Distribution, clearance and half-life

Why this matters to the anaesthetist

Every anaesthetic dose is, at bottom, a calculation of distribution (how much drug to put into the tank) and clearance (how much to keep pouring in to match what is draining out). Three parameters — the volume of distribution (Vd), clearance (CL) and the elimination half-life (t½) — together with bioavailability (F) and the context-sensitive half-time (CSHT), give the anaesthetist a quantitative framework for loading doses, maintenance infusions, redosing intervals and the prediction of recovery [2][6]. They are also the engineering basis of target-controlled infusion (TCI): the Diprifusor and open TCI pumps run a compartment model in software, computing the infusion rate required to hold a predicted plasma or effect-site concentration [9][10].

This topic is examined at every level of the anaesthetic fellowship: as a written multiple-choice or short-answer question on the definitions and equations, as a viva in which the candidate is handed a concentration-time graph and asked to derive Vd, CL and kelim, and as a clinical discussion of why remifentanil is context-insensitive and why a propofol infusion takes hours to reach steady state. The candidate who can move fluently between the equations and the bedside — between the hydraulic analogy and the patient on the table — is the candidate who passes. [1]

The one-compartment model

The one-compartment model is the simplest pharmacokinetic description: the body behaves as a single, well-stirred tank of volume Vd into which the drug is introduced and from which it is eliminated. Although no drug truly distributes instantaneously into every tissue, the model is a remarkably good approximation for drugs that equilibrate quickly between plasma and the tissues they reach, and it carries every concept the examiner needs [2].

Volume of distribution, the apparent volume

The first quantity the model defines is the volume of distribution: [1]

Vd equals the dose administered divided by the resulting initial plasma concentration (C₀). If you give 200 milligrams of a drug and measure a plasma concentration of 20 milligrams per litre immediately after injection, the Vd is 200 divided by 20, which is 10 litres. The crucial teaching point — and an examiner favourite — is that Vd is an apparent volume, not a real one. It is the volume the drug WOULD occupy if it were distributed at the same concentration throughout the body as it is in plasma. A drug that is avidly bound in tissues can have a Vd far larger than total body water (forty litres in an adult): propofol, thiopental and fentanyl have Vd values of many litres per kilogram precisely because they leave the plasma and sequester in fat and muscle. A drug that is large, ionised or heavily protein-bound and so confined to plasma has a tiny Vd: heparin and warfarin sit around three to five litres [2][4].

First-order elimination: a constant fraction, not a constant amount

In the one-compartment model the drug is eliminated by first-order kinetics: in any given time interval, a constant FRACTION of the drug present is removed. The rate of elimination is therefore proportional to the concentration: at high concentration a lot is removed per minute, and as the concentration falls the amount removed per minute falls with it. Plotting the natural logarithm of the concentration against time gives a straight line, and the concentration itself declines exponentially as C(t) equals C₀ times e raised to the power of minus kelim times t [2].

The contrast is with zero-order kinetics, in which a constant AMOUNT (not a constant fraction) is removed per unit time, producing a linear rather than an exponential decline. Phenytoin (above its Michaelis-Menten Km), ethanol at high dose, high-dose aspirin and theophylline at toxic concentration follow zero-order kinetics once their metabolising enzymes are saturated. The clinical danger of zero-order elimination is that a small dose increase produces a disproportionate rise in concentration — the mechanism of phenytoin toxicity. [1]

The elimination rate constant kelim

The elimination rate constant, written kelim (also k or kel), is the fraction of the drug removed per unit time, with units of inverse time (per minute or per hour). If kelim is 0.1 per minute, then 10 per cent of the drug remaining in the body is eliminated each minute. Because elimination is first-order, kelim is the slope of the log-concentration-versus-time line. It is related to clearance by kelim equals CL divided by Vd, which makes intuitive sense: a high clearance (a big drain) or a small Vd (a small tank) both make the concentration fall quickly. [1]

The elimination half-life t½

The elimination half-life is the time taken for the plasma concentration to fall by half. By solving the exponential equation, t½ equals the natural logarithm of 2 (which is 0.693) divided by kelim. Substituting kelim equals CL over Vd gives the second, more useful form: t½ equals 0.693 times Vd divided by CL. This single equation ties the three parameters together and is the most frequently examined relationship in pharmacokinetics [2][4].

[1]

The two-compartment model

Most intravenous anaesthetic drugs do not equilibrate instantly with all tissues. After a bolus, drug is distributed within seconds to the vessel-rich group (brain, heart, liver, kidney — the organs that receive the bulk of the cardiac output), more slowly to muscle and skin, and slowest of all to fat. A two-compartment model captures this by adding a peripheral compartment to the central one [6][5].

Central and peripheral compartments

The central compartment (compartment 1) is the vessel-rich space: plasma plus the well-perfused tissues with which the drug equilibrates rapidly. It is the compartment into which the drug is injected, from which blood is sampled, and in which the pharmacological effect is generated for a rapidly acting drug. Its apparent volume is V1 (or Vc). The peripheral compartment (compartment 2) represents the muscle, skin and fat into which the drug distributes more slowly. Its apparent volume is V2. The sum V1 plus V2 is the Vd at steady state (Vdss). [1]

The three rate constants

Transfer between compartments and out of the body is governed by first-order rate constants: [1]

• k12 — transfer from central to peripheral (distribution into tissue).
• k21 — transfer from peripheral back to central (return from tissue).
• k10 — irreversible elimination from the central compartment (metabolism by the liver, excretion by the kidney, and any other route of removal). [1]

Drug can only leave the body through the central compartment (k10), because the liver and kidney clear drug from blood, and the sampled compartment is blood. A third, deeper compartment (fat) is sometimes added, producing a three-compartment model — this is the model on which propofol TCI is actually built (the Marsh and Schnider models are three-compartment). [1]

The biphasic concentration-time curve: alpha and beta

After an intravenous bolus into a two-compartment system, the log-concentration-versus-time plot is no longer a single straight line but two lines — a bi-exponential decline: [1]

1. The distribution phase (alpha phase) is the steep early fall. The concentration drops rapidly not because the drug is being eliminated (k10) but because it is leaving plasma and entering the peripheral compartment (k12 greatly exceeds k21 and k10 in the first minutes). For thiopental and propofol this is the phase that ends the hypnotic effect: the patient wakes a few minutes after a bolus not because the drug has been metabolised but because it has redistributed away from the brain into muscle. [1]

2. The elimination phase (beta phase) is the slower, later fall. Once central and peripheral compartments have come close to equilibrium, the concentration declines at a rate set chiefly by metabolism and excretion (k10), and the curve becomes a shallow exponential. The half-life of this terminal phase is the beta half-life (t½β) — the number quoted in pharmacology texts as the elimination half-life [5][6].

The alpha half-life (t½α) is short — minutes for most anaesthetics — while the beta half-life is long — tens of minutes to hours. This single observation explains why the elimination half-life is a poor predictor of the duration of action of a single bolus: thiopental has a beta half-life of many hours yet puts a patient to sleep for only five to ten minutes, because recovery from a bolus is governed by redistribution (alpha), not elimination (beta). [1]

The three-compartment model and the effect-site compartment

For the lipophilic anaesthetics a third, slowly equilibrating compartment (fat) is added, giving a three-compartment model: a central compartment (V1), a rapidly equilibrating peripheral compartment (V2, muscle and skin) and a slowly equilibrating peripheral compartment (V3, fat), with the rate constants k12, k21, k13, k31 and k10. The concentration-time curve is then tri-exponential: a steep alpha phase, an intermediate phase, and a slow gamma (terminal) phase. This is the model on which propofol target-controlled infusion is actually built — the Marsh and Schnider models are both three-compartment. [1]

A further refinement is the effect-site compartment, a notional additional compartment linked to the central compartment by the rate constant ke0 (k-e-zero). The effect site is the biophase where the drug acts (the brain for a hypnotic, the neuromuscular junction for a relaxant). Because equilibration between plasma and effect site takes finite time, the effect-site concentration LAGS behind the plasma concentration on the way up (after a bolus) and on the way down — producing hysteresis on a concentration-effect plot. The t½ke0 is the equilibration half-life between plasma and effect site, and is the basis of effect-site targeting: a TCI pump in effect-site mode deliberately over-shoots the plasma concentration briefly to drive the effect site up to target quickly, then settles to maintenance. Propofol has a t½ke0 of about 1 to 3 minutes and remifentanil about 1 minute.

Volume of distribution in depth [1]

Definition and meaning

The volume of distribution has been defined above: Vd equals the dose divided by the extrapolated initial concentration C₀. In a multicompartment model there are several apparent volumes — V1 (central), Vd during the distribution phase, and Vd at steady state (Vdss, equal to V1 plus V2 plus …) — but the principle is unchanged: each is a proportionality constant relating the AMOUNT of drug in the body (or in a compartment) to the plasma concentration, and none is a real anatomical volume [2][4].

Why Vd varies between drugs

Three properties set the Vd: [1]

1. Lipid solubility. Highly lipophilic drugs cross cell membranes readily and partition into adipose tissue, giving a large Vd. Thiopental (oil/gas partition coefficient high, extremely fat-soluble) has a Vd of about 2 to 3 litres per kilogram — far above total body water. Propofol is similarly lipophilic and tissue-bound. [1]

2. Plasma protein binding. Only the FREE (unbound) drug can leave the vasculature. A drug that is heavily protein-bound in plasma (e.g. warfarin, 99 per cent bound, or propranolol) is largely confined to plasma and has a small Vd. Conversely, a drug that binds preferentially to TISSUE proteins is sequestered out of plasma and has a large Vd. [1]

3. Tissue binding. Active uptake or binding in specific tissues (digoxin in skeletal and cardiac muscle; amiodarone in fat and lung) can give Vd values of hundreds of litres per kilogram. The plasma concentration is then vanishingly small even when the total body load is large.

4. Degree of ionisation and pH partitioning. Only the unionised fraction of a drug crosses lipid membranes; the ionised form is effectively trapped on one side of the membrane. Weak acids are more unionised (and so more lipid-soluble) in an acidic environment, and weak bases are more unionised in an alkaline environment. This is the basis of ion trapping: aspirin (a weak acid) is trapped in the relatively alkaline mitochondrial matrix and across the placenta, and local anaesthetics (weak bases) accumulate in inflamed, acidotic tissue, where they ionise and become less effective. A drug's pKa relative to physiological pH therefore sets how much of it is in the membrane-permeant form and is a fourth determinant of its Vd. [1]

Typical values

A useful exam framework arranges drugs by their Vd: [1]

• Vd about 3 to 5 L (plasma volume): the drug stays in plasma — heparin, warfarin, monoclonal antibodies.
• Vd about 15 to 20 L (extracellular fluid): polar, water-soluble drugs — the non-depolarising muscle relaxants (rocuronium Vd about 0.2 to 0.3 L per kg, vecuronium similar), aminoglycosides.
• Vd about 40 L (total body water): moderately lipophilic drugs — ethanol, caffeine, digoxin partly.
• Vd many litres per kilogram (far above body size): highly lipophilic, tissue-bound drugs — thiopental (about 2.6 L per kg), propofol (about 2 to 10 L per kg), fentanyl (about 4 L per kg), diazepam (about 1 L per kg), amiodarone (about 60 L per kg), digoxin (about 7 L per kg) [2][4].

Clinical determinants of Vd

Vd is not fixed: it changes with the patient. Water content falls and fat content rises with age, so the Vd of water-soluble drugs shrinks and the Vd of lipophilic drugs grows in the elderly. Pregnancy adds plasma and extracellular volume (larger Vd for hydrophilic drugs) and raises total body fat later in gestation. Obesity enlarges the Vd of lipophilic drugs (use adjusted or lean body weight). Oedema, ascites and burns expand extracellular fluid and increase the Vd of polar drugs. Hypoalbuminaemia raises the free fraction and tends to enlarge the Vd for highly bound drugs. [1]

Protein binding and the free fraction

Only the free (unbound) drug is pharmacologically active: it alone leaves the vasculature, binds to receptors, and is available for glomerular filtration and hepatic uptake. Drugs bind chiefly to albumin (acidic and neutral drugs: warfarin, phenytoin, diazepam, thiopental) and to alpha-1-acid glycoprotein (basic drugs: lignocaine, propranolol, the muscle relaxants). Albumin falls in liver disease, nephrotic syndrome, critical illness, burns and malnutrition, raising the free fraction of acidic drugs; alpha-1-acid glycoprotein is an acute-phase reactant that RISES in inflammation and after surgery, lowering the free fraction of basic drugs. [1]

The clinical corollary is that in the hypoalbuminaemic, critically ill patient the same total drug concentration produces a higher free fraction and therefore more effect and toxicity — most important for highly bound, narrow-therapeutic-index drugs (phenytoin, warfarin, thiopental, digoxin). The total concentration usually falls as the free fraction equilibrates, so the net change in effect is often modest unless the drug is very highly bound AND has a low intrinsic clearance (capacity-dependent). For a high-extraction, flow-dependent drug, displacement from binding has little effect on clearance because the liver strips the drug regardless of whether it is bound.

Clearance in depth [1]

Definition

Clearance (CL) is the volume of blood (or plasma) from which the drug is completely removed per unit time. It has units of volume per time (millilitres per minute or litres per hour). Operationally, CL equals the rate of elimination divided by the plasma concentration (CL equals rate of elimination over C). Because elimination is first-order, rate of elimination equals CL times C, so CL is the constant of proportionality linking how fast drug leaves the body to how much is present [2][4].

The most important derived relationship links clearance to Vd and kelim: CL equals Vd times kelim (and therefore kelim equals CL over Vd). A drug with a large Vd can still have a short half-life if its clearance is high, and a drug with a small Vd can have a long half-life if its clearance is low. [1]

Clearance is additive

Total body clearance is the sum of all individual clearances — hepatic (CLH), renal (CLR), biliary, pulmonary and any other route. CL equals CLH plus CLR plus the rest. The contributions vary: for morphine, the liver dominates (CLH is most of total CL); for gallamine, the kidney dominates (excreted unchanged); for remifentanil, blood and tissue esterases dominate (no hepatic or renal dependence at all) [7].

Hepatic clearance and the extraction ratio

The liver clears drug from the blood flowing through it. The fraction of the drug removed in a single pass is the extraction ratio (E), a number between 0 and 1. Hepatic clearance equals hepatic blood flow times the extraction ratio: [1]

CLH equals liver blood flow times E. [1]

This deceptively simple equation, formalised in the well-stirred and parallel-tube models (Rowland, Benet and Graham 1973; Wilkinson and Shand 1975; Pang and Rowland 1977), divides drugs into two behaviourally distinct classes — the single most examined idea in hepatic clearance [1][2][3].

The intuition is mechanical. For a high-extraction drug the liver is so efficient it strips almost everything out of the blood that reaches it; the bottleneck is therefore how much blood arrives, which is liver blood flow. Reduce the flow (heart failure, haemorrhage, beta-blockade) and clearance falls in proportion. For a low-extraction drug the liver only clears a fraction of what arrives, so the bottleneck is the enzyme capacity and the free drug concentration at the hepatocyte; changes in liver blood flow barely matter, but enzyme induction (rifampicin, carbamazepine, chronic alcohol), enzyme inhibition (ciprofloxacin, fluconazole, grapefruit juice) or displacement from protein binding all change clearance [1][3].

The first-pass effect follows directly: a high-extraction drug given orally is largely cleared on its first transit through the liver before reaching the systemic circulation, so its oral bioavailability is low (oral morphine 20 to 40 per cent). This is why oral morphine needs a much larger dose than parenteral morphine for the same effect. [1]

Renal clearance

Renal clearance depends on three processes: glomerular filtration (driven by GFR and the free drug concentration; only unbound drug is filtered), tubular secretion (active transport of organic anions and cations into the tubule, e.g. penicillin, furosemide — can be saturated and competed for by probenecid), and passive tubular reabsorption (lipophilic, unionised drugs diffuse back across the tubular epithelium into plasma; the degree depends on urine pH and flow). Renal clearance falls with age (GFR declines by about 1 mL per minute per year after forty) and with renal disease, so renally cleared drugs (gentamicin, digoxin, enoxaparin, the water-soluble muscle relaxants) must be dose-adjusted by estimated GFR [2].

The ion-trapping concept belongs here: a weak acid is trapped in alkaline urine (it ionises and cannot be reabsorbed — the basis of forced alkaline diuresis in salicylate overdose), and a weak base is trapped in acidic urine. [1]

The elimination half-life in depth

The defining equation

The elimination half-life is the time for the plasma concentration to fall by 50 per cent during the elimination (beta) phase: [1]

t½ equals 0.693 divided by kelim, which equals 0.693 times Vd divided by CL. [1]

A large Vd (fat-soluble, tissue-bound) or a small CL (slow metabolism, renal or hepatic impairment) both lengthen the half-life [2][4].

Accumulation and the steady-state rule

When a drug is given by repeated dosing or constant infusion, the amount in the body rises until intake equals elimination — that point is steady state, at which the plasma concentration oscillates around a mean ( Css ). The time to reach steady state is governed solely by the half-life: after each half-life the concentration moves halfway from where it is to where it is going. [1]

• After 1 half-life: 50 per cent of steady state.
• After 2 half-lives: 75 per cent.
• After 3 half-lives: 87.5 per cent.
• After 4 half-lives: 93.75 per cent.
• After 5 half-lives: 96.9 per cent (clinically, steady state).
• After 7 half-lives: 99.2 per cent. [1]

The steady-state rule is therefore: it takes about five half-lives to reach steady state (and, by symmetry, about five half-lives to wash out after stopping). For propofol (t½β about 30 to 60 minutes) this is a few hours; for fentanyl (t½β about 3 to 4 hours) about a day; for diazepam (t½β about 20 to 43 hours, with an active metabolite) the better part of a week. This is why a benzodiazepine infusion accumulates dangerously over days and why a loading dose is used when a rapid effect is needed. [1]

Loading dose and maintenance rate

These two equations are the practical pay-off of the whole topic: [1]

• Loading dose (LD) equals Vd times the target concentration (Css). It fills the tank to the target concentration in one step, bypassing the five-half-life wait. For a drug with a large Vd the loading dose is large; for a polar drug with a small Vd it is small. [1]

• Maintenance rate (MD) equals CL times the target concentration (Css). At steady state the rate in equals the rate out, and the rate out is CL times the concentration, so the maintenance rate must equal CL times the target concentration [2].

A useful worked example: a drug with Vd of 0.7 L per kg in a 70 kg adult (Vd about 50 L) targeting a concentration of 5 mg per L needs a loading dose of 250 mg. If its clearance is 0.5 L per hour, the maintenance infusion is 2.5 mg per hour. These are the exact computations a TCI pump performs, thousands of times, for propofol and remifentanil. [1]

Half-life of common anaesthetic agents

A representative list (beta half-life unless stated): remifentanil about 10 to 20 minutes (but context-insensitive, see below); propofol 30 to 60 minutes (terminal t½ much longer, up to hours, but irrelevant clinically because redistribution dominates); thiopental 5 to 12 hours (yet a bolus lasts minutes — redistribution); etomidate 2 to 5 hours; ketamine 2 to 3 hours; rocuronium 60 to 90 minutes; vecuronium 50 to 70 minutes; suxamethonium under 1 minute (rapid hydrolysis by plasma cholinesterase); morphine 2 to 4 hours; fentanyl 3 to 4 hours; alfentanil 1 to 2 hours; diazepam 20 to 43 hours (plus active metabolite) [5].

Context-sensitive half-time (CSHT)

Why a new concept was needed

The elimination half-life is the half-life of the TERMINAL (beta) phase after a single bolus, when distribution is complete. But anaesthetists give drugs by infusion, and during a long infusion the peripheral compartments fill up with drug. When the infusion stops, that stored drug returns to plasma and slows the fall in concentration — so the time to a 50 per cent drop depends on how long the infusion ran. The elimination half-life cannot capture this. In 1992 Hughes, Glass and Jacobs proposed the context-sensitive half-time to fix the gap [6].

Definition

The context-sensitive half-time (CSHT) is the time required for the plasma (central compartment) concentration to fall by 50 per cent AFTER the end of an intravenous infusion that was designed to maintain a constant plasma concentration. The "context" is the duration of the infusion. The CSHT is therefore a function — CSHT(d) — not a single number: for each infusion duration there is a corresponding half-time [6].

The distinction is sharp: the elimination half-life is a property of the drug (a constant); the CSHT is a property of the drug AND the dosing situation (a curve). Hughes showed that for six common anaesthetic drugs the CSHT ranged from 1 to 306 minutes despite elimination half-lives of 111 to 577 minutes — the two measures bore no useful relation to each other [6].

How the CSHT behaves: the saturating and the flat

The shape of the CSHT-versus-duration curve separates the anaesthetic drugs into two clinically decisive groups: [1]

• Rising CSHT (saturation of distribution). For thiopental, fentanyl, alfentanil and (to a lesser degree) propofol, the CSHT rises as the infusion lengthens. In the first minutes the peripheral compartment is empty, so stopping the infusion lets the plasma concentration fall rapidly as drug redistributes OUT of plasma into tissue — the CSHT is short. But as the infusion continues, the peripheral compartment fills; once it is loaded, drug no longer leaves plasma (it is in equilibrium) and the concentration falls only by true elimination, which is slow. The CSHT therefore climbs and can far exceed the value after a brief infusion. After a many-hour fentanyl infusion the CSHT is measured in hours, not minutes [5][8].

• Flat CSHT (organ-independent metabolism). For remifentanil the CSHT stays at about 3 minutes regardless of how long the infusion has run. Remifentanil is metabolised by non-specific blood and tissue esterases (the same enzymes that hydrolyse esmolol and suxamethonium), which are so abundant and so unsaturated that clearance is independent of organ blood flow, hepatic function and renal function. There is no peripheral compartment to fill with active drug (the metabolite is essentially inactive), so there is nothing to slow the fall. Egan established remifentanil's pharmacokinetics in 1993 and Kapila confirmed in 1995 that the MEASURED context-sensitive half-time after a 3-hour remifentanil infusion was 3.2 minutes — against 47 minutes for alfentanil given at the same depth [7][8].

Clinical significance

The CSHT is the right number to choose an infusion opioid. Remifentanil is uniquely suited to long cases needing a rapidly titratable opioid and a rapid, predictable wake-up — cardiac surgery, neurosurgery, obese patients, and any setting where the duration of action must not depend on how long the drug has been given. Fentanyl and thiopental accumulate: the longer they are infused, the slower the recovery, so they are poor choices for prolonged infusion (this is the pharmacokinetic basis of the now-discarded high-dose fentanyl cardiac anaesthetic and of prolonged thiopental infusion). The CSHT also explains why propofol, despite a beta half-life of many hours, gives a rapid wake-up after a short TCI case (redistribution dominates) but a slow wake-up after a long infusion (the peripheral compartment fills and the CSHT rises) [6][8].

[1]

Bioavailability

Definition

Bioavailability (F) is the fraction of the administered dose that reaches the systemic circulation unchanged. For an intravenous bolus, by definition, every molecule enters the systemic circulation, so F equals 1. For any other route (oral, intramuscular, subcutaneous, transdermal, rectal, sublingual) some drug is lost before it reaches the systemic circulation, so F is less than 1 [2].

First-pass (presystemic) metabolism

For an oral drug the loss occurs at two sites. First, enzymes in the gut wall and the enterocytes (notably CYP3A4) metabolise a fraction of the drug before it is absorbed. Second, the absorbed drug enters the portal vein and must traverse the liver before reaching the systemic circulation; the liver extracts a fraction on this first pass. The combined loss is the first-pass effect, and it is large precisely for the high-extraction drugs (morphine, lignocaine, propranolol, verapamil). This is why oral lignocaine is useless for systemic anti-arrhythmic effect (it is cleared before it reaches the heart) and why oral morphine needs a dose about three times the parenteral dose. [1]

Determinants of F

Bioavailability is reduced by incomplete absorption (poor solubility, decomposition in gastric acid, gut motility), by gut-wall metabolism (CYP3A4, P-glycoprotein efflux), and by hepatic first-pass metabolism. Sublingual, transdermal, intramuscular and rectal routes partly bypass the portal system (the sublingual and lower-rectal venous drainage drains directly into the systemic circulation), which is why glyceryl trinitrate is given sublingually and why diazepam is effective rectally in status epilepticus. First-pass metabolism is reduced in liver disease and portosystemic shunting, increasing F (a hazard: the standard oral dose of a high-extraction drug becomes an overdose in cirrhosis). [1]

Using F in dosing

The oral dose that produces a given systemic exposure equals the intravenous dose divided by F. For a drug with F of 0.3, the oral dose must be about three times the IV dose. Bioavailability is also the correction factor in clearance calculations for non-IV dosing: the rate of elimination at steady state equals F times the dosing rate times the bioavailability.

Absolute and relative bioavailability [1]

Absolute bioavailability is the systemic availability of a non-intravenous dose compared with the intravenous dose, measured as the ratio of the areas under the concentration-time curve: F equals the AUC after the non-IV dose divided by the AUC after the IV dose (dose-corrected). Relative bioavailability compares one non-IV formulation with another (a generic against the originator) and is the basis of bioequivalence testing. [1]

Factors that reduce F are numerous: incomplete absorption (poor solubility, decomposition in gastric acid — penicillin G and insulin are destroyed orally), slow gut motility, gut-wall CYP3A4 and P-glycoprotein efflux (the mechanism of grapefruit juice interactions — grapefruit inhibits intestinal CYP3A4 and raises the F of felodipine, ciclosporin and some statins), and hepatic first-pass extraction (large for high-extraction drugs). Factors that raise F include liver disease and portosystemic shunting (less first-pass) and drugs that inhibit the relevant enzyme or transporter. The lower-rectal veins drain directly into the systemic circulation and so partly bypass the portal system, and the sublingual route drains straight into the systemic circulation — which is why glyceryl trinitrate is given sublingually and diazepam is effective rectally in status epilepticus. [1]

Anaesthetic relevance

Target-controlled infusion runs a compartment model

A TCI pump does not deliver a constant rate; it solves a compartment model in real time. The anaesthetist sets a TARGET plasma or effect-site concentration, and the pump computes the bolus and varying infusion rate required to achieve and hold it, using a drug-specific three-compartment pharmacokinetic model plus a pharmacodynamic (effect-site) model [9][10]. The two propofol models in common use are the Marsh model (weight-based, V1 scaled to weight, originally for children and adults) and the Schnider model (incorporates age, lean body mass and height — the basis of effect-site targeting) [9][10]. The Minto model is the analogous remifentanil model (incorporates age and lean body mass). The pump's plasma-concentration prediction is only as good as the model and the patient's resemblance to the study population — hence the interest in closed-loop delivery guided by a processed EEG.

Choosing drugs by their kinetics

The CSHT is the decision tool. For a brief case, almost any hypnotic or opioid works because redistribution dominates. For a long case, the CSHT of the chosen drug determines how quickly the patient will wake and breathe: [1]

Dosing in the altered patient

The pharmacokinetic framework tells the anaesthetist how to adjust dosing when the patient is not average. In the elderly, total body water falls, fat rises, albumin falls and hepatic blood flow and GFR decline — water-soluble drugs have a smaller Vd (a normal dose is too much), lipophilic drugs have a larger Vd and slower clearance, and the free fraction of highly bound drugs rises. In liver disease, high-extraction drugs clear more slowly (reduced blood flow and portosystemic shunting) and hypoalbuminaemia raises the free fraction. In renal failure, renally cleared drugs (morphine metabolites, the muscle relaxants gallamine and pancuronium) accumulate. In obesity, the Vd of lipophilic drugs is larger — dosing on total body weight over-treats; dose by lean or adjusted body weight. In pregnancy, plasma volume and cardiac output rise (larger Vd and higher CL) and albumin falls. In cardiac failure, hepatic blood flow falls and the clearance of flow-dependent drugs (lignocaine, morphine, propranolol) falls with it [1].

Weight-based dosing in obesity

Dosing the obese patient requires the right weight scalar, because the wrong one produces systematic under- or over-dosing. Total body weight (TBW) over-estimates the dose for most drugs, because although lipophilic drugs distribute partly into fat, the lean mass clears them. Ideal body weight (IBW) is derived from height and sex and ignores actual mass. Lean body weight (LBW) is the mass of non-adipose tissue and best predicts the Vd and clearance of most anaesthetics in obesity. Adjusted body weight is a correction of IBW for actual weight, used for some drugs. The practical rule: dose hydrophilic drugs (the muscle relaxants) on IBW or LBW; dose the propofol induction bolus on LBW to avoid over-shoot in the obese; and use LBW for remifentanil (the Minto model caps the weight input to prevent over-delivery). Suxamethonium is an exception — dose it on TBW, because plasma cholinesterase activity scales with total mass. [1]

Practical dosing examples

• Propofol induction: loading dose about 1.5 to 2.5 mg per kg (a bolus that fills the central compartment to the effective concentration, then redistributes).
• Propofol maintenance: 4 to 12 mg per kg per hour, or a TCI plasma target of 2 to 6 micrograms per mL.
• Rocuronium intubation: 0.6 mg per kg (Vd about 0.2 to 0.3 L per kg; redose at about 0.15 mg per kg guided by train-of-four).
• Remifentanil infusion: 0.05 to 0.3 micrograms per kg per minute, or a TCI effect-site target of 2 to 8 ng per mL — titratable to the stimulus and breathing, with a CSHT of about 3 minutes.
• Diazepam for sedation: a loading dose achieves sedation within minutes, but steady state takes about a week (t½ about 43 h) — the reason benzodiazepine infusions are avoided for long sedation. [1]

Factors that change Vd, CL and t½

• Age. Less total body water (smaller Vd for hydrophilic drugs — a normal dose of a relaxant is relatively too much in the elderly), more body fat (larger Vd for lipophilic drugs — slower clearance of thiopental, diazepam), less albumin (higher free fraction), reduced hepatic blood flow and GFR (slower clearance). Every drug lasts longer in the elderly.
• Obesity. Larger Vd for lipophilic drugs; dosing on total body weight over-treats — use ideal, lean or adjusted body weight. Higher cardiac output tends to raise clearance.
• Liver disease. Reduced clearance (most marked for high-extraction drugs such as lignocaine and morphine), less albumin (higher free fraction — more effect for the same total concentration), more portosystemic shunting (less first-pass, higher oral bioavailability).
• Renal disease. Reduced renal clearance — dose-adjust by estimated GFR. Active metabolites accumulate (morphine-6-glucuronide is more potent than morphine and is renally excreted).
• Pregnancy. Larger Vd (more plasma and extracellular water), less albumin (higher free fraction), higher cardiac output (higher clearance) — many drugs need a larger dose.
• Cardiac failure. Reduced hepatic blood flow reduces the clearance of flow-dependent drugs (lignocaine, morphine, propranolol) — the mechanism of lignocaine toxicity after an MI.
• Hypoalbuminaemia and protein displacement. A higher free fraction increases the effect and toxicity for the same total concentration, and can enlarge the Vd. Clinically important only for highly bound, narrow-therapeutic-index drugs (phenytoin, warfarin, thiopental) [2].

Red flags

[1] [1] [1] [1] [1] [1]

Examiner map and high-yield summary

[1]

The exam-critical content, in the order an examiner expects: (1) the one-compartment model — Vd as an apparent volume, first-order elimination, kelim, the exponential curve, t½ equals 0.693 over kelim; (2) the two-compartment model — central and peripheral compartments, the alpha distribution and beta elimination phases, the rate constants k12, k21 and k10, and why redistribution (not elimination) ends a bolus; (3) Vd in depth — apparent volume, the determinants (lipid solubility, plasma and tissue binding), and the typical values (thiopental high, muscle relaxants low); (4) clearance — CL equals rate of elimination over C equals Vd times kelim, hepatic versus renal, the extraction ratio and the flow-versus-capacity distinction (Wilkinson and Shand); (5) half-life — t½ equals 0.693 Vd over CL, five half-lives to steady state, loading dose equals Vd times target, maintenance equals CL times target; (6) the context-sensitive half-time — the Hughes definition, the rising curve for fentanyl and thiopental, the flat curve for remifentanil, and the clinical choice of infusion opioid; (7) bioavailability — F, first-pass metabolism, IV F equals one and oral F less than one; (8) anaesthetic relevance — propofol TCI and the Marsh and Schnider models, dosing in the altered patient, and the CSHT of common agents. [1]

References and further reading

• Wilkinson GR, Shand DG. Commentary: a physiological approach to hepatic drug clearance. Clinical Pharmacology and Therapeutics 1975;18(4):377-390. PMID 1164821.
• Rowland M, Benet LZ, Graham GG. Clearance concepts in pharmacokinetics. Journal of Pharmacokinetics and Biopharmaceutics 1973;1(2):123-136. PMID 4764426.
• Pang KS, Rowland M. Hepatic clearance of drugs. II. Experimental evidence for acceptance of the well-stirred model. Journal of Pharmacokinetics and Biopharmaceutics 1977;5(6):655-680. PMID 599412.
• Benet LZ. Clearance (nee Rowland) concepts: a downdate and an update. Journal of Pharmacokinetics and Pharmacodynamics 2010;37(6):561-565. PMID 21113650.
• Shafer SL, Varvel JR. Pharmacokinetics, pharmacodynamics, and rational opioid selection. Anesthesiology 1991;74(1):53-63. PMID 1824743.
• Hughes MA, Glass PSA, Jacobs JR. Context-sensitive half-time in multicompartment pharmacokinetic models for intravenous anesthetic drugs. Anesthesiology 1992;76(3):334-341. PMID 1539843.
• Egan TD, Lemmens HJ, Fiset P, et al. The pharmacokinetics of the new short-acting opioid remifentanil (GI87084B) in healthy adult male volunteers. Anesthesiology 1993;79(5):881-892. PMID 7902032.
• Kapila A, Glass PS, Jacobs JR, et al. Measured context-sensitive half-times of remifentanil and alfentanil. Anesthesiology 1995;83(5):968-975. PMID 7486182.
• Marsh B, White M, Morton N, Kenny GN. Pharmacokinetic model driven infusion of propofol in children. British Journal of Anaesthesia 1991;67(1):41-48. PMID 1859758.
• Schnider TW, Minto CF, Gambus PL, et al. The influence of age on propofol pharmacodynamics. Anesthesiology 1999;90(6):1502-1516. PMID 10360845. [1]

References

1. [1]Wilkinson GR, Shand DG. Commentary: a physiological approach to hepatic drug clearance Clin Pharmacol Ther, 1975.PMID 1164821
2. [2]Rowland M, Benet LZ, Graham GG. Clearance concepts in pharmacokinetics J Pharmacokinet Biopharm, 1973.PMID 4764426
3. [3]Pang KS, Rowland M. Hepatic clearance of drugs. II. Experimental evidence for acceptance of the well-stirred model over the parallel tube model using lidocaine in the perfused rat liver in situ preparation J Pharmacokinet Biopharm, 1977.PMID 599412
4. [4]Benet LZ. Clearance (née Rowland) concepts: a downdate and an update J Pharmacokinet Pharmacodyn, 2010.PMID 21113650
5. [5]Shafer SL, Varvel JR. Pharmacokinetics, pharmacodynamics, and rational opioid selection Anesthesiology, 1991.PMID 1824743
6. [6]Hughes MA, Glass PSA, Jacobs JR. Context-sensitive half-time in multicompartment pharmacokinetic models for intravenous anesthetic drugs Anesthesiology, 1992.PMID 1539843
7. [7]Egan TD, Lemmens HJ, Fiset P, et al. The pharmacokinetics of the new short-acting opioid remifentanil (GI87084B) in healthy adult male volunteers Anesthesiology, 1993.PMID 7902032
8. [8]Kapila A, Glass PS, Jacobs JR, et al. Measured context-sensitive half-times of remifentanil and alfentanil Anesthesiology, 1995.PMID 7486182
9. [9]Marsh B, White M, Morton N, Kenny GN. Pharmacokinetic model driven infusion of propofol in children Br J Anaesth, 1991.PMID 1859758
10. [10]Schnider TW, Minto CF, Gambus PL, et al. The influence of age on propofol pharmacodynamics Anesthesiology, 1999.PMID 10360845