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

  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

Which blood test is commonly used to monitor a continuous infusion of unfractionated heparin?

  1. AActivated partial thromboplastin time (aPTT)
  2. BSerum potassium
  3. CHaemoglobin A1c
  4. DINR (international normalised ratio, prothrombin time)
2.PharmacologyHard

The thalidomide disaster of the late 1950s and early 1960s is best known for which effect, and what did it lead to?

  1. ADeafness in children; the end of animal testing
  2. BLiver failure in adults; the ban of all sedatives
  3. CSevere limb defects in babies; stricter drug testing and regulation
  4. DHeart attacks in older adults; the start of generic medicines
3.Dosage calculationsMedium
024681010 mL

A child weighing 9 kg is prescribed 4 mg/kg of a drug. The stock solution contains 20 mg/mL. Draw up the dose: what volume V do you give?

9 kg4 mg/kg20 mg/mL
V = mL
4.Dosage calculationsHard
66 kg177 cmBSA = √(h·w/3600)135 mg/m²D = ? mg

A patient is 177 cm tall and weighs 66 kg. The prescription is 135 mg/m². Using the Mosteller formula BSA = √(height (cm) × weight (kg)/3600), find the dose D in mg.

177 cm66 kg135 mg/m²
D = mg
5.Clinical pharmacokineticsMedium
Vd = 7 L/kgC = 1 mcg/LLD = ? mcg63 kg · S = 1 · F = 0.7

Practice exercise (made-up values, not clinical guidance). A 63 kg patient is to be loaded with digoxin tablets to reach a level of 1 mcg/L. The volume of distribution is 7 L/kg and the tablets have a bioavailability F = 0.7. Find the total oral loading dose LD in mcg.

63 kgVd = 7 L/kgC = 1 mcg/LF = 0.7
LD = mcg
6.Clinical pharmacokineticsHard
93 kg82 · womanSCr 1.2 mg/dLCrCl → τ = ? h

Practice exercise (made-up values, not clinical guidance). An 82-year-old woman weighs 93 kg and has a serum creatinine of 1.2 mg/dL (106 µmol/L). Estimate the creatinine clearance with Cockcroft–Gault: CrCl (mL/min) = (140 − age) × weight (kg)/(72 × SCr in mg/dL), × 0.85 for women. The usual tobramycin regimen is 120 mg every 8 h for a creatinine clearance of 100 mL/min. Keeping the dose, the interval is lengthened in proportion to the fall in clearance. Find the new dosing interval τ. Round to one decimal place.

82 years93 kgwomanSCr = 1.2 mg/dL120 mg q8hCrCl normal 100 mL/min
τ = h

3Solutions

1.Pharmacology

Answer: A · Activated partial thromboplastin time (aPTT)

Why this is the answer

Unfractionated heparin is often monitored with the aPTT, and the infusion rate is adjusted according to a protocol. Low-molecular-weight heparins usually do not need routine aPTT checks.

Answer

A · Activated partial thromboplastin time (aPTT)
2.Pharmacology

Answer: C · Severe limb defects in babies; stricter drug testing and regulation

Why this is the answer

Thalidomide caused limb malformations (phocomelia) in thousands of babies. The disaster led to stricter rules on testing drugs for safety, including in pregnancy, and to systems for reporting adverse reactions.

Answer

C · Severe limb defects in babies; stricter drug testing and regulation
3.Dosage calculations

Answer: V = 1.8 mL

Drawing up a dose: volume = (prescribed dose/stock strength) × stock volume. Convert to the same units first, then check that the volume fits the syringe and lands on one of its graduations.

Dose from body weight

D = 4·9 = 36 mg

Volume

V = 36/20 = 1.8 mL

On the syringe

On this 10 mL syringe every small line is 0.2 mL.

Answer

V = 1.8 mL
4.Dosage calculations

Answer: D = 243.2 mg

Body-surface-area dosing: many cytotoxic and some paediatric doses are prescribed per square metre of body surface area: dose (mg) = dose per m² × BSA (m²). The Mosteller formula estimates BSA = √(height (cm) × weight (kg)/3600).

Body surface area

BSA = √(177·66/3600) = √3.245 = 1.801 m²

Dose

D = 135·1.801 = 243.2 mg

Answer

D = 243.2 mg
5.Clinical pharmacokinetics

Answer: LD = 630 mcg

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.

Volume of distribution

Vd = 7·63 = 441 L

Amount of active drug needed

Vd·C = 441·1 = 441 mcg

Loading dose

LD = 441/(1·0.7) = 630 mcg

Answer

LD = 630 mcg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: τ = 15.1 h

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.

Creatinine clearance (Cockcroft–Gault)

CrCl = (140 − 82)·93/(72·1.2)·0.85 = 53.07 mL/min

New interval

τ = 8·100/53.07 = 15.08 ≈ 15.1 h

Answer

τ = 15.1 h

In practice the interval is rounded to a convenient value such as 12, 24, 36 or 48 h.

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