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 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 comon...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.展开更多
目的：建立HPLC-MS法测定大鼠体内艾芬地尔的血药浓度,并研究酒石酸艾芬地尔在健康SD大鼠体内的药代动力学特征。方法：血浆样品碱化后采用乙酸乙酯液-液萃取处理,酮康唑为内标。采用C18色谱柱（5μm,4.6 mm×150mm）,以甲醇-p H 7...目的：建立HPLC-MS法测定大鼠体内艾芬地尔的血药浓度,并研究酒石酸艾芬地尔在健康SD大鼠体内的药代动力学特征。方法：血浆样品碱化后采用乙酸乙酯液-液萃取处理,酮康唑为内标。采用C18色谱柱（5μm,4.6 mm×150mm）,以甲醇-p H 7.20醋酸铵溶液为流动相,梯度洗脱（0-3 min,20%A→90%A,80%B→10%B）,流速0.6 m L·min^-1。质谱检测采用电喷雾（ESI）离子源,正离子模式,采用选择离子检测（SIM）方式检测,检测离子分别为m/z 326.3（艾芬地尔）、m/z 531.0（酮康唑）。选取健康SD大鼠[（250±20）g,雌雄各半],腹腔注射酒石酸艾芬地尔1 mg·kg-1后,采用建立的HPLC-MS法测定各个时间点（0、10、20、30、40、50、60、75、90、100、110、120、150、180、240、360 min,每个时间点6只）大鼠血浆中艾芬地尔的浓度,并计算其药代动力学参数。结果：艾芬地尔浓度在0.5-120μg·L^-1范围内,线性良好（r=0.9974）;日间、日内精密度RSD均小于10.5%,提取回收率均高于88%,专属性良好,血浆样品在本实验的条件下稳定,空白基质中的内源性物质不干扰待测组分和内标的测定。结论：本分析方法对血浆中艾芬地尔的检测具有专属性,且灵敏、可靠。酒石酸艾芬地尔经腹腔注射后在大鼠体内药动学模型为单室模型,其达峰浓度为113.79μg·L^-1,半衰期为2.42 h。展开更多
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 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.
