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

A patient with a fentanyl patch is given home-care advice. Which instruction is correct?

  1. AAvoid heating pads, hot baths and saunas over or near the patch
  2. BCut the patch in half if the pain is mild
  3. CApply each new patch over the same skin area
  4. DThrow used patches loose into the household bin with the packaging
2.PharmacologyHard

An older patient who has taken omeprazole for many years has muscle cramps, tremor and an irregular heartbeat. Which lab finding is most likely linked to the drug?

  1. AHigh serum sodium
  2. BLow serum glucose
  3. CLow serum magnesium
  4. DHigh serum calcium
3.Dosage calculationsMedium
500 mg+ 4.6 mLV = ? mL

A vial contains 500 mg of powder. The label says: add 4.6 mL of water for injection to give a total volume of 5 mL. The prescription is 100 mg. What volume V of the reconstituted solution do you give?

500 mg+ 4.6 mL → 5 mL100 mg
V = mL
4.Dosage calculationsHard
200 mg/5 mLV = ? mL

A patient weighs 57.2 lb. The prescription is 5 mg/kg as a single dose, and the stock contains 200 mg in 5 mL. Using 1 kg = 2.2 lb, what volume V do you give? Round to one decimal place.

57.2 lb5 mg/kg200 mg/5 mL1 kg = 2.2 lb
V = mL
5.Clinical pharmacokineticsMedium
110t (h)C (mg/L)1 h8 mg/L5 h2.6 mg/L

Practice exercise (made-up values, not clinical guidance). After an IV dose of tobramycin, the level is 8 mg/L at 1 h and 2.6 mg/L at 5 h. Assume first-order elimination. Find the half-life t½.

C1 = 8 mg/L (1 h)C2 = 2.6 mg/L (5 h)
t½ = h
6.Clinical pharmacokineticsHard
t (h)C (mg/L)Css​14 hC = ?

Practice exercise (made-up values, not clinical guidance). A theophylline infusion runs at 45 mg/h with no loading dose. The patient's clearance is 3 L/h and the half-life is 8 h. What is the level C after 14 h?

R = 45 mg/hCL = 3 L/ht½ = 8 ht = 14 h
C = mg/L

3Solutions

1.Pharmacology

Answer: A · Avoid heating pads, hot baths and saunas over or near the patch

Why this is the answer

Heat increases fentanyl absorption and can cause overdose. Sites are rotated, patches are never cut, and used patches are folded sticky sides together and disposed of safely, away from children and pets.

Answer

A · Avoid heating pads, hot baths and saunas over or near the patch
2.Pharmacology

Answer: C · Low serum magnesium

Why this is the answer

Long-term PPI use can cause hypomagnesaemia, which leads to cramps, tremor and arrhythmias. Other long-term risks include fractures, vitamin B12 deficiency and C. difficile infection.

Answer

C · Low serum magnesium
3.Dosage calculations

Answer: V = 1 mL

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 after mixing

500 mg/5 mL = 100 mg/mL

Volume

V = 100/100 = 1 mL

Answer

V = 1 mL
4.Dosage calculations

Answer: V = 3.3 mL

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.

Weight in kg

57.2/2.2 = 26 kg

Dose

5·26 = 130 mg

Volume

V = (130/200)·5 = 3.25 ≈ 3.3 mL

Answer

V = 3.3 mL
5.Clinical pharmacokinetics

Answer: t½ = 2.467 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.

Elimination rate constant

k = ln(8/2.6)/4 = 1.124/4 = 0.281 h⁻¹

Half-life

t½ = 0.693/0.281 = 2.467 h

Answer

t½ = 2.467 h
6.Clinical pharmacokinetics

Answer: C = 10.54 mg/L

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.

Steady-state level

Css = 45/3 = 15 mg/L

Rate constant

k = 0.693/8 = 0.08664 h⁻¹

Level after the given time

C = 15·(1 − e−0.08664·14) = 10.54 mg/L

Answer

C = 10.54 mg/L

ExamProblems · examproblems.com/courses/pharmacology