The Action Potential simulated by Mass Action Law Modelación de Potenciales de Acción generados mediante la Ley de Acción de Masas

En este trabajo se presenta un modelo matemático para potenciales de acción (PA), similar al modelo de Hodgkin y Huxley, utilizando la Ley de Acción de Masas para determinar las corrientes iónicas que atraviesan la membrana en cada célula excitable. Este modelo permite visualizar que la cinética de los canales iónicos (las velocidades de transición de un estado a otro), determina el curso temporal de las corrientes. Además, resalta que los tipos y la intensidad de las corrientes activadas en la membrana celular, determinan la morfología de los PA. Por lo anterior, a cada potencial de acción se le asociaron corrientes iónicas especificas, con esta condición, el modelo generó un sistema de ecuaciones diferenciales cuya solución es la función V=V(t), los resultados mostraron que esta función simula a los PA registrados experimentalmente.

Macroscopic currents of ionic channels using Mass Action Law: A mathematical model

In this work it proposes a mathematical model for ion channels based on two concepts, the Hodgkin and Huxley's as well as the Law of Mass Action in addition, we consider the kinetics of channels as a dynamic process of Markov`s chain. With the previous premises, a system of differential equations is proposed that when it is solved, all properties of the macroscopic currents are determined. The activation, deactivation, inactivation, and recovery of the inactivation concepts remain as processes that are part of a chemical reaction. With this system of equations, all the experimental protocols used in electrophysiology to characterize macroscopic currents can be modeled. Another advantage is that the model allows, with the same system of equations, to determine the properties of voltage-dependent channels regardless of the type of ion that pass through in the channel.

Thermodynamic Analysis and Experimental Investigation of Al and F Removal from Sulfuric Acid Leachate of Spent LiFePO4 Battery Powder

The co-precipitation thermodynamics of the Li+–Fe2+/Fe3+–Al3+–F−–SO42−–PO43−–H2O system at 298 K is studied, aiming to understand the precipitation characteristics. Based on the principle of simultaneous equilibrium and the mass action law, the missing Ksp values of AlF3 and FeF3 were estimated. The results of thermodynamic calculation demonstrate that Al3+ and F− in the sulfuric acid leachate could be preferentially precipitated in the form of AlPO4 and FeF3 by the precise adjustment of the final pH value. Only a small amount of P and Fe was lost by the precipitation of Fe3(PO4)2·8H2O, FePO4, and Fe(OH)3 during the purification process. Controlling the oxidation of ferrous ions effectively is of critical significance for the loss reduction of P and Fe. Precipitation experiments at different pH value indicated that the concentration of Al3+ and F− in the leachate decreased as the final pH value rose from 3.05 to 3.90. When the final pH value was around 3.75, aluminum and fluoride ion impurities could be deeply purified, and the loss rate of phosphate ions and iron ions could be reduced as much as possible. Relevant research results can provide theoretical guidance for the purification of leachate in the wet recycling process of lithium-ion batteries.

A Delay Differential Equation approach to model the COVID-19 pandemic

SEIR (Susceptible - Exposed - Infected - Recovered) approach is a classic modeling method that has frequently been applied to the study of infectious disease epidemiology. However, in the vast majority of SEIR models and models derived from them transitions from one population group to another are described using the mass-action law which assumes population homogeneity. That causes some methodological limitations or even drawbacks, particularly inability to reproduce observable dynamics of key characteristics of infection such as, for example, the incubation period and progression of the disease's symptoms which require considering different time scales as well as probabilities of different disease trajectories. In this paper, we propose an alternative approach to simulate the epidemic dynamics that is based on a system of differential equations with time delays to precisely reproduce a duration of infectious processes (e.g. incubation period of the virus) and competing processes like transition from infected state to the hospitalization or recovery. The suggested modeling approach is fundamental and can be applied to the study of many infectious disease epidemiology. However, due to the urgency of the COVID-19 pandemic we have developed and calibrated the delay-based model of the epidemic in Germany and France using the BioUML platform. Additionally, the stringency index was used as a generalized characteristic of the non-pharmaceutical government interventions implemented in corresponding countries to contain the virus spread. The numerical analysis of the calibrated model demonstrates that adequate simulation of each new wave of the SARS-CoV-2 virus spread requires dynamic changes in the parameter values during the epidemic like reduction of the population adherence to non-pharmaceutical interventions or enhancement of the infectivity parameter caused by an emergence of novel virus strains with higher contagiousness than original one. Both models may be accessed and simulated at https://gitlab.sirius-web.org/covid-19/dde-epidemiology-model utilizing visual representation as well as Jupyter Notebook.

Study of Reversible Platelet Aggregation Model by Nonlinear Dynamics

Blood cell platelets form aggregates upon vessel wall injury. Under certain conditions, a disintegration of the platelet aggregates, called “reversible aggregation”, is observed in vitro. Previously, we have proposed an extremely simple (two equations, five parameters) ordinary differential equation-based mathematical model of the reversible platelet aggregation. That model was based on mass-action law, and the parameters represented probabilities of platelet aggregate formations. Here, we aimed to perform a nonlinear dynamics analysis of this mathematical model to derive the biomedical meaning of the model’s parameters. The model’s parameters were estimated automatically from experimental data in COPASI software. Further analysis was performed in Python 2.7. Contrary to our expectations, for a broad range of parameter values, the model had only one steady state of the stable type node, thus eliminating the initial assumption that the reversibility of the aggregation curve could be explained by the system’s being near a stable focus. Therefore, we conclude that during platelet aggregation, the system is outside of the influence area of the steady state. Further analysis of the model’s parameters demonstrated that the rate constants for the reaction of aggregate formation from existing aggregates determine the reversibility of the aggregation curve. The other parameters of the model influenced either the initial aggregation rate or the quasi-steady state aggregation values.

SETTING UP A PROBLEM OF AIR-BORNE SOUND IN-SULATION CALCULATION FOR DOUBLE LAYER MASSIVE ENCLOSURES ON THE BASE OF THE MODELS WITH THE CONCENTRATED PARAMETERS

The calculation methods on the base of the concentrated parameters models, which were formed in the XX century, allowed to get simple and theoretically consistent solutions for the problems of one-layered building partitions sound insulation finding. The sound insulation estimation for the double-layered massive building partitions also is of scientific and practical interest, as double layer partitions are the particular case of the single layer enclosure's application. The concept of concentrated parameters includes the concentrated and the reduced masses, as well as the concentrated elasticity. The criteria for the object application as a specified kind of the concentrated parameters in the acoustical problems is the presence or the absence of the oscillation movement in it. The three calculation models with the application of the concentrated (discreet) parameters that to define the sound insulation of the massive double layer enclosures are given. The equations for sound insulation computation for one layer partition are represented. They were derived on the base of momentum law and energy conservation formulas under the continuity of energy flow conditions at the interface of different media. The three main paths of sound propagation from the room with the air-borne noise to the isolated room are shown. The two frequency range are separated on the way of the direct sound propagation: at the first, the surface density of the one of two layers and the air elasticity in the inter-layer gap influence on isolation; at the second one, the predominant role belongs to the summarized insulation by the "Mass Action Law" of the two layers. The indirect way's insulation is taken in account through the additional sound insulation graph drawing. The compound insulation curve is defined by the ways, where the sound energy transmittance is maximal at the standard frequency spectrum. The method of sound insulation calculation for the double layer partitions on the base of the concentrated parameters model application is revealed. As an example, the calculation of a prefabricated double layer inter-flat wall in the panel building was performed.

Mercury Removal from Aqueous Solution Using ETS-4 in the Presence of Cations of Distinct Sizes

The removal of the hazardous Hg2+ from aqueous solutions was studied by ion exchange using titanosilicate in sodium form (Na-ETS-4). Isothermal batch experiments at fixed pH were performed to measure equilibrium and kinetic data, considering two very distinct situations to assess the influence of competition effects: (i) the counter ions initially in solution are Na+ and Hg2+ (both are exchangeable); (ii) the initial counter ions in solution are tetrapropylammonium (TPA+) and Hg2+ (only Hg2+ is exchangeable, since TPA+ is larger than the ETS-4 micropores). The results confirmed that ETS-4 is highly selective for Hg2+, with more than 90% of the mercury being exchanged from the fluid phase. The final equilibrium attained under the presence of TPA+ or Na+ in solution was very similar, however, the Hg2+/Na+/ETS-4 system in the presence of Na+ required more 100 h to reach equilibrium than in the presence of TPA+. The Hg2+/Na+/ETS-4 system was modelled and analyzed in terms of equilibrium (mass action law) and mass transfer (Maxwell–Stefan (MS) formalism). Concerning equilibrium, no major deviations from ideality were found in the range of studied concentrations. On the other hand, the MS based model described successfully (average deviation of 5.81%) all kinetic curves of mercury removal.