Pharmacology: cram pack

Formula sheets, the key method steps for every topic and 6 practice problems, with full solutions at the back.

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1Formulas and methods

Dosage calculations

Dose from strength: volume = dose / strength
Weight-based dose: dose = mg/kg × body weight
Tablets: number = dose / tablet strength
Units: 1 g = 1000 mg, 1 mg = 1000 mcg

Method

Convert the ordered dose and the stock strength to the same unit.
Use desired over have times quantity: (D/H) × Q.
For weight-based doses, multiply by the weight in kg first, then divide the daily dose by the number of doses.
Estimate first and check that the answer is reasonable.

Clinical pharmacokinetics

Rate constant and half-life: k = ln 2/t½ = 0.693/t½
First-order decay: C = C₀·e^−kt = C₀·(1/2)^t/t½
Two levels: k = ln(C₁/C₂)/Δt
Volume and clearance: Vd = dose/C₀, CL = k·Vd
Loading dose: LD = Vd·C/(S·F)
Maintenance rate: R = CL·C_ss/(S·F)
Average steady state: C_ss,avg = S·F·D/(CL·τ)
Steady state: 1 − (1/2)ⁿ after n half-lives; ≈ 97% after 5
Infusion: C = (R/CL)(1 − e^−kt)
Interval and dose from peak and trough: τ = ln(C_peak/C_trough)/k, D = Vd·(C_peak − C_trough)
Cockcroft–Gault: CrCl = (140 − age) × kg/(72 × SCr mg/dL), × 0.85 for women
Renal adjustment: dose × CrCl/normal; Dettli Q = 1 − fe·(1 − CrCl/normal)

Method

Convert the half-life to a rate constant: k = 0.693/t½.
Turn per-kg values into totals: Vd (L) = L/kg × weight, CL (L/h) = L/kg/h × weight.
Pick the relation: C = C₀·e^−kt, LD = Vd·C/(S·F), maintenance rate = CL·Css/(S·F), τ = ln(Cpeak/Ctrough)/k.
For kidney function, estimate CrCl with Cockcroft–Gault first, then scale the dose or the interval.
Check the result: levels fall by half every half-life, and steady state takes about five half-lives.

2Practice problems

1.PharmacologyMedium

Warfarin works by:

ABlocking platelet aggregation through irreversible inhibition of COX-1
BDirectly inhibiting thrombin
CBlocking the vitamin K-dependent synthesis of clotting factors
DActivating antithrombin

2.PharmacologyHard

A drug has a volume of distribution of 40 L and complete bioavailability. Which loading dose gives a target plasma concentration of 2 mg/L?

A160 mg
B42 mg
C80 mg
D20 mg

3.Dosage calculationsMedium

A patient weighs 15 kg. The prescribed dose is 5 mg/kg per day, given in 3 equal doses. How many milligrams D are given per dose?

15 kg5 mg/kg/day3× per day

D = mg

4.Dosage calculationsHard

A patient weighs 114.4 lb. The prescription is 1 mg/kg as a single dose, and the stock contains 50 mg in 1 mL. Using 1 kg = 2.2 lb, what volume V do you give? Round to one decimal place.

114.4 lb1 mg/kg50 mg/1 mL1 kg = 2.2 lb

V = mL

5.Clinical pharmacokineticsMedium

Practice exercise (made-up values, not clinical guidance). After an IV dose of vancomycin, the level is 35 mg/L at 2 h and 17.5 mg/L at 10 h. Assume first-order elimination. Find the half-life t½.

C₁ = 35 mg/L (2 h)C₂ = 17.5 mg/L (10 h)

t½ = h

6.Clinical pharmacokineticsHard

Practice exercise (made-up values, not clinical guidance). An 85 kg patient on regular tobramycin doses is at steady state. The target is a peak of 6 mg/L and a trough of 1 mg/L, and the volume of distribution is 0.3 L/kg. Assuming rapid IV doses, what dose D raises the level from the trough to the peak?

85 kgVd = 0.3 L/kgC_peak = 6 mg/LC_trough = 1 mg/L

D = mg

3Solutions

1.Pharmacology

Answer: C · Blocking the vitamin K-dependent synthesis of clotting factors

Why this is the answer

Warfarin inhibits vitamin K epoxide reductase, reducing synthesis of factors II, VII, IX and X. It is monitored with the INR and reversed with vitamin K.

Answer

C · Blocking the vitamin K-dependent synthesis of clotting factors

2.Pharmacology

Answer: C · 80 mg

Why this is the answer

Loading dose = 40 L × 2 mg/L = 80 mg. The loading dose depends on Vd, while the maintenance dose depends on clearance.

Answer

C · 80 mg

3.Dosage calculations

Answer: D = 25 mg

Dose calculation: the amount to give equals what is prescribed divided by what you have, times the quantity it comes in: amount = (desired dose/stock strength) × stock volume. Always keep the units the same (convert g to mg, mg to mcg first) and check that the answer is sensible.

Total per day

5·15 = 75 mg

Per dose

D = 75/3 = 25 mg

Answer

D = 25 mg

4.Dosage calculations

Answer: V = 1 mL

Weight in kg

114.4/2.2 = 52 kg

Dose

1·52 = 52 mg

Volume

V = (52/50)·1 = 1.04 ≈ 1 mL

Answer

V = 1 mL

5.Clinical pharmacokinetics

Answer: t½ = 8 h

Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × C_ss. A loading dose is LD = Vd × C/(S × F), with S the salt factor (fraction of active drug in the salt) and F the bioavailability (1 for IV). From two levels, k = ln(C₁/C₂)/Δt; for an IV bolus Vd = dose/C₀ and CL = k × Vd. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.

Elimination rate constant

k = ln(35/17.5)/8 = 0.6931/8 = 0.08664 h⁻¹

Half-life

t½ = 0.693/0.08664 = 8 h

Answer

t½ = 8 h

6.Clinical pharmacokinetics

Answer: D = 127.5 mg

Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(C_peak/C_trough)/k and the dose that restores the peak is Vd × (C_peak − C_trough). The average steady-state level is C_ss,avg = S·F·dose/(CL·τ). An infusion rises as C = (R/CL)(1 − e^−kt). For a drug cleared by the kidneys, the dose is scaled with the creatinine clearance. The numbers are for practice only; at the bedside always follow local protocols and have high-risk doses double-checked.

Volume of distribution

Vd = 0.3·85 = 25.5 L

Dose

D = 25.5·(6 − 1) = 127.5 mg

Answer

D = 127.5 mg

In practice the dose is rounded to a convenient amount.

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