Mathematical model of bilirubin transport

The mathematical model of the bilirubin transport through liver is suggested. The model is sufficiently reflects the peculiarities of the bilirubin behavior under the different physiological conditions. The model is described by the system of difference-differential equations. The coefficients of the intensity of bilirubin transfer in normal liver are calculated.     

Mathematical modeling of thermal stresses in basic oxygen furnace hood tubes

The stress-strain history of Basic Oxygen Furnace hood tubes during thermal cycling has been computed using heat flow and stress analyses. The steady-state temperature distribution in a transverse section of the tube was computed at a location where gas temperature in the hood could be expected to be a maximum. Calculations were performed for peak gas temperatures in the range 1950 to 2480 °C (3500 to 4500 °F). The stress-strain history of an element of material located at the center of the tube hot face was traced for three consecutive cycles using elasto-plastic finite-element analysis. It has been shown that the state of stress in the element alternates between compression and tension as the tube successively heats and cools. Yielding and plastic flow occurs at the end of each half of a given cycle. It was postulated that owing to repctitive yielding, plastic strain energy accumulates causing failure of the tubes by fatigue in the low cycle region. Using fatigue theory a conservative estimate for tube life was arrived at. In-plant observations support this mechanism of failure, and the number of cycles within which tube cracking was observed compares reasonably with model predictions. Utilizing the heat flow and stress models it was recommended that tube life could be enhanced by changing the tube material to ARMCO 17-4 pH or AISI 405 steel or alternatively reconstructing hoods with AISI 316L tubes of reduced thickness. These recommendations were based on the criterion that low-cycle fatigue failure could be averted if the magnitude of the cyclic strain could be reduced or if macroscopic plastic flow could be prevented.     

Mathematical models of purine metabolism in man

The tachykinin NK1 receptor is widely distributed in both the central and peripheral nervous system. In the CNS, NK1 receptors have been implicated in various behavioural responses and in regulating neuronal survival and degeneration. Moreover, central NK1 receptors regulate cardiovascular and respiratory function and are involved in activating the emetic reflex. At the spinal cord level, NK1 receptors are activated during the synaptic transmission, especially in response to noxious stimuli applied at the receptive field of primary afferent neurons. Both neurophysiological and behavioural evidences support a role of spinal NK1 receptors in pain transmission. Spinal NK1 receptors also modulate autonomic reflexes, including the micturition reflex. In the peripheral nervous system, tachykinin NK1 receptors are widely expressed in the respiratory, genitourinary and gastrointestinal tracts and are also expressed by several types of inflammatory and immune cells. In the cardiovascular system, NK1 receptors mediate endothelium-dependent vasodilation and plasma protein extravasation. At respiratory level, NK1 receptors mediate neurogenic inflammation which is especially evident upon exposure of the airways to irritants. In the carotid body, NK1 receptors mediate the ventilatory response to hypoxia. In the gastrointestinal system, NK1 receptors mediate smooth muscle contraction, regulate water and ion secretion and mediate neuro-neuronal communication. In the genitourinary tract, NK1 receptors are widely distributed in the renal pelvis, ureter, urinary bladder and urethra and mediate smooth muscle contraction and inflammation in response to noxious stimuli. Based on the knowledge of distribution and pathophysiological roles of NK1 receptors, it has been anticipated that NK1 receptor antagonists may have several therapeutic applications at central and peripheral level. At central level, it is speculated that NK1 receptor antagonists could be used to produce analgesia, as antiemetics and for treatment of certain forms of urinary incontinence due to detrusor hyperreflexia. In the peripheral nervous system, tachykinin NK1 receptor antagonists could be used in several inflammatory diseases including arthritis, inflammatory bowel diseases and cystitis. Several potent tachykinin NK1 receptor antagonists are now under evaluation in the clinical setting, and more information on their usefulness in treatment of human diseases will be available in the next few years.     

Mathematical models for nonparametric inferences from line transect data

A general mathematical theory of line transects is develoepd which supplies a framework for nonparametric density estimation based on either right angle or sighting distances. The probability of observing a point given its right angle distance (y) from the line is generalized to an arbitrary function g(y). Given only that g(O) = 1, it is shown there are nonparametric approaches to density estimation using the observed right angle distances. The model is then generalized to include sighting distances (r). Let f(y/r) be the conditional distribution of right angle distance given sighting distance. It is shown that nonparametric estimation based only on sighting distances requires we know the transformation of r given by f(O/r).     

Mathematical modelling of drug transport in emulsion systems

Two mathematical models for the prediction of drug transport in triphasic (oil, water and micellar) emulsion systems as a function of micellar concentration have been developed and these models were evaluated by comparing experimental and simulated data. Fick's first law was used to derive a transport model for hydrophilic drugs, assuming that the oil/water (o/w) partitioning process was fast compared with membrane transport and therefore drug transport was limited by the membrane. Consecutive rate equations were used to model transport of hydrophobic drugs in emulsion systems assuming that the o/w interface acts as a barrier to drug transport. Benzoic acid and phenol were selected as hydrophilic model drugs. Phenylazoaniline and benzocaine were selected as hydrophobic model drugs. Transport studies at pH 3.0 and 7.0 were conducted using side-by-side diffusion cells. According to the hydrophilic model, an increase in micellar concentration is expected to decrease drug transport rates. The effective permeability coefficients (Peff) of drugs were calculated using an equation relating Peff and the total apparent volume of drug distribution (determined experimentally using drug/membrane permeability and partition coefficient values). The hydrophobic model was fitted to the experimental data for the cumulative amount of model drug in the receiver cells using a weighted least-squares estimation program (PCNONLIN). The oil/continuous phase partitioning rates (k1) and the membrane transport rates (k2) were estimated. The goodness of fit was assessed from the correlation coefficients of plots of predicted versus experimental data. The predicted data were consistent with the experimental data for both the hydrophilic and hydrophobic models.     

Mathematical models of current losses in bipolar cells

A thorough study of current losses in bipolar cells has been made for the development of the great energy-saving potential of bipolar cells. A proper equivalent circuit for bipolar cells has been proposed, and mathematical methods for computing current losses for all types of polar-ization have been developed. For linear polarization, the current losses can be computed by solving either a tridiagonal matrix or a second-order ordinary differential equation. These values can be used to evaluate the minimum current losses at given conditions. For other kinds of polarization, the current losses can be computed by similar methods if the necessary experiments of measuring the cell voltages of each electrolytic compartment have been made. These values can be used to design practical bipolar cells. Extensive experiments have been made to evaluate the effects of electrode polarization, electromotive force (emf) of the galvanic cell for the for-mation of electrolyzed substance, gaseous products, geometric dimensions of electrolytic cells, specific resistance of electrolyte used, and the total and ordinal number of electrolytic com-partments on current losses. This was the first time such systematic experimental research had been undertaken. Experiments showed that theoretical models were in good agreement with measured data and that DC energy consumption of 0.45 kwh/kg Pb for lead electrolysis from molten chlorides could be achieved in a cell with seven bipolar electrodes. GUANGWEN ZHAO, Visiting Professor, Department of Materials Science and Metallurgy, University of Cambridge, Cambridge, United Kingdom     

Mathematical model of oxygen transport in the cerebral cortex

To estimate the magnitude of hyperemia necessary to support oxidative metabolism in the cerebral cortex during functional activation, a mathematical model of O2 transport from capillary to tissue was developed. Radial and axial gradients of O2 pressure in tissue surrounding a single capillary were calculated at normal and increased cerebral metabolic rates for O2. Cone-shaped tissue geometry and nonlinear oxyhemoglobin dissociation were assumed. Local O2 consumption was assumed to be supported with local tissue pO2 greater than 1 mmHg. The distribution of tissue pO2 was also calculated during moderate hypoxemia (paO2=42 mmHg), using experimental values of red blood cell velocity measured in individual capillaries of the rat cerebral cortex using intravital video-microscopy. The model predicted that moderate increases (相似文献   

Mathematical models of Haemophilus influenzae type b

Electron microscopic anterograde autoradiography has been used to analyze the morphology and postsynaptic relationships of area 17 cortical terminals in the lateral division of the lateral posterior nucleus (LPl) of the cat and medial division of the inferior pulvinar nucleus (IPm) of the owl monkey. Such terminals are thought to arise exclusively from layer 5 in the cat and primate (Lund et al. [1975] J. Comp. Neurol. 164:287-304; Abramson and Chalupa [1985] Neuroscience 15:81-95). All labeled terminals in both nuclei exhibited the morphology of ascending "lemniscal" afferents. That is, they contained round vesicles, were large, made asymmetrical synaptic and filamentous nonsynaptic contacts, and were classified as RLs. These cortical RLs also exhibited the postsynaptic relationships of lemniscal afferents. Thus, they were presynaptic to large dendrites within glial encapsulated glomeruli, where a majority was involved in complex synaptic arrangements called triads. They also were found adjacent to terminal profiles with pleomorphic vesicles but never adjacent to small terminals containing round vesicles. Our results suggest that the layer 5 projection from area 17 provides a functional "drive" for some LPl and IPm neurons. Information carried over this "re-entrant" pathway (Guillery [1995] J. Anat. 187:583-592) could be modified within the LPl and IPm by both cortical and subcortical pathways and subsequently conveyed to higher visual cortical areas, where it could be integrated with messages carried through the well-documented corticocortical pathways (Casagrande and Kaas [1994] Cerebral cortex New York: Plenum Press).     

Mathematical models of diffusion-limited gas bubble dynamics in tissue

Mathematical models of bubble evolution in tissue have recently been incorporated into risk functions for predicting the incidence of decompression sickness (DCS) in human subjects after diving and/or flying exposures. Bubble dynamics models suitable for these applications assume the bubble to be either contained in an unstirred tissue (two-region model) or surrounded by a boundary layer within a well-stirred tissue (three-region model). The contrasting premises regarding the bubble-tissue system lead to different expressions for bubble dynamics described in terms of ordinary differential equations. However, the expressions are shown to be structurally similar with differences only in the definitions of certain parameters that can be transformed to make the models equivalent at large tissue volumes. It is also shown that the two-region model is applicable only to bubble evolution in tissues of infinite extent and cannot be readily applied to bubble evolution in finite tissue volumes to simulate how such evolution is influenced by interactions among multiple bubbles in a given tissue. Two-region models that are incorrectly applied in such cases yield results that may be reinterpreted in terms of their three-region model equivalents but only if the parameters in the two-region model transform into consistent values in the three-region model. When such transforms yield inconsistent parameter values for the three-region model, results may be qualitatively correct but are in substantial quantitative error. Obviation of these errors through appropriate use of the different models may improve performance of probabilistic models of DCS occurrence that express DCS risk in terms of simulated in vivo gas and bubble dynamics.     

浅析冶金运输企业汽车单车管理模式的选用

1 汽车单车管理是冶金运输的基础工作 单车管理是冶金汽车运输企业内一项最重要、最基本的基础工作。企业经营效益的高低,成本控制的实现与否,运输质量的优劣,设备技术状况的好坏,无不直接反映在单车管理上。随着整个社会市场竞争的加剧和冶金企业深化内部机制改革工作不断加快,使得汽车运输企业的内外部环境发生了深刻     

Mathematical modelling of peristaltic transport of a non-Newtonian fluid

The paper considers the phenomena of peristaltic transport of a non-Newtonian fluid represented as a power law fluid. The governing equations are the modified Navier-Stokes equations and the continuity equation in axisymmetric form. A solution is sought in terms of a perturbation series and it is shown the close proximity between analytical and numerical solutions when considering stream functions for various values of the flow behaviour index.     

Mathematical models for calculation of the electrochemical protection parameters of pipelines from electrochemical measurements

A mathematical model is proposed to calculate the transition resistance of anticorrosion coatings on a system of main pipelines in terms of the potential difference between the pipeline and soil surface, and the current along the line. A method to determine the optimum conditions for operating a cathodic protection system was devised. Values of the protection parameters of a pipeline calculated with the aid of a program developed on the basis of the proposed model are tabulated.Institute of Materials Science, Ukrainian Academy of Sciences, Kiev. Translated from Poroshkovaya Metallurgiya, Nos. 7/8(380), pp. 128–135, July–August, 1995.     

Mathematical and connectionist models of human memory: a comparison

Recent convolution-based models of human memory (e.g. Lewandowsky & Murdock, 1989), have accounted for a wide range of data. However such models require the relevant mathematical operations to be provided to the network. Connectionist models, in contrast, have generally addressed different data, and not all architectures are appropriate for modelling single-trial learning. Furthermore, they tend to exhibit catastrophic interference in multiple list learning. In this paper we compare the ability of convolution-based models and DARNET (Developmental Associative Recall NETwork), to account for human memory data. DARNET is a connectionist approach to human memory in which the system gradually learns to associate vectors, in one trial, into a memory trace vector. Either of the vectors can than be retrieved. It is shown that the new associative mechanism can be used to account for a wide range of relevant experimental data as successfully as can convolution-based models with the same higher-level architectures. Limitations of the models are also addressed.