When   Monday, March 30, 2009   Time   4:00 PM - 5:00 PM  
Where   Technological Instit M 416 2145 Sheridan Rd.   map it
Audience   - Faculty/Staff - Student - Public
Contact   Molly E Scanlon   +1 847 491 5586  
Group   McCormick-Colloquia Engineering Sciences and Applied Mathematics

Applied Math Colloquium

Title: Mathematical Modelling:  A Physiologically-Based Recirculatory Pharmacokinetic Model of Drug Distribution

Speaker: Dr. Tom Krejcie, Northwestern University

Abstract:

dentifying the basis of interindividual differences in reactivity to drugs with rapid onsets of effect and low margins of safety (intravenous anesthetics and analgesics) requires a detailed description of drug disposition (pharmacokinetics, PK) during the onset and offset of drug.  The PK model must be based on drug concentrations obtained frequently from the moment of injection into the blood stream, thereby accounting for the role of cardiac output and peripheral blood flow in drug distribution.  The initial drug concentration versus time relationship is a right-skewed distribution which can be described by several different mathematical formula.  We chose to use the Erlang probability density function, (a special case of the gamma distribution) to describe this early relationship because the model parameters can be interpreted physiologically, namely, converted to compartment volumes and blood flows.  The Erlang distribution is used as a mathematical description of flow through tanks-in-series.  Two parallel sets of tanks-in-series (sum of two Erlang functions) produce the drug concentration versus time relationship seen as a bolus of injected drug traverses the central circulation (heart and lungs) before entering the systemic circulation, as well as accounting for the delay in the first appearance of the drug at the arterial sampling site.  We then incorporated this model of the central circulation into a complete recirculatory PK model by including another, peripheral, Erlang distribution, and tissue compartments, in parallel, to model drug distribution throughout the body.  This recirculatory model of drug distribution also accounts for drug returning to the central circulation after little interaction with peripheral tissues (a physiologic drug shunt).  Our recirculatory PK model was developed from data in animals and was used to describe drug disposition in various paradigms of altered cardiovascular physiology.  Intravenous anesthetic induction dose requirements are generally assumed to be related to cardiac output, yet doses are decreased in both hypovolemia, with decreased cardiac output, and pregnancy, with increased cardiac output.  The common PK finding, in the paradigms we studied, is that an increased fraction of cardiac output not involved in tissue drug distribution increases early concentrations of rapidly administered drugs, increasing their initial intensity.