Applied mathematics and modelling · Maths EE idea · Accessible
Repeated doses and steady state
A research question to start from
How does the amount of a drug in the body behave under repeated doses, and how quickly does it approach a steady state?
A starting point, not your question: change the case, the comparison or the limit until it is yours. The research-question builder helps you check it.
Why it works as a maths EE
Geometric series and recurrence relations give exact formulas for a realistic process.
Mathematics you would need
- Exponential decay
- Recurrence relations
- Geometric series
- Limits
Much of this goes beyond the DP course. That is expected in a maths EE, but you must understand and explain everything you use.
One possible line of attack
- Model one dose with exponential decay.
- Derive peak and trough levels after n doses.
- Find the steady state and the time to approach it; discuss assumptions.
Scope and difficulty
Accessible. Accessible.
Pitfalls
- Medical claims beyond the model.
- Only numerical tables.
Where to start reading
Search a library catalogue or a university's open lecture notes for: repeated dosing geometric series steady state pharmacokinetics one compartment. Prefer textbooks, lecture notes and journal articles to a single website, and cite everything you use (how to reference a maths EE).
Make it your EE
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