Key Formulas & Equations
Volume of Distribution: Vd = Dose / C₀
Clearance: Cl = Dose / AUC = k × Vd
Elimination Rate Constant: k = 0.693 / t½
Steady-State Concentration: Css = F × Dose / (Cl × τ)
Loading Dose: LD = (Css × Vd) / F
Maintenance Dose: MD = (Css × Cl × τ) / F
Percent Ionization: % ionized = 100 / (1 + 10(pKa-pH))
Osmolarity: Osm = n × Molarity (n = particles per molecule)
Pediatric Dose (Clark's Rule): Child dose = (Weight/150) × Adult dose
Pediatric Dose (Young's Rule): Child dose = (Age/(Age+12)) × Adult dose
Corrected Calcium: Cacorr = Ca + 0.8(4 - albumin)
Anion Gap: AG = Na⁺ - (Cl⁻ + HCO₃⁻)
Core Concepts
Pharmacokinetics
The study of drug movement through the body: Absorption, Distribution, Metabolism, and Excretion (ADME). Determines how drugs reach their targets and how long they act.
Pharmacodynamics
The study of drug effects on the body, including mechanisms of action, receptor binding, dose-response relationships, and therapeutic vs toxic effects.
Drug Interactions
How drugs affect each other's actions when taken together. Includes pharmacokinetic interactions (absorption, metabolism) and pharmacodynamic interactions (synergism, antagonism).
Pharmaceutical Calculations
Mathematical computations used in pharmacy practice: dosage calculations, compounding measurements, IV flow rates, and unit conversions.
Pharmacology
The study of how drugs interact with living organisms. Includes drug classification, mechanisms, therapeutic uses, adverse effects, and contraindications.
Pharmaceutics
The science of drug formulation and delivery. Covers dosage forms, drug stability, bioavailability, and novel drug delivery systems.
Clinical Pharmacy
The application of pharmaceutical knowledge to patient care. Includes medication therapy management, pharmacovigilance, and evidence-based drug selection.
Toxicology
The study of adverse effects of chemicals on living organisms. Includes drug overdose management, antidotes, and poison control.
Worked Examples
Example 1: Half-Life and Clearance
Problem: A drug has Vd = 50 L and clearance = 5 L/hr. Calculate the elimination half-life.
Solution:
k = Cl/Vd = 5/50 = 0.1 hr⁻¹
t½ = 0.693/k = 0.693/0.1 = 6.93 hours
Example 2: Loading Dose Calculation
Problem: Desired Css = 10 mg/L, Vd = 20 L, F = 1.0. Calculate loading dose.
Solution:
LD = (Css × Vd)/F = (10 × 20)/1.0 = 200 mg
Example 3: Henderson-Hasselbalch
Problem: Aspirin (pKa = 3.5) in urine (pH = 6.5). Calculate ratio of ionized to unionized forms.
Solution:
pH = pKa + log([A⁻]/[HA])
6.5 = 3.5 + log([A⁻]/[HA])
log([A⁻]/[HA]) = 3.0
[A⁻]/[HA] = 1000:1 (mostly ionized, excreted in urine)
Practice Problems
Problem 1
A drug has t½ = 4 hours and Vd = 30 L. Calculate clearance.
Answer: Cl = 0.693 × Vd/t½ = 0.693 × 30/4 = 5.2 L/hr
Problem 2
Calculate maintenance dose for Css = 5 mg/L, Cl = 2 L/hr, τ = 8 hr, F = 0.8.
Answer: MD = (5 × 2 × 8)/0.8 = 100 mg
Problem 3
Order: Amoxicillin 250 mg. Available: 500 mg/5 mL. Calculate volume to dispense.
Answer: (250/500) × 5 mL = 2.5 mL
Problem 4
A 60 kg child needs a drug with adult dose 400 mg. Use Clark's Rule (weight in lbs).
Answer: 60 kg = 132 lbs; (132/150) × 400 = 352 mg
Problem 5
Calculate bioavailability if AUCoral = 80 mg·hr/L and AUCIV = 100 mg·hr/L.
Answer: F = (80/100) × 100% = 80%
Problem 6
A drug is 50% ionized at pH 5.0. What is its pKa?
Answer: When 50% ionized, [A⁻] = [HA], so pH = pKa = 5.0
Problem 7
Calculate steady-state concentration for dose = 200 mg, τ = 12 hr, Cl = 4 L/hr, F = 1.0.
Answer: Css = (1.0 × 200)/(4 × 12) = 4.17 mg/L