AltitudeOmics: Red Blood Cell metabolic adaptation to high altitude hypoxia

Red blood cells (RBCs) are key players in systemic oxygen transport. RBCs respond to in vitro hypoxia  through  the so-called  oxygen-dependent  metabolic  regulation,  which  involves  the competitive  binding  of  deoxyhemoglobin  and  glycolytic  enzymes  to  the  N-terminal  cytosolic domain  of  band  3.  This  mechanism  promotes  the  accumulation  of  2,3-DPG,  stabilizing  the deoxygenated state of hemoglobin, and cytosol acidification, triggering oxygen off-loading through the  Bohr  effect.  Despite  in  vitro  studies,  in  vivo adaptations  to  hypoxia  have  not  yet  been completely elucidated. Within  the  framework  of  the AltitudeOmics  study,  erythrocytes  were  collected  from  21 healthy volunteers at sea level, after exposure to high altitude (5260m) for 1, 7 and 16days, and following  reascent  after  7days  at 1525m.  UHPLC-MS  metabolomics  results  were  correlated  to physiological and athletic performance parameters. Immediate  metabolic  adaptations  were  noted as early as a few hours from ascending  to >5000m, and maintained for 16 days at high altitude.  Consistent with the mechanisms elucidated in vitro, hypoxia promoted glycolysis and deregulated the pentose phosphate pathway, as well purine catabolism, glutathione homeostasis, arginine/nitric oxide and sulphur/H2S metabolism. Metabolic adaptations were preserved one week after descent, consistently with improved physical performances in comparison to the first ascendance, suggesting a mechanism of metabolic memory.

A mathematical model of coal-fired fluidised bed boilers

A mathematical model of a large coal-fired fluidized bed boiler for power generation is synthesised. The effect of variations in the main parameters of the model on variables such as the background carbon concentrations in the bed, and the transient response of heat evolution are studied. The mechanisms of solids mixing within the bed, combustion and the flow of heat to the boiler tubes are shown to result in a characteristic dynamic response, knowledge of which is essential for the proper control and regulation of a practical system.

A mathematical model for assembly line balancing model to consider disordering sequence of workstations

Purpose – A binary integer programming model for the simple assembly line balancing problem (SALBP), which is well known as SALBP-1, was formulated more than 30 years ago. Since then, a number of researchers have extended the model for the variants of assembly line balancing problem.The model is still prevalent nowadays mainly because of the lower and upper bounds on task assignment. These properties avoid significant increase of decision variables. The purpose of this paper is to use an example to show that the model may lead to a confusing solution. Design/methodology/approach – The paper provides a remedial constraint set for the model to rectify the disordered sequence problem. Findings – The paper presents proof that the assembly line balancing model formulated by Patterson and Albracht may lead to a confusing solution. Originality/value – No one previously has found that the commonly used model is incorrect.

A mathematical model for dynamic efficiency using data envelopment analysis

In this paper we propose a data envelopment analysis (DEA) based method for assessing the comparative efficiencies of units operating production processes where input-output levels are inter-temporally dependent. One cause of inter-temporal dependence between input and output levels is capital stock which influences output levels over many production periods. Such units cannot be assessed by traditional or 'static' DEA which assumes input-output correspondences are contemporaneous in the sense that the output levels observed in a time period are the product solely of the input levels observed during that same period. The method developed in the paper overcomes the problem of inter-temporal input-output dependence by using input-output 'paths' mapped out by operating units over time as the basis of assessing them. As an application we compare the results of the dynamic and static model for a set of UK universities. The paper is suggested that dynamic model capture the efficiency better than static model. © 2003 Elsevier Inc. All rights reserved.

Immunological synapse: a mathematical model of the bond formation process:mathematical modelling of the immature synapse

The cell:cell bond between an immune cell and an antigen presenting cell is a necessary event in the activation of the adaptive immune response. At the juncture between the cells, cell surface molecules on the opposing cells form non-covalent bonds and a distinct patterning is observed that is termed the immunological synapse. An important binding molecule in the synapse is the T-cell receptor (TCR), that is responsible for antigen recognition through its binding with a major-histocompatibility complex with bound peptide (pMHC). This bond leads to intracellular signalling events that culminate in the activation of the T-cell, and ultimately leads to the expression of the immune eector function. The temporal analysis of the TCR bonds during the formation of the immunological synapse presents a problem to biologists, due to the spatio-temporal scales (nanometers and picoseconds) that compare with experimental uncertainty limits. In this study, a linear stochastic model, derived from a nonlinear model of the synapse, is used to analyse the temporal dynamics of the bond attachments for the TCR. Mathematical analysis and numerical methods are employed to analyse the qualitative dynamics of the nonequilibrium membrane dynamics, with the specic aim of calculating the average persistence time for the TCR:pMHC bond. A single-threshold method, that has been previously used to successfully calculate the TCR:pMHC contact path sizes in the synapse, is applied to produce results for the average contact times of the TCR:pMHC bonds. This method is extended through the development of a two-threshold method, that produces results suggesting the average time persistence for the TCR:pMHC bond is in the order of 2-4 seconds, values that agree with experimental evidence for TCR signalling. The study reveals two distinct scaling regimes in the time persistent survival probability density prole of these bonds, one dominated by thermal uctuations and the other associated with the TCR signalling. Analysis of the thermal fluctuation regime reveals a minimal contribution to the average time persistence calculation, that has an important biological implication when comparing the probabilistic models to experimental evidence. In cases where only a few statistics can be gathered from experimental conditions, the results are unlikely to match the probabilistic predictions. The results also identify a rescaling relationship between the thermal noise and the bond length, suggesting a recalibration of the experimental conditions, to adhere to this scaling relationship, will enable biologists to identify the start of the signalling regime for previously unobserved receptor:ligand bonds. Also, the regime associated with TCR signalling exhibits a universal decay rate for the persistence probability, that is independent of the bond length.

Dynamics of pulsed flow in an elastic tube

Internal haemorrhage, often leading to cardio-vascular arrest happens to be one of the prime sources of high fatality rates in mammals. We propose a simplistic model of fluid flow in our attempt to specify the location of the haemorrhagic spot, which, if located accurately, could possibly be operated leading to an instant cure. The model we employ for the purpose is basically fluid mechanical in origin and consists of a viscous fluid, pumped by a periodic force and flowing through an elastic tube. The analogy is with that of blood, pumped from the heart and flowing through an artery or vein. Our results, aided by graphical illustrations, match reasonably well with experimental observations.

DEA-R:ratio-based comparative efficiency model, its mathematical relation to DEA and its use in applications

We propose a new mathematical model for efficiency analysis, which combines DEA methodology with an old idea-Ratio Analysis. Our model, called DEA-R, treats all possible ratios "output/input" as outputs within the standard DEA model. Although DEA and DEA-R generate different summary measures for efficiency, the two measures are comparable. Our mathematical and empirical comparisons establish the validity of DEA-R model in its own right. The key advantage of DEA-R over DEA is that it allows effective integration of the model with experts' opinions via flexible restrictive conditions on individual "output/input" pairs. © 2007 Springer Science+Business Media, LLC.

Computer simulation of liquid flow patterns on distillation trays

This thesis describes work carried out to improve the fundamental modelling of liquid flows on distillation trays. A mathematical model is presented based on the principles of computerised fluid dynamics. It models the liquid flow in the horizontal directions allowing for the effects of the vapour through the use of an increased liquid turbulence, modelled by an eddy viscosity, and a resistance to liquid flow caused by the vapour being accelerated horizontally by the liquid. The resultant equations are similar to the Navier-Stokes equations with the addition of a resistance term.A mass-transfer model is used to calculate liquid concentration profiles and tray efficiencies. A heat and mass transfer analogy is used to compare theoretical concentration profiles to experimental water-cooling data obtained from a 2.44 metre diameter air-water distillation simulation rig. The ratios of air to water flow rates are varied in order to simulate three pressures: vacuum, atmospheric pressure and moderate pressure.For simulated atmospheric and moderate pressure distillation, the fluid mechanical model constantly over-predicts tray efficiencies with an accuracy of between +1.7% and +11.3%. This compares to -1.8% to -10.9% for the stagnant regions model (Porter et al. 1972) and +12.8% to +34.7% for the plug flow plus back-mixing model (Gerster et al. 1958). The model fails to predict the flow patterns and tray efficiencies for vacuum simulation due to the change in the mechanism of liquid transport, from a liquid continuous layer to a spray as the liquid flow-rate is reduced. This spray is not taken into account in the development of the fluid mechanical model. A sensitivity analysis carried out has shown that the fluid mechanical model is relatively insensitive to the prediction of the average height of clear liquid, and a reduction in the resistance term results in a slight loss of tray efficiency. But these effects are not great. The model is quite sensitive to the prediction of the eddy viscosity term. Variations can produce up to a 15% decrease in tray efficiency. The fluid mechanical model has been incorporated into a column model so that statistical optimisation techniques can be employed to fit a theoretical column concentration profile to experimental data. Through the use of this work mass-transfer data can be obtained.

Spray drier simulation and air flow pattern studies

The literature pertaining to the key stages of spray drying has been reviewed in the context of the mathematical modelling of drier performance. A critical review is also presented of previous spray drying models. A new mathematical model has been developed for prediction of spray drier performance. This is applicable to slurries of rigid, porous crust-forming materials to predict trajectories and drying profiles for droplets with a distribution of sizes sprayed from a centrifugal pressure nozzle. The model has been validated by comparing model predictions to experimental data from a pilot-scale counter-current drier and from a full-scale co-current drier. For the latter, the computed product moisture content was within 2%, and the computed air exit temperature within 10oC of experimental data. Air flow patterns have been investigated in a 1.2m diameter transparent countercurrent spray tower by flow visualisation. Smoke was introduced into various zones within the tower to trace the direction, and gauge the intensity, of the air flow. By means of a set of variable-angle air inlet nozzles, a variety of air entry configurations was investigated. The existence of a core of high rotational and axial velocity channelling up the axis of the tower was confirmed. The stability of flow within the core was found to be strongly dependent upon the air entry arrangement. A probe was developed for the measurement of air temperature and humidity profiles. This was employed for studying evaporation of pure water drops in a 1.2m diameter pilot-scale counter-current drier. A rapid approach to the exit air properties was detected within a 1m distance from the air entry ports. Measured radial profiles were found to be virtually flat but, from the axial profiles, the existence of plug-flow, well-mixed-flow and some degree of air short-circuiting can be inferred. The model and conclusions should assist in the improved design and optimum operation of industrial spray driers.

Analysis of the intraocular pressure pulse

This thesis was concerned with investigating methods of improving the IOP pulse’s potential as a measure of clinical utility. There were three principal sections to the work. 1. Optimisation of measurement and analysis of the IOP pulse. A literature review, covering the years 1960 – 2002 and other relevant scientific publications, provided a knowledge base on the IOP pulse. Initial studies investigated suitable instrumentation and measurement techniques. Fourier transformation was identified as a promising method of analysing the IOP pulse and this technique was developed. 2. Investigation of ocular and systemic variables that affect IOP pulse measurements In order to recognise clinically important changes in IOP pulse measurement, studies were performed to identify influencing factors. Fourier analysis was tested against traditional parameters in order to assess its ability to detect differences in IOP pulse. In addition, it had been speculated that the waveform components of the IOP pulse contained vascular characteristic analogous to those components found in arterial pulse waves. Validation studies to test this hypothesis were attempted. 3. The nature of the intraocular pressure pulse in health and disease and its relation to systemic cardiovascular variables. Fourier analysis and traditional parameters were applied to the IOP pulse measurements taken on diseased and healthy eyes. Only the derived parameter, pulsatile ocular blood flow (POBF) detected differences in diseased groups. The use of an ocular pressure-volume relationship may have improved the POBF measure’s variance in comparison to the measurement of the pulse’s amplitude or Fourier components. Finally, the importance of the driving force of pulsatile blood flow, the arterial pressure pulse, is highlighted. A method of combining the measurements of pulsatile blood flow and pulsatile blood pressure to create a measure of ocular vascular impedance is described along with its advantages for future studies.

Flow across microvessel walls through the endothelial surface glycocalyx and the interendothelial cleft

A mathematical model is presented for steady fluid flow across microvessel walls through a serial pathway consisting of the endothelial surface glycocalyx and the intercellular cleft between adjacent endothelial cells, with junction strands and their discontinuous gaps. The three-dimensional flow through the pathway from the vessel lumen to the tissue space has been computed numerically based on a Brinkman equation with appropriate values of the Darcy permeability. The predicted values of the hydraulic conductivity Lp, defined as the ratio of the flow rate per unit surface area of the vessel wall to the pressure drop across it, are close to experimental measurements for rat mesentery microvessels. If the values of the Darcy permeability for the surface glycocalyx are determined based on the regular arrangements of fibres with 6nm radius and 8nm spacing proposed recently from the detailed structural measurements, then the present study suggests that the surface glycocalyx could be much less resistant to flow compared to previous estimates by the one-dimensional flow analyses, and the intercellular cleft could be a major determinant of the hydraulic conductivity of the microvessel wall.

Multispectral fundus analysis

Purpose - To generate a reflectance model of the fundus that allows an accurate non-invasive quantification of blood and pigments. Methods - A Monte Carlo simulation was used to produce a mathematical model of light interaction with the fundus at different wavelengths. The model predictions were compared with fundus images from normal volunteers in several spectral bands (peaks at 507, 525, 552, 585, 596 and 611nm). Th e model was then used to calculate the concentration and distribution of the known absorbing components of the fundus. Results - The shape of the statistical distribution of the image data generally corresponded to that of the model data; the model however appears to overestimate the reflectance of the fundus in the longer wavelength region.As the absorption by xanthophyll has no significant eff ect on light transport above 534nm, its distribution in the fundus was quantified: the wavelengths where both shape and distribution of image and model data matched (<553nm) were used to train a neural network which was then applied to every point in the image data. The xanthophyll distribution thus found was in agreement with published literature data in normal subjects. Conclusion - We have developed a method for optimising multi-spectral imaging of the fundus and a computer image analysis capable of estimating information about the structure and properties of the fundus. Th e technique successfully calculates the distribution of xanthophyll in the fundus of healthy volunteers. Further improvement of the model is required to allow the deduction of other parameters from images; investigations in known pathology models are also necessary to establish if this method is of clinical use in detecting early chroido-retinopathies, hence providing a useful screening and diagnostic tool.