6.3 ADME Rates, Half-Lives, and Compartment Models

Absorption and Bioavailability

Absorption describes drug movement from the site of administration into systemic circulation. Bioavailability (F) is the fraction of administered dose reaching systemic circulation unchanged.

• Intravenous (IV) — F = 1.0; instantaneous peak; no absorption barrier.
• Intramuscular (IM) / Subcutaneous (SC) — water solutions absorb rapidly; oil depots slow release.
• Oral (PO) — the most common but most variable route; subject to gut transit, solubility, permeability, and first-pass metabolism in the gut wall and liver. Propranolol, morphine, and lidocaine have high extraction ratios and low oral bioavailability despite complete absorption.
• Sublingual / buccal — bypass portal circulation; nitroglycerin reaches systemic circulation quickly.
• Topical / transdermal — local effect or systemic delivery through intact skin.
• Rectal — partial bypass of first-pass; useful when vomiting or unconscious.
• Inhalation — local delivery to lung minimizes systemic exposure for beta-agonists and corticosteroids.

Distribution

Volume of distribution (Vd) is the apparent volume that would be required to contain the total body drug at the measured plasma concentration: Vd = Dose / C0. Vd is a theoretical, not anatomic, volume.

• Vd ≈ 3-5 L: drug largely confined to plasma (warfarin, heparin — high plasma protein binding).
• Vd ≈ 15-18 L: extracellular water (small polar drugs).
• Vd ≈ 42 L: total body water (ethanol, theophylline).
• Vd >> 100 L: extensive tissue or fat binding (digoxin ~500 L, chloroquine ~13,000 L, amiodarone ~60 L/kg).

Protein binding — acidic drugs bind albumin; basic drugs bind alpha1-acid glycoprotein (an acute-phase reactant, rises in inflammation). Only free drug distributes, is metabolized, and excretes; displacement interactions raise free fraction transiently but rarely matter clinically unless Vd is small and clearance is low.

Blood-brain barrier (BBB) — tight junctions and efflux transporters (P-gp, BCRP) exclude hydrophilic and large molecules; lipophilic small molecules cross by passive diffusion. Inflammation (meningitis) partially opens the BBB, allowing penicillin to reach therapeutic CSF concentrations.

Metabolism and Excretion

Hepatic clearance: CLh = Qh · E, where Qh is hepatic blood flow (~90 L/h) and E the extraction ratio.

• High-extraction drugs (E > 0.7; morphine, propranolol, verapamil) — clearance is blood-flow-limited; sensitive to hepatic blood flow changes (heart failure) but relatively insensitive to protein binding or enzyme induction.
• Low-extraction drugs (E < 0.3; warfarin, phenytoin, diazepam, theophylline) — clearance is capacity-limited; sensitive to enzyme induction/inhibition and protein binding.

Renal clearance combines glomerular filtration (GFR ~120 mL/min), active tubular secretion (OAT/OCT transporters in proximal tubule), and passive reabsorption (lipophilic weak acids/bases reabsorbed when urine pH favors the uncharged form).

Creatinine clearance (CrCl) is estimated by Cockcroft-Gault:

CrCl (mL/min) = [(140 − age) × weight (kg)] / (72 × SCr)

Multiply by 0.85 for females (standard Cockcroft-Gault sex correction). Many drug labels reference Cockcroft-Gault for renal dose adjustment. The 2021 CKD-EPI equation estimates GFR (eGFR) but is not always interchangeable for drug dosing.

Half-Life, Clearance, and Steady State

Half-life is the time for plasma concentration to fall by 50%: t1/2 = 0.693 · Vd / CL. It governs:

• Dosing interval — drugs with short t1/2 need frequent dosing or sustained-release formulation.
• Time to steady state — after 4-5 half-lives, accumulation equals elimination and the patient reaches ~94-97% of steady state. Doubling the dose does NOT shorten time to steady state; it only raises the steady-state concentration.
• Washout — similarly 4-5 half-lives for near-complete elimination.

Clearance (CL) is the volume of plasma cleared of drug per unit time: CL = Rate of elimination / C. Total body clearance is the sum of renal and non-renal clearances.

Compartment Models

In a two-compartment model, IV bolus produces a curve with an early steep distribution (alpha) phase as drug leaves plasma for tissues, followed by a slower elimination (beta) phase whose slope gives the terminal half-life used in dosing.

Linear vs Nonlinear Pharmacokinetics

Linear PK — clearance, Vd, and t1/2 are independent of dose; AUC rises proportionally with dose. Most drugs behave this way at therapeutic concentrations.

Nonlinear PK — saturable metabolism follows Michaelis-Menten kinetics: v = (Vmax · C) / (Km + C). When C approaches or exceeds Km, clearance falls and small dose increases produce disproportionate concentration rises. Phenytoin (Km ≈ 4 mg/L, Vmax ≈ 7 mg/kg/day) is the classic example: a 100 mg/day increment can carry a patient from subtherapeutic to toxic. Other examples: ethanol (zero-order at social doses), high-dose aspirin, theophylline at high doses.

Loading Dose, Maintenance Dose, and TDM

• Maintenance dose rate = Css,target · CL (for IV infusion) or Css,avg · CL / F (oral).
• Loading dose = Css,target · Vd / F; rapidly achieves therapeutic levels for drugs with long half-lives (amiodarone, digoxin, phenytoin, vancomycin).
• Peak (Cmax) and trough (Cmin) samples bracket the dosing interval; for aminoglycosides, peaks assess efficacy and troughs avoid nephrotoxicity. Vancomycin troughs (10-20 mg/L) target nephrotoxicity avoidance; newer Bayesian dosing uses AUC/MIC ratios.

Therapeutic drug monitoring (TDM) is essential for narrow-therapeutic-index drugs: aminoglycosides, vancomycin, digoxin, phenytoin, lithium, warfarin (INR), cyclosporine, tacrolimus, and anti-epileptics. Sampling at trough (just before next dose) is the standard for steady-state assessment.