(567bt) On Michaelis Menten Kinetics in Single Compartment Pharmacokinetic Models

Pharmacokinetics is derived from Greek words pharmacon that means drugs and kinetikos that means setting in motion. Drug can be absorbed by 13 different methods. Different forms of concentration change with time such as slow absorption, maxima and rapid bolus and constant rate delivery are possible. Factors that affect drug distribution are the rate of blood perfusion, permeability of capillary, biological affinity of drug, rate of metabolism of drug, rate of renal extraction, elimination of drug in the kidnes. BUN, blood urea nitrogen an end product in metabolism is removed from the blood in the Bowman's capsulte along with creatinine. A single compartment model with absorption and elimination was developed for systems that obey the Michaelis-Menten kinetics. Taylor series expansion was used. Expressions for higher order derivatives were obtained for dimensionless concentration. A infinite series expression for dimensionless concentration results as a function of dimensionless time and michaelis constant. The closed form analytical solution obtained was integrated. Both the integrated solution and infinite series solution were compared with side by side. The compartment model solution was obtained by inversion of Laplace transforms. The M & M solution is implicit and a more useful form was obtained by Taylor series expansion. Another method of solution was offered using the Lambert function.