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.

Refined plastic hinge analysis of steel frame structures comprising non-compact sections : II : verification

Application of "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A refined plastic hinge method suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in a companion paper. The method implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the method for the analysis of steel frames comprising non-compact sections is established in this paper by comparison with a comprehensive range of analytical benchmark frame solutions. The refined plastic hinge method is shown to be more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations.

Optical and biomechanical factors, associated with near work and myopia

Near work may play an important role in the development of myopia in the younger population. The prevalence of myopia has also been found to be higher in occupations that involve substantial near work tasks, for example in microscopists and textile workers. When nearwork is performed, it typically involves accommodation, convergence and downward gaze. A number of previous studies have examined the effects of accommodation and convergence on changes in the optics and biometrics of the eye in primary gaze. However, little is known about the influence of accommodation on the eye in downward gaze. This thesis is primarily concerned with investigating the changes in the eye during near work in downward gaze under natural viewing conditions. To measure wavefront aberrations in downward gaze under natural viewing conditions, we modified a commercial Shack-Hartmann wavefront sensor by adding a relay lens system to allow on-axis ocular aberration measurements in primary gaze and downward gaze, with binocular fixation. Measurements with the modified wavefront sensor in primary and downward gaze were validated against a conventional aberrometer using both a model eye and in 9 human subjects. We then conducted an experiment to investigate changes in ocular aberrations associated with accommodation in downward gaze over 10 mins in groups of both myopes (n = 14) and emmetropes (n =12) using the modified Shack-Hartmann wavefront sensor. During the distance accommodation task, small but significant changes in refractive power (myopic shift) and higher order aberrations were observed in downward gaze compared to primary gaze. Accommodation caused greater changes in higher order aberrations (in particular coma and spherical aberration) in downward gaze than primary gaze, and there was evidence that the changes in certain aberrations with accommodation over time were different in downward gaze compared to primary gaze. There were no obvious systematic differences in higher order aberrations between refractive error groups during accommodation or downward gaze for fixed pupils. However, myopes exhibited a significantly greater change in higher order aberrations (in particular spherical aberration) than emmetropes for natural pupils after 10 mins of a near task (5 D accommodation) in downward gaze. These findings indicated that ocular aberrations change from primary to downward gaze, particularly with accommodation. To understand the mechanism underlying these changes in greater detail, we then extended this work to examine the characteristics of the corneal optics, internal optics, anterior biometrics and axial length of the eye during a near task, in downward gaze, over 10 mins. Twenty young adult subjects (10 emmetropes and 10 myopes) participated in this study. To measure corneal topography and ocular biometrics in downward gaze, a rotating Scheimpflug camera and an optical biometer were inclined on a custom built, height and tilt adjustable table. We found that both corneal optics and internal optics change with downward gaze, resulting in a myopic shift (~0.10 D) in the spherical power of the eye. The changes in corneal optics appear to be due to eyelid pressure on the anterior surface of the cornea, whereas the changes in the internal optics (an increase in axial length and a decrease in anterior chamber depth) may be associated with movement of the crystalline lens, under the action of gravity, and the influence of altered biomechanical forces from the extraocular muscles on the globe with downward gaze. Changes in axial length with accommodation were significantly greater in downward gaze than primary gaze (p < 0.05), indicating an increased effect of the mechanical forces from the ciliary muscle and extraocular muscles. A subsequent study was conducted to investigate the changes in anterior biometrics, axial length and choroidal thickness in nine cardinal gaze directions under the actions of the extraocular muscles. Ocular biometry measurements were obtained from 30 young adults (10 emmetropes, 10 low myopes and 10 moderate myopes) through a rotating prism with 15° deviation, along the foveal axis, using a non-contact optical biometer in each of nine different cardinal directions of gaze, over 5 mins. There was a significant influence of gaze angle and time on axial length (both p < 0.001), with the greatest axial elongation (+18 ± 8 μm) occurring with infero-nasal gaze (p < 0.001) and a slight decrease in axial length in superior gaze (−12 ± 17 μm) compared with primary gaze (p < 0.001). There was a significant correlation between refractive error (spherical equivalent refraction) and the mean change in axial length in the infero-nasal gaze direction (Pearson's R2 = 0.71, p < 0.001). To further investigate the relative effect of gravity and extraocular muscle force on the axial length, we measured axial length in 15° and 25° downward gaze with the biometer inclined on a tilting table that allowed gaze shifts to occur with either full head turn but no eye turn (reflects the effect of gravity), or full eye turn with no head turn (reflects the effect of extraocular muscle forces). We observed a significant axial elongation in 15° and 25° downward gaze in the full eye turn condition. However, axial length did not change significantly in downward gaze over 5 mins (p > 0.05) in the full head turn condition. The elongation of the axial length in downward gaze appears to be due to the influence of the extraocular muscles, since the effect was not present when head turn was used instead of eye turn. The findings of these experiments collectively show the dynamic characteristics of the optics and biometrics of the eye in downward gaze during a near task, over time. These were small but significant differences between myopic and emmetropic eyes in both the optical and biomechanical changes associated with shifts of gaze direction. These differences between myopes and emmetropes could arise as a consequence of excessive eye growth associated with myopia. However the potentially additive effects of repeated or long lasting near work activities employing infero-nasal gaze could also act to promote elongation of the eye due to optical and/or biomechanical stimuli.

Distributed plasticity analysis of steel frame structures comprising non-compact sections

Application of 'advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. A primary objective was to produce a comprehensive range of new distributed plasticity analytical benchmark solutions for verification of the concentrated plasticity methods. A distributed plasticity model was developed using shell finite elements to explicitly account for the effects of gradual yielding and spread of plasticity, initial geometric imperfections, residual stresses and local buckling deformations. The model was verified by comparison with large-scale steel frame test results and a variety of existing analytical benchmark solutions. This paper presents a description of the distributed plasticity model and details of the verification study.

Pseudo plastic zone analysis of steel frame structures comprising non-compact sections

Application of `advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A concentrated plasticity method suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in this paper. The pseudo plastic zone method implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling. The accuracy and precision of the method for the analysis of steel frames comprising non-compact sections is established by comparison with a comprehensive range of analytical benchmark frame solutions. The pseudo plastic zone method is shown to be more accurate and precise than the conventional individual member design methods based on elastic analysis and specification equations.

Large-scale testing of steel frame structures comprising non-compact sections

Application of 'advanced analysis' methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A research project has been conducted with the aim of developing concentrated plasticity methods suitable for practical advanced analysis of steel frame structures comprising non-compact sections. A series of large-scale tests were performed in order to provide experimental results for verification of the new analytical models. Each of the test frames comprised non-compact sections, and exhibited significant local buckling behaviour prior to failure. This paper presents details of the test program including the test specimens, set-up and instrumentation, procedure, and results.

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.

Distinguishing attack on SOBER-128 with linear masking

We present a distinguishing attack against SOBER-128 with linear masking. We found a linear approximation which has a bias of 2^− − 8.8 for the non-linear filter. The attack applies the observation made by Ekdahl and Johansson that there is a sequence of clocks for which the linear combination of some states vanishes. This linear dependency allows that the linear masking method can be applied. We also show that the bias of the distinguisher can be improved (or estimated more precisely) by considering quadratic terms of the approximation. The probability bias of the quadratic approximation used in the distinguisher is estimated to be equal to O(2^− − 51.8), so that we claim that SOBER-128 is distinguishable from truly random cipher by observing O(2^103.6) keystream words.

Renormalization group interpretation of the Born and Rytov approximations

In this paper the method of renormalization group (RG) [Phys. Rev. E 54, 376 (1996)] is related to the well-known approximations of Rytov and Born used in wave propagation in deterministic and random media. Certain problems in linear and nonlinear media are examined from the viewpoint of RG and compared with the literature on Born and Rytov approximations. It is found that the Rytov approximation forms a special case of the asymptotic expansion generated by the RG, and as such it gives a superior approximation to the exact solution compared with its Born counterpart. Analogous conclusions are reached for nonlinear equations with an intensity-dependent index of refraction where the RG recovers the exact solution. © 2008 Optical Society of America.

Refined Plastic Hinge Analysis of Steel Frame Structures Comprising Non-Compact Sections: I: Formulation

Application of "advanced analysis" methods suitable for non-linear analysis and design of steel frame structures permits direct and accurate determination of ultimate system strengths, without resort to simplified elastic methods of analysis and semi-empirical specification equations. However, the application of advanced analysis methods has previously been restricted to steel frames comprising only compact sections that are not influenced by the effects of local buckling. A concentrated plasticity formulation suitable for practical advanced analysis of steel frame structures comprising non-compact sections is presented in this paper. This formulation, referred to as the refined plastic hinge method, implicitly accounts for the effects of gradual cross-sectional yielding, longitudinal spread of plasticity, initial geometric imperfections, residual stresses, and local buckling.

Stochastic linear multistep methods for the simulation of chemical kinetics

In this paper, we introduce the Stochastic Adams-Bashforth (SAB) and Stochastic Adams-Moulton (SAM) methods as an extension of the tau-leaping framework to past information. Using the theta-trapezoidal tau-leap method of weak order two as a starting procedure, we show that the k-step SAB method with k >= 3 is order three in the mean and correlation, while a predictor-corrector implementation of the SAM method is weak order three in the mean but only order one in the correlation. These convergence results have been derived analytically for linear problems and successfully tested numerically for both linear and non-linear systems. A series of additional examples have been implemented in order to demonstrate the efficacy of this approach.

Analysis of an internally mountable accelerometer balance system for use with non-isotropic models in shock tunnels

Knowledge of drag force is an important design parameter in aerodynamics. Measurement of aerodynamic forces at hypersonic speed is a challenge and usually ground test facilities like shock tunnels are used to carry out such tests. Accelerometer based force balances are commonly employed for measuring aerodynamic drag around bodies in hypersonic shock tunnels. In this study, we present an analysis of the effect of model material on the performance of an accelerometer balance used for measurement of drag in impulse facilities. From the experimental studies performed on models constructed out of Bakelite HYLEM and Aluminum, it is clear that the rigid body assumption does not hold good during the short testing duration available in shock tunnels. This is notwithstanding the fact that the rubber bush used for supporting the model allows unconstrained motion of the model during the short testing time available in the shock tunnel. The vibrations induced in the model on impact loading in the shock tunnel are damped out in metallic model, resulting in a smooth acceleration signal, while the signal become noisy and non-linear when we use non-isotropic materials like Bakelite HYLEM. This also implies that careful analysis and proper data reduction methodologies are necessary for measuring aerodynamic drag for non-metallic models in shock tunnels. The results from the drag measurements carried out using a 60 degrees half angle blunt cone is given in the present analysis.

The transient response of certain third-ordernon-linear systems

In this paper a method of solving certain third-order non-linear systems by using themethod of ultraspherical polynomial approximation is proposed. By using the method of variation of parameters the third-order equation is reduced to three partial differential equations. Instead of being averaged over a cycle, the non-linear functions are expanded in ultraspherical polynomials and with only the constant term retained, the equations are solved. The results of the procedure are compared with the numerical solutions obtained on a digital computer. A degenerate third-order system is also considered and results obtained for the above system are compared with numerical results obtained on the digital computer. There is good agreement between the results obtained by the proposed method and the numerical solution obtained on digital computer.

Influence of adhesive non-linearities on the performance and optimal length of adhesive bonded joints

An analytical study for the static strength of adhesive lap joints is presented. The earlier solutions of Volkersen [i], DeBruyne[2] and others were limited to linear adhesives. The influence of adhesive non-linearity was first considered by Grimes' et al[3] and Dickson et al [4]. Recently Hart-Smith[5] successfully introduced elastic-plastic behaviour of the adhesive. In the present study the problem is formulated for general non-linear adhesive behaviour and an efficient numerical algorithm is written for the solution. Bilinear and trilinear models for the nonlinearity yield closed form analytical solutions.

CFD analysis of high frequency miniature pulse tube refrigerators for space applications with thermal non-equilibrium model

High frequency, miniature, pulse tube cryocoolers are extensively used in space applications because of their simplicity. Parametric studies of inertance type pulse tube cooler are performed with different length-to-diameter ratios of the pulse tube with the help of the FLUENT (R) package. The local thermal non-equilibrium of the gas and the matrix is taken into account for the modeling of porous zones, in addition to the wall thickness of the components. Dynamic characteristics and the actual mechanism of energy transfer in pulse are examined with the help of the pulse tube wall time constant. The heat interaction between pulse tube wall and the oscillating gas, leading to surface heat pumping, is quantified. The axial heat conduction is found to reduce the performance of the pulse tube refrigerator. The thermal non-equilibrium predicts a higher cold heat exchanger temperature compared to thermal equilibrium. The pressure drop through the porous medium has a strong non-linear effect due to the dominating influence of Forchheimer term over that of the linear Darcy term at high operating frequencies. The phase angle relationships among the pressure, temperature and the mass flow rate in the porous zones are also important in determining the performance of pulse tuberefrigerator.