Nicholas Hill | University of Glasgow (original) (raw)

Papers by Nicholas Hill

Journal of Experimental Biology, 1997

Bioconvection occurs as the result of the collective behaviour of many micro-organisms swimming i... more Bioconvection occurs as the result of the collective behaviour of many micro-organisms swimming in a fluid and is realised as patterns similar to those of thermal convection which occur when a layer of water is heated from below. A methodology is developed to record the bioconvection patterns that are formed by aqueous cultures of the single-celled alga Chlamydomonas nivalis. The analysis that is used to quantify the patterns as a function of cell concentration, suspension depth and time is described and experimental results are presented.

Cmes-computer Modeling in Engineering & Sciences, 2013

A gas-liquid two-phase model for the simulation of a power-law fluid mold filling process with th... more A gas-liquid two-phase model for the simulation of a power-law fluid mold filling process with the consideration of phase change is proposed, in which the governing equations for the melt and air in the cavity, including the mass conservation, momentum conservation and energy conservation equations, are unified into one system of equation. A revised Enthalpy method, which can be used for both the melt and air in the mold cavity, is proposed to describe the phase change during the mold filling. Finite volume method on non-staggered grid is used to solve the system. The level set method is used to capture the interface evolution during the mold filling process. The interface evolution and the distributions of physical quantities such as velocity, pressure and temperature and so on are given. The “frozen skin” layers under different temperature and velocities conditions are discussed in detail. Numerical results show that increasing the temperatures of the melt and cavity is a better w...

Journal of Fluid Mechanics, 1988

Bioconvection ' is the name given to pattern-forming convective motions set up in suspensions of ... more Bioconvection ' is the name given to pattern-forming convective motions set up in suspensions of swimming microorganisms. ' Gyrotaxis ' describes the way the swimming is guided through a balance between the physical torques generated by viscous drag and by gravity operating on an asymmetric distribution of mass within the organism. When the organisms are heavier towards the rear, gyrotaxis turns them so that they swim towards regions of most rapid downflow. The presence of gyrotaxis means that bioconvective instability can develop from an initially uniform suspension, without an unstable density stratification. In this paper a continuum model for suspensions of gyrotactic microorganisms is proposed and discussed ; in particular, account is taken of the fact that the organisms of interest are nonspherical, so that their orientation is influenced by the strain rate in the ambient flow as well as the vorticity. This model is used to analyse the linear instability of a uniform suspension. It is shown that the suspension is unstable if the disturbance wavenumber is less than a critical value which, together with the wavenumber of the most rapidly growing disturbance, is calculated explicitly. The subsequent convection pattern is predicted to be three-dimensional (i.e. with variation in the vertical as well as the horizontal direction) if the cells are sufficiently elongated. n'umerical results are given for suspensions of a particular algal species (Chlamydomonas nizulis) ; the predicted wavelength of the most rapidly growing disturbance is 5-6 times larger than the wavelength of steady-state patterns observed in experiments. The main reasons for the difference are probably that the analysis describes the onset of convection, not the final, nonlinear steady state, and that the experimental fluid layer has finite depth.

Journal of Experimental Biology, 2000

Many amphibian tadpoles hatch and swim before their inner ears and sense of spatial orientation d... more Many amphibian tadpoles hatch and swim before their inner ears and sense of spatial orientation differentiate. We describe upward and downward swimming responses in hatchling Xenopus laevis tadpoles from stages 32 to 37/38 in which the body rotates about its longitudinal axis. Tadpoles are heavier than water and, if touched while lying on the substratum, they reliably swim upwards, often in a tight spiral. This response has been observed using stroboscopic photography and high-speed video recordings. The sense of the spiral is not fixed for individual tadpoles. In ‘more horizontal swimming’ (i.e. in directions within +/−30 degrees of the horizontal), the tadpoles usually swim belly-down, but this position is not a prerequisite for subsequent upward spiral swimming. Newly hatched tadpoles spend 99 % of their time hanging tail-down from mucus secreted by a cement gland on the head. When suspended in mid-water by a mucus strand, tadpoles from stage 31 to 37/38 tend to swim spirally dow...

Bulletin of mathematical biology, 2015

We investigate pattern formation by swimming micro-organisms (bioconvection), when their orientat... more We investigate pattern formation by swimming micro-organisms (bioconvection), when their orientation is determined by balance between gravitational and viscous torques (gyrotaxis), due to being bottom heavy. The governing equations, which consist of the Navier-Stokes equations for an incompressible fluid coupled with a micro-organism conservation equation, are solved numerically in a large cross section chamber with periodic boundary conditions in the horizontal directions. The influence of key parameters on wavelength selection in bioconvection patterns is investigated numerically. For realistic ranges of parameter values, the computed wavelengths are in good agreement with the experimental observations provided that the diffusion due to randomness in cell swimming behaviour is small, refuting a recently published claim that the mathematical model becomes inaccurate at long times. We also provide the first computational evidence of "bottom-standing" plumes in a three-dime...

Journal of Fluid Mechanics, 1992

The motion of a heavy sphere sedimenting through a dilute background suspension of neutrally buoy... more The motion of a heavy sphere sedimenting through a dilute background suspension of neutrally buoyant spheres is analysed for small Reynolds number and large Péclet number. For this particular problem, it is possible not only to calculate the mean velocity of the heavy particle, but also the variance of the velocity and the coefficient of hydrodynamic diffusivity. Pairwise, hydrodynamic interactions between the heavy sphere and the background sphere are considered exactly using volume integrals and a trajectory analysis. Explicit formulae are given for the two limiting cases when the radius of the heavy sphere is much greater and much less than that of the background spheres, and numerical results are given for moderate size ratios. The mean velocity is relatively insensitive to the ratio of the radius of the background spheres to that of the heavy sphere, unless this ratio is very large, whereas the hydrodynamic diffusivity increases rapidly as the radius ratio is increased. The pre...

A second order, conservative numerical scheme is used to solve the equations of bioconvection in ... more A second order, conservative numerical scheme is used to solve the equations of bioconvection in two dimensions with stress-free side walls. The model is based on the continuum model of Pedley, Hill & Kessler (1988) for a suspension of swimming, gyrotactic microorganisms. The suspension is characterized by five parameters: a Rayleigh number R, a Schmidt number S_c, a cell speed parameter W, a gyrotaxis number G and the aspect ratio lambda of the chamber. It is observed that for a deep chamber, at an initial stage of plume formation, the plumes are unstable to a varicose mode leading to the formation of large ``blobs'' as seen in experiments. As time increases, a sideways meandering instability also develops and ultimately it destabilises the plume. Simulation has also been done for periodic side wall boundary conditions. In order to explain these instabilities, a model for an infinitely long plume is derived and linear stability analysis predicts both varicose and meanderi...

Fluid Dynamics Research, 2005

... Platinum was evaporated at a shallow angle on a dried sample and then imaged using a ... View... more ... Platinum was evaporated at a shallow angle on a dried sample and then imaged using a ... View the MathML source Here the terms on the right-hand side both represent the effect of cell ... process in the cells&#x27; swimming behaviour, and View the MathML source is the rate of change ...

Annals of Biomedical Engineering, 2008

Bile flow is thought to play an essential role in the pathophysiological genesis of cholelithiasi... more Bile flow is thought to play an essential role in the pathophysiological genesis of cholelithiasis (gallstone formation) and in gallbladder pain. In this paper, we extend our previous study of the human biliary system (Li et al., 2007, J. Biomech. Eng., 129:164-173) to include two important factors: the non-Newtonian properties of bile, and elastic deformation of the cystic duct. A one-dimensional (1D) model is analyzed and compared with three-dimensional (3D) fluid-structure interaction simulations. It is found that non-Newtonian bile raises resistance to the flow of bile, which can be augmented significantly by the elastic deformation (collapse) of the cystic duct. We also show that the 1D model predicts the pressure drop of the cystic duct flow well for all cases considered (Newtonian or non-Newtonian flow, rigid or elastic ducts), when compared with the full 3D simulations.

Advances in Space Research, 1998

Experiments and calculations on the trajectories of micron-sized spheres, suspended in a fluid th... more Experiments and calculations on the trajectories of micron-sized spheres, suspended in a fluid that fills a closed container which rotates about an axis perpendicular to g, relate to the planning and interpretation of clinostat experiments. For low Reynolds number motion, the orbits are nearly circular, the radius being inversely proportional to the rotation rate. The swimming direction of microorganisms can be affected by light, gravity, vorticity etc. The trajectories of algae swimming in steadily rotating environments have been observed and compared with theoretical predictions for ideal gyrotactic microorganisms , thus providing some insights into the mechanisms of gravitaxis, gyrotaxis and the behaviour of the cells.

Journal of Theoretical Biology, 2005

When observing the two-dimensional movement of animals or microorganisms, it is usually necessary... more When observing the two-dimensional movement of animals or microorganisms, it is usually necessary to impose a fixed sampling rate, so that observations are made at certain fixed intervals of time and the trajectory is split into a set of discrete steps. A sampling rate that is too small will result in information about the original path and correlation being lost. If random walk models are to be used to predict movement patterns or to estimate parameters to be used in continuum models, then it is essential to be able to quantify and understand the effect of the sampling rate imposed by the observer on real trajectories. We use a velocity jump process with a realistic reorientation model to simulate correlated and biased random walks and investigate the effect of sampling rate on the observed angular deviation, apparent speed and mean turning angle. We discuss a method of estimating the values of the reorientation parameters used in the original random walk from the rediscretized data that assumes a linear relation between sampling time step and the parameter values.

A multiscale maximum entropy moment closure for locally regulated space–time point process models... more A multiscale maximum entropy moment closure for locally regulated space–time point process models of population dynamics

Proceedings of the International Conference on Statistics: Theory and Applications, 2019

Parameter estimation and uncertainty quantification in physiological modelling is a vital step to... more Parameter estimation and uncertainty quantification in physiological modelling is a vital step towards personalised medicine. Current state-of-the-art in this research area performs parameter optimisation, with very limited uncertainty quantification. This paper demonstrates the advantage of novel sampling methods, applied on a complex biological PDE system of the pulmonary circulation. The aim is to find an efficient and accurate method for the inference and uncertainty quantification of unknown parameters, relevant for disease diagnosis (pulmonary hypertension) from limited and noisy blood pressure data. The data likelihood is expensive to evaluate as it requires solving numerically a system of PDEs. Therefore, having a model that best trades off accuracy and computational efficiency is of uppermost importance. In this study, we employ fast Bayesian methods, namely MCMC algorithms coupled with emulation using Gaussian Processes, to achieve a computational speed-up. We compare the Delayed Rejection Adaptive Metropolis algorithm in a History Matching framework to the delayed acceptance Adaptive Metropolis algorithm. The first algorithm draws samples from the approximate posterior distribution, while the latter is guaranteed to generate samples from the exact posterior distribution asymptotically. In this paper we propose and derive the n-steps ahead delayed acceptance Metropolis-Hastings algorithm, which is a generalisation of the classical 1-step ahead delayed acceptance Metropolis-Hastings. We show the superiority of the n-steps ahead algorithm over the 1-step ahead method.

Physical Review Fluids, 2018

We study the effects of imposed three-dimensional flows on the trajectories and mixing of gyrotac... more We study the effects of imposed three-dimensional flows on the trajectories and mixing of gyrotactic swimming microorganisms , and identify new phenomena not seen in flows restricted to two dimensions. Through numerical simulation of Taylor-Green and ABC flows, we explore the role that the flow and the cell shape play in determining the long-term configuration of the cells' trajectories, which often take the form of multiple sinuous and helical 'plume-like' structures, even in the chaotic ABC flow. This gyrotactic suppression of Lagrangian chaos persists even in the presence of random noise. Analytical solutions for a number of cases reveal the how plumes form and the nature of the competition between torques acting on individual cells. Furthermore, studies of Lyapunov exponents reveal that as the ratio of cell swimming speed relative to the flow speed increases from zero, the initial chaotic trajectories are first suppressed and then give way to a second unexpected window of chaotic trajectories at speeds greater than unity, before suppression of chaos at high relative swimming speeds.

Frontiers in Physiology, 2019

International Journal of Applied Mechanics, 2016

In this paper, we present a mathematical model linking blood flow, shear-dependent endothelium pe... more In this paper, we present a mathematical model linking blood flow, shear-dependent endothelium permeability and intimal thickening (hyperplasia) of the arterial wall, which is an initial stage in the development of atherosclerosis. The key concepts are that the intimal layer swells in response to the presence of excess oxidised LDL (OxLDL) in foam cells. The hyperplasia disturbs blood flow, affecting endothelial permeability via the wall shear stress (WSS). These changes produce a feedback mechanism. LDL is transported through the arterial wall by advection and diffusion, and the concentration of LDL at each time step is assumed to be quasi-steady since it equilibrates on a fast time scale. The process is controlled by the slow timescale of the increase in concentration of OxLDL. We consider a section of uniform axisymmetric artery, and impose an initial local injury or ‘hotspot’ of relatively high permeability that enhances the influx of LDL, triggering the development of a bump-sh...

Heart, 2015

We compute and study critical pressures (Pc) for the initiation of the propagation of an existing... more We compute and study critical pressures (Pc) for the initiation of the propagation of an existing arterial dissection, which in general depends on the residual stress and pre-stretch of the artery, and the length and depth of the tear, using the Holzapfel-Gasser-Ogden mathematical model for the walls of the large arteries. For the simple case of a 2D tissue sample, increasing the length of the initial dissection lowers the value of Pc, but when the strip is supported by connective tissue, arrest of the dissection is obtained. A peeling test on a disc-shaped sample demonstrates that the orientation of collagen fibres plays an important role in the direction of propagation. To study the effects of residual stress on arterial dissection, we include residual stress, quantified by the opening angle when an artery is subject to a longitudinal cut. We show that Pc is approximately proportional to the opening angle, so that the observed loss of residual stress associated with ageing increases the likelihood of dissection. Finally the effects of the circumferential (arc) length and radial position of the initial tear in a cylindrical model of an artery are investigated. Pc decreases as arc length increases and as the initial dissection is placed closer to the lumen. Prolapse of the dissection into the lumen occurs when the initial tear close to the lumen and the arc length is large.

Journal of biological physics, 1999

If an excitable medium is moving with relative shear, the waves of excitation may be broken by th... more If an excitable medium is moving with relative shear, the waves of excitation may be broken by the motion. We consider such breaks for the case of a constant linear shear flow. The mechanisms and conditions for the breaking of solitary waves and wavetrains are essentially different: the solitary waves require the velocity gradient to exceed a certain threshold, whilst the breaking of repetitive wavetrains happens for arbitrarily small velocity gradients. Since broken waves evolve into new spiral wave sources, this leads to spatio-temporal irregularity.

Physical Review E, 1999

We consider an excitable medium moving with relative shear, subjected to a localized disturbance ... more We consider an excitable medium moving with relative shear, subjected to a localized disturbance that in a stationary medium would produce a pair of spiral waves. The spiral waves so created are distorted and then broken by the motion of the medium. Such breaks generate new spiral waves, and so a ''chain reaction'' of spiral wave births and deaths is observed. This leads to a complicated spatiotemporal pattern, the ''frazzle gas'' ͓term suggested by Markus et al., Nature ͑London͒ 371, 402 ͑1994͔͒, which eventually fills the whole medium. In this paper, we display and interpret the main features of the pattern. ͓S1063-651X͑99͒09407-6͔

Biomechanics and modeling in mechanobiology, 2014

A novel multiscale mathematical and computational model of the pulmonary circulation is presented... more A novel multiscale mathematical and computational model of the pulmonary circulation is presented and used to analyse both arterial and venous pressure and flow. This work is a major advance over previous studies by Olufsen et al. (Ann Biomed Eng 28:1281-1299, 2012) which only considered the arterial circulation. For the first three generations of vessels within the pulmonary circulation, geometry is specified from patient-specific measurements obtained using magnetic resonance imaging (MRI). Blood flow and pressure in the larger arteries and veins are predicted using a nonlinear, cross-sectional-area-averaged system of equations for a Newtonian fluid in an elastic tube. Inflow into the main pulmonary artery is obtained from MRI measurements, while pressure entering the left atrium from the main pulmonary vein is kept constant at the normal mean value of 2 mmHg. Each terminal vessel in the network of 'large' arteries is connected to its corresponding terminal vein via a netw...