Wednesday, November 4, 2009: 8:20 AM
Kohlberg (Camino Real Hotel)
Application of pharmacokinetics allows for the processes of liberation, absorption, distribution, metabolism and excretion to be characterized mathematically. Single and Multiple Compartment models can be used. The drug concentration may be asymptotically stable at large times or may reach a maxima at some said time or become completely depleted at some estimated time or the order of drug consumption may change at some intermediate time. The drug concentration in the blood plasma is derived for first order absorption with elimination using a single compartment model. The time where maximum concentration and infinite time drug accumulation in the urine can be calcualted usign this model. Also a separate expression is developed for the special case when the rate constant of infusion and elimination are equal to each other. For this case the earlier model prediction was a "blow-up" or singularity. The drug profile was found to be assymetric. The single compartment model was developed for second order absorption with elimination. The drug profile was found to be assymetric with a right tail. The single compartment model for the case of zeroth order absorption and elimination was developed. Type C behavior was found in the drug profile. A convex rise and a maxima and a concave fall was found in the drug profile. Complete depletion was found. For the case of Michaelis-Menten kinetics absorption with elimination, the expression was made more useful by Taylor series expansion of the derivatives of concentration of the drug in the plasma compartment. Four terms in the Taylor series gave a good fit with the integrated expression (implicit in C-t) especially for short times. The drug profile for absorption with Michaelis-Menten kinetics showed a maxima and complete depletion at large times. An aliter using Lambert function is also discussed.
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