Classical Michaelis-Menten and system theory approach to modeling metabolite formation kinetics

Abstract

When single doses of drug are administered and kinetics are linear, techniques, which are based on the compartment approach and the linear system theory approach, in modeling the formation of the metabolite from the parent drug are proposed. Unlike the purpose-specific compartment approach, the methodical, conceptual and computational uniformity in modeling various linear biomedical systems is the dominant characteristic of the linear system approach technology. Saturation of the metabolic reaction results in nonlinear kinetics according to the Michaelis-Menten equation. The two compartment open model with Michaelis-Menten elimination kinetics is theorethicaly basic when single doses of drug are administered. To simulate data or to fit real data using this model, one must resort to numerical integration. A biomathematical model for multiple dosage regimen calculations of nonlinear metabolic systems in steady-state and a working example with phenytoin are presented. High correlation between phenytoin steady-state serum levels calculated from individual Km and Vmax values in the 15 adult epileptic outpatients and the observed levels at the third adjustment of phenytoin daily dose (r=0.961, p<0.01) were found.

New Mathematical Methods in Pharmacokinetic Modeling

“…The latter is in strict contrast to mutually diverse models, commonly employed in pharmacokinetic, pharmacodynamic, and pharmacokinetic/pharmacodynamic modeling methods. The following examples of application of this technology can be found in the literature: modeling the drug dissolution (?urišová & Dedík 1997; Dedík & ?urišová 2002b), modeling the drug behaviour in the body (?urišová et al 1998), modeling the drug bioavailability in the blood circulation (Dedík & ?urišová 1994 & 1996), modeling the metabolite formation from the parent drug (Dedík & ?urišová 2002a; Popovič 2004), or modeling the drug effect (Dedík et al 2003). As expectable, the biological meaning of parameters of the resultant dynamic model of each of the given processes is fundamentally dependent on the nature the particular process, i.e.…”

Application of Modified Michaelis – Menten Equations for Determination of Enzyme Inducing and Inhibiting Drugs

“…There was a significant correlation between steady-state serum levels of phenytoin calculated from Vnax and Km values in epileptics. Single doses were initially administered followed by multiple doses (Popovic, 2004). Hence phenytoin could have zero order input and mixed order kinetic ouput in one compartmental model system (Lam and Chiou, 1979), suggesting that level of plasma phenytoin is not related linearly to dose and change in enzyme activity by co-administered drug , could alter plasma level of phenytoin.…”

Validation of the hepatic blood flow rate model for verapamil first-pass metabolism

“…The physiological blood flow rate model, used in this study, is based on the data cited earlier (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). The above-mentioned model was considered adequate for the examination of systemic availability and the firstpass elimination of verapamil, as the drugs behavior corresponded to the assumptions of the model (15)(16)(17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30).…”

“…For example, if verapamil is disproportionately distributed in favor of the erythrocytes, this may indicate that a fraction of the amount of verapamil associated with the red blood cells is 'tightly' bound and may not re-equilibrate sufficiently rapidly for it to become available to metabolic sites as the blood passes through the liver. On the other hand, it has been suggested (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14) that if the apparent partition coefficient of the drug between the plasma and the erythrocytes is very high, one can use plasma concentration data. In this case, however, the blood flow rate term in Eq.…”

“…Equations have been developed to estimate the extent to which an orally administered drug is metabolized on its first-pass through the liver by using only those concentrations determined after oral administration (1)(2)(3)(4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14). The investigators in question have pointed out that the following relation may be used to predict the maximum fraction of an orally administered drug reaching the systemic circulation: lation, Flow Rate is the hepatic blood flow rate (about 91.8 lIh in man).…”