Show the model answerAttempt it first — that is what makes it stick
What earns the marks10 marks
| (a) Three phases, named | 4 marks. Rapid distribution, slow distribution, then elimination. That sequence is the spine of the part |
|---|---|
| (a) The compartments themselves | Marks were allotted for describing the compartments involved, not only the phases they produce |
| (a) Draw one of two things | A labelled three-compartment model, or a labelled plasma concentration-time curve. Either was credited |
| (b) Loading, maintenance, termination | 6 marks. Three stages, each with its own pharmacokinetic process to explain |
| (b) How the loading dose is determined | Many did not include it. It is the central compartment volume times the target concentration |
| (b) What the loading dose is not | A recorded error was attributing it to maintaining the plasma level at steady state |
| (b) At least two models, with their inputs | And the patient parameters each one needs before it can compute a dose |
| (b) Plasma or effect site | The target may be set at either, and the question's own wording asks for both |
| (b) What governs the maintenance rate | Intercompartmental distribution and clearance, named as the two factors |
| (b) Context-sensitive half-time | Creditable when present, and its absence recorded as a mark loss |
4 marks
Propofol after a single intravenous bolus
A three-compartment model describes the body as a central compartment into which the drug is injected and from which it is cleared, connected to a fast peripheral compartment and a slow peripheral compartment that it fills and later draws back from. Nothing is metabolised anywhere except the central compartment. Every feature of the curve below follows from that arrangement.
| Compartment | Volume | What it corresponds to | Its role after a bolus |
|---|---|---|---|
| V₁, central | 6 to 40 L | Blood and the vessel-rich group: brain, heart, liver, kidney. Small, and the only compartment with a clearance term | Receives the whole dose in seconds, so the concentration peaks here. The brain sits inside it, which is why one arm–brain circulation is enough |
| V₂, fast peripheral | Larger than V₁ | Muscle, which is well perfused and takes up a lipid-soluble drug quickly | Drains the central compartment during the first minutes, then hands the drug back as the gradient reverses |
| V₃, slow peripheral | Very large | Fat, which is poorly perfused but has an enormous capacity for a drug this lipid soluble | Fills slowly and empties slowly. It is what makes the terminal half-life long and clinically uninformative |
| V(dSS), all three at steady state | 150 to 700 L, or 2 to 10 L/kg | Far larger than total body water, which is the signature of extensive tissue uptake rather than a real anatomical volume | Explains why plasma concentration falls so far so fast without any drug having been eliminated |
The three phases, in the order the concentration falls through them
Commonly lost: Quite a number of candidates explained the one-compartment model instead, and a few showed a wholly wrong understanding of the concept. A one-compartment model has a single exponential decay and therefore one half-life; it cannot produce the steep early fall that this question is about, and it cannot explain why a patient wakes minutes after a dose whose terminal half-life is measured in hours.
The figure below is one of the two drawings the question credits: a plasma concentration-time curve after 2 mg/kg, with the compartments alongside it. The therapeutic band runs 1.5 to 5 μg/mL, and the curve crosses the lower edge, the concentration at which a patient is expected to wake, within about eight minutes.
A single bolus wears off by redistribution, not by metabolism
Whole-blood propofol after 2 mg/kg. The concentration peaks within about half a minute and then collapses — and almost none of that collapse is elimination. The drug is moving out of the small, well-perfused central compartment into muscle, down a gradient the injection itself created. Consciousness returns when the blood concentration falls back through roughly 1.5 μg/mL, at about 8 minutes, while essentially all of the dose is still in the body. Two consequences follow, and both are examined. Give a second bolus and the gradient into muscle is smaller, so it lasts longer. Give an infusion for hours and the peripheral compartments fill, so when you stop, drug comes back — which is the whole reason the context-sensitive half-time exists.
6 marks
Propofol in a target-controlled infusion
A target-controlled infusion pump holds the same three-compartment model, solves it forward in time, and computes the infusion rate needed to reach and hold a concentration the anaesthetist sets. It calculates a concentration; it never measures one. The three stages below are the three things it has to do.
What the pump is doing, in three stages
The loading dose, and how it is determined
V1 is the central compartment volume in litres, the target concentration is in μg/mL (equivalently mg/L), and the product is a dose in milligrams. This is the single equation the question is built on, and the critique records that many candidates did not include how a loading dose was determined at all.
Because V1 is a model estimate rather than a measurement, the same target produces very different loading doses in different models. Take a 70 kg patient and a target of 4 μg/mL, the top of the usual maintenance range. Marsh describes V1 as 0.228 L/kg, giving V1 = 15.96 L and a loading dose of about 64 mg. Schnider fixes V1 at 4.27 L whatever the weight, so the same target asks for about 17 mg. That is a 3.7-fold difference for the same patient at the same target, which is why the two are used in different targeting modes rather than interchangeably, and why Schnider’s targets are not transferable to Marsh. The arithmetic is worth showing in the answer: it demonstrates that the equation is understood rather than quoted.
Commonly lost: A few candidates wrongly attributed the loading dose to maintaining plasma levels in the steady state. It does the opposite: the loading dose exists precisely because a maintenance infusion alone would take several time constants to reach the target. Loading fills a volume and is governed by V1; maintenance replaces a loss and is governed by clearance. Two doses, two parameters, two purposes.
Which model, and what it needs to know
| Parameter | Marsh | Modified Marsh | Schnider |
|---|---|---|---|
| V1 | Weight | Weight | Fixed at 4.27 L |
| V2 | Weight | Weight | Age |
| V3 | Weight | Weight | Fixed |
| k12 and k21 | Fixed | Fixed | Age |
| k13 and k31 | Fixed | Fixed | Fixed |
| k(e0), min⁻¹ | 0.26 | 1.21 | 0.456 |
| Clearance | Weight | Weight | Weight and height |
The question asks for the patient parameters needed to calculate the loading dose, and the table answers it directly. Marsh needs weight alone. Every one of its volumes and its clearance scales on the weight entered, so doubling the weight doubles V1 and doubles the induction dose. That is reasonable in a normally proportioned patient and wrong where the extra weight is adipose, because fat is V₃ and not V₁. Schnider needs age, weight, height and sex, the last three because it computes lean body mass, and it uses age for V₂ and for the intercompartmental rate constants. Its fixed V₁ makes its loading dose almost independent of weight.
Plasma or effect site
The target can be set at either, and the choice changes what the pump does at induction rather than what the drug does. Plasma targeting brings the plasma concentration to the target and holds it, letting the effect site fill behind it. Effect-site targeting deliberately overshoots the plasma concentration so that the effect site reaches the target sooner, then pauses the infusion while the two equilibrate.
What a target-controlled pump is actually doing
The pump holds a three-compartment model of the drug in software and solves it forward: it is calculating a concentration, never measuring one. Which concentration you ask it to hit changes the dose it gives. Ask for a plasma target and it delivers a bolus and keeps infusing, and the effect site arrives late. Ask for an effect-site target and it delivers a larger bolus and then stops, so the falling plasma concentration meets the rising effect-site concentration at the target with no effect-site overshoot — which is what the flat step in the right-hand panel is. Typical maintenance targets are 2.5–4 μg/mL for propofol with 3–6 ng/mL of remifentanil. The axes carry no numbers on purpose: the source figures carry none, and the shapes are the teaching.
What governs the maintenance rate
The critique names two factors, and they are separable. Clearance sets the floor: at true steady state, when no net transfer to the periphery remains, the infusion rate is simply clearance multiplied by the target concentration, and for propofol that clearance is high at 30 to 60 mL/kg/min. Intercompartmental distribution is everything above that floor: early in a case, most of the infusion is not replacing eliminated drug at all but keeping up with drug disappearing into muscle and fat. Steady state is approached, and in a case of ordinary length never quite reached.
Typical maintenance targets when propofol and remifentanil are run together are 2.5–4 μg/mL and 3–6 ng/mL, and the two are synergistic, so raising one target allows the other to come down for the same depth.
Termination, and why the context-sensitive half-time is the right number
When the infusion stops, the peripheral compartments are no longer absorbing drug but returning it. The time for the plasma concentration to fall by half therefore depends on how much has accumulated peripherally, which depends on how long the infusion ran. That is the context-sensitive half-time, and context is the duration of the infusion.
Move the infusion duration and read all six half-times at once
Context-sensitive half-time is the time for the plasma concentration to fall by half after an infusion stops, and context is how long the infusion ran. It is not the elimination half-life, and steady state is not part of the definition — an infusion can be stopped at any time. Drag the control and watch six agents separate: at ten minutes they are nearly indistinguishable, and by eight hours thiopentone has left the axis while etomidate has barely moved.
Two things set the shape of each curve. How high it rises is the ratio of distribution clearance to elimination clearance: if drug leaves the plasma into tissue much faster than it is eliminated, a reservoir accumulates and is handed back when the infusion stops. How long it keeps rising is the size and speed of the deep compartment — once that compartment is full, the curve plateaus.
Thiopentone and diazepam leave the axis because neither reaches a plateau inside eight hours. Thiopentone additionally saturates its own metabolism at high dose, so an infusion moves from first-order towards zero-order handling — a second reason its offset lengthens that the other agents do not share.
Propofol’s stays under 40 minutes even after eight hours, reading 38.1 minutes at that duration, because its clearance is high enough to keep pace with what the periphery returns. That is the property that makes a long total intravenous anaesthetic recoverable, and it is the reason this question ends where it does. Many pumps also display a decrement time, the predicted interval until the concentration falls to a value at which the patient is expected to wake, commonly 1.2 μg/mL for propofol.
Commonly lost: Candidates lost marks when no mention of the context-sensitive half-time was made, and when no diagram was used to illustrate the text. Both are recorded as reasons for lost marks rather than as missed opportunities, and both are cheap to supply: one curve and two sentences cover them.
If this came up in the viva
Viva points
Give one drug whose loading dose you would reduce and one whose maintenance rate you would reduce, and explain why they are different questions.
Answer
Loading dose = Vd × target concentration. It depends on volume alone. Reduce it for a hydrophilic drug whose Vd falls — digoxin, gentamicin.
Maintenance rate = clearance × target concentration. It depends on clearance alone. Reduce it for a drug whose clearance falls — morphine, or anything renally eliminated.
They are different questions because they are governed by different parameters. A patient in renal failure needs the same loading dose and a smaller maintenance rate.
Why does a smaller propofol dose produce a higher peak effect-site concentration, and why is onset still slower?
Answer
They are two separate changes that happen to point in opposite directions.
Higher peak: the central compartment is smaller, so a given dose is diluted into less volume and the plasma concentration driving transfer to the brain is higher.
Slower onset: cardiac output is lower and circulation time longer, so that concentration takes longer to arrive, and blood–brain equilibration is slower.
Hence: give less, give it slowly, and wait before repeating. The error is topping up before the first dose has arrived.
Does CSHT tell you when the patient will wake?
Answer
Not necessarily. During long, stimulating surgery, infusion rates will have been high, and the concentration at which waking occurs may be much less than half the concentration at the end of the infusion. Time to awakening may therefore substantially exceed the CSHT. This is why TCI pumps display a decrement time rather than a CSHT.
Define decrement time.
Answer
The time for plasma or effect-site concentration to fall by a specified percentage — 20%, 50%, 80%. CSHT is simply the 50% decrement time.
Why is propofol suitable for TIVA?
Answer
Its CSHT does not rise greatly even after several hours of infusion, unlike fentanyl.