scholarly journals The Mathematical Basis of the Interpretation of Tracer Experiments in Closed Steady‐State Systems

1951 ◽  
Vol 22 (4) ◽  
pp. 510-520 ◽  
Author(s):  
C. W. Sheppard ◽  
A. S. Householder
Keyword(s):  
Steady State ◽  
Mathematical Basis ◽  
Tracer Experiments

scholarly journals Estimates of Michaelis-Menten Constants for the Two Membranes of the Brain Endothelium

1984 ◽  
Vol 4 (2) ◽  
pp. 241-249 ◽  
Author(s):  
Albert Gjedde ◽  
Ove Christensen
Keyword(s):  
Steady State ◽  
Endothelial Cell ◽  
Transport Properties ◽  
Glucose Transport ◽  
Cell Membranes ◽  
Experimental Studies ◽  
Facilitated Diffusion ◽  
Capillary Endothelial Cells ◽  
The Individual ◽  
Tracer Experiments

Tracer studies on facilitated diffusion across the blood–brain barrier lead to the calculation of Michaelis-Menten constants that describe the rate of transport. However, the barrier consists of two endothelial cell membranes, and the relevance of single Michaelis-Menten constants in relation to the two cell membranes is unknown. We have formulated a model of two endothelial cell membranes and show that the measured Michaelis-Menten constants are simple functions of the properties of the individual membranes when transport across the endothelium is rapid ( P1 > 10−6 cm s−1). We also show that the Michaelis-Menten constants determined in tracer experiments describe facilitated diffusion in the steady state only if the two membranes have similar transport properties. As an application of this observation, we have examined three experimental studies that measure glucose transport in the steady state and show that the Michaelis-Menten constants for glucose transport calculated from the tracer experiments are equal to the constants calculated from the steady-state experiments. We conclude that the luminal and abluminal membranes of brain capillary endothelial cells have equal glucose transport properties.

Transport of bromide in the Bainsvlei soil: Field experiment and deterministic/stochastic model simulation. II. Intermittent water application

Soil Research ◽  
2005 ◽  
Vol 43 (1) ◽  
pp. 81 ◽  
Author(s):  
Ketema Tilahun ◽  
J. F. Botha ◽  
A. T. P. Bennie
Keyword(s):  
Steady State ◽  
Model Simulation ◽  
Soil Core ◽  
Water Fluxes ◽  
Water Application ◽  
Concentration Data ◽  
Average Pore ◽  
Continuous Application ◽  
Average Dispersion ◽  
Tracer Experiments

Despite the fact that non-uniform soil water content and variable input water fluxes are usually encountered in the field, tracer experiments have usually been carried out under steady-state conditions. The objective of this study was to analyse solute transport in a Bainsvlei soil under intermittent water application using Br– as a tracer. Sprinkler was used to apply water on a plot 200 by 200 cm. Soil core samples were taken every 20 cm to a depth of 160 cm several times during the experiment. The soil Br– concentration data were fitted to the steady-state convection–dispersion analytical model in the CXTFIT package. The average coefficients of determination yielded by this fit (r2 = 0.810) clearly support that the data could be analysed successfully with CXTFIT. The average pore-water velocity of 1.72 cm/day and average dispersion coefficient of 26.19 cm2/day determined from this fit are lower than the fitted values of the steady-state experiments. The Br– moved slower under the intermittent application of water than in the steady case, a conclusion supported by the deeper location of Br– peaks under continuous application than intermittent application after the same amount of water is applied.

scholarly journals Simulation of TiN/HfO2/Pt memristor I–V curve for different conductive filament thickness

2021 ◽  
Vol 7 (2) ◽  
pp. 45-51
Author(s):  
Andrey N. Aleshin ◽  
Nikolay V. Zenchenko ◽  
Oleg A. Ruban
Keyword(s):  
Steady State ◽  
Oxygen Vacancy ◽  
Energy Output ◽  
Cylindrical Shape ◽  
State Equations ◽  
Conductive Filament ◽  
Mathematical Basis ◽  
Bipolar Mode ◽  
Vacancy Flux ◽  
Quantitative Calculations

The operation of the TiN/HfO2/Pt bipolar memristor has been simulated by the finite elements method using the Maxwell steady state equations as a mathematical basis. The simulation provided knowledge of the effect of conductive filament thickness on the shape of the I–V curve. The conductive filament has been considered as the highly conductive Hf ion enriched HfOx phase (x < 2) whose structure is similar to a Magneli phase. In this work a mechanism has been developed describing the formation, growth and dissolution of the HfOx phase in bipolar mode of memristor operation which provides for oxygen vacancy flux control. The conductive filament has a cylindrical shape with the radius varying within 5–10 nm. An increase in the thickness of the conductive filament leads to an increase in the area of the hysteresis loop of the I–V curve due to an increase in the energy output during memristor operation. A model has been developed which allows quantitative calculations and hence can be used for the design of bipolar memristors and assessment of memristor heat loss during operation.

scholarly journals Identifiability of Regional Fluxes From Steady State Tracer Experiments

1997 ◽  
Vol 30 (2) ◽  
pp. 243-246
Author(s):  
Daniele Seno ◽  
Gianna Toffolo ◽  
Claudio Cobelli
Keyword(s):  
Steady State ◽  
Regional Fluxes ◽  
Tracer Experiments

Estimation of steady-state flux rates in metabolic systems by computer simulations of radioactive tracer experiments

1993 ◽  
Vol 9 (5) ◽  
pp. 573-580
Author(s):  
Hermann-George Holzhütter ◽  
Anke Schwendel ◽  
Tilman Grune ◽  
Jörn Quedenau ◽  
Werner Siems
Keyword(s):  
Steady State ◽  
Computer Simulations ◽  
Radioactive Tracer ◽  
Steady State Flux ◽  
Metabolic Systems ◽  
Tracer Experiments

scholarly journals SPECIALIZED SYMBOLIC COMPUTATION FOR STEADY STATE PROBLEMS

2013 ◽  
Vol 3 (1) ◽  
pp. 5-8
Author(s):  
Marcin Sowa
Keyword(s):  
Steady State ◽  
Programming Languages ◽  
Symbolic Computation ◽  
Optimal Algorithm ◽  
Operation Time ◽  
Mathematical Basis ◽  
Calculation Time ◽  
Implementation Scheme ◽  
Made In

An implementation of symbolic computation for steady state problems is proposed in the paper. A mathematical basis is derived in order to specify the quantities that the implementation will concern. An analysis is performed so that an optimal algorithm can be chosen in terms of the two chosen criteria – the operation time and memory needed to store symbolic expressions. The implementation scheme of the specialized class for symbolic computation is presented with the use of a general figure and by an example. The implementation is made in C++ but the presented idea can also be applied in other programming languages that share similar properties. A program using the proposed algorithm was studied for its efficiency in terms of calculation time and memory used by symbolic expressions. This is made by comparing the calculations made by the author’s program with those made by a script written in Mathematica.

scholarly journals Stochastic Chaos and Markov Blankets

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1220
Author(s):  
Karl Friston ◽  
Conor Heins ◽  
Kai Ueltzhöffer ◽  
Lancelot Da Da Costa ◽  
Thomas Parr
Keyword(s):  
Steady State ◽  
Functional Form ◽  
Lorenz System ◽  
State Density ◽  
Mathematical Basis ◽  
Stochastic Chaos ◽  
Internal States ◽  
The Lorenz System ◽  
Polynomial Expansions ◽  
Markov Blankets

In this treatment of random dynamical systems, we consider the existence—and identification—of conditional independencies at nonequilibrium steady-state. These independencies underwrite a particular partition of states, in which internal states are statistically secluded from external states by blanket states. The existence of such partitions has interesting implications for the information geometry of internal states. In brief, this geometry can be read as a physics of sentience, where internal states look as if they are inferring external states. However, the existence of such partitions—and the functional form of the underlying densities—have yet to be established. Here, using the Lorenz system as the basis of stochastic chaos, we leverage the Helmholtz decomposition—and polynomial expansions—to parameterise the steady-state density in terms of surprisal or self-information. We then show how Markov blankets can be identified—using the accompanying Hessian—to characterise the coupling between internal and external states in terms of a generalised synchrony or synchronisation of chaos. We conclude by suggesting that this kind of synchronisation may provide a mathematical basis for an elemental form of (autonomous or active) sentience in biology.

MATHEMATICAL ANALYSIS FOR THE INTERPRETATION OF IN VIVO TRACER INFUSION EXPERIMENTS

1972 ◽  
Vol 68 (2_Supplb) ◽  
pp. S26-S43 ◽  
Author(s):  
Erlio Gurpide
Keyword(s):  
Single Injection ◽  
Isotopic Data ◽  
Mathematical Basis ◽  
Hormone Research ◽  
Data Rates ◽  
Metabolic Reactions ◽  
Formal Procedures ◽  
Tracer Experiments ◽  
Schematic Form

ABSTRACT In vivo tracer experiments involving intravenous infusion of 1, 2 or 3 labelled hormones are described in schematic form. Formulae are provided to calculate from steady state isotopic data, rates of production and interconversion of circulating compounds, foeto-maternal production and transfer of hormones and rates of metabolic reactions occurring in an organ. Formal procedures to convert these formulae to expressions applicable to single injection experiments are outlined. The simplicity of the mathematical basis for the interpretation of most current experiments in hormone research is emphasized.

Analysis of steady-state carbon tracer experiments using akaike information criteria

Metabolomics ◽  
2021 ◽  
Vol 17 (7) ◽  
Author(s):  
Jeffry R. Alger ◽  
Abu Minhajuddin ◽  
A. Dean Sherry ◽  
Craig R. Malloy
Keyword(s):  
Steady State ◽  
Information Criteria ◽  
Akaike Information Criteria ◽  
Tracer Experiments
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