Abstract
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.
Highlights
The experimental, theoretical and computational analysis of rate of change with time of concentration and volume distribution of compounds administered externally such as drugs, metabolite, nutrients, harmones, toxins, in various regions of the human physiology is called pharmacokinetics [1,2]
The fluctuations in concentration depends on the dimensionless frequency resulting from the subcritical damped oscillations during absorption
This study deals with application of single compartment model pharmacokinetic analysis to systems: 1) that obey Michaelis-Menten kinetics and; 2) Krebs cycle kinetics
Summary
The experimental, theoretical and computational analysis of rate of change with time of concentration and volume distribution of compounds administered externally such as drugs, metabolite, nutrients, harmones, toxins, in various regions of the human physiology is called pharmacokinetics [1,2]. Compartmental methods [1] involve development of mathematical models to describe the change in concentration of drug with time. These models are similar to those developed in chemical reaction engineering and thermodynamics and biochemical kinetics. When the number of compartments in the model becomes large or when the kinetics becomes complex such as Michaelis-Menten or Krebs cycle no closed form analytical solution is possible [3]. Lundquist and Wolthers [4] presented integrated solutions for 1 compartment model with Michaelis-Menten kinetics This is a trancedental equation and not in a readily usable form. This study deals with application of single compartment model pharmacokinetic analysis to systems: 1) that obey Michaelis-Menten kinetics and; 2) Krebs cycle kinetics. In the case of Krebs cycle the implications of oscillatory systems are discussed
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