Pharmacology: cram pack

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

New problemsBack to the course

In the print window, choose “Save as PDF” to keep a copy on your device.

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

  1. Convert the ordered dose and the stock strength to the same unit.
  2. Use desired over have times quantity: (D/H) × Q.
  3. For weight-based doses, multiply by the weight in kg first, then divide the daily dose by the number of doses.
  4. 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·Css/(S·F)
Average steady state
Css,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(Cpeak/Ctrough)/k, D = Vd·(Cpeak − Ctrough)
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

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

2Practice problems

1.PharmacologyMedium

Why is IV promethazine given with great caution?

  1. AIt is a strong opioid that causes addiction
  2. BIt can cause severe tissue injury if it leaks or enters an artery
  3. CIt causes immediate kidney failure
  4. DIt causes a severe rise in blood pressure when it is given intravenously
2.PharmacologyHard

A woman with chronic hypertension who takes lisinopril is now pregnant. What is the key concern?

  1. ALisinopril works better in pregnancy, so the dose should be increased
  2. BLisinopril has no known fetal effects and should be continued
  3. CAll antihypertensives must be stopped in pregnancy
  4. DACE inhibitors harm fetal kidneys, so a safer drug is used
3.Dosage calculationsMedium
90 kg10 mg/kgD = ? mg

A patient weighs 90 kg and is prescribed 10 mg/kg as a single dose. Find the dose D in mg.

90 kg10 mg/kg
D = mg
4.Dosage calculationsHard
25k units250 mL? mL/h1500 units/h

An infusion contains 25000 units of a drug in 250 mL. The prescription is 1500 units per hour. At what rate R do you set the pump, in mL/h?

25000 units/250 mL1500 units/h
R = mL/h
5.Clinical pharmacokineticsMedium
VCss​ = 12 mg/LR = ? mg/hCL = 0.04 L/kg/h78 kg

Practice exercise (made-up values, not clinical guidance). A 78 kg patient receives a theophylline infusion. The clearance is 0.04 L/kg/h. What infusion rate R in mg/h gives a steady-state level of 12 mg/L?

78 kgCL = 0.04 L/kg/hCss = 12 mg/L
R = mg/h
6.Clinical pharmacokineticsHard
Vd = 7 L/kg0.2 → 0.8 mcg/LLD = ? mcg92 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 92 kg patient has a digoxin level of 0.2 mcg/L; the target is 0.8 mcg/L. The volume of distribution is 7 L/kg and the tablets have F = 0.7. What extra loading dose LD raises the level to the target?

92 kgVd = 7 L/kgC = 0.2 → 0.8 mcg/LF = 0.7
LD = mcg

3Solutions

1.Pharmacology

Answer: B · It can cause severe tissue injury if it leaks or enters an artery

Why this is the answer

Promethazine is a vesicant. Deep intramuscular injection is the preferred parenteral route, and if given IV it is diluted, given slowly into a well-running large vein, and stopped at once if the patient reports burning or pain.

Answer

B · It can cause severe tissue injury if it leaks or enters an artery
2.Pharmacology

Answer: D · ACE inhibitors harm fetal kidneys, so a safer drug is used

Why this is the answer

ACE inhibitors and ARBs cause fetal kidney damage, oligohydramnios and other problems, especially later in pregnancy. Drugs such as labetalol, nifedipine or methyldopa are used instead.

Answer

D · ACE inhibitors harm fetal kidneys, so a safer drug is used
3.Dosage calculations

Answer: D = 900 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.

Dose

10·90 = 900 mg

Answer

D = 900 mg
4.Dosage calculations

Answer: R = 15 mL/h

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.

Concentration

25000/250 = 100 units/mL

Pump rate

R = 1500/100 = 15 mL/h

Answer

R = 15 mL/h
5.Clinical pharmacokinetics

Answer: R = 37.44 mg/h

Clearance and volume: at steady state the dosing rate equals the elimination rate, so the maintenance rate = CL × Css. 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.

Clearance

CL = 0.04·78 = 3.12 L/h

Infusion rate

R = 3.12·12 = 37.44 mg/h

Answer

R = 37.44 mg/h
6.Clinical pharmacokinetics

Answer: LD = 552 mcg

Designing a regimen: with rapid IV doses the level falls from peak to trough during the interval, so τ = ln(Cpeak/Ctrough)/k and the dose that restores the peak is Vd × (Cpeak − Ctrough). The average steady-state level is Css,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 = 7·92 = 644 L

Rise needed

0.8 − 0.2 = 0.6 mcg/L

Loading dose

LD = 644·0.6/(1·0.7) = 552 mcg

Answer

LD = 552 mcg

In practice the dose is rounded to a convenient amount.

ExamProblems · examproblems.com/courses/pharmacology