Pharmacokinetics questions become easier when you identify what the examiner is asking before reaching for a formula. Are you trying to achieve an initial drug concentration, replace drug that has been eliminated, or predict how concentration changes over time?
This guide connects those questions to loading dose, maintenance dosing, clearance and half-life. Work through the examples, then attempt the five original single-best-answer questions without looking at the explanations. For a broader study schedule, see our MRCEM Primary revision guide.
The examples use hypothetical drugs and simplified models for examination revision, not patient prescribing. Unless stated otherwise, assume linear, one-compartment pharmacokinetics, constant parameters and no drug already present. Amounts refer to active drug, with no additional salt correction.
Which MRCEM Primary syllabus applies?
RCEM currently describes MRCEM Primary as 180 SBAs in three hours. The updated Basic Sciences Syllabus becomes the official reference from the 21 April 2027 examination onwards. Check the syllabus for your sitting rather than assuming an older subject weighting still applies. [1] [2]
1. Start with the unknown quantity
Loading, maintenance or elimination?
Write down the quantity you need and its expected unit. A loading dose should end in mg; a dosing rate may end in mg/hour; a half-life should end in a unit of time. This simple check can expose a wrong equation before you finish the arithmetic.
Question asks for | Start with | Expected unit |
|---|---|---|
Initial amount needed | Loading dose | mg |
Amount given per hour | Maintenance dosing rate | mg/hour |
Amount given each interval | Maintenance dose | mg/dose |
Time for concentration to halve | Elimination half-life | hours |
Know the symbols and units
Symbol | Meaning | Example unit or value |
|---|---|---|
Vd | Apparent volume of distribution | L, or L/kg before weight adjustment |
CL | Clearance | L/hour |
F | Bioavailability: fraction reaching systemic circulation | 0.5 for 50%; 1 for intravenous administration |
Ctarget | Target concentration | mg/L |
Css,avg | Average steady-state concentration | mg/L |
τ | Dosing interval | hours |
Use compatible units throughout. For example, 50 mL/min equals 3 L/hour: multiply by 60 to convert minutes to hours, then divide by 1,000 to convert millilitres to litres. The definitions and dosing relationships below follow standard pharmacokinetic principles summarised in UK Medicines Information guidance. [3]
2. Volume of distribution and loading dose
What does apparent volume of distribution mean?
Vd relates the amount of drug in the body to its measured plasma concentration. It is an apparent volume, not an anatomical compartment that can be measured with a scan. A large value can reflect extensive distribution outside plasma. [3]
Vd = amount of drug in the body ÷ plasma concentration
For example, if the body contains 240 mg of a hypothetical drug and the plasma concentration is 4 mg/L, Vd is 240 ÷ 4 = 60 L. Do not automatically substitute an administered oral dose for the amount currently in the body: absorption and elimination matter.
Calculate a loading dose
Loading dose = Ctarget × Vd ÷ F
A hypothetical intravenous drug has Vd = 40 L and a target concentration of 6 mg/L. Because intravenous bioavailability is 1, the calculated loading dose is 6 × 40 ÷ 1 = 240 mg. The units confirm the result: mg/L × L = mg. [3]
Adjust for body weight and bioavailability
Now consider a 70 kg adult, Vd = 0.6 L/kg, target concentration = 5 mg/L and oral bioavailability = 50%. First calculate total Vd: 0.6 × 70 = 42 L. Then calculate the loading dose: 5 × 42 ÷ 0.5 = 420 mg.
The corresponding intravenous calculation would give 210 mg. In this simplified model, a larger oral dose is required because only half reaches systemic circulation. Entering 50 instead of 0.5 would produce a 100-fold error. The equation estimates an amount; it does not determine a safe administration rate.
3. Clearance and maintenance dosing
Clearance is a volume per unit time
Clearance relates elimination rate to plasma concentration. It is expressed as a volume per unit time, such as L/hour, rather than an amount such as mg/hour. Maintenance input must replace the drug being eliminated to sustain the intended concentration. [4]
Maintenance dose rate versus dose per interval
Maintenance dosing rate = target steady-state concentration × CL ÷ F
Intermittent maintenance dose = Css,avg × CL × τ ÷ F
Suppose CL = 3 L/hour and the target concentration during continuous intravenous infusion is 8 mg/L. The required theoretical infusion rate is 8 × 3 = 24 mg/hour. This is a rate, not a single dose. [4]
For an oral regimen targeting an average steady-state concentration of 8 mg/L, with CL = 3 L/hour, F = 0.8 and an eight-hour interval, the calculation is 8 × 3 × 8 ÷ 0.8 = 240 mg every eight hours. The administered average rate is 30 mg/hour; multiplying by F gives a systemic input of 24 mg/hour.
With intermittent dosing, concentration generally fluctuates between peaks and troughs. An average target does not mean the concentration stays at that value throughout the interval. [3]
What if clearance falls?
If clearance in the infusion example falls from 3 to 1.5 L/hour, maintaining the same target requires 8 × 1.5 = 12 mg/hour. If Vd, target concentration and F remain unchanged, the loading-dose calculation is unchanged. This comparison assumes those parameters really are constant; illness can alter more than one parameter simultaneously.
4. Half-life and time to steady state
Relate half-life to clearance and distribution
t½ = 0.693 × Vd ÷ CL
In the simplified first-order model, Vd = 50 L and CL = 5 L/hour give t½ = 0.693 × 50 ÷ 5 = 6.93 hours. Halving clearance with unchanged Vd doubles this value. Increasing Vd with unchanged clearance also increases half-life. [4]
Why four to five half-lives is approximate
For a constant infusion starting from zero, the simple first-order model gives the fraction of eventual steady state after n half-lives as 1 − (½)n. The following values are calculated from that relationship.
Half-lives elapsed | Eventual steady-state concentration reached | Initial concentration remaining after stopping input* |
|---|---|---|
1 | 50% | 50% |
2 | 75% | 25% |
3 | 87.5% | 12.5% |
4 | 93.75% | 6.25% |
5 | 96.875% | 3.125% |
*Assuming no further absorption or administration and unchanged first-order elimination.
For a six-hour half-life, five half-lives take 30 hours. That corresponds to approximately 97% of the eventual steady-state concentration, not exactly 100%. Likewise, five half-lives after stopping input does not mean every molecule has disappeared.
Does a loading dose change half-life?
A loading dose can establish the desired concentration sooner, but it does not shorten the elimination half-life when the pharmacokinetic parameters remain unchanged. In an ideal one-compartment model, an appropriate intravenous loading dose followed by a matching infusion can establish the target immediately. [4]
5. First-order and capacity-limited elimination
Constant fraction versus constant amount
First-order elimination removes a constant fraction over equal time intervals. If the concentration halves every four hours, a sequence could be 32, 16, 8 and 4 mg/L. The amount removed becomes smaller, but the time taken to halve remains constant.
Zero-order elimination removes a constant amount per unit time. With fixed Vd, an illustrative concentration sequence falling by 4 mg/L each hour is 20, 16, 12 and 8 mg/L. Falling from 20 to 10 mg/L takes 2.5 hours, while falling from 10 to 5 mg/L takes 1.25 hours. There is no single concentration-independent half-life.
When the usual shortcut stops working
Capacity-limited elimination can arise when elimination pathways become saturated. A drug may behave approximately first-order at lower concentrations and approach zero-order behaviour at higher concentrations. Do not apply the same fixed half-life to every concentration range, particularly if a stem explicitly describes saturation.
6. Five original pharmacokinetics practice SBAs
These are original educational questions, not recalled or official RCEM questions. Apply the simplified assumptions stated at the start of this article.
Question 1: Weight-adjusted loading dose
A hypothetical intravenous drug has Vd = 0.5 L/kg. An 80 kg adult has no drug already present. What loading dose achieves an initial target concentration of 4 mg/L?
Question 2: Oral bioavailability
A hypothetical oral drug has Vd = 30 L, F = 0.6 and a target concentration of 10 mg/L. Ignoring elimination during absorption, what calculated loading dose is required?
Question 3: Maintenance dose
A hypothetical drug has CL = 4 L/hour and oral bioavailability of 0.5. What dose every six hours gives an average steady-state concentration of 5 mg/L?
Question 4: Elimination half-life
A drug follows first-order elimination with Vd = 60 L and CL = 6 L/hour. What is its approximate elimination half-life?
Question 5: Approaching steady state
A constant intravenous infusion starts with no drug present. The drug follows the simple first-order model and has a half-life of eight hours. Approximately how long is needed to reach 97% of its eventual steady-state concentration?
Answers and worked explanations
1. D — 160 mg. Total Vd = 0.5 × 80 = 40 L. Loading dose = 4 × 40 = 160 mg. A omits body weight; B reports the numerical Vd rather than the dose; C reports the body weight; E ignores the 0.5 L/kg factor.
2. D — 500 mg. Loading dose = 10 × 30 ÷ 0.6 = 500 mg. A uses 60 instead of 0.6; B multiplies by F; C ignores F; E would correspond to F = 0.5 rather than 0.6.
3. D — 240 mg. Dose = 5 × 4 × 6 ÷ 0.5 = 240 mg. A gives the numerical hourly dosing rate but labels it as a dose; B multiplies by F; C ignores F; E uses 24 hours rather than the stated six-hour interval.
4. C — 6.93 hours. Half-life = 0.693 × 60 ÷ 6 = 6.93 hours. A reverses Vd and clearance; B reports the constant alone; D omits 0.693; E is a tenfold arithmetic error.
5. E — 40 hours. Five half-lives give 96.875%, which rounds to approximately 97%. Five × eight = 40 hours. A, B, C and D represent one, two, three and four half-lives: 50%, 75%, 87.5% and 93.75%, respectively.
7. Common mistakes and quick answers
Five checks before choosing an answer
Convert percentages: use 0.5 for 50%.
Align time units: do not combine L/min with hours without conversion.
Check weight adjustment: convert L/kg to total litres when needed.
Distinguish dose and rate: mg/hour is not mg/dose.
Round at the end: retain intermediate values until the final calculation.
Does loading dose depend on clearance?
Clearance does not appear directly in the simplified loading-dose equation. With target concentration, Vd and F fixed, changing clearance alone does not change that calculated loading dose. Clearance does influence subsequent dosing requirements.
Does doubling a dose double half-life?
No, not under linear first-order kinetics with constant Vd and clearance. It doubles the initial concentration in the simple model. Reaching the same absolute lower concentration then takes one additional half-life; the half-life itself is unchanged.
Is steady state exactly reached after five half-lives?
No. A constant infusion starting from zero reaches approximately 96.9% after five half-lives in this model. The familiar rule describes a practical approximation.
Turn your calculations into confident SBA answers
Repeat one worked example without notes, explain why the units cancel, then change one variable and predict what happens before calculating. If you make a mistake, record whether it came from choosing the equation, converting units or performing the arithmetic.
Connect this practice with our overview of pharmacology concepts and drug classes, then practise retrieving the method from an unfamiliar question stem.
The StudyMedical MRCEM Primary question bank offers over 7,800 questions, explanations with teaching diagrams, custom topic-based quizzes, timed quizzes and the option to revisit previously incorrect answers. Try free sample questions without signing up and build regular SBA practice into your revision. [5]
