Capillary Agglutination Technology

In medical diagnostic tests, including pregnancy testing and tests for typed red blood cells, a small fluid sample is placed at one end of a capillary channel, which has been lined with a dried reagent. If the sample contains the analyte (the substance being tested for) then an agglutination reaction occurs between it and the reagent in the channel, and the agglutinated complexes progressively slow the flow and may even block the channel, partially or completely, so that the flow only reaches the far end very slowly, or not at all. The aim is that this should give a reliable detection of quite low concentrations of analyte in the sample. Platform Diagnostics asked the Study Group to construct a mathematical model of the process, so that, for known binding forces in the agglutination complexes, we can design the channel size and shape, and the fluid viscosity, to maximize the reliable detection of low concentrations. A key question is how the flow time depends on channel size, fluid surface tension and viscosity, (a) in the absence of agglutination, and (b) in the presence of agglutination

Resource allocation

This report discusses the problem of the allocation of resources: how should an organisation (such as MOD) invest bearing in mind the long term delay for the realization of investment strategies, and how might this apply in times of increasing budgetary constraints? After making certain simplifying assumptions, the Study Group constructed a prototype model based on the method of Optimal Control. This allows the decision maker to investigate the impact of particular investment strategies over a period of years, the impact being measured in terms of “quality” or “capability”. Interventions can be designed so that “quality” (Q) is maximized at a particular time, or so that the average quality over a given time interval is maximized. Both of these approaches are explored. This model shows reasonable behaviour when tested over a parameter set. It could be used as part of a systems approach to the defence budget as a whole, but the method itself is scalable to smaller (or larger) resourcing conundrums

Modelling the interactions between tumour cells and a blood vessel in a microenvironment within a vascular tumour

In this paper, we develop a mathematical model to describe interactions between tumour cells and a compliant blood vessel that supplies oxygen to the region. We assume that, in addition to proliferating, the tumour cells die through apoptosis and necrosis. We also assume that pressure differences within the tumour mass, caused by spatial variations in proliferation and degradation, cause cell motion. We couple the behaviour of the blood vessel into the model for the oxygen tension. The model equations track the evolution of the densities of live and dead cells, the oxygen tension within the tumour, the live and dead cell speeds, the pressure and the width of the blood vessel. We present explicit solutions to the model for certain parameter regimes, and then solve the model numerically for more general parameter regimes. We show how the resulting steady-state behaviour varies as the key model parameters are changed. Finally, we discuss the biological implications of our work

The drainage of a foam lamella

We present a mathematical model for the drainage of a surfactant-stabilised foam lamella, including capillary, Marangoni and viscous effects and allowing for diffusion, advection and adsorption of the surfactant molecules. We use the slender geometry of a lamella to formulate the model in the thin-film limit and perform an asymptotic decomposition of the liquid domain into a capillary-static Plateau border, a time-dependent thin film and a transition region between the two. By solving a quasi-steady boundary-value problem in the transition region, we obtain the flux of liquid from the lamella into the Plateau border and thus are able to determine the rate at which the lamella drains. Our method is illustrated initially in the surfactant-free case. Numerical results are presented for three particular parameter regimes of interest when surfactant is present. Both monotonic profiles and those exhibiting a dimple near the Plateau border are found, the latter having been previously observed in experiments. The velocity field may be uniform across the lamella or of parabolic Poiseuille type, with fluid either driven out along the centre-line and back along the free surfaces or vice versa. We find that diffusion may be negligible for a typical real surfactant, although this does not lead to a reduction in order because of the inherently diffusive nature of the fluid-surfactant interaction. Finally, we obtain the surprising result that the flux of liquid from the lamella into the Plateau border increases as the lamella thins, approaching infinity at a finite lamella thickness

Mathematical modelling of the overflowing cylinder experiment

The overflowing cylinder (OFC) is an experimental apparatus designed to generate a controlled straining flow at a free surface, whose dynamic properties may then be investigated. Surfactant solution is pumped up slowly through a vertical cylinder. On reaching the top, the liquid forms a flat free surface which expands radially before overflowing down the side of the cylinder. The velocity, surface tension and surfactant concentration on the expanding free surface are measured using a variety of non-invasive techniques. A mathematical model for the OFC has been previously derived by Breward, Darton, Howell and Ockendon and shown to give satisfactory agreement with experimental results. However, a puzzling indeterminacy in the model renders it unable to predict one scalar parameter (e.g. the surfactant concentration at the centre of the cylinder), which must be therefore be taken from the experiments. In this paper we analyse the OFC model asymptotically and numerically. We show that solutions typically develop one of two possible singularities. In the first, the surface concentration of surfactant reaches zero a finite distance from the cylinder axis, while the surface velocity tends to infinity there. In the second, the surfactant concentration is exponentially large and a stagnation point forms just inside the rim of the cylinder. We propose a criterion for selecting the free parameter, based on the elimination of both singularities, and show that it leads to good agreement with experimental results

Straining flow of a micellar surfactant solution

We present a mathematical model describing the distribution of monomer and micellar surfactant in a steady straining flow beneath a fixed free surface. The model includes adsorption of monomer surfactant at the surface and a single-step reaction whereby $n$ monomer molecules combine to form each micelle. The equations are analysed asymptotically and numerically and the results are compared with experiments. Previous studies of such systems have often assumed equilibrium between the monomer and micellar phases, i.e. that the reaction rate is effectively infinite. Our analysis shows that such an approach inevitably fails under certain physical conditions and also cannot accurately match some experimental results. Our theory provides an improved fit with experiments and allows the reaction rates to be estimated

Electrophysiological investigation of the effects of beak trimming in the domestic fowl (gallus gallus domesticus)

Beak trimming, the amputation of the anterior part of the beak, is used to reduce feather pecking and cannibalism amongst intensively reared poultry. This practice has been criticized on the grounds that it may cause the bird to suffer pain.The approach adopted in this thesis towards the study of pain perception in the chicken was to investigate the possibility of peripheral neural phenomena which may be related to acute and chronic pain sensation as a result of beak trimming.A review of the literature pertaining to the peripheral neural basis of cutaneous sensation in birds revealed that whilst mechanoreceptors and thermoreceptors are known to be present in the avian beak, the evidence for nociceptors has not been conclusive.Acute electrophysiological techniques were employed to study the primary afferent output from the beak, using a preparation developed for this purpose. Cutaneous nociceptors were discovered in the intact beak. An analysis of their stimulus response characteristics revealed many similarities with previously described mammalian cutaneous nociceptors. It was considered that the nociceptors would be activated during beak trimming, and would transmit nociceptive information to the central nervous system.In the trimmed beak, the nociceptor population showed a reduced sensitivity to heat. They therefore did not provide a peripheral neural basis for hyperalgesia following beak trimming.Abnormal spontaneous afferent discharges were recorded from the trimmed beak for up to 3 months following beak trimming. These discharges have many similarities to those resulting from peripheral nerve damage in mammals, and they may have had a similar origin in neuromas.It was concluded that the acute and chronic peripheral neural consequences of beak trimming can be compared with processes which can give rise to acute and chronic pain sensations in man.Further experiments are suggested to advance knowledge of the possibility of pain perception in the domestic fowl