For drugs obeying parallel first-order and Michaelis-Menten elimination kinetics,mathematical analysis concerning the optimum dosage regimen of intravenous infusion is conducted and following equations are derived:whe...For drugs obeying parallel first-order and Michaelis-Menten elimination kinetics,mathematical analysis concerning the optimum dosage regimen of intravenous infusion is conducted and following equations are derived:where Xo is the intravenous loading dose,Cb the plasma concentration level desired in clinical therapy,V the apparent distribution volume,k0 the rate constant of intravenouns infusion,K the first－order elimination rate constant,Vm the theoretical maximum rate of the Michaelis－Menten elimination process,Km the Michaelis constant.From this dosage regimen,plasma level maintains a constant Cb during the administration period.When K=0 the dosage regimen above is also suitable for drugs obeying Michaelis-Menten elimination kinetics.展开更多
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 u...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 frequency resulting from the subcritical damped oscillations during absorption. At low frequencies the fluctuations are absent. As the frequency is increased the fluctuations in concentration are pronounced. The fre-quency of fluctuations were found to increase with increase in frequency of oscillations during ab-sorption.展开更多
This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation contain...This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation containing a non-linear term related to Michaelis-Menten kinetics of enzymatic reaction. Approximate analytical expression of concentration of oxygen is derived using new Homotopy perturbation method for various boundary conditions. The validity of the obtained solutions is verified by the numerical results.展开更多
In this paper, we investigated stability and bifurcation behaviors of a predator-prey model with Michaelis-Menten type prey harvesting. Sufficient conditions for local and global asymptotically stability of the interi...In this paper, we investigated stability and bifurcation behaviors of a predator-prey model with Michaelis-Menten type prey harvesting. Sufficient conditions for local and global asymptotically stability of the interior equilibrium point were established. Some critical threshold conditions for transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation were explored analytically. Furthermore, It should be stressed that the fear factor could not only reduce the predator density, but also affect the prey growth rate. Finally, these theoretical results revealed that nonlinear Michaelis-Menten type prey harvesting has played an important role in the dynamic relationship, which also in turn proved the validity of theoretical derivation.展开更多
This paper compares the irreversible and reversible rate equations from several uni-uni kinetic mechanisms (Michaelis-Menten, Hill and Adair equations) and bi-bi mechanisms (single- and double- displacement equations)...This paper compares the irreversible and reversible rate equations from several uni-uni kinetic mechanisms (Michaelis-Menten, Hill and Adair equations) and bi-bi mechanisms (single- and double- displacement equations). In reversible reactions, Haldane relationship is considered to be identical for all mechanisms considered and reversible equations can be also obtained from this rela- tionship. Some reversible reactions of the metabolism are also presented, with their equilibrium constant.展开更多
Background： In India, rubber（Hevea brasiliensis） plantations cover -0.8 million ha of land, emphasizing its significant role in the Earth＇s carbon dynamics. Therefore, it is important to estimate the biomass stock...Background： In India, rubber（Hevea brasiliensis） plantations cover -0.8 million ha of land, emphasizing its significant role in the Earth＇s carbon dynamics. Therefore, it is important to estimate the biomass stocks of plantations precisely in the context of carbon management. Previous studies in India have focused on development of allometric equations for estimating aboveground biomass（AGB） through harvesting younger trees（up to 14 yr）only or on studies with small sample sizes without assessing model bias. The objective of this study was to develop biomass estimation models for different tree components in rubber plantations and assess model predictive performance at the stand level.Methods： A total of 67 trees were harvested from plantations of different ages（6, 15, 27 and 34 yr） in North East India and their diameter at 200 cm（D）, height and dry weights of different tree components were recorded. The data were used for evaluation of H-D and biomass estimation models at the stand level.Results： The Michaelis-Menten function was found to be the most appropriate model for estimating tree height among 10 commonly used H-D models. For estimation of AGB and coarse root biomass, a model that involves tree volume（i.e. D2 H） was found to provide better prediction than either D or H alone or a model that combines H, D and stand density. The estimated AGB varied from 28 Mg·ha-（-1） in 6 yr. old plantation to 169 Mg·ha-（-1） in 34 yr. old plantations.The coarse root biomass was estimated at 4 Mg·ha-（-1） for 6 yr. old plantation and 12 Mg·ha-（-1） for 34 yr. old stands.Conclusions： It is concluded that models involving tree volume are more appropriate for regional level biomass estimation than simple power-law models for individual stands. We recommend that the power-law model should not be used for estimation of AGB in plantations at different growth stages because power-law parameters can be biased due to data truncation.展开更多
We study kinetic models of reversible enzyme reactions and compare two techniques for analytic approximate solutions of the model. Analytic approximate solutions of non-linear reaction equations for reversible enzyme ...We study kinetic models of reversible enzyme reactions and compare two techniques for analytic approximate solutions of the model. Analytic approximate solutions of non-linear reaction equations for reversible enzyme reactions are calculated using the Homotopy Perturbation Method (HPM) and the Simple Iteration Method (SIM). The results of the approximations are similar. The Matlab programs are included in appendices.展开更多
文摘For drugs obeying parallel first-order and Michaelis-Menten elimination kinetics,mathematical analysis concerning the optimum dosage regimen of intravenous infusion is conducted and following equations are derived:where Xo is the intravenous loading dose,Cb the plasma concentration level desired in clinical therapy,V the apparent distribution volume,k0 the rate constant of intravenouns infusion,K the first－order elimination rate constant,Vm the theoretical maximum rate of the Michaelis－Menten elimination process,Km the Michaelis constant.From this dosage regimen,plasma level maintains a constant Cb during the administration period.When K=0 the dosage regimen above is also suitable for drugs obeying Michaelis-Menten elimination kinetics.
文摘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 frequency resulting from the subcritical damped oscillations during absorption. At low frequencies the fluctuations are absent. As the frequency is increased the fluctuations in concentration are pronounced. The fre-quency of fluctuations were found to increase with increase in frequency of oscillations during ab-sorption.
文摘This paper demonstrates the approximate analytical solution to a non-linear singular two-point boundary-value problem which describes oxygen diffusion in a planar cell. The model is based on diffusion equation containing a non-linear term related to Michaelis-Menten kinetics of enzymatic reaction. Approximate analytical expression of concentration of oxygen is derived using new Homotopy perturbation method for various boundary conditions. The validity of the obtained solutions is verified by the numerical results.
文摘In this paper, we investigated stability and bifurcation behaviors of a predator-prey model with Michaelis-Menten type prey harvesting. Sufficient conditions for local and global asymptotically stability of the interior equilibrium point were established. Some critical threshold conditions for transcritical bifurcation, saddle-node bifurcation and Hopf bifurcation were explored analytically. Furthermore, It should be stressed that the fear factor could not only reduce the predator density, but also affect the prey growth rate. Finally, these theoretical results revealed that nonlinear Michaelis-Menten type prey harvesting has played an important role in the dynamic relationship, which also in turn proved the validity of theoretical derivation.
文摘This paper compares the irreversible and reversible rate equations from several uni-uni kinetic mechanisms (Michaelis-Menten, Hill and Adair equations) and bi-bi mechanisms (single- and double- displacement equations). In reversible reactions, Haldane relationship is considered to be identical for all mechanisms considered and reversible equations can be also obtained from this rela- tionship. Some reversible reactions of the metabolism are also presented, with their equilibrium constant.
基金DST, GOI for funding (DST/IS-STAC/CO2-SR-224/14(c)-AICP-AFOLU-1)
文摘Background： In India, rubber（Hevea brasiliensis） plantations cover -0.8 million ha of land, emphasizing its significant role in the Earth＇s carbon dynamics. Therefore, it is important to estimate the biomass stocks of plantations precisely in the context of carbon management. Previous studies in India have focused on development of allometric equations for estimating aboveground biomass（AGB） through harvesting younger trees（up to 14 yr）only or on studies with small sample sizes without assessing model bias. The objective of this study was to develop biomass estimation models for different tree components in rubber plantations and assess model predictive performance at the stand level.Methods： A total of 67 trees were harvested from plantations of different ages（6, 15, 27 and 34 yr） in North East India and their diameter at 200 cm（D）, height and dry weights of different tree components were recorded. The data were used for evaluation of H-D and biomass estimation models at the stand level.Results： The Michaelis-Menten function was found to be the most appropriate model for estimating tree height among 10 commonly used H-D models. For estimation of AGB and coarse root biomass, a model that involves tree volume（i.e. D2 H） was found to provide better prediction than either D or H alone or a model that combines H, D and stand density. The estimated AGB varied from 28 Mg·ha-（-1） in 6 yr. old plantation to 169 Mg·ha-（-1） in 34 yr. old plantations.The coarse root biomass was estimated at 4 Mg·ha-（-1） for 6 yr. old plantation and 12 Mg·ha-（-1） for 34 yr. old stands.Conclusions： It is concluded that models involving tree volume are more appropriate for regional level biomass estimation than simple power-law models for individual stands. We recommend that the power-law model should not be used for estimation of AGB in plantations at different growth stages because power-law parameters can be biased due to data truncation.
文摘We study kinetic models of reversible enzyme reactions and compare two techniques for analytic approximate solutions of the model. Analytic approximate solutions of non-linear reaction equations for reversible enzyme reactions are calculated using the Homotopy Perturbation Method (HPM) and the Simple Iteration Method (SIM). The results of the approximations are similar. The Matlab programs are included in appendices.
