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

Why are many drugs started at lower doses in older adults?

  1. AKidney and liver clearance often decline, and sensitivity to drugs increases
  2. BOlder adults always weigh more than younger adults, so drugs last longer
  3. COlder adults absorb no drugs from the stomach
  4. DLower doses are cheaper for older patients
2.PharmacologyHard

Which strategy is most effective at preventing errors with IV insulin infusions?

  1. AWriting "U" for units on the order
  2. BUsing insulin syringes to measure large IV volumes
  3. CPreparing insulin infusions in advance and leaving them unlabelled
  4. DAn independent double check and a smart pump with a drug library
3.Dosage calculationsMedium
19 kgBSA = 0.78 m²135 mg/m²D = ? mg

A patient weighing 19 kg has a body surface area of 0.78 m². The prescription is 135 mg/m². Find the dose D in mg.

19 kgBSA = 0.78 m²135 mg/m²
D = mg
4.Dosage calculationsHard
00.10.20.30.40.50.60.70.80.911 mL

The prescription is 6200 units of a drug that comes as 10000 units/mL. Draw up the dose in the 1 mL syringe: what volume V do you give?

6200 units10000 units/mL
V = mL
5.Clinical pharmacokineticsMedium
Vd = 0.7 L/kgC = 20 mg/LLD = ? mg100 kg · S = 0.92 · F = 1

Practice exercise (made-up values, not clinical guidance). A 100 kg patient is to be loaded intravenously with phenytoin sodium to reach a phenytoin level of 20 mg/L. The volume of distribution is 0.7 L/kg and the salt factor is S = 0.92. Find the loading dose LD of phenytoin sodium in mg.

100 kgVd = 0.7 L/kgC = 20 mg/LS = 0.92
LD = mg
6.Clinical pharmacokineticsHard
t (h)C (mg/L)Css​t = ?95%

Practice exercise (made-up values, not clinical guidance). A theophylline infusion is started without a loading dose. The half-life in this patient is 9 h. How long t does it take to reach 95% of the steady-state level?

t½ = 9 h95% Css
t = h

3Solutions

1.Pharmacology

Answer: A · Kidney and liver clearance often decline, and sensitivity to drugs increases

Why this is the answer

Ageing reduces kidney function, changes body composition and often slows liver metabolism. Many drugs also have stronger effects on the ageing brain, so doses are started low and increased slowly.

Answer

A · Kidney and liver clearance often decline, and sensitivity to drugs increases
2.Pharmacology

Answer: D · An independent double check and a smart pump with a drug library

Why this is the answer

Independent double checks, standard concentrations and smart pumps with dose limits reduce insulin errors. "U" for units is avoided because it can be misread as a zero.

Answer

D · An independent double check and a smart pump with a drug library
3.Dosage calculations

Answer: D = 105.3 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).

Dose

D = 135·0.78 = 105.3 mg

Answer

D = 105.3 mg
4.Dosage calculations

Answer: V = 0.62 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.

Volume

V = 6200/10000 = 0.62 mL

On the syringe

On this 1 mL syringe every small line is 0.01 mL.

Answer

V = 0.62 mL
5.Clinical pharmacokinetics

Answer: LD = 1522 mg

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 = 0.7·100 = 70 L

Amount of active drug needed

Vd·C = 70·20 = 1400 mg

Loading dose

LD = 1400/(0.92·1) = 1522 mg

Answer

LD = 1522 mg

In practice the dose is rounded to a convenient amount.

6.Clinical pharmacokinetics

Answer: t = 38.9 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.

Rate constant

k = 0.693/9 = 0.07702 h⁻¹

Time to the given fraction of steady state

t = −ln(1 − 0.95)/0.07702 = 2.996/0.07702 = 38.9 h

Answer

t = 38.9 h

That is 4.322 half-lives.

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