Pharmacology Calculators

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Pharmacology is the science of drugs — how they interact with biological systems to produce therapeutic and toxic effects. It encompasses pharmacokinetics (PK: what the body does to the drug — absorption, distribution, metabolism, excretion) and pharmacodynamics (PD: what the drug does to the body — mechanisms of action, dose-response relationships, receptor binding). Understanding PK/PD principles is essential for rational drug dosing, predicting drug interactions, and developing new therapeutic agents.

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Pharmacokinetics (ADME)

  • Absorption: Entry into systemic circulation; oral bioavailability (F) = fraction absorbed × fraction surviving first-pass metabolism
  • Distribution: Volume of distribution (Vd) = drug in body / plasma concentration; high Vd = extensive tissue binding
  • Metabolism: Liver CYP450 enzymes transform drugs; first-pass effect can eliminate > 90% of oral dose for some drugs
  • Excretion: Primarily renal (water-soluble metabolites); half-life t₁/₂ = 0.693 × Vd / CL

Key PK Parameters

Half-life: t₁/₂ = 0.693 / k_elim = 0.693 × Vd / CL. Time to steady-state: ~5 × t₁/₂. After stopping: 50% eliminated per t₁/₂.

Clearance (CL): Volume of plasma cleared per unit time (L/h); CL = dose / AUC.

Pharmacodynamics

Drug effect vs. concentration relationship typically follows the Emax model: E = Emax × C / (EC₅₀ + C), a Michaelis-Menten-like equation. EC₅₀ = concentration for 50% maximum effect; Emax = maximum possible effect. The Hill equation adds cooperativity: E = Emax × C^n / (EC₅₀^n + C^n).

Therapeutic Index

TI = TD₅₀ / ED₅₀ (toxic dose for 50% of population / effective dose for 50%). Narrow TI drugs (warfarin, digoxin, lithium) require careful monitoring and dose adjustment. Wide TI drugs (most antibiotics, statins) have large safety margins.

Glossary

Pharmacokinetics (PK)
What the body does to the drug: Absorption, Distribution, Metabolism, Excretion (ADME); key parameters include bioavailability (F), volume of distribution (Vd), clearance (CL), and half-life (t₁/₂).
Therapeutic Index (TI)
TD₅₀/ED₅₀; ratio of toxic to effective dose; narrow TI drugs (warfarin, digoxin) require therapeutic drug monitoring; wide TI drugs have larger safety margins.
EC₅₀
The drug concentration producing 50% of the maximum pharmacodynamic effect; the inflection point of the sigmoid Emax dose-response curve; analogous to Km in enzyme kinetics.

Frequently Asked Questions

Pharmacokinetics (PK) describes what the body does to the drug: absorption (how it enters the body), distribution (how it spreads to tissues), metabolism (how it is chemically transformed, usually by liver CYP enzymes), and excretion (how it is eliminated). Key PK parameters: bioavailability (F), volume of distribution (Vd), clearance (CL), and half-life (t₁/₂). Pharmacodynamics (PD) describes what the drug does to the body: receptor binding, enzyme inhibition, ion channel modulation, and the resulting dose-effect relationship (EC₅₀, Emax). PK/PD integration determines dosing regimens to maintain drug concentrations within the therapeutic window.

Half-life (t₁/₂) = 0.693/k_elim = 0.693 × Vd/CL; the time for plasma drug concentration to fall by 50%. Key dosing implications: (1) Time to steady state ≈ 4–5 × t₁/₂ — regardless of dose frequency. (2) Time to complete elimination ≈ 4–5 × t₁/₂ after stopping. (3) Dosing interval is typically ~1 × t₁/₂ for most drugs (ensures adequate troughs without excessive peaks). Drug with t₁/₂ = 12 h dosed twice daily; t₁/₂ = 24 h dosed once daily; t₁/₂ = 3–5 days (like levothyroxine) allows weekly dosing.

Therapeutic index (TI) = TD₅₀ / ED₅₀ — the ratio of the toxic dose to the effective dose in 50% of the population. A wide TI (TI > 10) means the drug is safe at doses well above the effective dose — most antibiotics and statins. A narrow TI (TI < 3) means small overdoses can be toxic — warfarin, digoxin, lithium, aminoglycosides, phenytoin. Narrow-TI drugs require therapeutic drug monitoring (TDM) — measuring drug levels in blood to keep concentrations within the therapeutic window. Factors affecting TI: genetic variation in drug metabolism (pharmacogenomics), drug-drug interactions, kidney and liver function.

Cytochrome P450 (CYP) enzymes in the liver and gut are the primary metabolizers of drugs. Key enzymes: CYP3A4 (metabolizes ~50% of all drugs); CYP2D6 (antidepressants, codeine); CYP2C19 (proton pump inhibitors, clopidogrel); CYP2C9 (warfarin, NSAIDs). Drug interactions occur when one drug inhibits or induces a CYP enzyme affecting another drug's metabolism. Example: fluconazole (CYP3A4 inhibitor) increases warfarin levels → bleeding risk. Rifampin (CYP inducer) decreases many drug levels. Genetic polymorphisms create 'poor metabolizers' and 'ultra-rapid metabolizers' with very different drug responses.