An Application of Computer Algebra to Pharmacokinetics: The Bateman Equation

Exponentially decaying functions can be successfully introduced as early as high school. However, obtaining the equations for the resulting effect of absorption and elimination of drug processes acting simultaneously, even in simplified models like the single dose case in a one-compartment model wit...

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Bibliographic Details
Published in:SIAM review 2006-03, Vol.48 (1), p.133-146
Main Authors: Roanes-Lozano, Eugenio, González-Bermejo, Alfonso, Roanes-Macías, Eugenio, Cabezas, Justo
Format: Article
Language:English
Subjects:
Algebra
Algorithmics. Computability. Computer arithmetics
Applied sciences
Computer algebra systems
Computer science
control theory
systems
Differential equations
Dosage
Education
Exact sciences and technology
Exponential functions
Intravenous injections
Kinetics
Mathematical analysis
Mathematical functions
Mathematics
Medication administration
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
Ordinary differential equations
Pharmacokinetics
Pharmacology
Sciences and techniques of general use
Studies
Theoretical computing
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Summary:Exponentially decaying functions can be successfully introduced as early as high school. However, obtaining the equations for the resulting effect of absorption and elimination of drug processes acting simultaneously, even in simplified models like the single dose case in a one-compartment model with an order 1 kinetic (Bateman equation), requires one to solve a nontrivial differential equation. Therefore, this equation is normally taught to second- or third-year students in the schools of medicine and pharmacy. An alternative approach is presented that uses a computer algebra system to calculate a limit and allows one to bypass the use of differential equations.
ISSN:0036-1445
1095-7200
DOI:10.1137/050634074