Wednesday, November 4, 2009: 8:40 AM
Kohlberg (Camino Real Hotel)
Sometimes during absorption of drug into the human anatomy, Krebs cycle may be encountered. Reactions such as these can be represented by a scheme of Reactions in Circle. The essential steps in the Krebs cycle are the formation of: i) oxalic acid; ii) citric acid; iii) isocitric acid; iv) α-ketoglutaric acid; v) succyl coenzyme A; vi) succinic acid; vii) fumaric acid; viii) maleic acid. The kinetics of a sytem of: i) 3 reactions in circle; ii) 4 reactions in circle; iii) 8 reactions in circle and; iv) general case are derived. The conditions of the rate constants where the concentration of the reactant undergoes subcritical damped oscillations are obtained. For the n reactions in circle case a jacobian is written and the characteristic equation solved for complex roots. This happens for the case of 3 reactions when one of the rate constant is less than the square of the sum of the square root of the other two rate constants in the system. Vieta's substitution is used for solving the Laplace domain equation for the case of 4 reactions in circle. The conditions were subcritical damped oscillations in the drug infused is imposed in the single compartment pharmacokinetic model. The model solutions are developed by the method of Laplace transforms. The drug profiles were found to reach a maximum and reach a state of complete depletion after a said time. The fluctuations in concentration of the drug depends on the dimensionles frequency resulting from the subcritical damped oscillatiosn during absorption. At low frequencies the fluctuations were found to be absent. As the frequency is increased the fluctuations in concentration are pronounced. The frequency of fluctuations were found to incresae with increase in frequency of oscillations during absorption. A saw-tooth pattern was found under some conditions.