Zero-order Equations Research Articles

Mechanism of Cell-Mediated Cytotoxicity at the Single Cell Level

Abstract The kinetics and rate of T cell-mediated cytolysis was assessed by measuring the times required for lysis of isolated target cells by single cytotoxic lymphocytes. Single target cell lysis was determined microscopically by observing trypan blue uptake as a function of time of incubation of effector-target conjugates in agarose. Lysis of EL-4 target cells by alloimmune peritoneal exudate lymphocytes was initiated without a lag and was essentially complete at 2 hr. Both zero-order and first-order kinetics equations were analyzed for fit to the 0 to 2 hr lysis values. Statistically, the zero-order kinetic function could be rejected (p > 0.05), but the first-order kinetics function (p < 0.01) could not. This strong evidence for first-order kinetics of T cell-mediated cytolysis implies that within each CTL-target cell population, cytolysis occurs exponentially as a random decay process and that one event in the entire process of cytolysis is rate limiting. The first-order equation was then applied to measurements of the rate of cytolysis in many different individual effector-target cell combinations. Significant differences in the lytic rate were apparent when either the effector or target cells were varied, with the rate constants spanning a 5-fold range. The heterogeneity of lytic rates is consistent with the hypothesis that lytic efficiency is a function of both the effector and target cells used.

Dynamics of stationary ultra-long waves in middle latitudes

The dynamics of stationary ultra-long waves in middle latitudes are studied using a set of approximate linear equations for small perturbations about a zonal flow. the equations are derived by an expansion procedure based on the assumptions of planetary scales of variation and small mean superrotation. the zero-order equations reduce to a vertical structure equation containing no meridional derivatives. Analytical solutions are obtained for forced stationary waves in a model atmosphere consisting of three continuous layers, representing the troposphere, the lower stratosphere and the upper stratosphere. The waves are generated by thermal and topographic forcing in the model troposphere and propagate wave energy at zonal wavenumbers 1 and 2 into the upper stratosphere, where they are damped by Newtonian cooling. General relationships are found involving the zero-order fluxes of sensible heat and wave energy. These greatly clarify the dynamics of the waves, particularly in the lower stratospheric layer which links the regions of generation and dissipation. Taking realistic values of the parameters for northern middle latitudes in winter, the solutions for wavenumbers 1 and 2 show good agreement with observation. an examination of the sensitivity of the solution to changes in various model parameters shows that the meridional flux of heat by ultra-long waves in the troposphere is extremely sensitive to changes in the stratospheric wind profile and static stability. Since these waves are known observationally to account for a large fraction of the total poleward heat transport in northern middle latitudes in winter, a dynamical mechanism is suggested whereby variations in solar ultraviolet radiation or changes in the ozone content of the upper atmosphere could lead to climate change.

Development of Salbutamol Sulphate Sustained Release Pellets Using Acrylic Polymer and Polyvinyl Acetate Polymer and Evaluation of <i>In vitro</i> Release Kinetics

The nuclei of sustained-release pellets of salbutamol sulphate were prepared using extrusionspheronization technique followed by coating with the aqueous dispersion of methacrylic acid esters (Eudragit RS® 30 D) and commercial aqueous polyvinyl acetate dispersion (30% dispersion) (Kollicoat SR® 30 D). The coating polymers were applied to obtain a theoretical polymer load of 5%, 10%, 15%, 20% & 25 %( w/w) on the nuclei. Invitro dissolution studies of the coated pellets were performed in a USP paddle apparatus (type-2). Dissolution media was distilled water (500 ml), paddle speed was 50 rpm and it was preformed for 8 hours at 37°C (±0.5°C) temperature. Scanning Electron Micrographs (SEMs) of the nuclei & coated pellets were taken to study their surface morphology. The kinetics of the dissolution process was determined by analyzing the dissolution data using zeroorder, first order, Higuchi and Korsmeyer equations. The kinetic modeling of the dissolution profiles revealed that drug release mechanism ranged from diffusion controlled or Fickian transport to anomalous type or non-Fickian transport. T50% (MDT) and T90% values were calculated for each formulation. The higher MDT values were obtained with Eudragit® RS 30D where as Kollicoat® SR 30D showed comparatively low MDT values. MDT values were also increased with increasing polymer load on the nuclei. Key words: Salbutamol sulphate; Pellet; Aqueous dispersion; Eudragit® RS 30 D; Kollicoat® SR 30D; Extrusion spheronization; MDT. DOI: http://dx.doi.org/10.3329/dujps.v9i2.7895 Dhaka Univ. J. Pharm. Sci. 9(2): 109-118, 2010 (December)

Impact of Granulation and Effect of Polymers on Theophylline Release from Matrix Tablets

The effects of plastic, hydrophilic and hydrophobic types of polymers and impact of granulation process were investigated on the release profile of theophylline from matrix systems. A comparative release characteristics were evaluated by the use of polymers from different theophylline matrices. Matrix tablets of theophylline using Methocel K4M, Ethocel 20 cps, Kollidon SR were prepared separately by direct compression and moist granulation process. In this investigation the feasibility of moist granulation technique in the development of sustained release matrix tablet of theophylline was studied. The kinetics of the dissolution process was determined by analyzing the dissolution data using various kinetic equations, e.g. zero-order, Higuchi and Korsmeyer equations. The mean dissolution time (MDT) was calculated for all the formulations. The analysis of the dissolution data showed that the release process involves erosion and diffusion. Drug release was different from different classes of polymeric matrices and from tablets prepared by different manufacturing processes. The results showed that the profile and kinetics of drug release were the functions of polymer type, polymer content and granulation process. Key words: Theophylline, Moist granulation, Direct compression, Methocel K4M, Ethocel 20 cps, Kollidon SR doi: 10.3329/dujps.v7i2.2168 Dhaka Univ. J. Pharm. Sci. 7(2): 133-139, 2008 (December)

<i>In vitro</i> Release Kinetics Study of Ranolazine from Swellable Hydrophilic Matrix Tablets

The objective of this study was to design oral sustained release matrix tablets of Ranolazine usinghydroxypropyl methylcellulose (HPMC) as the retardant polymer and to study the effect of formulation factors suchas polymer proportion and polymer viscosity on the release of drug. In vitro release studies were performed usingUSP type II apparatus (paddle method) in 900 mL of 0.1N HCl at 100 rpm for 12 hours. The release kinetics wasanalyzed using the zero-order, first order, Higuchi and Korsmeyer-Peppas equations to explore and explain themechanism of drug release from the matrix tablets. In vitro release studies revealed that the release rate decreasedwith increase in polymer proportion and viscosity grade. Mathematical analysis of the release kinetics indicated thatthe nature of drug release from the matrix tablets was dependent on drug diffusion and polymer relaxation andtherefore followed non-Fickian or anomalous release. The developed controlled release matrix tablets of Ranolazineprepared with high viscosity HPMC extended release up to 12 hours.Key words: Ranolazine; Sustained release; Methocel E50 Premium LV; Methocel K100LV CR; Methocel K4M CR;Methocel K15M CR.DOI: 10.3329/dujps.v8i1.5333Dhaka Univ. J. Pharm. Sci. 8(1): 31-38, 2009 (June)

Lorentz-Invariant Equations of Motion of Point Masses in the General Theory of Relativity

After a general discussion of the problem of motion in the general theory of relativity a simple derivation of the law of motion is given for single poles of the gravitational field, which is based on a method originally developed by Mathisson. This law follows from the covariant conservation law for the matter energy-momentum tensor alone, without reference to any field equations, and takes the form of a geodesic of the (unknown) metric. Expanding this metric in terms of a power series in a parameter gamma and using the Minkowski proper time to parametrize the world lines of the particles, the (Lorentz-invariant) form of the approximate laws of motion follows. A method is developed to obtain the equations of motion (including the explicit form of the metric in terms of the particle variables) from Einsiein's field equations. A systematic linearization procedure leads to a series of second-order differential equations for the metric; the nth order approximation of the equations of motion, as well as the explicit form of the matter tensor in (n + l)st order, is obtained as an integrability condition on the (n + l)st order opproximation for the metric. No coordinate conditions are required to obtain themore » general form of the equations of motion; they are needed only to reduce the approximation equations to wave equations and thus to allow their explicit integration in terms of retarded or symmetric potentials. In developing the approximation method it is shown that consistency requires that any set of approximate equations is solved up to'' rather than in'' nth order; this implies that the form of the lower-order metric be maintained, but the motion corresponding to the nth order solutions rather than to lower order ones. In particular, the equations for the first- order metric imply zero-order equations of motion which restrict the particles to zero acceleration; the equations for the second-order metric imply first-order equation of motion involving the first-order metric, but without the previous restriction. In the retarded case the equations of motion contain retarded interactions and radiation terms of the form familiar from electrodynamics; no such terms appear in the symmetric case. The equations of the symmetric case are derivable from a Fokker-type variational principle. The relation of the results obtained to work on Lorentz-invariant equations by other autnors is discussed. In Appendix I a discussion of alternative derivations is prescnted; Appendix II contains remarks on Wheeler-Feynman type considerations for general relativistic equations of motion. (auth)« less

Configuration of a Plasma in an Axially Symmetric Magnetic Field

Closed form analytic solutions are obtained for the static configuration of a fully ionized low β density adiabatic plasma immersed in an externally applied axially symmetric magnetic field. There is introduced first a special orthogonal curvilinear coordinate system, one of whose coordinate curves coincides with the externally applied magnetic field. Then, by performing a perturbation expansion for a low β adiabatic plasma, a system of zero-order equations is obtained. Although this system of equations is incomplete, in that there are more unknowns than equations serving for their determination, a determinate integrable system of equations is obtained by specifying that the diagonal elements of the divergence of the zero-order heat flux tensor vanish. This system of equations is integrated to yield analytic results dependent on the boundary conditions imposed upon the plasma. Finally, it is shown that if a trapping criterion is to be satisfied, the boundary conditions imposed upon the plasma must satisfy certain inequalities.