Validation of a Mathematical Model of Arterial Wall Mechanics with Drug Induced Vasoconstriction Against Ex Vivo Measurements.

Experiments on intrapulmonary arteries (IPAs) isolated from rats maintained in normoxia and chronic hypobaric hypoxia showed that in normoxia, the IPA contractile sensitivity to KCl was not modified by gap junction inhibition. In contrast, chronic hypoxia induced an endothelium-independent hypersensitivity, which was suppressed by gap junction inhibition. For the theoretical analysis of these results, we developed a model of interconnected myocytes. Given that smooth muscle cells in IPAs are known to communicate via gap junctions, we regard the cytoarchitecture of the IPA as a spatial network, in which nodes represent individual smooth muscle cells and the links signify intercellular communication. A single-cell model that drives the dynamics of individual nodes includes the major elements of voltage-dependent Ca(2+) signalling. In addition, interindividual variability of SMCs is introduced by distributing the reversal potentials for K(+). Cell-to-cell connection consists of passive Ca(2+) diffusion and electrical coupling, and connection between cells is determined by the topology of the intercellular network. Model predictions indicate that the experimental results can be explained by topological modifications and not by changes in the number of gap junctions. According to the model, in normoxia the myocytes are connected in a complex network, whereas chronic hypoxia is related to loss of complexity, leading to hypersensitivity. Our results thus indicate that chronic hypoxia entails gap junction network rearrangements, leading to disturbances in the intercellular communication pathways.

Volatile anesthetics have been shown to have vasodilating or vasoconstricting actions in vitro that may contribute to their cardiovascular effects in vivo. However, the precise mechanisms of these actions in vitro have not been fully elucidated. Moreover, there are no data regarding the mechanisms of volatile anesthetic action on small resistance arteries, which play a critical role in the regulation of blood pressure and blood flow. With the use of isometric tension recording methods, volatile anesthetic actions were studied in intact and beta-escin-membrane-permeabilized smooth muscle strips from rat small mesenteric arteries. In experiments with intact muscle, the effects of-halothane (0.25-5.0%), isoflurane (0.25-5.0%), and enflurane (0.25-5.0%) were investigated on high K(+)-induced contractions at 22 degrees C and 35 degrees C. All experiments were performed on endothelium-denuded strips in the presence of 3 microM guanethidine and 0.3 microM tetrodotoxin to minimize the influence of nerve terminal activities. In experiments with membrane-permeabilized muscle, the effects of halothane (0.5-4.0%), isoflurane (0.5-4.0%), and enflurane (0.5-4.0%) on the half-maximal and maximal Ca(2+)-activated contractions were examined at 22 degrees C in the presence of 0.3 microM ionomycin to eliminate intracellular Ca2+ stores. In the high K(+)-stimulated intact muscle, all three anesthetics generated transient contractions, which were followed by sustained vasorelaxation. The IC50 values for this vasorelaxing action of halothane, isoflurane, and enflurane were 0.47 vol% (0.27 mM), 0.66 vol% (0.32 mM), and 0.53 vol% (0.27 mM), respectively, at 22 degrees C and were 3.36 vol% (0.99 mM), 3.07 vol% (0.69 mM), and 3.19 vol% (0.95 mM), respectively, at 35 degrees C. Ryanodine (10 microM) eliminated the anesthetic-induced contractions but had no significant effect on the anesthetic-induced vasorelaxation in the presence of high K+. In addition, no significant differences were observed in the dose dependence of the direct vasodilating action among these anesthetics with or without ryanodine at either the low or the high temperature. However, significant differences were observed in the vasoconstricting actions among the anesthetics, and the order of potency was halothane > enflurane > isoflurane. The Ca(2+)-tension relation in the membrane-permeabilized muscle yielded a half-maximal effective Ca2+ concentration (EC50) of 2.02 microM. Halothane modestly but significantly inhibited 3 microM (approximately the EC50) and 30 microM (maximal) Ca(2+)-induced contractions. Enflurane slightly but significantly inhibited 3 microM but not 30 microM Ca2+ contractions. Isoflurane did not significantly inhibit either 3 microM or 30 microM Ca2+ contractions. Halothane, isoflurane, and enflurane have both vasoconstricting and vasodilating actions on isolated small splanchnic resistance arteries. The direct vasoconstricting action appears to result from Ca2+ release from the ryanodine-sensitive intracellular Ca2+ store. The vasodilating action of isoflurane in the presence of high K+ appears to be attributable mainly to a decrease in intracellular Ca2+ concentration, possibly resulting from inhibition of voltage-gated Ca2+ channels. In contrast, the vasodilating actions of halothane and enflurane in the presence of high K+ appears to involve inhibition of Ca2+ activation of contractile proteins as well as a decrease in intracellular Ca2+ concentration in smooth muscle.

A power system is a nonlinear dynamical system. Understanding the dynamic behavior of a power system is necessary for its reliable operation. An equivalent mechanical model of a power system was proposed by K. Noda to help the physical interpretation of a power system behavior obtained by a mathematical model of a power system. The validity of the mechanical model was confirmed qualitatively. This study gives the quantitative validation of the mechanical model through experiments to assess the accuracy of the analogy between the mechanical and mathematical power system models. To this end, steady-state and transient stability of a power system, which are the local and global stability, are demonstrated. The cause of error of the mechanical model is discussed and the limitation on the application of the mechanical-mathematical model analogy is provided.

1. The pharmacological actions of the purine nucleotides beta-nicotinamide adenine dinucleotide (NAD), beta-nicotinamide adenine dinucleotide phosphate (beta-NADP), adenosine 5'-diphosphoribose (ADP-ribose), the vitamin nicotinamide and structural analogues of NAD and NADP were tested in the isolated perfused mesenteric arterial bed of the rat. Prejunctional effects of NAD were tested against sympathetic vasoconstriction at basal tone, and against sensory-motor vasodilatation at raised tone. 2. NAD and NADP had no vasoconstrictor action but were weak vasodilators of the raised-tone mesenteric arterial bed. A rank order of vasodilator potency of ADP >> ADP-ribose >> NADP > or = NAD = adenosine was observed. The P1-purinoceptor antagonist, 8-para-sulphophenyltheophylline (8-pST; 3 microM) inhibited vasodilator responses to NAD (pKB of 6.61 +/- 0.21, n = 7) and adenosine (pKB of 5.78 +/- 0.14, n = 6), but not those elicited by NADP, ADP and ADP-ribose. Nicotinamide, and analogues of NAD and NADP, namely nicotinamide-1,N6-ethenoadenine dinucleotide phosphate, beta-nicotinamide mononucleotide, nicotinamide hypoxanthine dinucleotide phosphate, nicotinamide hypoxanthine dinucleotide, nicotinamide guanine dinucleotide, and nicotinamide-1, N6-ethenoadenine dinucleotide had no vasoconstrictor or vasodilator actions (at doses of up to 50 nmol). 3. At basal tone, electrical field stimulation (EFS) (32 Hz, 1ms, 90 V, 5 s) at 2 min intervals elicited reproducible vasoconstrictor responses due to activation of sympathetic nerves. NAD and adenosine (10-100 microM) inhibited these responses in a concentration-dependent manner with similar potencies. Nicotinamide had no effect on sympathetic vasoconstriction at concentrations of up to 0.1 mM. Postjunctional effects of NAD (100 microM), as tested on constrictor responses to NA (5 nmol), accounted for approximately 60% inhibition at this concentration.4. In preparations in which tone had been raised with methoxamine (10-40 microM), EFS (8 Hz, 0.1ms,60 V, for 30 s) elicited vasodilatation due to activation of sensory-motor nerves. This vasodilatation was inhibited by NAD and adenosine (O.1-100 microM) in a similar concentration-dependent manner: pD2 values were 6.2 +/- 0.10 (n = 11) and 6.1 +/- 0.15 (n = 6) for NAD and adenosine respectively. Nicotinamide had no effect on sensory-motor vasodilatation at concentrations of up to 0.1 mM.5. Inhibition of sympathetic constriction by NAD and adenosine was antagonized by 8-pSPT (3 microM).Inhibitory effects of NAD and adenosine on sensory-motor vasodilatation were similarly antagonized by 8-pSPT (1 microM), pKB values were 6.72 +/- 0.21 for NAD and 6.36 +/- 0.22 for adenosine, resulting in parallel rightward shifts in the concentration-inhibitory effect curves.6. The adenosine deaminase inhibitor, pentostatin (1 microM), augmented the inhibitory effects of NAD and adenosine. Concentration-inhibitory effect curves for NAD and adenosine on sympathetic vasoconstriction and sensory-motor vasodilatation were shifted to the left without a change in the maximum.7. It is concluded that NAD can act as a modulator of sympathetic and sensory-motor transmission in rat mesenteric arteries via P1-purinoceptors possibly via direct actions but with a contribution of adenosine formed following breakdown of NAD or released pre- and/or post junctionally. Structure activity relationships of NAD, NADP, ADP and ADP-ribose showed that the P1-purinoceptor activity of NAD is abolished after removal of nicotinamide, or ribose plus nicotinamide, to yield the structurally-related ADP-ribose and ADP respectively, or when there is phosphorylation of the 2'-hydroxyl group of NAD to yield NADP.

A mathematical model of chest wall mechanics, based on a phenomenological approach to force balances, provides a quantitative framework for analyzing many types of chest wall movements by using orthogonal displacement coordinates. The moveable components of the ventilatory system include the rib cage, diaphragm, and abdomen. A distinction is made between the lung-apposed and diaphragm-apposed actions on the rib cage. The model equations are derived from "pressure" balances and geometrical relations of the compartments; the stress-displacement relations are hyperbolic. With this model we simulated stiff and flaccid chest wall behavior under normal and constrained conditions associated with abdominal compression, a Mueller maneuver, and a diaphragmatic isometric inspiration. We also examined situations that produce paradoxical as well as orthodox inspiratory movements. The results of these simulations were quantitatively consistent with available data from the literature. A phenomenon predicted by the stiff-wall model during quasi-static inspiration is that the rib cage displacement is negligible near residual volume, but then increases dramatically with lung volume. Since this mathematical model has a sound physical basis and is more comprehensive than previous models, it can be used to predict and analyze the behavior of the chest wall under a wide variety of circumstances.

In the field of geotechnical – soft soil improvement, the mathematical model or mechanical model is one of the important input parameters for the design calculations or studies. The determination of the appropriateness of the models has a great influence on the accuracy results of design and calculation as well as the sustainable stability of soft ground after improvement. On the contrary, the selection of inadequate calculation models will lead to increased costs of soft soil improvement, possibly even leading to the destabilization of the work and causing immense loss of people and property. Recently, many projects major highway after construction design in use has not meet the requirements of the standard, leading to wasted money and time of individuals, organizations, and the state of post-treatment. Therefore, the research and application of using mathematical or mechanical models in accordance with the new soft soil improvement method will greatly help as well as add additional options for soft soil improvement in Vietnam. The soft soil deformation is not only related to load but also to load time. The change in stress and deformation of weak soil over time is called rheology, and in this study is the viscoelastic behavior. From the above reasons, we try to apply a generalized Maxwell model to explain the viscoelastic behavior of a soft soil. In particular, the time-dependent behavior of a viscoelastic soft soil was represented by using the Maxwell rheological model. The Matlab programming code helps to solve numerically all the equation of the mathematical exhibition of the generalized Maxwell model results. We acknowledge that the generalized Maxwell model is superior in demonstrating the time-dependent behavior of soft soil. The results probably show that this is one of the effective models to predict the behavior of soft soils in ground improvement with GEC.

This work performs a local sensitivity analysis on a naval vessel manoeuvring mathematical model in order to identify the relevant input parameters, the force or moment coefficients, for the relevant outputs, such as yaw rate, drift, and peak overshoot. The mathematical model is solved, and the reference results are obtained. These results are compared with those obtained in sea trials for a real naval vessel in order to calibrate the mathematical model. The perturbation is induced in the external forces in surge, sway and yaw. Using a simple metric, it is possible to find and present the relevant parameters of the mathematical model for this naval ship.

The method of microwave radiometry is one of the areas of medical diagnosis of breast cancer. It is based on analysis of the spatial distribution of internal and surface tissue temperatures, which are measured in the microwave (RTM) and infrared (IR) ranges. Complex mathematical and computer models describing complex physical and biological processes within biotissue increase the efficiency of this method. Physical and biological processes are related to temperature dynamics and microwave electromagnetic radiation. Verification and validation of the numerical model is a key challenge to ensure consistency with medical big data. These data are obtained by medical measurements of patients. We present an original approach to verification and validation of simulation models of physical processes in biological tissues. Our approach is based on deep analysis of medical data and we use machine learning algorithms. We have achieved impressive success for the model of dynamics of thermal processes in a breast with cancer foci. This method allows us to carry out a significant refinement of almost all parameters of the mathematical model in order to achieve the maximum possible adequacy.

This paper establishes two-dimensional mathematical model and three-dimensional mathematical model of the mechanical structure elastic-plastic mechanics and according to Hooke's law and Drucker postulate analyzes the plastic relationship of the elastic-plastic mechanics. The first part of the paper introduces the parameter setting of finite element analysis of elastic-plastic mechanics. The second part establishes computer simulation model of elastoplastic. Finally, it analyzes bolt force using ANSYS software and applies it to computer simulation of elastoplastic force and air resistance of gymnast in the process of action showing which provides technical reference for the training of gymnasts.

In this study, two degrees of freedom planar compliant five-bar mechanism design is explored and synthesized to achieve a desired trajectory and to perform various defined tasks. The mechanism consists of five rigid links (including the ground) connected by the compliant large deflecting short beam joints and it is excited by the applied torques at the base links. The compliant five bar mechanism has not been explored in the literature for either a path tracking task or a function generation problem. The novelty of the compliant five bar mechanism presented in this paper is its large deflecting/rotating pivots joining the mechanism links. The mathematical model of the compliant five-bar mechanism is derived by using vector loop closures and dynamic inertia equations of the mechanism links. The dynamic response of the mechanism is investigated under the applied torques to the corresponding base links, using numerical 4th order Runge-Kutta methods. Compliant joints are represented by their equivalent torsional spring parameters so that the nonlinear large deflection equations of short beam joints are eliminated from the kinematic equations of the system using its equivalent Pseudo Rigid Body Model (PRBM). The torsional spring constants can be obtained, either by using nonlinear exact mathematical equations or by using geometrically nonlinear Finite Element Method software. The scope of this research is to derive a mathematical model of the system and to analyze the compliant five bar mechanism including the controller design for arbitrary predefined tasks to achieve the desired path for the end effector. The compliant five-bar mechanisms are superior to traditional rigid five-bar mechanisms in high precision tasks since compliant joints and links have no backlash and friction. This study explores path generation of compliant five bar mechanism resulting in high precision path tracking. The presented mechanism might be manufactured as a single piece using an injection molding technique or 3D printing by polypropylene and it is also suitable for a fully compliant Micro Electro Mechanical System fabrication. The mathematical model of the mechanism is validated by utilizing inverse-forward dynamic model. The tip point of the mechanism successfully follows the reference trajectory by employing model based PID controller.

Endothelin-1 (ET-1), a 21-residue potent vasoconstrictor peptide produced by endothelial cells, was reported to cause vasodilation in the systemic and pulmonary vascular beds. Therefore, in isolated perfused lungs from 7-day-old piglets, we studied the effects and the mechanisms responsible for the dilator effect of ET-1. ET-1 produced a mild transient decrease in perfusion pressure at low doses (less than 10(-7) M/g dry lung); at higher doses, a potent long-lasting vasoconstriction was noted. Indeed, the constrictor effect of ET-1 was at least equal to or greater than that of U-44069 and prostaglandin D2 (PGD2). When the vascular tone of the preparation was increased with U-46619, another stable endoperoxide analogue, the dilator response to low doses of ET-1 was increased, while the constrictor response remained unchanged. Indomethacin (2.8 x 10(-6) M) and glybenclamide (an ATP-sensitive potassium channel inhibitor) (10(-5) M) did not alter the responses to ET-1. The endothelium-derived relaxing factor (EDRF) inhibitor Nw-nitro-L-arginine (2 x 10(-4) M) not only inhibited the dilator response to ET-1 almost completely, but also potentiated the constrictor response. Finally, Nw-nitro-L-arginine alone had a mild vasoconstrictor effect in newborn pig lung. The results of these studies indicate that ET-1 has both vasodilator and vasoconstrictor activity in neonatal pig pulmonary vascular bed. This vasodilator activity may be mediated by EDRF.(ABSTRACT TRUNCATED AT 250 WORDS)

A role for prostaglandins in the regulation of the placental blood flows

The accumulation of low-density lipoprotein (LDL) is recognized as one of the main contributors in atherogenesis. Mathematical models have been constructed to simulate mass transport in large arteries and the consequent lipid accumulation in the arterial wall. The objective of this study was to investigate the influences of wall shear stress and transmural pressure on LDL accumulation in the arterial wall by a multilayered, coupled lumen-wall model. The model employs the Navier-Stokes equations and Darcy's Law for fluid dynamics, convection-diffusion-reaction equations for mass balance, and Kedem-Katchalsky equations for interfacial coupling. To determine physiologically realistic model parameters, an optimization approach that searches optimal parameters based on experimental data was developed. Two sets of model parameters corresponding to different transmural pressures were found by the optimization approach using experimental data in the literature. Furthermore, a shear-dependent hydraulic conductivity relation reported previously was adopted. The integrated multilayered model was applied to an axisymmetric stenosis simulating an idealized, mildly stenosed coronary artery. The results show that low wall shear stress leads to focal LDL accumulation by weakening the convective clearance effect of transmural flow, whereas high transmural pressure, associated with hypertension, leads to global elevation of LDL concentration in the arterial wall by facilitating the passage of LDL through wall layers.

mathematical modeling methods. The author analyzed the problems in the field of food technology and concluded that mathematical modeling is used in the following areas: clarification of technological process modes, designing recipes and assessing the quality of finished products, as well as predicting the shelf life of new products when they are put into production. The use of dihydroquercetin as a drug that prevents the oxidation of milk fat in the design of dairy products is substantiated. Mathematical modeling was carried out on the basis of experimental and analytical material obtained in laboratory and production conditions. Based on the maximum value of the objective functions, the optimal normalized mixtures and the maximum allowable concentration of dihydroquercetin were selected. The analysis of the received mathematical dependences and models is carried out, the system of linear equations is made. Purpose: to study the effect of natural bioflavonoid antioxidant on the oxidative processes of milk fat and the viability of lactic acid cultures and their associations by mathematical modeling in order to use it in the technology of a new product; conduct an analysis of mathematical dependencies and models, compose a system of linear equations. Methods: the article uses the method of mathematical analysis and the matrix method. Results and their significance: a mathematical model was developed for the dependence of the viability of probiotic cultures on the mass fraction of dihydroquercetin when designing recipes for a creamy-protein curd product, a matrix of the chemical composition of dairy ingredients was presented, and a system of linear equations for basic recipes was compiled. In the course of the study, the spatial configurations of dihydroquercetin, as well as its effect on the oxidative processes of milk fat, were studied. Mathematical modeling of experimental data on the study of the effect of dihydroquercetin on the viability of microorganisms with probiotic properties was carried out. The normalization of the complex of obtained results on the study of the influence of the mass fraction of dihydroquercetin on the fermentation process was studied. Controlled factors characterizing the process of fermentation of model media with dihydroquercetin have been determined. A rationing of the dihydroquercetin complex of more than 0.50% was established; the target function decreases to its minimum value of 0.53 with a mass fraction of dihydroquercetin of 1.00%.

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