremely complicated biological objects, interest lies in more basic experiments which seek to remove conflating factors and present a less complex environment within which cell migration can be experimentally examined. These include in vitro studies like the scratch assay or circle migration assay, and ex vivo studies like the colonisation of the hindgut by neural crest cells. The reduced complexity of these experiments also makes them much more enticing as problems to mathematically model, like done here. The primary goal of the mathematical models used in this thesis is to shed light on which cellular behaviours work to generate the travelling waves of invasion observed in these experiments, and to explore how variations in these behaviours can potentially predict differences in this invasive pattern which are experimentally observed when cell types or chemical environment are changed. Relevant literature has already identified the difficulty of distinguishing between these behaviours when using traditional mathematical biology techniques operating on a macroscopic scale, and so here a sophisticated individual-cell-level model, an extension of the Cellular Potts Model (CPM), is been constructed and used to model a scratch assay experiment. This model includes a novel mechanism for dealing with cell proliferations that allowed for the differing properties of quiescent and proliferative cells to be implemented into their behaviour. This model is considered both for its predictive power and used to make comparisons with the travelling waves which result in more traditional macroscopic simulations. These comparisons demonstrate a surprising amount of agreement between the two modelling frameworks, and suggest further novel modifications to the CPM that would allow it to better model cell migration. Considerations of the model’s behaviour are used to argue that the dominant effect governing cell migration (random motility or signal-driven taxis) likely depends on the sort of invasion demonstrated by cells, as easily seen by microscopic photography. Additionally, a scratch assay simulated on a non-homogeneous domain consisting of a ’fast’ and ’slow’ region is also used to further differentiate between these different potential cell motility behaviours. A heterogeneous domain is a novel situation which has not been considered mathematically in this context, nor has it been constructed experimentally to the best of the candidate’s knowledge. Thus this problem serves as a thought experiment used to test the conclusions arising from the simulations on homogeneous domains, and to suggest what might be observed should this non-homogeneous assay situation be experimentally realised. Non-intuitive cell invasion patterns are predicted for diffusely-invading cells which respond to a cell-consumed signal or nutrient, contrasted with rather expected behaviour in the case of random-motility-driven invasion. The potential experimental observation of these behaviours is demonstrated by the individual-cell-level model used in this thesis, which does agree with the PDE model in predicting these unexpected invasion patterns. In the interest of examining such a case of a non-homogeneous domain experimentally, some brief suggestion is made as to how this could be achieved.

Computer modeling of diffusion in biological tissues

Molecular-level computer simulations of restricted water diffusion can be used to develop models for relating diffusion tensor imaging measurements of anisotropic tissue to microstructural tissue characteristics. The diffusion tensors resulting from these simulations can then be analyzed in terms of their relationship to the structural anisotropy of the model used. As the translational motion of water molecules is essentially random, their dynamics can be effectively simulated using computers. In addition to modeling water dynamics and water-tissue interactions, the simulation software of the present study was developed to automatically generate collagen fiber networks from user-defined parameters. This flexibility provides the opportunity for further investigations of the relationship between the diffusion tensor of water and morphologically different models representing different anisotropic tissues.

Diffusion tensor of water in partially aligned fibre networks

Monte Carlo simulations were used to investigate the relationship between the morphological characteristics and the diffusion tensor (DT) of partially aligned networks of cylindrical fibres. The orientation distributions of the fibres in each network were approximately uniform within a cone of a given semi-angle (θ0). This semi-angle was used to control the degree of alignment of the fibres. The networks studied ranged from perfectly aligned (θ0 = 0) to completely disordered (θ0 = 90°). Our results are qualitatively consistent with previous numerical models in the overall behaviour of the DT. However, we report a non-linear relationship between the fractional anisotropy (FA) of the DT and collagen volume fraction, which is different to the findings from previous work. We discuss our results in the context of diffusion tensor imaging of articular cartilage. We also demonstrate how appropriate diffusion models have the potential to enable quantitative interpretation of the experimentally measured diffusion-tensor FA in terms of collagen fibre alignment distributions.

Characterisation of microvasulature changes after closed soft tissue trauma by contrast enhanced micro-CT imaging

INTRODUCTION It is known that the vascular morphology and functionality are changed following closed soft tissue trauma (CSTT) [1], and bone fractures [2]. The disruption of blood vessels may lead to hypoxia and necrosis. Currently, most clinical methods for the diagnosis and monitoring of CSTT with or without bone fractures are primarily based on qualitative measures or practical experience, making the diagnosis subjective and inaccurate. There is evidence that CSTT and early vascular changes following the injury delay the soft tissue tissue and bone healing [3]. However, a precise qualitative and quantitative morphological assessment of vasculature changes after trauma is currently missing. In this research, we aim to establish a diagnostic framework to assess the 3D vascular morphological changes after standardized CSTT in a rat model qualitatively and quantitatively using contrast-enhanced micro-CT imaging. METHODS An impact device was used for the application of a controlled reproducible CSTT to the left thigh (Biceps Femoris) of anaesthetized male Wistar rats. After euthanizing the animals at 6 hours, 24 hours, 3 days, 7 days, or 14 days after trauma, CSTT was qualitatively evaluated by macroscopic visual observation of the skin and muscles. For visualization of the vasculature, the blood vessels of sacrificed rats were flushed with heparinised saline and then perfused with a radio-opaque contrast agent (Microfil, MV 122, Flowtech, USA) using an infusion pump. After allowing the contrast agent to polymerize overnight, both hind-limbs were dissected, and then the whole injured and contra-lateral control limbs were imaged using a micro-CT scanner (µCT 40, Scanco Medical, Switzerland) to evaluate the vascular morphological changes. Correlated biopsy samples were also taken from the CSTT region of both injured and control legs. The morphological parameters such as the vessel volume ratio (VV/TV), vessel diameter (V.D), spacing (V.Sp), number (V.N), connectivity (V.Conn) and the degree of anisotropy (DA) were then quantified by evaluating the scans of biopsy samples using the micro-CT imaging system. RESULTS AND DISCUSSION A qualitative evaluation of the CSTT has shown that the developed impact protocols were capable of producing a defined and reproducible injury within the region of interest (ROI), resulting in a large hematoma and moderate swelling in both lateral and medial sides of the injured legs. Also, the visualization of the vascular network using 3D images confirmed the ability to perfuse the large vessels and a majority of the microvasculature consistently (Figure 1). Quantification of the vascular morphology obtained from correlated biopsy samples has demonstrated that V.D and V.N and V.Sp were significantly higher in the injured legs 24 hours after impact in comparison with the control legs (p<0.05). The evaluation of the other time points is currently progressing. CONCLUSIONS The findings of this research will contribute to a better understanding of the changes to the vascular network architecture following traumatic injuries and during healing process. When interpreted in context of functional changes, such as tissue oxygenation, this will allow for objective diagnosis and monitoring of CSTT and serve as validation for future non-invasive clinical assessment modalities.

Bacterial kinetics-controlled shape-directed biosynthesis of silver nanoplates using Morganella psychrotolerans

We show for the first time that by controlling the growth kinetics of Morganella psychrotolerans, a silver-resistant psychrophilic bacterium, the shape anisotropy of silver nanoparticles can be achieved. This is particularly important considering that there has been no report that demonstrates a control over shape of Ag nanoparticles by controlling the growth kinetics of bacteria during biological synthesis. Additionally, we have for the first time performed electrochemistry experiments on bacterial cells after exposing them to Ag(+) ions, which provide significant new insights about mechanistic aspects of Ag reduction by bacteria. The possibility to achieve nanoparticle shape control by using a "green" biosynthesis approach is expected to open up new exciting avenues for eco-friendly, large-scale, and economically viable shape-controlled synthesis of nanomaterials.

Non-invasive clinical measurement of the viscoelastic properties of tendon using acoustic wave transmission

Background. In isotropic materials, the speed of acoustic wave propagation is governed by the bulk modulus and density. For tendon, which is a structural composite of fluid and collagen, however, there is some anisotropy requiring an adjustment for Poisson's ratio. This paper explores these relationships using data collected, in vivo, on human Achilles tendon and then compares estimates of elastic modulus and hysteresis against published values from in vitro mechanical tests. Methods. Measurements using conventional B-model ultrasound imaging, inverse dynamics and acoustic transmission techniques were used to determine dimensions, loading conditions and longitudinal speed of sound in the Achilles tendon during a series of isometric plantar flexion exercises against body weight. Upper and lower bounds for speed of sound versus tensile stress in the tendon were then modelled and estimates of the elastic modulus and hysteresis of the Achilles tendon derived. Results. Axial speed of sound varied between 1850 and 2090 ms-1 with a non-linear, asymptotic dependency on the level of tensile stress (5-35 MPa) in the tendon. Estimates derived for the elastic modulus of the Achilles tendon ranged between 1-2 GPa. Hysteresis derived from models of the stress-strain relationship, ranged from 3-11%. Discussion. Estimates of elastic modulus agree closely with those previously reported from direct measurements obtained via mechanical tensile tests on major weight bearing tendons in vitro [1,2]. Hysteresis derived from models of the stress-strain relationship is consistent with direct measures from various mamalian tendon (7-10%) but is lower than previous estimates in human tendon (17-26%) [3]. This non-invasive method would appear suitable for monitoring changes in tendon properties during dynamic sporting activities.

Twitter and society : an introduction

Since its launch in 2006, Twitter has turned from a niche service to a mass phenomenon. By the beginning of 2013, the platform claims to have more than 200 million active users, who “post over 400 million tweets per day” (Twitter, 2013). Its success is spreading globally; Twitter is now available in 33 different languages, and has significantly increased its support for languages that use non-Latin character sets. While Twitter, Inc. has occasionally changed the appearance of the service and added new features—often in reaction to users’ developing their own conventions, such as adding ‘#’ in front of important keywords to tag them—the basic idea behind the service has stayed the same: users may post short messages (tweets) of up to 140 characters and follow the updates posted by other users. This leads to the formation of complex follower networks with unidirectional as well as bidirectional connections between individuals, but also between media outlets, NGOs, and other organisations. While originally ‘microblogs’ were perceived as a new genre of online communication, of which Twitter was just one exemplar, the platform has become synonymous with microblogging in most countries. A notable exception is Sina Weibo, popular in China where Twitter is not available. Other similar platforms have been shut down (e.g., Jaiku), or are being used in slightly different ways (e.g., Tumblr), thus making Twitter a unique service within the social media landscape.

Characterisation of the micro-architecture of direct writing melt electrospun tissue engineering scaffolds using diffusion tensor and computed tomography microimaging

This article describes the first steps toward comprehensive characterization of molecular transport within scaffolds for tissue engineering. The scaffolds were fabricated using a novel melt electrospinning technique capable of constructing 3D lattices of layered polymer fibers with well - defined internal microarchitectures. The general morphology and structure order was then determined using T 2 - weighted magnetic resonance imaging and X - ray microcomputed tomography. Diffusion tensor microimaging was used to measure the time - dependent diffusivity and diffusion anisotropy within the scaffolds. The measured diffusion tensors were anisotropic and consistent with the cross - hatched geometry of the scaffolds: diffusion was least restricted in the direction perpendicular to the fiber layers. The results demonstrate that the cross - hatched scaffold structure preferentially promotes molecular transport vertically through the layers ( z - axis), with more restricted diffusion in the directions of the fiber layers ( x – y plane). Diffusivity in the x – y plane was observed to be invariant to the fiber thickness. The characteristic pore size of the fiber scaffolds can be probed by sampling the diffusion tensor at multiple diffusion times. Prospective application of diffusion tensor imaging for the real - time monitoring of tissue maturation and nutrient transport pathways within tissue engineering scaffolds is discussed.

Integrated plasma-aided nanofabrication facility: Operation, parameters, and assembly of quantum structures and functional nanomaterials

The development, operation, and applications of two configurations of an integrated plasma-aided nanofabrication facility (IPANF) comprising low-frequency inductively coupled plasma-assisted, low-pressure, multiple-target RF magnetron sputtering plasma source, are reported. The two configurations of the plasma source have different arrangements of the RF inductive coil: a conventional external flat spiral "pancake" coil and an in-house developed internal antenna comprising two orthogonal RF current sheets. The internal antenna configuration generates a "unidirectional" RF current that deeply penetrates into the plasma bulk and results in an excellent uniformity of the plasma over large areas and volumes. The IPANF has been employed for various applications, including low-temperature plasma-enhanced chemical vapor deposition of vertically aligned single-crystalline carbon nanotips, growth of ultra-high aspect ratio semiconductor nanowires, assembly of optoelectronically important Si, SiC, and Al1-xInxN quantum dots, and plasma-based synthesis of bioactive hydroxyapatite for orthopedic implants.

Internal oscillating current-sustained RF plasmas : Parameters, stability, and potential for surface engineering

A new source of low-frequency (0.46 MHz) inductively coupled plasmas sustained by the internal planar "unidirectional" RF current driven through a specially designed internal antenna configuration has been developed. The experimental results of the investigation of the optical and global argon plasma parameters by the optical and Langmuir probes are presented. It is shown that the spatial profiles of the electron density, the effective electron temperature and plasma potential feature a great deal of the radial and axial uniformity compared with conventional sources of inductively coupled plasmas with external at coil configurations. The measurements also reveal a weak azimuthal dependence of the global plasma parameters at low values of the input RF power, which was earlier predicted theoretically. The azimuthal dependence of the global plasma parameters vanishes at high input RF powers. Moreover, under certain conditions, the plasma becomes unstable due to spontaneous transitions between low-density (electrostatic, E) and high-density (electromagnetic, H) operating modes. Excellent uniformity of high-density plasmas makes the plasma reactor promising for various plasma processing applications and surface engineering.

Discharge mode transitions in low-frequency inductively coupled plasmas with internal oscillating current sheets

Transitions between the two discharge modes in a low-frequency (∼460 kHz) inductively coupled plasma sustained by an internal oscillating radio frequency (rf) current sheet are studied. The unidirectional rf current sheet is generated by an internal antenna comprising two orthogonal sets of synphased rf currents driven in alternately reconnected copper litz wires. It is shown that in the low-to-intermediate pressure range the plasma source can be operated in the electrostatic (E) and electromagnetic (H) discharge modes. The brightness of the E -mode argon plasma glow is found remarkably higher than in inductively coupled plasmas with external flat spiral "pancake" coils. The cyclic variations of the input rf power result in pronounced hysteretic variations of the optical emission intensity and main circuit parameters of the plasma source. Under certain conditions, it appears possible to achieve a spontaneous E→H transition ("self-transition"). The observed phenomenon can be attributed to the thermal drift of the plasma parameters due to the overheating of the working gas. The discharge destabilizing factors due to the gas heating and step-wise ionization are also discussed. © 2005 American Vacuum Society.

Improvement of the mode II interface fracture toughness of glass fiber reinforced plastics/aluminum laminates through vapor grown carbon fiber interleaves

The effects of acid treatment, vapor grown carbon fiber (VGCF) interlayer and the angle, i.e., 0° and 90°, between the rolling stripes of an aluminum (Al) plate and the fiber direction of glass fiber reinforced plastics (GFRP) on the mode II interlaminar mechanical properties of GFRP/Al laminates were investigated. The experimental results of an end notched flexure test demonstrate that the acid treatment and the proper addition of VGCF can effectively improve the critical load and mode II fracture toughness of GFRP/Al laminates. The specimens with acid treatment and 10 g m−2 VGCF addition possess the highest mode II fracture toughness, i.e., 269% and 385% increases in the 0° and 90° specimens, respectively compared to those corresponding pristine ones. Due to the induced anisotropy by the rolling stripes on the aluminum plate, the 90° specimens possess 15.3%–73.6% higher mode II fracture toughness compared to the 0° specimens. The improvement mechanisms were explored by the observation of crack propagation path and fracture surface with optical, laser scanning and scanning electron microscopies. Moreover, finite element analyses were carried out based on the cohesive zone model to verify the experimental fracture toughness and to predict the interface shear strength between the aluminum plates and GFRP laminates.