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How Does the Slow Injection of a Medicine under the Influence of a Magnetic Field Affects the Spreading of Medical Substances

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Journal of Applied Mathematics and Physics 2021年第12期9卷 3115-3121页

作者： N. G. Gulko I. T. Selezov Department of Mathematics Ben-Gurion University of the Negev Beer-Sheva Israel Institute of Hydromechanics NAS of Ukraine Kiev Ukraine

The problem of excitation and the propagation of a nerve impulse by an axon (nerve fiber) for the case of a noninstantaneous function is studied. The application of no instantaneous step function of the heaviside type takes into account the time of delay. This generalizes the problem of the propagation of axon excitation to the case of an input impulse function’s noninstantaneous action with some increasing excitation. An exact analytical solution to the problem is constructed based on the Laplace integral transform and Ephros theorem. The propagation of the transmembrane potential was studied, in response to the switching on and off, for impulse of a constant current pulse delivered intracellularly at different points in time. The time analysis of excitation propagation along axon at different distances from the excitation point was performed.

关键词： Noninstantaneous Excitation heaviside function Transmembrane Potential Ephros Theorem Laplace Transform

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Real-Time Analytical Solutions as Series Formulas and heaviside off/on Switch functions for Multiple Intermittent Intravenous Infusions in One- and Two-Compartment Models

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Journal of Biosciences and Medicines 2022年第1期10卷 150-189页

作者： Michalakis Savva South University Savannah USA

Pharmacokinetic compartment models are the only models that can extract pharmacokinetic parameters from data collected in clinical studies but their estimates lack accuracy, explanations and physiological significance. The objective of this work was to develop particular solutions to drug concentration and AUC in the form of mathematical series and heaviside functions for repetitive intermittent infusions in the one- and two-compartment models, as a function of dose number and total time using differential calculus. It was demonstrated that the central and peripheral compartment volumes determined from regression analysis of the aminoglycoside antibiotic Sisomicin concentration in plasma represent the actual physiological body fluid volumes accessible by the drug. The drug peak time and peak concentration in the peripheral compartment were also calculated as a function of dose number. It is also shown that the time of intercompartmental momentary distribution equilibrium can be used to determine the drug’s apparent volume of distribution within any dosing interval in multi-compartment models. These estimates were used to carry out simulations of plasma drug concentration with time in the one-compartment model. In conclusion, the two-compartment open mammillary pharmacokinetic model was fully explained for the aminoglycoside antibiotic sisomicin through the new concept of the apparent volume of distribution.

关键词： Pharmacokinetics Intermittent Intravenous Infusion Multiple Doses Compartment Models heaviside function Apparent Volume of Distribution

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