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On Single Compartment Pharmacokinetic Model Systems that Obey Michaelis-Menten Kinetics and Systems that Obey Krebs Cycle Kinetics

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Journal of Encapsulation and Adsorption Sciences 2011年第3期1卷 43-50页

作者： kal renganathan sharma 不详

The integration of Michaelis-Menten kinetics results in a trancedental equation. The results are not in a form that is readily usable. A more usable form of the model solutions is developed. This was accomplished by using Taylor series expansion of dimensionless concentration u in terms of its derivatives. The infinite series expression for dimensionless concentration is given. It can be seen that for times t < , the Taylor series expression evaluated near the origin up to the third derivative is a reasonable representation of the integrated solution. More terms in the Taylor series expression can be added to suit the application. It can vary with the apparent volume, dosage, enzyme concentration, Michaelis constant and the desired accuracy level needed. The single compartment model solution was obtained by the method of Laplace transform. It can be seen from Figure 2 that the dimensionless drug concentration in the compartment goes through a maxima. The curve is convex throughout the absorption and elimination processes. The drug gets completely depleted after a said time. The curve is asymmetrical with a right skew. The systems under absorption with elimination that obey the kinetics that can be represented by a set of reactions in circle were considered. A system of simple reactions in circle was taken into account. The concentration profile of the reactants were obtained by the method of Laplace transforms. The conditions when subcritical damped oscillations can be expected are derived. A model was developed for cases when absorption kinetics exhibit subcritical damped oscillations. The solution was developed by the method of Laplace transforms. The solution for dimensionless concentration of the drug in single compartment for different values of rate constants and dimensionless frequency are shown in Figures 6-9. The drug profile reaches a maximum and drops to zero concen-tration after a said time. The fluctuations in concentration depends on the dimensionless

关键词： Single Compartment Models Michaelis and Menten Kinetics Reactions in Circle Subcritical Damped Oscillations Pharmacokinetics

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On Single Compartment Pharmacokinetic Model Systems that Obey Free Radical Copolymerization Kinetics and Multiplicity

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Journal of Encapsulation and Adsorption Sciences 2013年第3期3卷 77-92页

作者： kal renganathan sharma Advanced Technology Lone Star College-North Harris Houston USA

This study examines the issues in development of pharmacokinetic single compartment model for systems that obey free radical copolymerization kinetics. Copolymer composition as a function of reactivity ratios of comonomers for well mixed case was derived. For some cases, such as DEF-AN, diethyl fumarate and acrylonitrile system multiplicity in composition were found. The analysis is extended to n monomers. State space model expressions are used and the QSSA assumption is stated in state space equation form. Conditions when damped oscillations can be expected are noted. In addition to multiplicity in product composition, an account of reactivity ratios and other instances of multi- plicity were found during the pharmacodynamics of the free radical polymerization reactions. A careful study of initiated case, thermal case, 1 CSTR and 2 CSTRS was undertaken and results were presented. Numerical integration techniques were employed on the desktop computer. Steady state and transient state conversion for initiated case and thermal case for 1 CSTR and 2 CSTRs were calculated and plotted in Figures 7-9 and 12. No multiplicity was found in the thermal case for 1 CSTR in the dynamics of transient monomer conversion. Multiplicity was found in the initiated case for 1 CSTR in the dynamics of transient conversion of monomer. The multiplicity was found in the second CSTR for the case of 2 CSTRs in series. No multiplicity was found in the case of initiator decay.

关键词： Single Compartment Pharmacokinetics Copolymer Composition Reactivity Ratios Multiplicity State Space Model n Monomers

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Nanorobot Drug Delivery System for Curcumin for Enhanced Bioavailability during Treatment of Alzheimer’s Disease

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Journal of Encapsulation and Adsorption Sciences 2013年第1期3卷 24-34页

作者： kal renganathan sharma Advanced Technology Lone Star College Houston USA

Robotics has emerged as a collegiate course about 20 years ago at Stanford University, Stanford, CA. From the first IRB6, the electrically powered robot in 1974, the industry has grown over a 30-year period. A leading supplier of robots has put out over 100,000 robots by year 2001. Robot capable of handling 500 kg load was introduced in 2001, IRB 7000. A number of advances have been made in nanostructuring. About 40 different nanostructuring methods were reviewed recently [1]. Nanobots can be developed that effect cures of disorders that are difficult to treat. Principles from photodynamic therapy, fullerene chemistry, nanostructuring, X-rays, computers, pharmacokinetics and robotics are applied in a design of nanorobot for treatment of Alzheimer’s disease. The curcuma longa that has shown curative effects in rats’ brain with Alzheimer’s is complexed with fullerenes. The drug is inactive when caged. It is infused intrathecally into the cerebrospinal system. Irradiation of the hypothalamous and other areas of the brain where Alzheimer’s disease is prevalent lead to breakage of fullerenes and availability of the drug with the diseased cells. Due to better mass transfer, better cure is affected. The other plausible reactions such as addition polymerization of fullerene, polycurcumin formation and other hydrolysis reactions are modeled along with the drug action under the Denbigh scheme of reactions. The fractional yield of drug-curcumin interaction is a function of intensity of radiation, frequency of radiation, patient demographics, age, gender, and other disorders etc. Chromophore in curcumin is used as a sensor and computer imaging and feedback control design can result in more bioavailability for curcumin therapeutic action to cure Alzheimer’s disease. This study examines the principles used in the design, the strategy of the design of the nanorobot drug delivery system with a specific target and pharamacokinetic formulation of the associated competing parallel rea

关键词： Nanorobot Alzheimer’s Disease Curcuma Longa Photodynamic Therapy Intrathecal Infusion Denbigh Reaction Scheme

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Alternate Form of Damped Wave Conduction and Relaxation Equation a Capite Adcalcem in Temperature

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Journal of Physical Science and Application 2013年第1期3卷 46-53页

作者： kal renganathan sharma Advanced Technology Lone Star College University Park 20515 State Hwy 249 Houston TX 77070 USA

An alternate non-Fourier heat conduction equation is derived from consideration of translation motion of spinless electron under a driving force due to an applied temperature gradient. This equation is a eapite ad calcem,temperature. Elimination of the rate of change of velocity with respect to time leads to a non-Fourier heat conduction equation with a accumulation of temperature or ballistic term in it. The new constitutive heat conduction equation is combined with the energy balance equation in one dimension. The governing equation for transient temperature a partial differential equation （Eq. （23）） is solved for by the method of Laplace transforms. The problem considered is the semi-infinite medium with constant thermo physical properties with constant wall temperature boundary condition. A closed form analyticalexpression for the transient temperature was obtained （Eq. （36）） after truncation of higher order terms in the infinite binomial series and use of convolution and lag properties. This solution is compared with that obtained using the parabolic Fourier model and the damped wave model as presented in an earlier study. The predictions of Eq. （36） are closer to the Fourier model. The convex nature of the temperature curve is present.

关键词： Transport theory non-fourier conduction CWT constant wall temperature binomial infinite series.

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On Damped Wave Diffusion of Oxygen in Pancreatic Islets: Parabolic and Hyperbolic Models

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Journal of Encapsulation and Adsorption Sciences 2012年第3期2卷 33-41页

作者： kal renganathan sharma Advanced Technology Center & Biotechnology Institute Lone Star College CYFair Cypress TX & Department of Physics Texas Southern University Houston USA

Damped wave diffusion effects during oxygen transport in islets of Langerhans is studied. Simultaneous reaction and diffusion models were developed. The asymptotic limits of first and zeroth order in Michaelis and Menten kinetics was used in the study. Parabolic Fick diffusion and hyperbolic damped wave diffusion were studied separately. Method of relativistic transformation was used in order to obtain the solution for the hyperbolic model. Model solutions was used to obtain mass inertial times. Convective boundary condition was used. sharma number (mass) may be used in evaluating the importance of the damped wave diffusion process in relation to other processes such as convection, Fick steady diffusion in the given application. Four regimes can be identified in the solution of hyperbolic damped wave diffusion model. These are;1) Zero Transfer Inertial Regime, 0 0≤τ≤τinertia;2) Rising Regime during times greater than inertial regime and less than at the wave front, Xp > τ, 3) at Wave front , τ = Xp;4) Falling Regime in open Interval, of times greater than at the wave front, τ > Xp. Method of superposition of steady state concentration and transient concentration used in both solutions of parabolic and hyperbolic models. Expression for steady state concentration developed. Closed form analytic model solutions developed in asymptotic limits of Michaelis and Menten kinetic at zeroth order and first order. Expression for Penetration Length Derived-Hypoxia Explained. Expression for Inertial Lag Time Derived. Solution was obtained by the method of separation of variables for transient for parabolic model and by the method of relativistic transformation for hyperbolic models. The concentration profile was expressed as a sum of steadty state and transient parts.

关键词： C Type I Diabetes Simultaneous Reaction and Diffusion Michaelis and Menten Kinetics Damped Wave Diffusion Relativistic Transformation Hyperbolic Models Parabolic Models Islets of Langerhans

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On Thermodynamic Analysis of Substances with Negative Coefficient of Thermal Expansion

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Engineering（科研） 2013年第11期5卷 844-849页

作者： kal renganathan sharma Lone Star College-North Harris Houston USA

There are reports in the literature on the discovery of novel materials that were observed to shrink upon heating. Treatment of these materials in the same manner as the materials with positive coefficient of thermal expansion can lead to the misinterpretation of the laws of thermodynamics. This is because volume expansivity is usually defined at constant pressure. Negative values for volume expansivity can be shown using Maxwell’s reciprocity relations to lead to negative values for absolute temperature for ideal gas. For real systems, using Helmholz free energy analysis at equilibrium an expression for the volume expansivity was derived. It can be seen that this expression would be always positive for real physical changes, either heating or cooling. Isentropic volume expansivity is proposed as better suited for analysis of materials with negative thermal expansion, NTE and composites used in space such as Hubble telescope and Chandra telescope with zero coefficient of thermal expansion. This kind of a switch from isobaric to isentropic has precedence in the history of development of speed of sound.

关键词： Negative Thermal Expansion NTE Materials Helmholz Free Energy Second Law of Thermodynamics Speed of Sound Volume Expansivity

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Improvement of Biodiesel Product Yield during Simple Consecutive-Competitive Reactions

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Journal of Encapsulation and Adsorption Sciences 2015年第4期5卷 204-216页

作者： kal renganathan sharma Electrical Program San Jacinto College Pasadena TX USA

Biodiesel is a renewable fuel that can be made from vegetable oil and waste restaurant greases by catalysed transesterification reactions. Over 5 billion gallons of biodiesel was produced in 2010. The European Union and United States are seeing the sigmoidal portion of the growth curve in biodiesel production. Economic analysis such as profitability and annualized worth (AW) of a biodiesel plant in Taiwan is presented. With the revenue from glycerine byproduct recovery and with lower raw material costs, biodiesel may be profitable especially during days of higher gasoline prices. Multiple reactions of the consecutive-competive type may be used to model the methonolysis of trigylcerides. The reaction rate constant ratios and residence time in the reactor are important parameters in determining higher selectivity of FAME, fatty acid methyl ester product yield over glycerol by-product production. Illustrations of higher FAME yield, higher glycerol yield and cross-over from FAME to glycerol are shown for some values of reaction rate constant ratios and reaction scheme from triglycerides to diglycerides, monoglycerides and glycerol along with formation of FAME in each step by addition of methanol and catalyst is shown. Product distribution curves are presented in Figures 2-5 for different values or reaction rate constant ratios.

关键词： Biodiesel Transesterification Reactions Consecutive-Competitive Reactions Jatropha Curcas Oil Genomics Centrifugal Separation Optimization Profitability Method of Laplace Transforms

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